The Physicalist's Trilemma
On why simulationism is false and what consciousness tells us about the nature of physics.
What good’s a computerised nose?
~ Lou Reed, What’s Good (The Thesis)
For reasons best known to themselves – boredom, I suppose – the New Yorker recently1 decided to promote a 2016 article on the “simulationist” hypothesis. The idea is this: our descendants, endowed with vast computational resources, are likely to create simulated worlds, including simulations of us, their ancestors; these simulations vastly outnumbering the one, “real” world, we ought to conclude it’s likely that we’re in a simulation. LessWrong diasporan that I am, my tribal impulse is to defend Bostrom et al, who in failing to be the vulgar Epicureans that their opponents wish they were open themselves up to a certain amount of ridicule (“Nerds have convinced themselves they live in a video game,” was one insightful comment I came across). However, intelligent and thoughtful though Nick Bostrom is I think we have good reasons to think his hypothesis mistaken; and further to think that the computationalist orthodoxy is doomed just as the crude materialism of the 19th century was. I do not believe it plausible that, simulation or not, we live inside a computation – physics, I contend, is not computable, and those who believe it is are forced by their position to accept unattractive conclusions. The key to this is that Bermuda triangle into which all elegant theories of Being are almost inevitably lost: consciousness.
1.
The now-conventional belief that consciousness is a physical event seems well justified – not only can we inflict dramatic effects on consciousness by exposing the brain to certain chemicals (most saliently, psychedelics, but also alcohol and all manner of mind-altering potations), we also seem to be able to turn consciousness off entirely with general anaesthetics. A person under general anaesthesia is not asleep – in sleep, we have some level of awareness, whether that awareness is directed towards our dreams or at a low level towards our surroundings, or, as in a fever dream, towards some uncanny blend of the two – rather, under general anaesthetic consciousness ceases, and then, as the anaesthetic wears off, resumes; hence, the person under general anaesthetic experiences it as nothing; missing time. Between “count backwards from ten” and waking up in recovery there is a blink of darkness, and not much more than a blink. Other than that, there is not even darkness because darkness, while having no more content other than the eigengrau we see in the backs of our eyelids, is at least extended in time, whereas the experience of general anaesthetic has had all the time squeezed out.
As well as these up-stream effects on consciousness, we also observe downstream effects of consciousness – namely through the acts of conscious agents. Let’s abjure the Chalmerian quicksand of “p-zombies”, and observe only that the chief cause of consciousness discourse is the existence of its subject; if consciousness did not exist, we would not expect there to be so much philosophy addressing it. Empirically, consciousness both affects and is affected by the physical world. The most parsimonious explanation for this: consciousness is physical.
These facts are not impossible for dualisms to incorporate, but they do require some excuse-making (if the “interior” of consciousness exists separately to the physical stuff of the brain, why when certain processes of the brain are deactivated does consciousness also vanish?) In any case, I don’t purpose here to add to the travails of dualists, whose philosophy gives them enough pains without my help, and who, besides, tend already to reject computationalism as part and parcel of their rejection of physicalism. What I want to discuss here is a problem presented by consciousness to us physicalists.
2.
Take the science-fiction trope of the “uploaded mind” – a kind of simulationism in miniature. Brains are made of neurons; neurons of molecules; molecules of atoms; atoms of electron, protons, neutrons; these last (for the sake of argument) behave according to simple mathematical laws. Programs those laws into a computer and you can simulate the interactions of electron, protons and neutrons, therefore you can simulate the behaviour of atoms, therefore of molecules and so on, until one has a veridical simulation of a human brain. This simulation could be connected to a kind of nervous system and used to run a physical body, and if our simulation is accurate should reproduce the behaviour of a real person. Since consciousness plays a causal role in our behaviour, this could only be the case if the simulation is conscious; the human mind has been “uploaded” into the machine. To simplify the argument:
P1) Consciousness is physical (if you don’t believe this, you’re not a physicalist).
P2) Physics is computable.
C) Therefore consciousness is computable.
