Republicans VIII

 

The Party’s Over

The party's over
It's time to call it a day
They've burst your pretty balloon
And taken the moon away
It's time to wind up the masquerade
Just make your mind up the piper must be paid.

Is the Republican Party over?

A Venn Diagram is the perfect way to illustrate the Goldilocks principle, “Just Right”, when there are three outcomes from two diametrically opposed positions. The maximum condition is when the two positions intersect, overlap, and this creates three outcomes from the total of all conditions.  The first position that does not overlap is 1/3 of the total;  The area of the overlap, intersection of the first and second positions is 1/3 of the total. The area of the second position that does not overlap the intersection is 1/3 of the total. The total is thus always 1. The intersecting position might go by the name of Reagan Democrats or Rockefeller Republicans, etc. It is in this bi-partisan area that politics is most effective.

If one side becomes obsessed with ideologic purity and refuses membership to those who would work with the other position, the total will not change. In fact the excluded members may join with the other position. In this case the first position has 1/3 of the total. The second position has 2/3 of the total; the 1/3 that did not intersect with the other position PLUS the 1/3 that did previously  intersect. Excluding members because they were primaried out; were “RINOs”; spoke ill of other Republicans, etc. ........ or other  ideological tests ensure ideological purity becomes a self defeating effort.

Why has this become a problem for the  Republican Party? It goes back to its very beginnings. No individual Party member can be expected to have exactly the same position on every issue. If party membership is defined by only one issue, then there is the probability that membership would be offered to those with no other commonalities among its members. In the 1850s, the issue was the expansion of slavery into federal territories. The non-tax Whigs and the no-immigrant Know Nothings who may have had nothing in common with others who held anti-slavery positions were welcomed into the Republican Party. When slavery was abolished then the ideological position of the Party could become no-tax or no-immigrant, even and those who were anti slavery but pro-tax or pro-immigrant may be excluded from the party which they founded. It has taken almost two lifetimes, but the exclusion appears to have been accomplished. A party that excludes Richard Cheney, Liz Cheney, Adam Kinzinger and Mitt Romney and vilifies Jon Mc Cain may be ideological pure, but it is guaranteeing its own defeat.

Lawrence O’Donnell remarked that today’s Republican Party has become a cult of personality. He observed that the policies espoused by the current Republican nominee for President whether it is JD Vance or Ron Desantis, or even Donald Trump, Jr. are widely deplored, and yet those same policies espoused by Donald Trump, Sr are admired by many.  He concluded that it is the personality not the policies that are being endorsed. And since personalities have a limited lifespan, but one has to ask when Donald Trump, St.  is no more, is the Republican Party over?

Absolute

 

All in One

One love (hear my plea)
One heart
Let's join together and I'll feel alright
Let's join together (thanks and Praise to the Lord)
And I'll feel alright (and I will feel alright)

Is there also only One Absolute?

If there is an absolute and its absence, for example absolute zero, then the question becomes how many absolutes are there?

While it is true that life=ln(0 ± (sinh(x)+cosh(x))), if an absolute can be approached but not obtained, then the behavior approaching that absolute is said to be exponential. Since both sinh and cosh can be stated as exponentials, the two solutions are x and ‑x. https://dbeagan.blogspot.com/2024/09/sides.html

It is also true that while sinh(x) and cosh(x) are repeating functions,  they repeat only in imaginary planes every 2πi. These are also wave functions with positive and negative parts. They are positive during repeats of πi and are negative during the next following repeat of πi. Since it has already been said that the coefficient of the imaginary axis must confined to 0 in order to be real, this coefficient must be a relative zero not an absolute zero. Therefore x must practically be between 0 and π to be meaningful. Thus while it is true that one solution is x and one solution is -x, both solutions must have a coefficient of zero for the imaginary part in order to be real. That means that rather than a parabolic solution where the solution CAN be imaginary, this is more probably moving from one sheet of a two sheeted hyperboloid to the other sheet, The solution of x, and -x, therefore must also be between 0 and π. In that case, if the universe is one sheet of a two sheeted hyperboloid, then for  Pythagoras' Theorem to be true, then x as π must be the size of the universe. If c, a, and b are much less than the size of the universe then they are also much less than π. Then Pythagoras’ Theorem is c=√(a²+b²) is because the universe is locally flat while globally hyperbolic.

