Substantia. An International Journal of the History of Chemistry 3(2): 37-54, 2019 Firenze University Press www.fupress.com/substantia ISSN 1827-9643 (online) | DOI: 10.13128/Substantia-634 Citation: M. Henry, J.-P. Gerbaulet (2019) A scientific rationale for con- sciousness. Substantia 3(2): 37-54. doi: 10.13128/Substantia-634 Copyright: © 2019 Pr. M. Henry, J.-P. Gerbaulet. This is an open access, peer-reviewed article published by Firenze University Press (http://www. fupress.com/substantia) and distributed under the terms of the Creative Com- mons Attribution License, which per- mits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: All rel- evant data are within the paper and its Supporting Information files. Competing Interests: The Author(s) declare(s) no conflict of interest. Feature Article A scientific rationale for consciousness Marc Henry1,*, Jean-Pierre Gerbaulet2,* 1 Université de Strasbourg, UMR 7140, 4 Rue Blaise Pascal, 67000 Strasbourg 2 N-LIGHT Endowment Fund, 30 rue de Cronstadt, 75015 Paris E-mail: henry@unistra.fr; jpg@n-light.org Abstract. Consciousness is a concept that can be easily experimented but not easily defined. We show that the same observation applies to information, entropy and even energy. The best we can do is thus to generate and present “identity-cards” of these notions by listing their observable attributes with the help of mathematics, logics, information theory and thermodynamics. From a top-down approach starting from a view of reality based on a universal information field, emerges a ternary logical struc- ture of consciousness that further generates, through meaning, a dualistic space-time continuum populated with an infinite number of “things”. The validity of our logical structure is backed by quotations from topmost scientists and by various mappings such as famous previous models used in philosophy and science. Implications in neu- rosciences are also briefly discussed. Keywords. Consciousness, meaning, information, activity, matter, neurosciences. INTRODUCTION In a previous paper, a thought experiment arrived to the conclusion that consciousness has anteriority over energy and matter.1 Such a statement should not be a surprise for Eastern civilizations but seems to be in conflict with the materialism prevailing in Western civilizations, due to the devel- opment of science since Galileo’s first attempts to replace qualitative philo- sophical statements by observations and quantitative argumentation. This is illustrated in the first of two lectures held by Galileo Galilei at the Accadem- ia Fiorentina in 1588 in order to solve a literary controversy concerning the interpretation of Dante’s Inferno.2 In these lessons Galileo took the opportu- nity to show how mathematics could support a model suggested by the archi- tect Antonio Manetti and demonstrate that the model proposed by Alessan- dro Vellutello had parts that would have collapsed under their own weight. Shortly after he delivered his Inferno lectures, he also published a discourse on bodies in water, which refuted the Aristotelian explanation of why objects float in water.3 Galileo’s works thus paved the way to the intensive use of science and mathematics for giving rational explanations of natural phenomena. As evi- denced by his work on the structure of Dante’s inferno, quantitative consid- 38 Marc Henry, Jean-Pierre Gerbaulet erations are of considerable help for settling between several philosophical controversies. Accordingly, the playwright Eugen Berthold Friedrich Brecht has put the following words in Galileo’s mouth: “One of the main reasons why the sciences are so poor is that they imagine they are so rich. It isn’t their job to throw open the door to infinite wisdom, but to put a limit to infinite error. Make your Notes”.4 Figure 1 shows an illustration of the cur- rent scientific paradigm initiated by Galileo, in which every phenomenon is assumed to occur in a 4D space- time continuum called Minkowski’s space referred to as M4 space hereafter. A widespread view is that it exists a pyramidal hier- archy for scientific knowledge that is based on eight fun- damental disciplines: mathematics, physics, quantum mechanics, general relativity, electromagnetism, thermo- dynamics, chemistry and biology. In a previous paper, it has been advocated that such a pyramidal structure originating in the positivist thinking of the French phi- losopher Auguste Comte should be rejected and that a much better approach is to use group theory for reveal- ing the fundamental links between these autonomous disciplines.5,6 Fitting consciousness in such a material- istic frame is generally perceived as a “hard problem”,7 while fitting free will of living beings may be referred to as the “hard question”,8 domains where qualitative argu- ments predominate over falsifiable quantitative state- ments. The aim of this paper is then to show what sci- ence has to say about consciousness, independently of philosophical descriptions characterized by a total lack of consensus among thinkers. We were motivated in our approach by some remarks made by topmost scientists about the role played by consciousness in our universe. First, the importance of consciousness is obvious in quantum theory where the finite value of the quan- tum of action imposes that the observer always has an influence over what is observed. It is timely here to quote Werner Heisenberg, the father of matrix mechanics: “I think that modern physics has definitely decided in favor of Plato. In fact these smallest units of matter are not physical objects in the ordinary sense; they are forms, ide- as which can be expressed unambiguously only in math- ematical language (...). God is a mathematician”.9 One may also quote his enemy brother, Erwin Schrödinger, the father of wave mechanics: “As a matter of fact, I think that the material universe and consciousness are made out of the same stuff... But although I think that life may be the result of an accident, I do not think that of consciousness. Consciousness cannot be accounted in physical terms. For consciousness is absolutely fundamen- tal. It cannot be accounted for in terms of anything else”.10 Two weeks later, the same journalist asked to their com- mon mentor, Max Planck, this crucial question: “Do you think that consciousness can be explained in terms of matter and its laws? ”. Planck’s reply was: ”No, I regard consciousness as fundamental. I regard matter as deriva- tive from consciousness. We cannot get behind conscious- ness. Everything that we talk about, everything that we regard as existing, postulates consciousness”.11 Moving from physics to mathematics, it is worth quoting Eugene Wigner, the father of group theory applied in physics: “When the province of physical theo- ry was extended to encompass microscopic phenomena, through the creation of quantum mechanics, the concept of consciousness came to the fore again: it was not pos- sible to formulate the laws of quantum mechanics in a fully consistent way without reference to the conscious- ness. All that quantum mechanics purports to provide are probability connections between subsequent impressions (also called “apperceptions”) of the consciousness, and even though the dividing line between the observer, whose consciousness is being affected, and the observed physi- cal object can be shifted towards the one or the other to a considerable degree, it cannot be eliminated. It may be premature to believe that the present philosophy of quan- tum mechanics will remain a permanent feature of future Figure 1. A picturing of the current materialistic paradigm in West- ern science. Reality is manifested in a 4D-continuum (x,y,z,ic·t) called Minkowski’s space, having inaccessible zones out of a light cone associated to a given observer. On the left, a schematic hier- archy for scientific disciplines shown here as the progression: math- ematics (MT) → physics (PH) → quantum mechanics (QM) → elec- tromagnetism (EM) → thermodynamics (TH) → chemistry (CH) → biology (BL). General relativity (GR, not illustrated here) is repre- sented as a separate branch owing to the considerable difficulties met for merging this science with quantum mechanics. 39A scientific rationale for consciousness physical theories; it will remain remarkable, in whatever way our future concepts may develop, that the very study of the external world led to the conclusion that the con- tent of the consciousness is an ultimate reality”.12 It should thus be obvious that putting consciousness at the source of any reality is definitively not the prerog- ative of an Eastern way of thinking. This means that sci- ence, the Western way of thinking, has also something to say on this subject. It would thus be very nice if both ways of thinking could lead to the same conclusion. This was demonstrated in a previous paper using a thought experiment and showing that consciousness cannot be the result of neural activity.1 Here, we plan to develop the same idea using science’s language. We will show that concepts of consciousness, analogic information with meaning, digital information lacking meaning and information activity may be defined out of any space- time framework. Consequently, information necessar- ily preexists any other concept such as entropy, energy or matter that could be viewed as a mere mapping from a virtual information field towards the observable M4 space-time framework. To keep the paper at a reasonable length, the problem of the physical nature of the infor- mation field will not be discussed here but treated in a third paper.13 Consequently, we will present here only a static version of consciousness based largely on ther- modynamics. The scientific reason for such a choice is that thermodynamics aspects are universal and do not depends on mechanisms or physical implementation of the system. This is not true for dynamical aspects that are strongly implementation-dependent with mecha- nisms that are highly dependent on the physical struc- tures used for storing and processing information. Our methodology is inspired by David Bohm’s mod- el, addressing how the unfolding of an implicate order results in manifest order and structure as a result of the activity of a super-implicate order, which generates various levels of organization, structure, and meaning. According to Bohm, one finds at the root of capacities such as awareness, attention and understanding a pre- conscious “undivided state of flowing movement” – the actual and immediate activity of the holomovement. The nature of this movement can be discerned in a number of common experiences, such as listening to music. In such a model any transformation of consciousness must be a transformation of meaning, suggesting