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  Topic: Uncommonly Dense Thread 3, The Beast Marches On...< Next Oldest | Next Newest >  

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Joined: Jan. 2006

(Permalink) Posted: Sep. 06 2009,14:13   

Gilbert K. Dodgen:
Here’s another one: F = MA (force equals mass times acceleration) This is a fundamental law of physics, described in the most simple of all mathematical equations, that I use in my work creating finite-element analysis computer simulations of transient nonlinear dynamic systems. (All that means simulating real-life stuff, like cars crashing and figuring out how to design them so that they absorb the energy of impact and protect the human occupants.)

But here’s something very interesting about such a simple mathematical equation as F = MA. Force (e.g., lbf, or pound force) = Mass times Acceleration. Acceleration could be something like feet per second per second (ft. / sec.^2). Solving for Mass with simple algebra we get:

lbf / (ft. / sec.^2) or (lbf times sec.^2) / ft.

Thus, we calculate mass density by dividing mass by volume (in this case ft.^3), and we get:

lbf sec.^2 / ft.^4

How interesting! The simple equation F = MA leads to the concept of four-dimensional space.

Poor Gil. He uses the definition of mass density -- a definition that assumes three-dimensional space -- to reach the conclusion that space is four-dimensional. And then he fails to notice the discrepancy.

Here's your problem, Gil. The lbf is defined as 32 · lbm · ft/s2.  Substituting that into your derived equation for mass density, we get

mass density = (lbm·ft/s2)·s2/ft4 = lbm/ft3

Well, duh.  The very definition of mass density assumes three spatial dimensions, so of course we end up with ft3 in the denominator.  If you started with a definition of density that assumed 16 spatial dimensions, you'd end up with ft16 in the denominator.  A definition doesn't tell us anything about reality, Gil, especially if you screw up the algebra.

And the set of natural numbers is also the set that starts at 0 and goes to the largest number.  -- Joe G

Please stop putting words into my mouth that don't belong there and thoughts into my mind that don't belong there. -- KF

  15001 replies since Sep. 04 2009,16:20 < Next Oldest | Next Newest >  

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