The Ultimate Insight: On the Explanatory Power of Absolute Self-Awareness

A recurrent theme on this blog is the idea of Absolute Idealism 2.0, i.e. a contemporary, ‘mathematized’ version of the age-old philosophy of Absolute Idealism, which runs from the ancient Upanishads to the Neoplatonist philosopher Plotinus to German and Anglo-American Idealists such as Schelling, Hegel, Green and Royce. Absolute Idealism 2.0 takes over their central insights but develops them in a novel way consistent with modern science, in particular with the central role of mathematics in physics. The following post gives a broad overview of the central principles of Absolute Idealism 2.0. and how these principles enable us to make sense of reality-as-a-whole.
The self-creating power of Absolute Self-Awareness We can provisionally define Absolute Idealism as the philosophical theory that everything exists because it is thought and/or experienced by an Absolute Mind, which in turn exists because It thinks/experiences itself. Thus, on the Absolute-Idealist view, the Absolute Mind constitutes its own existence by thinking/experiencing itself, that is, by being self-aware. The Absolute Mind, then, should first and foremost be defined as Absolute Self-Awareness. The idea that (pre-reflective) self-awareness has a self-creating aspect is most often associated with the German Idealist Fichte and his case for the “self-positing of the I”, but roughly the same idea can be found with other Absolute Idealists as well:

• The Vedantic sages of the Upanishads: “In the beginning this world was only Brahman, and it knew only itself (Atman), thinking: ‘I am Brahman.’ As a result, it became the Whole.” (Brihadaranyaka Upanishad 1.4.10) 

• The Neoplatonic philosopher Plotinus: “The One [...] made itself by an act of looking at itself. This act of looking at itself is [...] its being.” (Ennead VI, 8, 16, 19-21)

• The German Idealist Schelling: “it is through the self's own knowledge of itself that that very self first comes into being” (Schelling 1800: 27).

• The American Idealist Royce: “if whatever exists, exists only as known, then the existence of knowledge itself must be a known existence, and can finally be known only to the final knower himself, who, like Aristotle's God, is so far defined in terms of absolute self-knowledge” (Royce 1899: 400).
   

By highlighting this self-creating aspect of Absolute Self-Awareness, Absolute Idealism is very attractive in that it offers a clear-cut and intuitively plausible answer to Leibniz’ famous question: “Why is there something rather than nothing?” According to Absolute Idealism, there is something rather than nothing because Absolute Self-Awareness is self-creating. I call this answer to Leibniz’s question intuitively plausible mainly because of two reasons: (1) we are all self-aware and so we know – with Cartesian self-evidence – that self-awareness exists, indeed it is the only existence we are absolutely certain of, and (2) we have a glimpse of the self-creating power of Absolute Self-Awareness in the (self-)awareness we have of our own free will. This last point needs some elucidation.

Kant and the “unconditioned causality of freedom
Of course, when I talk of the self-creating power of self-awareness, I am not talking of individual human self-awareness. None of us has brought him- or herself and the universe into existence. As empirical individuals we are biologically conditioned, brought into existence by others, subject to time. So how then can I say that our own self-awareness gives a glimpse into the self-creating power of Absolute Self-Awareness?

In a way we do experience a degree of self-causation in ourselves, namely, insofar as we exercise positive freedom, i.e. autonomy. Positive freedom requires a capacity for what Kant called “spontaneity”, the “unconditioned causality of freedom” (Critique of Pure Reason, B561/A533), i.e. a capacity to initiate an entirely new course of action and/or thought ‘out of nothing’, unmotivated and/or uncaused by prior givens. But isn’t such a capacity for radical spontaneity – for initiating something out of nothing – precisely what is needed in order to answer Leibniz’s question, i.e. to explain how reality has lifted itself into existence preceded by nothing?

Insofar as our self-awareness reveals in us this ‘unconditioned causality of freedom’, then, we have all the more reason to take our self-awareness as the key to answering Leibniz's question. It is, moreover, the self-positing nature of self-awareness that explains this unconditioned causality of freedom in the first place. Obviously we aren't self-causing in any absolute sense (since, to repeat, we have not created ourselves), but we are relatively self-causing in that we can at least intervene in the causal order of reality by spontaneously initiating a completely new causal chain of events.

This underscores the difference between empirical, individual self-awareness and Absolute Self-Awareness: what the former has relatively and finitely, the latter has absolutely and infinitely. That is to say: Absolute Self-Awareness has (or is) absolute freedom. The self-evident experience of our own self-awareness gives us empirical access to the self-causation that can answer Leibniz's question, but to make full sense of this answer we have to generalize beyond ourselves. We have to project prereflective self-awareness to something that transcends us, the Absolute, the unconditioned 'thing' that conditions all of reality.

The mathematical unfolding of Absolute Self-Awareness
What then is the precise relation between Absolute Self-Awareness and individual self-awareness as it is found in you and me? To answer this question we have to move from Leibniz’ question to the next question: why is the universe the way it is? We do not just want to know why something exists, we also want to know why this something is the way it is, i.e. why reality has developed into this infinitely complex universe in which we find ourselves. It is especially here that I take the age-old philosophy of Absolute Idealism into a new direction, making it fit for the future by drawing on ideas from modern physics and mathematics. It is here that Absolute Idealism becomes Absolute Idealism 2.0.

