A response to (the philosophizing of) Stephen Wolfram

Physics might catch up to the 'nature of time', but that will take more... time.

First of all, it might be interesting to readers that I point out that this post is as much a way to work towards my very own theories related to ecology (and its interactions with metaphysics and metaphysical perception) as it is a concrete response to Stephen Wolfram, and his writing on the nature of time, or a way to address metaphysics at large. To be clear, it remains all of these things.

From whence it came

Stephen Wolfram is a groundbreaking computer scientist who not only is an inventor of widely used software systems and interactive tools, he is also a congenial thinker and problem solver in the area where large language models and formal languages intersect (and will need to intersect). And so far so good, or, so amazing. But Wolfram is no exception to the rule that a person’s deep epistemic knowledge tends to influence, or so it would seem, their metaphysical commitments. I have, myself, a background in, among other things, physics, computation and simulation and have, using such practices, worked way back when on things ranging from our brain’s auditory pathways to plastic extrusion. I do not claim to be at Wolfram’s level in terms of computation or physics, I know enough to know my limitations. What has interested me however are deeper limits to computation than the epistemically verifiable. In other words, having become more of a philosopher than an engineer (understanding both worlds), I now think the time is ripe to work on some incongruences in both fields and in the places where they (can or can’t) overlap.

Before becoming a science entrepreneur writ large, Wolfram was an avid physicist, and now he is in the habit of drawing very fundamental conclusions from his computational approach to physics. If it were the case that these conclusions began and ended inside the realm of empirical physics, that would be one thing. But his impressive work on computational irreducibility and the so-called ruliad has, as hinted at in the preface, led him to speculate, with some confidence, on the nature of time. I am well aware that I have made an implicit claim here, so let me make it explicit: the nature of time is not necessarily a question of physics, and to the extent that a piece of the puzzle of time relates to physics, this must be convincingly shown in each instance where that case is made. This explicit claim is something I will keep at implicitly defending in this piece.

Let’s take a look at computational irreducibility and the ruliad before we focus on Wolfram’s claims about the nature of time and the Universe.

Computational irreducibility (CI) as a concept ties into the oft cited notions of e.g. turbulence, chaos, dynamic systems and so on. Whereas someone who looked at a mathematical or physical system from an un-computerized vantage point might say that a dynamic system is unpredictable, Wolfram who for good as well as historical (living in this day and age) reasons is a number cruncher prefers to use his term CI. So what is it to predict something? If a system is, in one way or other, sufficiently¹ simple, it is possible to infer a later state of the system analytically, or theoretically if you will. In such a case we do not need to track the system in order to understand what it will do next. There will be patterns clear enough for us to have precise foresight. In the general case, this tracking as well as the subject of the tracking could be continuous occurrences or sets of discrete ones. In the special case² of discrete or discretized systems, such tracking is what Wolfram calls computation³. If a system is CI, it is “unpredictable” unless the observer running and/or utilizing the computation is one (1) computational step away from the state of the system we are interested in knowing about. Such a system is made up of (i) a finite description (of some sort) of a given state, and (ii) a set of clear rules whereby one state shifts into the next. The way complexity unfolds, unless a system is very simple, it is not possible to forego the running of the steps (the interaction between each current state and the computational rules) as Wolfram likes to show. Now, Wolfram has furthermore stipulated the ruliad. A very nifty mathematical object that he claims is, or generates, the set of all possible computational rules. That is, all rules that make sense to, or one could even say make up, discrete and finite systems that we may want to observe, create or understand. In the world of such representations of symbols, quantities and so on, Wolfram has arrived at a very strong toolkit, and these very impressive theories to boot. Understanding how to view our computational efforts (related to irreducibility) and the positive and affirmative limits of the world of computation (the ruliad or something like it) we may well make more efficient and precise these efforts.

