From: Ben Houston (email@example.com)
Date: Thu May 17 2001 - 11:41:18 MDT
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:
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
> -----Original Message-----
> From: firstname.lastname@example.org [mailto:email@example.com] On
> Of my_sunshine
> Sent: Thursday, May 17, 2001 9:09 AM
> To: firstname.lastname@example.org
> Cc: email@example.com
> 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
> >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
> (1) I did not mean to imply, by my message, that a brain-like
> component was necessary to implement AI, but merely one option.
> (2) I am not a neuroscientist and am not up on cutting-edge knowledge
> neural operations, but this is what I meant by "Fourier computing"...
> (3) First, take a look at how the semantics of digital logic are
> 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
> 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
> 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
> 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
> in which the fundamental frequency of o is a (logical) function
> fundamental frequencies of v0 and v1.
> This is the important part: Any variable in the fourier
> 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
> outputs. Note that, in this perspective, frequency, amplitude,
> phase can all be given significance. What we have done is
> different semantic mapping to v by transforing v(t) into the
> This is, in some cases, how the human nervous system puts
> use. When sensing heat, for example, (using v = a1 cos w1) it is
> the value of a1, but the value w1, which conveys to the brain
> intensity of the heat. It is *more rapid*, not *more intense*,
> neuron firing which indicates a sensation of greater heat.
> 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
> (ask any EE), electronics which operate in this manner can be
> build entire computers. This is what I meant by "Fourier
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