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*> From: "Bollons Nicholas" <NSB195@psy.soton.ac.uk>
*

*> Date: Mon, 11 Mar 1996 16:47:49 GMT
*

*>
*

*> Some form of hypothetical propositional 'language' seems to be a lot
*

*> more plausible explanation than any 'on off' binary system.
*

A bit of a misunderstanding here: A binary code (for example, morse

code) IS propositional. The issue is about analog images (copies) vs.

arbitrary symbolic codes (computations), not binary vs nonbinary codes.

A binary code can express anything any other arbitrary code can express.

Arbitrary means it doesn't matter what the SHAPE of the symbols is; all

that matters is the rules for manipulating them. Remember the formula

for getting the roots of quadratic equations (X = -b =/ SQRT(b**2-4ac/2a):

It doesn't matter what symbols you use for "X" or "b" or "+": in fact,

it could all be written in binary code, as just 0's and 1's, though it

would be more complicated.

All these differences are just differences in the NOTATIONAL system, the

arbitrary symbols you choose to use. It's exactly the same as with

language: In English we call apples "apples," but we could have called

them "pommes," as in French, or we could have called them "X" or even

"011011000," or whatever it would be in morse code. The shape of the

symbols is arbitrary and does not matter: the symbols neither resemble

nor are causally connected with what they represent (stand for, refer

to).

With analog images, on the other hand, the shape of the image DOES

matter. A picture of an apple resembles an apple; it does not resemble

"apple" or "01101100001."

*> There is no way the divergence and mass of sensory input could be
*

*> explained in any 2 dimensional method.
*

Dimensions don't have anything to do with the binary/nonbinary

distinction. Binary code (0,1) is not 2-dimensional; it just has 2

symbols.

On the other hand, it is very possible that 2-dimensional"shadows" of

apples on our retinas, and further analog copies of that 2-dimensional

shadow higher up in or brains (the so-called "retinotopic" or analog

copies of the retina that I will talk a little about on Wednesday)

COULD encode all of our diverse sensory input.

A binary code would be symbolic, an analog copy would not be. If your

retina were divided into an on/off grid, the way the screen of a

computer is, then every "shadow" on it could be coded as a string

of 0's and 1's: 0's for every part that is dark, 1 for every part that

is light. Imagine a + shape projected onto a 5x5 grid. There are 1's

in the cells of the grid where the + casts a shadow, 0's everywhere

else:

00100

00100

11111

00100

00100

The rows of this grid could then be made into one very long line.

0010000100111110010000100

This line could be used as a binary code for reconstructing the +

on the grid, as long as we (arbitrarily) interpreted the first 0

as representing the upper left corner of the grid, the second 0 as

representing the 2nd..., the last 0 as representing the bottom right

corner.

Now look at the original +. Do you notice that right in the middle of

it, there is a 1, with a 1 above, below, left and right of it? Now look

at the long row that represents the grid. What has happened to this

above/below/left/right relationship? It's gone. At least it is no

longer visible (because the long row does not RESEMBLE the +, it merely

REPRESENTS it, as long as we use the arbitrary code, according to

which, say, the sixth binary symbol represents the beginning of the

second row of the grid. (Exercise: Which binary symbol in the long row

represents the middlemost 1 of the grid?)

The long row (also called a "vector") represents the "+" shape

symbolically: It does not resemble the +. There are merely rules that

can be applied to the otherwise arbitrary shape and position of the

binary symbols in the vector so that you can INTERPRET it as the +, and

indeed you can even use it to reconstruct the + if you want to.

Now consider what we would have had if the + had merely cast its shadow

on another surface. The other surface would look very much like the

original +. In particular, there would be a middle-most part of the

shadow that also had above, below, left and right of it parts that were

the same shapes as the parts that were above, below, left and right of

the corresponding middlemost part of the original +.

The shadow is an analog copy of the +, and it preserves the +'s spatial

shape. The binary vector does not preserve the shape, though it

preserves all the information ABOUT the shape (so you could reconstruct

the shape from it, and you could do other operations on it from which

you could figure out things about the shape -- for example, whether or

not the +'s shadow touches the bottom right corner of the grid (the part

that is represented by the last binary digit of the vector). Does it?

The fact is that although a symbolic code is arbitrary in its shape and

an analog copy is not, the symbolic code can DO just about anything the

analog copy can do (though not necessarily as simply or as efficiently).

A picture is worth a thousand words, but if you use enough words, you

can describe as much of a picture as you need to. Words can do

everything pictures can; you may just need a lot more of them to do it.

Can pictures do everything that words can do? The answer is no: The fact

that a picture's shape is not arbitrary, the fact that it resembles what

it represents, is both an advantage and a disadvantage: It allows you to

do certain things much more simply than with symbols (for example,

decide whether or not one shape overlaps with another, or matches it

when rotated); but it does not allow you to SAY anything. Symbols

describe; pictures merely depict. Many things cannot be expressed by

pictures. For example, how would you have explained what I've been

trying to explain in this message, by using only pictures, rather than

symbols, as I did? (I only used a picture once: to illustrate the +

grid.)

