mlevin@jade.tufts.edu (06/19/91)
I was just reading Z. Pylyshin's "Computation and Cognition", and at one point, he states something like: "the number of distinct human thoughts is uncountable." Does anyone have any arguments for or against the idea that the number of possible distinct human thoughts (or mental states) is uncountably infinite? Note I do not mean "astronomicallly large" - I mean infinite (and perhaps uncountably so) in the strict mathematical sense. It seems plausible to me; does anyone have a good argument either way? Mike Levin
erwin@trwacs.UUCP (Harry Erwin) (06/19/91)
mlevin@jade.tufts.edu writes: > I was just reading Z. Pylyshin's "Computation and Cognition", and >at one point, he states something like: "the number of distinct human >thoughts is uncountable." Does anyone have any arguments for or >against the idea that the number of possible distinct human thoughts >(or mental states) is uncountably infinite? Note I do not mean >"astronomicallly large" - I mean infinite (and perhaps uncountably so) >in the strict mathematical sense. It seems plausible to me; does >anyone have a good argument either way? The number of distinct human thoughts isn't even countably infinite in a quantum-mechanical universe, let alone uncountable. However, if we ignore that argument, the question boils down to whether the state of the brain is sensitively dependent to its state on a cauchy surface. I believe Paul Rapp has evidence that it is. So, although the number isn't infinite, it looks like it's uncountable. -- Harry Erwin Internet: erwin@trwacs.fp.trw.com
mlevin@athena.mit.edu (Mike Levin) (06/20/91)
In article <314@trwacs.UUCP> erwin@trwacs.UUCP (Harry Erwin) writes: >mlevin@jade.tufts.edu writes: > > >>thoughts is uncountable." Does anyone have any arguments for or >>against the idea that the number of possible distinct human thoughts >>(or mental states) is uncountably infinite? > >The number of distinct human thoughts isn't even countably infinite >in a quantum-mechanical universe, let alone uncountable. However, >if we ignore that argument, the question boils down to whether the >state of the brain is sensitively dependent to its state on a >cauchy surface. I believe Paul Rapp has evidence that it is. So, >although the number isn't infinite, it looks like it's uncountable. > >-- >Harry Erwin >Internet: erwin@trwacs.fp.trw.com I am sorry - I didn't specify the following in my original message. I am not looking for arguments from physics or neurobiology (but if you have an interesting one, let's hear it). I am specifically interested in arguments which do not assume a specific substratum for the mind, nor a specific theory of cognition. I am looking for people's ideas on this question from the point of view of philosophy or perhaps non-physiological psychology. An example of the kind of thing I have in mind: "there are an infinite number of possible objects, and upon considering each one, a person will/will not have a distinct mental state because ...". So I am more interested in arguments stemming from the higher-level concepts of "idea" or "thought" rather than the bottom-up approcah of trying to figure out how many states the brain can have, etc. In asking this question I realize that I am disregarding the behaviorist objection, and also (in trying to make this substratum- and theory-independent) appealing to each person's knowlege of what an idea or thought is. Mike Levin
yanek@panix.uucp (Yanek Martinson) (06/20/91)
In <1991Jun19.033316.18773@athena.mit.edu> mlevin@jade.tufts.edu writes: >at one point, he states something like: "the number of distinct human >thoughts is uncountable." Does anyone have any arguments for or >against the idea that the number of possible distinct human thoughts >(or mental states) is uncountably infinite? Note I do not mean >"astronomicallly large" - I mean infinite (and perhaps uncountably so) >in the strict mathematical sense. It seems plausible to me; does >anyone have a good argument either way? If you assume that all thoughts or mental states are physical events, states and connections of molecules in the brain then, because the number of molecules in your brain is finite, and states of every individual molecule (it's position charge, orientation, chemical bonding, whatever) are finit, then the number of possible permutations is very large, but finite. Most likely uncountable using today's technology, but not infinite.
