AN ATTEMPT TO ANALYSE THE DIFFICULTY FOR EUROPE TO NEGOTIATE WITH PRESIDENT VLADIMIR PUTIN
FROM THE INSEPARABLE CORE OF WAR/RELIGION OR RELIGION/WAR
WAR IS NOT MERELY GEOPOLITICAL — WAR IS, AT ITS CORE, RELIGIOUS
WEAPONS ARE A RELIGIOUS STATUS SYMBOL, A RELIGIOUS PARADE
Religion is an evolutionary survival strategy. Its structure is a mythical and ritual form of purposive human action. The attainment of the goal is situated evolutionarily as a gain/loss ratio which, through self-sacrifice, brings about a religious transcendent distinction between guilt and innocence. In this sense, there is an inseparable bond between hunting (hunter-gatherers) and religion, and between war and religion. The one is the other and the other is the one. They cannot be separated without touching the very essence of hunting and warfare.
Although highly schematic, I make the following distinctions:
- The plant and animal kingdoms: self-sacrifice is present there, but killing occurs only in the service of survival. Neither has religious meaning — or at least not the same meaning that hominids attach to it. Certain animal species manufacture tools. In animals and plants, religion is not an evolutionary survival strategy in the way it is in hominids.
- Among hunter-gatherers there occurred a first religious revolution as a survival strategy. In the Old Stone Age, these hunters fashioned highly sophisticated and refined stone tools. The capacity for abstraction underlying this knowledge was woven into the inseparable relationship between hunting and religion. The hunter is religiously both sacrificer and sacrificed (self-sacrifice), as is the animal. The animal sacrifices itself to the point of death, but is also the sacrificer for the hunter.
- With Homo sapiens, evolution went further. Homo sapiens made a technical invention not found among other hominids: the invention of the bow and arrow. This does not mean that sapiens was simply technically superior. The core lies again in the inseparable symbolic connection between hunting and religion. Evolution was very slow. But sapiens came to experience the hunt religiously more and more as warfare. Making a bow and arrow requires a greater capacity for abstraction than making a spear. A different meaning was gradually given to the original religious relationship. The hunter slowly becomes an innocent victor through self-sacrifice, and the prey a guilty loser. It was by coupling the religious duality of innocence/guilt to the self-sacrifice of the victor and the loss of the loser that this technical revolution became possible.
Hunting belongs to an older form of the religious. It is in warfare that the religious attains its true form. I express no preference in this. I merely observe. This does not mean that no violence existed among hunters at that time. But the religious meaning of the hunt evolved in a way we can trace.
In hunting, both hunters and prey (animals) are sacrificers and sacrificed (self-sacrifice). It is through the hunter’s self-sacrifice that the animal offers itself up to death. This is confirmed by rituals performed after the animal’s death. After death – insofar as the rituals are observed to the smallest detail – both the slain hunter and the slain animal become protective spirits for the group.
This does not mean that the distinction between guilt and innocence did not exist among hunters. But its meaning in relation to hunting was different. The first technical revolution (the fine working of stone) was also made possible by this distinction, but in a different way. Evolution was enabled by a religious ‘purposiveness’. The meaning of the whole matter is encoded in the words themselves.
In French we have ‘efficace’: effective, efficacious, operative. The origin is Latin: efficax (nominative), efficacis (genitive), meaning: effective, powerful, operative. It is derived from the Latin verb efficere: to bring about, to achieve, to make succeed.
The first religious revolution connects innocence with the attainment of the goal, and guilt with failure. The brain became programmed in this way. The hunter who was eaten by wild beasts missed his goal. And the animal killed by the hunter also missed its goal (to kill the hunter). Evolutionarily, an exceptional religious symmetry was employed by hunters in this relationship. With sapiens, this symmetry gradually becomes an asymmetry.
Hunters employed the following symmetry: by virtue of their innocence – the self-sacrifice – both belong to the benevolent side of a higher ambivalence. I repeat that the structure is as follows: the hunter is in reality a sacrificer/sacrificed, and the animal is in reality a sacrificer/sacrificed. Mythico-religiously, after both their deaths, they are purely the sacrificed (both having undergone self-sacrifice), whereby both are innocent as an evolutionary gain for the group, notwithstanding the loss of their deaths.
In warfare, the attacker enters only into the mythical self-sacrifice; he is mythically not a sacrificer. The sacrificer is precisely challenged by virtue of this self-sacrifice, whereby the innocence of the attacker will be confirmed. The structure within the above framework is then as follows: the attacker sacrifices himself, thereby becoming transcendently innocent, and by virtue of the self-sacrifice itself is always the victor, always, until he loses the war. The enemy is merely the chosen sacrificer who confirms the innocence and evolutionary gain for one’s own side. After the victory, the enemy does not become a protective spirit as in the hunt. The loser must be punished. He underwent a religiously guilty defeat and is accordingly humiliated, killed, raped, sold into slavery, etc. This was so in antiquity, but also still today. The punishment of the loser (repression, etc.) goes hand in hand with the ritual purification of the victor, whereby the victor maintains the distinction in society even after the victory. The victor obtained the victory through self-sacrifice, and the sacrificer-loser must be punished for his loss. For the victor: self-sacrifice and innocence. For the loser: no self-sacrifice but guilt (Versailles, where the Belgians were not welcome because they had ‘sacrificed’ too little — they did not belong among the victors).
The structure is as follows: the attacker is a sacrificer/sacrificed and the designated enemy is a sacrificer/sacrificed. Yet this is not the mythical core without which a war cannot be waged. Wars belong to the religious as a form of evolutionary gain. The enemy is first provoked (in various ways). The attacker needs a sacrificer in order to confirm his own self-sacrifice as innocent. This innocence, obtained through self-sacrifice itself, always confirms the status of victor.
Can I demonstrate my thesis in another way? If I am correct, the inseparable core of war/religion (religion/war) must also be apparent from the symbolism of weapons themselves. Weapons are religious status symbols that serve religiously for adornment, decoration, parure, parrying and parade. They have primarily a religious meaning for the group, as markers of identity. They refer to the religious connection between innocence and an individual (the right to carry a sword or weapon) or collective status symbol. The desire to possess the atomic bomb is primarily a religious status symbol of religious innocence (the fatality-god – victory – innocence). Religious regimes are religiously obsessed by it (the madness-god). ¹
If one fails to account for this inseparable connection between war and religion, or vice versa, negotiating with an ‘enemy’ becomes impossible and untenable. Untenable because each side always sees itself as the victor, by virtue of self-sacrifice and innocence. Each side will ultimately always win the war, even if the war has been lost (the Nuremberg mentality of Göring).
PRESIDENT VLADIMIR PUTIN AND THE MYTHIC-RELIGIOUS PILLAR OF THE WAR IN UKRAINE
Timothy Snyder views contemporary Russian politics not merely as the product of geopolitical interests or accidental propaganda, but as a mythically constructed vision of the past that legitimises the current aggression in Ukraine. Central to this is what he calls the ‘politics of eternity’.
It is a mode of religious thinking in which an empire sees itself as historically untouched, inherently innocent and permanent through time. In practice, this means that official Russian rhetoric constructs a narrative in which the state and the people are continuously portrayed as innocent. Russia (and especially Putin) is always in the right, acting with historical justification, regardless of the facts of reality. This myth of eternal, timeless continuity (which is inherent to the religious itself, even beyond earthly time; this eternity exists solely in the service of orthodox self-sacrifice) – for instance traced back to the supposed early unity of Russia, Belarus and Ukraine through the conversion of Vladimir the Great in 988 – creates a sense that the current state is a natural, rightfully existing entity, independent of historical errors or guilt. This inherently religious narrative construction makes it far easier to present interventions such as the war against Ukraine as the restoration of a legitimate historical order rather than an invasion of a sovereign country.
The religious dimension may be apparent from the following.
Snyder demonstrates that the Kremlin under Putin cultivates a religious narrative in which Russia sees itself as the continuous victim of enemies and threats, reaching back to the Soviet period and the enormous losses under Stalin and in the Second World War. This narrative of permanent suffering and harsh history is deployed to legitimise current policy and to present enemies as inherently hostile, as hostile sacrificers (who must enable the good self-sacrifice).
In this narrative, historical victims are not merely remembered but religiously instrumentalised to create a sense of collective innocence and the moral superiority of the victor through self-sacrifice itself. The past is thus framed as evidence that Russia has always suffered innocently and therefore has the right to defend itself against new ‘threats’.
Although Snyder does not go into detail on religious doctrines, he describes how the religious is deployed as national symbolism as part of the religion (like all modern authors, Snyder reduces religion to ideology – religions without transcendence – whereas what is at stake here is precisely the transcendence of innocence, which legitimises wars) of the politics of eternity.
In this context, historical figures, myths about the origins of the Russian state and religio-cultural references play a role in constructing continuity and legitimation.
The Orthodox victims of communism (the Soviet Union) are now elevated to the status of heroes. This means that the Orthodox Church also employs a religious language that elevates victims of Stalinism to heroes – that is, to symbols of national salvation and self-sacrifice for the fatherland – even though they were persecuted by Stalin as members of the same church!
Snyder’s central point is that this reinterpretation of the past is not genuine historical inquiry but political myth-making (in reality religious myth-making). The suffering of the Russian people (including victims of Stalinist violence) is not seen as a sign of guilt or moral complexity, but as proof of a collective innocence that is continuously threatened by enemies/sacrificers other than the communist ones. In this narrative, the past is not used to accept responsibility, but to legitimise current power and to unite the population emotionally around an ideal of an innocent, restlessly threatened nation.
We cannot avoid it, though Snyder does not go this far: as religious innocent self-sacrifices, the murdered Orthodox become protectors of the fatherland (good guardians) precisely by virtue of their innocent self-sacrifice as evolutionary gain for Putin’s current religion (through which he seeks to ensure his own continuity).
This mythical reconstruction (the indivisibility of religion and war) of the past replaces classical historical interpretation with a myth that describes the past as always already correct, what Snyder calls the ‘politics of eternity’. It means that history does not serve to draw lessons or acknowledge responsibilities, but to prove that current policy is necessary, justified and free from guilt. In this logic, Russia cannot possibly be responsible for aggression; rather, Ukraine is, for example, an unnatural deviation from a supposed ‘historical truth – the only religious truth being the innocence of the victor’ – and thereby a legitimate target for intervention. The attacker needs a hostile sacrificer (the permanent threat) in order to transform his self-sacrifice into innocence, from which only permanent evolutionary gain follows.
Snyder links this to the broader religious influence of philosophers – in reality modern theologians – such as Ivan Ilyin, whose work was promoted by the Russian elite to construct a vision of Russia as a unitary state led by one person, rooted in a history destined by divine or transcendent origin and thereby exempted from all responsibility. In this religion (for it is far more than philosophy or ideology), evil is seen as something external to the nation itself, which helps to present the war as a struggle against ‘evil’ and not as an act of aggression.
In Snyder’s analysis, this mythological approach to the past forms the foundation of propaganda and political legitimation. The war in Ukraine is packaged in narratives such as the supposed unity of the two countries, the defence of historical lands, and the protection of a ‘Russian world’, whereby the invasion can be presented internally as something honourable and necessary. This reinforces the perception of historical innocence, which according to Snyder is better understood as an ideological construction than as a realistic historical judgement.
Snyder argues that these myths are not objectively true, but that they are politically operative (purposive, effective): they reduce feelings of guilt, define the enemy as inherently wrong or aggressive, and form an ideological framework – actually a religious framework -) in which one’s own warfare is presented as justified action. Thus warfare not only changes material reality but becomes ideologically and narratively embedded in a vision in which one’s own actions are seen as innocent and necessary.
My starting point goes further than Snyder’s. The core is not a religious transformation of politics, but the inseparable bond of war/religion or vice versa. The relationship between the religious and the secular is far more complex than is generally assumed. Religious transcendence does not become secular; it relocates.
Snyder argues that the Russian war against Ukraine cannot be analysed without understanding how the narrative of historical innocence and eternal correctness functions. It creates a story in which one’s own aggression appears legitimate, innocent and even necessary for the restoration of a historically ‘rightful order’, thereby generating ideological (actually religious) gain, while the failure or collapse of that narrative is presented as an existential threat.
UNDER WHAT CONDITIONS IS NEGOTIATION POSSIBLE?
In the analysis of contemporary Russian politics, and especially the role of Vladimir Putin, it becomes clear that conventional geopolitical approaches fall short when one fails to recognise the deeper religious and mythical structures of the Kremlin. Putin does not act merely as a rational actor weighing national interests against costs and benefits (economic sanctions can cause a great deal of pain; they do not change the religious dimension), but from a narrative closely connected to a mythical vision of Russian history and religious identity. In this narrative, Russia is presented as the continuous victim of external and internal threats (endlessly seeking out sacrificers in order to legitimise one’s own innocence through self-sacrifice). Russia is historically innocent, absolutely religious, and precisely for that reason morally justified in its actions. The religious knows no relativity, everything is always absolute.
In this framework, every attempt at negotiation that proceeds solely from classical geopolitical logic fails. The simple weighing of territorial interests, economic costs or strategic risks completely ignores the religious dimension in which Putin operates. For him, every action, every compromise and every gesture carries a symbolic religious significance – rooted in the evolutionary survival strategy – anchored in the mythical reconstruction of the past and in collective religious identity.
The diplomatic approach must be twofold. On the one hand, the counterpart must be made to feel that one fully knows and sees through the religious narrative. This must be done without rejecting it and without yielding to it.
Effective diplomacy in this context requires that proposals be formulated in a way that appears to respect the religious symbolic and ritual goal of Russia (a diplomatic ruse is essential here), while strategic interests and factual realities are preserved.
The determination of a non-negotiable boundary is essential here. The religious is in itself absolute and universal. A boundary is always a relative marker (hence the enormous problem of giving boundaries an absolute religious meaning, which ancient Rome attempted to do).
Concessions or proposals that undermine the mythical vision of Russia or threaten to erode the sense of collective self-sacrifice will automatically be rejected or transformed into myth-making through propaganda.
The challenge therefore lies not in convincing Putin with rational arguments, but in anticipating how each diplomatic gesture is interpreted within his mythico-religious logic. Proposing solutions that connect with the sense of historical continuity, national protection and moral legitimacy makes it possible to engage in a dialogue that remains both operationally and strategically relevant.
In this light it can against be argued that the traditional geopolitical toolkit is fundamentally inadequate when dealing with an actor who primarily sees action as the continuation of a mythical and religious narrative.
Every form of communication, negotiation or proposal must be structured on the basis of insight into the historical myths, the religious dimension of victims and enemies, and the central role of symbolic self-sacrifice. The success of diplomacy in this framework is not measured by rational concessions, but by the capacity to operate within the narrative universe of Russian leadership politics, keeping the perception of innocence, justice and historical continuity intact while strategic goals can nonetheless be secured.
The question is whether Europe is capable of this. Europe takes it as an absolute given that Russia is a secular state and that religion plays only a minor role. This is Europe’s great mistake in this matter.
The insight into this religious dimension opens the possibility of a new strategy of interaction. By showing Putin that one has complete knowledge (without more) of the mythical structures of Russian religious identity, self-sacrifice and historical innocence, one can condition negotiations in a way that respects his symbolic logic without surrendering factual interests. The challenge is not to unmask the myth as a weapon, but to acknowledge its workings and to use it to achieve practical results. In this approach, diplomatic acts become ritually charged, symbolically meaningful and psychologically effective, whereby the illusorily experienced evolutionary gain of Putin is not confirmed in material terms, but acknowledged as a narrative instrument that can be deployed to achieve concrete and strategic outcomes.
In reality, the elite in Russia has an illusory sense of evolutionary religious gain. This sense of gain has several dimensions, including a necessary dimension for remaining in power. This sense is illusory because religions themselves (and this applies to all world religions) have reached their entropic maximum with regard to this evolutionary survival strategy. For Russia, this is the real drama that is unfolding. They are using an evolutionary strategy that no longer works, and which is therefore deployed and ‘sweated out’ to the extreme, the utmost, by continuing to make sacrifices.
One must simultaneously explicitly acknowledge and analyse the limits of this mythical logic. Religion, like all evolutionary survival strategies, has an entropic moment at which its original adaptive value is fully attained and thereafter declines. The mechanisms that historically brought cohesion, cooperation and material advantage are still present in their symbolic form. Yet they no longer generate any real evolutionary advantage. In the context of Russia, this means that the sense of strategic advantage and moral justification flowing from symbolic self-sacrifice is illusory. What Putin and his elite experience as a survival gain functions in reality as a self-destructive mechanism, because the religio-mythical narratives no longer yield material or strategic advantages but exclusively feed the perception of success.
A diplomatic strategy that acknowledges this duality combines understanding and confrontation in a subtle way. Acknowledging the religious and mythical dimension communicates respect for the narrative logic that drives Russia, whereby the elite feels understood and is seemingly confirmed symbolically in their myth.
At the same time, one can analytically demonstrate that the supposed evolutionary gain of this logic has reached its maximum and that the pursuit of this symbolic self-sacrifice dynamic, when intensified, can only lead to self-destruction. This opens space for negotiations in which the Russian elite is confronted with the limits of its own mythological worldview without its mythical perception of innocence and justice being wholly threatened.
In this approach, diplomacy is no longer a game of purely material concessions or power politics, but an interaction at the level of myth, symbolism and entropic insight. One acts within the reality of the Russian narrative while simultaneously allowing the illusorily experienced evolutionary advantages to be discovered. In this way, one can steer Putin and his elite towards choices that, despite their mythical logic, minimise the risk of total self-destruction and secure strategic outcomes. The insight that religion functions at its entropic maximum transforms the perception of self-sacrifice dynamics from a supposed gain into an analytical instrument with which the limits of Russian action can be negotiated.
A PLAN OF ACTION
In a practical framework for negotiations with Russia, diplomatic action is concentrated on interaction with a narrative system that anchors moral and symbolic meaning in every political and military gesture. The first step is the explicit identification of the mythico-religious universe in which the Russian elite operates. Every step must be constructed as an acknowledgement of the symbolic coherence of their narrative. This means that proposals, concessions and communications are formulated in such a way that they do not undermine the perception of collective innocence, self-sacrifice and historical continuity, while at the same time the actual interests of the negotiating party are safeguarded.
The second step is the strategic deployment of entropic insight. By demonstrating that the religio-mythical mechanisms have reached their evolutionary maximum, one can highlight the illusorily experienced gain of self-sacrifice and warfare as potentially self-destructive. This is achieved by formulating proposals in which the Russian elite is confronted with the limits of its narrative universal legitimation, without its mythical self-image being damaged. The aim is to create symbolic and psychological pressure that moves them towards choices that are materially and strategically advantageous for the negotiating party, while the perception of the narrative’s continuation remains intact.
The third element is the construction of proposals that transform the illusorily experienced evolutionary gain into pragmatic stability. This can be done, for example, through gestures and framing that confirm the sense of symbolic success, while in reality material and political risks are reduced. The dialogue is structured in such a way that the narrative of self-sacrifice dynamics and historical justification is deployed to guide the Russian elite towards decisions that are operationally and strategically favourable.
The fourth element is the anticipation of mythical interpretations of actions and concessions. Every diplomatic gesture must be evaluated with regard to how it is interpreted within the religio-mythical framework, with particular attention to symbolic self-sacrifices, historical continuity and perceptions of moral superiority. Through this anticipation, escalation can be avoided while the illusorily experienced evolutionary gain is simultaneously modulated towards a pragmatic outcome.
The whole forms a dynamic framework in which diplomacy is measured not by material concessions alone, but by the capacity to navigate within the symbolic universe of the counterpart, to exploit the entropic limits of religion and to steer the perception of self-sacrifice dynamics. This framework makes it possible to exercise controlled influence over choices that at first sight spring from religious and mythical logic, while the actual outcomes remain materially and strategically manageable.
Philippe De Keukelaere
¹ The United States developed the atomic bomb during the Second World War as a response to German plans to do the same. It was, among others, Albert Einstein who informed President Roosevelt of this. The religious dimension in the United States at that time consisted in the desire to win the war, but this was merely a reaction to the far deeper religious meaning that can be discerned in National Socialist religion.
Sources
This text is greatly indebted to the following authors:
- Ludovic Slimak, Le dernier Néandertalien, 2023; ISBN 978-2-4150-0492-7
- Timothy Snyder, The Road to Unfreedom, 2018; ISBN 978-90-263-4329-2
THE FUSION MOMENT: CONSCIOUSNESS AS AN AUTOREFERENTIAL CONTROL SYSTEM
An interdisciplinary inquiry from mathematics, neurology and evolutionary biology
I. The inadequacy of existing theories of consciousness
The question of the nature of consciousness has, in the twentieth and twenty-first centuries, yielded two dominant yet fundamentally unsatisfying answers. On the one hand, there is epiphenomenalism, which regards consciousness as a causally impotent by-product of neurological processes. On the other hand, there is the quantum-mechanical theory of Roger Penrose and Stuart Hameroff, which anchors consciousness in a non-algorithmic quantum phenomenon occurring within the microtubules of nerve cells. Both positions encounter serious theoretical and empirical objections, making an alternative conceptualisation of consciousness necessary.
