Variance

 

Room to Move

May seem peculiar
How I think o' you
If you want me darlin'
Here's what you must do.
You gotta free me
'Cause I can't give the best
Unless I got room to move.

Does the universe give us room to move?

The universe is infinite and expanding. But because it allows us to be free, there is choice, it has a known variance, which should NOT be confused with its size. That variance allows for all of these choices to occur. If each choice is binary, e.g. heads/tails, true/false, the odds of each choice is 0.5 and statistics tells us that the variance of the universe must be s²π²/3. Because the odds of choice, s, are 50%, its variance is 0.91. If there was no choice then s would be 0, reflecting that there is only one outcome, i.e. only true, and the odds of deviating from that outcome is 0% and the variance would thus be zero. 

The universe in which we live has choice, and thus has to include all of those choices. At the point where the universe incudes all of those choices, there is a transition to a universe where the choice has already been made ( e.g. there is effectively no further choice). This point is the absolute as given by Einstein’s Theory of Relativity. In the Theory of Relativity, the absolute is the speed of light. That is you can only approach an absolute, but you can not be an absolute. This describes exponential behavior. In Traffic Engineering, the approach is to the absolute which is capacity of a road. In Fluid Mechanics, it is the capacity of a channel. In Traffic Engineering, you are in a uncongested domain before reaching that capacity. In Fluid Mechanics you are in a laminar flow domain before you approach that capacity. It is suggested that the universe  in which we live is only the turbulent, chaotic, part of the domain where there is choice. There must be a transition to the orderly domain, which has a zero variance. But in both domains,  the universe is infinite so not only are we free in our domain, but in both domains we have room to move.

Good Intentions

 

Don't Let Me Be Misunderstood

Baby, do you understand me now?
Sometimes I feel a little mad
But don't you know that no one alive can always be an angel
When things go wrong I feel real bad.
I'm just a soul whose intentions are good
Oh Lord, please don't let me be misunderstood

But the road to Hell is paved with good intentions

C.S. Lewis and J.R.R. Tolkien were more than contemporaries and acquaintances.  They both belonged to a group they called the Inklings and thus supposedly read and commented on each others works while in progress.  J.R.R. Tolkien is the author who created The Lord of the Rings, The Hobbit, and whose estate has authorized the Amazon series The Rings of Power.  C.S. Lewis is perhaps best known today for his Narnia series which contained  The Lion, the  Witch, and the Wardrobe.  But he is also the author of That Hideous Strength, the last volume of his Perelandra trilogy.

Both men lived through, and were deeply affected by, the hellish evils of WWI and WWII and the rise of fascism. Their works reflect this.  J.R.R. Tolkien also appears to be a strong believer in the monarchy, if not a Jacobite, who also believed in the battle of ultimate good and ultimate evil. He set his tale in a completely imaginary world.  C.S. Lewis appeared to be less of a monarchist, who appeared to believe that people were neither inherently good nor evil, but could be deceived to unknowingly support what later tuned out to be fascism. He also set his story as much as possible in the “real” world.  The “science” in the Perelandra trilogies is woefully out of date, and the theology is, being positive, at least imaginative.  But the lessons about having good intentions, but unknowingly supporting the evils of fascism, are unfortunately all too pertinent today.

Truth III

 

Battle Hymn of the Republic

Mine eyes have seen the glory of the coming of the Lord
He is trampling out the vintage where the grapes of wrath are stored
He hath loosed the fateful lightning of his terrible swift sword
His Truth is marching on

Are you in favor of the Truth?

There seems to be a fixation that the Truth is about Dominance, while nothing could be further from the…doh….Truth. The Truth is about CERTAINTY, not DOMINANCE. A majority of the Supreme Court, a 5-4 decision, might be the truth, or it might merely be dominance. So how do we get it get to certainty?

The current judicial system provides the  answer. A uniramous jury has a certainty of 99.97%. That is because a unanimous jury verdict of guilty is only 1 of 4096 outcomes. (A unanimous verdict of NOT guilty is also only one of of 4096 outcomes.)  That jury verdict can not be completely certain due to statistics. Also that jury verdict might be only a false positive, which is why there are appeals, if: the evidence presented to the jury is false; the jury is biased and can not fairly judge the evidence; or there has been jury tampering. A criminal jury verdict of 7-5 is not only hung, a mistrial, it could only reflect dominance, not certainty.

Any verdict should be about Certainty, not Dominance. That is why Trial by Combat, which was never a part of Roman Law, the Law of Moses, the Code of Hammurabi, etc., is considered to be barbaric and has been all but eliminated. But requiring unanimity gives tremendous power to a single holdout. That holdout may require that their position, the lowest common denominator, be accepted by the group. But there is a way to get certainty, not dominance without requiring unanimity. Statistics provides an answer to this in the square root of the variance; and the Z-score, the justices in the dominant decision divided by the mean of those justices, expressed as a percentile.