that everything, including ourselves, is a generalized kind of meaning.14 Quoting Bohm himself about such an approach: “As in the discussion of reason, it was shown how one level of thought will organize the next level. This can go on to pro- duce a structure that may develop indefinitely with rela- tively closed loops of many kinds. This implies that con- sciousness is organized through a generative order whose totality is in many ways similar to the totality of the gener- ative and implicate order that organizes matter. It is now possible to look into the question of how consciousness and matter are related. One possibility is to regard them as two generative and implicate orders, like separate but parallel streams that interrelate in some way. Another possibil- ity is that basically there is only one order, whose ground includes the holomovement and may go beyond. This order will unfold into the two orders of matter and mind, which depending on the context will have some kind of relative interdependence of function. Yet at a deeper level they are actually inseparable and interwoven, just as in the com- puter game the player and the screen are united by par- ticipation in common loops. In this view, mind and matter are two aspects of one whole and no more separable than are form and content”.15 Finally, the scientist that has most investigated a consistent connection between physics and psychol- ogy is beyond any doubts Ernst Mach: “If psychical life is to be harmonized at all with the theories of physics, we are obliged, I reasoned, to conceive atoms as feel- ing (ensouled). The various dynamic phenomena of the atoms would then represent the physical processes, whilst the internal states connected therewith would be the phe- nomena of psychic life. If we accept in faith and serious- ness the atomistic speculations of the physicists and of the early psychologists on the unity of the soul, I still see no other way of arriving at a tenable monistic conception.”16 From such a survey of what have been said about consciousness by some greatest men in science, it should be clear that the consciousness-brain relationship should be understood as a unity and not as a duality between spirit and matter. A formal proof of the validity of such a statement has been given previously.1 Now, it seems that time is ripe to go one step further and analyze at the light of the knowledge accumulated over the XXth century and over the first fifth of the XXIst century how such a monist view fits into modern science. Our philo- sophical position will thus be that it is possible to map brain activity onto computability with the immediate implication that consciousness should be external to the brain/brains for reasons listed below. We agree that postulating non-biology based brain/mind activity, is seriously disputable and we do not pretend to solve con- clusively a debate that has agitated mankind during mil- lenaries. Our aim is rather to allow the reader interested in the phenomenon of consciousness to deepen his own thoughts about the ontologic questioning: “What Is”, by providing a safe scientific guideline to the complex bot- tom-up approach of reality, and a hint of the simple and powerful top-down avenue to the same. 40 Marc Henry, Jean-Pierre Gerbaulet A LOGICAL APPROACH TO CONSCIOUSNESS As stated by David Bohm, one of the most striking attributes of consciousness is its ability to make order emerge from chaos. Consequently, logics should be at the very root of consciousness. It has been proven in 1913 by the American mathematician Henry Maurice Sheffer (1882-1964) that the Boolean algebra could be derived from the use of a single binary NAND logical operator (alternative denial) represented by the so-called Sheffer stroke (↑).17 This remarkable property has the consequence that NAND gates are now crucial compo- nents of today’s computers, for instance, through the use of flash memories. Accordingly, as all logical operations of binary logic may be encoded with just a single logical connector, high-performance computing processors may be readily developed. This immediately suggests basing consciousness on NAND operations. Accordingly, let P and Q be two propositions that can be either true or false. The alternative denial opera- tion is then defined as being such that v(P↑Q) = 1 in all cases except when v(P) = v(Q) = 1, in which case v(P↑Q) = 0. Consequently, if P stands for a proposition such as “I am”, three primitive concepts immediately emerge: - Negation: ¬P = P↑P that could be interpreted as “I am not” - Tautology: ⊤ = (¬P↑P) = P↑P↑P meaning “I am who I am” - Contradiction: ⊥ = ¬⊤ = ⊤↑⊤ = P↑P↑P↑P↑P↑P or “I am who I am not”. Our claim is that we are facing the very basis of any kind of consciousness, in other words, its “identity card”. Accordingly, the negation operation allows defin- ing what is outside, the tautology what is inside, while the contradiction allows for the existence of incomplete- ness, that is to say the inevitable existence of undecid- able propositions in any kind of coherent computing sys- tem using numbers.18 The other attributes of conscious- ness then logically follow as soon as the Sheffer stroke is applied to at least two different propositions P and Q. It is for instance possible to introduce the concept of cau- sality through the use of an implication operator: - Implication: (P ⇒ Q) = P↑(P↑Q) Setting P = Q, one recovers the tautology under a new form (P ⇒ P) that could be translated as “If Me, then Me”. In fact, causality allows defining the existence of “time” seen as a never-ending succession of causes (P) and effects (Q). Irreversibility is very easily introduced at such a level, by the mere fact that the truth table of the proposition (P ⇒ Q) is different from the truth table of the reverse proposition (Q ⇒ P). The implication allows also introducing the concept of “inhibition”, another crucial attribute of consciousness: - Inhibition: (P ⊣ Q) = (P ⇒ Q)↑(P ⇒ Q) = [P↑(P↑Q)]↑[P↑(P↑Q)] It is worth noticing that implication and inhibition are dual concepts, as it is possible to write: (P ⇒ Q) = (P ⊣ Q)↑(P ⊣ Q). Both operations refer to the same condi- tional statement “If … then …” and differ by the output: “go outside” for implication and “go inside” for inhibi- tion. The existence of an active and expansive mode of action, or “Yang” mode using implication, as well as the existence of a complementary passive or contrac- tive mode, or “Yin” mode using inhibition typical of Eastern philosophies, is thus logically deduced. From a neuronal standpoint, this implies the existence of two modes of autonomy: sympathetic or active, as well as parasympathetic or inhibitive. Alternation between awake state (active consciousness) and sleepy state (pas- sive consciousness) is also described using this logical implication. The former explains the existence in the brain of a default mode network (DCN) associated to introspection, self-referencing, emotional regulation and mind wandering, all anti-correlated to the latter, a task control network (TCN) associated to top-down regula- tion of sensorimotor processing in control of oriented attention.19 It has thus been proved that shutting down the DCN was positively correlated with behavioral per- formance (implication), while reinforcing it interferes with task control, leading to degraded behavioral perfor- mance (inhibition). Another attribute of consciousness is its ability to discriminate things. This is possible through the use of two other logical operators: - Equivalence: (P ⇔ Q) = [(P↑P)↑(Q↑Q)↑(P↑Q)] - Incompatibility: (P ⊕ Q) = (P↑P)↑(Q↑Q)↑(P↑Q)↑(P↑ P)↑(Q↑Q)↑(P↑Q) Translated into words, this gives “If Me then You and If You then Me” for equivalence the very basis for affinity or attraction and “If Me then not You and if You then not Me”, the basis for repulsion. Such operations explain the structuration of groups of conscious beings into clans, parties, societies, religions, etc. Finally, consciousness has also the ability to unite things (synthesis) according to a conjunction mode (P ∧ Q) = (P↑Q)↑(P↑Q) translating as “Me and You” or to 41A scientific rationale for consciousness separate things (analysis) through a disjunction mode (Q∨P) = (P↑P)↑(Q↑Q) translating as “Me or You”. Conse- quently, through synthesis conscious beings interact for sharing something independently of any kind of affinity, while through analysis, they gather for increasing diver- sity and wealth. These last two modes form the basis of any culture whether scientific, artistic or philosophic. It is obviously quite amazing that all these funda- mental attributes of consciousness derive from the exist- ence of a single logical operation corresponding to the “alternative denial”. From a symbolic viewpoint, such a denial has been represented many times under the symbol of the Ouroboros, i.e. a dragon biting its tail, which clearly suggested by its circular shape, an exterior (negation), an interior (tautology) and an incomplete- ness (contradiction), owing to the self-referencing of the symbol where the beginning also corresponds to the end (Figure 2). To conclude, this section on formal logics, it is worth noticing that consciousness may a priori proceed according to three different types of logics, depending on the meaning given to contradiction. - The first logical mode is based on the allowance for the “reductio ab absurdum” proof, in which one deduces from a contradiction (¬P ⇒ ⊥) that P or ¬¬P are true statements (elimination of the double negation). Here we have the rational and coherent thinking mode typical of classical physics, based on Boolean algebra.20 - The second logical mode rejects “reductio ab absur- dum” proofs, by stating that contradictions are per- fectly allowed, but that starting from a contradic- tion which is false by nature, one may deduce any kind of true propositions (⊥ ⇒ P explosion’s prin- ciple). Here we have the typical thinking mode of quantum physics stating that quantum objects may have contradictory descriptions such a wave/parti- cle duality for instance. Mathematically speaking, this corresponds to intuitionistic logic character- ized by the use of multi-valued Heyting algebra.21 Using intuitionistic logic, it may be shown that the double negation has an autonomous status that can- not be assimilated to an affirmation. On the other hand, it is always true that ¬¬¬P = ¬P. The explo- sion principle typical of Heyting algebra has physi- cal consequences such as the existence of a big bang for inert matter explaining the observed diversity for matter. At a psychical level, the intuitionistic logic may clearly be associated to the unconscious mind, explaining why dreams are so difficult to interpret using the Boolean conscious