Epiphenomenalism holds that consciousness exists, but that it plays no causal role whatsoever in the course of physical processes. Consciousness is, in this view, merely a shadow of neurological activity — present, but functionally irrelevant. The devastating consequence of this position is that it logically undermines itself: if conscious reasoning has no causal force, then no one can ever adopt the conviction that epiphenomenalism is true for good reasons. The conviction itself would not arise from conscious reasoning, but from blind neurological causality. Epiphenomenalism thereby saws off the branch on which it sits.
Penrose attempts to escape this problem by grounding consciousness in a non-algorithmic quantum process, the so-called Orchestrated Objective Reduction. His starting point is that mathematical insight — the moment at which a mind grasps why a theorem is true — can never be reduced to a formal computational process, as demonstrated by Gödel’s incompleteness theorems. Consciousness then requires a physical substrate that is equally non-algorithmic, which Penrose locates in the quantum collapse within neuronal microtubules. The criticism of this model is, however, overwhelming: quantum coherence decoheres in the warm and wet biological environment of the brain too rapidly to play a functional role in cognition. Moreover, it remains unclear how quantum collapse could account for the qualitative, subjective dimension of consciousness.
What follows proposes an alternative theory that endorses neither epiphenomenalism nor Penrose’s quantum hypothesis, but instead understands consciousness as an autoreferential control system whose core lies in what we shall call the fusion moment — a timeless intersection of anticipatory information and proactive execution.
II. The fusion moment: a timeless mathematical structure
The starting point of the theory proposed here is an apparently paradoxical neuroscientific fact: in an experienced table tennis player, tennis player or cricketer, the ball moves too quickly for the conscious reaction time of the brain to adequately guide the motor response. Yet the player responds accurately and fluidly. The standard explanation is that the brain constructs an anticipatory internal model of the trajectory, speed and expected position of the ball, and that the motor action is already initiated before the conscious awareness of the situation has fully taken shape. This fact, corroborated by Benjamin Libet’s research into the temporal relationship between brain activity and conscious decision-making, suggests that consciousness does not follow a linear chain of cause and effect.
The theory proposed here holds that a fusion moment occurs in the brain between two simultaneously active processes: on the one hand, the anticipatory information that represents the not-yet-executed action as a possibility; on the other hand, the proactive execution information that prepares and selects the action. This fusion moment is, in mathematical terms, timeless — in the sense that it has no duration in the ordinary temporal meaning of the word. It is a singularity — a point outside the time axis — analogous to an eigenvalue in linear algebra or to the point of convergence in a commutative diagram from category theory. At this point there is no before or after; anticipation and execution are simultaneously present as two sides of the same mathematical structure.
The movement described by the fusion moment is mathematically that from image to source: from the information — which contains the stroke as potentiality — the system moves toward the source of that stroke, which is already present in fused form within the information. Information here anticipates the source, in the sense that the stroke as possibility is already contained within the informational structure before it is played. This is related to the concept of retrocausality in quantum mechanics, as developed in John Cramer’s transactional interpretation, and to the Platonic idea that mathematical entities are discovered rather than constructed. The brain discovers the correct stroke before it calculates it.
With regard to the lateralisation of this process, the left hemisphere — specialised in sequential processing, language production and motor planning — initially carries the anticipatory information: it prepares the stroke as a structured, executable sequence. The right hemisphere — specialised in holistic pattern recognition, spatial processing and contextual understanding — embodies the executive source: it realises the stroke as a whole, embedded in spatial and contextual reality. At the fusion moment, however, this relationship is inverted. At the timeless intersection, the two hemispheres exchange functions: what was information becomes source, and what was source becomes information. This inversion is not incidental but constitutes the very core of the fusion moment — it is precisely this reversal that renders the system autoreferential, as it mirrors its own structure and recognises itself therein. The timeless connection between the two hemispheres is possibly mediated by the corpus callosum, which functions as the anatomical locus of this inversion.
III. Consciousness as the recognition of a potential memory
Consciousness, as the theory developed here proposes, is the recognition of what a memory could have been. This formulation calls for careful explication, since it differs substantially from both the standard conception of consciousness as epiphenomenon and from consciousness as a quantum phenomenon.
Consciousness is not a registration of what has already been — that would reduce it to a purely retrospective phenomenon. Neither is it an anticipation of what is yet to come — that would make it a purely prospective phenomenon. Consciousness is the recognition of a potential memory: a structure that has not yet existed in time as an actual memory, but which was present as a possibility within the fusion moment. At the moment when the fusion moment is realised — that is, when the stroke is played as it was anticipated — the system recognises in the executed action precisely what it carried as potentiality. This is not a memory of the past, but the acknowledgement of a structure that encompasses time, as it were.
This renders consciousness autoreferential in a very precise, mathematical sense: the system anticipates itself, executes itself, and recognises itself in the execution. The structure is analogous to a fixed point in the mathematical sense — a point at which the function finds itself again: f(x) = x. The stroke that was anticipated is the stroke that was played; the system has recovered its own state. Consciousness is this moment of self-recognition — not as mystical intuition, but as a mathematically precisely definable autoreferential process.
IV. The control moment: the discrete zero and its biological correlate
When a successful stroke confirms the fusion moment, that fusion moment transforms into what we call the control moment. Mathematically, this control moment is a discrete zero — not an emptiness, but a boundary point between two states that simultaneously connects and separates them. The discrete zero is the point at which the system has verified its own coherence: anticipation and reality coincide, the circle closes, the mirror symmetry is complete.
The mirror symmetry around the fusion moment can be understood as follows: to the left of the discrete zero lies the anticipatory potentiality — the information that contains the stroke as possibility; to the right of the discrete zero lies the realised reality — the stroke as it was played. The left hemisphere initially carries the anticipatory information — the stroke as a prepared sequence. The right hemisphere embodies the executive source — the stroke as spatial whole. At the fusion moment, however, this is inverted: what was information becomes source, and what was source becomes information. It is precisely this inversion that renders the system autoreferential — it mirrors its own structure and recognises itself therein. The zero itself is the point of coincidence, the moment at which potentiality and reality prove to be each other’s mirror images. This is the autoreferential moment par excellence: the system recognises itself in the mirror of its own realisation.
The biological correlate of this control moment is an experience of reward and, more deeply, of what can only be described as innocence. This term requires careful elucidation. Innocence, in the sense intended here, is not a moral category but a systemic state: it is the state in which the system is fully coherent with itself, in which no discrepancy exists between anticipation and realisation, and in which consequently no correction is required. The player who strikes the ball cleanly need make no negative corrective movement; the system has confirmed itself. The biological sense of wellbeing that ensues — presumably mediated by dopaminergic and endorphinergic processes — is the bodily expression of mathematical coherence. The feeling of satisfaction is not merely an emotion; it is a biological signal indicating that the system has reached its own fixed point.
V. The missed stroke: broken symmetry, guilt and the biological drive toward restoration
When a stroke is missed, a fundamentally different dynamic arises. The fusion moment is not confirmed; the discrete zero is not reached; the mirror symmetry breaks. Anticipation and reality do not coincide, and the system finds itself in a state of asymmetry — an outstanding debt to reality which, from the internal logic of the system, demands resolution.
The biological correlate of broken symmetry is an experience of punishment and, symmetrically opposed to the innocence of the successful stroke, of guilt. Here too, guilt is not a moral category but a systemic one: it is the state in which the system is not coherent with itself, in which the anticipatory structure and the realised reality do not coincide, and in which a corrective movement is consequently necessary. From an evolutionary perspective, the missed stroke has yielded no advantage; the system registers a deficit and mobilises cortisol-driven restorative processes.
This mechanism, already complex at the individual level, becomes still more striking when scaled to the collective. The supporters of a losing football team share a collective fusion moment: the anticipation of victory has become a shared psychological structure, a collective identity seeking its confirmation in the outcome of the match. When that confirmation fails to materialise, the collective experiences a broken symmetry — a collective guilt in the systemic sense — which biologically activates the same restorative impulse as the individual missed stroke, but now at a scale where the primitive, phylogenetically older reaction patterns dominate. The violence that may ensue is, in this analysis, not an irrational outburst but a biologically driven attempt to force the missing discrete zero: through violence, the system attempts to restore the symmetry of which it was deprived by the loss.
VI. The evolutionary challenge: from guilt to information
The theoretical insights developed in the preceding sections lead to a conclusion that is both modest and radical: the only way to prevent the violence arising from collective broken symmetry is not forgiveness — for forgiveness still operates within the logic of guilt and restoration, as an anticipatory return of guilt to the one who bears it — but rather the transformation of the very coding of the missed stroke itself. (1)
Forgiveness acknowledges the guilt and returns it; it leaves the underlying systemic structure intact. What is needed is a fundamentally different coding of the moment of broken symmetry: not as guilt requiring restoration, but as information that can be retained and integrated. This means that the missed stroke is no longer registered as a deficit activating the biological restorative impulse, but as a data point that enriches the future anticipatory structure — as a potential memory that further develops the system.
This transition is evolutionarily extraordinarily difficult. The biological system has been constructed over millions of years of evolution to code loss as an existential threat and to activate the restorative impulse immediately and forcefully. The amygdala, which processes the emotional significance of experiences, is phylogenetically old and fast; the prefrontal cortex, which is capable of metacognition and the recoding of emotional reactions, is evolutionarily younger and slower. At the moment of maximum biological pressure — loss, broken symmetry, cortisol peak — prefrontal regulation is most vulnerable to being overridden by the more primitive reaction patterns.
What is required is that the individual or collective, at the moment of broken symmetry, adopts a meta-position with respect to its own biological reaction: the system must be able to observe itself from the outside while feeling the restorative impulse from within. This is not, as stated earlier, a matter of moral superiority or forgiveness, but of a neurological capacity that can be developed through training, culture and conscious practice. Whether and how this capacity can be cultivated at the collective level remains one of the most urgent questions facing contemporary society.
VII. Conclusion: consciousness as a mathematical-biological coherence system
The theory developed here offers an alternative to both epiphenomenalism and Penrose’s quantum hypothesis. Consciousness is neither a causally impotent by-product of neurological processes nor a non-algorithmic quantum phenomenon, but an autoreferential control system whose core lies in the timeless fusion moment — the point at which anticipatory information and proactive execution converge.
Consciousness is the recognition of what a memory could have been: an autoreferential moment at which the system recognises its own potentiality in the realised reality. When this recognition is complete — when the discrete zero is reached and the mirror symmetry is whole — the system experiences coherence, reward and innocence. When the recognition fails — when the symmetry breaks — the system experiences incoherence, punishment and guilt, and mobilises a biological restorative impulse which, in its most primitive expression, may result in violence.
The theory connects, in a consistent manner, the mathematics of the fusion moment, the neurology of the two cerebral hemispheres, the evolutionary biology of reward and punishment, the phenomenology of innocence and guilt, and the social psychology of collective violence. Its practical implication is that the prevention of violence is not primarily a moral or political task, but a neurological and evolutionary one: the development of the capacity to recode broken symmetry as information rather than as guilt. Whether the human species is capable of taking this evolutionary step systematically remains an open and urgent question.
(1) What I write here is not a value judgement concerning forgiveness. I merely observe that it is insufficient with respect to what is treated here.
Philippe De Keukelaere
Selected references
Penrose, R. (1989). The Emperor’s New Mind. Oxford University Press — ISBN 978-0-19-851973-7
Penrose, R. (1994). Shadows of the Mind. Oxford University Press — ISBN 978-0-19-853978-0
Hameroff, S., & Penrose, R. (2014). Consciousness in the universe: A review of the ‘Orch OR’ theory. Physics of Life Reviews, 11(1), 39–78 — DOI: 10.1016/j.plrev.2013.08.002
Libet, B. (1985). Unconscious cerebral initiative and the role of conscious will in voluntary action. Behavioral and Brain Sciences, 8(4), 529–539 — DOI: 10.1017/S0140525X00044903
Damasio, A. (1999). The Feeling of What Happens: Body and Emotion in the Making of Consciousness. Harcourt — ISBN 978-0-15-100369-5
Dehaene, S. (2014). Consciousness and the Brain: Deciphering How the Brain Codes Our Thoughts. Viking — ISBN 978-0-670-02543-5
Cramer, J. G. (1986). The transactional interpretation of quantum mechanics. Reviews of Modern Physics, 58(3), 647–688 — DOI: 10.1103/RevModPhysics.58.647
Whitehead, A. N. (1929). Process and Reality: An Essay in Cosmology. Macmillan — ISBN 978-0-02-934570-7
Thom, R. (1972). Stabilité structurelle et morphogenèse. W.A. Benjamin — ISBN 978-0-201-40685-3
Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik, 38, 173–198 — DOI: 10.1007/BF01700692
QUANTUM MATHEMATICS
FROM CAUSALITY TO TASTE, A LASTING TENSION
QUANTUM MATHEMATICS AS AN EPISTEMOLOGICAL (from the Greek ‘epistēmē’ = knowledge, and logos = reason or discourse; epistemology is the philosophy of knowledge, the study of how we know, what we know, and under what conditions something may rightly be considered knowledge) PATH TOWARD STABILITY?
THE PROBLEM OF INFORMATION AND UNITARITY
Quantum mathematics starts from an unresolved question in contemporary theoretical physics. What is the status of information? More precisely, the question concerns whether information is fundamentally preserved in all physcal processes, or whether there exist conditions under which information is irreversibly lost. This question is not peripheral but touches the core of both quantum mechanics and relativity theory. Within quantum mechanics, information preservation is regarded as a fundamental principle. The time evolution of an isolated quantum system is described by unitary transformations, which by definition are reversible and do not allow for any loss of information. In this context, information preservation does not necessarily mean that information always remains practically accessible, but rather that it is, in principle, never destroyed. At the same time, relativity theory introduces situations in which this self-evidence comes under pressure. In particular, the presence of observational horizons, such as those associated with black holes, appears to imply that information may definitively disappear from the observable universe. This gives rise to a tension that has been the subject of intense debate for several decades.
The so-called information problem is often approached as a conflict between two concrete theories. Om the one hand quantum field theory, and on the other general relativity. In many analyses, the search is directed toward a dynamical solution. One then looks for a new theory of quantum gravity, a correction to existing field equations, or a refinement of thermodynamic descriptions.
Yet one may ask whether the problem is exclusively of a dynamical nature. An alternative reading suggests that the conflict arises from a deeper structural deficiency, namely from an unclear or inconsistent definition of what is meant by ‘information’. In many contexts, information is implicitly equated with measurable quantities, observable correlations, or statistically accessible microstates. This identification, however, is not self-evident and may become problematic in extreme physical regimes. When information is defined exclusively through its measurability, information loss appears inevitable as soon as measurability disappears. The question then arises whether this truly concerns a loss of information, or merely a loss of access to information.
A crucial distinction that often remains implicit in the literature is that between information preservation and information accessibility. Information preservation concerns the question of whether the structural content of a system remains intact. Information accessibility concerns the question of whether this content can be read out, measured, or reconstructed by an observer. In thermodynamic descriptions, and particularly in contexts dominated by statistical averages, information accessibility is severely limited. This does not necessarily mean, however, that information itself has disappeared. It may equally well mean that information remains present in a form that is no longer operational or vectorial. The failure to make this distinction explicit contributes to the apparent paradoxes surrounding information loss. What is interpreted as destruction may in fact be a transformation from readable information into a non-readable, yet structurally preserved, form.
An additional source of confusion concerns the concept of entropy and the role of zero. In many physical contexts, a state of maximal entropy is associated with the loss of order, meaning, and information. Zero thereby acquires the meaning of an endpoint, namely a state in which nothing can be further distinguished. This interpretation, however, is not unproblematic. Entropy is a measure of the number of accessible microstates, not necessarily of the existence of structural information. Nor does zero have to mean that there is nothing. Zero may also indicate a perfect balance or symmetry, in which opposing contributions exactly cancel each other without the underlying structure disappearing. Without an explicit structural definition of zero and entropy, it remains unclear rather to a state in which information is fully delocalized or disoriented.
The persistent tension between quantum-mechanical unitarity and relativistic thermodynamics suggests that a purely dynamical solution may be insufficient. Even highly refined theories remain implicitly dependent on prior assumptions about what information is, how it is carried, and under which conditions it may be regarded as preserved. Is another approach possible? This is the question posed here. Not the introduction of new dynamics, but the explicit formulation of a structural criterion for information preservation. Such a criterion would precede specific theories and function as a touchstone. It makes visible the conditions under which one can coherently speak of the preservation or loss of information. It is in this context that, in the following part, a quantum-mathematical basic structure will be introduced. This structure does not claim to be a physical law, but offers a formal framework in which information preservation, mirroring, and zero-balance are defined in an explicit and verifiable manner. It constitutes the formal reference point on which the subsequent analysis will rest.
THE QUANTUM-MATHEMATICAL BASIC STRUCTURE
This section introduces a quantum-mathematical structure that is not intended as a dynamical law or physical equation, but as a structural criterion for information preservation. The proposed structure functions as a formal framework that specifies how information can exist and be preserved, independently of measurability, dynamics, or statistical description. It is not read temporally and does not describe a process in time, but should be understood as a relational configuration in which information is fixed through symmetry, mirroring, and balance.
The quantum-mathematical basic structure is expressed by the following formal relation between source and information:
with the control condition:
These two expressions together form a single formal unit. The arrow and the fusion symbol F do not indicate a cause – effect relationship, but a structural correspondence. The relation does not describe a transfer in time, but a simultaneous presence of source structure and information structure within one closed configuration.
The numbers 1, 2, and 3 are referred to in this framework as source numbers. They are not measured values, but structural elements. The choice of these three numbers is principled, they constitute the minimal discrete set in which identity, distinction, and differentiation jointly occur. The number 1 represents unity and identity, the number 2 introduces distinction and polarity, and the number 3 guarantees multiplicity and coherence. No single source number carries information by itself. Information arises exclusively from the configuration of the three numbers as a whole. The notation 1+2+3 must therefore be read not arithmetically, but structurally.
The tilded numbers 1̃, 2̃, (3)̃ are referred to as information numbers. They are neither new values nor negations of the source numbers. The tilde sign indicates a change of status, not a change of content. Mirroring here means that the same structural content is preserved while its operational orientation changes. Whereas source numbers may be conceived as active and vectorial, information numbers are structurally present without necessarily being accessible or readable. The mirroring is not a geometrical symmetry, but an information-status symmetry: the content is preserved, while access may disappear.
The symbol F occupies a central position in the formula and is called the fusion point. It is not an operator in the usual mathematical or physical sense and must not be interpreted as an operation that destroys or combines something in an energetic sense. The fusion point expresses that source numbers and information numbers are structurally identical, despite their different status. Formally, for each element it holds that:
Fusion here means identification without annihilation. There is neither loss nor increase of content. The fusion point functions as the structural hinge on which the zero-balance rests.
The zero that appears in the control condition has a specific meaning. It does not indicate a void to be filled, absence, or destruction. Zero here signifies perfect structural balance. When the source configuration and the mirrored information configuration exactly coincide, zero appears, despite the fact that the full content remains present. Zero functions as a control condition that guarantees the preservation of information without energetic or structural residue. In this sense, zero represents a state of maximal symmetry and redundancy, not of dissolution.
Because the set of source numbers is finite and closed, and because the mirroring is exact, the structure forms a closed and structurally unitary system. Unitarity is not defined here through time evolution or operators, but as an invariant property of the structure itself. A system that satisfies these conditions may lose information in terms of accessibility, but not in terms of identification.
This quantum-mathematical basic structure does not claim to be a physical theory. It introduces no forces, no fields, and no dynamics. Its methodological status is that of a structural reference framework. The formula functions as a touchstone. It makes visible whether and how existing theories implicitly or explicitly respect information preservation. In this sense, it operates at a level that precedes specific physical descriptions and prepares the transition toward further analysis.
QUANTIC FUSION, THE REVERSAL OF THE READING DIRECTION, AND AUTO-REFERENTIAL DISPERSION
This section situates quantum mathematics explicitly as a mathematics of resonance and as a mathematics of taste symmetry. Quantum mathematics is not a new mathematics and introduces no new science. It functions as a meta-mathematics that tests the unitarity of scientific statements against their symmetric unity with respect to their auto-referential character. This test is carried out via the zero function, and always with reference to the smallest element. Within this meta-relation, no foundation is posited and no origin is fixed; instead, the fusion value of the elements is examined in relation to the preservation of information.