alphonce@cs.ubc.ca (Carl Alphonce) (06/20/91)
In article <314@trwacs.UUCP> erwin@trwacs.UUCP (Harry Erwin) writes: >mlevin@jade.tufts.edu writes: > > >> I was just reading Z. Pylyshin's "Computation and Cognition", and >>at one point, he states something like: "the number of distinct human >>thoughts is uncountable." Does anyone have any arguments for or >>against the idea that the number of possible distinct human thoughts >>(or mental states) is uncountably infinite? Note I do not mean >>"astronomicallly large" - I mean infinite (and perhaps uncountably so) >>in the strict mathematical sense. It seems plausible to me; does >>anyone have a good argument either way? > >The number of distinct human thoughts isn't even countably infinite >in a quantum-mechanical universe, let alone uncountable. However, >if we ignore that argument, the question boils down to whether the >state of the brain is sensitively dependent to its state on a >cauchy surface. I believe Paul Rapp has evidence that it is. So, >although the number isn't infinite, it looks like it's uncountable. > >-- >Harry Erwin >Internet: erwin@trwacs.fp.trw.com A minor point: if something is uncountable, it is infinite. In fact, finite < countable (countable infinite) < uncountable (uncoutably infinite) at least as far as I can recall from my logic / set theory courses.
costello@DEC-Lite.Stanford.EDU (Tom Costello) (06/20/91)
In article <1991Jun19.173307.10704@athena.mit.edu>, mlevin@athena.mit.edu (Mike Levin) writes: |> In article <314@trwacs.UUCP> erwin@trwacs.UUCP (Harry Erwin) writes: |> >mlevin@jade.tufts.edu writes: |> > |> > |> >>thoughts is uncountable." Does anyone have any arguments for or |> >>against the idea that the number of possible distinct human thoughts |> >>(or mental states) is uncountably infinite? |> > |> >The number of distinct human thoughts isn't even countably infinite |> >in a quantum-mechanical universe, ||> >[stuff deleted] |> >-- |> >Harry Erwin |> >Internet: erwin@trwacs.fp.trw.com |> |> I am sorry - I didn't specify the following in my original message. |> I am not looking for arguments from physics or neurobiology (but if |> you have an interesting one, let's hear it). | |> mental state because ...". So I am more interested in arguments |> stemming from the higher-level concepts of "idea" or "thought" rather |> than the bottom-up approcah of trying to figure out how many states |> the brain can have, etc. In asking this question I realize that I am |> disregarding the behaviorist objection, and also (in trying to make |> this substratum- and theory-independent) appealing to each person's |> knowlege of what an idea or thought is. |> |> Mike Levin This sounds like Russell's quote, that ``there is a simple arithmetical proof that there are less things in heaven and earth than are dreamt of in my philosophy''. This is based on the cardinality of the power set of all things being greater than the set of all things. To say the number of possible thoughts is uncountable is stretching the idea of countability from math to philosophy. In mathematics the term means there exists no one to one correspondence in the system, of the set to the set of natural numbers. The term is relative to the system doing the correspondence, a set can be countable to one system and uncountable to another. The fact that we have the concept of uncountable is not enough to prove we have uncountable thoughts. This follows simply from the fact there are countable models of ZFC. In fact given that there is presumably a model of all possible thoughts, of some infinite cardinality,that is there is a model of all concepts and all relations on concepts , there must therefore be a model of cardinality aleph 0, by the downward Lowen Skolem theorem, this of course assumes that the language of thought is countable, but this seems reasonable even to dualists on purely behavourialist grounds. The great danger in using concepts like uncountable in philosophy, or ai, is that the person using them usually has an agenda. That is something along the line of, ``there are an uncountable number of possible thoughts therefore the physical symbol hypothesis is false.'' Using uncountable for arguments like this is pure rhetoric, and shows a lackl of understanding of the term. In fact I cannot think of any particular use of uncountable in ai that wuld not be entirely equivalent to its use in pure logic, or formal systems, and thus its use in describing thoughts assumes rather than rejects the physical symbol hypothesis. Tom.
