ada612@csc.anu.oz.au (09/21/90)
Here is a basic question about digital simulations of analog computing
systems such as the human brain is currently taken to be. Namely, is there
any theorem that shows that this is in general possible, assuming
that the precision of the arithmetic is fixed (or, equivalently,
I hope, if the device has a fixed upper bound on the time needed
to compute the state at t_{i+1} from that it at t_i).
More precisely, discussions of brain simulations (as in Hofstadter's
Book-of-Einstein's-Brain scenario) assume that one can can simulate
a brain by breaking the passage of time into small intervals, and
using the equations governing the evolution of the system to
compute the state at t_{i+1} from that at t_{i}, furthermore using
approximations to physical & mathematical constants such as e and pi.
For this procedure to be convincing, we need to know that as our
time-interval size decreases and arithmetic precision increases, the
predicted state of the system at t (given initial conditions for t_0)
converges to a limit. This is obviously true for the kinds of well-
behaved systems that we look at in baby Calculus, but is it provable or
plausibly conjecturable for brains?
Reasons for suspecting that it isn't are:
I: A semi-ignorant reading of the semi-popular literature on chaos theory
suggests that it might be possible to set up systems that passed
through critical periods t_c with the property that tiny differences
in the state at t_c would magnify into big differences at a later
time t, such that the states calculated for t_c with different
approximation methods produced non-convergingly different answers
at t.
II: The conclusion that a fixed-precision simulation of a brain is possible
leads immediately to the conclusion that a finite-state machine can simulate
the brain, which leads to one of the following conclusions, which I find
implausible:
A) a finite state machine can be a sentient being.
B) a finite state machine can simulate the behavior of a sentient
being without being sentient.
Note the importance of the proviso that the simulation be fixed-precision.
If we allow the precision of the simulation to grow as the calculation
proceeds, it ceases to be finite state, but also, the time needed to
calculate the next state function would increase as the simulation
proceeded, and we wouldn't really have a functional equivalent to
a brain. Thus an algorithm might be able to provide a sort of
semi-simulation of a brain (with the time scale expanding as the
simulation proceeded) without leading us to conclude either (A) or
(B) for algorithms.
Avery Andrews ada612@csc.anu.oz.aumiron@fornax.UUCP (Miron Cuperman) (09/23/90)
What is a sufficient condition for a simulation of a brain to be good enough? The noise induced by the finite precision of the simulation must be on the order of magnitude of normal noise we experience. If that is so, the simulation is adequate. There is no a-priori reason to assume we cannot build a simulation with the same amount of noise as in nature. Chaos does not influence the possibility of simulation in any way. The brain may be sensitive to some perturbances. Since the simulation will posses the same amount of noise, it will cause the same amount of perturbances. Brains MUST be equivalent to finite state machines. Any precision beyond the energy of natural noise has no influence. Conclusion: Brains are finite state machines with noise. Therefore there is no a-priori reason why they cannot be simulated. -- By me: Miron Cuperman <miron@cs.sfu.ca> "Do not go gentle into that good night, Rage, rage against the dying of the light" - Dylan Thomas, 1933
jacob@latcs1.oz.au (Jacob L. Cybulski) (09/26/90)
From article <1292@fornax.UUCP>, by miron@fornax.UUCP (Miron Cuperman): > Brains MUST be equivalent to finite state machines. Any precision beyond > the energy of natural noise has no influence. > > Conclusion: Brains are finite state machines with noise. Therefore there > is no a-priori reason why they cannot be simulated. I think your reasoning is a bit illogical. It is your assumption that brains are equivalent to finite state machines, and I cannot see any convincing argument that this is the case. The subsequent conclusion is thus unacceptable. I do agree, however, with you and others that some aspects of mental manipulation could be simulated as if the part of the brain responsible were a finite state machine (I am not even sure if the term "part" is appropriate here). Jacob
ada612@csc.anu.oz.au (09/26/90)
