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Re: [Phys-L] Fwd: [PTSOS] spacetime simulator: flexible conduit?



On 07/17/2012 05:52 PM, Ken Caviness wrote:

But I really doubt whether even 1% of the people notice or learn
incorrect physics from the non-fitting parts of the demo. It should
be taken only as an analogy: the heavy mass deforms the surface,
it's no longer flat, and marbles on the no-longer flat surface behave
differently! That much is shared by the demo and the actual theory.
As good as many analogies, I'd say.

We agree that all analogies are imperfect ... but I insist they
are not all _equally_ imperfect.

Sometimes one analogy is apt in one respect while another is apt
in another respect, such that taken together they tell far more
of the story than either one separately. Ask yourself what goes
in the middle of the following diagram, such that it is in some
ways related to the set of blue things and in some ways related
to the set of triangular things:
http://www.av8n.com/physics/img48/blue-triangle.png

One should never overreact *or* underreact to the imperfections of
an analogy. Deciding which analogy to use, and how to use it, is
sometimes not easy. It requires judgment.
a) Sometimes tricky tradeoffs must be made.
b) Sometimes not. Sometimes one analogy is Pareto superior to another.

One question that is almost always fair game is this: How much would
it cost to come up with a better analogy?

In the present case, before you run off and spend time and money
building a trampoline, consider how much better *and* cheaper it
would be to stock up on masking tape plus a collection of suitable
curved objects.

I suggest that students making geodesics using tape will actually
learn something useful. They will learn about how geodesics actually
behave. This has application to geography, navigation, and aviation
(great circles), optics (Fermat's principle), classical physics
(principle of least action), plus quantum mechanics ... as well as
to general relativity.

The trampoline trick is deceptive. Virtually everything that the
youtube video says about curved spacetime will have to be unlearned.
In contrast, none of the tape geodesic ideas will have to be unlearned.
Sure, there are imperfections in the tape model, but it is rather
obvious what the imperfections are, so nobody is going to be deceived.

Not all analogies are equally imperfect!

The geodesic lesson (compared to the trampoline trick)
a) requires less cost and less laborious preparation;
b) has less downside in terms of deceptions and misconceptions; and
c) has more upside in terms of correct conceptions and applications.

Looks like a win/win/win to me.