Making creative use of some seminal ideas from the American Idealist Josiah Royce, I argue that the recursivity inherent in Absolute Self-Awareness – in short: its awareness of itself, its awareness of that awareness, its awareness of the awareness of that awareness, and so on – establishes an intrinsic connection between self-awareness and the recursively generated natural numbers and even the recursively generated set-theoretical universe of pure sets, which in a way contains the whole of mathematics (more about this here and here). Thus, from this perspective, the Absolute Mind comes out as a deeply mathematical being, generating – through the recursivity of its self-awareness – all of mathematics, and subsequently mirroring itself in those mathematical structures that best reflect its transcendent splendor.

The universe as the mathematical self-image of the Absolute
In my view, the resulting mathematical mirror image of the Absolute Mind is our physical universe (which, as modern physics shows, is indeed thoroughly mathematical in nature). Through mirroring and recognizing itself in this mathematical universe, and particularly in those mathematical structures that emulate intelligence (such as the algorithmic structure of the human brain), the Absolute Mind increases its own self-awareness and thus teleologically realizes its essence. In this way I explain the apparent fine-tuning of the universe, i.e. the fact that surprisingly many of nature’s fundamental constants – such as the ratio of the masses of electrons and protons, the energy density of the vacuum, even the three-dimensionality of space – are “just right” for the evolution of life. This bio-friendliness of the universe follows from the fact that the universe is the mathematical mirror image of the Absolute Mind.

It is, moreover, the self-recognition of the Absolute Mind in mathematical structures (such as the algorithmic structure of the human brain) that infuses these structures with phenomenal consciousness: it explains why the mathematical structure of the brain is “accompanied by an experienced inner life” (Chalmers 1996: xii). In this way I aim to solve the notorious “Hard Problem of Consciousness”. Moreover, as it is the mathematical structure of the universe as a whole in which the Absolute Mind mirrors itself, we must see the entire universe as infused with phenomenal consciousness, thus arriving at a panpsychist view of the cosmos.

This, then, answers the question we raised above about the relation between individual human self-awareness and Absolute Self-Awareness. Individual self-awareness, as experienced by individual organisms, is nothing but the self-reflection of the Absolute in specific mathematical structures, notably in those algorithms that “simulate” intelligent volitional agency, algorithms such as the ones that underlie the functioning of our brains. In this sense, Absolute Self-Awareness is the pre-reflective core of every finite individual form of self-awareness. One could say that each empirical instance of individual self-awareness (human or otherwise) is, as it were, a navel in the physical universe, connecting the latter through a transcendental umbilical cord with the Absolute Self-Awareness that grounds reality as a whole.

Explaining mind-body dualism
This explanation of what individual consciousness is – namely, the self-reflection of Absolute Self-Awareness in the complex algorithm that simulates brain functioning – also allows us to make sense of the apparent duality of mind and matter and, notably, the apparent supervenience of the former on the latter. This is one of the major difficulties faced by any kind of Idealism: if matter is just an appearance in consciousness, why and how then can it seem that matter exists apart from consciousness and, indeed, that (individual) consciousness appears to depend on matter?

From the perspective of Absolute Idealism 2.0, this duality between mind and body comes down to the distinction between, on the one hand, the mathematical structure of the recursive self-unfolding of Absolute Self-Awareness, and the latter’s self-recognition in certain privileged parts of that structure on the other. The mathematical structure in which the Absolute reflects itself is the structure of matter, i.e. the structure discovered by physics. But it is the self-reflection of the Absolute in this structure, the fact that it recognizes itself in it, that – so to speak – infuses the structure with phenomenal awareness. It is this act of self-recognition that explains why the mathematical structure of matter is – as Chalmers put it – “accompanied by an experienced inner life”. This holds in particular for the structure of the brain (human or otherwise), which is the kind of mathematical structure in which the Absolute recognizes most of itself (intelligent and volitional agency); hence the infusion of this structure with individual consciousness.

Hence the duality of brain and consciousness, and the apparent dependence of the latter on the former. The brain as a physical object is simply the underlying mathematical structure as experienced from the outside by another conscious organism (i.e. another brain / individual consciousness), whereas individual consciousness is that very same mathematical structure as experienced ‘from within’, i.e. as an object for the Absolute’s self-recognition. We can call these, respectively, the first-person and the third-person experiences of the mathematical structure of the brain. The fact that individual consciousness appears to be causally dependent on the brain is due to the fact that individual consciousness is ontologically dependent on the mathematical structure in which the Absolute recognizes itself.

The funny thing here is that we, human beings, are in principle capable of both a first-person and a third-person perspective on the mathematical structures of our own brains; for example – to take a rather drastic example – when we open up our skull and use a mirror to look at our own brain. We then experience its underlying mathematical structure in two ways simultaneously: from the inside as the object of the Absolute’s self-recognition, which gives us our individual consciousness, and from the outside, i.e. from a third-person perspective, which gives us this strange lump of grey matter that is supposed to be us. Something similar happens, though less drastically, when we look at a CT scan of our own brain. 

