X-Message-Number: 15312
References: <>
Date: Wed, 10 Jan 2001 19:12:59 +0000
From: "Joseph Kehoe" <>
Subject: Turing rides again

>Hi everyone!
>
>Someone other than Mike Perry also seems hypnotized by Turing machines.
>He claims that a human brain could be imitated (if I read him right)
>by a single fast processor. While a very small brain could probably
>be imitated, it doesn't follow from that that much larger brains
>could be so imitated. The problem becomes exponentially harder the
>more neurons used. I would like to see his explicit calculations on
>this issue.


This may be true but not necessarily if neurons only form connections to local 
neurons.

This would be less than exponential growth if that were the case. I am not an 
expert in Brain

biology but I believe this to be the case.  If each neuron had a limit of 
neurons that it could

connect to then growth would be less than NP which means there is no theoretical
barrier to

our imitating it on a single processor. A brain twice as large as mine does not 
imply each

neuron has twice the connections just that there are more neurons with a similar
amount of connections each.

A fully interconnected graph grows exponentially but the brain is not fully 
connected and is made

up of local regions (a neuron can only connect to another neuron if it is within
a certain radius-
radius size is not that important)

Then the graph grows at the rate of the SUM of each subgraph.  As long as each 
subgraph

is not exponential (guaranteed by the limiting radius) then the entire graph 
cannot be exponential.


If someone can show that there is no upper limit on the number of connections a 
single neuron can make then this argument falls flat but I doubt anyone can (any
brain surgeons on this list?;-)).


Also using one of the off the shelf hardware solutions would provide speed ups 
of an order of magnitude or more.

I do not remember who sells them but they used to slot into your PC and run NN 
simulations very fast.

Whether the hardware is a parallel processor, single processor, or specialised 
NN simulator does not
really matter we can use whatever we prefer.


>He also disliked what I said about another issue which may affect
>whether or not a Turing machine could imitate a human brain: he claimed
>that imitations showing growth and loss of neurons and changes in their
>connections had already been implemented. Again, I'd like to see his
>references. The work on computer models of brains is one which I
>try to follow myself, not because I believe that computers (as we
>know them now) could imitate complete brains but because it does
>produce one way to test our ideas about how brains do various
>operations.


The paper was a technical report from - U. of Stanford Cal. (I think) but I read
it about 6 years ago in a previous existance as a lecturer and cannot find it 
now as I put all that stuff in storage (somewhere).

The idea is fairly simple. Once a node connection strengths all go down to zero 
it is dead. Using a sigmoid squashing function we would let it approach zero but
never actually get there, then it is (practically) dead but can regrow over 
time.
The simplest approach.

Start off with N nodes each with K connections where N and K are the max limits 
of what is possible.

e.g. if a human has a maximum of 400000000 neurons over her lifetime and each 
neuron can have a theoretical (biological) max of 50000 connections to its 
neigbhours  then let N=400000001 and K=50001.

Set the unused connections to ~0 and the used connections to their appropriate 
strengths. Run the sim.  Each node can approach the max no. of allowed 
connections if needed and the number of nodes can approach the max if needed 
also.
To remove a node set its connection strengths to ~0
To create one pick one with connections near 0 and let it increase in strength.
All this should happen automatically using old fashioned back propagation

I have not done any research on NN in a lonnnggg time so please don't ask for 
details.  You should find them in most NN books.

>I will finally point out that in my discussions I have quite deliberately
>NOT claimed that we could not produce a device which imitated the
>workings of a human brain. That's not what I'm talking about at all.
>I have suggested problems with producing COMPUTERS which imitate
>human brains COMPLETELY ... at least any computers as we now know
>them. The question I am raising is that of whether or not Turing
>machines provide an adequate model for ALL thinking/feeling machines.
>Of which human beings provide one case (and note that I did not
>say "thinking" or "feeling" alone).


This all seems reasonable. I do not claim Turing machines can reproduce brains 
just that I have not heard of a theoretical obstacle that we know of that 
disallow them to do so. Time will tell.  I believe that they may do so within 
the next couple of decades but you never can tell...

Developing a conscious machine will prob. be easier than a machine that imitates
a human intelligence perfectly (or as near as).


>And no, our present machines fail utterly to match living things
>on some characters essential to living in the real world: self-repair
>one of the most outstanding ones. Without self repair an independent
>creature isn't going to survive very long at all.


True but writing a self repairing Turing machine (on paper) does not seem that 
dificult a task. Reproducing turing machines are  easy enough so a self 
repairing one that uses checksums to correct errors on its own input tape would 
seem easy enough. (The turing machine is the tape - input tape=DNA) Just don't 
ask me to do it I am way past the stage of being able to write those things out 
quickly.


Reproducing Turing machine - a set of input symbols that contains instructions 
for the machine to make copies of itself and repeat.... (I believe we did one in
college eons ago but not too sure)

Self repairing - the sequence of symbols contains instructions for the machine 
to check the checksum and use that to repair any errors. You could also tell it 
that once it has run the checksum it should reproduce itself if you wanted.

Joseph.

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