Real time and real-time

So far, all is dandy. We have to agree with Wolfram in the discrete case (he has QED’d the hell out of it) and by the very nature of where science stands we have to say that analogously, the world at large is also unpredictable in a similar manner. But the problem arises when Wolfram is not satisfied with “a similar manner”. He in fact claims the world not only to be accessed computationally (by e.g. us who engage in the intersubjective practice of science) but that it is constituted by computation:

We get closer as soon as we start thinking in computational terms. Because then it’s natural for us to think of successive states of the world as being computed one from the last by the progressive application of some computational rule. And this suggests that we can identify the progress of time with the “progressive doing of computation by the universe”.

First of all there is a number of ways in which we can begin disproving this claim about identifying time’s progression with the universe doing computation, and they’re all clichés: the cart before the horse, mixing up map and territory, and so on. Because: Wolfram has forgotten that it is the pragmatic efforts of science that have made computation possible. Those efforts that, leaning on empirical piecemeal (albeit thanks to diligent scientists: systematic) data that came from the world of flux (the one we are trying to understand) affords⁴ discretization and computation, rendering a scientific revolution helping us (intersubjective thinkers) interact with and understand this world, or Universe if you will. It is the fact that we employ computation as well as observation that we can say more and more things about the world, it is not the case that it is because the world is conducting computation that we exist, along with everything else.

But, kudos, for Wolfram’s approach is rather cocky and entrepreneurial! For if I knew⁵ that I could truncate, parse and rearrange the Universe and not just some local and fleeting part thereof in this fragmentary way and in doing so, not just arrive at good ways to continue to live in my local and fleeting world (whether “I” am me or, let’s say, a civilizational set of intersubjective thinkers-and-actors) then I should be rather omniscient. For when I, as it were, tapped into computation as such, would I then be touching the very universe more profoundly than when I do anything else? Make love? Have some illusion shattered whilst reading a poem? Am engulfed by profound music? Seeing the holistic structure, rather than working through the steps, of some mathematical idea? I find it is absurd to think that such a computational regimen has any ontological resemblance to irreducible reality, be it anthropocentric such as in the examples above or not.

Secondly, as I hinted at above, I am not against venturing into a discussion about time with physics (even discrete systems) at our disposal, but when one does so one cannot simply assume the conclusion⁶. Here, the assumption is made in the most hand-wavy way possible, with an appeal to it being “natural for us to think of successive states of the world as being computed one from the last by the progressive application of some computational rule”. But who is “us”? A particular subset of computer scientists who have stood on the shoulders of computational giants in order to do (meta)physics? Clearly not us “intersubjective thinkers” that I have claimed to part of above. Because if we ask a complete layperson (who may or may not have interesting ways of sharing with us about their first-hand experience of time) or a vast number of philosophers, physicists, mathematicians and so on (with tools handed down through generations for theorizing on, and making tentative sense of, time) one is very unlikely to find this attitude at all, and even less so to find people who find it “natural”. What Wolfram very much wants to reach is in fact some conclusions about the computational nature of time but this is what he starts off with as an assumption with absolutely no back-up in terms of either reasoning (some appeal to philosophical notions), data or simulations (which he is arguably first-rate at). The kinds of simulations Wolfram leans on to make his case simply show a universe that is ruled by his ruliad, they do not show the universe at large:

So, here is a grand theory of patterns running at an impressive speed inside a well-contained Olympic stadium where huge feats are performed. But this says very little about the motions of the world outside the stadium. Wolfram isn't doing the proper work of scrutinizing or making clear (his) first principles. Granted: there is absolutely no intrinsic need to “do philosophy” when one addresses time (although for my money, it’s wise to do so). But to the extent that Wolfram labels the writing in question “philosophy” next to labeling it physics, he is thus errant.

The above is actually sufficient to send Wolfram back to the drawing board, especially as he hammers down his point one more time (“That time is a reflection of the progress of computation in the universe is an important starting point. But it’s not the end of the story”). But let’s hear more of the story. Because I will have to admit, I don’t see where this is going ;-).

If the underlying system is computationally irreducible, then to work out its future behavior requires an irreducible amount of computational work. But it’s a core feature of observers like us that we are computationally bounded. So we can’t do all that irreducible computational work to “know the whole future”—and instead we’re effectively stuck just doing computation alongside the system itself, never able to substantially “jump ahead”, and only able to see the future “progressively unfold”.