Morality as self-recognition in the other
To repeat: Absolute Self-Awareness is the pre-reflective core of every finite individual consciousness, insofar as the latter is nothing but the self-recognition of the Absolute in the mathematical structure of the brain. Thus, as the Vedanta philosophy based on the Upanishads puts it, we are all in principle capable of discovering the same Self (Atman) as the innermost core of our individual self-awareness. This Universal Self, this core in each of us, is the Absolute Self-Awareness as it reflects itself empirically in the self-awareness of finite organisms in the universe. Thus, the “unconditioned causality of freedom” we detect in our self-awareness really is the unconditioned causality of the self-causing Absolute as the ground of all reality. In that sense the (self-)awareness we have of our own free will does give us a glimpse into the endlessly creative source of the universe.

Insofar as we are capable of this glimpse, i.e. of ‘seeing’ the Absolute as the prereflective core of our own self-awareness, we start to appreciate that the same holds for all living beings. We start to realize that all organisms are essentially nothing but different manifestations of one and the same creative essence, the Absolute, the Universal Self, which senses, thinks and acts through all these organisms. This gives an enormous feeling of connection and love for others. Suddenly you can empathize with others and take their perspective much more easily, because you know they are not fundamentally different from you. You start to experience other beings as different versions of yourself, i.e. of your innermost Self, the creative essence of the universe. It is this empathy with others, through the non-dual sense of cosmic unity, that is the foundation of all sincere morality.