If the three dimensions of that hyperboloid are space, time and imagination, and imagination is confined to be zero in order to be real, this can also be stated that  negative coefficients of i are worse than real,  and positive coefficients of i are better than real. Time also can be defined as the past is negative, and the future is positive, if the present reality is 0. This means that both time and i, imagination, must also be infinite. This means that only space can be constrained to zero and real values and thus be absolute. If there is an absolute, for example absolute zero temperature, then the question becomes how many absolutes are there? Temperature is directly proportional to velocity, and velocity is merely the derivative of space with respect to time. This means that temperature and space are effectively the same thing. This suggests that if there is an absolute zero of temperature, this means that space has the same absolute zero. If the dimensions of time and i must NOT be absolute,  and the dimension of space has to be an absolute, then there is no such thing as negative space. What is from our flat perspective perceived as negative space is merely one sheet of a two sheeted hyperboloid and thus there is only one absolute, just as there is only one volume. The three dimensions of this volume are space, time, and imagination, and only space is absolute. Again, temperature is merely the derivative of space with respect to time. Absolute zero temperature means space is absolute. If neither time not i, imagination, can be absolute, then there is only one remaining dimension that can be absolute.

Beliefs

 

I Believe

I believe for every drop of rain that falls
A flower grows
I believe that somewhere in the darkest night
A candle glows
I believe for everyone who goes astray, someone will come
To show the way
I believe, I believe

What do you believe?

Must  followers of Science, Technology, Engineering and Math, STEM, disciplines be atheists? When I was first working, a co-worker said that someday since I was an engineer, I would stop believing in God and become an atheist.  Now almost 45 years later, it still has not happened.  I have instead realized that the position that was being put forward is merely one of nomenclature. Scientists believe in an absolute and the absence of an absolute.  For example they believe in a temperature of absolute zero. Theists believe in God and the absence of God.  Exchange absolute for God, and they are both saying the same thing. Technologists believe in an absolute, even though technologists have never obtained either an absolute or an absolute zero. Theists believe in God, even though theists have not seen God or the absence of God.

Instead what scientists and other technologists believe is that through research and study they can discover  how the absolute/God works, NOT that there is no absolute/God. If there are rules, those rules are the mind of God. The problem is the belief that understanding how rules works means that if you follow those same rules that YOU are then God. It does not mean that studying the rules, or personally testing those rules, means you don’t believe in the rules.  In the New Testament of the Christian Bible, when the Apostle Thomas doubts that the others have seen the Risen Christ he is not saying that there is no Risen Christ, only that he personally needs the proof that there is a Risen Christ. He won’t accept the word of others that there is a Risen Christ. Christ himself does NOT chastise Thomas for this doubt.  Christ instead appears before Thomas, and asks Thomas to inspect his wounds.  But Thomas did not say that by inspecting those wounds he had become the Risen Christ, only that he believed in the Risen Christ.

If the rules are those of the absolute/God, knowing those rules means that you believe in the rules, not that you ARE the rules.

Ceilings II

 

O Death

Well I am death, none can excel
I'll open the door to heaven or hell
Whoa, death someone would pray
Could you wait to call me another day

If life is a building, then birth is the floor and death is the ceiling.

The Bill of Rights to the US Constitution concentrates on establishing rights (ceilings and floors) on individuals beyond which the state can not operate. The Constitution itself also set some floors for its officers, but unfortunately did NOT set ceilings. This was done because the life expectancy at the time of writing of the Constitution was such that any ceilings that needed to exist would be beyond the limits that death already imposed. Thus a minimum age for as President as 35 years was written into the constitution, but no maximum age was established. At the time, life expectancy was only 40 years. Admittedly that was skewed by death in childhood but even a 35 year old might on average only be expected to live an additional 30 years in 1796. Thus setting a ceiling of 75 years for taking the oath of the presidency could be considered to be an unnecessary ceiling when death might come earlier.

However life expectancies have changed. It is now conceivable to live to 100 or more years. So if there is a floor, we can no longer count on death imposing a cut-off before a ceiling is needed. By never acknowledging that the People as individuals were giving to die, no ceilings were set. If instead the People collectively are expecting to live forever, then ceilings shouldn’t be ignored.

