Subject: Re: [MATHEDCC] Real world negatives
From: Kirby Urner (urner@alumni.Princeton.EDU)
Date: Tue Jan 11 2000 - 10:04:58 EST
On Thu, 2 Dec 1999 03:40:04 -0700, you wrote:
>Here's another example: If someone appears to walk forwards,. consider that
>positive, if backwards negative. If you show a film forwards consider that
>positive, if you show it backwards, consider that negative. So if you film
>someone walking backwards and show it forwards, positive "times" negative
>is negative, and they appear to walk backwards. Same if you film someone
>walking forwards and show it backwards. But if you film someone walking
>backwards and show it backwards, they appear to walk forwards. Or negative
>times negative is positive.
>
Yes, as a mnemonic this works:
Forward shown forward is forward (+ * + = +)
Forward shown backward is backward (+ * - = -)
Backward shown backward is forward (- * - = +)
One might need to explain a little how viewing successive
frames of film relates to the mathematical operation of
"multiply". One might explain that "to multiply" is simply
to add repeatedly, which in this context means to "view
successive frames of film" (i.e. to view additively).
Indeed, I think film makes a useful pedagogical tool in
many contexts. For example, in physics:
A frame of film captures (photo-records) a mass moving
at some velocity (mv) for some time (the duration of
the shot, e.g. 1/125th of a second), and through some
distance (slower speed film will show more blurring,
indicating a different start and end position): mv d/t.
Since mvd is a unit of "action", you can speak of a frame
as "action packed" (double meaning). It flashes by in
time t, i.e. with frequency f (f=1/t). These are energy
units: E = mvd/t or hf (where h = the "minimum action"
i.e. Planck's constant).
If energy frames are conveyed quickly (as though frames
were "buckets of energy", the film being a kind of
conveyor belt, in the sense of showing energy being
expended), then you have more "power" in the picture
(or "scenario"). Speed up the film and you see a
process which expends the same energy more quickly
-- more power (P = Ef).
Does this make sense to the physics teachers among you?
I've gone into more detail at my website, for any
wishing to follow up.
>Now for the real question: in which major film was this latter technique
>used to make someone appear to walk forwards, albeit in an odd manner?
>Hint: the director was one of the people doing the walking, and it was
>desired that the walk look odd.
>
>Karl Schaffer ---------------> schaffer@admin.fhda.edu
>(408) 864-8214 (offc) -------> De Anza College, 21250 Stevens Creek Blvd.
Sounds like a very clever director.
Kirby
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