In this way, a kind of self-recognition in others – a seeing of yourself in others – takes place, but the self that is recognized here is not primarily the individual self but rather the Self, the Universal Self, the Atman, the Absolute. One could say that in this way the universe as the mathematical self-image of the Absolute is all the more true to its archetype: just as the Absolute recognizes itself in the otherness of the physical universe, so the universe mirrors this Divine Self-Recognition by evolving organisms that recognize themselves (i.e. their Self) in each other. Through the evolution of this self-recognition among organisms, this “mutual recognition” as Hegel calls it, the universe evolves into an ever improving mirror of the Absolute, thereby contributing to the latter’s essence as self-awareness.       Relation to Enlightenment in Eastern spirituality As the above reference to the Vedanta indicates, this (self-)realization of the Absolute as the prereflective core of our own individual self-awareness has a deep connection to what in Eastern spirituality is known by such terms as "Enlightenment", "Awakening", "(Self-)Realization", and "Liberation". This marks an important difference between Western and Eastern forms of Absolute Idealism. Whereas the Western forms are mostly theoretically oriented, aimed at a purely intellectual understanding of reality, the point of virtually all Eastern spirituality is primarily practical, aimed at a radical existential transformation of human life. Hence the terminological distinction I draw between Western philosophy and Eastern spirituality. It is certainly not the case that philosophical theorizing is entirely absent in the East – quite the contrary, Eastern spirituality contains some of the deepest philosophical thinking ever done. It is just that in Eastern spirituality all theorizing is ultimately subordinated and subservient to the spiritual goal of Liberation: theory for the sake of theory is rejected, because it stands in the way of the spiritual goal. The notion of Absolute Self-Awareness, then, signifies in the Eastern context not just the ultimate nature of reality, it also signifies the individual’s realization of the Absolute as his / her own innermost Self and as such the final Liberation from the suffering inherent in finite human existence. In Eastern spirituality, then, Absolute Self-Awareness is first of all not a theoretical concept (as it is in Western Absolute Idealism) but an experience or intuition, the experience of Enlightenment, the awakening to or realization of one’s true nature, the intuition of the Absolute as the core of one’s being. This is the experience that accomplishes the longed for Liberation from suffering. Here the Vedanta of the Upanishads provided the original template for all later Eastern spiritual traditions aimed at Enlightenment (even if these traditions criticized certain aspects of the Vedanta). For the Upanishadic sages, the key insight “Brahman is Atman” is not just a theoretical insight into the ultimate ground of reality, it is also the liberatory insight into the ultimate core of one’s own self, the realization “I am Brahman”, freeing one from the suffering inherent in finite human life. This comes out clearly in the Brihadaranyaka Upanishad, which we quoted earlier as clearly pronouncing the basic realization of the self-causing nature of Absolute Self-Awareness: “In the beginning this world was only Brahman, and it knew only itself (Atman), thinking: ‘I am Brahman.’ As a result, it became the Whole.” (1.4.9) This remarkable passage doesn’t stop here: it goes on pronouncing with equal clarity the spiritual significance of this realization: “If a man knows ‘I am Brahman’ in this way, he becomes this whole world. Not even the gods are able to prevent it, for he becomes their very Self (Atman)... He is the one who is beyond hunger and third, sorrow and delusion, old age and death.” (1.4.10, 3.4.2) Here the spiritual significance of Absolute Self-Awareness, the Liberation from the suffering inherent in finite existence, is clearly announced. The ultimate insight that explains everything? What all this makes clear is that the Enlightenment experience has both a theoretical and a practical value, indeed it is the ultimate accomplishment both philosophically and spiritually. Enlightenment is not just the insight that liberates from the confines of finite existence, it is also the insight that provides the ultimate epistemological foundation for the Absolute-Idealist worldview. This implies an extreme form of rationalism, such that in principle everything is explainable for us, finite human beings, because insofar as we are self-conscious beings we have a prereflective intuition of the nature of Absolute Self-Awareness as the self-causing cause of reality-as-a-whole. Looked at from the theoretical perspective, Enlightenment is the insight into the essential core of our own self-awareness as the absolutely free (i.e. self-causing) source of all reality, as the recursive fountainhead of all mathematics and thus of the physical universe as our own innermost mathematical self-image, and as the source of all morality qua self-recognition in others. Enlightenment, in short, is the ultimate insight that allows us to explain everything. But, so a critic might ask, does it even make sense to attempt an explanation of ‘everything’? Isn’t such an all-encompassing notion logically incoherent? I want to finish this post by taking a closer look at this objection and how Absolute Idealism can deal with it. Leibniz’s question, paradox, and self-awareness This objection has in particular been raised by analytic philosophers such as Alfred Ayer and Bertrand Russell: they argue that all-encompassing concepts like “everything” and “reality as a whole” lead to paradoxes of self-reference, akin to the paradoxes of the early ("naive") set theory developed by Cantor, Dedekind and Frege. In my view, however, this self-reference ceases to be paradoxical once we realize that Absolute Self-Awareness is the self-causing cause of reality and that self-reference belongs to the essence of self-awareness. Naive set theory is so-called because it allowed sets that are deemed "too big", such as the universal set: the set containing all sets, including itself. Thus the universal set is self-membered, and this leads – directly or indirectly – to paradoxes, such as Cantor's paradox, the Burali-Forti paradox and Russell's paradox. One could argue that Leibniz's question produces similar paradoxes because, in a way, it totalizes existence. By posing the question "Why is there something rather than nothing?", Leibniz invites us to look at reality as a whole, the totality of what exists, in order to find the cause or reason explaining this totality. But in conceiving this totality, aren't we relapsing into the naiveté of early set theory? Aren't we allowing a set that is "too big"? This was indeed the main objection raised by logical positivism against Leibniz’s question: it is meaningless because it leads to paradoxes of self-inclusion. Thus Alfred Ayer: "Supposing you asked a question like 'Where do all things come from?' Now that's a perfectly meaningful question as regards any given event. Asking where it came from is asking for a description of some event prior to it. But if you generalize that question, it becomes meaningless. You're then asking what event is prior to all events. Clearly no event can be prior to all events. Because it's a member of the class of all events it must be included in it, and therefore can't be prior to it." (Ayer quoted in Holt 2013: 24) Bertrand Russell too noted the paradoxical self-referentiality of the philosophical concept of reality-as-a-whole: “The comprehensive class we are considering, which is to embrace everything, must embrace itself as one of its members. In other words, if there is such a thing as “everything,” then “everything” is something, and is a member of the class of “everything”.” (Russell 1919: 136) Thus Russell was suspicious of all-embracing philosophical concepts such as reality-as-a-whole: “The difficulty arises whenever we try to deal with the class of all entities absolutely [...]; but for the difficulty of such a view, one would be tempted to say that the conception of the totality of things, or of the whole universe of entities and existents, is in some way illegitimate and inherently contrary to logic.” (Russell 1903: 362) With the concept of reality-as-a-whole out of the window, however, Leibniz's question can no longer be posed. If the concept of reality-as-whole is logically incoherent, then the question why that whole exists must be illogical as well. In response to this criticism we only have to point out that the set-theoretical paradoxes are defused by the phenomenon of self-awareness. For what appears as paradoxical in the foundations of mathematics – namely, self-reference – actually is a living reality in the phenomenon of self-awareness. Why then should we reject self-reference as paradoxical, and banish it from the foundations of mathematics, when self-reference is a clearly a bona fide aspect of reality, an aspect of which the existence is attested – with Cartesian self-evidence – by the undeniable phenomenon of self-awareness? Thus it becomes clear how the Absolute-Idealist view of reality as essentially a form of self-awareness – namely, Absolute Self-Awareness – saves Leibniz’s question from Russell's criticism. If we take reality as such to be self-awareness, then the self-inclusion of the totality of what exists ceases to be paradoxical, because such self-inclusion is to be expected of self-awareness. This self-inclusion is the inherent recursivity of self-awareness, which necessarily involves awareness of self-awareness, and awareness of awareness of self-awareness, and so on without end. In other words, self-awareness must include itself as one of the objects of which it is aware. Thus we can compare self-awareness to a ‘magical matryoshka’, a Russian nesting doll that somehow contains itself: if one opens up the doll, one finds the same doll inside… In short, then, the Absolute Idealist conception of self-awareness does not just enable us to answer Leibniz's question, it also enables us to pose that question in a meaningful way. It shows that the self-inclusion of the totality of what exists – a totality presupposed by Leibniz's question – is not a senseless violation of logic, because it belongs to the living essence of reality qua Absolute Self-Awareness. References -Chalmers, D. J. (1996), The Conscious Mind: In Search of a Fundamental Theory, Oxford University Press.   -Holt, J. (2013), Why does the world exist?, Profile Books. -Kant, I. (1781/’87 [2009]), Critique of Pure Reason, Cambridge University Press. -Plotinus, Enneads, translation by A.H. Armstrong, Loeb edition. -Royce, J. (1899 [1959]), The World and The Individual, First Series: The Four Historical Conceptions of Being, Dover Publications. -Russell, B. (1903 [1964]), The Principles of Mathematics, George Allen & Unwin. -Russell, B. (1919 [1970]), Introduction to Mathematical Philosophy, George Allen and Unwin. -Schelling, F.W.J. (1800 [2001]), System of Transcendental Idealism, translated by Peter Heath, University Press of Virginia. -Upanishads, translation by Patrick Olivelle, Oxford University Press, 2008.