There should be ceilings on how old its officers could be in order to take their oaths. There should also be term limits on each of those offices, NOT lifetime appointments. Those terms can be long enough that they are generational, not as nominated by the present voters. If the adult voting age is 18 years, then an 18 year term limit is consistent with being a regent for most wards of the state before they achieve full voting status. The nomination of most federal officers is by the President. If a President is limited to two term, then most federal officers should also be limited to two terms, unless otherwise specified. Not acknowledging death, allows death to win.

Branding

 

You Don’t Know Me

You give your hand to me
And then you say hello
And I can hardly speak
My heart is beating so
And anyone can tell
You think you know me well
Well, you don't know me

Maybe to be known, you need better branding!

When I was  a young engineer, I was working on what became known in Boston on I-93, the South East Expressway as the Zipper lane. That was NOT what it was called by us engineers.  We called it the SEXway ( South East eXpressway) Reversible Movable Barrier Separated High Occupancy Vehicle Lane.  Rolls trippingly off the tongue doesn’t it! 😉

The basic concept is that confected, concrete Jersey barriers are stored against the median on both sides of the South East Expressway and moved as needed.  The traffic was highly directional during peak hours, northbound in the morning and southbound in the afternoon.  While the traffic was such that it warranted an additional lane during the peak hour in the peak direction, there was not the right of way to add an additional lane. But there was an extra lane in the reverse direction.  But that traffic was already going at expressway speeds in the opposite, off peak, direction so it could not be safely taken.  A lane could be taken if that lane was separated by a physical barrier, but then that barrier would be needed to be removed, and switched to the opposite side only hours later each day.  If only there was a physical barrier that could be moved twice a day when needed, and thus the concept of movable barriers was developed.  The barriers could be moved to create the lane in the early morning, and stored against the median in the afternoon.  In the afternoon, the process would need to be reversed in the opposite direction.  Once the kinks were worked out, a design was developed, and the barriers were put in place.  Because there was only a single lane, to entice and reward drivers to use this lane, and to prevent it from being overloaded upon opening, entry would be restricted to High Occupancy Vehicles (e.g. carpools and buses).  But there was still that name.

The branding of the lane was taken care of by the newspaper headline writers.  The machine that moved the connected barriers appeared like it was opening a big Zipper, when it was stored it appeared to be closing a Zipper, and the lane that it created allow you to Zip into Boston from the suburbs. Would it have been as successful under the original name?  Maybe.  But the Zipper lane by which it is known is MUCH better branding.  There is an article Parker Molloy dealing with another example.  What is formally known as  “coherence bias” by journalists might be better branded as “sane-washing”. The intent is cleaning up a speech by journalists which informs only about the policies, but does not convey about the character of the speaker.  The intent is good and is informative on policy but is depriving any information about character.  Knowing it is “coherence bias” is interesting.  Calling it “sane-washing” is not only better branding, ... it gives the reader the proper information.

Electoral College II

 
Alma Mater

Alma Mater, we hail thee
With loyal devotion
And bring to thine altar
Our off 'ring of praise

We love our college, but do we love the Electoral College?

The Electoral College was created  because the Slave States wanted to include slaves among the population that determines federal voting strength, but still wanted to control the vote of their slaves. The compromise was that federal voting strength was based an enslaved person being counted as 3/5 of a person, and the establishment of the Electoral College. Given that history, and the fact that slavery was abolished, does the  Electoral College serve any purpose today?

The Electoral College is also a reminder that the winner of a Presidential election also represents those states from which the winning candidate for President received no votes.The President represents not only all of the people, but he must represent ALL of the States as well. A President needs to be backed not only by a plurality of voters, but by a plurality of States as well.

The Electoral College membership is set as equal to the number of Congressional (House and Senate) seats,  plus a few electoral votes for federal districts and territories. It is arguable that the number of seats in the House, the largest share of Electoral College votes is out of whack, but that is a different matter and can and should be solved by a different process. https://dbeagan.blogspot.com/2024/04/zero-sum.html. 

The problem is the size of the Electoral College, not the College itself.  Arguably, the Electoral College still serves a purpose and let us  bring "our off'ring of praise", and not call for its abolishment. 

