Joined: Jan. 2006
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