Choices II

 

Waist Deep in the Big Muddy 

Well, I'm not going to point any moral,
I'll leave that for yourself
Maybe you're still walking, you're still talking
You'd like to keep your health
But every time I read the papers
That old feeling comes on;
We're, waist deep in the Big Muddy
And the big fool says to push on. 

It sure is Muddy, but how Big  is the universe? 

Our universe allows choices. Thus it has to be big enough to accommodate all of those choices. Choices are inherently random. (Well, maybe her hairdresser knows! In a previous blog post I said that the absolute, God, was like Rick Blaine from Casablanca. I guess that I am now suggesting that God is like Clairol. Oh, well, I guess when it comes to blasphemy, "In for a penny, In for a pound".😉 )

An individual  may not like the choices made by others, but that is not the point. “Stuff happens!” A random normal (unbiased)  distribution is the logistics distribution, also known as the
sech-squared distribution. If the median choice is 50% then s, the range parameter of that distribution, must be 0.5.  The odds of a choice ( e.g. a coin flip of heads and tails) is 50%, regardless, if the result,  choice, can only be heads (e.g. 100%) or tails (e.g. 0%). If s is 0.5 then the variance, size, to accommodate all of the choices is  0.5²π²/3. 

The fact that it involves squares is important. While any number can be expressed as the sum of two numbers regardless of the surface, a square can also be expressed as the sum of two squares but with different results depending on the surface. (I.e., if the surface is flat, then the answer must satisfy Pythagoras’ theorem). If we are in a flat surface (universe) then also taking Einstein’s Theory of General Relativity into account, the choices should also satisfy E=mc².  Then a flat, Euclidean, relativistic mass equation, m, would be m₀/√(1-(v/c)²), where m₀ is the rest mass at a velocity, v, of zero compared to the speed of light, c. However if the universe is hyperbolic, then Pythagoras’ theorem does not apply, and the relativistic mass equation is instead m=ln(cosh(v/c)cosh(m₀)±sinh(v/c)sinh(m₀)). This does not have the problem of becoming imaginary when the velocity exceeds the speed of light. It becomes undefined, is an acknowledgement that the velocity can NOT exceed the speed of light. However this equation suggests that the mass becomes infinite, an absolute, when v=c. To prevent that, it is suggested that as velocity approaches the speed of light, its relativistic mass transitions from the existing chaotic portion of the universe and enters a non-chaotic, orderly, portion of the universe. ( The division between these two portions is what is called the Big Bang).  The variance, size, of the chaotic portion of universe is equal to the size of the orderly portion of the universe. At the transition,  the relativistic mass equation is rotated by 90 degrees counterclockwise, and becomes a maximum when the speed in the orderly portion decreases to zero. 

Thus the equation of relativistic mass, m, in the orderly universe must satisfy 
XXXX, where the transition occurs when the relativistic mass is m_t and the ratio of the velocity to the speed of light is 1. This is a rotation of the chaotic equation by 90° and a translation of the origin from a ratio of velocity to the speed of light of 0 and a mass equal to the rest mass to an origin of (1,m_t). Because it was already said the maximum relativistic mass, m_m, in the orderly domain occurs when the velocity is zero then 0=XXXX . The variance of the orderly universe must also be equal to the variance of the chaotic universe. This means that m_t occurs at m_m*.5*π/√3. 

I would propose that the maximum relativistic mass be called the Warp Factor, which means that in the original  Star Trek, Mr. Scott should have said, “Aye sir. I can give you Warp Factor  ½*π/√3, and maybe a wee bit more!”.