Choice III

 

Uncle John’s Band

I live in a silver mine and I call it beggar's tomb
I got me a violin and I beg you call the tune
Anybody's choice, I can hear your voice
Wo, oh, what I want to know, how does the song go

What are the limits of anybody’s choice?

You might seem stationary, but the Earth is rotating.  The Earth is also revolving about the Sun.  The Sun is revolving about the center of the Milky Way galaxy.  The Milky Way galaxy is expanding from the center of the universe, which is the Big Bang.   Thus while you seem stationary, it is only because it is the perspective from your moving frame of refence that is the Earth.  In an inertial frame of reference, which adjusts for all of the rotating, revolving and expanding, you are hardly stationary.

Black holes are singularities where light can not escape.  However if light, and matter, can not escape, then releasing energy can also not increase the entropy of the Universe. Thus Black Holes might function similar to the Big Bang, the origin of the universe in an inertial frame and serve as the transition between the current universe and the universe before the Big Bang. It appears that, prior to the Big Bang, hyperbolic geometry, was rotated by 90 degrees.  Thus a Black Hole might also involve not only a singularity where light can not escape, but also a rotation of any geometry by 90 degrees.

A black hole in three dimensional Minkowski space, where the dimensions are space, time and possibilities, would be at the same space, and same time in our conventional universe, but then the only rotation could be around the axis of possibilities. Thus it is suggested that if our portion of the universe is one of choice, then the portion of the universe prior to the Big Bang might have not allowed choice. 

The probability of a choice was given by Nobel Laureate Daniel McFadden as exp(x_aβ)/(exp(x_aβ)+exp(x_bβ), that is the probability of making a choice x_a, is a function of the utility of that choice and the utility of not  making that choice, x_b. This has a shape of a sigmoid curve.  It is also true that this looks very similar to the hyperbolic tangent, tanh, which is  

tanh(x)=(exp(x)-exp(-x))/(exp(x)+exp(-x)).

This says that x is a function approaching an absolute, which is what exponential behavior is, and  also approaching the opposite of that absolute.  As x becomes very large, exp(-x) becomes very small and the minus term in the numerator can be ignored.  If you also say that there is no opposite of an absolute, this same function would be ½*tanh(x)+½, where the negative absolute is eliminated by the constant (i.e. it is shifted up to being no absolute), and the amplitude of tanh is adjusted to reflect that there is an absolute, 1 and the absence of that absolute, 0.  This can also be shifted such that it is a normal distribution, where the median is equal to the mean is equal to the mode and it follows the 68/95/99 rule, and is ½*tanh(x-µ)+½, where µ is the mean location.  This is also the Cumulative Distribution Function of the logistics distribution, 1/(4*s)*tanh((x-µ)/(2*s))+½ , where s is 0.5.  Fifty percent, 0.5,  is also the probability of making an unbiased normal choice. If the Cumulative Distribution Function, CDF, is as above, then its Probability Density Function, PDF, also has a variance, σ² , given as s²π²/3. If  s =0.5 this means that if choice happened in a normal hyperbolic universe, then that choice has a standard deviation, σ, of .5π/√3=.9069. The  probability of making the same choice as the absolute when x= μ is 50%  If x is increasing to infinity, then by x= μ+3σ, 99.97% of everyone making a choice of the absolute will have made that choice.  

In a Black Hole not only does the relative mass become infinite but the relative time also becomes infinite.  If time is infinite and there is choice, then even if the PDF <1, then the CDF=1.