active mode. - The third logical mode corresponds to minimal logic that simply gives no special treatment to the contra- diction.22 It follows that using minimal logic, there is no difference between the formula ⊥ and any other kind of formula F. This means that it is here possi- ble to associate contradiction at any formula F, the negation becoming P ⇒ F. This is obviously the most amazing mode where nothing can be denied, as eve- rything is true by essence. It is also the “Anything goes” apothegm of the philosopher Paul Feyera- bend.23 Here one may speak of oneness, i.e. the feel- ing of the deep unity of the universe. This is also the kind of logic depicted by the Ouroboros (Figure 2). MEANING, INFORMATION, COMMUNICATION, LANGUAGE The above formulation leads to an identity card of consciousness, which is a mapping of its basic logical attributes. This is the only safe attitude when facing a concept that cannot be defined in an absolute manner. By experimenting consciousness, we meet the above attributes and by trying to go beyond that, we per- form an act of faith that is out the scope of a scientific Figure 2. The mythical Ouroboros or snake biting its tail. Left : representation from a Greek manuscript, Codex Parisinus Graecus 2327, fol. 196, written in 1478 by Theodoros Pelecanos. Top right: representation from another Greek manuscript entitled Chryso- poeia of Cleopatra from Codex Marcianius Graecus 299 (Venice), written probably during the 11th century. Inside the Ouroboros, a text stating “Hen to Pan” translating as “All in One”. Bottom right: Zen’s ensō (Japanese world meaning “circle”) is a circle that is hand- drawn in one or two uninhibited brushstrokes to express a moment when the mind is free to let the body create. 42 Marc Henry, Jean-Pierre Gerbaulet approach. Moreover, as it is consciousness that gives the three possible meanings to contradiction, it should come first, before the two other concepts that are “meaning” and ‘information”. Accordingly, with logical thinking, we are at the very root of scientific knowledge corresponding to Pla- to’s world of abstract ideas. The logical attributes of consciousness introduced above apply to any kind of proposition. Meaning is then the way chosen by con- sciousness for treating contradiction along 3 fundamen- tal modes (rejection, acceptation or detachment). How- ever, in order to make the connection with our observ- able physical world, we cannot stay at such an abstract level and we see in the information concept an obvious “fuel”. The idea is then to state that when consciousness meets information, a meaning emerges through applica- tion of its three modes and nine ways of reasoning. The notion of meaning may then be applied either internally for introspection (DCN mode of the brain) or externally to act and communicate (TCN mode). Figure 3 shows an illustration of our viewpoint. As demonstrated by the Palo Alto school of think- ing, it is absolutely impossible to “not communicate”.24 Any silence or omission always carries a deep meaning suggesting that meaning is hierarchically superior to information. Now, “to communicate” means exchang- ing information through a language that may be digital or analogic. Information is thus not a primary attribute of consciousness, but always a secondary attribute of it that can be non-reflexive (digital mode, TCN) or reflex- ive (analog mode, DCN). Consequently, upon any information exchange, it is mandatory to consider two levels of language: the object- oriented language dealing with raw information, and a meta-language taking as object the language itself, thus dealing with more abstract structures. If the object-ori- ented language is perfectly suited for digital communi- cation at a bit-level, it is however devoid of any mean- ing. Consequently, the role of the meta-language is to give meaning to the object-oriented language, thus plac- ing analog communication above the digital one. Such a viewpoint is also in agreement with Gödel’s incomplete- ness theorems18 stating that languages able to close on their selves contain unavoidable contradictions (and if they don’t, they contain undecidable issues). In order to decide of the truth of an object-oriented language L, it is thus mandatory to go at an upper ML (meta-language) level to find the resources needed for referring to all the expressions of L. In other words, the truth for L is located in ML and not in L. Similarly, the truth for ML will be located a still upper level MML and so on without ever ending. This shows that a language cannot contain an adequate true predicate for itself and truth cannot be defined at this level: it should be defined using a superior language. It then transpires that any communication has always two aspects: the content (raw information) and the relation (meaning or interpreted information). As it is the relation that organizes the content, it follows that such a relation can only be a meta-communication. It should also be realized that, in any communication, the emitter may have more information at its disposal than the receiver, even it the receiver thinks that he has exact- ly the same amount of information (or vice-versa). It is then very dangerous to think that another party holds the same amount of information as oneself and will draw the same conclusions from a given communication. The trouble with the analogic language is that a large amount of the elements constituting the morphol- ogy and the syntax of the digital language is missing and that it is the role of the translator to re-insert the missing elements. Consequently, upon translation of an analogic material into a digital one, it is mandatory to introduce the logical truth functions that are absent in the analogic communication mode. This is particularly true at the level of negation, which does not exist at all in minimal logic, heavily used in analogic communica- tion modes. Any exchange of communication can thus be identified as symmetric or complementary depending on the fact that one considers similarities or differences. Figure 3. A pictorial representation of a conscious being (Me), represented here as a body and a Mind living in a material world, and using its consciousness to give meaning (?) to information rep- resented by a pen and a book. Consciousness has been symbolized on the head of the conscious being by the mantra “Om”, the cosmic sound of Atman, identical in essence with Brahman, the Self, the only reality (in Hinduism). 43A scientific rationale for consciousness Moreover, in any cognitive act, a clear distinction should be made between the fact of perceiving (raw information or object-oriented digital language) and the fact of understanding what has been perceived (informa- tion carrying meaning or analogic meta-language). This allows defining the meaning as information within a context. Alternatively, one may say that «  A bit of infor- mation is definable as a difference, which makes a differ- ence  ».25 These two kinds of information may be easily confounded in the common language, despite the fact that raw and interpreted information do not act at the same level of communication. INFORMATION ACTIVITY Up to now consciousness appears as a primordial entity embedded in a kind of non-dual universal field filled with a “substance” named information, and has the ability to give meaning to the information stored in such a field through three logical modes and nine logical tools. Upon information exchange two levels of communication have been identified: digital language or analogic meta-language. The next step is then trying to define what could be an “object” in a world holding only information. Our postulate is that consciousness, focusing on a certain amount of information measured in bits, isolates within the non-dual field what we will call an “information pool”. Obviously, such an infor- mation pool would be first characterized by a certain number of binary digits (bits), the storing medium being the “stuff “ evoked by E. Schrödinger in a 1931 interview and from which the illusion of matter could be created.10 As consciousness is able to give meaning to a given information pool, it directly follows that some pools will be perceived by consciousness as holding highly mean- ingful groups of bits that could be used for building an “identity card” for the pool. Obviously, such highly meaningful bits will be eagerly kept within the pool and not transferred towards another pool, because such a transfer would cause an identity loss. Accordingly, the notion of “ego” is clearly introduced and identified. Consequently, besides the information content, one should also introduce an information availability meas- uring the strength of each ego. Being a conscious infor- mation pool, each ego may exchange information with another ego that could hold less-meaningful bits, in which case the information availability will be high. At an upper level, ego may accept transferring its meaning- ful bits towards the universal information field, under- going a dissolution process. The notion of information availability thus introduc- es a fundamental “duality” within the non-dual infor- mation field. For instance, one may consider an infor- mation pool having low information availability. This basically means that the identity of such an information pool should be preserved during information exchanges. In such a case, one may speak of a static “volumetric” information pool. Alternatively, one may come across an information pool having high information availability. This means that we encounter in such a case a dynamic “radiating” information pool having no “volume” owing to the ease of transferring information. Such dynamic information transfers allow introducing the concept of “time” in order to characterize the “speed” of any infor- mation transfer and the associated bandwidth. A space-time frame filled with matter and radiation thus emerges as a direct consequence of consciousness giving meaning to various pools of the information field. As consciousness has three modes of logical inference, we may identify three ways of perceiving space and time (figure 4) giving rise to three modes of apprehension of reality: by computing with numbers (wakefulness), by using symbols loaded with meaning (awareness) or by trying not to understand or describe by just living here and now (mindfulness). On such a ground, it is possible to introduce a new concept, information activity, defined as the product of information content by information availability and characterizing the overall intensity of information trans- fers between information pools. Furthermore, this leads to a distinction between emitters that send information and receivers that accept