From <1292@fornax.UUCP> miron@fornax.UUCP (Miron Cuperman) >What is a sufficient condition for a simulation of a brain to be good enough? >The noise induced by the finite precision of the simulation must be on the >order of magnitude of normal noise we experience. If that is so, the >simulation is adequate. Reflecting on my original question, this seems right: since neural behavior is sloppy and imprecise, the roundoff errors of fixed precision digital simulations shouldn't make any difference to the quality of performance. >Brains MUST be equivalent to finite state machines. Any precision beyond >the energy of natural noise has no influence. > >Conclusion: Brains are finite state machines with noise. Therefore there >is no a-priori reason why they cannot be simulated. But this seems wrong, because brains can also *grow* while they operate, which is not something that finite state machines can do. Turing machines on the other hand can grow in the rather limited sense that they amount of tape they have written on can get larger, but brains can add new active computational agents, in the form of synapse connections. This is clearly a more radical form of extensibility (if you're interested in what can be done in real time). Avery Andrews (ada612@csc.anu.oz.au)
cowan@marob.masa.com (John Cowan) (09/28/90)
In article <1990Sep26.202658.2906@csc.anu.oz.au> ada612@csc.anu.oz.au writes: >From <1292@fornax.UUCP> miron@fornax.UUCP (Miron Cuperman) > >>What is a sufficient condition for a simulation of a brain to be good enough? >>The noise induced by the finite precision of the simulation must be on the >>order of magnitude of normal noise we experience. If that is so, the >>simulation is adequate. > >Reflecting on my original question, this seems right: since neural >behavior is sloppy and imprecise, the roundoff errors of fixed precision >digital simulations shouldn't make any difference to the quality of >performance. Turing actually makes this very point in "Can Machines Think?". He points out that while a digital computer cannot exactly simulate the behavior of an (analog) differential analyzer (because the digital machine has only finite precision), it can approximate the random error in the analyzer's behavior to an arbitrarily close degree. >>Conclusion: Brains are finite state machines with noise. Therefore there >>is no a-priori reason why they cannot be simulated. > >But this seems wrong, because brains can also *grow* while they operate, >which is not something that finite state machines can do. Turing >machines on the other hand can grow in the rather limited sense that >they amount of tape they have written on can get larger, but brains >can add new active computational agents, in the form of synapse connections. >This is clearly a more radical form of extensibility (if you're interested >in what can be done in real time). I don't understand the sense of your final parenthesis. Neglecting it for a moment, the claim that brains are superior to Turing machines because they can add "new active computational agents" seems clearly wrong. The universal Turing machine has a fixed finite-state repertoire and a single tape, like any Turing machine. However, the tape may be thought of as logically divided into two tapes. The H-tape contains a symbolic representation of the finite-state part of the TM being simulated by the UTM, and the S-tape is the simulated tape of the simulated TM. In the standard UTM, the H-tape contains both the unchanging representation of the finite-state machine hardware, and the changing representation of the current state. The machine hardware representation (MHR) is not changed during operation of the UTM. However, there is no problem with constructing a variant UTM which is allowed to change the MHR. In particular, the amount of MHR table space can grow without bound, since the H-tape is of infinite length. (The easiest way to simulate an H-tape/S-tape pair is to use alternate cells of the physical tape.) Of course, such a modified UTM cannot simulate an oracle (an infinite-state machine) because it would take infinite time to "grow" the representation of such a machine on the H-tape. OTOH, a brain cannot grow to infinite size (and processing power) in less than infinite time either. Turing machines are notoriously slow in "arbitrary time units": they have to work confoundedly hard to overcome the limitations of serial access. But I don't see that "real time" has much to do with it. If the modified UTM hardware is made fast enough, within quantum limits, surely it could simulate an arbitrarily fast finite-state device? -- cowan@marob.masa.com (aka ...!hombre!marob!cowan) e'osai ko sarji la lojban
ada612@csc.anu.oz.au (10/02/90)
Re: Message-ID: <270367E4.160B@marob.masa.com>
From: cowan@marob.masa.com (John Cowan)
>>But this seems wrong, because brains can also *grow* while they operate,
>>which is not something that finite state machines can do. Turing
>>machines on the other hand can grow in the rather limited sense that
>>they amount of tape they have written on can get larger, but brains
>>can add new active computational agents, in the form of synapse connections.
>>This is clearly a more radical form of extensibility (if you're interested
>>in what can be done in real time).
>
>I don't understand the sense of your final parenthesis. Neglecting it for>
>a moment, the claim that brains are superior to Turing machines because they
>can add "new active computational agents" seems clearly wrong.
