What Is Consciousness?

Great Debates
161

I don’t believe any of those things needs to be proven. To claim anything is encoded in the digits of Pi is an extraordinary claim, and the burden of proof is on the one making the claim, not the one refuting it. In any event, the claim cannot be proven for the same reason it cannot be disproven; the task is simply too onerous.

Not all infinities are the same. Take Galileo’s paradox: there are two infinite sets. One is the set of all whole numbers (1, 2, 3, 4, 5, …) and the other is a square of the members of the first set (1, 4, 9, 16, 25, …). Which set has more members in it? At first glance, one might think the first set does, since it contains all the numbers from the second set as well as the numbers in between, but since both sets are infinite, one must conclude that they are actually the same size. Seems counterintuitive from a finite point of view, but makes sense logically. Infinities are not all the same and may not actually include every conceivable possibility within them. Pi is just one of many infinite possibilities.

162

It isn’t really an “extraordinary” claim at all, given the nature of infinity. In fact, it would be miraculously unlikely if any given sequence of digits didn’t appear.

True, but not relevant here. Pi has been proven to have the properties required. The distribution of digits is indistinguishable from a random series. It has been tested to ridiculous depths, and the distribution, among the first million or so digits, shows exactly the same properties as a random distribution. e.g., the decimal string “111” shows up about once in every thousand three digit strings, and so on.

Yes, it is certainly possible to construct sequences of digits that do not behave akin to random sequences, but pi isn’t one of those.

163

I have no doubt that Pi is an infinite sequence with no discernible pattern, apart from the pattern of being unpredictable. However, that does not prove that anything that can exist is encoded in the digits of Pi. In fact, it probably means just the opposite.

Just because we want something to exist, that it would be cool if it existed, does not mean that it exists. Life elsewhere in the universe would be really cool, but so far we have no proof that life as we know it exists anywhere else but on earth. If we altered the meaning of “life” to include volcanic activity, why then we could include Io, the actively volcanic moon of Jupiter as proof of extraterrestrial life. But since we seem to restrict our definition to organic life, we are at a loss, even though the chances seem to be good for the possibility of ET life simply based on the math. But still nothing so far.

Another consideration: if the works of Shakespeare or any other writer were to be encoded in the digits of Pi, then Pi would no longer be an infinitely random number because at least a portion would become predictable. Either Pi never repeats and is random or it is not. It cannot be both.

164

How do you figure?

Up to the our ability to measure it, every single digit occurs about one time in 10. Every two-digit string occurs one time in 100. Every three-digit string occurs one time in 1,000. And so on.

There is no reason to believe this does not continue indefinitely. Every possible 10-million digit string will probably occur, roughly once in every 10^10,000,000 digits.

Since pi is infinite, every conceivable 10-million digit string will probably occur, not only once, but again and again, infinitely.

Why would you argue that this property abruptly ceases at some arbitrary boundary?

No one here has made any argument based on personal desires.

The numbers 01 through 99 occur in pi. Several times. The numbers 001 through 999 occur many times in pi. The digits “999” occur, on average, once every 3,000 digits, all throughout the entire length of pi. Does this mean, by your reasoning, that pi’s digits are no longer random?

I was just playing poker. The dealer dealt me a full house, nines and threes. Does that mean the deal was not random?

(Let’s leave aside the fact that pi’s digits are not random; pi has a very specific fixed value, because of its geometric nature. Pi’s digits appear random; they pass every known test for randomness.)

165

Only if you believe Chalmers’ account of implementation. But as I mentioned to eburacum45, it suffers from the problem that in order to perform any given computation, the system does not actually have to satisfy this notion of implementation—that is, for, say, computing the digits of pi, it need not be the case that the rock, or the wall, ‘satisfies the strong state-transition conditionals’ in order to get out the result of the computation. So if consciousness likewise is a result of computation alone, then again the system need not satisfy Chalmers’ account of implementation.

That’s an important point: for every number, there exists some encoding under which it contains the works of Shakespeare: an encoding is just a mapping between code words and plaintext, so the encoding that maps ‘1’ to the complete Shakespeare is a perfectly good one. So it’s not surprising that there is some way to ‘decode’ Shakespeare from the digits of pi. However, it is (or would be—more on that later) surprising that every possible code will find the complete works of Shakespeare somewhere in those digits.

