Absolutely VI

 

Let’s Hear it for the Boy

Let's hear it for the boy
Let's give the boy a hand
Let's hear it for my baby
You know you gotta understand
Oh, maybe he's no Romeo
But he's my lovin' one-man show
Oh, whoa-oa-oa
Let's hear it for the boy

And lets hear it for the tie.

In any contest between two parties there are three outcomes: win, loss AND tie.  We don’t often think about ties because so many contests have tie breakers such as: extra innings, sudden death, overtime, extra time, shoot outs, goal kicks, etc., so that those ties eventually become either wins or losses. But they were still ties in the first place.

It will be a tie if both  of those parties in the contest are NOT absolutes.  If one of the parties is an absolute, then the absolute should always win, or else it is not an absolute.  If both of the parties are absolutes, then what?  Then one of the absolutes must lose, which means that party can not be an absolute.  However, if there is only one absolute then that absolute can win every contest, because that absolute could only pay against another party who was not an absolute.

Thus the only way for Game Theory to be consistent with absolutes, is for there to be only one absolute.  Then that one absolute will always win, never tie. 

 

 

Imposssible II

 

Impossible

Impossible! But the world is full of zanies and fools
Who don't believe in sensible rules
And won't believe what sensible people say
And because these daft and dewy eyed dopes
Keep building up impossible hopes
Impossible things are happening every day!

I think the song means imPROBABLE.

If the odds are a million to one, not NO chance, that is the very definition of improbable but not impossible. This is because of how zero is treated and that relates to dominance and certainty. There are two types of zero, an absolute zero and a relative zero. An absolute zero is the absence of an absolute. A relative zero is the midpoint between two absolutes. They may look the same, but just as a human may not see any difference, while a computer makes a distinction between 0 and “0”, it is because of the absolute that there is a difference between dominance and certainty, although they may look the same.

Certainty is the probability of an outcome subtracted from 1. Dominance is when one party of an outcome is greater than any other party. Thus a zero as an absolute is different than a zero as a relative. If there are a positive integer number members of a group,  it can  only reflect certainty if the number of outcomes is also zero. The probability before any outcome is zero and the certainty is 100%. However the moment that there are any outcomes, the certainty by definition is always less than 100%, while the dominance is assured as long as one outcome for one party of the contest is greater than an other party of the same contest.

For example let’s assume that there are 9 members of a group, say the number of justices on the current supreme court. A 9-0 decision may appear certain but the moment the justices have made a decision it is no longer certain. That 9-0 decision is only one of 2⁹, 512, possible outcomes. The dominance of that 9-0 outcome is 100%, but the certainty is only 1-1/512=99.8%. An 8-1 decision also has a 100% dominance, but there are 9 possible outcomes that could give that 8-1 decision, so its certainty is 1-9/512, 98.24%. A 7-2 decision is still 100% dominant, but there are 36 possible outcomes that could be 7-2 making its certainty only 1-36/512, 92.97% even if it is 100% dominant. There are 84 possible outcomes, a certainty of 83.59% for a 6-3 decision, while it is still 100% dominant. There are 126 possible outcomes, a certainty of 75.39% for a 5-4 decision, while it is still 100% dominant. There are 256 possible outcomes for every remaining decision, a certainty of 50.0% while every one of those decisions is 0% dominant.

In any contest between two parties, where neither party is an absolute,  one of those parties may be dominant, but by definition that party can not be 100% certain. Dominance can be 100%, but that is NOT certainty. Lack of dominance does not determine that its is impossible, only that it is improbable.

Electoral College III

 

Sophisticated Lady

Educated lady with your college degree
Amazes me why you just can't see
Learned everything from your books on the shelf
But no one ever taught you how to think for yourself

You may be educated but are you electoral?

The sovereign of our country is "We the People" but the name of our country is the United States.  The President should be the choice of the people AND of the states.  The Electoral College is is a means of ensuring that the President is the choice of both.  It ensures that the choice has not only the support of the people.  but also a broad representation of the states.

Is the current system flawed? Absolutely.  The method of selection of Electoral College votes in Nebraska, with its famous "Blue Dot" instead of a "Winner takes all" means that the choice is one of both the people AND the state.  The attempt to change Nebraska's electoral policy on the eve of the current election is not only cynical, it shows how deeply flawed is the current system.  Every state should aspire to be like Nebraska, NOT Nebraska should aspire to be like every other state.

