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Re: [Phys-l] Equations (causal relationship)



Hi Rick-
Good question, because it focuses on a major weakness in the teaching of math in this country.
What is algebra? It is a formal, systematic method of reasoning.
You start with a relationship (F=ma, or its differential, vector equivalent) and deduce consequences of that relationship. Using algebra, and obeying its rules, guarantees that the result is logically equivalent to the starting point. In this way you discover that a huge class of physical phenomena is consistent with that relationship. It is not that nature is obeying the rules of algebra, it is that your conclusions are correctly obtained if you correctly apply the rules of algebra.
Sometimes, of course, you reason correctly and obtain a result that is different from the physical result. When that exciting event occurs you are guaranteed that your starting principle was incorrect.
High school algebra teachers, many of them, have never learned that algebra is nothing but a system for reasoning.
Regards,
Jack




On Mon, 1 May 2006, Rick Tarara wrote:

Let me change something that I earlier presented BY BOLD ASSERTION to a
question, even though I risk the wrath and the ridicule of the demi-god(s)
of this list.

IS PHYSICS ALGEBRA?

Just because we write an algebraic equation to relate physical quantities,
do ALL THE RULES of algebra necessarily apply to the physics. Must nature
obey our artificial mathematical rules? Can't forces cause accelerations
even in the equation we have used to MODEL this can be rewritten to
_suggest_ that accelerations cause forces--or that nothing causes anything!
Does physical causality have to follow our attempts to represent the physics
with algebra?

Rick

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Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, Indiana
rtarara@saintmarys.edu
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----- Original Message -----
From: "John Denker" <jsd@av8n.com>

The criticism of my example is entirely without merit.
It looks to me like grasping at straws.

The community has a choice:
-- We can accommodate a few people who have strongly-held opinions, or
-- We can rely on the axioms and bedrock principles of mathematics.

I've always had good luck going with the principles. I recommend we go
with the principles.


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