Bob is drinking tea, let’s say. In a few moments he has a number of sense impressions: the smell of the tea, the smoothness of the porcelain handle against forefinger and thumb, the resisting weight of the mug as he lifts it, the almost imperceptible clink of mug coming away from saucer, porcelain to lips, a headier smell, first hot vapour passing the lips, and then –
The conscious perception of these experiences comprise, if physicalism is true, a succession of physical events in Bob’s brain. If our physicalism is thorough-going – allowing consciousness its effective power, as well as its power to be affected – then any simulation of these physical events must also instantiate Bob’s consciousness. Which is to say: if we run a physical simulation of Bob’s brain in these moments on a computer, there must be a real Bob “inside” the computer experiencing it.
And this, indeed, is probably the conventional view among physicalists – hence such rarefied hypotheses as Bostrom’s simulationism. But this conclusion – that consciousness is computable – leads to problems, and they have to do with what computation actual is. It’s easy enough to imagine electrical signals buzzing back and forth on a circuit board and to think that this analogises to the explosive intracranial signalling between neurons which seems to be the cause of, or identical with, consciousness, and that therefore our electrically excited circuit board might achieve the same ends by slightly different means. But computation is not about circuit boards; a computation is a mathematical abstraction which we instantiate using circuit boards by forcing some physical property of the circuit board (say, the state of a transistor) to behave reliably like some part of the abstraction we’re interested in (say, a one or a zero – or Symbol A or Symbol B, as we might better call them). This is not the only way, however, that we can instantiate a computation. There are many models of computation but the most well-known is Turing’s state machine; we can say that for every computation there is at least one Turing machine that realises it.
3.
So what is a Turing machine? Imagine a single, one-dimensional tape divided up into squares. Each square contains a symbol taken from a finite alphabet — in the canonical case, an alphabet containing only two symbols, “0” and “1”, but any number of symbols is permitted. The machine has a pointer indicating its location on the tape, and keeps track of its own “state” — it could be in, say, State 1, State 2, or State 3 — but again any finite number of states is permitted. At each step it reads the symbol at its current location, and then according to its state follows a finite list of instructions — it might move left along the tape, move right, change state, change the symbol at its current location, or a combination of these. And that’s it — that’s all computation is. Obviously a Turing machine can be automated, as long as the tape is machine-readable, but equally the computation can be performed by hand.
Now imagine we take the computation from our “uploaded mind” scenario — Bob’s moment of tea-induced reverie — and instead of running it on silicon and electricity, we pay a guy minimum wage to follow instructions from a book, writing and erasing symbols in pencil on a long paper tape, shuffling it back and forth in his hands, consulting the book, making little notes of the machine’s current state, back to the tape… To believe that consciousness is computable is to believe that this system instantiates the consciousness of Bob — that Bob’s mind has been “uploaded” into the tape. Suddenly it seems rather less plausible. Now, before you bravely straighten your rationalist spine and bite the bullet, let’s line up a few more and see what your appetite’s like.
4.
Here’s a section of our man’s tape — a brief snippet of the computation which, if we take the “uploading” hypothesis seriously, comprises Bob’s conscious experience:
Here we see that this Turing machine uses an alphabet of two symbols, a “1” and a “0”. But of course nothing at all depends on the form those symbols take. We could just as well choose to use smiley and frowny faces instead, and the result will be isomorphic. Like this:
A bit messy but mostly readable — except symbol 4. We know it should be a “0” or a frowny face, but the form itself is ambiguous. If we interpret it as a frowny face, then this tape is part of the computation which instantiates Bob’s consciousness; but if we interpret it as a smiley face, this is no longer Bob. And in fact, each of the faces on the tape can be interpreted however we like — even though they look quite unambiguous to us, the smiles are not identical to one another, and nor are the frowns. There is nothing about the physical representation of the symbols on the tape that constrains our interpretation of them, and this part of the tape could therefore be the equivalent of 101001, 101101 or 111111. This is also true after our minimum-wage Turing machine operator makes a change to the tape; and therefore the operations performed are themselves open to interpretation. In short, which computation is happening is not an objective physical fact; computation is read into physical events.
(One might wonder, if this is the case, why computers work at all. But our computers are not only abstract Turing machines; we build into our computers machines to interpret the computations performed — screens which light up, speakers which emit sounds, printers, punch-cards etc. There may be no objective fact of the matter as to which computation has been performed, but we extract the results we want through mechanical necessity; the machine behaves like the computation we’re interested in to the purposes we’re interested in.)