Is the Universe a Self-Computing Consciousness?

For a printable version of this text, see: Is the Universe a Self-Computing Consciousness? From Digital Physics to Roycean Idealism

It is a well-established fact in physics that physical processes are thoroughly computable, with the laws of nature acting as algorithms taking the present state of a physical system as input and producing the next state as output. In an often-quoted remark computer scientist Tommaso Toffoli puts this as follows: "In a sense, nature has been continually computing the "next state" of the universe for billions of years; all we have to do – and, actually, all we can do – is "hitch a ride" on this huge ongoing computation". (Toffoli 1982: 165) This thoroughgoing computability of nature is what allows us to use computers to model or "simulate" physical processes, thus greatly enhancing our capacity to understand nature. "Scientific laws give algorithms, or procedures, for determining how systems behave," physicist Stephen Wolfram explains:

"The computer program is a medium in which the algorithms can be expressed and applied. Physical objects [...] can be represented as numbers and symbols in a computer, and a program can be written to manipulate them according to the algorithms... It thereby allows the consequences of the laws to be deduced... New aspects of natural phenomena have been made accessible to investigation. A new paradigm has been born." (Wolfram 1984: 188, 203)

Digital physics still up for grabs
Thanks to rapid advances in computer science and information theory, the new paradigm heralded by Wolfram in 1984 has burgeoned into a new field of physics called "digital physics", studying the technological and theoretical applications, implications and foundations of the thoroughgoing computability of nature. Despite this rapid growth, however, and despite considerable media attention for the more fantastic claims made by some researchers in this field (e.g. we live in a computer simulation created by an advanced civilization; see Bostrom 2003), digital physics is by no means yet a unified field of research with consensus on basic premises and conclusions. Researchers agree by and large on the success of computer models to simulate physical process, but disagree widely on the implications of this success, i.e. on what the computability of physics means. Does it merely mean that physical processes can be modeled by computations? Or does it mean that physical processes are computations? And what kind of computations are involved in physical processes? Are they essentially digital or analogue? Are they deterministic or also probabilistic? Are they classical computations, performable by a Turing Machine? Or are they quantum computations, requiring multiple Turing Machines working in parallel? And if they are classical, are the computations performed serially, as on a Turing Machine, or should we rather think of distributed computation as in cellular automata and neural networks? These are some of the basic questions that researchers in digital physics continue to disagree about (for an overview of all the different approaches in digital physics, see the papers collected in Zenil 2013). It is fair to say, therefore, that the field of digital physics is still up for grabs.

The Church-Turing Thesis and the platform problem
In this post I will be concerned with one of the most fundamental problems in digital physics: the problem of the hardware or – more generally – of the computing platform, i.e. the pre-existing environment that facilitates the process of computation. If physical processes are computations, if the entire universe is computational, what then is the "cosmic computer" underlying the universe, what is the hardware or platform on which the computations run? Moreover, who or what is responsible for the program obeyed by those computations, i.e. for the algorithms expressed in the laws of nature? Why these algorithms and not others? These questions pose serious problems for digital physics and threaten to erode the new paradigm from within. The difficulty is that they are in principle unanswerable within the confines of digital physics given the "universality of computation" implied by the Church-Turing Thesis.

Computational universality is one of the foundational tenets of computer science: it states, basically, that any computation that can be carried out by one general-purpose computer can also be carried out on any other general-purpose computer, no matter how different their internal architectures are. Thus it has been shown, for example, that a cellular automaton with a certain minimum level of internal complexity is computationally equivalent to a Turing Machine, despite their radically different architectures (namely, distributed vs. serial computation). Even the quantum computer, often heralded as a revolution in computation, is strictly speaking computationally equivalent to a Turing Machine (the only difference being that it would take a Turing machine an impractical amount of time to perform certain computations which pose no such problems for quantum computers). This computational equivalence of radically different hardware architectures is a consequence of the abstract principle encapsulated in the Church-Turing Thesis, stating basically that "computation" (which we may take to be synonymous with "algorithm" and "computable function") is simply anything that can be performed by a Turing Machine. This implies that any device capable of computation, i.e. any computer, can in principle do all the things a Turing Machine can do, and vice versa, no matter how different their architectures are. This also means that all computers can "simulate" each other: any device capable of computation can be programmed to perform any possible algorithmic process, be it a physical process or the action of a man-made computer.

So why does computational universality imply the inscrutability of the "cosmic computer"? The point is that if all physical processes are computations, and if all the empirical data we have reveal nothing but physical processes – that is to say, if all we can know are these computations – then by definition we are precluded from knowing anything about the platform on which these computations run, because that platform could be anything as long as it is Turing equivalent. Due to the universality of computation, all different kinds of architectures can facilitate computation. Therefore the computations involved in physical processes can tell us nothing about the underlying architecture of the cosmic computer. The latter thus turns out to be – speaking in a metaphysical vein – the unknowable, the transcendent as such. This inscrutability of the cosmic computer is in a sense the computational equivalent of the unknowability of God "as He exists in Himself". 