The elementary fusion formula that makes this possible is:
1 + 2 + 3 F^(1,2,3,)
This formula is not conventionally read from left to right, but from right to left. The numbers in superscript are information numbers. The number immediately following the F sign is the vector. The numbers to the left of the F sign are the source numbers. The sign F is the fusion sign and always refers to zero as the symmetric correctness check. In the case of addition, this check is directly visible: the sum of the information numbers must be equal to the sum of the source numbers. The number 1 following the F sign thereby possesses two tastes. On the one hand that of a vector number, on the other that of an information number. In the case of division, this relation is inverted.
The vector, which is always equal to the smallest source number, functions as the key to the reconstruction of the source. From the right-hand side, the left-hand side must always be ‘reconstructible’. In a structure such as
600 : 2 : 5 : 6 F 2, 120, 100, 300
in order to complete the symmetry fully and to respect the F = 0 axis, the number 2 must be present on both sides of the formula. On the right-hand side it appears as a discrete vector that initiates the unlocking of the source 600. On the left-hand side the same number functions as the smallest source number. This dual presence is not accidental, but a structural requirement.
The zero point here is not merely the mirror in which the operation tilts from division to multiplication. It is also the point at which the relation reverses its reading direction, from right to left. In this reversed reading, the system does not lose coherence but rather regains it. What appears is not a static observable dispersion, but an auto-referential observable dispersion.
The dispersion on the right-hand side is not a passive or accidental scattering of elements, comparable to gas particles in a room. It is an active, self-referential dynamic in which the system experiences itself in its own dispersion. It is not a statistical dispersion that can be measured externally, but an auto-referential dispersion that is internally generated and perceived. This is a fundamental quantum feature: the system is simultaneously the source and the measurement of its own dispersion.
In classical physics, the observer measures a dispersion that already exists. In the structure described here, dispersion arises precisely because the system observes itself. The information that disperses is at the same time that which makes this dispersion possible. What disperses is not merely information, but the relation between information and its source. Observation forms part of the dispersion itself and is not a measurement after the fact, but a moment of simultaneous emergence. Auto-referential observable dispersion is thus a state in which the system generates and observes its own dispersion.
The information that expands is simultaneously the carrier and the measure of that expansion. The zero point F = 0 forms in this structure the boundary between two forms of expansion: a centrifugal, distributive expansion and a centripetal, unifying expansion. At this point there is no longer an opposition between the classical, auto-referential observable dispersion, not static observable dispersion.
The dispersion on the right is not a passive, accidental scattering of elements, but an active, self-referential dynamic. The system experiences itself in its own dispersion. It is not a statistical dispersion that can be externally measured, but an auto-referential dispersion that is internally experienced and generated. This is fundamentally quantum. The system is simultaneously the source and the measurement of its own dispersion.
In classical physics, the observer measures a dispersion that already exists. Here, dispersion arises from the fact that the system observes itself. The information that disperses is simultaneously that which enables the dispersion. The dispersion on the right-hand side is therefore not a static, observable scattering of data, but an auto-referential observable dispersion. It is a dynamic in which the system experiences itself as the field of its own expansion. What disperses is not only information, but the relation between information and its source. Observation is part of the dispersion itself. It is not a measurement after the fact, but a moment of simultaneous emergence. Auto-referential observable dispersion is a state in which the system generates and observes its own dispersion.
The information that expands is simultaneously the carrier and the measure of that expansion. Thus the zero point F = 0 forms the boundary between two forms of expansion. The first is centrifugal and distributive, the second is centripetal and unifying. At this point there is no longer an opposition between classical division and multiplication; both processes are complementary, one the expression of the other.
FORMAL EQUILIBRIUM, ENTROPIC DISPERSION, AND AUTO-REFERENTIAL STABILITY
The formal equilibrium of quantic fusion can be expressed as a structural relation between entropic dispersion and auto-referential stability. This equilibrium is not understood as a transition from disorder to order, nor as a dynamical process with a final state, but as a mirrored relation between two limit behaviours of energy and information. Formally, this relation can be represented as
E_∞ ↔ oneselfescence (F = 0) ↔ E_0,
where E_∞ stands for maximal entropic dispersion and E_0 for minimal energetic concentration.
The term oneselfescence does not denote a physical mechanism here, but a structural transition state in which energy restructures itself through reflection around the fusion point F = 0.
In this configuration, the fusion point does not mark the end of a process, but the mirror moment at which the reading direction of the relation can be reversed. On the left, energy appears as entropic expansion, unlimited in its dispersion and without preservation of vectorial structure. On the right, energy appears as auto-referential stability, not as fixation, but as concentrated presence that preserves itself through continuous reorganization. The mirror sign that carries this relation does not express causality, but reciprocity between energy and information.
What moves from right to left in this structure is not merely the direction of the formula, but the movement of meaning itself. The transition proceeds from dispersion to concentration, from division to multiplication, and from information to form. The zero point thereby functions as the restorative mirror of the system. It is the point at which loss regains its identification without being annulled. Entropic dispersion appears here not as destruction, but as a movement toward maximal uniformity in which structure temporarily loses its readability without disappearing.
Fusion, in this context, does not describe a struggle between order and disorder, but an oscillation between two forms of energy. On one side lies a state in which information loses itself in its own dispersion; on the other side, a state in which the same information reclaims itself as stable presence. The tension between the two is not an opposition, but a rhythmic interaction in which the system continuously empties itself in order to recognize itself anew.
When this oscillation reaches its centre, the fusion point F = 0, the movement does not solidify into standstill, but into clarity. At this point, energetic information becomes visible as concentrated meaning, not as metaphor, but as a structural effect of coherent self-reflection. The zero point is therefore not a boundary, but a phase transition in which expansion contracts maximally without losing its content.
The loss that occurs here is not destruction, but a reduction to the vectorial core. Through this contraction, the system gains in intensity. Energy relinquishes its dispersion in order to allow itself to be discovered as information. Thus a state of dynamic stability emerges, one that does not rest on stillness, but on continuous resumption. The entropic side seeks the boundary of its loss, while the informational side preserves what appeared to be lost. Between the two lies the fusion point as a self-referential mirror in which energy transforms itself into insight.
Quantic fusion appears here as a state of reciprocal radiation. Energy does not stabilize through immobility, but through the resonance of its own reflection. On the left, entropic dispersion dominates without preservation of readability; on the right, auto-referential stability appears, in which information preserves itself by allowing itself to circulate. Hence the reading from right to left.
At the zero point, the change of taste takes place: the transition from loss to meaning and from expansion to concentration. There the system recognizes itself as a coherent field that does not attain its equilibrium through closure, but through mirroring.
THE CONTROL: THE ZERO TEST
Control within this structure does not take the form of a verification of a result and is neither an empirical test nor a concluding step. It appears as a zero test. The zero test is the symmetric correctness check to which the fusion sign F always refers. It does not evaluate an outcome, but an approach.
THE CONVENTION OF QUANTIC MATHEMATICS
Quantic mathematics is read from right to left.
From the right, we first encounter the information numbers, followed by the vector, which is always the smallest source number. The right-hand side is composed on the basis of the information from the left-hand side through the change of taste of the left-hand elements.
In divisions, a witness number appears on the right, which undergoes the taste change of an information number, and on the left a witness number that likewise undergoes the taste change of a source number.
The first numbers on the right (when read from the right) are the information numbers. Then comes the vector. Then the fusion sign. The fusion sign reflects the auto-referential character of the quantic assertion, in which the right-hand information numbers and the left-hand source numbers always converge to the zero function. The fusion number is the self-remembrance of the number 0 in the symmetric test: it tests the coherence of the relation itself by verifying whether source and information exactly correspond under reversal of the reading direction.
The zero test is performed by not reading the formula linearly, but from right to left. From the information side, the source side must be ‘reconstructible’ again. This is the sole requirement of the control. When this reconstruction is possible, zero appears. Zero is not calculated here and not derived; it appears exclusively as a structural indication of symmetric correctness.
Zero is not a result and not an endpoint. It does not indicate a fillable void, nor a disappearance. Zero appears only when, upon reversal of the reading direction, no difference arises between source and information. It marks the point at which the relation fully closes without surplus or deficit. In this sense, zero is not an outcome, but a state of perfect balance between both sides of the structure.
The zero test can be performed per element. In a structure of the form
600 : 2 : 5 : 6 F 2, 300, 120, 100
each information number is individually brought into relation with its corresponding source number. The source number 2 corresponds with the information number 300, the source number 5 with 120, and the source number 6 with 100. Each information number must, together with its corresponding source number, make the source 600 visible again. The control does not consist in the sum of these relations, but in their individual symmetric validity.
The role of the vector is essential here. The number 2 possesses two tastes: on the right it appears as the unlocking vector, on the left as the smallest source number. This dual presence is not the consequence of the zero test, but the condition under which the zero test can take place. Without this vector, reconstruction is impossible and symmetric correctness cannot be tested.
When zero does not appear, the structure itself is not incorrect, but is being read incorrectly. Zero remains absent when the formula is interpreted linearly, when the reading direction is not reversed, when the vector loses its dual taste, when source and information numbers are interchanged, or when dispersion is conceived as merely statistical rather than auto-referential. In all these cases, a difference appears that does not belong to the structure, but to the reading.
The zero test is not a closure and not a one-time operation. It can be carried out anew with each reading. Where zero appears, the symmetric correctness of the relation is present under reversal of the reading direction. Where it does not appear, the difference lies not in the structure, but in the manner in which it is read. Zero is the number that, as absent, becomes present through remembrance.
Their summation must lead to the same result, mirrored in the zero difference that constitutes the maximal entropy of the system.
AN EXAMPLE
Initial structure in the case of a division
Ω : ν₁ ν₂ ν₃ ← F = 0 ← v : ṽ₁ ṽ₂ ṽ₃
600 : 2: 5: 6: F 2, 300, 120, 100,
On the right we have the INFORMATION (vector v and information numbers ṽᵢ).
Left: we have the SOURCE
, which is discovered from the left.
THE MAIN STRUCTURE — THE FORMULA
Left: what appears as source
Right: what is given as information
Arrow to the left: reading direction
F = 0 : symmetric control (no operation)
THE EXAMPLE
The left source side is in principle not introduced but discovered.
RIGHT — INFORMATION SIDE (POINT OF DEPARTURE)
2 functions on the left as the vector
(dual taste: on the left the vector, on the right a source number)
300, 120, 100 are information numbers
WHAT DOES F = 0 MEAN HERE?
The expression is read from right to left and verified:
All information relations reconstruct the same source.
Therefore, the absent number zero appears:
F = 0
Zero is not a result,
but the auto-referential centre of the reconstruction.
THE FORMAL SUMMARY (S_RH)
When (and only when) the above relations close, the following holds:
This formula:
– does not begin as a structure to be founded
derives nothing
– summarizes what can be structurally discovered in an auto-referential manner
Information is on the right, the source on the left.
The formula is read from right to left.
Zero appears when information can fully reconstruct the source.
THE TASTES
Element | Tastes |
vector (2) | information and unlocking |
| ν_i | source number and filter |
information numbers | reconstructive, not dynamical |
| Ω | invariant, discovered |
zero (F = 0) | symmetry control |
Information is located on the right, the source on the left.
The formula is read from right to left.
Zero appears when information can fully reconstruct the source.
Within this structure, the absent zero is primarily understood as a fusion number.
Zero is the fusion number that auto-referentially represents the mirrored-symmetric structure.
– Zero is not a source number.
– Zero is not an information number.
– Zero is not a vector.
– Zero is the point at which source and information structurally coincide.
In fusion, zero is a self-remembering absent number, from which the exactness of the fusing symmetry becomes evident by virtue of maximal entropic dispersion with preservation of information.
In certain cases, however, 0 can also change taste and, for example, become an invisible information number or an invisible source number.
FIRST ROLE OF ZERO: FUSION NUMBER OF THE MIRRORED-SYMMETRIC STRUCTURE
As stated above, zero expresses the auto-referential symmetry between source and information.
On the left lies the source side, which in classical mathematics appears as a mathematical operation and, in the quantic context, as a quantic reduction discovered through the fusing taste changes originating on the right.
On the right lies the information structure.
Zero occupies the structural centre, the fusion point (F).
In a reduction that does not yield zero, zero undergoes no taste change.
Zero carries the fusion.
Zero tests the symmetric, mirrored, auto-referential character of the operation.
SECOND ROLE OF THE NUMBER ZERO: WHEN THE QUANTIC OUTCOME IS ZERO DUE TO A REDUCTION PROCESS
When a classical operation (for example subtraction) arithmetically yields zero, corresponding quantically to a reduction to the vector value, the smallest element, a special situation arises.
Quantically expressed, this occurs when the source numbers reduce to zero.
This zero is not a new element, but a resumption of the fusion number in a modified taste state.
Here, it is not the value that changes, but the taste (function) of zero.
THE DOUBLE SYMMETRIC TASTE CHANGE IN THE CASE OF A CLASSICAL ZERO RESULT
When, quantically expressed, reduction to zero occurs (arithmetically, the left-hand operation yielding zero), such that zero as the remembering number changes taste to a vector, the following holds:
Zero does not appear on the left as a source number.
Zero does not appear on the right as an information number.
Zero temporarily assumes both functions.
This requires a double symmetric taste change:
- a) To the left (information taste)
Zero functions as a self-remembrance indicating that no information is missing and that information has been fully absorbed into structure.
- b) To the right (source taste)
Zero functions as a recognizably absent fusion point indicating that no source difference remains; the classical source has been fully recovered.
Zero becomes neither an information number nor a source number but carries both tastes without becoming an element.
THE COINCIDENCE OF THE THREE TASTES
In this exceptional state, one may state that the
source taste, information taste, and vector function coincide together in a single point.That point is:
– not on the left,
– not on the right,
– not a number,
– but the fusion point itself.
– the vector function is suspended,
– the information function is suspended,
– the source function is suspended,
– without anything disappearing.
Zero primarily functions as a fusion number that auto-referentially carries the mirrored-symmetric structure. When an operation yields zero in classical mathematics (on the right-hand side), and, quantically, reduces to zero from the information on the left-hand side, it is not the value of zero that changes, but its functional taste. In that case, a double symmetric taste change occurs, whereby zero appears neither as a source number nor as an information number but temporarily carries both functions. In this state, source function, information function, and vector function coincide in a single structural point.
When zero appears, everything is absent, yet everything coincides as presence.
THE SYMMETRIC BASIC FORMULA AND THE DISCRETE NUMBERS
The symmetric basic formula expresses the structure of fusion in a concrete relation of discrete numbers. It defines and discloses the source not by addition or expansion, but by symmetric decomposition around the fusion point . The formula reads:
1+2+3 F^1,2,3
Within this relation, the number appears on both sides of the formula. On the right-hand side, it appears as an information number and as the vector that initiates the unlocking. On the left-hand side, the same number functions as the smallest source number. This dual position is not a redundancy, but a structural necessity that makes the symmetric reading direction possible.
At the conceptual level, this yields the abstract relation:
OCCAM DISTINCTION BETWEEN THE CLASSICAL AND THE QUANTIC MATHEMATICAL STANDARD
Before introducing the classical mathematical formulation, it is necessary to make a methodological distinction that does not constitute a value judgment but indicates a difference in standard. Classical mathematics operates within a framework in which symmetry is not fixed in advance, but is approached through dynamical, analytical, or statistical processes. Limits, integrals, and normalizations function as instruments to reach or approximate a state of equilibrium. Within this standard, zero does not appear as a criterion, but as an outcome, a state that one seeks to realize within a predefined dynamic.
This does not mean that classical mathematics is deficient, but that it employs a different norm. Symmetry is not a structural starting point, but a regulative ideal. It can be checked, approximated, or restored, but it is not guaranteed a priori.
The coherence of the classical description is therefore operational. It rests on the consistency of calculations, on the correctness of assumptions, and on the stability of limit processes. Within this standard, one may strive toward symmetry without ever presupposing it as an intrinsic criterion.
The classical formulation that follows must be understood, in this sense, as an approximative description of equilibrium. It is technically closed and arithmetically coherent, but its symmetry remains conditional. Zero appears only at the end of a trajectory and remains dependent on the chosen dynamics, distributions, and boundary conditions. Symmetry here is the result of a process, not its foundation.
Opposed to this classical standard stands the quantum-mathematical structure proposed in this work. This structure introduces no new dynamics and replaces no existing theory, but applies a different norm. It does not treat symmetry as a state to be reached, but uses it as a structural criterion. Zero does not appear here as an endpoint, but as a fusion point. It is the sign that source and information mirror each other exactly. Rather than describing a trajectory toward symmetry, this approach makes visible the conditions under which one can meaningfully speak of preservation at all.
The difference between both standards is therefore not substantive, but methodological. Classical mathematics unfolds meaning through expansion. It employs extension, dynamics, and calculation in order to approach equilibrium. The quantum-mathematical structure, by contrast, concentrates meaning through symmetry. It replaces a chain of conditions with a single structural test. In Occam terms, this does not mean that one approach is superior to the other, but that they fulfill different functions. The classical standard develops and computes. The quantum-mathematical standard controls and tests.
Within this Occam distinction, the quantum-mathematical formula is not an alternative to the classical formulation, but its metanorm. Where classical mathematics shows how a system moves toward symmetry, the quantum-mathematical structure shows when that symmetry is structurally meaningful. The two standards are therefore complementary: one describes the path, the other the criterion.
CLASSICAL MATHEMATICS APPROACHES SYMMETRY;
THE QUANTUM-MATHEMATICAL STRUCTURE DETERMINES WHEN SYMMETRY HOLDS.
In classical mathematical and physical descriptions, the equilibrium between energy, mass, and information is developed through a sequential chain of derivations, limits, and integrations. In your text, this appears explicitly in the following form:
This formulation is explicitly dynamical.
It employs:
– time derivatives
– spatial derivatives
– divergences
– limit processes
– and an integral over an infinite volume.
Equilibrium appears here only at the end of a computational process.
Zero is a result, not a given. The value appears as an integrated outcome of a long trajectory of differential conditions.
Classical mathematics preserves its coherence here through explicit control at each individual level: energy, mass, information, and space are verified step by step. The price paid for this is the length and complexity of the formulation.
- a) It makes the sequential nature explicit:
– local differential balance,
– the limit F→0
The global integral state
This is exactly how classical physics operates.
(b) It clearly exposes the problem. Symmetry appears only in the limit. The number zero appears as a state to be reached. The global value (100) appears only afterward.
This makes visible that symmetry is not given, but derived.
(c) It unifies energy, mass, and information, not structurally, but operationally, as required by the classical standard.
- b) Why it nevertheless cannot be symmetrically closed (and does not need to be)?
The structural limitations are the following:
(a) Zero is conditional
= 0
which implies that zero is
– dependent on dynamics,
– dependent on boundary conditions,
– dependent on convergence.
Zero is here a result, not a criterion.
(b) The limit
A limit is approached, never reached;
symmetry therefore remains ideal, not structurally present.
(c) The global value (100) breaks symmetry
– this introduces a residual value,
– confirms that zero is not absolute,
– and shows that symmetry holds only locally or asymptotically.
Within the classical mathematical and physical standard, symmetry necessarily appears as a state to be approached. Derivations, limit processes, and integrations are directed toward minimizing or eliminating a residual term so that an equilibrium or zero condition can be reached. What remains after these procedures is typically interpreted as residue. A term that carries no foundational meaning and that, ideally, should vanish in the limit. In the classical framework, this residual value has no positive status, rather, it marks the incompleteness of the approximation and must be eliminated in order to restore symmetry.
Within the quantum-mathematical structure proposed here, this perspective shifts fundamentally. What appears in the classical standard as a residue to be discarded is no longer treated as noise or artifact, but as an irreducible structural element. The residual value is not eliminated, but isolated and recognized as the smallest building block against which the symmetric relation is calibrated. It does not function as a sign of failure, but as a carrier of structure. The transition from classical to quantic therefore does not consist in a numerical reinterpretation of the residue, but in a change of its status, from a deviation to be removed to a foundational criterion.
This difference does not indicate a deficiency of classical mathematics, but a difference in norm. In the classical standard, simplicity is achieved through purification. One removes what does not contribute to global equilibrium. In the quantum-mathematical approach, simplicity is achieved through concentration: one retains precisely that which is no longer reducible. Where classical mathematics lets its residual value disappear in order to approach symmetry, the quantum-mathematical structure grounds itself on that minimal remainder in order to fix symmetry structurally. In Occam terms, this does not imply a multiplication of assumptions, but a shift in what is considered essential.