Here’s the problem: whether or not some set of physical events corresponds to some computation is a question that can only be answered relative to some rules of interpretation, but the correspondence between physical events and conscious experience must be absolute; either there is a Bob drinking tea or there isn’t! Ironically, it turns out there is nothing more objectively real than subjective experience. We can dispense with our formal Turing machine, because we can interpret any physical circumstance as part of our computation. We can say: this puddle represents a 1 at such-and-such a place on our tape; this leaf represents a 0 — just as we can and do say a transistor in some particular state represents a 1 and black marks that look like “0” represent a 0. We can therefore impose some rules-of-interpretation on, say, an ant colony, and Bob’s conscious experience can be read into the activities of that colony. Does that mean that “inside” the colony there is a real Bob having real experiences?
As the title suggests, I think we have three ways of dealing with this problem. I will present them in order of diminishing badness, as is traditional.
The First Horn: Deny, Deny, Deny
I’ve led you down a little garden path and maybe you don’t like where we’ve ended up. The natural course of action is to attempt to go back. My argument hinges on an assertion: that there is no objective correspondence between physical states and and instantiated computational states; that whether or not a computation has taken place is subject to interpretation. Can this assertion be denied?
To do so would require one to propose an objective mapping between physical states and computations therein instanced; to be able to say (in principle) if-and-only-if such-and-such physical events occur does such-and-such a computation take place. I’ve already given my reasons above why I think this can’t be the case, but at risk of being repetitive let me try to provide more clarity. Let’s have a look at another version of Bob’s tape:
The computation only uses two symbols, which can be called “0” and “1”. But the physical machine representing the computation uses (at least) six different symbols, shown here. We know how to group the 1s together — to treat 1s written in different fonts as if they were identical — but how does reality know? Why couldn’t the rule instead be that an symbol written in Times New Roman is a “1” and any symbol written in any other font is a “0”? If this was the case, the above segment of tape would read “000000”. And consider that no matter how similar we make all our 1s, there will always be some physical differences between them — if nothing else there’s the fact that they appear at different physical locations. If two symbols on our tape shared all physical attributes they wouldn’t be two symbols at all — they’d be the same thing.
And consider further: the order in which the symbols are presented isn’t objective either. We have a tape with a far-left end and a far-right end, but we could have a mapping where, say, the 64th symbol on the physical tape represents the 1st symbol on the Turing machine’s tape. So we see that computation entirely open to interpretation.
The Second Horn: Go Mad With Reason
The second strategy, ever popular amongst rationalists, is to square up one’s jaw and commence to biting bullets. We could maintain that consciousness is computable and that computations can be interpreted into diverse physical events, if only we’re willing to admit that all conscious states are instantiated. Bob’s consciousness can be said to be uploaded in an ant colony? Very well — Bob exists in that ant colony. We accept the absurdity.
Indeed, this does seem to be a live position: Max Tegmarck’s proposed “Level 5 multiverse”, or mathematical universe hypothesis (muh MUH), asserts that mathematical structures, including computations, have independent reality — all mathematically real structures are physically real — and that those which contain consciousnesses naturally instantiate those consciousnesses. Which is to say, it’s a form of platonism which refuses (I think quite sensibly, if you’re going to be a platonist) to distinguish between potentiality and actuality. For those of us who reject mathematical platonism2, this position is untenable, but it must be admitted that platonism remains highly popular, especially among professional mathematicians. The bullet-biting option remains, therefore, an option, if you want it.
There is another problem with it, however — although this argument is kind of backwards. Our empiricism functions by making observations under conditions where we could have made a different observation if reality was different. To test the theory of general relativity, we looked to see whether there was any gravitational lensing of light passing close to the sun; had there been no such lensing, it would have been strong evidence again general relativity. But what Tegmarckian theory must suggest is that both observations will be made; both conscious states being computable, and all computations having independent reality, there will be two versions of the observer: one which sees the lensing and one which doesn’t (as well as those versions of the observer which see: red spots, their own face, five small bowls of ragu, the standard of St. Iago de Compostela, or the text of The Very Hungry Caterpillar3). That both observations will be made is guaranteed beforehand; it follows therefore that we could learn nothing from observations. Now, if the MUH is true, then, yes, that’s simply the case; it’s no good saying, “We really want to be empiricists” — it simply wouldn’t work. But I’m betting Max Tegmarck et al don’t want to admit that. It wouldn’t only be to “bite the bullet”; it would be to close out the all-you-can-eat bullet buffet.