chalmers@bronze.ucs.indiana.edu (David Chalmers) (06/20/91)
In article <1991Jun19.033316.18773@athena.mit.edu> mlevin@jade.tufts.edu writes: > I was just reading Z. Pylyshin's "Computation and Cognition", and >at one point, he states something like: "the number of distinct human >thoughts is uncountable." Does anyone have any arguments for or >against the idea that the number of possible distinct human thoughts >(or mental states) is uncountably infinite? Note I do not mean >"astronomicallly large" - I mean infinite (and perhaps uncountably so) >in the strict mathematical sense. It seems plausible to me; does >anyone have a good argument either way? It's arguable that the number of distinct thoughts an individual can have is finite, but the number of distinct *beliefs* is at least countably infinite. e.g. I believe "1 < 2", "1 < 3", "1 < 4", and so on. The difference being that thoughts presumably have to be explicit, while beliefs can be implicit (tacit). One might argue that even a tacit belief has to be finitely specifiable, in which case there can't be an uncountable number of them. -- Dave Chalmers (dave@cogsci.indiana.edu) Center for Research on Concepts and Cognition, Indiana University. "It is not the least charm of a theory that it is refutable."
me@csri.toronto.edu (Daniel R. Simon) (06/20/91)
In article <1991Jun19.033316.18773@athena.mit.edu> mlevin@jade.tufts.edu writes: > I was just reading Z. Pylyshin's "Computation and Cognition", and >at one point, he states something like: "the number of distinct human >thoughts is uncountable." Does anyone have any arguments for or >against the idea that the number of possible distinct human thoughts >(or mental states) is uncountably infinite? Note I do not mean >"astronomicallly large" - I mean infinite (and perhaps uncountably so) >in the strict mathematical sense. It seems plausible to me; does >anyone have a good argument either way? > >Mike Levin And can they all dance on the head of a pin? "There *is* confusion worse than death" Daniel R. Simon -Tennyson (me@theory.toronto.edu)
dave@tygra.Michigan.COM (David Conrad) (06/20/91)
In article <1991Jun19.033316.18773@athena.mit.edu> mlevin@jade.tufts.edu writes: > I was just reading Z. Pylyshin's "Computation and Cognition", and >at one point, he states something like: "the number of distinct human >thoughts is uncountable." Does anyone have any arguments for or >against the idea that the number of possible distinct human thoughts >(or mental states) is uncountably infinite? ... It seems plausible to me; >does anyone have a good argument either way? > >Mike Levin I think the argument would rest on the analog, as opposed to digital, nature of the brain. Since the potential across a synapse when it fires can be at any value, i.e. it is not quantized, then one could make use of the uncountably infinitely many real numbers between any two points on the number line. The question is, is our intelligence dependant on the analog nature of the brain, or can it be simulated on a finite state machine? This question has sparked much debate, as you might well imagine. David R. Conrad dave@michigan.com -- = CAT-TALK Conferencing Network, Computer Conferencing and File Archive = - 1-313-343-0800, 300/1200/2400/9600 baud, 8/N/1. New users use 'new' - = as a login id. AVAILABLE VIA PC-PURSUIT!!! (City code "MIDET") = E-MAIL Address: dave@Michigan.COM
erwin@trwacs.UUCP (Harry Erwin) (06/21/91)
alphonce@cs.ubc.ca (Carl Alphonce) writes: . . . . >> The number of distinct human thoughts isn't even countably infinite >>in a quantum-mechanical universe, let alone uncountable. However, >>if we ignore that argument, the question boils down to whether the >>state of the brain is sensitively dependent to its state on a >>cauchy surface. I believe Paul Rapp has evidence that it is. So, >>although the number isn't infinite, it looks like it's uncountable. ----- >> >>-- >>Harry Erwin >>Internet: erwin@trwacs.fp.trw.com >A minor point: if something is uncountable, it is infinite. In fact, > finite < countable (countable infinite) < uncountable (uncoutably infinite) >at least as far as I can recall from my logic / set theory courses. You're correct, which is why I said "it looks like it's uncountable." There is some very recent work that indicates you can simulate chaos satisfactorily with a 16-bit word size. For all practical purposes, there are an uncountable number of thoughts, but if you look at it carefully, there are probably only a finite (but very large) number. -- Harry Erwin Internet: erwin@trwacs.fp.trw.com
thomas@ckgp.UUCP (Michael Thomas) (06/21/91)
Hi everyone:
Okay, how about this, you must agree that a number is a
thought and a floating point number is a thought. So as long as you can
count (produce numbers) then you are producing a countable number of thoughts
well I will start and count a number every second from now. You count
the numbers that I'm saying, when you stop, The Brain/mind will have
reached an uncountable number of thoughts. (and if you didn't catch it:
If you want to know how many thoughts is uncountable I will tell you
because I'm counting.... 8^)
If you think a number isn't a thought/idea, why not? a number
is a symbol for something in the world there are three apples and four
chairs. So If I'm counting say the number of different names in the world
and any possible name I could come up with then I could go on forever
and ever and ever (until I died.)
