DOCTORJ@SLACVM.SLAC.STANFORD.EDU (Jon J Thaler) (03/24/91)
One thing that has always bothered me about the comparison between computers and brains is that (most) computers are finite state machines, while it is not obvious to me that brains are. It is well known that mathematical modelling of continuous systems on disctrete lattices will miss some classes of solutions entirely, so I have trouble following the arguments based on analogies between computers and brains. Can someone out there shed some light on this for me?
kludge@grissom.larc.nasa.gov ( Scott Dorsey) (03/25/91)
In article <91082.223501DOCTORJ@SLACVM.SLAC.STANFORD.EDU> DOCTORJ@SLACVM.SLAC.STANFORD.EDU (Jon J Thaler) writes: >One thing that has always bothered me about the comparison between >computers and brains is that (most) computers are finite state machines, >while it is not obvious to me that brains are. It is well known that >mathematical modelling of continuous systems on disctrete lattices >will miss some classes of solutions entirely, so I have trouble following >the arguments based on analogies between computers and brains. Can someone >out there shed some light on this for me? Maybe in the real world everything is discrete. For example, the current flowing along a wire is not a continuous value, because it's actually the flow of individual electrons, each with a fixed charge. And since all neurotransmitters consist of individual molecules, perhaps the brain is also really a discrete system. That's not to say that it's not a very fine-grained one, though, that would be very difficult to model. But if it were an easy problem, it wouldn't be quite as enjoyable to work on. --scott
jeg@ZYX.SE (Jan-Erik Gustavsson) (03/25/91)
I apologize if this is the wrong forum but... Could someone please provide me with the e-mail address to professor Rawls at Harvard University (probably at the philosophy department). -- ----------------------------------------------------------------------------- Jan-Erik Gustavsson, ZYX Sweden AB, Styrmansgatan 6, 114 54 Stockholm, Sweden Phone:+46-8-6653205 Fax:+46-8-6674831 E-mail:jeg@zyx.se -----------------------------------------------------------------------------
maxwebb@ogicse.ogi.edu (Max G. Webb) (03/27/91)
>One thing that has always bothered me about the comparison between >computers and brains is that (most) computers are finite state machines, >while it is not obvious to me that brains are. It is well known that >mathematical modelling of continuous systems on disctrete lattices >will miss some classes of solutions entirely, so I have trouble following >the arguments based on analogies between computers and brains. Can someone >out there shed some light on this for me? > The 'apparent' continuity in the response of neurons is not too relevant, due to the low precision in the device. Whatever each neuron is computing, it is not computing it to 32 bits accuracy! Having infinite precision in one number is equivalent in power to having infinite # of (sequentially accessible) bits of memory. (of course) Hence, discrete devices should have no problem simulating such neurons. Simply set the smallest delta between two numbers in your representation to 1/2 the relative inaccuracy of the neuron between two different presentations of the same stimuli. Max. -- Max Webb | maxwebb@cse.ogi.edu | 20 nw 16th, #315, Portland Or, 9209
kolen-j@retina.cis.ohio-state.edu (john kolen) (03/29/91)
>One thing that has always bothered me about the comparison between >computers and brains is that (most) computers are finite state machines, >while it is not obvious to me that brains are. It is well known that Computers are discrete systems until they encounter environmental factors which interact with them at a physical level. Radiation is one such factor, while heat is another. Each can change the behavior of the system in unpredictable ways. Designers add in shielding, cooling fans, redundant parts, to prevent such occurences. A stupendous effort is expended to build computers so they behave as discrete systems, but it is not apparent that nature went to such extremes. Rather, it exploited the natural state-like properties of continuous dynamical systems. By changing from one attractor to another, state-like behavior can be obtained. This method does entrench a particular type of attractor, i.e. the attractors can be fixed points, limit cycles, or strange (chaotic) attractors, all that is necessary is some way to uniquely identify them. John -- John Kolen (kolen-j@cis.ohio-state.edu)|computer science - n. A field of study Laboratory for AI Research |somewhere between numerology and The Ohio State Univeristy |astrology, lacking the formalism of the Columbus, Ohio 43210 (USA) |former and the popularity of the latter
magi@utu.fi (Marko Gronroos) (03/29/91)