How so? It still continues to be a very real phenomenon in need of explanation. Even if I might not be able to striclty answer the question of whether you are conscious, I can certainly say that I am conscious, and I can look for an explanation of this fact. And this explanation itself will be objective: it will explain how certain systems produce conscious experience.

The ‘nature of infinity’ is a complete red herring here. What is needed is the property of normality: normal numbers include every conceivable sequence of digits in proportion to its length. There are infinite, non-repeating numbers that are non-normal, for which you can’t argue that Shakespeare’s works should turn up somewhere (simply take 0.101001000100001…, which fails to include the digits 2-9). There are in fact infinitely many such numbers, even though almost all infinite non-repeating numbers are in fact normal.

And this is wrong: pi is strongly conjectured, but not proven to be normal. In fact, even though almost every number is normal, this property is known of very few. An example is Champernowne’s number, given by the digit expansion 0.1234567891011121314…, which has the property that every conceivable digit string occurs by construction.

166

Good HMHW,

Then if my rock has a:

Subscript m=the number of components of human knowledge
state ‘B’ that is a necessary consequent of state ‘A’
state ‘A’ that is a necessary consequent of state ‘B’
environment such that it at sometime finds itself in state ‘B’

I will then observe the subsequent sequence of states for m transitions
I will observe states B1,A1,B2,A2…Bm,Am

I then map the states thus:

B1=Library of Congress
A1=Google Data Bank
B2=Current contents of the cloud
A2=Watson
.
.
.
((Am+Am^2)/2)=Sum total of all knowledge

The physical system is not computational. The mapping attributes computation to an uninvolved medium that is observed but has only 2 states and no input or output. The computation is external to the physical system

So, the premise that *all physical systems are computational *is false.

My rock is a physical system
My rock is (not computational)
.:Therefore some physical systems are (not computational)

I assume that folks smarter than me are working on the problem of quantum computing and may come up with great wonders. But, the problem is similar to Maxwell’s Demon. It will always require the equivalent of a Hilsch Vortex for implementation.

Crane

167

That’s not what follows from your argument. At best, it shows that there are some ways to map the states of a physical system to a process that is not a computation—but it’s not clear to me it does even that. Of course, this then does not establish that you can’t map the states of a physical system to those of a computation.

And again, this:

Is simply not a premise the argument needs. All I need is that there is some way to map the states of a physical system to those of a computation, which is easily possible.

168

HMHW,

The Universal Turing Machine (UTM) is, by definition, a system that can perform the computations of any other computational system. The Contra Positive is not true. This means that all computing systems cannot perform the functions of a UTM. Perhaps because there are no complete UTMs.

Your PC and the sheet rock wall are not UTMs.

However:

A UTM can perform the operations of any physical computational system
If it is demonstrated that consciousness is a function of a physical computational system
.:Then If a physical UTM could be constructed it would be conscious

These are definitions and have nothing to do with research into the nature of consciousness.

Crane

169

Yes. And as I explained already, that’s the reason why the discussion is couched in terms of finite-state automata, which are not universal TMs, but suffice to capture any program that can be executed on finite-memory machines, such as desktop PCs or our brains. You only need a large enough set of states to emulate a FSA, which can for a macroscopic object always be achieved by a sufficient fine-graining of phase space.

170

HMHW,

“Is simply not a premise the argument needs. All I need is that there is some way to map the states of a physical system to those of a computation, which is easily possible.” HMHW

A=A is not computation. A+B=C is computation. For A+B=C the computing engine has transformed the information. The output differs from the input.

A word processor is not a computer although computers may be used to perform word processing.

The internal oscillator of your computer has two states. State 2 is a necessary consequent of state 1 and state 1 is a necessary consequent of state 2. If you map the Declaration of Independence to state 1 and the Constitution to state 2 - your computer will present you with the Declaration of independence in state 1 and The Constitution in state 2.

A=A
B=B

No computation has taken place. It is not a physical computing engine.