Election 2024

 

Centerfield

Oh, put me in, coach

I'm ready to play today

Put me in, coach

I'm ready to play today

Look at me, I can be centerfield

How does a coach decide who will play?

It has been said that over a baseball season you will win 1/3 of your games and lose 1/3 of your games and it is what happens in that remaining 1/3 that determines the success of your season. In a season of 162 games, then you should lose no more than 2/3 of 162, or 108 games. Tell that to the 2024 Chicago White Sox! This statement should be in REGULATION games, those NOT going to extra innings, you will win 1/3, etc. Losses in extra innings only prove the point and tie breakers should be deducted from the total of 162 games played.

The reason is that there are three outcomes to every game win, loss, AND tie. The games that end in a tie after regulation are NOT being counted as ties. It is the same in any contest such as an election, but in elections policies AND character are being considered. 1/3 will chose one policy, 1/3 will chose the other policy, and 1/3 will chose character as the tie breaker because they can’t decide on policy alone. There are those elections that are only about policies. Arguably the 1972 election of Richard Nixon vs, George McGovern was on policy ( Nixon’s character was not widely known until AFTER the election.)  And the 1964 election of Lyndon Johnson vs, Barry Goldwater was on character. This means that unless the opinion on policies and character changed between 1964 and 1972, that 60% of the population prefer Republican policies and 60% of the voters will choose on character.

If we start with the premise that 1/3 will choose Republican policies, then that means that the Republican base is 33% of the electorate. Similarly 33% of the electorate will chose Democrat policies. This means that one-third will of the voters will be unwilling or unable to decide on policies alone and will revert to character as a tiebreaker. If 60% of those voters think that Kamala Harris has the better character, then she  should receive 60% of that 33.3%, or an additional 19.8%, for a total of 52.8% while  Donald Trump will only receive 40% of that 33.3% or an additional 13.3% for a total of 46.2%. A larger difference than that indicates that the character is more than an 60/40 split. But it must be remembered that a Harris victory does NOT mean a victory of Democratic policies. It only means that Harris won on character.

Debates and elections are illustrative of character, not policies. How you debate is more important than what you debate. Does this mean that the election has been decided?  It might be. (Pennsylvania started early voting on Sept 11^th. November 5^th is just the finish line.) But electoral college voting strength is not the popular vote. Play ball!

Listen

 

Joy to the World

Singin' joy to the world
All the boys and girls now
Joy to the fishes in the deep blue sea
Joy to you and me

Did you watch the Hariis-Trump debate last night!

James Carville was wrong. " It is the economy, stupid" only if you are concerned with policies.  But if a voter is also concerned with who is going to represent him, IT'S CHARACTER, STUPID. And I am so relieved that Kamala concentrated on her character and not her policies. 

You might chose on history, but you are counting on that history being a trend to indicate the future, because elections are about the future, not the past.  Picking only on the past is like being the MLB Yankees in free-agent binging.  How has that worked out for them?  The Yankees need to remember that you play Old Timers Games before the real game, not during the real game.  When you are voting, will you remember?

Discontinuity II

 

Crossroads

I went down to the crossroads
Fell down on my knees
Down to the crossroads
Fell down on my knees
Asked the Lord above for mercy
Take me, if you please

A discontinuity is a crossroads.

I have suggested that there is a discontinuity that is formed when a function crosses its inverse. When this happens at a physical surface it is a physical discontinuity. But there are instances when it is NOT a physical discontinuity but only an apparent discontinuity.
https://dbeagan.blogspot.com/2024/09/rebound.html

At this crossroads there is the decision of  to whether to continue, or take the road which turns back, because the inverse goes in the opposite direction so one of its legs is in the direction from which the original function came. I have suggested that when this is the situation, such as occurs for example when the capacity of a road is reached, or the capacity of a water channel is reached, this crossroads is also the intersection between what is observable and that which is unobservable. At the crossroads there is the option of continuing into the unobservable or changing to the path at that takes you back to the observable. Lord, take me please into the unobservable.

Ceilings

 

One Man’s Ceiling is Another Man’s Floor

I was walking with my dogs
And the night was black with smog
When I thought I heard somebody call my name
Remember: one man's ceiling is another man's floor, goddamn
One man's ceiling is another man's floor

It’s just apartment house rules.