information. But in order to behave as a potential information sender, the emitter has Figure 4. In our approach space and time are creation of con- sciousness and should be perceived along three different modalities according to the status given to the contradiction. The digital time is useful for a rational comprehension with the brain, the analog time for intuitive comprehension with the heart and the timeless time for immediate comprehension with the gut. 44 Marc Henry, Jean-Pierre Gerbaulet to handle both the emitted information and the context, the context being here defined as the amount of infor- mation not transmitted and kept by the emitter. This means that an emitter has a consciousness allowing it to discriminate between the information that should be emitted and the context that should not be emitted. It then logically follows that emitters should have necessar- ily higher information contents than receivers and that information should flow from pools having higher infor- mation contents towards pools having lower information content. Moreover, if it happens that two pools of informa- tion have the same information content, there is nei- ther emitter nor receiver and one may then be allowed to define a new single pool of information by adding the information contents of these two pools. In other words, information pools are thus doomed to always increase in size and should never decrease, leading to the logical conclusion that information content behave as the con- cept called entropy in thermodynamics. Such an identi- fication of the information content with entropy is then in full accordance with the Shannon/von Neumann definition of entropy26, giving further confidence in this interpretation. Consequently, we meet here thermodynamics, a science sharing with consciousness the ability to deal with information at a meta-language level and with energy and matter at an object-oriented level. Staying at an information level, one may say that entropy meas- ures the amount of digital information available on one hand,26 while, on the other hand, complexity or thermo- dynamic depth27 corresponds to the amount of infor- mation rejected at an analogic level. Alternatively, one may speak of digital information and analogic exforma- tion that is treated by consciousness to define a context not transmitted during the communication.28 It then becomes possible to reconcile the two conflicting inter- pretations of entropy. At a digital level of object-oriented language, one finds the Shannon-Von Neumann thermo- dynamic entropy, while at the analogic level of the meta- language, one meets the cybernetics negentropy of Wie- ner/Schrödinger.29 A fundamental error is here to think that it is possible to obtain the meaning (cybernetics negentropy) by merely changing the sign of the amount of information (thermodynamics entropy). It should also be clear that assimilating entropy to disorder and negentropy to order, as done in most ther- modynamics textbooks, should be completely avoided. This is because there is no order or disorder at a digital level, such notions belonging to the analogic realm of consciousness observing things. At a digital level, infor- mation corresponds to what is unexpected, and there are more unexpected things in a disordered situation than in an ordered one.28 Moreover, it follows from Gödel’s incompleteness theorems that it is impossible to know if there is order or disorder at a digital level. Order and disorder are thus clearly subjective notions located at the level of the digital meta-language and, as such, they have nothing to do with thermodynamics. It follows that discriminating between pools of information according to their information contents allows distinguishing between potential emitters hav- ing high information contents and receivers having low information contents. However, it should be clear that, at this level, nothing is “observable”. In other words, we are moving in a virtual world where everything is perceived as made of information. Here, it is worth quoting the great physicist John Archibald Wheeler: “I think my life in physics is divided into three periods ... I thought at first that everything was made of particles .... In my second period everything was made of fields ... In this third, my impression is that everything is made of information”.30 Figure 5 shows a translation of Wheeler’s statement. It is also worth noticing that David Bohm has also intro- duced in 1985 the notion of activity of meaning, a non- mechanical reality associated to enfoldment and unfold- ment and quite close to the information activity concept discussed here.14 The next step is then to introduce fundamental coupling constants, the role of which is to set a limit between what can be observed (matter) and what cannot be observed (information, entropy and energy). ENTROPY AND TEMPERATURE The first constant has the role of giving physical meaning to the abstract notions of information con- tent, information availability and information activ- ity. As shown in figure 6, there is an identity in logical structure between communication and measurements in Figure 5. The three fundamental modes of perception of conscious- ness gives rise to the three basic models of reality: viewed as infor- mation at a primordial source level, viewed as fields during propa- gation and viewed as particles upon Manifestation as matter. 45A scientific rationale for consciousness quantum physics.31 This suggests generalizing the entro- py concept used in statistical thermodynamics to the information theory. Accordingly, the mathematician John von Neumann when asked by Claude Shannon to suggest a name for his newly discovered uncertainty function lucidly stated: “You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statisti- cal mechanics under that name, so it already has a name. In the second place, and more important, no one real- ly knows what entropy really is, so in a debate you will always have the advantage”.32 It thus should be no surprise that a great confusion exists in science about the definition of entropy that merely reflects the great difficulty of defining conscious- ness. Such difficulties in definitions stem from the fact that entropy or consciousness cannot be defined explic- itly as they are both primary concepts. However, in the spirit of what has been done for introducing consciousness, the best way to introduce entropy to a material world is to describe its fundamen- tal attributes.33 Replacing the unobservable “informa- tion pool” by its visible counterpart, the “body” or the “soma” in Bohm’s language,14 it appears that entropy is a “stuff ” that can be transferred, poured out, cumulated or distributed among bodies. Each body contains more or less entropy depending on its information content, the entropy of the whole system being equal to the sum of the entropies of its parts. Rubbing, grinding, heat- ing or performing a chemical reaction, are examples of processes able to generate entropy. Entropy also has the property of being unable to cross thermally insulated walls, meaning that if it can be created, it is doomed to increase and never decrease in any isolated system. When entropy is poured into a body, this body becomes warmer, meaning that a body without entropy is abso- lutely cold. Any entropy increase also causes changes in volume, in shape, changes the state of aggregation as well as electric or magnetic properties. Finally, it is rath- er easy to measure the amount of entropy in a body: for example, the volume loss of ice while melting is directly proportional to the amount of entropy added. It follows from such an analogy that our first coupling constant should be an entropy. Now, knowing that entropy S measures also the information content, it comes that temperature T is readily assimilated to infor- mation availability, while information activity takes the figure of energy W through a fundamental relationship: W = kB·T measured with a physical unit named “joule” (symbol J). Such a unit is well adapted to the human body char- acterized by an average resting metabolic rate of 3611 J·kg-1·h-1,34 corresponding to an average power of 105 watts (1W = 1 J·s-1). A more convenient energy scale for discussing elementary phenomena in the visible universe is the zepto-joule (symbol zJ), with 1 zJ = 10-21 joules. On such a scale, the universal entropy constant takes the value kB = 0.0138 zJ·K-1 also known as Boltzmann’s con- stant in memory of the Austrian physicist Ludwig Boltz- mann, the father of statistical thermodynamics. Such a “quantum of entropy” allows discriminating between a non-observable world involving entropy changes such that S < kB and the visible universe where S ≥ kB. ACTION AND FREQUENCY Now, let us consider the situation where informa- tion sent by an emitter is captured by a receiver and then re-emitted without any loss towards the sender, restoring the initial situation. As the final state is the same than the initial one, the process may occur a sec- ond time and so on without interruption, leading to the concept of “vibration” characterized by the number of cycles performed per unit of time, i.e. by a frequency f. It should be obvious that activity and frequency have to be related in some way through a second universal cou- pling constant relating this aspect of the information world to the physical world. Such a coupling constant h is well known in physics under the name of “quantum of action” with a new relationship: W = kB·T = h·f where h is Planck’s constant, with h = 663 zJ·fs, (1 femto-second (fs) = 10-15 s). As for the quantum of entropy, the quan- tum of action L allows discriminating between a non- observable world involving action changes such that L < h and the visible universe where L ≥ h. It is worth noticing that the fact that physical action L is quantified is a mere consequence of the quantifica- tion of information in bits. In other words, quantum physics, one of the most fundamental theories of mod- ern science, emerges quite naturally from informa- Figure 6. Similarity in logical structure between information theo- ry and quantum theory meaning that information content for the mind should correspond to entropy for the body. Adapted from J. Rothstein (1951).31 46 Marc Henry, Jean-Pierre Gerbaulet tion theory.35 With such a link in hand, movement in the information world becomes what is called “kinetic energy” in the physical world, whereas structural infor- mation has his physical counterpart named “poten- tial energy”. The first law of thermodynamics stating that the total energy should always be conserved stems from the fact that, once created, information can never be destroyed. Thus, at the scale of the whole