Lighten Up

Rant 25: Now that Facebook has a billion followers it might be a good rant to quote Hyman Rickover, the father of the US Nuclear Navy. A paraphrase of his quote is: "Great minds discuss ideas, ordinary minds discuss events, small minds talk about people." To which I would add: The mindless talk only about themselves.

Now, back to ideas: It is a simple property of sinusoidal waves that they exhibit the same shape (periodicity) in both space and time. Once you can imagine how that can be expressed it becomes obvious. I have never seen it expressed except to show the same two two- dimensional graphs plotted as amplitude versus distance and amplitude versus time, that is just to change the name of the horizontal axis. But a pseudo-3D plot of these two axes perpendicular to each other, called an orthogonal projection, shows some interesting relations. We can color code the amplitude with red at the crest (maximum amplitude) and violet at the trough (minimum amplitude)using the rainbow sequence (ROYGBIV). The while lines are sine waves running parallel to each axis. The graph shows what looks like a corrugated sheet cut at 45 degrees to the bends. It also clearly shows that any point (height) on the wave moves at the velocity of the wave - which is any upward (vertical) line (same color) on the graph since distance/time=velocity.

Cast in Stone

RANT24: It's been six months since my last rant and one year since I started. The original premise was that the more you complain the longer God let's you live. My leukemia has me on a week of chemotherpy every 4 weeks. What's worse is I've run out of ideas to blog on my phenomenal cosmology gig. No matter because I'm pretty sure I'm only ranting to myself. One note, like Boltzmann's tomb, my obelisk now sports two 5.5x16" ceramic tiles of the equations of the previous two rants - cast in stone as it were.

A Simpler Spacetime Distance

RANT 23: In Rant 21 it all started out OK but got bogged down in some tedious math. It has occurred to me that there's a much straighter road to the result that is really more dramatic. The axes in Rant 21 of Imag vs Real vs Time really harken back to a similar set of axes in Rant 6 where I tried to show that the Argand axes of Re and Im can be expanded into perpendicular planes. If now we apply the cross (vector)product to Re X Im we still get the third perpendiculcar axis BUT it will still lie in the Im plane. IF that axis is in fact TIME then it must be multiplied by i, the square root of -1. Now when we consider the Pythygorian theorem in "spacetime" to obtain what is called the "proper distance" (D) which includes the time axis as well as the space axis, we would write D^2 = R^2 + (iT)^2 = R^2 - T^2. We know that R^2 = X^2 + Y^2 + Z^2 so D = Square Root of (X^2+Y^2+Z^2-T^2). This is precisely the formula used by Einstein that showed that time is not disconnected from space and that SPACETIME is a integrated concept.