The power of both English and of mathematics and other forms of

computation is the power of symbols: strings of objects (e.g., 0's and

1's) whose shapes are arbitrary but can be used to express anything

that can be expressed in words. To express something in words is to

PROPOSE something. A proposition is a statement, whether in English or

in maths ("the cat is on the mat," "1 + 1 = 2"). Propositions are either

true or false, whereas pictures are neither "true" nor "false," they are

merely pictures. They are not saying anything. (Remember what I said

about Magritte's picture of the pipe and the statement about the pipe?

Pictures are not statements.)

*> How, for instance would you
*

*> process hearing and sound ? No 00010's could be used to represent the
*

*> individuality of all the pitches and tones used in music.
*

Yes they could. A picture (or sound) may be worth a thousand symbols,

or even more, but if you use ENOUGH symbols, you can represent the

sound as close closely as you like. (Think of the Mona Lisa -- in just

black and white, to make it simpler -- represented as a very long

vector of 0's and 1's: Not a single detail would be missing; all the

information about the Mona Lisa would be there. In fact, you could use

the code to make a machine draw the Mona Lisa a million times. It's

just that the code itself, the long vector of symbols, from which the

picture could be drawn, would not itself resemble the Mona Lisa; it

would merely represent it, symbolically.)

So it need not be true that the brain's "code" is analog: It could be

symbolic (propositional), as Pylyshyn suggests. The retina, after all,

is really just a huge grid, and the rods and cones in it could be like

binary 0's and 1's. (They're not, as it turns out, but not because

symbols couldn't have done the job; in computer screens' bit-maps they

DO do the job.)

*> A form of 'logical language' (Kosslyn's pseudo English) would work in
*

*> well with the use of A.I in research, as both human and computer
*

*> would seem to use a language for coding input and performing output
*

*> with the language as the medium for both.
*

Not sure what you mean here. The fact is that Artificial Intelligence

(AI) uses mostly just symbols and rules. And using symbols and rules, it

can do many (perhaps all) the things people can do. This power of

symbolic computation is part of what made people like Pylyshyn and

Fodor conclude that computation is what the brain does too -- that

symbols are the "language of thought." Kosslyn (and Anderson, cited in

Kosslyn's chapter) replied that although symbols COULD do it all, there

seems to be evidence that in people's brains there is analog processing

going on too, and that this is not surprising, because in certain cases

analog processing would be more efficient than symbols and computation.

Shepard's mental rotation (also described in the Kosslyn chapter) is a good

example.

*> We all know that a computer does not have a Homunculus (for if it
*

*> did it would also probably have a mind)
*

It's supremely unlikely that a computer has a mind; so a homunculus is

not a problem for computational explanations of the mind. But does it

have to be a problem for imagistic (analog) explanations? The answer is

that analog processing is also possible without the need of a homunculus

to "see" the picture. A machine could do internal rotation and matching

of analog "shadows" without any more need for a homunculus to "look at"

the internal images than there is a need for a homunculus to understand

the internal symbols in a computer.

*> But it does have something
*

*> very similar to one - A Central Processing Unit (C.P.U). This in
*

*> practise processes all the internal information of output and input
*

*> from a variety of different areas.
*

The computer's CPU is not like a homunculus; it's a purely mechanical

device that is designed to switch circuits, i.e., manipulate 0's and 1's

on the basis of their shapes, much as when you mindlessly calculate the

roots of a quadratic equation. All of that can be done mechanically. No

need for a homunculus at all.

*> Could some processing unit exist
*

*> in the brain other than the homunculus ? Processing data in a
*

*> logical and computational way ? Brain Imaging (using P.E.T) has
*

*> identified certain areas that are active during certain functioning
*

*> (retinotopical mapping). This makes the brain a multidimensional organ
*

*> in which different areas perform different functions just like in a
*

*> computer. Could these areas then portray to a C.P.U which processes
*

*> information or data. A logical Homunculus ? Is there any data to
*

*> indicate the physical existence of such a thing ?
*

You've confused a few things here: Computation is the manipulation

of symbols with arbitrary shapes, on the basis of rules. Retinotopic

maps in the brain are analog projections of the retina, so their shape

is NOT arbitrary. Internal rotation of these analog shapes would not be

symbol manipulation, it would be analog processing.

Dimensions have nothing directly to do with the symbol/image

distinction. The brain does, however, represent 3-dimensional space,

and might do it in an analog or a symbolic way, or both. It also

represents many other dimensions of sensory variation (sounds, smells,

etc.), and, again, could do it either way. If we are to explain HOW our

brain does all those things, and use that to explain our minds,

however, then we need to find an explanation that does NOT require a

homunculus in there, looking at the images or understanding the

symbols, otherwise our work starts all over again, as we try to explain

how IT's mind works...

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