universe, information exchanges are necessarily without losses.36 Alternatively, Planck ’s constant can also be inter- preted as the multiplicative scale factor setting the scale of classical zero-point radiation appearing in classical electromagnetic theory, as relativistic classical electron theory with classical electromagnetic zero-point radia- tion gives many results in agreement with quantum the- ory.36 Consequently, the identification made here would remain valid even if quantum mechanics was finally proved to be fundamentally wrong. Such an uncer- tainty in the validity of quantum theory stems from its well-recognized incompatibility with general relativity, another most important physical theory, as both theories diverge on the evaluation of vacuum energy density by more than 120 orders of magnitude!!!5, 37. LIGHT, MATTER AND ELECTROMAGNETISM It should also be obvious that the distinction between static spatial-like information and dynamic time-like information cannot be a fundamental one as it is consciousness that gives meaning and identity to the various pools of bits. Consequently, a third universal constant should exist, intimately associating space with time. The basic postulate of equivalence between space and time stemming from the theory of relativity is thus logically introduced. By this definition, the third univer- sal constant should be a speed c = 299 792 458 meters per second (m·s-1) giving an upper limit for the transfer of information between information pools. The fact that such a constant should not be infinite is here direct- ly related to the fact that it belongs to the realm of the physical world where pools of information always have a finite number of bits. It then follows that two kinds of entities should exist in a physical universe: those able to propagate with the maximum allowed speed c, known as “photons”, and those propagating at speeds v < c, known as “matter”. In the second case, one may assign to a material object with an energy W, an inertial coefficient m or “mass”, linked to it by m = W/c2. As for the quantum of entropy or the quantum of action, the speed of light c allows discriminating between a non-observable world involving speeds v such that v > c and the visible universe (light cones) where v ≤ c (see figure 1). At this stage we have in hand a possible justification for the observation of a physical universe where energy, the physical counterpart of information activity, could manifest itself through three kinds of variables (tem- perature, frequency and mass) corresponding to various kinds of information availability, linked through a fun- damental equivalence relationship: W = kB·T = h·f = m·c2. However, such a picture applies to an observable universe having movement occurring in a single direc- tion through translation. In order to be able to perform rotations, a 2D-spatial frame is required, requiring introduction of a fourth universal coupling constant e being a quantum of electrical charge with a physical unit named coulomb (symbol C) and such that e = 0,106 atto-coulombs (symbol aC), with 1 aC = 10-18 C. Associated to this new aspect of information activ- ity, one should have a new variable measuring static information availability corresponding to the so-called electrical potential U (SI unit volt V or energy per cou- lomb) and leading to another fundamental equivalence relationship: W = kB ·T = h·f = m·c2 = e·U. Here, the reason for the quantification of electrical charge is that it is a fourth possible manifestation of the same stuff named information that is naturally quanti- fied in bits. As for the quantum of entropy, the quantum of action or the speed of light, the quantum of charge e, allows discriminating between a non-observable world involving charges q such that q < e and the visible uni- verse where q ≥ e. Finally, one may combine translations with rotations to allow for spiral movements, requiring a fifth coupling constant related to the existence of magnetism. However, as electricity is linked to static rotations and magnetism to dynamic screw rotations, this new dynamic aspect of information availability µ0 = 4π·10-7 H·m-1 corresponds to a magnetic inductance (SI unit henry H or V·s2·C-1) per unit length. This leads to yet another fundamental equivalence relationship: W = kB·T = h·f = m·c2 = e·U = (µ0·e·c)·I involving an electric current I = dq/dt, measuring the rate of variation in electric charge q with time t. Intro- duction of a magnetic permeability for empty space 47A scientific rationale for consciousness means that such a medium should be considered as a “substance” having an electric permittivity ε0 = 1/(µ0·c2) corresponding to a capacitance (SI-unit farad F or C·V-1) per unit length. WHAT IS ENERGY? According to the present formulation, energy should be considered as the manifestation of information activ- ity in M4 space-time. As information activity is driven by consciousness through the meaning, energy and entropy should be considered as an attribute of a mani- fested consciousness. However, it is worth noticing that in the material M4 world, energy is indeed a mongrel concept. This fuzzy nature of the energy concept was well perceived by the French mathematician Henri Poin- caré: “In every particular case we clearly see what energy is, and we can give it at least a provisory definition; but it is impossible to find a general definition of it. If we wish to enunciate the principle in all its generality and apply it to the universe, we see it vanish, so to speak, and nothing is left but this – there is something which remains con- stant“.39 Translated in our language, this means that energy as an attribute of consciousness may exist under an infi- nite number of different forms. As energy is the shadow of information activity and as information activity was defined as the product of information content by infor- mation availability, we have in hand a universal “reci- pe” for talking about energy in a manifest world. Each form of energy should then be considered as a product of a “coordinate” measuring the amount of something (a “thing” being, for consciousness, a pool of information with interesting conserved properties) by an associated “propensity” ruling spontaneous or natural transfers of such things between different parts of a thermodynamic system. Let us briefly demonstrate that all forms of ener- gy known in M4 comply with such a universal recipe. A first coordinate could measure for instance the entropy content S of a body with an associated propensi- ty corresponding to its temperature T, their product dW = T·dS being called “thermal energy”. The propensity is identified by stating that spontaneous evolution always occurs when entropy flows from a part with a high tem- perature towards another colder part, the reverse evolu- tion needing another external form of energy. At ther- mal equilibrium, all temperatures have to be equalized to the same value, meaning that parts at similar temper- atures do not exchange entropy anymore. A second coordinate would measure the weight of a body, that is to say the product of its mass m by a char- acteristic constant acceleration g = G·M/R 2 provided by another bigger mass M of size R where G = 66.7384 pJ·kg-2·m is Newton’s gravitational constant. To this coordinate, one may associate a propensity correspond- ing to altitude h, their product dW = d(m·g)×h being called “gravitational energy”. Stating that spontaneous evolution always occurs when a part at high altitude moves towards a lower altitude identifies the propensi- ty. At gravitational equilibrium, all altitudes have to be equalized to the same value meaning that parts at the same altitude do not move anymore. The reverse evolu- tion consisting on moving from a low altitude towards a higher one cannot be spontaneous, needing the mobili- zation of another form of energy. A third coordinate would measure the amount of momentum p of a body, that is to say the product of its mass m by its speed v (p = m·v) associated to a propen- sity corresponding to its speed, their product dW = v·dp being called “kinetic energy”. The propensity is identi- fied by stating that spontaneous evolution always occurs when a part of high speed changes towards a state of low speed, the reverse evolution needing another external form of energy. At kinetic equilibrium, all speeds have to be equalized to the same value, meaning no more exchange of momentum between parts moving at the same speeds. A fourth coordinate would measure the amount of space (volume V) occupied by a body associated to a propensity corresponding to the pressure P inside the body, their product dW = -P·dV being called “mechani- cal energy”. The propensity is identified by stating that spontaneous evolution always occurs when a part of high pressure changes towards a state of low pressure, the reverse evolution requiring another external form of energy. At mechanical equilibrium, all pressures have to be equalized to the same value, meaning no more vol- ume variations for parts having the same pressures. A fifth coordinate would measure the amount of electrical charge Q at the surface of a body associated to a propensity corresponding to the electrical potential U, their product dW = -U·dQ being called “electrical ener- gy”. The propensity is identified by stating that sponta- neous evolution always occurs when a part of high elec- trical potential changes towards a state of lower electri- cal potential, the reverse evolution requiring another external form of energy. At electrical equilibrium, all potentials have to be equalized to the same value, mean- ing no more exchange of charge between parts at the same potential. A sixth coordinate would measure the amount of electric flux V·D (where D stands for electric flux den- sity measured in C·m-2) within a given volume V asso- 48 Marc Henry, Jean-Pierre Gerbaulet ciated to a propensity corresponding to the electric field E, their product dW = E·d(V·D) being called “dielec- tric energy”. The propensity is identified by stating that spontaneous evolution always occurs when a region where the electrical field is high changes towards a state of lower electrical field, the reverse evolution requiring another external form of energy. At equilibrium, elec- trical field should be the same everywhere in the vol- ume meaning no more exchange of electric polarization between different spatial regions. A seventh coordinate would measure the amount of magnetic flux V·B (where B stands for the magnetic flux density measured in Wb·m-2) within a given volume V associated to a propensity corresponding to the mag- netic field H, their product dW = H·d(V·B) being called “magnetic energy”. The propensity is identified by stat- ing