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Re: [Phys-l] irresistible force v. immovable object



Here's an equally valid question:

What happens if a blorp comes into thermal contact with a slurg and all the
marfs are turned into storgs?

Who cares? There's no such thing as either an unstoppable object or an
unmovable object. Everything can be stopped and everything can be moved.
As John pointed out, this is not a physics question, it's a philosophy one.
Just so long as students understand the domain of the problem, you can tell
them whatever you want. Hell, go ahead and agree that the world will end.
But no matter what you tell them, it isn't physics.


On Wed, Feb 23, 2011 at 11:53 AM, John Denker <jsd@av8n.com> wrote:

On 02/23/2011 07:26 AM, Connie Tyree wrote:

A student posed the following question: What would happen if a
theoretically unstoppable object collides with a theoretically unmovable
object? He predicts everything...the world...would end. I know the world
will not end...what is the opinion of this group?

There are a couple of answers:

1) Philosophers have fussed over this question for thousands
of years. Feynman liked to use this example (among many
others) to argue that most philosophy is useless.

2) Questions like this come up all the time in physics. Newton
invented calculus in order to do physics, and in particular
to solve some physics problems that fall into this category.

3) There is a whole family of similar problems, including:
infinity divided by infinity
zero times infinity
zero added to itself infinitely many times
zero divided by zero
zero to the zeroth power
longitude of the north pole
hue of a black object
et cetera

Roughly speaking, the procedure for dealing with such problems
goes like this: Imagine a very large but finite force acting
on a very large but finite object. Do the math. Then imagine
an even larger force and an even larger object. Do the math
again, and compare answers. If you can show that the answer
must converge to some definite value, then we call that value
the _limit_ and take it as the answer to the question.

The answers are often surprising. Depending on details of the
physical situation, the answer could be zero, or one, or infinity.
Indeed it could be anything from minus infinity to infinity,
inclusive. So guessing is not recommended. You have to do
the calculation carefully, or you will get spectacularly wrong
answers.

Another possible answer is that the limit may not exist. For
example, in many situations, the longitude of the north pole
does not have any definite value. That is, you can /try/ taking
the limit, but you will get a different value each time, so the
limit does not exist. This example is not a serious problem,
because in the cases where it does not exist, the longitude
doesn't matter.

In other cases, if the limit does not exist, it may be because
you have built an unphysical model of the physical situation.
The only recourse is to build a better model. For example,
rather than talking about infinite temperature you are better
off building a model in terms of /inverse temperature/ and
letting the inverse temperature go to zero. Ditto for a lens
with an infinite focal length: you are better of building a
model in terms of inverse focal length. You may have seen
eyeglasses measured in units of diopters. The diopter is the
SI unit of inverse focal length.
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