The Third Horn: Back to Reality
Let us say we accept the inherent subjectivity of the mapping between physics and computation. Let us say also that we reject the reality of all conscious states which is implied by the radical mathematical platonism of Tegmarck (in order to preserve the possibility of empiricism). What options does it leave us? We must reject the premise with which we began: that a conscious mind can be simulated by a computer. But remember the argument from earlier:
P1) Consciousness is physical.
P2) Physics is computable.
C) Therefore consciousness is computable.
Since we’re rejecting C), we must also reject either P1), P2), or both. As physicalists we cannot reject P1) — we’re therefore obliged to come to the conclusion that physics is not computable.4
This initially seems like a problem. The whole thrust of modern physics has been an attempt to describe the entire physical world using linear equations — precisely the kind of thing computers are good at. The goal has been to establish some mutually compatible mathematical formulae which can account for all physical occurrences since — well, since there have been things to account for. But consider that, as yet, this project remains frustrated. The physical world seems be to subject to two domains of governance: the relativistic and the quantum mechanic, for which domains we can give no single account. There is therefore no set of physical circumstances, no matter how limited, which we can simulate exactly. Many expect that, in the long run, general relativity and quantum mechanics will be reconciled, and that the resultant grand-unified theory will be computable (in principle) — but there is no guarantee.
Imagining a non-Turing-computable physical law is trivial. Take this toy example: imagine we had a universe with one Euclidean spacial dimension, discrete units of time, and a single particle with a single property: its coordinate relative to it’s starting position — call this D. Say that at time T the particle is at location D=Σ(T), where Σ is the Busy Beaver function. The behaviour of this particle would be, in principle, predictable (if you could solve the Busy Beaver game fast enough), and perfectly deterministic, yet there could never be any computer, no matter how powerful, that could simulate its behaviour for an arbitrary length of time; the existence of such a computer would violate Turing’s halting theorem.
Obviously this is nothing like our universe, and as far as I know there are no physical analogues to the Busy Beaver function, but it serves to show there’s nothing in principle demanding that a lawful universe be computer-simulable. Note also that others have reached the same conclusion for different reasons. Roger Penrose (for the feverish credentialists among you: Nobel Prize winner Roger Penrose) has long suspected that physics can’t be computed because human reason seems to overspill the limits of formal systems given by Gödel’s incompleteness theorem: we come to mathematics with understanding, not mere calculation. This blog post — written in response to the same New Yorker piece that began this discussion — makes the slightly weaker claim that known physical processes can’t be simulated on physical computers.
Anyway: here’s where I put down my marker: in the long run, I expect physics to defy computation — and dismiss, therefore, the likelihood that we’re living in a simulation. That’s not what reality is. But having said this, what are the implications for the “uploaded mind”? Under this scenario, we don’t end up with an uploaded mind which, other than being conscious, behaves exactly as the mind being simulated would. Rather, the simulation is simply defective: it will produce the wrong results. Indeed, if we knew enough about physics, we would realise this beforehand; the project would be abandoned as impossible.
A Fourth Horn?
Well — hang on. Doesn’t this argument prove too much by too little? Essentially the argument is this: computation is subjective, consciousness is objective, and therefore the latter is not a species of the former. Could we not say, after all, that, yes, computation is subjective, that physics and consciousness are computable, but that consciousness is not instantiated by virtue of the computation being performed — that other conditions need to obtain to make this happen. Could we not imagine that the behaviour of all particles is simulable, but that the presence of the real particles (or, for all we care, fairy dust) is needed in order for conscious experience to happen?