that spontaneous evolution always occurs when a region of high magnetic field changes towards a state of lower magnetic field, the reverse evolution requiring another external form of energy. At magnetic equilib- rium, magnetic field should be the same everywhere in the volume, meaning no more exchange of magnetiza- tion between different spatial regions. An eighth coordinate would measure the amount of matter N within a given volume V associated to a pro- pensity corresponding to the chemical potential µ, their product dW = µ·dN being called “chemical energy”. The propensity is identified by stating that spontaneous evolution always occurs when a region of high chemi- cal potential changes towards a state of lower chemical potential, the reverse evolution requiring another exter- nal form of energy. At chemical equilibrium, chemical potentials should be the same everywhere in the volume, meaning no more exchange of matter between different spatial regions. As shown above and as stated by Poincaré, if the energy concept can be easily defined in a particular situation as the product of an energy coordinate by an energy propensity associated to such a coordinate, it is impossible to give it a definition covering all possible situations. The only thing that could be said about ener- gy without going into details is that “it exists something that remains constant during any evolution”. Obviously, such a general definition corresponds more to a postu- late than to a scientific statement derived from empirical evidence. Our scheme nicely relates this postulate to the existence of consciousness. This suggests that energy could also be rigorously introduced in psychology and spirituality. For instance, Sigmund Freud was the first one to formulate a scientif- ic theory of psychological facts by introducing the idea of the existence of a new form of energy called “mental energy”. Accordingly, it was rather easy to introduce a coordinate measuring the amount of thoughts N coming from the “Id” with an associated propensity that Freud called “libido” acting as a kind of chemical potential that could be related for instance to glucose consump- tion within the brain40 or to the amplitude of the 0.1 Hz component of heart rate variability.41 Within such a framework of thinking, knowledge of a total metabolic energy M could be divided by Boltzmann’s constant kB to retrieve a “psychic temperature” ψ = M/kB as well as an associated mental energy dW = ψ·dN. It is worth noticing that such an energetic approach of mental activity has been criticized and rather linked to a degree of controllability with mental fatigue associated to a lack of desire and not to a lack of energy.42 Here, it seems better to identify “desire” with information activity defined as explained above as the product of information content by information availability. The same holds for Qi or Prana that would better be viewed as information activity rather than “spiritual energy”. Again, such mis- use of the term energy directly stems from the intrinsic vagueness of the concept. The vagueness of the energy concept is also well illustrated by the fact that one may also consider only two kinds of energy: a first one describing the ability to change position of a body (kinetic energy) and a second one describing the ability to change the relative disposi- tion of its constituting parts (potential energy). By con- trast, entropy has a single meaning: measuring the infor- mation content in the world of consciousness and as the spreading of energy over all the accessible degrees of free- dom in M4. The reason for the existence of the second law is then to distinguish between reproducible experiments in M4 and non-reproducible ones that are “virtual”.43 Accordingly, during mental activity, everything is possible, and the fact that an event is reproducible or not does not matter anymore. The fact that self-organized structures and diversity in M4 stem from a flux of entro- py44 may also be logically related to an information flux in the information field of consciousness. Finally, it is worth noticing that it is possible to avoid speaking about energy and entropy as two differ- ent entities in thermodynamics. It is the “free energy” concept or ”chemical potential” defined as the total energy corrected of any entropy variation at a given tem- perature.45 The trouble here is that the expression “free energy” may also be interpreted as the energy contained in the physical vacuum, i.e. as “zero point energy”.37 A much better way is then to associate to each substance an “activity” variable, noted “a”, with the value a = 1 when the system contains only this substance (pure state) and the value a = 0 when the substance is com- 49A scientific rationale for consciousness pletely missing in the system. Intermediate values (0 < a < 1) will thus describe any kind of mixture contain- ing a given substance in variable amounts. Using such an “activity” concept avoids facing the troublesome energy/entropy duality, with just a single rule stating that exchanges of energy, entropy or matter always occur from spatial regions having a high activity, towards spa- tial regions having a low activity. This is a much satisfy- ing alternative way of stating that energy should always be conserved (first law) and that entropy should always increase (second law). It then appears that the activity concept is not only a convenient way of giving a direc- tion to any kind of evolution, but that thanks to its uni- fied nature, it could also be considered as a more funda- mental concept than energy or entropy considered sepa- rately. This is why activity has been put at the forefront and energy/entropy in the back in our previous paper.1 DISCUSSION In this paper we have proposed associating the con- cept of consciousness to the operation of a single alter- native denial logical operator (↑) acting on pools filled with information and giving meaning to them. Using the computer metaphor, pools with meaning then cor- respond to software, while pools devoid of meaning correspond to raw data. The ensemble of all informa- tion pools forms an information field that we may call “supra-consciousness”. At this level of minimal logic, there is no special treatment for the contradiction (⊥ = P↑P↑P↑P↑P↑P) that cannot be considered as the negation of a tautology (⊤ = ¬P↑P). At a second level of intuition- istic logic (meta-consciousness), contradiction is viewed as the mother of any kind of truth (⊥ ⇒ P), the negation having the property that ¬¬¬P = ¬P. At a third level of Boolean logic (rational consciousness), contradiction is used by consciousness to infer that something is true (if ¬P ⇒ ⊥ then ¬¬P ⇒ ¬⊥ = ⊤). Such a ternary approach of consciousness is by no means new and has already been explored by Ernst Mach by considering that Nature consists of the ele- ments given by the senses.16 In other words, Mach was convinced that what we usually call sensations are the true elements - elements in the sense that no further res- olution has yet been made of them - of the world. Then, the primitive man first takes out of them certain com- plexes of these elements that present themselves with a certain stability and are most important to him. Conse- quently, every physical concept is nothing but a certain definite connection of the sensory elements denoted by symbol A, B, C..., and every physical fact rests therefore on such a connection. These elements are the simplest building stones of the physical world that we have yet been able to reach. In our approach such complexes of elements may be mapped with the notion of “informa- tion pool”. In his analysis, Mach was indeed obliged to introduce three kinds of complexes noted ABC (i.e. ¬P = P↑P = things out of the body), KLM (⊤ = (¬P↑P) = P↑P↑P = the body) and αβγ for anything else (⊥ = ¬⊤ = ⊤↑⊤ = P↑P↑P↑P↑P↑P = the spirit). With these three complexes, one may for instance derive the existence of conscious I (ego) as (KLM + αβγ) facing an external world (ABC) made of things. But this is not the only possibility as one may have a pure spirit as αβγ fac- ing a material world (ABC + KLM). A third combina- tion could also be a material body (KLM) facing a spirit impregnating all things (ABC + αβγ = God). Finally, one could also envision a non-dual and non-local conscious- ness (ABC + KLM + αβγ = Atman). But, if Mach has derived such a scheme from its scientific empirical expe- Figure 7. Eight common forms of energy in the observable M4 space. In each case, energy corresponds to the product of a coor- dinate measuring an amount (highlighted in blue) by an associat- ed propensity (highlighted in red) taking at equilibrium the same value everywhere in the system. Other forms of energy not repre- sented here may also exists such as for instance interfacial energy dW = γ·dA where A is the coordinate measuring the amount of area and γ a propensity called surface tension. One may also cite elastic energy, dW = x·d(k·x) where k·x is the coordinate measur- ing the amount of tension and x the propensity corresponding to a length. In fact it exists an infinite number of energy forms accord- ing to the meaning given by consciousness to the manifestation of information activity. One may thus even define a psychic energy, dW = ψ·dN, where N is the coordinate measuring the amount of thoughts and ψ the associated propensity that could correspond to the intensity of desire for instance. 