A Nash Equilibrium says that to ensure that 95.8% of the individuals will join the group, that 4.2% have to be blocked from achieving their User Optimal. It does not say that those 4.2% are being punished, only that they are being capped at the mean/median of the group plus two Standard Deviations. So those 3.2% are being capped at 45.8% MORE than the median. This includes anyone among that 95.8% who might have otherwise been among that 4.2%.

A minimum wage, standard deduction, earned income credit, poverty line, etc. is a floor below which individuals in the group should not be allowed to fall. In order for the group to have decent shelter, shouldn’t there also be a ceiling. A ceiling is neither good nor bad. It can prevent you from climbing, but it also can provide you with protection. A ceiling that is imposed only on a selected group, like a Glass Ceiling on women, is bad. But a ceiling that is imposed by the group, for the good of the group, as long as it applies to all members of that group, can be good.

Groups

 

United We Stand

For united we stand, divided we fall
And if our backs should ever be against the wall
We'll be together, together, you and I

We will hang together, or we will  hang separately.

Anything that increases the size of the group, unites us, is good. Anything that decreases the size of the group, divides us, is bad. This includes :

Voter suppression

The group making decisions should be as large as possible. Anything that limits voting in the group, when only voters make decisions for the group, including those excluded from voting, is bad.

Discriminatory laws or any segregation.

There always will be wards of the state. If the state is the people, then wards are the children who have not yet become the people. But excluding anyone from the group, making them wards, on the basis of race, sex, income, sexual orientation, immigration status, ethnicity, caste, etc. has the same impact as voter suppression.

Opposing Anti-trust

Monopolies (only one seller) and monopsonies (only one buyer) are bad for a reason. They decrease competition, choices, of the group. That is why mergers are looked at askance. They are a first step on the road towards monopolies/ monopsonies. 

Anti Union Activities

This includes right to work, firing union organizers, opposing the minimum wage,child labor, OHSA, etc.  The people uniting is good.  Their organizing does not make you bad.  If it offends you, but does not effect you, try to remember this is about the other guy.

Stock-buy backs

They only increase the value per existing investors, they do NOT increase the number of investors.

Market Segmentation

Market segmentation that directs advertising towards certain markets is good. It offers more choices to those markets as buyers. Market segmentation that only offers price differentiation by market when the product has no reason to be segmented, is bad.

Eliminating Competition

Actions to buy up competitors to put then out of business, pricing at a loss to drive competitors our of business, or anything that decreases the number of competitors. It may be good for you , but it is bad not only for that competitor, but anyone working for that competitor as well as your existing and potential customers.

Focusing on the short term and not the long term

The future, long term is where growth of the group will occur.  The short term is only the current group, with no increase. Since members of the group will be  constantly dying, focusing on the short term is accepting that the group will get smaller.

Solutions

 

1, 2, 3

1-2-3, oh, that's how elementary it's going to be
C'mon, let's fall in love, it's easy
Like takin' candy from a baby

1-2-3 is elementary, NOT deterministic.

I am a fan of three. For example https://dbeagan.blogspot.com/2024/02/three.html. A system  has three part: 1) an input; 2) a process; and 3) an output. Just because an input is deterministic, it does NOT mean that the process has to be deterministic, or the output has to be deterministic. For example take a coin. It has only two sides. What could be more deterministic than that. Flipping that coin is random NOT deterministic. The outcome is NOT deterministic either. It is 50% the coin is heads AND 50% that the coin is tails. So while the input was 100%, a coin,  the output AND the process are random.

When the input and process are combined into a scenario,  that also does not mean that the scenario has therefore become deterministic and therefore the output is deterministic. It still depends on the process. If the process was not deterministic, the output won’t be deterministic because the scenario can’t be deterministic. If a process is random, then it has a variance of more than zero. Goldilocks is a solution when the process is deterministic: not too hot, and not too cold; not too hard, and not too soft; just right, halfway between the two extremes. But if a process is random, its variance is NOT zero, then the output can not be Goldilocks, and Nash Equilibriums govern. At equilibrium the solution is 5/6 of the variance, σ², which is identical to the mean, μ, plus two times the square root of the variance, σ. Only when the variance is zero, will the solution be the mean, just right.

Sides

 

Both Sides Now 

I've looked at life from both sides now
From win and lose and still somehow
It's life's illusions I recall
I really don't know life at all 

You don’t need to pick a side, or repeat both sides.  Life IS both sides. 