The classical approach eliminates its remainder; the quantum -mathematical approach recognizes it as meaning-bearing.
c/ Correct positioning with respect to the formula
The classical formula makes visible how symmetry is dynamically pursued through derivations, limits, and integrations. It is coherent within its own standard, but its zero remains a limit value and its equilibrium an approximated state. The quantum-mathematical formulation,
by contrast, introduces symmetry not as a goal, but as a criterion, and replaces the limit process with a structural zero condition.
THE QUANTUM-MATHEMATICAL FORMULATION (THE AFOREMENTIONED FORMULA)
Or, expressed structurally and discretely:
600 :2 :5 :6 F (= 0) 2, 300,120,100
Within the quantum-mathematical structure there is no limit in the classical sense, in which a threshold value is approached through iteration toward infinity. In classical mathematics, symmetry appears as the result of multiplying thresholds and conditions that mutually compensate and counteract one another. Each step introduces a new correction, so that equilibrium can only be approximated through an accumulation of constraints.
The quantum-mathematical approach follows a different logic. The transition to zero does not occur through an asymptotic process, but through a structural inversion. Time is not eliminated, but recovered. What appears in the classical description as loss, residue, or remainder is here understood as the smallest building block of the structure. Instead of thresholds that neutralize one another, taste states are distinguished, each resisting symmetry in its own way, yet without reinforcing that resistance. They are not removed by compensation, but overcome by fusion.
The end therefore functions as a beginning, not on the basis of a founding cause, but through recognition, as an act of remembering. Zero does not appear as the endpoint of a calculation, but as the moment at which source and information recognize one another and temporal ordering becomes reversible (which is remembrance). Symmetry is not achieved by removing obstacles, but by the coincidence of tastes in a common structural point.
THE OCCAM CONTROL: LENGTH VERSUS STRUCTURE
The difference between both formulations is not a difference in content, but a difference in the economic organization of meaning.
In the classical formulation, equilibrium is proven.
In the quantum-mathematical formulation, equilibrium is tested.
The classical formula exhibits a high degree of explanatory detail, but low Occam economy. Each new aspect requires a new term, a new derivative, or a new integral. The quantum-mathematical formula, by contrast, contains no superfluous steps. It introduces no dynamics that are not necessary for control. Zero functions here as a single touchstone:
- a) if zero appears upon reversal of the reading direction → structural coherence
- b) if it does not appear → an error in the reading, not in the structure.
In the classical formula, zero is the endpoint of a process.
…
In the quantum-mathematical structure, zero is the starting point of the test: (source)-(info) = 0 ⇒”symmetric correcties “
Zero is therefore not calculated, but recognized.
Quantum mathematics is not a new theory, but a metamathematical reduction. It shows that what in the classical formulation becomes visible only after extensive computation is already present as a structural relation.
In Occam terms, this means:
– no multiplication of assumptions,
– no addition of dynamics,
– no extension of space–time structures,
but a single symmetric control: F = 0
DISCRETE OBSERVATION
The advantage of quantum mathematics therefore lies not in its capacity to explain more, but in its capacity to require less. Where classical mathematics reaches stability through length, quantum mathematics reaches stability through symmetry. The long classical equation and the compact quantum structure do not contradict one another. They relate as development and test, as calculation and control, as extended causality and structural Occam balance.
FORMAL ECONOMY AND STRUCTURAL SUPERIORITY OF THE QUANTUM-MATHEMATICAL FORMULATION
The comparison between the classical and the quantum-mathematical formulations makes clear that the distinction between them is not primarily substantive, but formal and methodological. Both approaches describe the same coherence between energy, mass, and information, but they do so according to radically different principles of ordering, control, and economy.
The classical formulation, as used in the original text,
is explicitly sequential.
Each physical or informational aspect appears as a separate term, acquiring meaning only through its position in a longer chain of derivatives and integrals. The coherence of the whole is safeguarded by an accumulation of local controls.
The quantum-mathematical formulation, by contrast, is:
or, in its structural formulation,
This is a structural measure.
The question posed is:
How much of the source remains structurally preserved after passing through three independent constrictions?
This is a measurement.
How does structural preservation manifest itself?
states that preservation holds;
allows us to discover how that preservation is structurally realized.
THE CONNECTION BETWEEN BOTH FORMULAS
Step 1 — Reinterpretation of
In the quantum-mathematical context:
The ‘deltas’ are structural, not dynamical.
Step 2 — When does F = 0 hold?
F = 0
Holds exactly when:
– the source, after constriction, can be fully reconstructed from the information side
– no residual value remains (the residual value is the first building block of quantum physics)
– the symmetric zero test succeeds.
This is precisely what
tests.Step 3 — Structural equivalence
The relation can be formulated as:
Or, more explicitly:
Why is this not a derivation?
There is no cause – effect relation between these expressions. They do not stand in a deductive sequence.
Their relation is the following:
Formula | Role |
| ΔM+ΔI=0 | universal criterion |
| concrete particular structure |
The relation expresses the general criterion of structural information preservation.
The ratio :
concretizes this criterion within a discrete quantum-mathematical structure.
Where the first formula establishes that no residue occurs, the second makes explicit how this residue-free equilibrium is realized through constriction, fusion, and symmetric control.
In Occam terms, this yields:
Quantum mathematics replaces succession by a single global relation. What is classically distributed over time, space, and chains of derivations is compressed into one symmetric configuration. This is not a loss of information, but a change of tastes, understood here as representational levels.
In the classical formulation, control is external. Each individual term must be verified. Whether it is correctly defined, whether the limit exists, whether the integral converges, and whether zero is eventually reached. The coherence of the whole emerges only after this sequence of checks.
In the quantum-mathematical formulation, control is intrinsic. Zero does not appear after calculation, but as a consequence of structural symmetry. The only requirement is that the reading direction can be reversed and that source and information reconstruct one another exactly. If this condition fails, the error lies not in the structure, but in the reading.
This renders the quantum formula structurally stable. It is insensitive to local variations as long as the global relation remains intact.
The classical formula is inseparably bound to time. Derivatives, limits, and integrals all imply temporal development. Stability appears only after time has elapsed, as the endpoint of a process.
The quantum-mathematical formula, by contrast, is reversibly temporal. It does not describe an evolution, but a state of balance. Time does not function as an independent parameter, but as a consequence of the chosen reading direction. When that direction is reversed, what appears classically as a cause can function quantum-mathematically as a recovered origin. One does not found, one fuses. Stability is not postponed until the end of a process, but is present within the process itself as an auto-referential possibility.
This constitutes a fundamental advantage. The quantum formula renders time reversible at the structural level without introducing any new assumptions.
In classical mathematics, information is closely tied to discrete representation. What cannot be calculated, integrated, or measured disappears from the formal framework. As a result, information loss is frequently identified with loss of accessibility.
Classical mathematics recognizes discrete numbers.
In classical mathematics, discrete numbers are :
– countable,
– distinguishable (each element is individually identifiable),
– non-continuous (no values lie between successive elements),
– position-bound (their meaning depends on their place within a sequence or – structure).
In practice, classical mathematics does not fully know how to treat these numbers. By their properties, they are already quantum. In quantum mathematics, these numbers are handled explicitly on the basis of their properties.
The quantum-mathematical formula makes this distinction explicit. Information can be preserved without being operationally readable. The transition from source numbers to information numbers is not destruction, but a change of taste. Zero guarantees that the structural content remains intact, even when its vectorial form disappears.
In classical mathematics, one seeks the unattainable value of continuity. In discrete mathematics, one studies discrete properties. Quantum mathematics goes one step further. Discrete numbers are not treated according to their value, but according to their tastes. This allows fusion between numbers while preserving identification (a unique notion expressing discreteness).
This makes the quantum formula particularly suitable as a touchstone for theories involving horizon formation, entropy, or decoherence.
According to Occam’s principle, the formulation that preserves coherence with the fewest assumptions deserves preference. In this respect, the advantage of the quantum-mathematical formula is evident:
it introduces no additional variables,
it avoids dynamical assumptions,
it requires no limit processes,
it replaces a long chain of conditions with a single symmetric control.
The classical formula remains necessary for concrete calculations and predictions.
The quantum-mathematical formula does not replace it, it tests it.
It functions as a meta-criterion indicating whether an extended description is structurally coherent.
The strength of the quantum-mathematical formula lies not in simplicity as reduction, but in simplicity as concentration. Where classical mathematics unfolds meaning through expansion, quantum mathematics preserves meaning through symmetric reflection of different tastes, whose exactness is ensured by testing against the discretely absent number zero at the point of fusion.
At the moment of extreme contraction – the extreme entropic moment – the discreteness of number (the indivisibility of the digit) ensures preservation of information, even as entropy spreads simultaneously.
This raises the final distinction. Quantum physics and quantum mathematics are not identical. Quantum mathematics provides quantum physics with an auto-referential structural framework, enabling the construction of a bridge between relativity theory and quantum physics.
Philippe De Keukelaere
NEW
HOW TO QUANTIZE THE CONFLICT OVER GREENLAND THROUGH QUANTUM MATHEMATICS AS AN EVOLUTIONARY ADVANTAGE
THE ARCTIC SYMMETRY MATRIX: INFORMATION DISSEMINATION AND QUANTUM STABILITY FROM THE DISCRETE VECTOR GREENLAND.
AN EVOLUTIONARY ADVANTAGE FOR THE U.S., DENMARK, AND GREENLAND
We propose a model of total energetic fusion between the United States and Denmark, centred around Greenland. In this quantum structure, Greenland functions as the smallest vector, which is nonetheless crucial for information preservation.
We demonstrate that the input of energy (in the broadest sense) and resources by both poles in a state of entropic maximum leads to a dissemination of information-energy from this central vector, whereby an unshakeable symmetry regarding the zero-axis is guaranteed. Furthermore, we introduce the concept of quantum law, which does not arise from external arbitration, but from the internal consistency of the quantum structure itself.
THE MATHEMATICAL ARCHITECTURE
PRESERVATION VIA THE VECTOR
The following mathematical quantum formula demonstrates how information-energy moves:
600,/: 2,/: 10,/: 6,/: 5,/ F “2”,/ “10”,/ “6”,/ “5”,/ 300,/
In this quantum formula, the “2/” is the discrete vector (Greenland). Although this appears to be the smallest element in the equation, it functions as the central processor of the fusion (F).
A/ INFORMATION PRESERVATION AND AUGMENTATION
The information-energy brought in by the poles (the 600/) is stored by the vector Greenland and immediately redistributed across both poles.
B/ SYMMETRY GUARANTEE
This process guarantees that the symmetry relative to the zero (as a self-referential benchmark) is maintained, regardless of the size of the individual input. Thus, Greenland becomes a state within the United States and Denmark while maintaining its independence.
C/ GREENLAND AS A SOURCE OF SYMMETRIC DISSEMINATION
In this system, Greenland is an independent state that functions as a quantum axis. The preservation of information within this vector ensures a constant balance:
INFORMATION-ENERGY DISSEMINATION
When the U.S. makes an additional investment, this energy is directly mirrored and disseminated across the entire matrix via the vector Greenland.
DUAL INTEGRATION
Greenland remains symmetrically connected at every level as a state of the U.S. and a state of Denmark. The informative differences in their input are neutralized by the vector Greenland into a state of quantum stability.
GAIN THROUGH LOSS AS AN EVOLUTIONARY ADVANTAGE OF THE ZERO-AXIS
The ‘loss’ of binary control is the condition for activating this information-energy.
THE BINARY SYMMETRY: GAIN THROUGH LOSS
FOR THE U.S.
By bringing its resources undifferentiated into the fusion, the U.S. loses the burden of unilateral security enforcement, but especially the burden of a lingering conflict with Europe, whereby the U.S. loses an ally, which weakens unilateral security enforcement. (1)
The gain is that the vector Greenland preserves and disseminates their information-energy, making their strategic presence militarily invulnerable and entirely efficient within the symmetry. If one looks vertically at the U.S. on the globe, one sees that the evolutionary advantage lies in the fact that the U.S. gains no right flank through a conflict with Europe. The first thing a strategist must do is look at the terrain with their own eyes and clearly realize that we do not live in a perfect world where everything is possible.
FOR EUROPE
By bringing its resources undifferentiated into the fusion, Europe ‘loses’ the burden of unilateral enforcement, which they otherwise cannot guarantee, but especially the burden of a lingering conflict with the U.S., whereby Europe loses an ally.
The gain here is likewise that the vector Greenland preserves and disseminates their information-energy, making their strategic presence militarily invulnerable and entirely efficient within the symmetry. If one looks vertically at Europe on the globe, one sees that the evolutionary advantage lies in the fact that Europe gains no left flank through a conflict with the U.S. Here too, the first thing a strategist must do is look at the terrain with their own eyes and clearly realize that we do not live in a perfect world where everything is possible.
FOR DENMARK
They lose the necessity for defensive sovereignty, which they as a small country cannot fulfil. The gain is that they resonate more with the increased information-energy disseminated over their layer from the vector Greenland. Unity within Europe, NATO, and the necessary alliance of the U.S. for the defense of Europe.
QUANTUM STABILITY THROUGH INFORMATION PRESERVATION
The stability of this system is inherent in the preservation of the smallest vector. Because the information-energy from Greenland is disseminated over both poles, a state of maximum quantum stability arises. Neither pole can disrupt the balance without breaking the information axis (Greenland), which would lead to a direct loss of their own stored information-energy. The system thus mathematically enforces its own peace.
TOWARD A NEW FORM OF QUANTUM LAW AS AN EVOLUTIONARY ADVANTAGE
Just as classical mathematics retains its value through the introduction of quantum mathematics, so classical law retains its value with the introduction of quantum law. We observe that classical law at the international level, not everywhere, as international treaties are concluded daily is in certain cases (and there President Donald Trump has a point) no longer operational. We must not, however, fall into a closed dark hole. (2) We therefore propose a new source of international law: quantum law. (3)
THE SELF-REFERENTIAL ZERO POINT AS A SOURCE OF PUBLIC INTERNATIONAL LAW
Quantum law (quantic law) does not arise from the rational reduction of a conflict to a common denominator to be imposed. In the Arctic Symmetry Matrix, the law arises from the rational reduction of the conflict from the self-referential zero point of the quantum structure.
The law “is” not there beforehand. It crystallizes at the moment an action is tested against the zero-axis (the vector Greenland). An act is ‘lawful’ when it simultaneously and symmetrically preserves the information-energy of the U.S. and Denmark. The zero point functions as a constant mirror. Every deviation from the symmetry is recognized by the structure itself as an ‘information error.’
LAW AS INFORMATION PRESERVATION
The evolutionary advantage of quantum law is that it no longer consumes energy to enforce a ‘common denominator.’ Instead, it guards the integrity of differences through information preservation within the undifferentiatedness of the entropic moment. The law is the guardian of the self-referential character that the system safeguards as stability.
Quantum law implies that the energy released by the American investment disseminates across the Danish layer. The law is the algorithmic guarantee that the information of the ‘loss’ is directly converted into the gain of quantum stability. The law tests to ensure this quantum stability through information preservation and augmentation.
THE SHIFT FROM CONFLICT TO SYMMETRIC RESOLUTION
In the quantum structure the law is the internal consistency of the matrix by quantum review.
The conflict is traced back to the zero point of the vector Greenland. This is the quantum conflict reduction.
It is examined whether the proposed action preserves the symmetry of the 600/ (the total energy) relative to the 0 (the state of rest). This is the symmetry check.
The outcome is a rebalancing of the information-energy by means of a quantum legal testing of the preservation of the self-referential character through proper information preservation and proper information augmentation.
THE SYMMETRIC STATE OF REST (300)
The transition to the Arctic Symmetry Matrix is an evolutionary necessity. By positioning Greenland as the independent, discrete vector (2/), a system is created in which information preservation leads to superior energy for all involved. The 300/ is the proof of this state of rest: a condition in which the information-energy of the U.S. and Europe is fully fused and symmetrically distributed, with Greenland as the unshakeable zero point of the new Arctic reality. Quantum law has thus become the highest form of stability, arising from the quantum structure itself.
Philippe De Keukelaere
(1) The importance of allies is no longer deemed necessary in geopolitics. This is a grave mistake. The loss of an ally is not a loss of power in the classical sense of the word, but always a loss of energy. Think of Napoleon and Hitler.
(2) Religious regimes, such as that of Iran, quickly fall into closed black holes, whereby the religious figures in power can only maintain their power by sacrificing and destroying their people as a proposed religious self-sacrifice and self-destruction. Religions have no quantum potential and can only exceed their maximum entropic moment through violence and war. They thereby produce a paramilitary organization (they can do no more), which murders its own people. The paramilitary Revolutionary Guard (what’s in a name) in Iran numbers 150,000 men and serves only to maintain the power of the religious figures by murdering their own people.
(3) In Belgium, professors Jan Ronse (marginal review) and Chaïm Perelman (reasonableness versus unreasonableness) were precursors of quantum law from the perspective of testing and evaluation (although their doctrines are not the same as quantum law).
Ronse from the perspective of Dutch legal theory, in TPR 1977, 207 tot 222.
On page 209, Ronse wrote: “I may assume that the concept of marginal review already belongs to the conceptual arsenal of Belgian jurists, especially after they have heard or read the particularly interesting lecture that M. Wiarda delivered in Brussels.” footnote (4). Footnote (4) refers to M. Wiarda, De rechter tegenover vage rechtsnormen, R.W., 1973–1974, 177 et seq.
Where the classical private law doctrine of marginal review prohibits the judge from sitting in the decision-maker’s chair, quantum law lifts this principle to a higher level: the testing no longer takes place by an external actor, but through the inherent resistance of the quantum structure itself against asymmetry, as a legal self-referential energy test. It is not a marginal review, but a quantum review (I will return to this later).
SALT AND BLACK HOLES
PART I MIRRORED LOGIC (GELO) AS QUANTUM MATHEMATICS
SALT AND BLACK HOLES
PART I: THE LOGIC EMPLOYED – MIRRORED LOGIC (new name: GELO) AS QUANTUM MATHEMATICS
A/ PRELIMINARY WARNING (Forewarned is forearmed)
This text employs connections that are not customary within established science. The question is whether this text can still be situated within the “standard” framework of known science. It may be read as a text constructed in an alchemical manner.
The text contains synthetic connections that may raise questions.
An unusual linkage is made between three formulas (see Part II, later) that belong to entirely different domains of physics and that cannot be mathematically derived from one another or combined into a linear model.
I establish this linkage through the rational mediation of Mirrored Logic.
It is, in other words, quite clear in such an approach that one departs from the standard of classical mathematics and instead approaches classical mathematics from the perspective of the cultural meaning that this mathematics has acquired. This is not a critique of the intrinsic value of classical mathematics, but rather of the cultural significance it currently holds.
Therefore, I will first provide the counterexample of Oswald Spengler’s use of classical mathematics (the standard) as a new cultural norm and form, based on the mathematical formula that he employs in an unscientific manner in his work Der Untergang des Abendlandes. Umrisse einer Morphologie der Weltgeschichte, first volume, Vom Sinn der Zahlen, pp. 144–211.
On page 182 (on page 182, Spengler uses the following standard formula). It is the only composite / complete formula that Spengler employs as such.
THE COUNTEREXAMPLE OF OSWALD SPENGLER
An interesting example in this respect is the relationship between the philosophy of culture of Oswald Spengler and the modern striving toward an ever-greater process of becoming-more (surplus-becoming). Central to this discussion is Spengler’s analysis of Faustian culture, in which infinity is not conceived as a finite goal, but as a direction of becoming.
This is clarified through Spengler’s interpretation of infinitesimal calculus, his comparison with the construction of Gothic cathedrals, and his notion of nobility (for Spengler, only blood nobility counts) as the bearer of form and continuity.
The starting point is the following. As soon as infinitesimals and limit processes are wrongly interpreted as realizable or accumulable quantities, the striving toward surplus value derails and becomes a process of becoming-more, which leads to the self-destruction of structure and form. This is the mathematical derailment (not the mathematics self) at the origin of the mythical pillar of wars.
The difference with Oswald Spengler lies in the fact that his unscientific approach remains a mere striving (incidentally, as in Nietzsche, with a number of exceptions), whereas National Socialism will interpret this striving as realizable, as in the notion of the Thousand-Year Reich.
INFINITESIMALS IN THE FORMAL MATHEMATICAL STRUCTURE
In classical analysis (prior to modern axiomatic precision), one makes use of the infinitesimal, often denoted by the symbol
An infinitesimal is a positive quantity that is not zero, but smaller than any measurable magnitude.
Formally, this is expressed as
Thus, is greater than zero, but smaller than any conceivable finite measure.
It is important to note that can never be measured, cannot be realized, and functions exclusively as a direction of approximation.