Crane

171

Well, that’s not right. Fully formalized, say in terms of partial recursive functions, of course the identity function is a computation.

But that’s of course not at all what happens here. Rather, we have A = Declaration of Independence, B = Constitution. Basically, you’ve got a database—a device that returns some data if it is put in some state (by input, or, in your example, by the internal oscillator). It might be a trivial computation, but it’s a computation nonetheless.

And again, even if you find a mapping that takes the states of a physical system to states of a process that is not a computation, then this does not mean that you can’t use the physical system to implement a computation—the negation of ‘there exists a mapping such that a system S implements a computation’ is not ‘there exists a mapping such that a system S implements no computation’—which is what your argument seeks to establish—but ‘there exists no mapping such that a system S implements a computation’. But this is false.

172

Ah! I beg your pardon. I had thought this specific one of pi’s properties had been proven.

Certainly, the digits show “randomlike” properties as far as anyone has ever been able to examine them, but, of course, that isn’t a proof.

173

HMHW,

One of the possible maps is the null case.

OK, show me the set of maps that will compute sin x / x in the interval x=10 thru x=90 for 3 states. Remember you have no input or output.

Crane

174

Of course I’ve got output: the FSA state. And for the program you propose, you’d first construct the FSA computing the values in a row, then simply map the states the FSA cycles through to the state of the physical system. This would likely not be a 3-state FSA, but again, you can set the number of states you require simply by graining the system’s phase space. Alternatively, you can use the convention that state n of the system is mapped to a different state every time it occurs.

Chalmers discusses the implementation of a FSA cycling to the states A and B, i.e. producing the sequence ABABABA…, and how to map that to a rock. The mapping for any other FSA works in exactly the same general way, so I see nothing to be gained in drawing up more examples.

175

HMHW,

Then you are performing the calculations and listing them on your maps. The maps are called when the states are detected. There is no input to the rock and there is no output from the rock and there is no computation other than what you did to fill in your forms.

C’mon Man!

Chalmers is right - your maps are irrelevant to any discussion of consciousness.

Crane

176

No. I’m not mapping the results of the computation to the states of the rock, but the program that computes those results. That program, I must know, of course—but nothing about the results.

There’s no input alright (which is not a restriction, since any input can always be recontextualized as part of the program), but there is output—the states of the rock, viewed via the mapping—and there is computation: the evolution of the rock, from one state to the next.

This is not what Chalmers says. He in fact agrees with the gist of the argument, he merely argues that the notion of implementation the argument uses is not appropriate; and I think he’s wrong on that, as I have elaborated.

Just take another look at how the example of the ABABABAB automaton is implemented. Then recall that every computation performed by a finite state automaton can be viewed as such a string of states. These are implemented in exactly the same way. There’s nothing particularly difficult or deep about this.

177

Must of been sometime in1976, I was contacted by a group in Chicago to make a briefcase system with a cable for input only. The cable was to have a clamp that fit over an 8080 microprocessor. The system would be connected to the 8080 for some period of operation. The computer in the briefcase would then recreate the program the 8080 was running. The system in the briefcase was a higher speed 16 bit micro.

I determined that it could not be done, essentially for the reasons given by Chalmers. The customer sent a lawyer and some non-disclosure agreements and information on the schematics of the target system. It still could not be done. I began to believe that they wanted to rip off software from games that were in joints owned by the mob. I demurred.

The observation was more intimate than your ‘scope’, but mapping all of the functions, of the system observed, was not possible.

Crane

178

That’s a nice little anecdote, but I fail to see how it’s supposed to be relevant to the discussion. I’m not trying to duplicate the FSA on the rock, I merely want to implement it performing a specific computation—there’s a difference.

179

There doesn’t seem to be any lower bound on the number of particles in this hypothetical ‘rock’, so we could presumably map any FSA to a rock consisting of no more than two particles. This seems to reduce the argument to garbage.

I fail to see how the idea has any impact on the idea of consciousness as computation; if consciousness is caused by computation alone, (as seems very likely indeed) it may be difficult or even impossible to map that computation to the physical states of the brain/body system, and the conundrum presented by Searle and formulated by Chalmers seems to indicate some possible reasons for error. In the same mass of brain tissue that contains my consciousness, there are enough states to map everyone else in the world’s consciousness as well (nay- the universe).