If a surface is hyperbolic then there is a hyperbolic, non-Euclidean solution for the hypotenuse of a triangle on that surface. If life is a complex number, x + y*i, and we are living in reality, y=0, then that solution is cosh(life)=cosh(x)*cosh(y), which is life=ln(cosh(x) ± sinh(x)) beause cosh(0)=1. By subtracting cosh(x) from each solution, and because cosh(x) is symmetrical, that is cosh(-x) is equal to -cosh(x), this can also be stated as life=ln(0 ± (sinh(x)+cosh(x))). If an absolute can be approached but not obtained, then the behavior approaching that absolute is said to be exponential. Since both sinh and cosh can be stated as exponentials, the two solutions are x and -x. This, and the surface being hyperbolic, is consistent with the two sheets of a hyperboloid. If our universe is one of those sheets, then it has the opposite sign of the other sheet. If our universe is observable, then there must exist an unobservable universe that has the opposite sign of any value in our universe. 

Or to put it in New Testament terms, “The first shall be last, and the last shall be first.”  And life always has both a certain term, cosh(x) and an uncertainty term, sinh(x), which means that uncertainty is a consequence of being on a hyperbolic surface. Any value from an absolute will have two solutions, the value and its opposite. Or from an absolute, again in New Testament terms Galatians 3:28, “There is neither Jew nor Gentile, neither slave nor free, nor is there male and female, for you are all one in Christ Jesus”. In other words, remember on Election Day, there is neither liberal nor conservative, neither Democrat nor Republican, for you are all one in America.

Affirmative Action III

 

I’m Sorry

I'm sorry, so sorry
Please accept my apology
But love was blind
And I was too blind to see

Oops I made a mistake, but IMHO so did the Supreme Court!

I took the position that Affirmative Action is always a good thing in a previous blog post,  https://dbeagan.blogspot.com/2022/08/affirmative-action.html, while the US Supreme Court overturned Affirmative Action in its 2024 opinion on college admissions.  IMHO, we were both guilty of being false. I was being a false positive. I was saying that Affirmative Action was always being used for good, and therefore the decision was wrong. The Supreme Court was saving that Affirmative Action is always bad, and IMHO that is a false negative. As it turns out MIT and other elite schools are finding that the racial constitution of the incoming freshman classes is less diverse racially, but is more diverse economically.  Huh?

There is a wealth inequality in the United States that has a racial component. On average Whites are wealthier than Blacks and Hispanics.  But that doesn’t mean that some Blacks and Hispanics aren’t wealthier than some Whites. What the elite colleges were apparently doing is admitting the wealthiest minorities. In that fashion they could be more racially diverse, but NOT more economically diverse. If they had used NO bias, the incoming class should be just like the overall society. By only admitting wealthy minorities, those colleges could be more diverse racially, while being not being economically diverse. The lack of Affirmative Action, as it was being used in admissions, just  might have highlighted the fact that colleges were being less diverse than the general population when it comes to wealth, even if they appeared to be closer to the general position for minority status. In the words of Martin Luther King Jr., the goal is to judge on “the content of one’s character, not the color of one’s skin.”  

So is the goal of Affirmative Action wrong? IMHO, not in the least. 

Was the way in which it was being administered producing a false positive? Apparently.

Division?

 

Born Free

Stay free
Where no walls divide you
You're free as a roaring tide
 So there's no need to hide
Born free
And life is worth living
But only worth living
'Cause you're born free

Walls ARE meant to divide you.

The opposite of freedom is to have walls.  The phrase after all is “Divide and Conquer.”  If you accept walls, then you are accepting being conquered.  If life is a Zero-Sum game with walls, then when you win, you take something from others.  If life is a game of growth, not Zero-Sum,  then everyone could have more at the end than at the beginning.

A motto of the United States is “E pluribus unum.  Out of many, one” .  It is the United States, NOT the Divided States. Don’t build or accept walls.

Confused

 

Dazed and Confused

Been dazed and confused for so long it's not true
Wanted a woman, never bargained for you
Lots of people talk and few of them know
Soul of a woman was created below, yeah

Are you confused?

Many of the problems of the world are that some very basic concepts are being confused.