SURPLUS VALUE AS INCREASE THROUGH ADDITION (INFINITE PROCESS OF BECOMING)
In modern economic or political contexts, “surplus value” is often conceived as an increase through addition:
In contemporary economic and political discourses, “surplus value” is often implicitly understood as a quantitative increase through discrete addition. This conception can formally be represented as an iterative step:
Although this representation is mathematically correct and is legitimately applied within various formal models (such as discrete dynamical systems or iterative processes), it is conceptually limited when it is elevated to a general model of growth, value, or historical destiny. The reduction of “more” to countable addition neglects the distinction between a finite step and a process of becoming that is, in principle, non-terminating.
When surplus value is conceived as a limit process, attention shifts from the addition of units to a structural orientation without completion. In such a perspective, “more” is not a realizable endpoint, but a direction in which the process continuously proceeds without ever culminating in a definitive state. The distinction between a discrete step and a limit structure is crucial here: whereas the former proceeds by accumulation, the latter presupposes a dynamic of continuous approximation without closure.
This conceptualization makes clear that the problem does not lie in the formal validity of discrete growth models, but in their uncritical generalization into normative or ontological schemas. Surplus value, conceived as a limit process, does not refer to maximal realization, but to a structural logic of uninterrupted becoming-more.
THE EXAMPLE OF THE SPENGLERIAN STRUCTURE: LIMIT INSTEAD OF STEP
Faustian striving does not function in this manner. It follows a limit process:
One continuously approaches a subsequent state without ever reaching an endpoint.
There is no completion, no maximum, only permanent becoming-more.
This is, as stated above, the great difference between Spengler’s unscientific approach and the new interpretation that National Socialism will give to it.
SPENGLER’S INTERPRETATION OF INFINITESIMALS
In Der Untergang des Abendlandes, Spengler states that mathematics is culturally bound.
Greek culture knows finite forms and measurable objects.
Faustian culture knows infinite processes and a boundless direction.
In Spengler, the framework of meaning shifts. He uses mathematical forms not as definitions, but as symbols of a cultural attitude. This becomes visible in the only explicit series of formulas that he records in his text:
This series of formulas belongs entirely to standard mathematics, but its function in Spengler is non-computational. (2)
For the first element holds
where is Euler’s number, with value
For the second element holds
For the third element holds
where and therefore .
This concerns a power with a complex exponent, strictly defined within complex analysis.
The deviation in Spengler does not lie in the mathematical correctness of these expressions, but exclusively in their interpretative status.
GOTHIC CATHEDRALS SHARE THE SAME STRUCTURE IN SPENGLER’S VIEW
When Spengler discusses the construction of cathedrals, he does not employ a formula. The cathedral is a morphological example of the exact same structure that is symbolically represented in the series of formulas mentioned above. No single generation possesses the final result. The value lies in the continuity of form. Completion is not a prerequisite for meaning.
It is a historical fact that many Gothic cathedrals collapsed before their completion because the builders aimed too high. In Antwerp, they simply lost heart (partly due to a lack of funds), and the second tower was never finished.
DETERMINATION
The formula employed by Spengler reads
It is the only explicit mathematical notation in Spengler. It belongs entirely to standard mathematics. Spengler’s deviation does not consist in syntax, but in symbolic rereading.
WHERE SPENGLER INTERPRETATIVELY DEVIATES FROM STANDARD MATHEMATICS
Spengler uses these structures not as mathematical definitions, but as cultural symbolism: he allows “number,” “boundary,” “direction,” and “infinity” to function as signs of a Western (Faustian) attitude toward life.
In mathematics, the limit is not situated outside mathematics.
The limit is a strictly mathematical concept that is entirely situated within mathematics and formally defined there. It possesses no symbolic, cultural, or existential meaning outside this formal framework. Any attribution of such meaning is not a mathematical extension, but an interpretative transposition into another discursive domain.
In Spengler, the limit structure becomes symbolic. It concerns the “soul” of a culture and its relation to infinity.
Spengler thus leaves mathematics and enters another domain, namely a morphological philosophy of culture.
Mathematics states objectively what a limit is.
Spengler states subjectively what a limit means for a culture.
SPENGLER’S SYMBOLIC REREADING
FROM LIMIT TO DESTINY-DIRECTION
THE INSANE FATALISTIC FAUSTIAN, NIETZSCHEAN RELIGIOUS BELIEF IN BECOMING IN OSWALD SPENGLER’S VIEW
Within Spengler’s framework, the limit character (approximation without symbolic reinterpretation) becomes a symbol of a culture that is structurally oriented toward the distant, the unattainable, and the infinite. This symbolic step can be interpreted as follows:
– the limit becomes a direction (Richtung);
– the infinite process becomes a mode of existence (becoming as destiny).
Mathematically, this is not conceived as a discrete step
but as an unclosable process, formally expressed by
This process is grounded in Spengler’s view as a blood nobility that preserves the form (the morphomlogical) as a counter-revolution. This constitutes the religious anchor in Spengler’ view. In National Socialism this was adopted, but interpreted differently, as is now the case in many contemporary religious sects. (3)
The mathematical approach is transformed into a tragic, fatalistic magnitude that leads to madness.
At this level, the possibility arises to think becoming-more without it being a simple addition. Cultural identity is sought in a permanent boundary process without closure.
THE REINTERPRETATION OF NATIONAL SOCIALISM AS RELIGION
National Socialism can (structurally) be described as a political-religious rereading and misreading of this symbolism.
There is a reversal of interpretation. From the limit as boundary-direction to the limit as a realizable endpoint.
In standard terms, this can be formulated as follows: one treats the limit as if there existed a finite step in which it is “reached,” as if
were a normative command.
This is not a mathematical theorem, but a structural analogy: a limit structure is religiously transformed into maximization and an imperative of realization.
Where Spengler (tragically) still preserves the unattainable within becoming-more, the religious approach of National Socialism sacralizes the “more” (religious becoming-more) as proof of truth and destiny.
The formulas used are pure standard mathematics (analysis).
Spengler uses no formulas, but shifts the level of meaning.
He transforms mathematical boundary structures into cultural symbols.
An ideological religion of “increase” can then reread this symbolism as a duty of realization, whereby limit-thinking derails into maximization and destruction of form.
THREE REGISTERS OF LIMIT-THINKING: MATHEMATICS, SPENGLER, NATIONAL SOCIALISM
One and the same formal structure – the limit – assumes a different function in three fundamentally distinct registers: the mathematical register, that of Oswald Spengler, and the National Socialist register. The distinction between these registers is crucial, because confusion among them has not only theoretical but also historical and destructive consequences.
THE LIMIT IN STANDARD MATHEMATICS
In formal mathematics, the limit is a strictly defined concept. It belongs entirely to the internal domain of mathematics and functions there as an exact instrument for describing processes of approximation. A limit is not an object, not a goal, and not a realizable state, but a structural relation within a formal system. It possesses no normative, existential, or cultural meaning. Any attempt to load the limit with meaning or destiny necessarily leaves the domain of mathematics itself.
Within this register, the limit is value-neutral, non-teleological, and in principle uncompleted. Its strength lies precisely in the fact that it never needs to be “reached.”
THE LIMIT IN SPENGLER: SYMBOLIC TRANSPOSITION (SCIENTIFICALLY INCORRECT)
In Spengler, no mathematical but rather a symbolic shift takes place. He does not adopt formal mathematical structures – including limit-thinking and infinitesimals – as definitions, but as cultural signs.
In a strict scientific sense, this approach is incorrect and does not conform to standard mathematics. Spengler does not use mathematical concepts in accordance with their formally and axiomatically defined meanings, but transfers them into a symbolic and cultural interpretive framework. Concepts such as limit, infinitesimal, and infinity therefore no longer function within the formal domain of mathematics. His approach is not a mathematical extension, but a non-scientific, interpretative transposition.
At the same time, the limit in Spengler ceases to be a mathematical instrument and becomes an expression of a Faustian attitude toward life: an orientation toward the distant, the infinite, and the unattainable. Decisive is the fact that this transposition does not result in realization. It remains a striving, a direction without completion. Even where his approach is unscientific, it preserves the tragic awareness of unclosability. The limit remains a boundary, not a goal.
THE NATIONAL SOCIALIST DERAILMENT: FROM LIMIT TO IMPERATIVE AS A RELIGIOUS MAXIMAL ENTROPIC MOMENT WITHOUT INFORMATION PRESERVATION
National Socialism breaks with this restraint. What in Spengler remains symbolic and tragic is here taken literally and transformed into a normative command. The limit is no longer understood as a direction, but as a realizable endpoint. The infinite process is reduced to a project that must be completed.
This shift is not a mathematical error, but an ideological misreading: a formal structure is stripped of its uncompleted character and transformed into an imperative. Where mathematics knows no goal and Spengler no completion, National Socialism demands realization. In this way, limit-thinking derails into maximization, and striving into destruction.
The distinction between these three registers is not merely analytical, but normatively necessary. As soon as mathematical structures are absolutized outside their own domain, the risk arises that direction is confused with goal and approximation with destiny. Spengler’s thought marks a scientifically invalid yet culturally influential border zone; National Socialism fully transgresses that boundary.
The catastrophe thus does not arise from mathematics itself, but from the ideological demand to realize the unattainable. Where the limit is abolished, form disappears as well.
Mirrored Logic as a form of quantum mathematics that operates exclusively with discrete numbers offers a way out of entropy without information preservation. Quantum mathematics represents a return to the mathematical limit, not as a foundational principle, which was severely damaged by Spengler and National Socialism and therefore too often employed unscientifically (leading to a dramatic increase in instability), but as a fusion with information preservation, in which the number zero becomes the anchor point of the rupture as a possibility of stability.
B/ THE STARTING POINT OF MIRRORED LOGIC
When we examine the following formula from GELO:
GELO form:
+3/, +6/, F 3/, “9”/
(F denotes fusion.)
we can observe an increase of information through a reduction of being.
CLASSICAL MATHEMATICAL FORM
3 + 6 = 9
Here, 9 is the information value, while 3 is the vector value.
By reducing the information value 9 in relation to the vector 3, information is preserved by first identifying the smallest building block (the number 3) of the structure on the left-hand side of F, based on the vector on the right-hand side, which always remains identical (unless the smallest building block is 0).
The smallest number on the left-hand side is always equal to the first number on the right-hand side. From this number, the smallest structural component is always known.
The second number (6) is discovered by subtracting the first number on the right-hand side from the information value 9.
In an addition, 9 is the sum of the two numbers on the left-hand side. The second number can therefore be found simply by subtracting the vector from the sum.
With multiple digits, the remaining values of the structure can be reconstructed from the vector, which always represents the same smallest amount on the right-hand side.
THE LOGICALLY MIRRORED FORMULA
GELO form:
5/, +10/, +20/, +40/, F 5/, “15”/, “25”/, “45”/
The Mirrored Logic represents information through the fusion (the symbol F) of both sides of F, with preservation of information through a reduction on the left-hand side of F.
ANALYSIS OF VECTOR DETERMINATION IN THE FORMULA
GELO form:
5/, +10/, +20/, +40/, F 5/, “15”/, “25”/, “45”/
In this specific sequence, the vector can be identified by allowing the reasoning to fuse (not to be founded) from the smallest number: the number 5 (placed after the symbol F), which functions as the vector.
The symbol F (fusion) is the tipping point or zero point in Mirrored Logic.
The number 5 (to the left of F) is the source value. This is the value directly connected to F as the starting point of the reasoning.
The number 5 is simultaneously the vector. It is the active unit or “step” that determines the relations in the rest of the formula.
From the right-hand side, the left-hand side can be reconstructed using the preserved information (15, 25, 45).
CLASSICAL VECTOR CALCULATION
Vector v = 5
15 − 5 = 10
25 − 5 = 20
45 − 5 = 40
VECTOR ANALYSIS TABLE
Information | Vector | Structure | Logic
15 | 5 | 10 | 15 − 5 = 10
25 | 5 | 20 | 25 − 5 = 20
45 | 5 | 40 | 45 − 5 = 40
The 5 placed after the symbol F is the driving force (the vector) that governs the distance and proportionality between the numbers within the mirrored system.
The initial left-hand structural configuration derives its information from the mirrored informational structure on the right-hand side.
THE MEANING OF ZERO AS A DISCRETE STATE (THE INFORMATION-ZERO)
When zero is treated as a discrete state within Mirrored Logic, reduction to 0 is not an endless annihilation, but the attainment of a specific phase state.
In Mirrored Logic, zero is not the absence of value, but the ultimate simplification of the information matrix.
This constitutes a fundamental mathematical distinction.
ZERO AS THE ENTROPIC MAXIMUM IN CLASSICAL MATHEMATICS
In classical mathematics, division by zero leads to infinity (∞), the point at which the calculation “breaks”.
In the classical approach, division by zero is indeed an undefined entropic state. In Mirrored Logic, it represents the ultimate entropic transition.
Here we reach the core of the paradox. In classical mathematics, zero is an endpoint, because 0 always remains 0.
One could argue that reduction to zero is not the end of value, but the point at which the calculation endlessly destroys itself in entropic repetition.
ZERO AS ENTROPY AND INFORMATION
In classical mathematics, zero is often regarded as a lack of value.
In Mirrored Logic (GELO), by contrast, zero is the fullness of chaos, the state in which all information is so perfectly distributed that no distinction can be made.
This is exactly what physics designates as the entropic maximum.
ZERO AS A STATE OF COMPLETE SATURATION
Where classical mathematics states that a value “disappears” once it is reduced to zero, Mirrored Logic states that the value has reached its informational expansion limit.
Zero is the mathematical representation of the state in which the fundamental information matrix is fully dispersed.
It is not the absence of information, but its omnipresence.
THE SELF-DESTRUCTION OF THE CALCULATION
When a mathematical operation results in zero, the calculation does not “destroy itself” out of weakness, but because it has reached the entropic maximum. (2)
In this final phase, any further operation (increase or decrease) becomes irrelevant. Information has transitioned from a discrete, countable unit into an infinite field of possibilities.
This does not imply that classical mathematics becomes worthless. On the contrary, it is precisely from classical mathematics that the entropic maximum can be identified. Abandoning classical mathematics would mean abandoning the standard of the second law of thermodynamics, which is not intended. Confusion arises from symbolic misuse of zero. Zero is not “nothing”, but proof of the complete absorption of the vector by information. (The confusion arises from the symbolic use of language concerning the figure 0. It is a zero that is taken to mean nothing. Expressions such as “he is a nobody,” “a complete zero,” or “a disposable human being” are misleading, not only in ordinary speech, but also within classical mathematics, especially when one begins to speak about the structural foundations of quantum mathematics).
THE MATHEMATICAL DETERMINATION
In Mirrored Logic, zero is the symbol of the absolute interface.
Reaching zero means reaching the maximal surface (A) of the Bekenstein – Hawking formula and the maximal configuration space (W) of Boltzmann (to be discussed in the next part).
Zero is therefore not the starting point of maximal entropy, but the terminal point of increase.
In classical arithmetic, zero functions as a definitively self-destructive closed “black hole”. Once a number reaches zero in a multiplication, information disappears:
10 × 0 = 0
In Mirrored Logic (GELO) and in quantum information theory, zero is not a destroyer, but a specific state within a dynamic system.
ZERO AS A DISCRETE STATE IN MIRRORED LOGIC (GELO)
In GELO, zero (0) is regarded as a position on the axis of mirroring, an equilibrium point between opposing vectors or informational states.
Classical view:
0 = absence of value
GELO view:
0 = active resting state or fusion equilibrium (F)
Within this logic, reaching the state 0 does not signify the end of information, but a return to source information.
According to Shannon’s information theory, the choice between 0 and 1 represents the smallest possible unit of information (one bit):
H = −∑ pᵢ log pᵢ
From this it follows that 0 contains as much potential information as 1.
THE ZERO VECTOR IN MIRRORED LOGIC
GELO form:
0,/ F −5/, “5/,”
Left side (Source): the smallest value is 0.
Right side (Vector): the vector equals 5.
Fusion into zero:
Because the vector (the step) equals the source value, the remaining distance to the equilibrium point is zero.
This is crucial for the following reason.
In classical mathematics one would say: information is lost.
In the GELO, however, this configuration means:
0 = (Vector 5) ⇔ (Structure 5)
Zero here functions as a witness. It indicates that the vector has perfectly filled the structure. There is no remainder, which signifies maximal symmetry.
Zero is obtained when the smallest value on the left equals the vector. This is the point at which “motion” (the vector) and “being” (the structure) become one and fuse. This is the moment of full quantum saturation.
In this case, the vector is not equal to the general feedback zero, but to the information value 5. Within the entire system, zero as the smallest building block becomes the greatest building block. Hence, within this logic, the number 5 must submit.
THE QUANTUM PARALLEL AND THE STRUCTURAL FUNCTION OF ZERO
Mirrored Logic (GELO) exhibits striking similarities with the quantum-mechanical interpretation of informational states.
Where classical mathematics considers zero a destructive value, GELO views zero as a fusing ground state. It is not a foundation, but a state that carries the latent potential of all information.
THE QUANTUM GROUND STATE AS AN ANALOGUE OF ZERO
In quantum mechanics, the state |0⟩ is not empty, but the ground state of a qubit.
To transition to the excited state |1⟩, energy is required. In GELO, this energy is interpreted as a vectorial impulse: the force that displaces a system from equilibrium (0).
In this model, zero preserves the full informational potential of the system. It forms the starting point of the reversible transformation between equilibrium |0⟩ and excitation |1⟩.
ZERO AS THE FUSION POINT OF VECTORIAL INFORMATION
In GELO, zero is not conceived as the absence of structure, but as the fusion point (F) between two complementary vectors:
V_net = V⁺ + V⁻
where:
V⁺ is the expansive vector (positive informational direction),
V⁻ is the contractive vector (negative direction).
Their fusion at zero expresses complete symmetry and is mathematically written as:
V⁺ + V⁻ = 0
In this case, information is not destroyed but folded into itself, a process that corresponds in quantum physics to superposition.
SUPERPOSITION AND INFORMATION CONSERVATION
A qubit in superposition can be written as:
|ψ⟩ = α|0⟩ + β|1⟩
with the normalization condition:
|α|² + |β|² = 1
The state |0⟩ is never fully eliminated; it forms the basis upon which every superposition rests.
In GELO, this means that every informational shift can be traced back to a symmetric ground state: zero.
Zero thus functions as the carrier of informational space, not as its negation.
THE INFORMATION CONSERVATION LAW IN GELO
In Mirrored Logic, the following conservation relation applies:
I = S + V + F
where:
I is the total informational content of the system,
S the structural component,
V the vectorial component (energy of displacement),
F the fusion component (symmetry or zero state).
When the system is in the zero state, the following holds:
S + V = 0
Total information is then concentrated in a resting point of maximal coherence.
Zero thus constitutes the archive of complete symmetry.
THE ENTROPIC ZERO AS AN INFORMATIONAL FREEZER
From a thermodynamic perspective, zero in GELO is comparable to absolute zero (0 K).
At that temperature, entropy is minimal. Particle motion ceases, but the structure of the system remains intact.
Informationally, this is a state of perfect freezing: a total contraction of mass in which information is not lost, but fully conserved.
To “thaw” this state, a vectorial stimulus (energy, frequency, or impulse) is required, through which latent information becomes active again.
This reversibility forms the core of GELO logic.
STATEMENT
In Mirrored Logic, zero (0) represents the ultimate informational state.
It is a state in which energy, structure, and vectors are fully balanced.
Zero does not destroy; it gathers.
It does not erase; it archives.
It does not end; it stabilizes.
Zero is the witness of perfect symmetry:
the point at which all information converges into a state of maximal coherence.
VECTORIAL RECONSTRUCTION OF INFORMATION FROM THE ZERO STATE
The transition from the zero state to an active informational structure constitutes the most dynamic aspect of Mirrored Logic (GELO).
While zero was defined in the previous section as a ground state of maximal symmetry, this phase describes the reversible activation of that symmetry through a vectorial impulse.
VECTORIAL ACTIVATION: FROM POTENTIAL TO EXPANSION
The zero state |0⟩ contains the full potential information of the system.
To activate this latent information, a vectorial component (V) is introduced, determining the direction and intensity of informational displacement:
I_active = |0⟩ + V
where:
|0⟩ is the symmetric ground state,
V is the vectorial energy (direction and amplitude),
I_active is the activated informational state.
This transformation may be interpreted as the transition from a compressed entropic state to a de-structured informational expansion.
The vector functions as the “receiver of memory”: the energy that restores stored structure into usable data.
THE FUSION RELATION BETWEEN ZERO AND VECTOR
This transition is described by the following fundamental GELO equation:
F(0, V) = S
Here, zero functions not as a starting point, but as an equilibrium reference.
Every vectorial addition displaces the system from that equilibrium, and the magnitude of displacement determines the degree of informational differentiation:
ΔI = f(V)
The vector (V) is therefore not merely a direction, but also a measure of informational disturbance: a unit of difference that temporarily breaks the symmetry of zero.