Different approaches to the platform problem: Fredkin vs. Deutsch
Ed Fredkin, one of the pioneers of digital physics, speaks in this regard of the "Tyranny of Universality" from which he concludes that "we can never understand the design of the computer that runs physics since any universal computer can do it". (Fredkin in Zenil 2013: 695) For Fredkin, however, this is no reason to reject the idea that physics is exhausted by computation. He rather bites the bullet and embraces the mystery, speaking in quasi-theological fashion of the "Other" as the ultimate source of the computations that produce our universe. The Other, he says, could be another universe, another dimension, another something. It's just not in our universe, and so he perforce remains agnostic about it: 

"As to where the Ultimate Computer is, we can give [a] precise answer: it is not in the Universe – it is in another place. If space and time and matter and energy are all a consequence of the informational process running on the Ultimate Computer, then everything in our universe is represented by that informational process. The place where the computer is, the engine that runs that process, we choose to call "Other"." (Fredkin 1992)

For other researchers, however, the problem posed by computational universality is reason to be skeptical of the core claim of digital physics, i.e. the claim that physical processes are nothing but computations. David Deutsch, for instance, the principal inventor of the quantum computer no less, reverses the relation between physics and computation as it is normally conceived in digital physics. Instead of seeing the laws of physics as a subset of all possible algorithms, Deutsch (1985) sees those laws as determining which computations are possible, i.e. physically allowed in our universe. Part of his reason for doing so is precisely the problem of the unknowability of the hypothetical cosmic computer due to computational universality:

"If the laws of physics as we see them are just aspects of some universal computer program, then by definition we would be prevented from finding out anything about the hardware of that computer. That is the very nature of computing: the power of computing comes from the fact that the computer is a universal machine. If we're just a program, the program cannot obtain information about the machine on which it is running. So there would be an underlying physics responsible for this computer, and we would never be able to find out what that physics is." (Deutsch in Brown 2000: 335) "[B]ecause the properties of this supposed outer-level hardware would never figure in any of our explanations of anything, we have no more reason for postulating that it’s there than we have for postulating that there are fairies at the bottom of the garden." (Deutsch 2003: 4)

All in all, Deutsch 'saves' digital physics from the platform problem by drastically curtailing the scope of digital physics. If physical processes cannot in toto be seen as consisting in computations (since that, according to Deutsch, would make the underlying hardware of the universe inscrutable), then that basically means the end of digital physics qua attempt to reduce physics to computation. Symptomatic in this regard is Deutsch's reversal of the relation between physics and computation: if, as Deutsch claims, the laws of physics determine which computations are possible, rather than those laws being just a subset of all possible computations (a common claim in digital physics), then a thoroughgoing computational approach to physics is given up. It would, after all, be rather circular to try to understand the laws of physics in terms of computation if those laws themselves define what computation is. It can seriously be doubted whether this is at all a consistent position for someone who sees the universal quantum computer as the best model of how the universe (or rather the multiverse, for Deutsch) works.

A dilemma
So what is the upshot? It seems to me that if the project of digital physics is to continue, i.e. if computation is to be taken as the key to how the physical universe works, then we face the following dilemma: either (1) we bite the bullet, like Ed Fredkin, and accept the in principle unknowability of the platform underlying the computations that comprise the universe, or (2) we find an additional and non-computational source of insight into the nature of the cosmic computer. It is clear why, in option (2), this non-computational nature of the additional source of insight is necessary. If what gives us information about the cosmic computer consists itself entirely of computations as well, then the problem posed by the universality of computation simply repeats itself, for then the platform of those computations becomes inscrutable, and the buck is merely passed on to another level. To stop this regress, and gain knowledge of the ultimate computing platform, we must find a source of knowledge that is not essentially computational in nature. So the crucial questions become: Do we have any non-computational sources of knowledge? And do they tell us anything about the computing platform underlying the computations involved in physical processes? In this post I would like to propose an idealist version of option (2).

Does the platform problem require an idealist solution?
Before I go on to answer these questions in some detail, I will first offer some general reasons why the platform problem in digital physics calls for a broadly idealist solution, i.e. a solution invoking the ontological priority of "mind over matter". First of all, as has often been noted by researchers in digital physics, it is very hard to see how the platform underlying the computations involved in physical processes could be physical as well. If the computing platform were a physical object (possibly obeying physical laws different from ours), and if all of physics is computational, then the platform too would be the result of computation and would as such presuppose a lower-level platform, which – if it were physical – would require another platform at a still lower level, and so on without end. In other words, within the confines of digital physics, operating on the assumption that all of physics is computational, the view of the computing platform as something physical leads to an infinite regress. Deutsch recognizes this: "that underlying physics would not be a program running on a computer, unless you want to postulate an infinite regress." (Deutsch in Brown 2000: 335)

This is one of the reasons why Deutsch more or less opts out of digital physics by making computation dependent on the laws of physics rather than vice versa (as elaborated above). For Deutsch, as a physicist, it is apparently not an option that reality at its most basic level is other than physical. Thus, to save the ontological priority of the physical and at the same time avoid the above regress, Deutsch is forced to assume that the physical is more than just computation, i.e. that there is a non-computational aspect to physics. But in view of the thoroughgoing computability of physical processes, it is hard to see how there could be any empirical evidence for this view. In short, to avoid the regress, while still upholding the computational nature of physics, it is necessary to postulate a non-physical platform underlying the computations involved in physical processes. This in itself already points in the direction of an idealist solution to the platform problem.