Are the 435 congressional-based electoral votes awarded to the states flawed?  Absolutely, but that number is not a feature of the Electoral College.  The number itself is NOT a constitutional requirement but the cowardly abandonment of the Congressional mandate to apportion seats after a decennial census that is based on a compromise after the 1910 Census.  A fairer way to apportion House seats would be the Wyoming Rule under which California would have 68, instead of 52, House of Representative seats and the total seats in the House would be 574 instead of 435.

The Electoral College Compact, that a state awards its votes to the winner of the national popular vote, ensures only that the President is the choice of the people, but that might not be the choice of the states.  The Electoral College is intended to be a means to ensure that the choice represents the people AND the states.  As wrong as it is for the loser of the popular vote but the winner of the Electoral College to be the President, it would also be wrong to see the winner of the popular vote but the loser of a revised Electoral College to be President. Two wrongs never make a right. It is possible that the winner of the presidential election could have a majority of the people but that support be concentrated in a narrow representation of states.  A revised Electoral College might prevent this from happening.

It is not the Electoral College that is flawed.  It is suggested that the number of votes in the Electoral College and the awarding of those votes on a "winner takes all" basis that is flawed.  As long as we are the United States then the President should be the choice of the people AND the states. 

That there are battleground states is evidence that the current system is flawed.  There should be battleground congressional districts.  The election should be not people OR states but people AND states. Countries that are divided, like Christians and Muslims in Lebanon, have other power sharing agreements that may only be customs which can be violated.  The Electoral College is an attempt to peacefully recognize and deal with those divisions in the law.

Absolutely V

 

Try

Try, try, try just a little bit harder
So I can love, love, love him, I tell myself
'Cause I'm gonna try, oh yeah, just a little bit harder

There is no Try.

With apologies to Yoda’s “Do or not Do. There is no Try”,  “Good or no Good. There is no Evil”.  Yoda was not saying that there is no such thing as trying. And the second statement is not saying that there is no such thing as evil.  What both statements are saying is that the choice is about an absolute.  Trying is not an absolute, neither is evil.  Thus the G.W. Bush and cronies' conception of the world as a battle of Good vs. Evil elevates Evil to that of an absolute.  There is only one absolute and that is Good. Good is not merely the absence of Evil, it is the presence of Good, which means that Evil is NOT an absolute.

Climate Change V

 

Cell Block Tango

He had it coming'
He had it coming'
He only had himself to blame
If you'd have been there
If you'd have heard it
I betcha you would have done the same

Nobody could have seen it coming?  Really?  Really?

G. W. Bush famously said that nobody could have foreseen the disaster in New Orleans caused by Hurricane Katrina and that he and FEMA Administrator Brown did a great job.  I beg to differ.  Katrina struck New Orleans on August 29, 2005.  I worked on a report for the US DOT, Impacts of Climate Variability and Change on Transportation Systems and Infrastructure- Gulf Coast Study, Department of Transportation, Washington, DC, March 2008, which studied the impact of climate change on the Gulf Coast. It studied the impact of hurricanes, their wind, rain, and storm surges, as well as sea level rises in the coastal areas of the United States from Mobile Bay, Alabama, to Galveston Bay, Texas.  That study and that geographic area were chosen in part because of an article in Scientific American, Drowning New Orleans, in the October 2001 issue which discussed the impact of a hurricane on the levees and dikes protecting New Orleans.  Katrina accidentally provided a natural experiment with which to examine and validate those methods in our study.  Also Hurricane Rita struck Houston and Galveston on September 24, 2005.  By that time evacuation plans had been developed for Houston and the success of those evacuation plans could also be evaluated.

Could anyone have predicted the date and the hour in which a hurricane would strike? No, but the impacts were known in advance. The impacts of Katrina were very much in keeping with the article in Scientific American less than 4 years earlier.  The evacuation plan for Houston called for the orderly, timed evacuation of the city in only 1 vehicle per household.  A meeting was held to evaluate the findings of the study which included the very persons who prepared the evacuation plan for Houston.  They admitted that they also had to evacuate but they used every car in their households, as many as 3 cars per household, as soon as the evacuation of any geography had begun, without waiting for their turn just like everyone else. It is any wonder that the roads during the evacuation were jammed.  IOW do as I say, not as I do.  Great job, Brownie!!! You are not to blame!!!!