RECONSTRUCTIVE INFORMATION CYCLES
GELO assumes that every vectorial activation is part of a cyclic process.
When the vector reaches maximal amplitude, a return to the zero state occurs:
V_max → |0⟩
This process is analogous to the oscillation of a quantum system between the states:
|0⟩ ↔ |1⟩
The vectorial transition is interpreted as a Rabi oscillation: a rhythmic movement between potential and actualization.
Zero is therefore not static, but rhythmically active: it pulsates, restructuring information through continuous fusion and defusion with the vector.
THE LAW OF REVERSIBLE SYMMETRY
The fundamental conservation equation of GELO is expressed as:
V_out + V_in = 0
This expresses the principle of reversible symmetry: every vectorial outflow has a complementary inflow that restores equilibrium.
The total informational value remains constant:
ΔI = 0
From this it follows that zero is not only the center of symmetry, but also the anchor of information conservation, a kind of energetic “pulse frequency” that guarantees system integrity.
ENTROPIC RESTRUCTURING
When a vector disrupts equilibrium, entropy increases locally.
However, in GELO the total entropy of the system remains conserved, because the zero state absorbs the increased disorder and restructures it:
ΔS_sys + ΔS_zero = 0
Here, zero functions as an entropic regulator. It gathers the information generated by disturbance and reorganizes it into a new, coherent state.
This property renders zero in GELO non-destructive, but self-correcting. It is the feedback mechanism of mirrored logic: a dual rational system that contains its feedback internally, not externally.
MATHEMATICAL REPRESENTATION OF RECONSTRUCTION
The reconstruction of information can be modeled as an iterative function:
I_{n+1} = f(I_n, V)
Each iteration generates a new vectorial state relative to the equilibrium of zero.
The structure is recursive, meaning that each new vector is rooted in the symmetry of the previous one.
This iterative dynamic renders GELO non-linear, yet self-referential.
THE EPISTEMOLOGICAL IMPLICATION
From an epistemological perspective, this implies that knowledge (information) is never detached from its zero state, the state of maximal potential.
Vectorial activity is merely a momentary differentiation within a continuous field of symmetry.
Zero is therefore not the “destruction of the self” through self-sacrifice, but the structurally absent self transformed into information.
It is not excess being (additive accumulation) striving toward infinite becoming and self-destructive entropic maximum; it is a temporary absence of being in which the self attains its full energy, despite the entropic maximum.
STATEMENT
In Mirrored Logic, the vector is the key to the reactivation of zero.
Without the vector, zero remains potential but immobile. With the vector, it becomes creative and expansive.
Zero preserves, the vector moves, and their interaction constitutes information as a living system.
THE COMPUTATIONAL PROJECTION OF GELO – FROM VECTOR TO INFORMATION PROCESSING
Mirrored Logic (GELO) can be understood as a structural information model in which each number, vector, and zero state fulfills a specific logical role.
The dynamics of fusion (equilibrium) and differentiation (vectorial expansion) form the basis of a computational paradigm closely related to quantum information science, yet grounded in deterministic symmetry rather than probabilistic uncertainty.
THE LOGICAL UNIT: THE MIRRORED BIT (G-BIT)
In classical computing, the fundamental unit is the bit, which can assume only two values:
0 or 1
In GELO, by contrast, we define the mirrored bit or g-bit, which contains not only the values 0 and 1, but also their vectorial relation:
g = { |0⟩ , V }
where:
|0⟩ denotes the symmetric zero state (equilibrium),
V denotes the vectorial deviation (direction of activation).
Each g-bit therefore contains information about both state and transition.
The g-bit is not static but dynamically reflective: it knows not only what it is, but also where it is moving.
GELO OPERATORS
The basic operations in GELO are not defined as absolute logical gates (such as AND, OR, NOT), but as vectorial transformations within a symmetric field.
The fundamental operators are defined as follows:
Reflection operator (ℜ):
ℜ(V) = −V
This reflects the vectorial direction without destroying informational content.
Fusion operator (Φ):
Φ(V, −V) = 0
Two opposing vectors fuse into equilibrium; this is the formal representation of informational symmetry.
Activation operator (Α):
Α(0) = V
This activates the zero state by assigning a vectorial component.
Unfolding operator (Ω):
Ω(V) = S
This produces the concrete informational instance (the expression of structure in time or space).
THE ARITHMETIC FUNCTION OF THE MEDIATOR NUMBER
In earlier sections, the mediator number (B) was defined as half of the total structure:
B = S / 2
and as the coupling between structure and vector:
B = f(V)
In computational terms, B functions as a regulation factor or “buffer” that determines how the symmetric zero state translates into discrete informational states.
It is the internal clock number of GELO: a stable median frequency that synchronizes all transformations.
GELO AS DETERMINISTICALLY TRACEABLE AUTO-REFERENTIAL DETERMINATION (MEASUREMENT IN THE G-BIT)
In contrast to classical quantum information theory, where the state of a qubit is determined only upon measurement, the g-bit remains deterministically traceable.
The state of the g-bit can be described as:
ψ = α|0⟩ + βV
with the condition:
|α|² + |β|² = 1
The difference with the qubit lies in interpretation.
In quantum mechanics, superposition remains indeterminate until measurement.
In GELO, superposition is fully structured. Each ratio corresponds to a specific vectorial configuration at a defined informational level.
Thus, GELO preserves both the mathematical quantum energy of superposition and the requirement of deterministic symmetry, in which the “self” is preserved as information through self-referential mirroring within the system.
THE INFORMATIONAL TRANSFORMATION CYCLE
The computational cycle of GELO can be summarized as:
0 → Α → V → Ω → S → ℜ → −V → Φ → 0
Each cycle consists of four phases:
activation: releasing the vector from zero,
unfolding: manifesting information,
reflection: mirroring the vectorial state,
fusion: restoring equilibrium in zero.
This cycle constitutes the “breathing” of information within GELO, in which information is never lost, but continuously transformed, restructured, and stabilized.
APPLICATIONS IN INFORMATION PROCESSING
GELO provides a theoretical framework for:reversible computation (no information loss),
informational compression (using zero as archive),
symmetric encryption (where the key is the vectorial mirror of the encoded state),
and even non-deterministic quantum emulation (where g-bits allow classical hardware to simulate quantum behavior deterministically, without probabilistic fluctuation).
STATEMENT (WHAT HAVE WE LEARNED TODAY?)
Mirrored Logic presents a universal principle:
all information arises from equilibrium, moves through asymmetry, and returns to symmetry.
Zero is the memory of this process.
The vector is its breath.
Information is its form (the structural paradox).
Formally summarized:
I = { 0, V, B }
where 0 is memory, V is motion, and B is the measure of their coherence.
GELO demonstrates that logic, mathematics, and physics are merely three perspectives on a single structure: THE MIRROR OF INFORMATION.
Zero does not destroy; it informatizes (preserves as reconstructible information).
The vector does not found; it fuses.
Their fusion constitutes the foundation of all computable reality.
C/ WHAT IS MIRROR LOGIC FOR THE KWANTUMMATHEMATICS
Where classical mathematics regards reduction to zero as a neutralization of value, mirrored logic understands it as a transition toward infinite entropy.
The point at which a calculation “breaks” through division by zero marks, in mirrored logic, not nothingness but the attainment of an information-theoretical singularity (the non-sacrificial self, the salinity of the calculation). In this state, the fundamental information matrix is no longer bounded by numerical magnitudes but has dissolved into a state of maximal configurational freedom.
Here, the numerical zero does not function as an unfillable void, but as the discrete symbol of the transition toward the infinite background matrix.
Within this mirrored logic, the number zero likewise does not serve as an indicator of nullity (maximal entropy as destruction or self-annihilation), but as a discrete numerical endpoint marking the transition to the entropic maximum. Where classical reduction to zero is interpreted as a loss of value, zero here functions as the mathematical threshold to infinite configuration space: the state in which the information matrix liberates itself from the structural constraints of volume.
THE SEARCH FOR THE ABSENT IN QUANTUM MATHEMATICS
The absent – present informational source and the entropic maximum of zero.
In quantum mathematics, the absent is not emptiness, but an absent–present informational source. This source forms the bridge between the unstructured potential of the source and the determined outcome. The purpose of mathematical observation is to cause the entropic maximum of zero (the witness number) to be discovered. This witness number structures the information for the left-hand side, thereby allowing the vector to acquire its true meaning.
THE SYNTHETIC QUANTUM STRUCTURE: MULTIPLICATION
In this mode, factors construct reality from source potential.
GELO FORM:
2,/ × 10,/ × 6,/ × 5,/ F “2”,/ “10”,/ “6”,/ “5”,/
CLASSICAL FORM:
2 × 10 × 6 × 5 = 600
ANALYSIS OF THE ABSENT – PRESENT SOURCE
In this construction, 300 is the absent–present informational source. Although not physically written, this number is the witness that structures the entropic maximum of the source value 600.
The presence of the vector F,2,/ activates this informational source. The vector indicates that 300 is the stable zero-point reference from which the coefficients on the right-hand side acquire their structural form.
THE REDUCTIVE QUANTUM STRUCTURE: DIVISION
In the mirrored logic of division, the source functions as the starting value, while the right-hand side displays the breakdown toward the witness number.
GELO FORM:
600,/: 2,/: 10,/: 6,/: 5,/ F “2”,/ “10”,/ “6”,/ “5”,/ 300,/
CLASSICAL FORM:
600 ÷ 2 ÷ 10 ÷ 6 ÷ 5 = 1 (with witness 300)
ANALYSIS OF THE ABSENT–PRESENT SOURCE
Here, the vector 2 is the absent–present informational source. In this system, 300 must appear explicitly in order to unlock the entropic maximum of zero.
The number 300 functions as the observation that reduces the “chaos” of 600 into a structured image. Without 300, the absent vector 2 could deliver no structural information to the left-hand side. The witness number compels zero to reveal vector 2 as the active initiating source.
THE IMPORTANCE OF THE ABSENT
Quantum mathematics teaches that information acquires meaning only through the relation between the present and the absent–present informational source. The entropic maximum of zero functions here as fusion testimony.
It is the witness number that objectifies the transition from source to result. Whether we use 300 to prove the vector (division) or the vector to understand 300 (multiplication), the objective remains the structuring of information for the left-hand side of F.
Epistemologically, one may state that quantum physics compels us to recover the memory of the absent. In this sense, quantum mathematics is Proustian.
THE REDUCTIVE QUANTUM STRUCTURE
DIVISION AND THE WITNESS NUMBER
In quantum mathematics, a value that is “absent” (such as vector 2 in the division sequence) can never be observed directly. It requires a witness in order to become knowable. The number 300 is this witness.
Why is 300 the witness?
300 “sees” what has happened to the source value 600. Without 300, 600 would remain a closed entity.
The witness testifies to the rupture caused by the absent vector. Vector 2 does not appear as a result, but 300 points toward it. It effectively states: “I exist only because 600 passed through 2.”
300 is the witness that halts the entropy (indeterminacy) of 600. At the moment 300 appears, the information for the left-hand side is structured: the absent vector 2 has been discovered.
REPETITION OF THE FORMULA
GELO FORM
600,/: 2,/: 10,/: 6,/: 5,/ F “2”,/ “10”,/ “6”,/ “5”,/ 300,/
In this sequence, 300 is the witness that reveals the absent–present informational source (vector 2). In quantum mathematics, 300 is the witness number that reaches the entropic maximum of zero.
The witness reveals the absent. Vector 2 itself remains invisible in the result, but 300 testifies to its action.
Because the informational values (10, 6, 5) are identical to the source values, 300 is the only number capable of betraying the absent vector 2. It is the necessary observer that confirms the transition from source to vector and delivers the identity of the absent.
Without a witness, there is no proof of the act (division) or of the agent (the vector). In the formula, 300 is the anchor point that compels the left-hand side to disclose its information.
In this sense, in the above formula, the number 2 is a mediator number that becomes present through its absence.
THE ZERO
IN CLASSICAL MATHEMATICS
In classical mathematics, zero (0) functions as:
a dividing boundary between positive and negative numbers (− ↔ 0 ↔ +),
the neutral element in addition (x + 0 = x),
and the symbol of absence – it means “nothing,” or “no quantity.”
It’s a separator, not a generator.
It splits the continuum of values into two opposing domains (positive and negative).
IN GELO (QUANTUM – INFORMATIONAL CONTEXT)
In the GELO structure, zero is not a dividing line, but a structural equilibrium point – a field of potentiality that holds both polarities in coherence.
That means:
ZERO IS NOT THE MIDPOINT BETWEEN OPPOSITES, BUT THE UNIFIED STATE PRIOR TO DIFFERENTIATION
It does not divide posit
ive and negative; it contains them in potential.
Instead of being nothing, it is everything in latency, an informational zero-point field.
In this interpretation, zero is the origin-state of symmetry, not the boundary of opposition.
CONCEPTUAL ANALOGY IN THE MIRROR SYSTEM
In classical logic: 0 is the absence of 1.
In GELO logic: 0 is the potential of 1 and −1 simultaneously.
So the zero state isn’t neutral because it lacks polarity; it’s neutral because it precedes polarity.
It’s non-dual, not mid-dual.
IMPLICATIONS
If we remove the assumption that 0 divides positive and negative, then:
“Opposition” becomes a mode of manifestation, not a fundamental reality.
The “zero point” becomes a field of coherence, not a static midpoint.
Every positive manifestation implicitly contains its absent–present negative as structure, rather than as opposition.
This aligns perfectly with the former GELO phrase:
“300 is the absent–present informational source… the stable zero-point reference from which the coefficients acquire their structural form.”
That is: the “zero” (symbolized by 300) is not absence, but the unseen balance that structures what appears.
A NEW OBJECTIVITY TROUGH A NEW MIRROR
Classical mathematics is founded upon a mirror that divides. It reflects reality through opposition, constructing knowledge upon the distance between what is seen and what sees. In this dualistic structure, zero functions as the dividing line, the surface of the mirror where the image and its source remain apart. Positivity and negativity, affirmation and negation, being and non-being are distributed on opposite sides of this reflective plane. Truth, in this scheme, arises from separation. To know something objectively is to observe it without participation. Yet this very detachment renders classical logic ambivalent. The mirror reflects, but it does not recognize itself in what it reflects. Its image is precise yet incomplete, always dependent on an invisible observer outside its frame. The classical mirror is clear, but asymmetrical.
The difference between these two mirrors marks the transition from classical to quantum objectivity. In the classical model, knowledge is gained by distance, by stepping back from the mirror to avoid distortion. The observer remains unseen, and objectivity depends on this absence. In the quantum model, however, the mirror itself becomes aware: each half sees itself as it is seen, without ambivalence. There is no outside to the reflection. Observation and being, subject and object, exist as conjugate states of one coherent image. What is reflected is not the other, but the self as relational field. The mirror ceases to separate perception from reality, it becomes the medium of their unity.
From this perspective, zero is no longer the point of division but the transparent surface of universal reflection. It is not the midpoint between positive and negative, but the undivided origin where both sides of the mirror are already one. Classical mathematics interprets zero as the absence of magnitude. Quantum mathematics understands it as the presence of symmetry, the place where differentiation begins without fracture. The mirror of classical logic shows two halves that cannot meet; the mirror of GELO logic shows each half seeing itself as seen. This self-symmetry eliminates ambivalence. Every polarity is a reflection within one surface, not a conflict across two domains.
Such a transformation redefines what objectivity means. Classical objectivity is founded on the exclusion of the observer; quantum objectivity is founded on the inclusion of the observer in the reflective act. The first aspires to clarity through distance; the second achieves coherence through resonance. Objectivity, in this new sense, is not the absence of subjectivity but the equilibrium of mutual reflection. It is the condition in which each element of reality mirrors every other without distortion, a state of transparent reciprocity rather than detachment. Truth arises not from the separation of mirrors but from their alignment, when the image and its reflection coincide perfectly.
To think within this framework is to move from an epistemology of distance to an ontology of reflection. Mathematics becomes a language of mirrors, each operation a gesture of self-recognition within the field of zero. The non-ambivalent zero thus becomes the key to a new logic of being: a mirror that does not divide the world into opposites, but allows it to see itself in itself. Classical objectivity is the mirror of distance; quantum objectivity is the mirror of coherence. The former reflects difference; the latter reflects identity. Through the lens of the GELO structure, reality ceases to be a system of separate images and becomes the single, self-seeing mirror of existence.
In classical logic, Being and Self are separated. Being is the object, the external reality that appears; the Self is the subject, the observer who perceives. Between them stands the mirror that divides. Zero, in this framework, is the sign of distance — the boundary where perception ends and existence begins. Objectivity depends on this distance: to know is to step back from what is known. Yet in doing so, the Self becomes absent from the Being it observes. It knows the world but does not participate in it. Knowledge is achieved through separation, and thus it remains ambivalent — the Self perceives what it cannot become.
In the quantum or GELO logic, this relation transforms entirely. The mirror becomes transparent. Zero no longer divides Being and Self but joins them as two dimensions of the same reflective field. The reflective surface does not stand between, but within. Being and Self are no longer opposite poles of perception; they are reciprocal aspects of one process of reflection. Being is the content of reflection – that which appears; Self is the function of reflection – that through which appearing becomes possible. Both belong to one and the same coherent event. The mirror is not the image of division but the locus of convergence, the space in which seeing and being-seen occur as a single phenomenon.
In this sense, the non-ambivalent zero functions as the center of self-being, not as the absence of value, but as the still point where presence becomes aware of itself. Zero is not the void between opposites; it is the self-reflective equilibrium that holds both in potential. It is not emptiness, but the awareness of Being as its own reflection. Thus, the zero-point is the true axis of identity, the point at which Being recognizes itself as Self, and Self discovers itself as Being.
We may therefore say that in the GELO framework, Being and Self do indeed coincide, but not through fusion or erasure of distinction. They coincide through the removal of asymmetry. They remain distinct as two facets of one transparent mirror, yet this mirror is no longer opaque. What the Self sees is Being; what Being reflects is Self. In the classical mirror, the Self looks at Being. In the quantum mirror, Being sees itself through the Self. The boundary dissolves, yet the integrity of both remains intact.
In this convergence, knowledge ceases to be the representation of an external world and becomes the world’s recognition of itself. Classical thought knows through separation; quantum-reflective thought knows through coherence. In this new mirror, Being and Self are no longer two sides of a division but one act of reflection, the world seeing itself as it is seen.
Philippe De Keukelaere
NEW TEXT
THE EVOLUTIONARY CYCLE OF HIGH-ENERGY STELLAR REMNANTS
FROM SUPERNOVA EXPLOSIONS TO QUANTUM MECHANICAL DISSIPATION
WHAT WILL REVOLUTIONIZE THE HUMAN SCIENCES.
Black Hole Explosions? Offprint from: Nature, Vol. 248, No. 5443, 1 March 1974. After : HAWKING, Stephen William.
[London: Macmillan, 1974].
First edition, extremely rare offprint issue, and Hawking’s own file copy, of his most important article, predicting that black holes emit radiation, now known as ‘Hawking radiation’. This would cause relatively low mass black holes (less than 1012 kg) to ‘evaporate’ completely in a time less than the age of the universe. The discovery that black holes radiate was a complete shock to the scientific community since it had been assumed that nothing, not even light, could escape from a black hole (that was, of course, why they were called black holes!). Hawking’s Royal Society obituary stated: “It is fair to say that Stephen’s discovery [of Hawking radiation] ranks as one of the most important results ever in fundamental physics” (Carr, et al.). John Archibald Wheeler once said that just talking about Hawking radiation was like “rolling candy on the tongue” (ibid.). Hawking’s doctoral advisor, Dennis Sciama, said of Hawking radiation, “That’s a work of genius, in my opinion, that discovery” (Sciama, Oral History). At the heart of Hawking’s theory is an equation (see below) relating the entropy of a black hole, or equivalently the amount of information it contains, to its surface area (the two are proportional). The Harvard physicist Andrew Strominger, who collaborated with Hawking on one of his last works, wrote: “The [area/entropy] equation stands alongside the Einstein equation and the Schrödinger equation among the most important equations of 20th-century physics. However, unlike the other equations, which describe distinct areas of physics, the area/information law unites disparate areas, as indicated by the striking appearance [in the equation] of nearly all the most basic constants of nature” (Page et al.). This formula, which Hawking wanted to have engraved on his tombstone, suggests a profound and hitherto unsuspected relation between general relativity, quantum theory, and thermodynamics. The formula gives a glimpse of a future theory of quantum gravity, the holy grail of theoretical physics. “The challenge of uniting quantum theory and general relativity in a successful theory of quantum gravity has arguably been the greatest challenge facing theoretical physics for the past eighty years. One avenue that has seemed particularly promising is the attempt to apply quantum theory to black holes. This is in part because, as purely gravitational entities, black holes present an apparently simple but physically important case for the study of the quantization of gravity. Further, because the gravitational force grows without bound as one nears a standard black-hole singularity, one would expect quantum gravitational effects (which should come into play at extremely high energies) to manifest themselves in the interior of black holes. In the event, studies of quantum mechanical systems in black hole spacetimes have revealed several surprises that threaten to overturn the views of space, time, and matter that general relativity and quantum field theory each on their own suggests or relies on … it has become increasingly clear that there are profound connections among general relativity, quantum field theory, and thermodynamics … In particular, a remarkable parallel between the laws of black holes and the laws of thermodynamics indicates that gravity and thermodynamics may be linked in a fundamental (and previously unimagined) way. This linkage strongly suggests, among many things, that our fundamental ideas of entropy and the nature of the Second Law of thermodynamics must be reconsidered, and that the standard form of quantum evolution itself may need to be modified” (Stanford Encyclopedia of Philosophy). Nobel Laureate Kip Thorne wrote: “Few, if any, of Einstein’s successors have done more [than Hawking] to deepen our insights into gravity, space and time’, and Roger Penrose stated ‘We remember Newton for answers. We remember Hawking for questions. And Hawking’s questions themselves keep on giving, generating breakthroughs decades later. When ultimately we master the quantum gravity laws, and fully comprehend the birth of our universe, it will be by standing on the shoulders of Hawking’ (Carr et al.). We are not aware of any other copy of this offprint having appeared on the market.
