A few years ago I outlined the so-called “triviality argument” that consciousness cannot be reduced to the process of computing a particular kind of computer program. At the core of the argument is the recognition that there is no unique, objective way to define computational states in the physical world. Consequently, it is always possible to find some (perhaps complicated) mapping of arbitrary physical states onto the states of a computer program that generates conscious experiences. (The example I used in the earlier post was the fluctuating orientations of the magnetic moments in a hot iron bar.) If consciousness could be reduced to a purely computational phenomenon, we would be forced to conclude that all sorts of inanimate objects like hot iron bars are conscious purely by virtue of this arbitrary mapping.

The post generated some lively discussion on Hacker News and Reddit, and I had some good conversations with a number of people about it offline. A number of commenters raised various objections to the argument as I presented it, but most of the objections centered around the leap I made from a computer that manipulates rocks in a field to the randomly fluctuating states of atoms in an iron bar. The iron bar is not a real computer, according to their argument, because the mapping from its states to the state of a Turing machine is totally arbitrary. Moreover, because this mapping is purely random, producing this mapping essentially requires you to perform the computation yourself — so, to the extent that any computation is being performed, it’s really you who are computing, not the iron bar.

I think these objections are incorrect and I still believe that a careful understanding of what a computer really is will force us to accept that if consciousness can be reduced to a special kind of computation, then a hot iron bar is conscious (as is a pail of water, or a brick, or a wall, etc.). So in this post I want to make the leap from the “rocks in a field” computer to the iron bar a little more deliberately so we can see what is really going on in the argument.

To this end, let’s walk through a series of thought experiments. This will be a reducto ad absurdum, so throughout this I will assume that consciousness can be reduced to a particular kind of computation. In other words, I will assume that by running a particular computer program, I can generate a new, independent, conscious being. As in the last essay, I’ll call this program consciousness.exe. Let’s see where we end up.

Some assumptions

Before we proceed, I am going to lay out a couple of assumptions. The first is that the existence of a conscious being should not depend on some other conscious being recognizing it as being conscious. If I were somehow the lone survivor of a terrible catastrophe that destroyed the rest of humanity, I will assume that I would remain conscious, even though no one else would be around anymore to recognize it. If the computational theory of consciousness is correct we must extend the same courtesy to computers — we will have to accept that a computer that is executing the consciousness.exe program is conscious even if no other conscious beings recognize it as such.

My second assumption is that the Church-Turing thesis holds. That is, any computation can be performed with a suitable Turing machine. In particular, if consciousness can be reduced to a computation, then there exists some Turing machine which will generate a conscious being when it is executed.

My third assumption is that all of these thought experiments take place in a universe which is governed purely by the laws of classical physics — in other words, this is a universe in which quantum mechanics does not exist and whose physics is completely deterministic. The fact that this doesn’t describe the real universe isn’t relevant for our purposes since any computable function can be computed by a Turing machine which operates purely by the laws of classical mechanics. Even if the brain somehow took advantage of some quantum computational processes, these can be simulated with a classical Turing machine (even if it possibly runs less efficiently).

Thought Experiment № 1

Wherein I become a Turing machine in the desert

Let’s imagine we are out in a desert, much like the Mojave, but far larger. It is an endless flat plain littered with rocks. To pass the time, I draw a very long grid on the ground with two rows, one to the north and one to the south. In each column I place a rock in either the northern row or the southern row. If the rock is in the southern row I consider it a “0” and if it is in the northern row I consider it a “1.” These two rows will correspond to the ticker tape of a Turing machine.

Beneath these two rows, I draw a set of \(N\) boxes and I place a rock into one of these boxes. This set of boxes corresponds to the state of the Turing machine. If I have drawn \(N\) boxes on the ground, I have an \(N\)-state Turing machine.

Now I start to operate by a set of rules. I start by standing at one of the columns on the input row, look at which row the rock is in along with what state I am in, and then I update my state and possibly change the rock from the bottom row to the top row or vice versa. Then I move either left or right depending on the rule, and start the process all over again. Eventually I get to a special state that tells me that I am done.

