Re: Computation and Cognition

From: HARNAD Stevan (
Date: Wed Mar 13 1996 - 13:57:42 GMT

> From: "Nottingham Andy" <>
> Date: Wed, 13 Mar 1996 11:31:20 GMT
> It seems that all we have been doing with computation is showing what
> a computer can do and how it can simulate what a person does.

Actually, in showing that a computer can do what a person does we have
shown HOW something, anything, can do what a person can do. Until we
showed that, we had no idea how anything at all could do what people
can do.

If you think the computer is somehow not doing it the "right" way, you
need to give reasons and evidence. The fact that it's a computer, doing
computation, isn't a reason or evidence, because we don't know how
brains (or anything else) do it. If one doesn't know how it IS done, how
can one say how it ISN'T done?

> Isn't this just like behaviourists watching rats run a maze in order to
> study human behaviour. The only conclusions in that kind of study are
> how the rat behaves, and in computation the only conclusions are how
> a computer does things.

The differences is that behaviourists described merely WHAT the rats
did, not HOW. When a computer does something you can do, we also have
(at least one) explanation of HOW it can be done. "One" sounds better than
"none"; and unsually the only way to reject one explanation is by finding
another one that does at least as well.

> A computer processes all information as 0's or 1's or combinations of
> these characters. In a person surely it is not just a case of neurons
> firing and not firing but also the rate at which they fire, which
> possibly adds another dimension to human computation

Yes, but the rate of firing is just another quantity, which could just
as well be a symbol. There are many ways to build a computer; most
computers use a location code: information is stored in registers. But
they could just as well use a frequency code. That's the remarkable
thing about symbols and codes: Their "shapes" don't matter. Only the
rules for manipulating them ("algorithms") matter.

So the fact that brain signals vary in frequency is no more evidence
AGAINST the idea that the brain is a computer than the fact that neurons
fire in an on/off way is evidence FOR the idea that the brain is a
computer. There are many different kinds of computers, just as there are
many different codes, and symbol-shapes. The relevant thing is not the
hardware, in computation, but the software, i.e., the symbols and rules. The
hardware details do not matter. What matters is what the symbol system
does: what the symbol manipulation rules are doing. What physical
"shape" they happen to take is irrelevant, because their shape is
arbitrary in relation to what they represent.

But there is ONE way in which the firing frequency of the brain might be
a hint that there's more going on in there than just computation:
Remember what I said about analog processing? Suppose the task is to say
whether or not pairs of acoustic frequencies (sounds that differ in
pitch, i.e., in how fast they are vibrating) are the same. And suppose
the brain represents frequency with an analog code, as frequency. That
means a higher pitched sound would make a neuron fire faster and a low
pitched sound would make it fire slower.

If that were true, then the task of matching frequencies could be done
without symbols, just as matching picture shapes can be done without
symbols, by analog processing alone. If two neurons fired at the same
frequency, the sounds would be reported as matching, otherwise as not

In reality, the brain does not happen to represent sound frequency as
neuron firing frequency. It instead translates the sound frequency into
a spatial representation: Higher pitched sounds activate a higher part
of the cochlea, which is part of the inner ear, and lower pitched sounds
activate a lower part of the cochlea. The representation is still
analog, though, because the spatial representation has the same property
I described for the grid onto which the shadow of a visual object is
projected: It preserves the "structure" or "geography" of the object.

In the case of the visual shadow, you have an object, and you have its
shadow (image, analog representation). The middle point of the + shape
is physically above, below, to the left and to the right of other parts
of the + in both the object and the image. The same is true of the
cochlear "image" of acoustic pitch, except higher and lower pitch has
been transformed into higher and lower parts of the cochlea: An acoustic
property has been smoothly transformed into a spatial property, but the
resemblance is preserved, in that the structure or topography is still

This kind of a transformation is called an analog transformation.
(You may recognise it as an "isomorphism" or point-to-point mapping,
from mathematics.) The mapping from object to image is point-to-point
("retinotopic," in the case of vision) and preserves all the
point-to-point "topography" around each point. It doesn't matter that
acoustic points have been transformed into spatial points. The
structural resemblance is still there. And so is the causal connection,
because analog transformations can usually be inverted: You can transform
the object into the image, and you can inverse-transform the image into
the object. In the brain there is usually a series of analog
transformations. There are over fifteen copies of the retinotopic map,
higher and higher in the brain, and there are also higher analogs of the
cochlear map, as well as of the body-image map (which is also called
the somatosensory "homunculus," a "good" homunculus, because it is
merely an analog map of the body, not to be confused with the "bad"
homunculus that we are trying to avoid in explaining the mind, because
it too would have to have a mind, which would have to be explained; no
such problem with the little body-image maps in our heads).

It is analog representation in the brain that is the real rival to
computation, not frequency coding. And oddly enough, it is through
computer simulations that Kosslyn and others have shown that analog
processing can, like symbol processing, do some of the things people
can do, without any need for a homunculus.

Computers can simulate even things that are not computers: A computer
can simulute the air, and it can simulate an airplane, and so it can be used
to design and test new airplanes that we have not yet built. Once
tested by computer simulation, such a plane can be successfully built
the first time we try, and if the simulation has managed to anticipate
all of the relevant properties of air and flight (if the "picture" has
been described by enough symbols and symbol manipulation rules, and
described correctly), then the plane should not even need to be tested,
because it has ALREADY been tested by simulation.

In practice, computer simulation alone is not quite enough in airplane
design, but the point is that simulation can even give us information
about noncomputational structures and process, like airplanes and
flying. That's how it can also give us information about analog
processes like mental imagery.

So Kosslyn has shown that cognition is not just computation; it may be
analog processing as well.

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