From: Glenn Morton <glennmorton@entouch.net>

Date: Mon Jun 20 2005 - 21:32:36 EDT

Date: Mon Jun 20 2005 - 21:32:36 EDT

Thanks, David, I was hoping to elicit something from you.

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

*> From: D. F. Siemens, Jr. [mailto:dfsiemensjr@juno.com]
*

*> Sent: Monday, June 20, 2005 5:55 PM
*

*>
*

*> I'm breaking this up and considering just the one part in my response. in
*

*> order to avoid building up a massive file. This considers just the matter
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*> of math. I noted logic in a separate post.
*

*>
*

*> What follows in Glenn's post seems to me to take us out of math into
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*> physical theory. I want to stick to math. First, contemporary number
*

*> theory begins with the null class, which contains nothing, and goes on
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*> from there. I guess this could be viewed as constructing the whole out of
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*> nothing, but I rather think that there has to be a class in order to
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*> construct other classes, not to mention mathematicians to do the
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*> constructing. But a mathematical class is an abstraction, whether null or
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*> containing members. There are concrete classes, like the class of all
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*> Thomas Jefferson's descendants, recently perceived to be larger than
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*> earlier admitted. Note that the number that applies, yet unknown, is a
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*> class which is clearly different from the persons living, dead, and yet
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*> to be born, making up the physical class.
*

*>
*

*> What can I construct out of numbers? out of points, lines, plane figures,
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*> solids, hypersolids? alephs and omegas? Nothing! A scientists uses the
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*> various mathematical constructs to formulate theories that describe
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*> aspects of the universe, ideally.
*

If I understand your point here, you don't think that the universe can come

out of mathematics--I get this from the question and from the obvious

mention that one has to have mathematicians to do math. What can I construct

out of numbers?....Nothing!. It sounds like you are an inventionalist where

it comes to math. I would respond that you don't need mathematicians to do

math at all. Monkeys, do math, if you include counting as a subset of math.

They can count

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Human baseball players when chasing a ball do a form of complicated internal

calculus to put their hand where the ball will be. Chimpanzees, when

hunting monkeys, have been observed to calculate where the monkey will be

and go there. That is a form of math. So, math is not something that exists

only because mathematicians exist.

The point with both the math and logic part of that essay were that math and

logic had to exist at the very beginning. If it came out of nothing (and

nothing lacks an ability to store such information) one has a problem.

Biochemical systems are mathematical information processing machines. They

have internal clocks (another form of math before mathematicians). The laws

of gravity are also mathematical in nature. So math seems to pre-exist

mathematicians.

*>But who confuses E=mc^2 with any part
*

*> of the word she lives in? Everybody but a few folks who have an ax to
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*> produce /ex nihilo/ in order to grind it separate description from
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*> construction. There are various spots where /creatio ex nihilo/ is
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*> tacitly called upon without acknowledgement of the Creator.
*

Actually physicists discussing the origin of the universe start with the

mathematical laws in order to derive the creation of the universe. So, I

would suggest that at least that class of people "confuse" the laws that

lead to E=mc^2 with the existence of the world in which they live, as well

as the mathematicians who are Platonists.

Concerning the last sentence, calling upon creation ex nihilo without

tacitly calling upon a creator is done all the time, but I can't see what

ontological importance you place on such an activity. From your logic

portion,

I would presume that you think one can't derive the universe from

mathematics because it too should be a category mistake. However, that may

support my case in that physical theory almost always starts discussion of

the creation with mathematics already in existence?

Given that some suggest that mathematics is built on the structure of our

brains and has no more reality than the self delusion of seeing patterns in

snow on the TV (which actually happens).

From your Logic reply:

*>While it is true that bits have physical exemplification, I see this as
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*>essentially analogous to geometry's essential pieces. A point A and line
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*>AB have the same area and the same volume, 0. But the diagram drawn to
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*>represent these entities has a finite area and a finite volume, whihc is
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*>ignored. A polygon ABCDE has an area, but the volume is theoretically
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*>still 0. The physical exemplification of the bit is concrete, but the
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*>intent of the bit is purely abstract.
*

Given the deep connection between information and entropy, I would beg to

differ that information is purely abstract. When you compute on a computer

and store everything in memory, no entropy is created, the universe's

entropy remains constant. But, when you destroy the information, that is

when entropy rises. Entropy is lost information and if entropy is physical

then so is information.

*>
*

*>There is a further problem, the assumption that logic is strictly
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*>digital. But none of Aristotle's three calculi are digital. They cannot
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*>be translated into contemporary calculi. Further, "true" is not a bit,
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*>though it can be represented as a bit in some metalanguages. But this
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*>gets us into some high-powered abstractions.
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*>
*

I really don't want to defend Zeilinger's idea but it was one that needed to

be included because somehow, the universe acquired logic and the universe

acquired math--even before the existence of logic. Zeilinger's hypothesis

would have to be considered.

*>Most formalized logics involve two values, which can be represented by 1
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*>and 0--true/false for statements, valid/invalid for arguments. But then
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*>there is the little problem of wffs, which are totally content dependent.
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*>An extension of this notion leads to fuzzy and multi-valued logics, which
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*>clearly are not amenable to encapsulation in bits. Related problems have
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*>been discussed for the language available in familiar logics. The classic
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*>term is "bald," which does not allow a sort into two bins. the
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*>requirement for valid arguments.
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*>
*

*>Finally, logic is abstract, but the universe is concrete. Perhaps one can
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*>construct a weird version of Berkeley's idealism out of nothing but
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*>logic, but I doubt it. Even the bishop required God as the source of all
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*>impressions. To state the problem differently, to try to construct the
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*>universe out of bits is to make a gross category mistake.
*

Logic is also fuzzy as you noted. You are referring only to the classical

type of logic where one has true/false. Fuzzy logic the truth values vary

from 0 to 1. And quantum logic is even fuzzier. Due to superposition, a

quantum computer can represent 4 or more numbers simultaneously. So just

because formalized logic is limited, it doesn't necessarily mean that

quantum logic is subject to the same limitations.

Do I think the universe comes out of logic? No, but the idea may not be as

big a category mistake as you think. We don't know why the universe is

'concrete' if we don't know why the universe exists, because to exist is to

somehow be concrete.

Received on Mon, 20 Jun 2005 20:32:36 -0500

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