For concreteness, we can imagine that the set of rules I play this game by has the effect of sorting a list. I am not a very good computer scientist, so I decide to use a bubble sort algorithm. I can arrange the rocks on the input rows to encode whatever list of integers I desire. Then I follow the steps of my program and when I finish in the halting state, the sequence of rocks on the grid describes the same list that I started with, but sorted.

If, instead, I operate by the special rules of the consciousness.exe program, I will produce a new, independent conscious being for the duration that it runs. Before I run this program, I set up the input tape so that the input to the computer’s senses will simulate the sensation of sitting in an armchair, enjoying a cup of tea. As I operate the system, I carefully observe exactly what manipulations I make to the rocks. I then repeat this process for many different inputs: the experience of taking a walk in a forest, eating an egg salad sandwich, watching the sunset at the beach, and so forth. As I manipulate the rocks, I memorize every configuration that they take. I have a very good memory.

The moral of the story: A Turing machine merely manipulates a sequence of bits by a particular set of rules. By predetermining the right set of state transitions and starting with the right set of inputs, I can use these rocks to compute any computable function. If we believe that consciousness is a consequence of executing a particular kind of computer program, this implies that I will be able to generate a conscious being by shuffling the rocks in this desert in the appropriate way.

Thought Experiment № 2

Wherein I tire of my game and automate it

I am a busy man and I don’t have time to stand around in the desert all day playing around with rocks. So I build an automaton to do it for me. In fact, I build two automata. One of these plays the first game of sorting lists, and the second runs the consciousness.exe program.

Both automata are complicated devices chock full of pulleys and gears, but they do exactly what I did all by myself. When I press the “START” button each one stands at a particular column on the grid of rocks and detects whether the rock is in the upper or lower row; it consults which state it is in by looking at which of the \(N\) state boxes has a rock in it; then, depending on the rule, it moves the rock in the input row from the top to the bottom or vice versa, updates the state rock, and moves left or right. It continues to do this until it puts the state rock into the “HALT” box at which point it shuts down (assuming it ever arrives at this point). This is a very complicated machine to build, but after I am done I am confident that it will always carry out the rules of the Turing machine I have programmed.

To test it out, I use the first automaton to sort some lists. Then I use the second automaton to simulate the experience of sitting in an armchair drinking a cup of a tea. In both cases, the automata manipulate the rocks in precisely the same way as I did when I was playing these games myself.

The moral of the story: A Turing machine doesn’t require a conscious observer to manually make the state changes. Its behavior can be completely automated. This, indeed, is the whole point of building a computer.

Thought experiment № 3

Wherein I discover my machine’s clone

Having automated my work, I relax by taking a long hike in the desert. One day during my travels I come across a very long line of rocks in two rows and a pair of machines that look identical to the ones I have built. I open them up and everything on the inside is just the same as the one that I built, with exactly the same set of pulleys and gears. I do not know who built this device or why.

I test the left one out by arranging some rocks on the grid to represent an unsorted sequence of numbers. I press “START” and the machine begins to sort the list of numbers, making exactly the same manipulations that my machine did.

Then, I test the right one out by arranging some rocks on the grid to represent the sensory input of sitting in an armchair enjoying a cup of tea. I press “START” and once again the machine manipulates the rocks in precisely the same way that my own machine did.

The moral of the story: It does not matter who built the computer or what their intention was in building it. It is only necessary that the device correctly follows the rules of the Turing machine.

Thought Experiment № 4

Wherein I discover a mysterious Turing machine

I continue my hike. A few days later, I discover a scene that is almost identical to the one I saw last — two rows of rocks and a pair of devices that appears very nearly identical to mine. The one difference is that this time the machines have been welded shut, so I can’t open them up and see what’s going on inside. But I wonder if maybe these are Turing machine just like the ones I built earlier.

So I arrange the rocks on the input rows to give the machine on the left a list of integers in some arbitrary order, press the “START” button and watch it trundle along and shuffle the rocks. Lo and behold, it does exactly the same thing as my own Turing machine did. Every change to the input row is the same, every state update is the same, and every move left or right is the same. I try running the machine on many different inputs and every time I run it, it behaves exactly the same as the machine I built did.