Yes the mind can conceive an uncountable number of thoughts/ideas...
--
Thank you,
Michael Thomas
(..uunet!ckgp!thomas)thomas@ckgp.UUCP (Michael Thomas) (06/21/91)
In article <1991Jun19.195149.19583@panix.uucp>, yanek@panix.uucp (Yanek Martinson) writes: > In <1991Jun19.033316.18773@athena.mit.edu> mlevin@jade.tufts.edu writes: > > > >at one point, he states something like: "the number of distinct human > >thoughts is uncountable." Does anyone have any arguments for or > >against the idea that the number of possible distinct human thoughts > >(or mental states) is uncountably infinite? Note I do not mean > >"astronomicallly large" - I mean infinite (and perhaps uncountably so) > >in the strict mathematical sense. It seems plausible to me; does > >anyone have a good argument either way? > >If you assume that all thoughts or mental states are physical events, states >and connections of molecules in the brain then, because the number of molecules >in your brain is finite, and states of every individual molecule (it's position >charge, orientation, chemical bonding, whatever) are finit, then the number of >possible permutations is very large, but finite. Most likely uncountable using >today's technology, but not infinite. Wait a second, 8^) did you say that all thoughts or mental states are physical events? You didn't really say that states and connections of molecules in the brain are thoughts then? I'm sorry but there is no way on earth that you are going to be able to make me believe this. YES, I understand what you are saying, but to directly tie thought&& idea directly to connections of molecules in the brain, is not going to "fly." I am sorry 8^) but since the brain works with stimulus and all stimulus is a wave/frequency you will have a hard time turning a frequency into a single molecule. Plus the brain is a "living", "moving", "growing", "breathing" thing. It is always in motion and not sitting still in molecules. And even if you are correct mathmatically the combination of those molecules activity and their pattern of activity. Thought isn't a single event but an on going one. so when you count up the growing combinations of molecules and add there activity across the spectrum of their pattern of activity you get an infinite number of thoughts still. thanks for listening.... -- Thank you, Michael Thomas (..uunet!ckgp!thomas)
dagmar@brainiac.raidernet.com (Greble Dagmar) (06/21/91)
mlevin@jade.tufts.edu writes: > > I was just reading Z. Pylyshin's "Computation and Cognition", and > at one point, he states something like: "the number of distinct human > thoughts is uncountable." Does anyone have any arguments for or > against the idea that the number of possible distinct human thoughts > (or mental states) is uncountably infinite? Note I do not mean > "astronomicallly large" - I mean infinite (and perhaps uncountably so) > in the strict mathematical sense. It seems plausible to me; does > anyone have a good argument either way? You might want to try to define 'distinct human thoughts' a little further (and then bring world peace, too :) ), but as I see it what Pylyshin has put forth is undeniably true, althought I wouldn't go so far as to say infinite in that manner you did, simply because we humans are a finite number, composed of a finite number of atoms, etc... I would say that they are completely uncountable unless one wishes to classify, and sub-classify, and sub-sub-classify as to make even the Dewey Decimal System seem like a breeze. Hence, you've got to define the 'distinctness' of the thought itself, or you end up 'combing spaghetti'. I think that we could possibly put an upper limit to them (big maybe) on a sheerly chemical/biological basis, but it still wouldn't give us much of an analysis of what's going on in one's head. -- _-----_ ------------------------------------------------------------------- = \:/ = Save Mother Earth or Die! : Greble Dagmar... Occult Theologian =_ : _= (This is not a joke.) :...!uunet!mjbtn!raider!brainiac!dagmar -- ----- -------------------------------------------------------------------
dirish@csc-sun.math.utah.edu (Dudley Irish) (06/21/91)