Mean and median.  Mixing up these terms, which sound similar, can lead to unintended things. https://dbeagan.blogspot.com/2018/08/wonderful-world-dont-know-much-about.html

Effective and Marginal.  The US Tax Code changed in the 1980s because people did not understand the difference between effective (e.g. first derivative) and marginal ( e.g. second derivative) and that has led to more than 40 years of extra income for high income taxpayers.  https://dbeagan.blogspot.com/2024/08/laffer-curve.html

Dominance and Certainty.  The ruling of a panel of judges should be certain.  It should not merely be dominant. A unanimous jury approaches certainty.  A 5-4 panel of judges is merely dominant.  https://dbeagan.blogspot.com/2024/06/dominance.html

If we have dazed and confused ourselves, shame on us.  If others have taken advantage of us because they are dazing and confusing us, shame on them. And shame on us.  Don’t be confused.  The first thing a stage magician learns is to distract the audience so they can't tell they are being tricked.  If you don’t know, take the time to find out before you act, you are effectively letting others act for, and possibly trick, you.

Nash Equilibriums III

 

All about the Bass

Because you know I'm all about that bass
'Bout that bass, no treble
I'm all about that bass, 'bout that bass, no treble
I'm all about that bass, 'bout that bass, no treble
I'm all about that bass, 'bout that bass, hey

I beg to differ. It’s all about the Math!

I know that Math is Hard, but bear with me. Math may be the explanation, and the solution, to our current problems. This might sound strange but what mathematicians would call infinity, a scientist might call an absolute, an ethicist might call Truth, and an Evangelical would call God, But all can be analyzed/approached the same way.

Let’s suppose the existence of infinity/absolute/Truth/God. The absence of these things would be death, flat-lined. A flat-line has no Amplitude, no variance. The presence of these things must therefore have an Amplitude according to the formula ½A²=σ², where A is the amplitude and σ² is the variance. Infinity/absolute/truth/God as a wave, the opposite of a straight line, must be ...doh...infinite. A wave is an infinitely repeating function of π, which is merely saying that while a wave is infinite, there might be no difference between its behavior at π, 2π, 3π, …nπ, …∞π. If there is an absolute that repeats as a function of π, it must have a repeating median/mean, μ, of π /2.

Individuals can act like a wave. (Don’t believe me! Have you never seen a crowd at a stadium doing the wave!). So how do you get many individuals to perform like a wave. A normal (The mathematical name for it. Not a moral judgement!) distribution of individuals is the logistics, hyperbolic secant squared,  distribution, 1/4s*sech²((x-μ)/2s). S is a function of the variance, according to the formula σ²=s²π²/3. That function is also known as the Probability Distribution Function, PDF.

While ordinary wave functions repeat with a period related to π,  hyperbolic wave functions, such as sech, repeat with a period related to πi, where i is the imaginary number, i=√-1. ( I know math is hard, but the kids in Algebra know this!). Also for functions of x, f(x), there is a derivative of that function, f’(x), which is the slope of that function, and an integral of that function F(x)=∫f(x)δx, which is the area under that function. The derivative of the logistics distribution is
-1/8s²*sech²((x-μ)/(2s))*tanh((x-μ)/(2s)). The integral of the logistics function, which also goes by the name Cumulative Distribution Function, CDF, is 1/2*tanh((x-μ)/(2s))+1/2. ( again Math is Hard. Feel free to check with the kids taking AP Math!)

All of this to say that a wave function, its derivative, and its integral can be defined for any value of x given only two parameters: the median, μ,  which is akin to the phase of the wave, and the range, s, which defines the amplitude of the wave. There are three behaviors that are of interest. The first is User Optimal, UO,  defining only the median, as μ=0 and allowing any value for s. This can be defined as “Only I matter,” “Second place is first loser”, “Winning is the only thing”, “All’s fair” , etc. The second behavior is System Optimal, SO where you accept infinity/absolute/Truth/God/π and thus the median must be π/2, but you say that  you always are 100% certain. The problem is that since you are only an individual, according to the logistics distribution you must also be 40% certain at either 1/3π or 2/3π, and 6% certain at either 1/6π or 5/6π, etc. This means that you then have to be much more than 100% certain if you add all of these together. While being more than 100% certain sounds great, it is mathematically impossible. In fact the integral, CDF, of the logistic function when μ=π/2 and s=.25, which is consistent with being 100% certain at μ, starts at 50% certain at x=0, while the certainty should not be 50% until  x=π/2.

