**From:** Ben Houston (*ben@exocortex.org*)

**Date:** Thu May 17 2001 - 11:41:18 MDT

**Next message:**Eliezer S. Yudkowsky: "Re: PHYSICS/SPACE: Legitimate time traval proposal"**Previous message:**my_sunshine: "Re: Fourier computing?"**In reply to:**my_sunshine: "Re: Fourier computing?"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Hi Dave,

Interesting... I do see what you are talking about but it doesn't seem

to be that related to observed neural codes.

Here is a book that I've been reading recently -- just found it a month

ago. It's got pretty good descriptions of what neuron-firing actually

represent and how people are implementing mathematical models of such:

http://eliza.cc.brandeis.edu/abbott/book/

If you want to discuss anything in the book send me an email -- I think

that I've got a grasp now on most of it but talking about it is always

helpful.

Cheers,

-ben houston

http://www.exocortex.org/~ben

*> -----Original Message-----
*

*> From: owner-sl4@sysopmind.com [mailto:owner-sl4@sysopmind.com] On
*

Behalf

*> Of my_sunshine
*

*> Sent: Thursday, May 17, 2001 9:09 AM
*

*> To: sl4@sysopmind.com
*

*> Cc: sun@faclib-0119.unh.edu
*

*> Subject: Re: Fourier computing?
*

*>
*

*> This still seems (at least borderline) relevant to sl4...
*

*>
*

*> First, let me say two things, then I'll answer your question...
*

*>
*

*> >neurons and their respective neural codes. I have never heard of
*

*> >Fourier computing though. And, I was until now unaware that there
*

was a

*> >need to "invent the kind of component which the human brain uses." I
*

*> >guess I have been in the dark about something -- could you fill me
*

in?

*>
*

*> (1) I did not mean to imply, by my message, that a brain-like
*

computing

*> component was necessary to implement AI, but merely one option.
*

*>
*

*> (2) I am not a neuroscientist and am not up on cutting-edge knowledge
*

*> about
*

*> neural operations, but this is what I meant by "Fourier computing"...
*

*>
*

*> (3) First, take a look at how the semantics of digital logic are
*

mapped to

*> voltage levels:
*

*>
*

*> Operands: binary voltages
*

*> # we map voltage intervals to boolean values...
*

*> (0.5 V <= v <= 1.5 V) -> boolean(v,1)
*

*> ~(0.5 V <= v <= 1.5 V) -> boolean(v,0)
*

*>
*

*> Operations: logic gates
*

*> # we map the domain (v0,v1), through a logical function, to a
*

range

*> (o).
*

*> boolean(v0,0) A boolean(v1,0) -> boolean(o,0) # logical OR
*

*> boolean(v0,0) A boolean(v1,1) -> boolean(o,1)
*

*> boolean(v0,1) A boolean(v1,0) -> boolean(o,1)
*

*> boolean(v0,1) A boolean(v1,1) -> boolean(o,1)
*

*>
*

*> But, neurons don't work like this...
*

*>
*

*> Let's take a first-order fourier decomposition of v:
*

*> v(t) = a1 cos w1*t + noise... and disregard the value a1
*

*>
*

*> Remap operands:
*

*> (30/s <= w1 <= 40/s) -> boolean(v,1)
*

*> ~(30/s <= w1 <= 40/s) -> boolean(v,0)
*

*>
*

*> Remap operations:
*

*>
*

*> We can symbolically expand any line (all lines) of the logic
*

table:

*> i.e., boolean(v0,0) A boolean(v1,0) -> boolean(o,0) becomes
*

*> ~(0.5 V <= v0 <= 1.5 V) A ~(0.5 V <= v1 <= 1.5 V) ->
*

*> ~(0.5 V <= o <= 1.5 V)
*

*> and so on until the truth table has been expressed as a
*

*> (complicated)
*

*> piecewise function o = logicalOr(v0,v1).
*

*>
*

*> Likewise can we construct o = logicalOr(v0,v1) using the fourier
*

*> interperetations of v0, v1, and o. It would look something like:
*

*> ~(30/s <= w0 <= 40/s) A ~(30/s <= w1 <= 40/s) ->
*

*> ~(30/s <= o <= 40/s) ....
*

*> The piecewise function o = logicalOr(v0,v1) can thus be
*

constructed

*> in which the fundamental frequency of o is a (logical) function
*

of

*> the
*

*> fundamental frequencies of v0 and v1.
*

*>
*

*> This is the important part: Any variable in the fourier
*

*> decomposition
*

*> of a function f(x) can be used to carry data, i.e.:
*

*> v(t) = a1 cos (w1*t+p1) + a2 cos (w2*t+p2) + ...
*

*> a1, a2, w1, w2, p1, and p2 can all be used to encode inputs and
*

*> store
*

*> outputs. Note that, in this perspective, frequency, amplitude,
*

and

*> phase can all be given significance. What we have done is
*

employed a

*> different semantic mapping to v by transforing v(t) into the
*

time

*> domain.
*

*>
*

*> This is, in some cases, how the human nervous system puts
*

neurons to

*> use. When sensing heat, for example, (using v = a1 cos w1) it is
*

not

*> the value of a1, but the value w1, which conveys to the brain
*

the

*> intensity of the heat. It is *more rapid*, not *more intense*,
*

*> neuron firing which indicates a sensation of greater heat.
*

Clearly,

*> the brain has some way of semantically mapping such frequencies,
*

*> since I can tell hot from luke warm from scalding....
*

*>
*

*> By constructing circuits which implement these mathematical
*

*> functions
*

*> (ask any EE), electronics which operate in this manner can be
*

used

*> to
*

*> build entire computers. This is what I meant by "Fourier
*

computing".

*>
*

*> Dave
*

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