I am sure that that you have all heard the old saw, "You can never step into the same river twice." I would similarly argue that you can never have the same thought twice. Thus, for as long as you live you are constantly having different thoughts. There are two questions here. First, does this sequence map to the integers or to the real numbers, in other words, is the sequence of brain states countably infinite or uncountably infinite. The other question is whether because people only live a finite time we want to accept that the sequence of thoughts has an end or whether we want to take a theoretical stance where we don't view the sequence as ending. Now, be careful. Remember the number of real numbers from zero to one is uncountably infinite. If you believe that thoughts map to the real numbers rather than the integers this still leaves you with an uncountable number of thoughts. Also, the number of rational numbers from zero to one is countably infinite. Thus if between every pair of thoughts there is another thought, then even if we take the sequence as ending, it still is countably infinite. So you simply must decide whether thoughts are continuous or not. I don't have a clue as to how to decide this issue. Now, before you think to flame me for a screwup in my understanding of cardinal number theory, I will warn you that my favorite mathematics professor taught a set theory class two quarters ago that I sat in on. I seriously believe that I remember all this stuff correctly. Though what it has to do with AI, I don't know. -- Dudley Irish / dirish@math.utah.edu / Manager Computer Operations Center for Scientific Computing, Dept of Mathematics, University of Utah The views expressed in this message do not reflect the views of the Dept of Mathematics, the University of Utah, or the State of Utah.
erwin@trwacs.UUCP (Harry Erwin) (06/22/91)
dave@tygra.Michigan.COM (David Conrad) writes: >>...previous article... >I think the argument would rest on the analog, as opposed to digital, nature >of the brain. Since the potential across a synapse when it fires can be at >any value, i.e. it is not quantized, then one could make use of the >uncountably infinitely many real numbers between any two points on the >number line. The question is, is our intelligence dependant on the analog >nature of the brain, or can it be simulated on a finite state machine? >This question has sparked much debate, as you might well imagine. Judy Dayhoff (U. Md) is looking at this issue. Based on some similar things that I've seen in multiprocessing systems, I suspect the instantaneous state of the brain is sensitive to _when_ individual synapses fire, so my personal belief is that the analog nature of the brain is an important component of intelligence. No proof, tho. Bernardo Huberman has been involved in some research that seems to indicate that chaotic processes are particularly efficient at pattern recognition (via rapid phase-locking), which may be why Paul Rapp has seen chaos in brainwaves. Sander van der Leeuw was interested in my point that a deterministic system controlled by a chaotic pattern detector is chaotic as a whole. That is a good description of the way many cultures operate. -- Harry Erwin Internet: erwin@trwacs.fp.trw.com
vu0208@bingvaxu.cc.binghamton.edu () (06/25/91)
In article <1991Jun19.033316.18773@athena.mit.edu> mlevin@jade.tufts.edu writes: > I was just reading Z. Pylyshin's "Computation and Cognition", and >at one point, he states something like: "the number of distinct human >thoughts is uncountable." Does anyone have any arguments for or >against the idea that the number of possible distinct human thoughts >(or mental states) is uncountably infinite? Note I do not mean >"astronomicallly large" - I mean infinite (and perhaps uncountably so) >in the strict mathematical sense. It seems plausible to me; does >anyone have a good argument either way? > >Mike Levin If not infinite then multiple thoughts DO occur concurrently in a human brain!! 1) I remember reading somewhere about a poet who could write with both left and right hands, and at times he was writing two different poems simultaneously! 2) A personal experience: I have had many times NESTED-DREAMS! That is, Dream in a dream at most to 3 levels. At each level I have communicated from the nth-level to (n-1)th level of the nested-dreams. ------- This is purely my theory: Human brain may be strongly-processing one thought (on which it is concentrating) but in the back-ground lots of thoughts are being processed (weakly) (here I use strong and weak thoughts to define the degree if concentration). Now once the current thought-process is completed or require more information then one/or more of the back-ground process-thoughts share/send the information to/from the strong-thought. And this thinking process goes on until fewer thoghts are left (resulting in a conclusion or action) or all the thoughts are connected together to reach some new discovery/invention by the brain.