Then I set up some input to simulate the experience of sitting in an armchair drinking a cup of tea, and press the “START” button on the machine on the right. Once again I am astonished to see that the machine manipulates the rocks in precisely the same way that my own purpose-built machine did.

The moral of the story: It does not matter if I understand how the computer works for computation to be occurring. It is sufficient that the system make the correct state transitions. One might object that this system is not actually computing since these machines could just be operating randomly and I just happened to get lucky on the inputs that I gave them. But this objection is not tenable in this universe. Since this universe is operating by the laws of classical mechanics, everything is completely deterministic. There is no randomness. In both the case of my purpose-built Turing machines and the case of these mysterious Turing machines, there is simply a physical system operating by the laws of physics. Whether or not I understand how the system manages to correctly obey the transition rules of the abstract Turing machine is irrelevant. (And moreover this is necessary for the computational theory of consciousness to work since otherwise a conscious being would require some other conscious being to understand its computational mechanism, which we assumed from the outset is not the case.)

Thought Experiment № 5

A Turing machine on uneven ground

Some time later I go on another hike through the desert, this time with my friend Alice. We encounter another row of rocks and a pair of machines that look identical to the ones I built. I tell Alice about the machines I saw in the past and how one of them sorts lists and the other simulates consciousness and I suggest that maybe these two do the same. So we arrange the rocks on the input row to correspond to some list and press “START” on the left machine. This time, though, the machine does not correspond at all to the state transitions of my machine. We try running the machine on all sorts of inputs, but in every case there is no correspondence to the machine I built. I tell Alice that this machine must be broken.

But after watching it for a while, Alice notices something. We had assumed that the northern row of rocks corresponds to “1”s and the southern row corresponds to “0”s. But the ground is somewhat uneven. In each column, one of two positions is higher than the other. If we designate the higher position to be a “1” and the lower position to be a “0”, then the machine behaves identically to the one that I built. We set up an unsorted list of integers using this new encoding and indeed when the machine finishes the list has been sorted. Then we set up an input that simulates the experience of sitting in an armchair enjoying a cup of tea and press “START” on the second machine. With this new encoding, the second machine makes exactly the same state transitions that my own purpose-built Turing machine did.

The moral of the story: There is no unique correspondence between the physical states of the system and the states of the Turing machine. Moreover, a machine could have been computing at some point in the past even if at the time I did not understand what its encoding was.

Thought Experiment № 6

A Turing machine on shaky ground

We continue our hike and arrive in an area with a strange geological phenomenon. Once every second, an earthquake rumbles through the area. We see that there is another long set of rows with rocks and a pair of machines that look identical to my own. But because of the earthquakes, we notice that periodically some of the rocks randomly move from the top row to the bottom row or vice versa. We set up a list of integers to sort, press “START” on the left machine and see what happens.

As we watch the machine go, we notice that there are little seismometers in each column. They seem to be keeping track of how many times a rock got jostled by an earthquake. When the machine arrives at a particular column, in checks the seismometer and if there were an even number of jostles, it treats the northern row as a “1” and if there were an odd number it treats it as a “0”. Once we figure this out, we see that every move the machine makes corresponds exactly to the Turing machine that I made.

Likewise I set up the rocks to encode the experience of sitting in an armchair enjoying a cup of tea and then press the “START” button. Accounting for the random fluctuations due to the earthquakes, the machine makes precisely the same state transitions that my purpose-built machine did.

The moral of the story: The encoding of a Turing machine does not need to be particularly simple in the physical world. In this case, the encoding is the result of an XOR between two bits: the bit from the position of the rock, and another bit that the seismometer tracks.

Thought Experiment № 7

A Turing machine in a resonant canyon

We find yet another pair of machines in this region with earthquakes. However, in this place, there are no longer two rows of rocks. Instead there are \(M\) pairs of rows. \(M\) is quite large. By my estimate, it is larger than a million. In each column, every pair of rows has one rock in the northern or southern box. As before, the earthquakes come once per second and sometimes randomly jostle the rocks from the northern to the southern box or vice versa. We press the “START” button on the left machine and watch it go, but with all the random motions of the rocks, we do not understand what is going on.

