Posted by
glen e. p. ropella-2 on
Nov 01, 2009; 4:43pm
URL: http://friam.383.s1.nabble.com/Crutchfield-s-Is-anything-ever-new-tp3917261p3927634.html
Thus spake Ted Carmichael circa 10/30/2009 03:33 PM:
> In response to Glen's comments, I would say that his differentiation between
> thoughts and actions is also a somewhat arbitrary choice of scale. I agree
> that how two people shoot a basketball is usually more easily translated
> between them than how they calculate the product of two numbers. When I
> shoot a basketball, I follow the same general procedure (knees bent, one
> hand on the side of the ball and one hand behind it, etc) that other people
> do. But my physical structure is still different than another person's, so
> I have refined the general procedure to better match my physical structure.
> (Or not, since I usually miss the basket.)
Yes, you're onto something, here. But I wouldn't consider it a matter
of general vs. specific for throwing a basketball. Any general method
you may think exists is an illusion. Let's say you're learning how to
do it from a coach and several fellow players. For each other person
you watch do it, their method is particular to _them_. In such a case,
there is no general method. You may _imagine_ some illusory general
method in your head. But when the method is executed, it is always
particular.
Now consider the coach's _description_ or model of the method. Even in
that case, the description, the words, the actions the coach executes
with his mouth and hands in an attempt to communicate an idea are
particular to him. The descriptive actions are particular to him. Even
in that case, there is no general method. Any general method you may
think exists is pure fiction. What matters is the particular actions.
Induction is a myth. [*]
It's not general vs. specific. It is abstract vs. concrete. You're
observation of either the coach's description or your fellow players'
methods is chock full of errors and noise. In order to cope with such
noise and translate from their actions to your actions, you have to fill
in the blanks. You are totally ignorant of, say, how fast to twitch
your eyes while you're maintaining focus on the basket... or how fast to
twitch your hand/finger muscles while holding the ball. You can't
observe those parts of the method when watching your fellow players.
And such information is totally absent from the coach's description.
So, you have to make that stuff up yourself.
And you make it up based on your _particular_ concrete ontogenetic
history. And, hence, when you execute the method, it is also particular
to you.
However, because your hands, fingers, and eye muscles are almost
identical to those of your fellow players and your coach, the method is
transferable despite the huge HUGE _HUGE_ number of errors and amount of
noise in your observations.
> Two different people calculating a product, however, may use two totally
> different methods. One person may even have a larger grammar for this,
> utilizing more methods for more types of numbers than the second person.
> (In effect, he has more of his brain dedicated to these types of tasks,
> which give him the power to have a larger "math" grammar.) So it's probably
> more precise to say: at a certain scale 'actions' can be mapped between two
> people but 'thoughts' cannot be.
It's less a matter of scale than it is of noise and error. When
calculating a product (or doing any of the more _mechanical_ -- what
used to be called "effective" -- methods), the amount of noise and error
in the transmission from one to another is minimized to a huge extent.
Math is transferable from person to person for precisely this reason.
It is _formal_, syntactic. Every effort of every mathematician goes
toward making math exact, precise, and unambiguous.
So, my argument is that you may _think_ that you have different methods
for calculating any product, and indeed, they may be slightly different.
But the amount of variance between, say, two people adding 1+1 and two
people throwing a basketball is huge, HUGE, _HUGE_. [grin] OK. I'll
stop that. Because (some) math is crisp, it's easier to fill in the
blanks after watching someone do it.
Now, contrast arithmetic with, for example, coinductive proofs. While
it's very easy to watch a fellow mathematician add numbers and then go
add numbers yourself. It's quite difficult to demonstrate the existence
of a corecursive set after watching another person do it. (At least in
my own personal math-challenged context, it's difficult. ;-) You can't
just quickly fill in the blanks unless you have a lot... and I mean a
LOT of mathematical experience lying about in your ontogenic history.
Typically, you have to reduce the error and noise by lots of back and
forth... "What did you do there?" ... "Why did you do that?" ... "What's
that mean?" Etc.
Hence, it's not a matter of scale. It's a matter of the amount of
error, noise, and ignorance in the observation of the method. And it's
not about the transfer of the fictitious flying spaghetti monsters in
your head. It's a matter of transferring the actions, whatever the
symbols may mean.
> If you go down to the lower level processes, all of our neurons behave in
> approximately the same ways. So at this scale they can be mapped, one
> person to another. I.e., when thinking, one of my neurons is just as easily
> mapped to one of your neurons as my actions are to your similar actions.
Right. But similarity at various scales is only relevant because it
helps determine the amount of error, noise, variance, and uncertainty at
whatever layer the abstraction (abstracted from the concrete) occurs.
Note I said "layer", not "level". The whole concept of levels is a red
herring and should be totally PURGED from the conversation of emergence,
in my not so humble opinion. ;-)
* I have what I think are strong arguments _against_ the position I'm
taking, here. But I'm trying to present the argument in a pure form so
that it's clear. I'm sure at some point in the future when I finally
get a chance to pull out those arguments, someone will accuse me of
contradicting myself. [sigh]
--
glen e. p. ropella, 971-222-9095,
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