But we can presumably restrict our enquiries to the consciousness that has detectable input and output systems for now, I think.

180

Well, you’ll note that I always specified a macroscopic object. Putnam solves the problem differently, by requiring an open system: if even those two particles are in continuous interaction with an environment, they will effectively traverse an arbitrary number of distinguishable states. That’s all that’s needed.

Fundamentally, the argument is nothing but this: take a FSA with n states, s[sub]1[/sub], s[sub]2[/sub],…,s[sub]n[/sub]. Any computation carried out using this FSA is a sequence of those n states. Say, without loss of generality, that sequence is s[sub]1[/sub]s[sub]3[/sub]s[sub]8[/sub]. Knowing this sequence is tantamount to knowing the result of the comptuation: there is a table such that it takes the states to human-intelligible results.

You can imagine each state to be, for example, the entire configuration of a PC—all the bits in its memory. Initialized in a starting state, it will then transition to various other states—changing the contents of its memory. This is the performance of the computation. At some point, it must either repeat (since we have a finite memory), or reach some final state. If it reaches a final state, then the configuration it has at that point, the data in its memory, is the result of the computation. Using a suitable table, you can translate the memory content to something human-intelligible—say, the first k digits of pi. This is the result of the computation.

All you need, in order to perform that same computation using a rock, say, is for that rock to have a sufficient amount of states—which as I said, can always be achieved by a sufficient fine-graining of its phase space (for a macroscopic object; for an open system, you have likewise a guarantee of sufficient states, by noting that it will, in general, never revisit the exact same point in phase space twice). Then, you only need a mapping of the rock’s states to the states of the FSA. Using this mapping, you can observe the rock, and deduce the evolution of the FSA—in our example, the sequence of states s[sub]1[/sub]s[sub]3[/sub]s[sub]8[/sub]. Where you get that mapping from is of no consequence—the argument needs only for it to exst.

So having the rock in hand, and the mapping, you can deduce the exact sequence of states the FSA goes through. Know knowing how to translate that sequence to something human-intelligible, you can, from there, obtain the result of the computation. But this translation is once again just a mapping—say, from states of the FSA to numbers. You can compose this mapping with the mapping from states of the rock to states of the FSA, to give you a mapping from states of the rock to something human-intelligible.

But then you’re in exactly the same situation you were with the original FSA in hand: the FSA performs some evolution, which, using your mapping, you can translate into, say, the digits of pi. In exactly the same way, the rock performs some evolution, which, using your mapping, you can translate into the digits of pi. So with the same justification you had in saying ‘the FSA computes the digits of pi’, you can say ‘the rock computes the digits of pi’; it’s precisely the same situation: not knowing the digits of pi beforehand, and only using a physical system, and a table that tells you how to interprete the states of that system (which, for convenience, is often implemented in the form of a monitor for modern-day computing systems; in earlier days, you had things like, e.g., punchcards), you will learn the digits of pi—the outcome of the computation.

Note that we haven’t done anything to the rock but to look at it. If we look at it differently, we can bring out other computations—any computation that an inputless FSA is able to implement (which is any computation a PC, or any finite system, can implement). So if there is now a computation that gives rise to consciousness, then there is a way to look at the rock such that it performs that computation—using nothing but an (extremely large) lookup table taking the rock’s states to the states of the computation.

But if that’s true then it either means that the rock is conscious when looked at in a particular way—which is a strange conclusion: how could the presence of consciousness depend on who’s looking how? Or, the rock should best be taken to perform any computation that can be ‘brought out’ by using the appropriate translation—but then, the rock would have conscious experience, and moreover, all possible conscious experiences simultaneously. Neither seems a palatable conclusion.

And what consciousness does have them? After all, in the earlier discussion, nobody seemed to disagree that there could be beings behaviourally indistinguishable from us, that nevertheless have no conscious experience—formulated differently, beings that have all our inputs and outputs, without consciousness. So those inputs and outputs are in no sense inputs and outpurs of consciousness, as they’re there with or without it.