However, after studying this region for a long time, Alice notices something peculiar. There seems to be a strange resonance along the north-south axis. This causes the earthquake to only ever jostle an even number of rocks. By applying an XOR across the entire column, she realizes that this corresponds to the 0 or the 1 that the Turing machine is working with.

Armed with this knowledge, we set up the rocks to represent an unsorted list of integers. Then we press “START” again and observe that the machine correctly implements our bubble sort algorithm given this encoding. Then we set up the rocks to simulate the experience of sitting in an armchair and press “START” on the machine on the right and watch as the rocks proceed to go through exactly the same state transitions as my purpose-built machine.

The moral of the story: The encoding can be a function of a large number of physical bits.

Thought Experiment № 8

A Turing machine in another resonant canyon

As our journey through the desert proceeds we find a pair of machines in a region that looks identical to the one that came before. There are \(M\) pairs of rows (\(M\) being very large), and two machines. As before, earthquakes jostle the position of the rocks every second.

We set up some rocks to represent an unsorted list of integers and press “START” on the left machine, but we see something strange. The states all seem correct, but only on the even time steps. On the odd time steps they are sometimes wrong.

After mulling this over for a time, Alice realizes what is going on. On even time steps, we take an XOR across all \(M\) rows, but on odd time steps, we omit the very furthest row. Once we have taken this into account, the state transitions all match up exactly what we expect to run bubble sort on our list.

We then set up the rocks to simulate the experience of sitting in an armchair and press the “START” button on the right machine. With our newfound knowledge of how to interpret the states, we observe that the state transitions are exactly as they were for my original machine.

The moral of the story: The encoding need not be fixed in time.

Thought Experiment № 9

The subterranean Turing machine

Our hike continues and we arrive at an area with two long rows of rocks and another set of boxes corresponding to states, but there’s no machine there. There’s just a pair of buttons on the ground that both say “START.” We press the left one and to our astonishment the rocks start to move, seemingly of their own accord. We notice that their movements correspond exactly to the movements of the list-sorting Turing machine I had built. We spend a long time investigating this strange place. We feed it all sorts of lists and every time the rocks end up with a sorted list. Then we arrange the rocks to encode the experience of sitting in an armchair enjoying a cup of tea and press the “START” button on the right. Once more the rocks shuffle about on their own and every transition matches that of my purpose-built Turing machine executing the consciousness.exe computer program.

Eventually Alice pulls out her metal detector and realizes that something is going on underground. After some digging, we discover that there is a tunnel underneath the rocks and there is a machine that looks identical to the one I built in the tunnel. Rather than manipulating the rocks from above, where we could see it, it seems to have been manipulating them from below, where we couldn’t.

But other than its location the behavior of this machine is absolutely identical to the first machine I came across. This raises the question — before we figured out that this machine was in the tunnel, was it computing anything? We put in inputs and observed that it was producing the correct state changes. By the computational theory of consciousness, the system must have been computing — and conscious — all along.

The moral of the story: It doesn’t matter if we see or understand the mechanism by which these state changes take place. All we have to do is verify that the state changes are proceeding according to the correct rules.

Thought Experiment № 10

The ghostly machine

Now Alice and I arrive at a place that looks much the same as before with a pair of rows and a pair of buttons in the ground that both say “START.” Once again we press the one on the left and watch with astonishment as the rocks start to shuffle about seemingly of their own accord. We encode a list of unsorted integers and find that when the machine stops the integers have been sorted. Likewise we encode the simulated experience of sitting in an armchair enjoying a cup of tea and press the right button. And again the rocks start shuffling about on their own and at every point in time their positions match the positions of the rocks that my purpose-built Turing machine produced..

Now we start to investigate the place looking for what could be causing the rocks to move. We don’t see anything around us. Alice pulls out her metal detector, but finds nothing underground. After a long and thorough investigation we are stumped.

I finally conclude to Alice, “I think that the winds must have blown in just the right way to make this system look like it’s computing. But it couldn’t really have been computing. We seem to have gotten lucky.”

Alice responds, “That may be true, but it doesn’t matter. We may consider this series of events to be ‘lucky,’ but ‘luck’ doesn’t really exist here. Our world is governed by the laws of classical mechanics and is completely deterministic. It doesn’t matter how the rocks ended up getting into the correct spots. It just matters that they did. This system performed the computation just as well as the previous one with the underground Turing machine did.”