maxwebb@ogicse.ogi.edu (Max G. Webb) said: > The 'apparent' continuity in the response of neurons is not too > relevant, due to the low precision in the device. Whatever each > neuron is computing, it is not computing it to 32 bits accuracy! 32 bits? Integer? Not floating point? How about sight? You can see the Sun, which is -27 magnitudes, and a galaxy that is +6 magnitudes. The brigthness difference is 32 magnitudes ==> approx. 10^13 ==> 10 000 000 000 000. 32 bits is only 4 294 967 296. Ok, ok, neurons don't fire 10 000 000 000 000 times as fast when watching the Sun than when watching a star, but this is just an example of dangers of using fixed-range numbers. How about using floats?? What happends if you put your fancy CCD-camera in direct sunlight? Your Cray blows up? :-) > Having infinite precision in one number is equivalent in power > to having infinite # of (sequentially accessible) bits of memory. > (of course) Yes, of course! What a scientific breakthrough! WOW! But exactly becouse of this they use a rotated '8' - symbol in mathematics and exponents for smaller numbers. B-> > Hence, discrete devices should have no problem simulating such > neurons. ARGH! Not again! There is a BIG difference between discrete in quantity and discrete in time/space, computers are f*cking discrete in time/space!!!!!!! > Simply set the smallest delta between two numbers in > your representation to 1/2 the relative inaccuracy of the neuron > between two different presentations of the same stimuli. How can you assume that we would have the same accuracy (smallest delta) in the first (test) and the second (actual use) representation/simulation? Why represent the same stimuli to the both simulations if the first one already has processed it? I can understand why someone wants to run speed tests in computers, but this sounds suspicious... Did I understand your message clearly or why does it sound so suspicious? Sorry about flames, but I'm sorry if I misunderstood you (hopefully...). ------------------------------------------------------------------------------- Marko Gronroos ! Tel. +358-21-445613 ! Karvataskunkatu 10 H 100 ! ! Computer Scientists do it 20610 Turku ! ! with bigger hardware. Finland ! ! ------------------------------------------------------------------------------
sarima@tdatirv.UUCP (Stanley Friesen) (04/08/91)
In article an article DOCTORJ@SLACVM.SLAC.STANFORD.EDU (Jon J Thaler) writes:
<One thing that has always bothered me about the comparison between
<computers and brains is that (most) computers are finite state machines,
<while it is not obvious to me that brains are.
In my biologist persona, I rather tend to disagree. The brain appears to
me to be quite discrete. It is simply not *binary*. Why you ask?
Let me preset a few simple facts about neurotransmission.
1. Firing of a neuron is an all or none response. There is no such thing
as weak or strong signals.
2. A neuron may only fire up to a certain maximum rate, due to a refractory
period after each firing.
Thus the behavior of a neuron is in fact directly mappable onto a discrete
system. As near as I can make out from my reading on the subject a single
neuron encodes its data in *unary* rather than binary.
< It is well known that
<mathematical modelling of continuous systems on disctrete lattices
<will miss some classes of solutions entirely, so I have trouble following
<the arguments based on analogies between computers and brains. Can someone
<out there shed some light on this for me?
As near as I can tell all relevent properties of neurons can be adequately
modeled by discrete mathematics.
--
---------------
uunet!tdatirv!sarima (Stanley Friesen)sarima@tdatirv.UUCP (Stanley Friesen) (04/11/91)
In article <MAGI.91Mar28191353@polaris.utu.fi> magi@utu.fi (Marko Gronroos) writes: >32 bits? Integer? Not floating point? > How about sight? You can see the Sun, which is -27 magnitudes, and a >galaxy that is +6 magnitudes. The brigthness difference is 32 >magnitudes ==> approx. 10^13 ==> 10 000 000 000 000. 32 bits is only >4 294 967 296. > Ok, ok, neurons don't fire 10 000 000 000 000 times as fast when >watching the Sun than when watching a star, but this is just an example >of dangers of using fixed-range numbers. How about using floats?? This is an invalid argument. It is easily established that human sensitivity to light (and to most other stimuli) is *logarithmic* is nature. This is why the magnitude scale is logarithmic. Thus the brain hardly needs to encode such large 'values' as 10,000,000,000,000, it need only encode, say 13 (or perhaps 27). And indeed this appears to be what it does, the values I suggested fall within the observed range of variation in firing rate of neurons. Thus it appears that a single *byte* would be sufficient to encode the data transfered by a single neuron! Essentially the brain seems to use about one digit of mantissa and about three or four digits of exponent. A sort of 'short float' format. >Yes, of course! What a scientific breakthrough! WOW! But exactly >becouse of this they use a rotated '8' - symbol in mathematics and >exponents for smaller numbers. B-> Quite, and this is also essentially what a neuron does. Each neuron has a resting firing rate that could be said to represent an exponent of zero, with a depressed rate representing a negative exopnent and an increased representing a positive exponent. The maximum firing rate, determined by the refractory period of the neuron, represents machine infinity (i.e. MAXVALUE) -- --------------- uunet!tdatirv!sarima (Stanley Friesen)