sena@infinet.UUCP (Fred Sena) (06/26/91)
>In article <1991Jun19.033316.18773@athena.mit.edu> mlevin@jade.tufts.edu writes: >> I was just reading Z. Pylyshin's "Computation and Cognition", and >>at one point, he states something like: "the number of distinct human >>thoughts is uncountable." Does anyone have any arguments for or >>against the idea that the number of possible distinct human thoughts >>(or mental states) is uncountably infinite? ... It seems plausible to me; >>does anyone have a good argument either way? >> >>Mike Levin I think that there is some confusion here between "uncountable" and "infinite". I don't believe that they are the same thing at all because I think that there are many things that are uncountable yet finite. For example, if I were to ask you the number of cars that are running on the roads at a particular instant, the number would be uncountable because you can't be everywhere at once to count them and the number of cars would change as you were in the process of counting. I think that everyone would agree that the number would be finite as well, since there are a finite number of cars. I think that the reason why thoughts in the brain are uncountable is because the brain is an uncertainty machine. You cannot measure the number of thoughts because all forms of measurement will cause the actual state to change. As soon as you ask someone how many thoughts they are having, you are changing the number of thoughts that they have because they have to start to think about you question instead of whatever they were spontaneously thinking before you asked them. Besides, what do we consider to be a "thought" anyways. It's not exactly something that you can really measure. Do you count words, symbols, or both? The subconscious speaks to the conscious through symbols. --fred -- -------------------------------------------------- Frederick J. Sena sena@infinet.UUCP Memotec Datacom, Inc. N. Andover, MA
alphonce@cs.ubc.ca (Carl Alphonce) (06/26/91)
In article <2773@infinet.UUCP>, sena@infinet.UUCP (Fred Sena) writes: |> |> I think that there is some confusion here between "uncountable" and "infinite". |> I don't believe that they are the same thing at all because I think that |> there are many things that are uncountable yet finite. |> |> For example, if I were to ask you the number of cars that are running on the |> roads at a particular instant, the number would be uncountable because you |> can't be everywhere at once to count them and the number of cars would change |> as you were in the process of counting. I think that everyone would agree |> that the number would be finite as well, since there are a finite number of |> cars. |> I agree that there is some confusion about this. The terms finite, infinite, countable, and uncountable, all have precise mathematical definitions. However, they are also used in contexts where it is not clear whether the mathematical meaning or the "common" meaning is the one which was meant to be conveyed. Maybe some attempt can be made to indicate when a "technical" meaning of a word is what is to be conveyed, so that these (fruitless) discussions can be avoided in future. For those who are familiar with the mathematicaal definitions of these terms, feel free to stop reading here. For those unfamiliar, here is a (hopefully) non-technical (hopefully) brief summary: Without getting technical, we may loosely define the terms as follows: A set is finite if there are n elements in the set (where n is a natural number). (Alternately, where one defines 0 to be {} (ie: the "empty" set - the set with no members) 1 to be succ(0) = {0} = {{}} 2 to be succ(1) = {0,1} = {{},{{}}} . . . n+1 to be succ(n) = {0,1,...,n}, one can say that a set A is finite if there is a one-to-one mapping from A to some natural number n.) A set A is infinite if there is no natural number n such that there is a one-to-one mapping from A to n. If we let N, the set of natural numbers, be the set {0,1,...,n,...}, then a set A is said to be countable if there is a one-to-one mapping from A to N. Note that (obviously) the set natural numbers is countable. Furthermore, the set of even numbers is countable (take the one-to-one mapping to be f:x -> 2x), and the set of prime numbers is countable (let f be the function mapping n to the n-th prime number). Even the rational numbers are countable. However, there are some uncountable sets also. The set of real numbers, for example, is uncoutable. Thus, there is no one-to-one mapping from the set of natural numbers to the set of real numbers. For a proof of this, see any good logic or set theory book. Carl. alphonce@cs.ubc.ca
gin001@cdc835.cdc.polimi.it (Mauro Cicognini) (06/27/91)
