keiths
Posts: 2041 Joined: Jan. 2006

Gilbert K. Dodgen: Quote  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 finiteelement analysis computer simulations of transient nonlinear dynamic systems. (All that means simulating reallife 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 fourdimensional space. 
Poor Gil. He uses the definition of mass density  a definition that assumes threedimensional space  to reach the conclusion that space is fourdimensional. And then he fails to notice the discrepancy.
Here's your problem, Gil. The lb_{f} is defined as 32 · lb_{m} · ft/s^{2}. Substituting that into your derived equation for mass density, we get
mass density = (lb_{m}·ft/s^{2})·s^{2}/ft^{4} = lb_{m}/ft^{3}
Well, duh. The very definition of mass density assumes three spatial dimensions, so of course we end up with ft^{3} in the denominator. If you started with a definition of density that assumed 16 spatial dimensions, you'd end up with ft^{16} 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
