Martian Math Memo
Typos fixed. Original version. Followup.
Re: Developing a Metaphysics for Physics
From: kirby urner <kirby.urner@xxxxxxxxx>
To: math4wisdom@xxxxxxxxx
Date: Sun, 3 Sep 2023 09:25:16 -0700
Hi Andrius —
We overlap in our interest in using our Newtonian heritage, in terms of units, of time, distance, mass etc. to build up a picture of “what’s happening”.
The information that “something is moving at high speed” doesn’t fully give a sense of its potential to do damage (one way to look at it; to add entropy), until we also have the thing’s mass. Say we already know its direction (is it coming towards Earth?) as speed means velocity in this case, an arrow. Size will come into it too of course, but we’re folding that idea into its mass by suggesting we have information about its material, say from a spectrogram.
Photons don’t break our bones, because they’re almost massless at light speed (no mass at rest) — energized, they have momentum.[1] Photons at high enough frequencies (gamma rays) will do significant cell damage.[2]
The two multiplied together: mv, gives our Newtonian idea of momentum p. Momentum: p = mv.
A Volkswagen bug (car) driving along the freeway in the “action frame” of a movie, looks to be still in that moment.
Lights, camera, action: I’m linking to the film making language game — not just my idea.
Terry Bristol, whom you met for discussions of thermodynamics (its intellectual history), once organized a Math Summit here in Oregon, at Oregon State University (Corvallis), featuring math world superstars of that day:
Keith Devlin
Ralph Abraham
Roger Penrose
… [3]
These guys had all been speakers in Terry’s ISEPP public lecture series. [4]
I’ve always remembered how Keith Devlin, in his talk, was especially keen on the topic of: using filmmaker language to teach calculus concepts.
The process of using faster and faster film speeds, to devote more and more frames to each slice of time, is akin to “differentiating towards a limit” of “infinitely subdivided” wherein every frame of a flying arrow is truly still (Zeno’s paradox). Projecting said film gives us the cumulative effect of “a scenario” i.e. “the integral effect” of all the slices.
So one frame of film shows a road-bound VW of momentum p (mv), moving for some distance (mvd, pd).
There’s a delta t (the duration of the frame) in which said action (pd) is registered.
Every frame, recording an action, is therefore also an “energy bucket” in that the pd (action) “in a time frame” = pd/t = mvd/t = mvv = energy units E (in terms of Newtonian units, not bothering with coefficients).
Expressed in other (familiar, textbook) units: action = mvd = h (units of action); hf = E (action per time frame) = h/t given f (frequency) = 1/t.
We’re sensitive to when familiar actions (“man walking” “horse running”) are too slow or too fast in a film, perhaps intentionally. We might say such a scenario is “unrealistic” or “the physics is wrong” e.g. something with a lot of momentum seems to turn on a dime. “In reality, that should take a lot longer” we’re thinking.
Or maybe it’s just that people move in a too frenetic manner, like in old films from WW1 played back at the the post-WW2 24 frames per second. Using computers, we’ve slowed them down (and added color). [5]
Here enters our notion of “power”: energy per time frame (E/t).
P = E/t (energy expended per time frame) i.e. (mvd/t) / t.
t = time
f = frequency (1/t)
m = mass
d = distance
p = momentum = mv
h = Planck action = mvd
E = energy = p/t = hf
P = power = E/t
Possibly useful going forward?
As for an observer being “outside the universe” that’s perhaps a definitional (semantic) matter.
If we define our universe to be inter-subjective, then might we never need to imagine being outside it or seeing it as an object?
Kirby
[1] https://youtu.be/V_fKYrrsVT4
[2] https://nbviewer.org/github/4dsolutions/School_of_Tomorrow/blob/master/isotope_decay.ipynb