Provenance: the estate of Professor Stephen Hawking (1942-2018).
“The simplest picture of a black hole (the term was coined by Wheeler in 1967) is that of a system whose gravity is so strong that nothing, not even light, can escape from it. Systems of this type are already possible in the familiar Newtonian theory of gravity. The escape velocity of a body is the velocity at which an object would have to begin to travel to escape the gravitational pull of the body and continue flying out to infinity, without further acceleration. Because the escape velocity is measured from the surface of an object, it becomes higher if a body contracts and becomes more dense. If the object were to become sufficiently dense, the escape velocity could therefore exceed the speed of light, and light itself would be unable to escape … Taking relativistic considerations into account, however, we find that black holes are far more exotic entities” (SEP).
The existence of black holes in the context of general relativity was predicted by the German astronomer Karl Schwarzschild who, in 1915, found the first exact solution to Einstein’s equations, which Einstein had perfected just one month earlier. This solution described the gravitational field, or equivalently the nature of the spacetime, outside a spherically symmetric mass. In Schwarzschild’s solution there was a sphere concentric with the mass, later called the ‘event horizon’, such that nothing, not even light, could escape from inside the event horizon to the outside. There was a singularity at the centre of the black hole at which the notions of space and time broke down. Later, solutions of Einstein’s equations were found which described rotating black holes, and black holes with an electric charge. It is important to emphasize that, in general relativity, a black hole is a purely gravitational object: a black hole is not a thing in spacetime; it is instead a feature of spacetime itself.
Physicists, notably including Einstein himself, were initially sceptical that Schwarzschild’s solution described anything that could exist in the real universe. Indeed, in 1939 Einstein wrote a paper purporting to show that black holes could not exist. But at almost the same time, J. Robert Oppenheimer and his student Hartland Snyder published a paper which gave a precise mechanism whereby a collapsing star could become a black hole.
It was only in the 1960s that important results on the nature of black holes began to appear. One of the first was the ‘no-hair’ theorem (so called by Wheeler), which states that black holes are completely characterised by just three externally observable quantities: their mass, electric charge and angular momentum. All other information (for which ‘hair’ is a metaphor) about the matter that formed a black hole or is falling into it ‘disappears’ behind the event horizon and is therefore permanently inaccessible to external observers. The no-hair theorem was followed by the discovery of the four ‘laws’ of black holes:
- The surface gravity of a stationary black hole is constant over its entire surface.
- A change in the total mass of the black hole is determined in a fixed way by changes in its area, angular momentum, and electric charge, so that the total quantity is conserved.
- (The Area Theorem) The total surface area of a black hole never decreases.
- No physical process can reduce the surface gravity of a black hole to zero.
There is an obvious formal analogy between these laws and the laws of classical thermodynamics: the 0th law of thermodynamics states that a body in thermal equilibrium has constant temperature throughout; the 1st law is a statement of the conservation of energy; the 2nd law states that entropy never decreases; and the 3rd law states that it is impossible to reduce the temperature of a system to zero by any physical process. Accordingly, if in the laws for black holes one takes ‘stationary’ to stand for ‘thermal equilibrium’, ‘surface gravity’ to stand for ‘temperature’, ‘mass’ to stand for ‘energy’, and ‘area’ to stand for ‘entropy’, then the formal analogy is perfect. In the early 1970s, Jacob Bekenstein suggested that this was more than an analogy: he argued that a black hole should be assigned an entropy proportional to its area.
“Stephen was highly sceptical [of Beckenstein’s suggestion] because black holes would then have a non-zero temperature. Any object with a temperature emits black body radiation, but black holes were thought to be unable to emit anything. Stephen began to study how particles and fields governed by quantum theory would [interact with] a black hole. Earlier studies [by the Soviet astrophysicists Yakov Zeldovich and Alexei Starobinsky] had shown that an incoming wave could be amplified by scattering off a spinning black hole and had even indicated, as an extension, that a spinning black hole could … caus[e] spontaneous particle emission that spins the black hole down.
“At the Krakow meeting on Cosmology in September 1973, Stephen met Zeldovich and Starobinsky, who pointed out to him this spontaneous emission. Stimulated by these discussions, Stephen discovered a few months later, much to everyone’s surprise, that all black holes, even those that do not spin and thus have no spin energy to extract, emit particles at a steady rate. Initially, he thought there must be a mistake in his calculation. That black holes could emit particles went against the long-held belief that black holes could only be absorbers and never emitters of anything. The result refused to go away. What finally convinced Stephen was that the outgoing particles had precisely a thermal spectrum—the black hole created and emitted particles and radiation just like any hot body … This phenomenon came to be known as Hawking radiation.
“For a non-rotating black hole [of mass M], the temperature is given by Stephen’s most famous equation,
T = hc3/16π2GkM,
where h is Planck’s constant, c is the speed of light, G is Newton’s gravitational constant, and k is Boltzmann’s constant. [This implies that] the entropy S of the black hole can be identified as
S = πAkc3/2Gh
[where A is its surface area]” …
“Consequently, an isolated black hole emits thermal radiation and so loses mass. Since the temperature is inversely proportional to the mass, the temperature increases, leading to a runaway process and eventually, it is presumed, to the disappearance of the black hole. The process takes an inordinately long time for a solar-mass black hole, about 1067 years. But for small black holes, which could have been formed in the early universe, their lifetimes could be much shorter. For example, a black hole of mass 1012 kg will last about 1010 years, approximately the current age of the universe” (Carr et al.).
“Although careful to be discreet until he was ready to make an official announcement, [Hawking] could not resist telling Dennis Sciama, the man who had helped shape his early career. Afterward, the shocking news spread through Hawking’s inner circle. Martin Rees, a colleague at Cambridge [and future President of the Royal Society and Astronomer Royal] welcomed a visit from Sciama with ‘Have you heard? Have you heard what Stephen had discovered? Everything is different, everything has changed!’” (Larsen, p. 42).
“Stephen first announced this result at a meeting on quantum gravity at the Rutherford Laboratory on 15-16 February 1974, and it was published in Nature shortly afterwards [the offered paper]. The prediction has now been derived in several different ways and it is such a beautiful result—unifying quantum theory, general relativity and thermodynamics—that most experts accept that it is correct” (Carr et al.). “Hawking wrote a longer, more complete description of his discovery and submitted it to Communications in Mathematical Physics in March, 1974. He did not receive any acknowledgement, and a year later inquired as to the status of his paper. He was told that the journal had lost his manuscript and was asked to resubmit it. When it was finally published, the submission date was erroneously listed as April 1975” (Larsen, p. 43).
Hawking’s first picture to understand his radiation was in terms of ‘virtual particles.’ “According to Einstein’s special theory of relativity, mass can be converted into energy and energy can be converted into mass [namely, a particle-antiparticle pair]. According to … the Heisenberg Uncertainty Principle, it is possible to create energy out of nothing so long as the energy debt is paid back in a very short period of time … The energy is, in a sense, borrowed from the very fabric of the universe – from the vacuum, as it is called. This happens randomly every second of every day, with the borrowed energy creating a particle-antiparticle pair (called a virtual pair, since they only exist temporarily). After the passage of a minute amount of time, the pair rejoins and annihilates, repaying the energy debt to the universe. As strange as this may sound, it has been verified experimentally. Parallel metal plates in a vacuum set very close together will feel a tiny attractive force due to the presence of the virtual pairs – this is called the ‘Casimir effect.’
“Suppose the creation of the particle-antiparticle pair happened just outside the event horizon of a black hole. If one of the members of the pair fell into the black hole, the remaining particle could not annihilate with its partner when the time was up, and the energy debt appears to be unpaid. A real particle or antiparticle has been created, seemingly from nothing, or, rather, it looks to an outside observer as if it leaked from the black hole! But the energy needed to create the particle had to come from somewhere – namely from the black hole itself. In this way, the energy of the black hole, or, better yet, its mass (since mass and energy are convertible, according to Einstein) decreases, and the black hole radiates away” (Larsen, p. 41).
The existence of Hawking radiation creates two deep problems for physics: ‘naked’ singularities and the ‘information loss paradox’. Work by Hawking, the Oxford physicist Roger Penrose and others in the late 1960s established several singularity theorems which showed that, if certain physically reasonable premises were satisfied, then in certain circumstances singularities could not be avoided. These theorems indicate that our universe began with an initial singularity (the Big Bang), and that in certain circumstances collapsing matter must form a black hole with a central singularity. While spacetime singularities are frequently viewed with fear and suspicion, physicists offer the reassurance that, even if they are real, we expect them to be hidden away behind the event horizons of black holes. They could not therefore affect the universe outside the event horizon. A naked singularity, on the other hand – one that is not hidden behind an event horizon – seems to imply a profound breakdown in the fundamental structure of spacetime: even determinism itself would collapse entirely near a naked singularity. The existence of Hawking radiation raises the possibility that naked singularities could actually be formed in our universe: as a black hole emits Hawking radiation, its event horizon shrinks, and eventually (in a finite time) disappears altogether, apparently leaving the singularity at the centre of the black hole exposed.
We noted above that when a black hole is formed, by the collapse of a star, for example, all information about the star (e.g. the elements of which is composed) is lost, except for the three quantities mass, electric charge, and angular momentum. This was not regarded as a problem, as it could be assumed that this information was somehow stored inside the event horizon of the black hole, even though it was inaccessible. But if the black hole eventually disappears as a result of emitting Hawking radiation, it seems that the information about everything that fell into the black hole will be irretrievably lost – the Hawking radiation is random (it has no relation to the original information). This loss of information is a serious problem because it seems to imply that black holes cannot be described by quantum mechanics. In standard quantum mechanics, a knowledge of the quantum state of a physical system at one time is sufficient to determine it, via Schrödinger’s equation, at any later time: this implies that quantum evolution “preserves information”. Although Hawking agonized about the paradox on and off over the next 40 years, it was only in one of his very last works that a solution began to appear. In a 2016 joint paper with Strominger and the Cambridge physicist Malcolm Perry, Hawking suggested that the vacuum of general relativity might provide a ‘memory matrix’ THAT PRESERVES THE INFORMATION IN THE UNIVERSE, even after a black hole has evaporated. (I emphasise)
Carr, Ellis, Gibbons, Hartle, Hertog, Penrose, Perry, & Thorne, ‘Stephen William Hawking CH CBE. 8 January 1942 – 14 March 2018,’ Bibliographical Memoirs of Fellows of the Royal Society, Vol. 66, June 2019 (royalsocietypublishing.org/doi/10.1098/rsbm.2019.0001). Page, Taylor, Preskill, Hertog, Ellis, Guth, Unruh, Strominger, Rocek, Galfard, Berry, Carr & Hartle, ‘Stephen Hawking (1942-2018),’ Physics Today, 14 March 2018 (physicstoday.scitation.org/do/10.1063/PT.6.4.20180314a/full/). Hawking, Perry & Strominger, ‘Soft hair on black holes,’ Physical Review Letters, vol. 116, 231301 (2016). Larsen, Stephen Hawking: A Biography, 2005. Sciama, Oral History Interview, 14 April 1978, American Institute of Physics (aip.org/history-programs/niels-bohr-library/oral-histories/4871).
THE EVOLUTIONARY CYCLE OF HIGH-ENERGY STELLAR REMNANTS
FROM SUPERNOVA EXPLOSIONS TO QUANTUM MECHANICAL DISSIPATION
WHAT WILL REVOLUTIONIZE THE HUMAN SCIENCES.
A preliminary synthesis, an imperfect synthesis of current scientific insights regarding the final stages of massive stars (M > 8 M☉). Central to hereby are the energetics of supernovae and gamma-ray bursts (GRBs), the threshold values for black hole formation, and the theoretical process of black hole evaporation via Hawking radiation. The emphasis lies on the transition from matter to energy and the long-term evolution of the cosmos.
INTRODUCTION
In contemporary 2026 astronomy, supported by multi-messenger observatories, we understand that the death of a star is not an endpoint but a transformation. The most powerful explosions in the universe act as both the source of chemical complexity (nucleosynthesis) and potential threats to biological systems in nearby galaxies.
THE DYNAMICS OF STELLAR EXPLOSIONS
When the nuclear fuel of a massive star is exhausted, the iron core collapses under its own gravity. This results in:
Supernovae: An explosion with a luminosity of billions of suns, responsible for the dispersal of heavy elements such as iron, gold, and calcium.
Gamma-Ray Bursts (GRBs): Relativistic particle jets originating at the birth of a black hole. These “cosmic fireworks” can sterilize biospheres at distances of thousands of light-years by destroying atmospheric ozone layers.
THE FORMATION OF COMPACT REMNANTS
The mass of the remaining core determines the ‘fate’ of the star, dictated by the Tolman-Oppenheimer-Volkoff (TOV) limit:
- Neutron Stars: If the core mass remains between ~1.4 and 2.2 M☉, the collapse is halted by neutron degeneracy pressure.
- Black Holes: If the mass exceeds the TOV limit, a complete gravitational collapse occurs, leading to a singularity.
THE END OF BLACK HOLES: HAWKING RADIATION
Black holes are not eternal. According to the principles of quantum field theory in curved spacetime, as formulated by Stephen Hawking, these objects slowly ‘evaporate’:
Mechanism: near the event horizon, particle pairs are created. One particle falls in while the other escapes, leading to a net loss of mass (M).
Evaporation Time: the lifespan is proportional to M³. For stellar-mass black holes, this process takes approximately 10^67 years.
The Final Explosion: As the mass decreases, the temperature of the black hole rises exponentially. The final phase manifests as a burst of high-energy gamma radiation, converting the remaining mass into pure energy in a fraction of a second.
The life cycle of matter in the universe reaches its most extreme form in black holes. Although they appear to be the ultimate ‘trap’ for matter, Hawking radiation ensures that all mass eventually returns to the universe as radiation. Future missions, such as the Nancy Grace Roman Space Telescope, remain essential for validating these frontiers of physics.
THE PARADOX OF INFORMATION AND ENTROPIC DECAY
The transition from a collapsing star to an evaporating black hole introduces one of the deepest conflicts in modern physics: ‘the Black Hole Information Paradox’. This process is governed by the interplay between gravitational entropy and the fundamental laws of quantum mechanics.
Bekenstein-Hawking Entropy
A black hole is not merely a geometric vacuum; it possesses a massive amount of entropy. Unlike classical systems where entropy is proportional to volume, a black hole’s entropy is proportional to the surface area of its event horizon:
This implies that as a star collapse into a black hole, the enormous amount of information (the “microstates”) that constituted the star is encoded on the two-dimensional boundary of the horizon. This aligns with the Second Law of Thermodynamics: the total entropy of the universe must increase, and the formation of a black hole represents the most efficient way to “pack” entropy into a finite region of space.
The Information Paradox
The problem arises during Hawking Radiation. If a black hole evaporates completely, what happens to the information that fell into it?
Quantum Unitarity
A core principle of quantum mechanics is that information cannot be destroyed; the initial state of a system must be uniquely recoverable from its final state.
The Conflict
Hawking’s original calculation suggested that the outgoing radiation is purely thermal (random). If the radiation is random and the black hole disappears, the information about the original star is lost forever, violating the laws of physics.
Information Preservation via Entanglement
Current insights suggest that information is preserved. As the black hole evaporates, the entanglement between the interior and the exterior radiation increases. After a certain point (the Page Time), the information begins to ‘leak’ back out through subtle correlations in the Hawking radiation.
The Final Dissipation
In the context of the long-term evolution of the cosmos, this process signifies the ultimate increase in entropy. The “ordered” information of a star is processed by the black hole and eventually redistributed across the universe as “scrambled” Hawking radiation. While the information is technically preserved (satisfying quantum laws), the entropy increases to its maximum possible state, leading the universe toward a state of thermal equilibrium, or “heat death,” where no more work can be performed.
REFERENCE
Hawking, S. W. (1974). Black hole explosions? Nature, 248 (5443), pp. 30-31.
How Do Wars End? The Taste of the Innocent Loser
The Discovery in the Caves of Goyet (Belgium, 40,500–45,500 BCE): When War (The Hunt for Humans?) and Religion Were Still One
The Unrecognized Discovery of Sigmund Freud to End Wars
The Spoils of War (Women, Territory, Gold—the Billions) as Primary Drivers (Casus Belli) for Wars
The discovery of cannibalism in the caves of Goyet was a process that unfolded over several years and decades, but the crucial scientific breakthrough took place in 2016.
The Original Excavations (1860–1930)
The caves were first investigated by the geologist Édouard Dupont in 1868. At that time, thousands of bones and artifacts were collected and brought to the Royal Belgian Institute of Natural Sciences (RBINS) in Brussels. It was already known that human remains were among them, but methods to analyse them in detail did not yet exist.
The Rediscovery in the Archive (2004–2012)
Archaeologist Hélène Rougier and her team began to re-examine the vast archive of Dupont’s excavations. To everyone’s surprise, among the animal remains (horses, reindeer), they discovered numerous bone fragments that were not from animals, but from Neanderthals.
The Publication of Scientific Proof for Cannibalism (2016)
Scientific confirmation of cannibalism came in July 2016. After years of microscopic research and DNA analysis, the team published the results in Scientific Reports [3].
This research demonstrated that four facts were scientifically established:
The bones showed cut marks indicating filleting.
The bones were intentionally broken to extract bone marrow.
The bones were used by Neanderthals as tools (retouchoirs).
The bones belonged to “strangers”; it was a form of “exocannibalism.”
This discovery took place not in the cave itself but in a laboratory and museum archive. Because human and animal bones had become mixed during the original 19th-century excavations, modern scientists could only determine what had truly happened using advanced techniques such as high-resolution microscopy and isotope analysis.
If we wish to go further than what has been scientifically demonstrated, we enter the realm of falsifiable hypotheses. Here, I proceed from several hypotheses, which, however, can also be read in combination with one another.
The Hunger, the Calories
The most obvious hypothesis is that of hunger and the search for calories. This explanation is generally applied to such discoveries and concerns an economic event: there is food scarcity, and one remedies this by seeking nourishment where possible.
The fact that this food was not sourced from one’s own population can be explained by the greater economic convenience of fetching food from another group rather than from within one’s own. This fits within a survival strategy. Obtaining food from one’s own group would have only worsened the crisis. After all, the question would have been: who are we going to eat first?
It should be clear that, under such a premise, the risk of internal violence should not be underestimated. However, the question remains whether acquiring such food from one’s neighbours could have proceeded non-violently. Although this cannot be demonstrated scientifically, it is highly likely that such acts would have involved conflict.
Another question is whether such behaviour must always be linked to the search for calories. Is it explicable solely as an economic survival strategy, or could more have been at play? In this economic interpretation, the victims are those of food scarcity.
A Religious Hunt for Humans? Religion as a First Form of War
In the animal world – particularly among apes- it has been observed that certain hunts are not primarily linked to acquiring food or calories. Such hunts serve as religious or bonding rituals within the group. Through the hunt, a new connecting hierarchy is established or reinforced within animal groups, concerning the distribution of food and females.
Hunting, and war-as-hunting, can thus be seen as the earliest forms of religious bonding rituals, traces of which already appear in the animal world. Central to this ritual process is the consumption of the spoils of war. In this assumption, the victims are not those of hunger, but of war.
Why Eat the Loser? Sigmund Freud
I propose a renewed reading of Sigmund Freud, and more specifically Chapter 4 of Totem and Taboo.
