Re: How can I tell if F is a string or if it is a number?
- From: tchow@xxxxxxxxxxxxx
- Date: 23 Apr 2008 17:34:14 GMT
In article <2beb583b-ae0e-4ebf-9f16-c6de8642867e@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Pioneer1 <1pioneer1@xxxxxxxxx> wrote:
On Apr 15, 12:08 pm, tc...@xxxxxxxxxxxxx wrote:
No. F is not an abbreviation, not even a meaningless one.
Okay. What is it? Does it have a meaning? If it does, its meaning is
not coming from observations. Then, where does it come from?
F stands for the numerical value of the force, where "force" is a concept in
our physical theory of the world.
No. ma is not an abbreviation for mR/T^2. F is not an abbreviation
for ma.
So why does it cancel? It's not a placeholder. It's not a temporary
variable. It's not a label. It's supposed to be a "physical" quantity
but it cancels out of formulas.
Canceling in formulas happens whenever you have more than one equation for an
unknown. Suppose you have two coins of unknown weight. By doing some
experiments you find that the difference in weight is 4 and the sum of the
weights is 10. So I can let X be the weight of one coin and let Y be the
weight of the other coin. I get the equations
X = Y + 4
X = 10 - Y
I can cancel out X to obtain the equation Y + 4 = 10 - Y, whence Y = 3
and X = 7. Does the fact that I have canceled out X mean that X is an
"abbreviation" for "Y + 4"? No. X is the weight of the coin. X = Y + 4
is not a definition, but a fact that you obtained from experiment.
Elimination of variables is just a mathematical technique for solving
equations. The fact that you can eliminate a variable doesn't mean that
the variable doesn't mean anything or is just an abbreviation; it just
means that you can make progress in *solving* the equations.
Perhaps you understand the coin-weighing example but still have trouble
making the leap to F = ma. So let's take another coin-weighing example.
Suppose I have a balance beam that has unequal length arms. One arm has
length A and the other arm has length B. If I put a weight X on one side
and a weight Y on the other side and they balance, then I have the "physical
law" AX = BY. Here we have an equation involving multiple variables. Does
this mean that "A" is an abbreviation for "BY/X"? No. A is the length of
the first arm. AX = BY is a generalization from many empirical observations.
It is not a mathematical identity, but a physical law.
What if I find some other physical laws that also involve A, X, B, and Y,
and that allow me to solve for these quantities by eliminating variables?
Would that mean that A suddenly becomes an abbreviation for "BY/X"? No.
A is the length of the first arm. Even if you manage to find some other
equation for A that allows you to eliminate A and solve for some other
unknowns, A continues to denote the length of the first arm.
--
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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