>
> <discussion of UTMs which I omit for brevity)
The sense of my final parenthesis is that I find the standard idealizations
of computability theory to be a very dubious framework for thinking
about brains. Computability theory is about what can be done eventually,
whereas brains have to keep up with the real world, always providing some
sort of output in response to the current input.
Consider for example the following basis, which seems to be fairly widely
accepted, for believing that a computer or robot is sentient: if it looks
like a brain (at the relevant level of structure) and acts like a brain,
it should be presumed to be/have a mind. But `fixed horsepower'
computing devices will neither look nor act like brains. In Searlespeak,
one might say that their causal powers differ from those of brains in a
non-mystical and functionally relevant way. So why suspect them of sentience?
Avery Andrews (ada612@csc.anu.oz.au)weyand@csli.Stanford.EDU (Chris Weyand) (10/03/90)
In <1990Oct2.221006.3024@csc.anu.oz.au> ada612@csc.anu.oz.au writes: >The sense of my final parenthesis is that I find the standard idealizations >of computability theory to be a very dubious framework for thinking >about brains. Computability theory is about what can be done eventually, >whereas brains have to keep up with the real world, always providing some >sort of output in response to the current input. So don't use computatbility theory. I mean there really is a difference between computers such as the MacIIcx I'm using right now and Turing Machines. The main one being that TM's can't be fitted with an array of sensors and effectors or anything else physical since they themselves are not. Also, sure computatbility theory talks about what functions can be computed and is not concerned with time or space efficiency. But we who program real computers are very concerned with those issues. Just because the theory says little about efficiency doesn't mean that computations can't be done efficiently. >Consider for example the following basis, which seems to be fairly widely >accepted, for believing that a computer or robot is sentient: if it looks >like a brain (at the relevant level of structure) and acts like a brain, >it should be presumed to be/have a mind. But `fixed horsepower' >computing devices will neither look nor act like brains. In Searlespeak, >one might say that their causal powers differ from those of brains in a >non-mystical and functionally relevant way. So why suspect them of sentience? You can't disprove a statement X by simply saying X is not true! I think a better test of sentience would be if it acts like a mind then it may be presumed to be a mind. Acting like a brain presumably involves sending chemical/electrical signals here and there and that doesn't sound very interesting. After all the brain of a frog acts like a brain. Chris Weyand weyand@cs.uoregon.edu -=- weyand@csli.stanford.edu
smoliar@vaxa.isi.edu (Stephen Smoliar) (10/14/90)
In article <15631@csli.Stanford.EDU> weyand@csli.Stanford.EDU (Chris Weyand) writes: >In <1990Oct2.221006.3024@csc.anu.oz.au> ada612@csc.anu.oz.au writes: > >>The sense of my final parenthesis is that I find the standard idealizations >>of computability theory to be a very dubious framework for thinking >>about brains. Computability theory is about what can be done eventually, >>whereas brains have to keep up with the real world, always providing some >>sort of output in response to the current input. > >So don't use computatbility theory. I mean there really is a difference >between computers such as the MacIIcx I'm using right now and Turing Machines. >The main one being that TM's can't be fitted with an array of sensors and >effectors or anything else physical since they themselves are not. Also, sure >computatbility theory talks about what functions can be computed and is not >concerned with time or space efficiency. But we who program real computers >are very concerned with those issues. Just because the theory says little >about efficiency doesn't mean that computations can't be done efficiently. > Efficiency is only part of the story. More important is that computability theory is concerned with FUNCTIONS, in the strict mathematical sense of the word, which is to say a relation which associates with every element from some domain space at most one element from a range space. Within this theory computation is a finite process which eventually halts given any domain element for which such an association exists. However, there are plenty of things that computers do which cannot be reduced to such functions. For example, operating systems do not halt in a finite amount of time and return a function value (at least they are not designed to do so). If we want to talk about simulating a brain, we would do better to consider an operating system as an appropriate metaphor than a function which computes a polynomial. Computability theory may then tell us about certain functions which we may want to build as COMPONENTS of such a system, but that does not guarantee that we shall gain any insights about building the whole system. ========================================================================= USPS: Stephen Smoliar USC Information Sciences Institute 4676 Admiralty Way Suite 1001 Marina del Rey, California 90292-6695 Internet: smoliar@vaxa.isi.edu "It's only words . . . unless they're true."--David Mamet