50 Marc Henry, Jean-Pierre Gerbaulet rience, we get the same result from the mathematical structure of logics based on propositions about the world linked into complexes through the Sheffer’s stroke (↑). It was also deduced that space and time also have a triple interpretation (digital, analogic and both attrib- utes) as well as physical reality (particles, fields and information). The fact that the time sensation is inti- mately associated to consciousness has already been analyzed in details by Ernst Mach16, and before him by Saint Augustine (time was a feature of consciousness named animus) and Plotinus (time is generated by the soul or psyche while eternity is the quality of the spir- it or nous).46 The evolution towards a ternary aspect of time was perceived in the Middle ages by Meister Eckart by adding the notion of Nu ̂as, the intersection of time and eternity. Eckart was thus talking of the Nu ̂ (=Now) in which time dissolves into eternity, a concept also identified by Sufi masters as Ibn al-waqt i.e. “son of the moment”, free from the chains of past and future. The fact that time is a feature of the activity of consciousness was also well perceived in Hinduism (ksana) and Bud- dhism (U-ji). However different these spiritual ways may be, they all require three actions: focusing on the interi- or (internal analog time), body exercise to strengthen the will (external digital time) and some kind of regulation of breath (timeless time). We have also introduced the concept of information activity in relation with the physical notions of entropy and energy with a fundamental relationship: W = kB·T = h·f = m·c2 = e·U = (µ0·e·c)·I. On the other hand Ernst Mach has clearly identified five basic elements for sen- sations: time-sensation related to consciousness, color- sensation and space-sensation related to the sight/touch pair, tone-sensation related to the ear/voice pair and matter-sensation related to the taste/smell pair.16 Follow- ing our approach an immediate mapping emerges: color/ temperature (T) through Wien’s displacement law, tone/ frequency (f ) through the existence of music, matter/ mass (m) through the notions of atoms and molecules. Such a mapping leaves space-sensation mapped to the existence of static charges (electricity) and time-sensa- tion mapped to the existence of moving charges (mag- netism). Moreover, as movement needs specification of an inertial referential frame, a complete equivalence between electric and magnetic field and thus of space with time is expected. This is in agreement with the basic postulate of special relativity. This could be a quite convincing argument in favor of putting a single concept (information) at the source of Mach’s five elemental-sen- sations associated to a physical world. But one may also make a mapping with the five Pla- tonic solids of antiquity: tetrahedron (fire/color-sensa- tion), octahedron (air/tone-sensation), cube (earth/mat- ter-sensation), icosahedron (water/space-sensation) and dodecahedron (ether/time-sensation). In such a symbolic language, the space/time equivalence could be mapped to the mathematical duality existing between dodeca- hedron and icosahedron. As cube and octahedron are also dual geometries, this also suggests another equiva- lence between tone (frequency) and matter (mass) in full agreement with quantum field theories based upon the equivalence h·f = m·c2. Finally, the fact that the tetrahe- dron is its own dual could be mapped to the well-known fact that colors may be generated either by addition (unequal RGB-triples) or by subtraction (dual unequal CMJ-triples), the white-sensation (light) being produced by equal RGB-triples and the black-sensation (darkness) by equal CMJ-triples. Noticing that the wood grows from the earth and that the metal drops as meteorites from the sky (ether), we also have a mapping connection with the five Chinese elements. Obviously, one could argue that such mappings are just coincidences occurring by chance. Such a posi- tion would in fact be the only reasonable conclusion in a bottom-up approach where the “big” is explained by the properties of the “small” holding the ultimate truth. However, in the top-down approach used here, where it is the big that is the ultimate reality that could be frag- mented in a infinite number of ways into an infinite number of small illusory entities, these mapping based on mathematical ideas are just the glint of the profound unity and coherence of the information field holding supra-consciousness. Going to neurosciences, it is satisfying to see that three kinds of consciousness states have also been iden- tified: C0-consciousness for unconscious processing, C1-consciousness for having an information in the mind calling for an action on the outer world and C2-con- sciousness for introspection or meta-cognition.47 A pos- sible mapping would be to associate supra-consciousness (detachment from contradiction) to unconscious infor- mation monitoring C0, meta-consciousness (accepta- tion of contradiction) to introspective C2-consciousness and rational consciousness (reject of contradiction) to extrovert C1-consciousness. It is worth noting that three levels of consciousness (type I primary, type II oriented outwards and type III oriented inwards) was also devel- oped by Jean-François Houssais48 or by Philippe Guil- lemant (anima, me and self ).49 Referring to Block’s con- cepts of A-consciousness (availability of information for use) and P-consciousness (perception of information),50 it should be clear that here a fundamental ingredient is missing, explaining the considerable difficulties met by such a reduction from three modes to only two modes.51 51A scientific rationale for consciousness Taking such a triple structure of consciousness for real then leads to the unavoidable conclusion that the current M4 framework is too narrow and should be enlarged by adding at least two dimensions to it. The need for such an enlargement from M4 to a V6 space, where the letter ‘V’ stands for Verity or Virtual, is already obvious in physics where general relativity is not compatible with quantum physics and is strongly suggested by the conformal invariance of Maxwell’s equations.5 This point will be fully developed in a third paper13. Another important point that has not been addressed here is the physical nature of the informa- tion field. Speaking of information without referring to the kind of memory used for storage is obviously not a tenable position from a scientific viewpoint.52 Taking for granted the metaphor of the computer, we know that memory is a crucial component for information process- ing. Here, we have proposed to link consciousness to an information field without referring to the kind of mem- ory used for computing. In an annex to this paper, we have recapitulated the main technologies currently used for building memory devices for artificial intelligence design. In biology, we find neurons that can fire (spike of action potential or bit 1) or not (no spike or bit 0). These all-or-nothing pulses are the basic language of the brain supporting a brain-computer metaphor. Even, if there are good reasons for criticizing such a metaphor53, all the standard arguments about why the brain might not be a computer are nevertheless rather weak nowadays.54 Viewing consciousness as a “secretion” of neural activity, the problem appears to be awfully complex and unsolv- able owing to Gödel’s incompleteness theorems18 stating that all consistent formal systems, that concern them- selves with numbers, contain formulas about those very systems that are undecidable within the systems them- selves. As self-reference is key for deriving meaning from elements that in themselves do not have meaning such as strings of bits, symbols, neuronal firing, etc., we are forced, in order to keep coherence, to kick consciousness out of neurons and brain activity as proposed here. It thus emerges in the brain a blind spot, something pre- sent but unable to be represented from within the sys- tem, which could be called the conscious “self ”.55 But, in contrast with Vukadinovic austere conclusion viewing consciousness as a nothingness having no independent existence apart from the brain, we argue that such a nec- essary blind spot is the door by which supra-conscious- ness enters the brain.) Last but not least, our approach is closely related to Eastern traditions emphasizing that consciousness is the ultimate reality and that matter is just “maya” or illusion. Amazingly, such a nature consciousness was clearly per- ceived by the great mathematician Henri Poincaré, in a paper written in 1906 and added to French editions of his book “Science and hypotheses”: “One of the most surpris- ing discoveries that physicists have announced in the last few years is that matter does not exist”.56 Recognition of this basic fact is also the reason why defining conscious- ness is generally perceived as a hard problem.7 As quoted by the cognitive neuroscientist Marcel Kinsbourne: “What makes any problem hard is that something false but attrac- tive stands in its way”.8 Here the thing that is fundamen- tally wrong but nevertheless quite attractive is obviously the fact that matter and spacetime exists by itself. CONCLUSION To conclude, it should be recognized that from a sci- entific viewpoint based on the mathematical structure of logics that at least three levels of consciousness have to be distinguished in any discussion about such a concept that can be experimented : - A rational consciousness giving an autonomous sta- tus to the logical operation of negation, to which no contradiction is possible since a double negation is equivalent to an assertion. Rational consciousness finds itself associated to digital information, object- oriented languages at the level of communication, or to thermodynamic entropy in the physical world. - A meta-consciousness that admits the existence of contradiction, which allows for double negation to acquire an autonomous status different from the one of the assertion. Meta-consciousness is linked to analogic information, to meta-languages carrying meaning in communication, or to cybernetic entro- py, also named negentropy, that we can relate to the existence of living systems. - A supra-consciousness that does not attribute any specific status to contradiction, which amounts to making the operations of negation and implication equivalent. Supra-consciousness, for its part, tran- scends digital/analogic duality of information, for, at this level, only positive assertions linked by non- local causality chains exist. The existence of supra-consciousness is usually ignored in neurosciences but was anticipated by top- most scientists: Max Planck (theory of quanta), Wer- ner Heisenberg (matrix mechanics), Erwin Schrödinger (wave mechanics), Eugene Wigner (group theory), John A. Wheeler (cosmology), Henri Poincaré (theory of cha- os), David Bohm (Aharonov-Bohm effect), Albert Ein- stein (theory of relativity) and Ernst Mach (theory of sensations). We have given here scientific arguments for 52 Marc Henry, Jean-Pierre Gerbaulet the necessity of using a top-down approach where con- sciousness generates space/time/matter/energy concepts from an universal stuff named information instead of the usual bottom-up scenario where space/time/matter/ energy secretes consciousness as an emergent property of complex systems. It should be clear that our approach does not claim to be a kind of universal and transcen- dental truth that cannot be falsifiable by doing experi- ments. As shown in a third paper,13 it is perfectly pos- sible within the proposed framework to formulate falsifi- able assertions after considerations of dynamical aspects of information processing. To do this, we will have to introduce physical mechanisms allowing comput- ing quantitative data that may be checked against well- designed experiments. It is our hope that the argumen- tation developed here will be of some help for perform- ing well-designed experiments about the phenomenon of consciousness in a very next future. REFERENCES 1. J.