A normal distribution follows the 68/95/99 rule. This means that 68% of the outcomes are found between the mean plus 1 Standard Deviation, the square root of the variance; 95% of the outcomes are found between the mean plus 2 Standard Deviations; and 99% of the values are found between the mean plus 3 Standard Deviations. A verdict from a single judge might be dominance or might be certainty. A normal distribution might require an infinite number of justices but there can not be an infinite number of justices making a decision. Assuming a normal distribution, 68% of the bench, would seem to be the desirable number of the justices to determine certainty rather than dominance. For a 9 justice Supreme Court, this would mean that no decision would be considered certain unless it had 68% of the Court. But 68% of 9 is 6.12 which, because justices are not fractions, would require a 7-2 decision, to have a certainty above 68%. 68% of ten justices, adding a justice to the current court, would be 6.8 which would also round to 7 justices. Thus to reflect certainty, rather than dominance, it is suggested that decisions should require 7 of 9 justices, include 94.0% of the outcomes; or 7 of 10 justices, include 91.9% of the outcomes. If one justice is removed from the Supreme Court, the mean would be 4, the median would be 4, but the mode would be evenly split between 3 AND 4. A dominant vote would require a 5-3 decision, which includes 89.4% of the outcomes, and that is its certainty. Or if two justices are removed from the current court so that there are seven justices, then the mean is 3.5, the median is 3.5, but the mode is 4. A 4-3 vote is not only dominant, but it also has a Z-score of 4/3.5. That reflects a certainty of  87.3%

If, politically, it would be difficult to remove justices from SCOTUS, it is recommended that a justice be added to SCOTUS and, that to reflect certainty, its decisions require 7 of the 10 justices on SCOTUS. It is also noted that a 10-member court could be split, 5-5 which would never reflect dominance. A 6-4 vote might merely reflect dominance, not  certainty.

Stewards

 

Everybody Wants to Rule the World 

Acting on your best behavior
Turn your back on Mother Nature
Everybody wants to rule the world 

Don't  turn your back please. Be a steward, NOT a ruler. 

In the  creation story in the Bible,  God in the English text appears to give man dominion over the Earth  (Genesis 1:28).  But the Bible was not written in English.  It was written in ancient languages and translated many times, eventually into English.  It is not reasonable to assume dominion is the correct concept and that has given Man the right to dominate and possess absolute control over the Earth.  If that is the case, then God has given his sovereignty over the Earth to Man, and this sovereignty is thus no longer God’s. Instead it is more reasonable to assume that God has retained his sovereignty and has merely made Man his steward and caretaker. This is in keeping with the Israelites’ belief in the Old Testament that the land in its entirety belongs to God and not to his people and that  “the Earth is the Lord’s and the fullness thereof” (Psalm 24:1). 

In fact, it is questionable that the Bible ever supports dominance of any group over any other group.  If we are supposed to be stewards, our brother’s keepers, Good Shepherds, etc. then dominance is never supported.  Dominance is not even the best game strategy, except in two player contests.  This does not mean being a pushover.  The best game  strategy is being tough but fair.  https://dbeagan.blogspot.com/2021/05/tough-but-fair-beats-always-being-nasty.html.

Superman

 

Don’t Mess Around With Jim

You don't tug on Superman's cape
You don't spit into the wind
You don't pull the mask off that old Lone Ranger
And you don't mess around with Jim

If you are tugging on Superman’s cape to ask for help, then that’s different.

Like Jerry Seinfeld, I am an enormous Superman fan.  Superman ( created by Jerome Siegel and Joe Shuster) fights for Truth, Justice, and the American Way or as I would prefer to say Certainty, Mercy and Pluralism.  The Superman origin story is a thinly veiled retelling of the Moses story where, instead of a baby being saved in a basket in the bulrushes of the Nile, he is saved in a rocket escaping the dying planet of Krypton.  He is adopted by the Kents and he grew up to bring oppressors to justice.  He believed in the government of the People, which was also true of Batman (created by Bob Kane, nee Kahn) until the 1980s, when those who disagreed with Batman must be crazy and were confined to Arkham Asylum, not jail. It went from a situation where both costumed heroes assisted the government, to one in the late 1980s where Superman supported a corrupt government and was opposed by an individualistic Batman (The Dark Knight Returns).  At the height of Superman’s popularity in the 1940s, he assisted the downtrodden by capturing oppressors FOR the government, functioning much like a Golem in Jewish folk tales.

In the most recent incarnation on TV, Superman and Lois, he has saved a Russian village from an avalanche and a North Korean submarine.  While these are often considered to be enemies of America, Superman is for what was once America’s shining example, its pluralism, supporting all, not just American WASPs.  For him love of country is NOT merely hatred of other countries.  He is  the living embodiment of “My county right or wrong. If it is right, keep it right. If it is wrong, make it right.”  “Might for Right", not “Might makes Right”

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.

Debt Ceiling II

 

Burning Down The House

Ah, watch out
You might get what you're after
Cool babies
Strange but not a stranger
I'm an ordinary guy
Burning down the house.

Debt ceiling deal anyone?

In the game of chicken that is the debt ceiling negotiations, the House Freedom Caucus that installed Kevin McCarthy as Speaker is prepared to crash and burn the United States’ economy.  This should not be a surprise.  Since they do not view the elected sovereign of the United States as their sovereign, they also do not view the economy as their economy.  Uh, “This land is your land, this land is my land” and all that jazz.  There is not a Democratic economy and a Republican economy.  There is only the United States economy.  The sovereign of the United States is NOT the President.  The President, of either party, is only the current steward of the People and their economy. This is confusing the ceremonial sovereign, the President, with the actual sovereign, the People. If you crash the economy, then you are crashing the People’s economy. Why should we ever let you be stewards of that economy, if there is any economy left after you try to burn down the house.