vu0208@bingvaxu.cc.binghamton.edu () writes: >In article <1991Jun19.033316.18773@athena.mit.edu> mlevin@jade.tufts.edu writes: >> I was just reading Z. Pylyshin's "Computation and Cognition", and >>at one point, he states something like: "the number of distinct human >>thoughts is uncountable." Does anyone have any arguments for or >>against the idea that the number of possible distinct human thoughts >>(or mental states) is uncountably infinite? Note I do not mean >>"astronomicallly large" - I mean infinite (and perhaps uncountably so) >>in the strict mathematical sense. It seems plausible to me; does >>anyone have a good argument either way? >> >>Mike Levin >If not infinite then multiple thoughts DO occur concurrently in a >human brain!! >1) I remember reading somewhere about a poet who could >write with both left and right hands, and at times he was writing two >different poems simultaneously! >2) A personal experience: I have had many times NESTED-DREAMS! That >is, Dream in a dream at most to 3 levels. At each level I have >communicated from the nth-level to (n-1)th level of the nested-dreams. >------- >This is purely my theory: >Human brain may be strongly-processing one thought (on which it is >concentrating) but in the back-ground lots of thoughts are being >processed (weakly) (here I use strong and weak thoughts to define the >degree if concentration). Now once the current thought-process is >completed or require more information then one/or more of the >back-ground process-thoughts share/send the information to/from the >strong-thought. And this thinking process goes on until fewer thoghts >are left (resulting in a conclusion or action) or all the thoughts are >connected together to reach some new discovery/invention by the brain. I think very interesting the experience of having nested dreams, although it never occurred to me. I think also very reasonable that many thoughts be carried on at once, since a vast number of processes surely go on inside the brain simultaneously: just think of all the self-supporting systems and the self-regulation systems. So, as the autonomous nervous system is able to do many things at once, also thecentral nervous system (that is, the conscious part) is likely to be able to do so, too. The rest is experience. As for the number of thoughts (that is, mind processes) that can go on at once, I think that we need first a more precise definition of what we mean with the word. Of course, if the definition is loose enough, we may end up as well saying that we have uncountably infinite thoughts going on in a single moment, just because we cannot really measure them, or identify them well enough. Personally, I think that their number may be very large, but not infinite, due to the finite number of neurons in the brain. Of course, this is only an idea, that comes to me quite natural. But common sense is often wrong. Let's not forget we are dealing with living things. And a network that can change itself as it needs. ------------------------------------------------------------------- Sapere aude! Habe mut dich die einige verstanden zu bedienen! (I. Kant)
t-rmason@microsoft.UUCP (Richard MASON) (06/29/91)
Newsgroups: comp.ai.philosophy Subject: Re: how many distinct thoughts can a person have? Summary: Expires: References: <1991Jun19.033316.18773@athena.mit.edu> <1991Jun20.083708.13355@tygra.Michigan.COM> Sender: Reply-To: t-rmason@microsoft.UUCP (Richard MASON) Followup-To: Distribution: usa Organization: Microsoft Corp., Redmond WA Keywords: In article <1991Jun20.083708.13355@tygra.Michigan.COM> dave@tygra.Michigan.COM (David Conrad) writes: >In article <1991Jun19.033316.18773@athena.mit.edu> mlevin@jade.tufts.edu writes: >>Does anyone have any arguments for or >>against the idea that the number of possible distinct human thoughts >>(or mental states) is uncountably infinite? ... It seems plausible to me; >>does anyone have a good argument either way? >> >I think the argument would rest on the analog, as opposed to digital, nature >of the brain. Since the potential across a synapse when it fires can be at >any value, i.e. it is not quantized, then one could make use of the >uncountably infinitely many real numbers between any two points on the >number line. The question is, is our intelligence dependant on the analog >nature of the brain, or can it be simulated on a finite state machine? >This question has sparked much debate, as you might well imagine. It seems to me very unlikely that a synapse has an uncountably infinite number of relevant states, i.e. that any difference in the potential across a synapse results in a different synapse state and therefore a different overall thought. Doesn't this imply that as a voltage-measuring device, a synapse is an instrument of infinite accuracy, infinitely superior to any voltmeter we could ever construct? This seems an absurdity. So it seems to me more likely that there is some limit on the accuracy of a synapse potential, therefore synapse potential is in effect quantized. If we add to this statement an upper limit on the maximum potential that can exist across a synapse, it would seem that the number of distinct possible brain-states is finite. Very large, but finite. ========================================================================= Richard Mason t-rmason@microsoft.com All opinions are my own.