-P. Gerbaulet, M. Henry, 2019, Substantia, 3(1), 113-118. 2. Galileo Galilei, MSS Filza Riniccini 21, insertion 19, Bibl. Naz. Cent. Di Firenze, 1588, pp. 1-29. Reprinted in Le Opere di Galileo Galilei Vol. 9, Firenze, 1899, pp. 31-57. 3. Galileo Galilei (1612), Apresso Cosimo Giunti, Fire- nze, 1612; Reprinted as Discourse on bodies in water, translated by Thomas Salusbury, University of Illinois Press, Urbana, 1960. 4. B. Bretch, Leben des Galilei, translated as “Life of Gali- leo” by John Willet, (Eds.: John Willet & Ralph Man- heim), Bloomsbury, London, 1980, p. 73. 5. M. Henry, Inference : Int. Rev. Sci. 2016, Vol. 2, issue 4; http://inference-review.com/article/super-saturated- chemistry 6. E. Scerri, M. Henry, Inference : Int. Rev. Sci. 2017, Vol. 3, issue 1; https://inference-review.com/letter/on-the- madelung-rule 7. D. J. Chalmers, J. Consciousness Stud. 2018, 25, 6. 8. D. C. Dennett, Phil. Trans. R. Soc. B 2018, 373, 20170342. 9. W. Heisenberg, Natural Law and the Structure of Mat- ter, Rebel Press, London, 1970, pp. 32, 43. 10. J. W. M. Sullivan, Interviews with great scientists. IV – Prof. Schrödinger, The Observer, London, January 11, 1931, p. 15-16. 11. J. W. M. Sullivan, Interviews with great scientists. VI - Max Planck, The Observer, London, January 25, 1931, p. 17. 12. E. P. Wigner, Symmetries and reflections, Indiana Uni- versity Press, Bloomington, 1967, pp. 171-184. 13. M. Henry, “Consciousness, Information, Electromag- netism and Water”, Substantia (submitted). 14. L. Nichol, The essential David Bohm edited by Lee Nichol with a reminiscence by H.H. The Dalai Lama, Routledge, Taylor & Francis Group, London, 2003. 15. D. Bohm & F. D. Peat, Science, Order and Creativity, Routledge, Taylor & Francis Group, London, 2010, pp.182-183. 16. E. Mach, Contributions to the analysis of the Sensa- tions, Translated by C. M. Williams, The Open Court Publishing Co, Chicago, 1897, p. 183. 17. H. M. Sheffer, Trans. Amer. Math. Soc., 1913, 14, 481. 18. K. Gödel, Monatsh. Math. Phys., 1931, 38, 173. 19. X. Wen, Y. Liu, L. Yao, M. Ding, J. Neurosci. 2013, 33, 6444. 20. G. Boole, An investigation of the laws of thought on which are founded the mathematical theories of logic and probabilities, Walton and Maberly, London, 1854. 21. A. Heyting, Sitzungsberichste Preuss. Akad. Wiss. Phys. Math. Klasse, 1930, 42, 57, 158. 22. I. Johansson, Compositio Mathematica, 1936, 4, 119. 23. P. Feyerabend, Against method, 3rd Ed., Verso, Lon- don, 1993. 24. P. Watzlawick, J. Beavin-Bavelas, D. A. Jackson, Prag- matics of Human Communication, W. W. Norton & Company, New York, 1967. 25. G. Bateson, Steps to an Ecology of Mind, Jason Aron- son Inc., London, 1972, pp. 276, 321,460. 26. C. E. Shannon, Bell Syst. Tech. J. 1948, 27, 379. 27. S. Lloyd, H. Pagels, Ann. Phys.1988, 188, 186. 28. T. Nørretranders, The User Illusion, Viking, New York, 1991. 29. N. Wiener, Cybernetics or control and communication in the animal and the machine, John Wiley & Sons, New York, 1948. 30. J. A. Wheeler, K. Ford, Geons, Black Holes and Quan- tum Foam. A Life in Physics, W.W. Norton & Co., New York, 1998, pp. 63-64. 31. J. Rothstein, Science 1951, 114, 171. 32. M. Tribus, E. C. McIrvine, Scientific American 1971, Vol. 225 No. 3, p. 180. 33. G. Job, T. Lankau, Ann. N. Y. Acad. Sci. 2003, 988, 171. 34. R. G. McMurray, J. Soares, C. K. Caspersen, T. McCurdy, Med Sci Sports Exerc. 2014, 46, 1352. 35. C. Rovelli, Int. J. Theoret. Phys. 1996, 35, 1637. 36. M. Horodecki, R. Horodecki, A., U. Sen, Found. Phys. 2005, 35, 2041. 37. T. H. Boyer, Phys. Rev. D. 1975, 11, 790. 38. A. Vilenkin, Science. 2006, 312, 1148. 53A scientific rationale for consciousness 39. H. Poincaré, Science and Hypothesis, chapter VIII, Walter Scott Pub. Co. Ltd., New York, 1905, pp. 147- 148. 40. M. T. Gailliot, R. Baumeister, Personality and Social Psychology Rev. 2007, 11, 303. 41. S. H. Fairclough, K. Houston, Biological Psychology. 2004, 66, 177. 42. G. R. J. Hockey, in Cognitive fatigue: multidisciplinary perspectives on current research and future applica- tions (Ed.: P.L. Ackerman), American Psychological Association, Washington, DC, 2011, pp. 167-188 43. E. T. Jaynes, Am. J. Phys. 1965, 33, 391. 44. I. Prigogine, Time, structure and fluctuations, Nobel Lecture, 8 December 1977. 45. W. J. Gibbs, The scientific papers of J. Willard J. Gibbs, Vol. 1, Longmans Green and Co, London, 1906. 46. W. Achtner, Neue Zeitschrift Für Systematische Theolo- gie Und Religionsphilosophie, 2009, 51, 268. 47. S. Dehaene, H. Lau, S. Kouider, Science 2017, 358, 486. 48. J.-F. Houssais, Les trois niveaux de conscience, Guy Trédaniel, Paris, 2016. 49. Ph. Guillemant, La physique de la conscience, Guy Trédaniel, Paris, 2015. 50. N. Block, Behavorial and Brain Sci. 1995, 18, 227. 51. J. E. Bogen, S. Bringsjord, D. Brown, D. J. Chalmers, D. Gamble, D. Gilman, G. Güseldere, A. Murat, B. Mangan, A. Alva; E. Pöppel, D. M. Rosenthal, A. H. C. van der Hejiden  ; P. T. W. Hudson, A. G. Kurvink, N. Block, Ned, Behavorial and Brain Sci.1997, 20, 144 52. R. Landauer, Physics Today 1991, May 23. 53. R. M. Biron, J. Comput. Higher Educ. 1993, 5, 111. 54. G. Marcus, Face It, Your Brain Is a Computer, The New York Times 2015, June 28, p. SR12. 55. Z. Vukadinovic, The Incomplete Self: Gödel and The Brain, Epoché 2018, Issue #14. 56. H. Poincaré, Science and Hypothesis: The complete text, Chap. 14, Bloomsbury academic, London, 2018, p. 163. ANNEX Here we describe for readers not familiar with tech- nological aspects of information processing, the main techniques used to build artificial or natural memory devices. In the physical M4 world, information is read or written on a material substrate that could be poly- carbonate covered by aluminum for optical disks, a fer- romagnetic material for tapes or hard-disks, silicon for memory chips, or a metal-oxide semiconductor for flash memories. In all cases, one have to encode a succession of bits that can be zero (0) or one (1). For optical compact disks, one uses lasers of dif- ferent wavelengths: λ = 780 nm for CD, λ = 650 nm for DVD and λ = 450 nm for BluRay to read and write bits. Upon writing, the laser beam etches bumps (called pits) into the plastic surface, a bump representing the number 0 or leave a flat unburned area on the disc, called a land, representing the number 1 forming a continuous spiral of about 3–5 billion pits. The burned polycarbonate is then coated with an aluminum layer that reflects light. Upon reading, the laser flashes up onto the shiny side of the CD, with the lands reflecting the laser light straight back (bit 1), while the pits scattering it (no reflection or bit 0). For recordable compact disk (CD-R), there is a layer of dye between the protective polycarbonate and the ref lective aluminum. For writing information, a high-power is used able to heat the disc in order mak- ing a tiny black spot on it. Upon reading, the laser light is completely absorbed by black spots (bit 0) while hit- ting unburned areas the laser light reflects straight back (bit 1). Such technologies cannot be used to manufac- ture rewritable compact disks (CD-RW). Instead of hav- ing a layer of dye, a CD-RW has a layer of metallic alloy AgInSbTe that can be crystalline and transparent to light (bit 1) or amorphous and opaque blocking light (bit 0). When a laser hits this material, tiny little areas can be changed back and forth between the crystalline and amorphous forms, allowing reading and writing infor- mation at will. Ferromagnetic materials used in magnetic tapes, magnetic hard drives, and magnetic random access memory can also be used for information storage because they magnetic state can switched between two states using a magnetic field that is generated by electric currents. Here, a conductive layer forms a program/erase line for altering the logic value stored in the device. A bit one or a bit zero can be stored in the ferromagnetic region depending upon a direction and a magnitude of current flow through the conductive layer. By contrast memory chips use MOSFET transistors made of sili- con to store information that is basically a three-termi- nal device with terminals named as Source, Gate, and Drain. Gate voltage controls the flow of current between source and drain. If gate voltage exceeds a particular threshold voltage, a current flows (bit 1) while below if gate voltage is below the threshold; there is no cur- rent (bit 0). The drawback is that as soon as the power is turned off, all the transistors revert to their original states—and the memory loses all the information it has stored. To overcome this problem, flash transistors have 54 Marc Henry, Jean-Pierre Gerbaulet been developed having a second gate (control gate) above the first one (floating gate). Oxide layers through which current cannot normally pass separate the two gates. In this state, the transistor is switched off storing a bit zero. But upon application of a positive voltage between the drain and control gate, electrons get pulled in a rush from source to drain. A few also manage to wrig- gle through the oxide layer by a process called tunneling and get stuck on the floating gate storing a bit one. The electrons will stay there indefinitely, even when the posi- tive voltages are removed and whether there is power supplied to the circuit or not. Putting a negative voltage between the drain and the control gate repels the elec- trons back the way they came, clearing the floating gate and making the transistor store a zero again. Substantia An International Journal of the History of Chemistry Vol. 3, n. 2 - September 2019 Firenze University Press Chemical Industry and Sustainability Vittorio Maglia Novel water treatment processes Mojtaba Taseidifar1, Adrian G. Sanchis1, Richard M. Pashley1,*, Barry W. Ninham2 Is aberrant N-glucosylation relevant to recognise anti-MOG antibodies in Rett syndrome? Feliciana Real-Fernández1,2, Giulia Pacini2, Francesca Nuti1, Giulia Conciarelli2, Claudio De Felice3, Joussef Hayek4, Paolo Rovero2, Anna Maria Papini1,* Hydrogen-like quantum Hamiltonians & Einstein separability in the case of charged radical molecules Han Geurdes A scientific rationale for consciousness Pr. Marc Henry1,*, Jean-Pierre Gerbaulet2,* Derjaguin’s Water II: a surface hydration phenomenon Ilya Klugman, Anna Melnikov1, Drew F. Parsons2 Leonardo da Vinci – The Scientist Walter Isaacson B. V. Derjaguin* and J. Theo. G. Overbeek. Their Times, and Ours Barry W. Ninham Sadi Carnot’s Réflexions and the foundation of thermodynamics Pier Remigio Salvi, Vincenzo Schettino Vladimir Vasilyevich Markovnikov (1838-1904) – the eminent Russian chemist, author of one of the best known empiric rule in organic chemistry Aleksander Sztejnberg