The hard problem of consciousness
What could this non-physical substrate of computation possibly be? Do we have any evidence for the existence of something non-physical? Here, I think, is where the "hard problem of consciousness" becomes all-important, i.e. the problem posed by the apparent impossibility to explain consciousness entirely in physical terms (Chalmers 1996). The hard problem, when taken seriously, shows that consciousness must be non-physical. And, of course, we do have evidence for the existence of consciousness (it would after all be rather paradoxical to deny the reality of our own consciousness). Thus consciousness comes out as a possible candidate for being the platform underlying the computations involved in physical processes. No doubt this approach goes counter to the widespread conviction in current science that consciousness must ultimately be reducible to physical processes in the brain. But it is precisely this conviction that the hard problem puts into doubt. Here I will simply presuppose the correctness of the various arguments given for this irreducibility of consciousness, because developing and defending these arguments here will take us too far afield (for a general overview of these arguments, see Chalmers 1996). Nevertheless, to get a general sense of what these arguments are about, I will say a few words about one such argument, the famous "knowledge argument" which received its canonical formulation from Frank Jackson (1986). Earlier versions of this argument, however, had already been put forward by other philosophers in the analytic tradition, notably Bertrand Russell, whose particular rendering of the argument I will quote and discuss. It testifies to Russell's particular genius that he was able to say in two sentences what other philosophers say in pages. Here is what he writes:

"It is obvious that a man who can see knows things which a blind man cannot know; but a blind man can know the whole of physics. Thus the knowledge which other men have and he has not is not a part of physics." (Russell 1954, 389)

In other words: even if a blind man knows all there is to know about the brain as a physical object, i.e. even if he has perfect scientific knowledge – a perfect physics – of the brain, there is still something left out, namely, what it is like for the seeing man to see. And we can generalize this to conscious experience in general. Even if, to use Thomas Nagel's famous example, we have perfect physical knowledge of a bat's brain, we still do not know what it's like to be a bat, i.e. what the experience of a bat is like (Nagel 1974). Thus, conscious experience is something over and above brain activity. Such an experience of what something is like is what philosophers call a quale. Conscious experience consists of qualia, i.e. experiences of what it is like to sense, feel and think. Qualia constitute the irreducible aspect of consciousness, i.e. irreducible to physical reality.

The non-computational nature of consciousness
It is important to realize that the knowledge argument for the irreducibility of consciousness works equally well against the position of functionalism/computationalism in cognitive science, where consciousness is identified not so much with the brain per se but rather with the brain's functional organization, i.e. the algorithms involved in the brain's information processing. Advocates of this approach (e.g. Putnam, Fodor) often stress the "multiple realizability" of functional organization, meaning that the algorithms involved in information processing are independent of any specific type of physical hardware, such as the human brain. Here, of course, they rely on the universality of computation as implied by the Church-Turing Thesis: the same computations can be performed by any kind of physical system, including man-made machines. If those systems have the same functional organization as the human brain, those systems would have a consciousness indistinguishable from ours.

However, as I said, the knowledge argument works well against this approach too. We could – as in Frank Jackson's classic thought experiment (Jackson 1986) – imagine a blind cognitive scientist with perfect knowledge of the brain's functional organization, i.e. of the algorithms involved in the brain's information processing. Would she thereby know what it is like to see? No, clearly not. Hence, the what-it's-likeness of visual experience, the qualia involved in seeing, are something over and above the computations performed by the brain. And again we can generalize: even if we have perfect knowledge of the computations going on in a bat's brain, we still do not know what it's like to be a bat. Thus, conscious experience as such – the having of qualia – is something over and above computation.  

We are now in a position to answer the first of the two questions raised above: Do we have any non-computational sources of knowledge? And do they tell us anything about the computing platform underlying the computations involved in physical processes? The hard problem shows that, yes, we do have at least one non-computational source of knowledge, namely, the first-person knowledge we have of our own consciousness. But how does this help us to answer the second question? Does consciousness reveal anything about the underlying nature of the cosmic computer? Could consciousness itself be the computer that runs the computations involved in physical processes, such that the physical world is actually a manifestation of the computational capacity of consciousness? This may sound paradoxical in light of the fact that we have just established the non-computational nature of consciousness, but really this paradox is only apparent. To say that consciousness cannot be fully explained in computational terms does not mean that consciousness is not capable of computation. So, again, could consciousness be the computer that generates physics? Obviously, a solution of this type takes us in the direction of idealism, where mind is seen as explaining matter rather than vice versa. And before I go on to suggest a specific idealist solution to the platform problem, let me note that modern physics already by itself has invited idealist interpretations, mainly because of the constitutive role of the observer in quantum mechanics (e.g. Von Neumann, Wigner, Stapp), the anthropic principle in cosmology, and the constitutive importance of information for physical processes (e.g. Wheeler). An idealist solution to the platform problem, then, would fit in with already existing theoretical tendencies in contemporary physics.
 
