Re: How can I tell if F is a string or if it is a number?

In article <c3d12d4f-028d-4568-87eb-c7254c6f2a39@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Pioneer1 <1pioneer1@xxxxxxxxx> wrote:
Okay, I read your earlier post again. My only question is about the
ambiguity of the equality sign in physics. One of the meaning of the
equality sign is that it says, "any time you see ma you can replace it
with F." But, as I understand it, it also defines a proportionality.

Let me try to restate your question using somewhat more standard terminology.
Your question is whether the symbol "F" is merely an *abbreviation* for the
longer expression "m*a".

The answer is no. There isn't any way to "test this mathematically"; you
just have to learn what notational convention people are using.

The fact that, during calculations, you can substitute "F" for "m*a" or
vice versa does not in itself imply that "F" is an abbreviation for "m*a".

It may help to think of the situation this way. Acceleration and force are
separate physical concepts. Acceleration is the rate of change of velocity.
Force is a more slippery concept but intuitively we all have a sense of what
the force of gravity or a magnetic force is. From the standpoint of pure
logic, there is no necessary connection between force and acceleration. The
fact that, in the actual universe that we live in, force is proportional to
acceleration, is somewhat surprising. Logically, things could have turned
out otherwise; it's only empirically, by performing experiments, that we
know that force is proportional to acceleration. This empirical observation
is known as Newton's second law of motion: F = m*a.

The assertion that F = m*a is therefore telling us something about the
universe that we happen to live in. If "F" were just an abbreviation for
"m*a" then that would be just a purely logical fact and would not tell us
anything about what physical laws happen to hold in our universe.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
.

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