The moral of the story: Since it is not necessary that we understand how the system works or that it was designed with the intention of computing a particular function, all that matters is that the states of the system correspond to the states of an abstract Turing machine. The machine itself is irrelevant and does not even need to exist as long as the system ends up transitioning through the correct sequence of states.

Thought Experiment № 11

A ghostly machine in a resonant canyon

Our long sojourn continues and we once more end up in a region with earthquakes and the strange geological resonance we saw before. But as in our last encounter, we do not see any machines, just two buttons on the ground labelled “START.” We press the button on the left and watch the rocks go. Armed with our knowledge from our last experience in the resonant canyon, we apply an XOR to the columns and observe that the resulting bits correspond to the states of my list-sorting Turing machine.

Then we set up an input that represents the experience of sitting in an armchair enjoying a cup of tea and press the “START” button on the right. Again, after we apply an XOR across every column, we observe that although the rocks seem to be shuffling around randomly, every state of the system corresponds to the state of my purpose-built Turing machine.

Now we get to work looking for the machinery that is causing the rocks to move about. But as in our last encounter, we are unable to discover anything, even after years of searching.

The moral of the story: If we accept that the systems in Thought Experiments № 7 and № 9 compute, we must accept that this system computes. We may not understand how the system is operating and the encoding may be complicated, but there is nevertheless a direct mapping between the states of the system and the states of a Turing machine performing the computation. The computational theory of consciousness forces us to accept that this grid of rocks is conscious.

Thought Experiment № 12

Alice hunts for consciousness in a grid of rocks

Alice and I finally come to one last vista, also in earthquake country. Here, as in our last encounter, there is a vast grid of rocks, although the geological resonance seems different than before. We do not quite understand how it works. Here the \(M\) pairs of rows is exceedingly large, more than \(10^{15}\). We see the same pair of “START” buttons on the ground. We press the left button and watch what the rocks do. We cannot make any sense of it for a long time. But we are persistent and after decades of study, Alice says, “I’ve figured it out! The system is not using all \(M\) rows. It is only using a subset of the rows. If we account for that and apply an XOR, the system was sorting a list all along!”

Then we press the “START” button on the right and watch the rocks move. Again, after decades of study, Alice says, “This system is computing, too! This system is also using a subset of the rows, it’s just a different subset this time and now it’s running the consciousness.exe program.”

I tell her, “You’re nuts! There’s no way this system is computing. There are so many rows here that you could always find some subset that encodes any sequence of binary strings! This system ran for \(T\) time steps and \(M\) is many orders of magnitude larger than \(T\). The probability that the random fluctuations here would produce some subset of rows that matched the series of binary strings that encode the Turing machine is nearly 1!”

Alice responds, “But that doesn’t matter! There’s no rule that says I can’t pick and choose which rows I want to be included in my ‘system.’ In every place we’ve been, there have always been more rocks lying around than the ones in the rows for the Turing machine. In those cases we only included the rocks that were convenient for us, and I am doing exactly the same thing now. All you need is a mapping from the physical states of your system to the states of the Turing machine that you built. And I found that mapping! This field of rocks is conscious.”

“Wait a second,” I say. “You had to do an awful lot of work to find the right set of rocks that mapped onto the consciousness.exe Turing machine. I think that we cannot ignore your contribution ot the computation. Perhaps the subset of rocks you found is conscious, but it is only conscious in combination with the computations you yourself did to find those rocks.”

Alice responds, “That’s a clever argument, but it can’t be true for two reasons. All I was doing was checking different combinations of rows to see if they were computing the consciousness.exe program. Checking that a computation is valid is not the same thing as doing the computation itself. Think back to the first machine you encountered out here in the desert — was the machine conscious only because you were there checking that its results were correct? Sure, I had to do a bit more work to do this validation, but there is fundamentally no difference between what you were doing then and what I am doing now.