Wolfram is right that aspects that we may define, denote (and so on) and that take place in some (contextually) sufficiently deep future (be it one second or 10,000 years) are not aspects that we can predict mentally with any accuracy. And he may also be right that the reason for this is that we “are” in principle computationally bounded. At least our cognitive apparatuses that deal in these defined terms that are able to handle as symbols and/or well-defined mental concepts seem to be, when attacking the aforementioned type of predictive problem. We are epistemologically limited, stupid. But that is not the same thing as “us”, or any other hypothetical observer having, “core features” the likes of computational boundedness visavi a world that is computationally irreducible (the latter, here, was critiqued in my above section).

Let’s look at this in two ways: (i) there is no obvious reason to assume that the process by which we make demarcations in the world is constituent of our (ontological) core or the core of the world (ontologically speaking). Or, importantly, to any relation in-between the two⁷, and if one wants to argue that there is then one takes on a heavy burden of proof. This is true whether one thinks one is going to succeed with some kind of Popperian way of showing this or some wholly other way. And (ii), all of the things that happen to us, or that we do, or some mixture thereof, and that we call successful “knowing:s of the future” are hardly down to processes that are computational and/or conscious and/or mappable. Whereas we can statistically prove that somebody is good at grokking the subtle cues involved in the playing of poker, it is fiendishly difficult to somehow map/mathematize what this skill entails. Physiologically, psychologically, what have you. And not only that: for the computational explanation to hold we would have to prove in real-time that it was computation that took place in the world of the poker table. It doesn’t end there, we would have to prove that, experientially and functionally, this is what took place from the vantage point of the successful body-language reader. Or else how would we say that computation was the core of such a successful observer (and actor)? It’s in fact an absurd notion, which by proxy proves that there is a fruitful distinction to be made between computation and intuition, and that this difference is not just woo-woo.

The same goes of course for many things that happen to humans that don’t involve a lot of formality or theory or mathematics, such as bodily functions/expertise, communicative prowess, and so on. And then we have only ruled out, and granted, the special case of humans doing formality, theory, math. What about the world “in-itself” (whatever we think about such a notion philosophically)? Why would quantum systems (or any conceivable agent, dead matter, system, world, partial world…) be doing computation the way computers and our minds sometimes do in order for us to parse the formal, the theoretical and the mathematical?

Imaginary guitar notes and imaginary vocals exist only in the imagination of the imaginer!

Let’s move on! Wolfram says that: “we experience time because of the interplay between our computational boundedness as observers, and the computational irreducibility of underlying processes in the universe”. Now, there seems to be an illuminating contrast here between what Wolfram has been talking about above (the world) and now “we experience” when he addresses time. But the same kind of argument starts cutting both ways, because whereas we cannot say that quantum states unfold via computation just because we like to understand them using computation, we cannot say that we experience time because of our tendency not to be able to predict what is going on. Although intuitively it makes sense that somehow there is a kind of expediency in only experiencing that which we (our consciousness) must, so to speak, put under study because we are not, in real-time, in possession of the means to predict this or that (sub)aspect of our experience, it has not been sufficiently proven that time as such occurs as an experience due to such gaps in understanding/computation. In fact, although the experience of time is far from the only fundamental first-person experience/intuition we have, if it were this easy then it is likely that the discussion around qualia and the “hard problem” would have looked way different the last decades. Now, I surely think that psychologists and cognitive scientists could use a healthy dose of Wolfram, but in order for these points to come across (also to people like me) they need to be fleshed out way more and with more philosophical sophistication.

The quote above goes on: “If we were not computationally bounded, we could “perceive the whole of the future in one gulp” and we wouldn’t need a notion of time at all”. And as said, although he may have a point (it is not theoretically unsound like the postulations about the world at large) it still assumes too much about our ability to categorize correctly. Because even if we knew what was going to happen in a sensory sense, we would not necessarily know the reasons why it did (and this distinction should be clear, and important, to a physicist!). So whether one argues from some pure notions of information theory or from (e.g. biological) evolution there may well be a reason to experience time, and that which we know will happen (in a sensory sense) in order for us to gather deeper data (and store it as salience, memory, capacity for reflection) on that which happens. This can, in turn, aid our (evolutionary need for) explanatory models and thus our experience would not just be optimized for the brute-force understanding of the here and now.