Quadratic

 

Zero, My Hero

What's so wonderful about a zero? It's nothing, isn't it?
Sure, it represents nothing alone
But place a zero after one, and you've got yourself a ten
See how important that is?
When you run out of digits, you can start all over again
See how convenient that is?
That's why with only ten digits including zero
You can count as high as you could ever go
Forever, towards infinity
No one ever gets there, but you could try 

Zero is even more important than that! 

In a previous blog post  https://dbeagan.blogspot.com/2024/10/absolute-zero.html I suggested that zero as the coefficient of the imaginary part of a complex number on a hyperbolic surface is important.

The solution  of quadratic equation ax²+bx+c is typically given as x=(-b±√(b²-4ac))/(2a) if x is a real number or if x is a complex number on a Euclidean, flat, surface.  However if x is the real part of a complex number on a non-Euclidean hyperbolic surface then the quadratic equation is really ax²+bx+c+0²i and its solution is x=ln(cosh((-b±√(b²-4a*c))/(2a))±sinh((-b±√(b²-4a*c))/(2a))). Then if b²‑4a*c is negative, and its square root is imaginary, since the solution of cosh(ki) is always real but the solution of sinh(ki) is always imaginary, the solution of x will be imaginary. This is true for the period of 5/6, 83.3%, of the solutions where the traditional solution of the quadratic equation is the approximation as well as  the period of the remaining 16.7%, 1/6, where the approximation no longer applies.

The approximation means that in this case the real part will itself contradictorily be a complex number, a+b*i+0²i. For the remaining 16.7%, 1/6, the approximation will be the negative of that complex number, while the hyperbolic solution will always give the correct complex number.

For other solutions where the imaginary coefficient should always be zero, the hyperbolic solution always applies. Thus the relativistic dilation is γ=ln(cosh(√(1-v^2/c²))±sinh(√(1-v^2/c²))); Pythagoras’ Theorem is c=ln(cosh(√(a²⁺b²))±sinh(√(a²⁺b²))); in statistics the coefficient of EVERY moment about the mean is 0 not just odd moments; the real radius, r,  of a complex number, x+y*i in Cartesian coordinates translated to polar coordinates, re^iθ, is  r=ln(cosh( (√(x²⁺y²))±sinh(√(x²⁺y²))), etc. 

Hyperbolic

Three Blind Mice 

Three blind mice, three blind mice
See how they run, see how they run
They all ran after the farmer's wife
She cut off their tails with a carving knife
Did you ever see such a sight in your life as three blind mice?

In addition to blind mice, what about Blind Men and the Elephant?

The Blind Men and the Elephant is an ancient Indian parable that has roots in Buddhist, Hindu, and Jain texts, that discussed the limits of perception, and the importance of complete context, and is a poem by John Godfrey Saxe. It is also the subject of the of illustration below.

This is the phenomena that is responsible for the flat Earth Fallacy. If you use only your own perception, the Earth looks Flat, even though the Earth is a sphere. Mathematically it would be described as being locally flat, but globally spherical. If we only use our local perception it looks flat. The issue is that we are so small compared to the radius of that sphere, that it looks flat, just as the surface of a beach ball would look flat to an ant on that beach ball.  Just like the blind men who mistook the elephant as being a spear, a snake, a rope, a fan, a tree, or wall depending on what part of the elephant they were perceiving, or as Saxe’s poem goes

So oft in theological wars,
    The disputants, I ween,
Rail on in utter ignorance
    Of what each other mean,
And prate about an Elephant
    Not one of them has seen!

What we perceive as straight lines and parabolas might both only be parts of a hyperbola. A hyperbola looks like a straight line at great distances from its vertex and looks like a parabola close to its vertex. What we perceive as straight lines and parabolas in flat space might only be different parts of the same hyperbola……IOW space might be locally flat and universally hyperbolic.

That space is hyperbolic is NOT a unique idea. It was proposed by Mabkhout (Mabkhout, 2012). He pointed out that if space is hyperbolic and the Einstein field equations are solved in hyperbolic space, the need for dark matter and dark energy goes away. This is hardly the limit of this proposal. It has implications on mathematics, physics, statistics, EVERYTHING. Don’t be blind.

Mabkhout, S. (2012). The infinite distance horizon and the hyperbolic inflation in the hyperbolic universe. Phys. Essays, 25(1), p.112.