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... 

References
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