Wolfram subsequently brings in the ruliad, and there isn’t much to add here other than to reiterate the fact that since he has not proven that time progresses as (or is experienced thanks to the limitations in) computation, then there is no reason why an object that summarized possible rules could have anything to say about time.

So What in the End is Time?

Asks Wolfram. And he comes back to his favorite CI-concept, but now it is more clear that he contradicts himself: “To begin with, the fact that time can robustly be thought of as “progressing”, in effect in a linear chain, is a consequence of computational irreducibility—because computational irreducibility is what tells us that computationally bounded observers like us can’t in general ever “jump ahead”; we just have to follow a linear chain of steps”. In other words, in wanting to show that the (apparent) progressing nature of time (it may well be thus) is due to CI, he invokes the fact that CI tells us that we cannot jump ahead. But what is cause and what is effect here⁸? If you will, the reasoning is circular. And in a theory that, on top of this, itself invokes a causal metaphysics (linear, progressive), mixing-up the cause and the effect in the scientific detective work as such is of course very ironic.

To conclude, the world is not computational and time is not a side-effect of computational limits. These are category errors, or in the words of Pauli: not even wrong. Physics might catch up to the nature of time, but, if so, that will take more time.

That’s it for now. I hope that I, like Stephen, have been wrong in interesting ways.

1. Here it is important to see that the systems we are talking about are all the kinds of systems that are “Popperian”, that is: the only claims about the system that make sense are falsifiable. If the system is defined in a lofty way, then claims about future states of the system can be arbitrarily vague, unfalsifiable and/or afford an arbitrary amount of backpedaling once we are to compare prediction and reality. Of course, physics does not deal in such lofty systems, nor should it.

2. It is not the main focal point here, but part of what Wolfram sets out to do is to claim that the universe is fundamentally discrete in nature. This is not something he or anyone else has succeeded in proving, hence the set of instances where systems appear to us as discrete must be called a “special case”.

3. Imagine that you are standing on a beach and you see a pelican living its life in the surroundings. It might fly, in might waddle, it might swim, it might hunt, socialize, display mating behavior and so on. When you observe this bird, and you may be mesmerized, you are apt to have a holistic experience of movement, flow and of your sense of belonging to nature, and you may also have some notions in yourself that you are trying to understand what the pelican will do next. And depending on your experience with pelicans, you may be more or less good at this. This scenario is one of tracking and one of prediction. If we imagine that a science drone did all of this pelican-watching, for some reason, it would need to compute in order to predict and, importantly, in order to track. Computation would be its tracking.

4. This in itself reiterates the old dialectics of empiricism and rationalism. So I should be clear and say that I do not need to prove that rational categories necessitate having first access to data. That may or may not be the case. What I am saying is that, pragmatically, having access only to rational categories affords us nothing with respect to the world.

5. Note that this reductio ad absurdum I am employing is not Laplace’s demon. For I am not saying that the Wolframian metaphysician knows and computes everything, he “merely” knows with certainty (as indeed Wolfram seems to do) that the unfolding of the world is reducible to computation. Which in and of itself is quite a striking level of knowledge.

6. I think that a statement like the following, found later in the piece under scrutiny: “At the lowest level the state of the universe is represented by a hypergraph which captures what can be thought of as the “spatial relations” between discrete “atoms of space”. Time then corresponds to the progressive rewriting of this hypergraph.” needs two comments. First, there are plenty of them from Wolfram and we see others in my text here outside of footnoting. Second, we can refute them at once from the mere fact that it is assumed (rather absurdly) that the universe IS represented by a hypergraph. Even saying CAN BE rather than IS would be something in need of a lot of backing up.

7. Which is in fact what we, Wolfram included, are trying to discuss and not something, again, that we should assume prematurely.

8. Is either “ontic”, is either “ontological”? “Epistemological”? Wolfram isn’t stating on what levels of the world CI takes place, and he isn’t stating what the metaphysical status of the progression is either. We are left in the dark.