There are two problems with this position. The first: say that we simulate the philosopher David Chalmers. If all the physical processes which make up David Chalmers are computable we should be able to reproduce all of his behaviours — including his writing of philosophical papers on the nature of consciousness. But the real particle, or fairy dust, or whatever, is absent from the simulation; the simulation oughtn’t to be conscious (if it is, we’re once again skewered on the 2nd horn) — so why is it writing papers about consciousness? To put it another way, this proposal is only half-physicalism. Consciousness is left as an epiphenomenon: it is associated with physical events but makes no difference in the physical world. An uncomfortable position.
The second objection is deadlier: this position contradicts itself. It maintains that all physical processes are computable, that consciousness is caused by physics — and yet that the cause of consciousness lies somewhere outside that computation. These three propositions cannot be reconciled. I therefore reject the proposal of a tetralemma; this fourth horn will not do.
Coda on physicalist ontology
“Physicalist” and “materialist” are used interchangeably, but in truth they’re very different positions. Materialism was a hypothesis of the 18th and 19th centuries, and has long been dead to us — it was killed by physics itself. It proposed a limited ontology: space, time and matter (which is to say corporeal substance extended in space). Faced with phenomena that seems apparently immaterial, like light, it proposed several theories to cope. First, that light was made up of minute corpuscles. Secondly, when it was shown that light behaved like a wave, that it was a wave in some otherwise undetectable substance: the luminiferous aether. After the Michelson–Morley experiment this could not be maintained, and materialism died. Nobody any longer believes that matter is fundamental — we explain it as an effect of quantum mechanics. Nobody even believes that the volume occupied by a particle or object can be well-defined. So what is physicalist ontology now?
In truth, nobody know. In an effort to reconcile his theism and his materialism, Thomas Hobbes proposed that God, too, was made of a corporeal substance. A modern physicalist would not even know the difference between a corporeal and an incorporeal substance. Our commitment is to say: whatever is is physical. What does it mean for something to be physical? It is something that obeys the laws of physics. But what are the laws of physics? We work to discover them by observing reality… We’re therefore committed to saying that whatever exists is whatever behaves like reality. Not a statement I would expect non-physicalists to disagree with. Physicalism, then, is not a metaphysical commitment at all, but an epistemological one: it is a commitment to empiricism and science, and the belief that reality can be discovered by these means, but says nothing presumptuous about what reality actual is — or at least, it ought not. But it is typical of human folly that a project which begins by describing phenomena using mathematics should end up concluding that mathematics is what lies behind the phenomenon; hence computationalism and simulationalism, the beliefs that we live, as it were, inside an equation. But reject these easy — and, being easy, inadequate — answers and we are left with the Hard Problems of Being and Consciousness both, and the suspicion that these are somehow related. These questions are capital-H Hard not because of the difficulty of choosing between hypotheses, but because in our hypothesis space there seems to exist not a single one which achieves satisfaction. Not only don’t we know what kind-of-thing does exist, we struggle to think of a single one which could exist. Science is not, as Auden put it, “happy to answer/ That the ghosts who haunt our lives/ Are handy with mirrors and wire”, rather all our science leaves us standing once again on the precipice, staring down into that vertigo-inducing mystery of Being, asking ourselves (because we can’t quite think of the right question) “Why is there anything at all?”5 Reality remains for the physicalist — perhaps especially for the physicalist — a cause for utter bafflement.
Our wonder, our terror remains.
~ W. H. Auden, The Sea and the Mirror
It was recent when I started writing this.
Obviously I’m not getting into it now. I’ll just say: we can have a real “mathematics of self-inconsistent things” — indeed, this is the other side of Gödel’s incompleteness theorem — but we could not have a self-inconsistent reality. Mathematics is the exploration of the necessary consequences of human-invented games; it has no independent reality.
And this is confining ourselves to the sense of sight; every other type and combination of experience must also have its reality — which proposition, if understood and believed, would be cause enough for a permanent state of terror.
Dualists of course reject P1) — but in doing so they’re obliged also to reject P2) anyway. Consciousness does have effects on the physical world, whether or not it is itself physical. Physics therefore would be a computation which did not contain all the information to predict physical outcomes — a computation with sudden, inexplicable discontinuities isn’t.
The answering of which question only Leibniz, I think, has made any progress on.