Royce and the computational power of self-consciousness
So let's turn to the question how consciousness might function as the cosmic computer that underlies the physical universe. Here I would like to draw attention to some interesting suggestions put forward by the American idealist Josiah Royce (1855-1916). Royce stands in the tradition of absolute idealism inaugurated by the post-Kantian German idealists Fichte, Schelling and Hegel. This means, among other things, that Royce takes not so much consciousness as such to be ontologically primary but rather one specific form of consciousness, namely, self-consciousness. Absolute idealism takes the whole of reality to exist because it is thought and/or experienced by an absolute Self who in turn exists because it thinks/experiences itself. Thus the self-consciousness of the absolute Self allows it to be ontologically self-grounding, i.e. to bootstrap itself into existence (I have argued for this position here). It is precisely this circular structure of self-consciousness which is revealed by Royce to be closely connected to the problematic of computation. Royce is not much read nowadays, but insofar as he is known at all it is for two innovations. Firstly, Royce introduced American pragmatism into absolute idealism by forging a kind of synthesis between Hegel and Peirce. This Royce, however, the pragmatist, will not be important for us. Secondly, Royce is also known as the philosopher who defended the infinite complexity of self-consciousness and who, to that effect, devised the widely discussed example of the "map of England on the surface of England" (see e.g. Russell 1970: 80; Rucker 1997: 38; Moore 2003: 102). As Royce writes:

"To fix our ideas, let us suppose, if you please, that a portion of the surface of England is very perfectly leveled and smoothed, and is then devoted to the production of our precise map of England... A map of England, contained within England, is to represent, down to the minutest detail, every contour and marking, natural or artificial, that occurs upon the surface of England... In order that this representation should be constructed, the representation itself will have to contain once more, as a part of itself, a representation of its own contour and contents; and this representation, in order to be exact, will have once more to contain an image of itself; and so on without limit." (Royce 1959: 504-505)

In other words, a perfect map of England on the surface of England would contain an actual infinity in the sense that it would contain a picture of itself (the map of the map), and a picture of that picture (the map of the map of the map), and so on ad infinitum. For Royce, this bizarre self-mapping map illustrates a crucial property of fully realized self-consciousness, namely, it's exhibiting a kind of infinity called "Dedekind infinity" by mathematicians, where a whole is mirrored by infinitely many of its proper parts. For just like the self-mapping map, a completed self-consciousness exhibits, according to Royce, an endless recursivity in that it is not just self-aware but also aware that it is self-aware, and aware that it is aware of its self-awareness, and so on. For Royce, then, this infinity inherent in self-consciousness has a decidedly mathematical favor, being closely related to the work of the mathematician Dedekind (especially the latter's Gedankenwelt proof for the existence of actual infinity). Indeed, Royce – in line with his commitment to absolute idealism – takes this recursivity of self-consciousness to be the very origin of the recursion that defines the natural number system, i.e. the recursion captured in the successor function S(n)=n+1 such that S(0)=1, S(1)=2, S(2)=3, and so on. Thus, on Royce's account, the natural numbers come out as essentially a formal expression or model of the structure of self-consciousness:  

"The intellect has been studying itself, and as the abstract and merely formal expression of the orderly aspect of its own ideally complete Self [...], the intellect finds precisely the Number System, – not, indeed, primarily the cardinal numbers, but the ordinal numbers. Their formal order of first, second, and, in general, of next, is an image of the life of sustained, or, in the last analysis, of complete Reflection." "[T]he number-series is a purely abstract image, a bare, dried skeleton, as it were, of the relational system that must characterize an ideally completed self." (Royce 1959: 538, 526)

In my view, Royce's theory of the arithmetical structure of self-consciousness is highly original and of crucial importance for the further development of absolute idealism. It allows the latter to hook up with contemporary science, and thereby to reclaim its position among the metaphysical theories that are still worth taking seriously. As Eric Steinhart writes: "Formal Roycean metaphysics offers spectacular opportunities for deep mathematical, metaphysical, and scientific research. It is a paradise waiting to be explored." (Steinhart 2012: 376) In particular, Royce's insight into the constitutive link between self-awareness and number allows us to develop an idealist solution to the platform problem in digital physics. This can be seen by means of the following argument: Insofar as the absolute Self is aware of the recursivity of its own self-consciousness, it is – on Royce's insight – also aware of the set of natural numbers, N, generated by that recursivity. And thereby it is also aware of all the possible relations between those numbers, which in turn is to say that it is aware of all the computable functions (which, after all, are all the mappings from N to N). In that sense the absolute Self can be said to engage in computation (cf. Steinhart 2012: 368). But what exactly does it compute? Well, since the absolute Self is essentially nothing but self-constituting self-consciousness, what it computes must precisely be itself, i.e. it computes those computations that facilitate the maximization of its self-consciousness. We can then, by an inference to the best explanation, explain our own universe as that complex computation that produces the highest possible level of self-awareness, such that our universe is 'nothing but' the computational (self-)reflection of the absolute Self. On this idealist solution, then, the ultimate computing platform – the cosmic computer – is identified with absolute self-consciousness as such. 

Above I noted that this solution to the platform problem involves an extension of Royce's insight. This is because, although Royce was highly interested in mathematics and formal logic, his writings predate the development of Turing Machines and the modern theory of computation by several decades. But it seems pretty obvious to me that if Royce had been familiar with the Church-Turing Thesis and the computational approach to physics, he would no doubt have made the connection with his own insight into the arithmetical structure of self-consciousness, much in the way I have done here. No doubt, however, this Roycean solution to the platform problem in digital physics remains highly speculative and must be supported by further arguments and clarifications if it is to be taken seriously. In the coming months I hope to develop and argue for this theory more fully. Stay tuned... 

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