“But even if you are still not convinced,” Alice continues, “we can just set up the system in exactly the same state as when we found it. This time I won’t do any checking at all. But because the system will deterministically evolve in precisely the same way, I don’t need to check the results anymore — I know that the subset of rows I had identified earlier will map precisely onto the state transitions of the consciousness.exe computer program. Are you going to claim that the system was conscious the first time it was run but not the second? That is the same as saying that a conscious being cannot exist without an external observer to verify that it is conscious, and we’ve already establihsed that that cannot be so.”

The moral of the story: A computer is a mapping of physical states to the states of a Turing machine, but the collection of physical states that constitutes the computer does not need to be physically contiguous. Just as a computation may be distributed across hundreds of computers in data centers across the globe, the computation could consist of an arbitrary subset of the rows of rocks.

A Dramatic Plot Twist

Wherein a hot iron bar attains consciousness

I now reveal that this whole time Alice and I are microscopic beings. What we thought to be a field of rocks is in fact a bar of iron. The two rows of rocks correspond to the magnetic orientation of the iron atoms. The grid of rocks corresponds to a long column of iron atoms in this bar. The earthquakes we were observing are in fact thermal fluctuations in the bar. When Alice claimed that the field of rocks in the last thought experiment was conscious, she was really claiming that a hot bar of iron is conscious.

The moral of the story: The computational theory of consciousness forces us to accept that a hot iron bar is conscious.

Conclusions

Throughout this series of thought experiments I’ve endeavored to show that a physical computer is nothing more than a system with a mapping from its physical states to the states of an abstract Turing machine. This mapping does not need to be especially simple, nor does anyone need to know how the physical system has managed to correctly update its physical states to match the corresponding updates of the Turing machine. The mapping just needs to exist.

In every experiment I paired the consciousness.exe computer program with a computer program that runs bubble sort to highlight the conceptual difference between sorting — which is fundamentally a computational process — and consciousness — which I believe is a physical process. Even in the reducto ad absurdum of the final thought experiment, once an appropriate mapping is found, the hot iron bar is indeed executing the bubble sort algorithm. I started with an unsorted list, ended up with a sorted list, and at every step of the way, the state of the list matched what I expected from the bubble sort algorithm. The work Alice had to do find this mapping did not involve sorting the list herself, anymore than I am somehow contributing to my laptop’s computations if I probe its voltage states with an oscilloscope. [¹] Likewise, if consciousness were simply a matter of running the consciousness.exe computer program, we would have to accept that the hot iron bar is conscious.

At root, computational processes require the existence of an indpendent observer to provide the mapping between the physical states of the system and the abstract states of a Turing machine. It’s not necessary that the observer validate every intermediate step of the computation, or even the input and output (assuming they have confidence from the physics of the system that the rules of the Turing machine will be obeyed). But they must provide the mapping. By contrast, consciousness exists independently from any external observers. No one needs to provide the mapping between the states of the neurons in my brain to the abstract states of a Turing machine in order to imbue me with consciousness.

I have also tried to present examples where the kinds of physical states we’re considering are at least somewhat physically straightforward. But the physical states can, in principle, be arbitrarily complicated as well. We can imagine taking a cubical box one meter to the side and measuring the positions of all the air molecules inside as a function of time. If the seventh place decimal digit of the distance from the \(x\)-axis is even, then we consider it to represent a 0 and otherwise a 1. Or we could do this for the sixth place digit and with respect to the \(y\)-axis. Or we could do it in base 11. Any physical system with enough degrees of freedom will have a subset of its elements that encode the state transitions of an arbitrary Turing machine.

At the end of all of this, the computational theory of consciousness forces us into a position of panpsychism — and an especially extreme form of panpsychism at that. We have to accept that not only are all things conscious, but they contain all consciousnesses, including yours and mine. This conclusion is absurd on its face. The implication is that consciousness cannot be completely reduced a special form of computation.

To my mind, consciousness must involve a physical process in some way. These physical processes surely involve some computation, but the computation must be done with respect to a particular physical system — and so, they cannot be a pure computational process, since such processes are independent of the physical systems that perform them. So while we can use a computer to simulate the activity of the neurons in a brain, such a simulation will not actually produce a consciousness because it lacks the physical component that produces consciousness (whatever that might be).

Footnotes