The difficulty lies in uncovering the dynamics of ritual consumption (theophagy and exocannibalism) from a new perspective. Contrary to theories that view eating the god or enemy as an appropriation of power or vitality, we may see it as a ritual assimilation of innocence. In exocannibalism, the central issue is a change of taste, making the eating of the enemy (real or symbolic) necessary.
Based on a rereading of Freud’s Totem und Tabu and the Polemos of Heraclitus, one can posit that the victor becomes morally bankrupt (guilty) through his victory, whereas the loser retains innocence in his defeat. Consuming the body – viewed as the information carrier of this innocence – is not a triumph but a necessary compensation for the winner’s guilt.
The history of religions shows a persistent phenomenon of physically internalizing the divine or the enemy. From the Aztec teocualo (eating the god Huitzilopochtli in the form of tzoalli dough) to the Christian Eucharist, and from archaic exocannibalism to the symbolic consumption of the enemy (as in the Viennese legend of the croissant), the common thread is assimilation.
Traditionally, this assimilation is interpreted as a transfer of power—the eater takes over the strength of the eaten. This text proposes a fundamental reversal of that view. What if the eater is not the “strong one” seeking power, but the “guilty one” seeking innocence at a moment of extreme entropy (killing and eating the enemy)?
For Heraclitus, War (Polemos) is not merely destructive but also productive; through War, new orders arise in the world. The Primal Father (War) is both the Destroying and the Creating Father. As long as the Father lives (War itself, in Freud), there is chaos and oppression.
The desire for the father’s women is the spoils of war for which the murder—the war against the Father – is committed. Without this specific object of desire, the sons’ aggression would never have led to collective murder. The woman becomes the ultimate treasure – the Spoils of War. In the Primal Horde (Urhorde), the Father holds the monopoly on all women, possessing them as exclusive property. For the sons, the women are the forbidden fruit, the means of existence denied to them. The “War” (the sons’ revolt) is essentially a robbery, they seek to seize the Father’s possessions.
One could say that the sons are jealous of the Father’s wealth and start a war to conquer the loot. But more is at play. The sons wage war because they believe they have lost something – their being, their self – represented mythically as animals in relation to the Primal Father. Yet the loot continually points back to the victor’s guilt, which is why the victor attempts ritually to restore innocence, to move from chaos and disorder toward a renewed cultural order. This ritual may take the form of eating the enemy. In this way, the loot disappears, and the guilty victor assimilates the innocence of the defeated.
The cannibalistic ritual is the guilty victor’s attempt to reclaim the loser’s innocence. In that sense, it is a restoration ritual: it transforms the guilt of acquisition into renewed innocence through symbolic loss.
This dynamic finds its anthropological foundation in Freud’s work. In Totem und Tabu (1913), Freud describes the primal murder, where the sons (the victors) kill and consume the father (the loser). Crucially, Freud does not let social order (Kultur) arise from the victory itself but from the psychological crisis that follows. The victors do not celebrate power; they are overcome by guilt consciousness (Schuldbewußtsein).
Freud writes:
“So schufen sie aus dem Bewußtsein der Schuld heraus die beiden Grundtabus des Totemismus, mit denen die Anfänge der Moral unausbleiblich gegeben waren.”
(“Thus they created out of their filial sense of guilt the two fundamental taboos of totemism, which for that very reason inevitably corresponded to the two repressed wishes of the Oedipus complex.”) [1]
“Die Gesellschaft ruht nun auf der Mitschuld an dem gemeinsam begangenen Verbrechen…”
(“Society is now based on complicity in the common crime…”) [2]
Culture is thus the monument of the guilty victor. The ritual meal repeats the attempt to bring the Father (the loser) back to life within one’s own body – to ‘launder’ the guilt of murder, as in the Roman general’s triumphal sacrifice of the white bull.
The figure of the Primal Father or Loser aligns with Heraclitus’s concept of Polemos (War/Strife). Heraclitus states in Fragment 53:
“War is the father of all and the king of all; and some he has made gods and some men, some bond and some free.” [4]
In the Freudian reading, the Primal Father becomes the embodiment of conflict. His death – the ultimate battle – creates the distinction between War (the dead Father/totem) and Man (the guilty sons). Whereas Heraclitus saw struggle as a cosmic, innocent necessity, the sons moralize it. Having won the Polemosthrough parricide, they bear the burden of victory. The loser (the Father/God), withdrawn from guilt by his defeat, becomes sacral and innocent.
However terrible such rituals may seem, it is through them – through the change of taste (from guilt to innocence) in eating the enemy or a substitute – that the preservation of the idea of “the innocence of the loser” emerges as the true end of the Primal Father.
In eating a “truly present god” (as in transubstantiation) or symbolically eating the enemy, one consumes the spoils of war for their sacral meaning- the taste -. The only thing truly “present” is the taste of the booty consumed. That is what it is about: the taste of the loser’s innocence (later reflected in ritual sacrifices), which sacrally transforms the victor’s guilty consciousness into innocence.
Thus, humanity gradually discovered that the loser of a war is innocent because of his loss, and the victor is guilty because of his victory. While most sacral restoration rituals emphasize increased power through victory, their unspoken, unconscious meaning (in Freud) is the restoration of innocence. Freud discovered that wars become unnecessary as soon as humankind recognizes, within consciousness itself, the innocence of the loser.
Philippe De Keukelaere
Bibliography
Freud, Sigmund. (1913). Totem und Tabu. Einige Übereinstimmungen im Seelenleben der Wilden und der Neurotiker. In Gesammelte Werke, Band IX. London: Imago Publishing.
Heraclitus. (ca. 500 BC). Fragments.
Rougier, Hélène et al. (2016). Neandertal cannibalism and Neandertal bones used as tools in Northern Europe. Scientific Reports 6, Article number: 29005.
Notes:
[1] Freud, S., GW IX, p. 176 (Chapter IV: “Die infantile Wiederkehr des Totemismus”).
[2] Freud, S., GW IX, p. 179.
[3] Rougier, H. et al., Scientific Reports 6, 29005 (2016).
[4] Diels-Kranz, Die Fragmente der Vorsokratiker, 22 B 53.
Sunday Morning
The Ukrainian artist Vostyslaf Voronko
HOW PIETER BRUEGEL THE ELDER, AS A REPRESENTATIVE OF FLEMISH PAINTING, DISCOVERED THE RELATIONSHIP BETWEEN WAR AND SELF-DEIFIED GURUS (gurus are not leaders)
INTRODUCTION
My source is the book by Leo Spaepen: de Bruegelcode, 2025.
My intention is, with respect to the evolutionary possibility of achieving peace, to examine which element, the gently mirroring self, can connect itself from self-consciousness with another element (that stabilizes the oxytocin and dopamine levels in our brains to a violence-inhibiting level) as a necessary condition for the realization of peace.
It is, however, important to first give a counterexample.
The discoverer of it (I repeat that this is as important as discoveries from the ‘hard’ sciences, which are also important) is an artist, Pieter Bruegel the Elder.
I draw my information from the aforementioned source, but will mainly draw a connection between two artworks by Bruegel. The Triumph of Death (Prado, Madrid) and The Tower of Babel (the version – there are two –, in my eyes equally valuable versions – that hangs in the Kunsthistorisches Museum in Vienna). First I will treat the two paintings separately based on the information I found in the aforementioned book. From there I will make the connection.
One of the valuable elements of Spaepen’s book is the anchoring of the artist in the particular Flemish painting tradition (which is still not generally accepted, because for example only one of his paintings is in a Flemish museum, Dulle Griet, purchased in 1894 by a German merchant in Antwerp, Fritz Mayer van den Bergh, for 486 Belgian francs (116)).
His quest to connect the meaning of the themes with the turbulent history from Bruegel’s time is convincing.
Spaepen discovers the various nuanced dimensions in Bruegel’s artworks.
I have already written about The Triumph of Death. At the time I did not have the information that I have now found in Spaepen’s book. My thesis is that besides the particular anchoring of Bruegel’s work, this work also has a universal meaning regarding the phenomena we try to objectively discover in a positivist way. I will try to demonstrate this by making the connection between the two aforementioned paintings.
THE TRIUMPH OF DEATH
Spaepen analyzes the painting from three planes (he cuts the painting into three parallel parts from north to south). He talks about the background, the middle ground, and the foreground. The foreground is a panoramic landscape that he identifies from left to right.
a) The background (which can also be read as a foreplan, because the self-sacrifice and self-destruction from this plan approach us – when read vertically -)
On the left, he recognizes the chalk cliffs of the North Sea coast of the French Cap Gris-Nez and Cap Blanc-Nez. On the right, the yellow sand dunes of the Netherlands (94).
On the left there is war and the battle rages. In the middle we have an advancing army of skeletons, who advance from the hills inland (95). Spaepen states that the viewer thereby feels the threat. There are attempts to stop the advancing army of corpses, but they fail (95). On a dune to the right there is an explosion. The painting shows mainly executions of heretics on the right. There are torture wheels (also on the left) and emaciated corpses hanging from gallows. Beheaded corpses. Part of a corpse is approached by a dog, there are dead skeletons (bones), etc…
Rightly, Spaepen states that the religious conflict is also raging fully on the right. He writes: “Together with the advancing army of skeletons, those scenes make it clear to us: the religious conflict has also fully erupted here, because the breeding ground for it, hatred, is as present here as in France.” (95)
My thesis is (I use Spaepen’s elements), that we have on the left the violent aspect of war, the battle itself. On the right we have what feeds the war (Spaepen’s breeding ground), namely the violent mythical pillar. The most important, however, is situated in the middle. This is Bruegel’s brilliant invention. The war comes toward us from self-sacrifice and self-destruction. By turning back time and painting already deceased skeletons, he discovers the core of what a war is. Why do I state that it is Bruegel who discovered self-sacrifice and self-destruction (which comes toward us) as the core of the war phenomenon?
In 2008 (the institution was only recognized as a university in 2014), in the wing that formerly belonged to the Walpole-Waldegrave family, I tried in Twickenham (Greater London) (in 20 minutes, my short speaking time) to demonstrate that from the Neolithic to the present there is a human sign language (already present in the late Paleolithic; for example, already appearing in the ‘Grotta dell’Addaura’ in Sicily) that symbolically religiously depicts the necessity of self-sacrifice – self-destruction. It is the raised arms (in religions this is still a gesture of offering). Remarkable in Bruegel’s painting is that the leader of the oncoming skeleton army is not a corpse, but a giant, or deity (the god of war?) – with a living human body – with raised arms. He is unarmed. Only a second corpse giant (or god) who follows him on his heels is armed with a spear and ready to throw. Bruegel is a dual artist. Spaepen also notices this in his book (albeit in another context as double meaning).
Spaepen’s analysis is valuably innovative. He starts from a horizontal plan.
My thesis is that there is also a vertical plan. The vertical plan starts from the left side, the tower, from where the skeleton army departs, further along a walled chapel, where we get the impression (?) that the skeletons are enjoying themselves as in a tavern. It could also be that they learn the ‘offering gesture’ (as body language) there. The outstretched arms could point to this. Most of the skeleton army is further painted as a right angle, of which the ‘right angle’ touches a torture wheel on the right side.
The endpoint is a cross, which is the mirror image of the giant or god with raised arms. Would Protestants and Catholics both engage in battle, from a mythical religious pillar or the necessary self-sacrifice of an exemplary executed person as a model? The self-destruction of a mythical tragic hero, whom all self-sacrificers must imitate as tragic war heroes?
If we follow the same line, we find that it is now the skeletons who are fighting each other. A reference to the division within the camps? On the Reformed side, the Lutherans, the Calvinists and the Anabaptists. But also the Catholic side was very divided, between the more tolerant (William of Orange – who remained Catholic for a long time –, Egmont, Hoorn, and even – albeit to a much lesser extent – Margaret of Parma), and the extremes, King Philip II of Spain and for a long time (until he fell from grace; he was eventually also made a scapegoat due to the merciless attitude of King Philip II) Cardinal Granvelle.
Suddenly when we look to the south, we discover a naked man. The man looks at the approaching army in the distance, and more specifically at the giant or god (here rather god) with raised arms. He would like to make the same gesture (Bruegel’s humor, who had the nickname Bruegel the droll – in the sense of the French drôle and not in that other meaning… which the word did not yet have – later Bruegel was even compared to Pallieter (21), which is not quite correct; he did have a deep sense of humor), but has a big problem. He is naked and must hide something with his other hand. It is perhaps far-fetched. Yet I ask the question: could the man symbolize the erotic sacrificial ‘mania’ (the Greek word), inherent to the gurus, who as self-deified gods wage wars of aggression (more on the meaning of self-deification in Bruegel later), and therefore have others sacrifice themselves as human offerings like tragic heroes did.
The man walks toward a walled, lifeless garden.
In the middle of that garden stands only one dead tree. In the garden, a corpse is buried by a corpse, there are skulls, and two large skeletons who make a snake-like movement to ring two death bells. The bells are the size of those found in Gothic cathedrals. There is clearly a reference to your ancestor Adam (and he looks like him!), who together with his spouse (Madam Eve) was expelled from the Garden of Eden, and now wants to return to this ultimate place of self-sacrifice and ‘self-destruction’ that the Garden of Eden has become.
It has become a walled city of graves, where only corpses and corpse remains live. If we follow the line from the tower (French side), to the right (to the Dutch side), further to the south, we find that the line is snake-shaped. Would Bruegel be suggesting a connection between war as the original sin of humanity?
I do not dare to claim that far. What is certain for me is that the mythical pillar of war – which Bruegel discovered – is the original sin of humanity. The original sin is a denial that we could rediscover and objectify from a renewed positivist perspective, but that we – not out of denial – but mythical blindness do not want to see. The deepest layer is the self-sacrifice and self-destruction of the own self and the self of the own people. Here we touch the particular Flemish aspect of Breugel. He expresses this self-sacrifice from the religious mythical, particularly from his time, but also universally. The story of Adam and Eve is an old Jewish literary story, but it undeniably has a universal meaning (it wants to address all humanity in literary form).
Philippe De Keukelaere (to be continued).
THE MOST IMPORTANT WORK OF ART (PAINTING) IN WORLD HISTORY
PIETER BRUEGHEL THE ELDER UNDERSTOOD THE (MYTHICAL) STRUCTURE OF EXTREME VIOLENCE
THE TRIUMPH OF DEATH.
INTRODUCTION
In the Prado Museum in Madrid hangs a painting by Pieter Brueghel the Elder from 1562. This artwork is as important for world history as Einstein’s scientific work.
It is so significant that it should actually be displayed in a separate room. It is worth visiting the Prado Museum just for this painting.
In this painting, I find all (yes, all) the structuring elements of my analysis regarding contemporary extreme collective violence.
The painting is a synthesis of the meaning of this violence for humanity. Brueghel sees reality through the eyes of the people, which is why his ‘genius’ is often overlooked.
SOME ELEMENTS
I/ The ambivalent goddess of fate – the supreme god
At the bottom right (when looking at the painting), our ambivalent goddess of fate sits calmly, away from the chaos of war. She holds a musical score in her hand.
The benevolent side plays music with a mandolin, while the malevolent side, a skeleton representing death, plays the violin.
II/ The self-deified incarnate gods
Above the table (with a white tablecloth), we see the empress (the emperor’s wife) in a red dress. She is still alive but is already being gripped by death – the skeleton holding her above her golden belt.
Her self-deification falters due to the total destruction caused by extreme violence in war. As an ambivalent incarnation of the fate goddess belonging to the benevolent side of divine ambivalence, she now moves to the malevolent side of death.
She joins what the people have always been in relation to the fate goddess and the incarnate gods.
She makes a final, futile gesture to save her divine status, raising both arms. This is the oldest sacrificial gesture of humanity, but she does it not for herself. She looks at us.
It is an attempt to preserve her divine status at the last moment by perpetuating the self-sacrifice of the people, which nourishes that status with blood. However, there is no blood – the symbol of self-sacrifice – to be seen anywhere.
The violence is so extreme because the self-sacrifice of the people is over. The malevolent side of the fate goddess is now only death. The empress will also be destroyed by death.
The skeleton actually performs the opposite sacrificial gesture with its long arms, indicating the disappearance of the sacrifice and the dominance of death. The skeleton laughs. It is the triumph of death as the (new) malevolent side of divine ambivalence towards the people.
At the bottom right lies the emperor in military attire. He doesn’t look well; he is dying. His self-deified incarnation is also faltering. A skeleton holds an hourglass in front of him with one hand. Not days but seconds are numbered. The emperor also looks at us with the deadly gaze of despair.
Not primarily because he is going to die, but because he realizes there is a shift in violence. Death as death replaces any possibility of deadly self-sacrifice. Violence can no longer be hidden as good violence through self-sacrifice, supported by the mythical pillar.
With his left hand, he points to a skeleton looting. Here too, the disappearance of the people’s sacrificial possibility is evident, now reduced to just death. The skeleton kneels and, like with the empress, performs the opposite sacrificial gesture. The sacrifice is over; now only death reigns. The same posture and gesture are seen in the skeleton burying a coffin above the round building – what remains of a church tower. The benevolent symbols (saints, good self-sacrifices) of the religious building were replaced by the malevolent symbols of death.
The sacrificial gesture (raised arms) is futilely replicated by many living people, taken to the extreme by the naked woman being pulled towards a collective grave by a kind of ‘container.’
III / The sacred, religious can no longer mythically hide violence as good violence.
Extreme violence reveals violence; it becomes visible, making it even more extreme.
The role of religions is to provide a mythical pillar, allowing the distinction between good and bad collective violence. This implies that collective violence is not presented as violence but as a sacrificial event, a self-sacrifice of the victim.
This conceals the violent nature of the violence.
When this mythical possibility disappears, when the sacrificial possibility disappears, only the assimilation of the people with death remains, belonging to the malevolent side of the incarnate self-deified leaders of the supreme god, the fate goddess.
We must interpret this weakening of the (totally misunderstood) mythical pillar in the sense that René Girard gave to the weakening of ‘belonging.’
“It seems to me that history bears out Proust’s analysis. The decline of feudalism exacerbated feudal conflicts. After the Reformation, when religious fervor waned, religious wars increased. At the end of the eighteenth century in France, the ‘noble reaction’ aroused by the weakening of the nobility helped trigger the Revolution. The First World War, that paroxysm of national conflicts, announced the decline of nationalism.” (Belonging, Contagion, 2016, 1 -12).
However, there is a difference. The shift from the people’s sacrificial possibility to the death of the people is the last and most violent step. That is what Brueghel discovered first.
Hence, this painting is the most important in world history.
The large shields behind which the skeleton armies try to hide point to that impossibility. They can hide nothing anymore. They are coffins with crosses. Religion can no longer make the mythical distinction between good and bad violence and can no longer wrap good violence as a good religious self-sacrifice.
The pursuing crowd – the people who should become a pursuing crowd to ultimately sacrifice themselves – of dead skeletons no longer achieves any sacrifice. It is not even a sacred lynching anymore. The people’s relationship to self-sacrifice has disappeared; only the relationship to death itself remains. The people are driven alive to a collective grave like cattle, to the grave as a slaughterhouse.
The larger the religious symbols, the less they can hide good collective violence with the religious sauce of the mythical.
In this painting – the upper part – there are still individual human sacrifices. There is a stark contrast between what happens below and above (in heaven) in this regard. The heaven of ‘self-sacrifice’ to hide good violence as violence is gone.
To the right above the rock, a skeleton pulls a man from the rock by grabbing his throat.
This skeleton makes the sacrificial gesture, matching the same sacrificial posture of the falling man, who does the same sacrificial movement with his legs in falling direction.
The end of sacrifice because death itself has replaced the sacrifice. Heaven (the mythical pillar of (self)violent sacrifice) is gone. Individual (self) sacrifices can no longer hide violence as violence, allowing death to dominate everything.
Thomas Hobbes would formulate it as follows: it is the genocide of every people against every people. Primarily against their own people. This indicates the weakening of the mythical pillar. It is a violence shift like no other in human history.
James Ensor has taken up this theme. For him, only death and the people remain. No sacrificial gesture remains.
IS THERE A WAY OUT? HOPE FOR HUMANITY?
THE QUIET HOPE OF THE SOFT SELF, MIRRORING ITSELF AS SELF-AWARENESS.
My thesis is that man has a biological, organic, internal brake against violence. A possible – it is a choice given to us by evolution – soft internal ever-withdrawing mirroring mediation. Through which a continuously recurring movement (recurring self-reflection) occurs in the own self. As a result, it does not sacrifice itself, it does not destroy itself in function of a greater being, felt by a wrong perception of the self of the other.
These endless internal self-reflective mirror movements are the most essential non-sacrificial, indestructible anchor point in our individual humanity.
Philippe De Keukelaere (to be continued)