This is like the scene at the door to the back room in Casablanca. UO behavior is asking ”Do you know who I am?”  SO behavior is throwing all UOs out of the Club. The third behavior, the Nash Equilibrium (for reasons that would make your head hurt) is saying that μ=π/2 and s= 0.51451 and this is like saying “I know who you are. You’re lucky your cash is good at the bar.”     https://www.youtube.com/watch?v=aALbiGJpw7c.  An ideal single wave would be s=.55139 which is consistent with a value of s=.5 (twice the SO value) on a hyperbolic non-Euclidean surface because of the use of the hyperbolic secant, from a perfect multiple wave. The derivative of this function and its integral under all of these behaviors are shown below. 

Figure 1 Derivative, dPDF, of logistic function

Figure 2 Certainty, PDF, of logistic function 

Figure 3 Integral, CDF, of logistics function

Those following a User Optimal, UO,  strategy will  try to get those following a System Optimal,  SO, strategy to join them by saying that "I will act like you are correct ( the quiet part NOT out loud being especially since as a UO, I can accept any s) if you act like my median of μ=0 is correct". Instead if the SO wants to be like perfection, then it should adopt a Nash Equilibrium, NE, strategy. The best strategy is not to win, UO, and not the common good, SO, but to quote mathematician John Nash from Ron Howard’s Oscar winning A  Beautiful Mind, is  “to win for the common good,” a Nash Equilibrium. If you are a SO plan to join with NEs, NOT with UOs, if you want to be perfect.

Rebound

 

Red Rubber Ball

And I think it's gonna be all right
Yeah, the worst is over now
The mornin' sun is shinin' like a red rubber ball

But how does that red rubber ball bounce?

A bounce, rebound, occurs when an object, such as a particle, encounters a discontinuity. That discontinuity can be a physical surface, or it can be merely observational, that is the ability to observe, and measure, may be the actual reason that there appears to be a  discontinuity..

If a particle is moving, and is not acted upon by a force, that particle moves in a straight line. That is Newton’s Law of Inertia. However this is only true if space is flat. It is more proper to say that a particle moves along the geodesic in its space. If the space is flat, then the geodesic is a straight line. But if that space is not flat, for instance is spherical or hyperbolic, then it is non-Euclidean, and only flat space is Euclidean.

We say that the Earth is a sphere, and we live on the Earth’s spherical surface. That is why the shortest distance between two points on earth is more properly a Great Circle Distance. While this is true, it might be only of interest to airplane pilots and others who measure vast distances. When the distances involved are far less than the radius of the Earth, then the solution for the hypotenuse of a triangle on that spherical surface is cos(c/R)=cos(a/R)*cos(b/R), where R is the radius of the Earth/spherical surface, and it is virtually identical to the solution on a classical flat Euclidean surface, cos(c)=cos(a)*cos(b), as can be verified by using the series for the trigonometric functions. Both of these are equal to Pythagoras’ Theorem, c=√(a²+b²). It is therefore customary to say that the distances on Earth  are spherical globally but are flat locally. Might this also be true for space?

The solution for the hypotenuse of a triangle on a hyperbolic surface uses hyperbolic trigonometric functions, cosh(c)=cosh(a)*cosh(b). This has a different solution than the classical solution. The classical solution relies on the circular identity, cos²+sin²=1.  In hyperbolic space the identity cosh²-sinh²=1 applies. Additionally space may not be merely what can be observed, it might be that which can not be observed, i. In this case reality having a coefficient of zero for that which can not be observed can be expressed as a complex number which is reality plus zero imagination, r+0*i. If reality is the solution of a triangle r²=(a²+b²)+0^2*i, then its solution in hyperbolic space is
ln(cosh(a²+b²) ± sinh(a²+b²)) because cosh(0²) is 1,  where the ± indicates that there are two solutions. Because cosh is symmetrical while sin is symmetrical, and for small values of a²+b² compared to the size of the universe, sinh(a²+b²), the uncertainty, is also small. This can be also expressed as a single solution, ln(cosh(a²+b²)+sinh(a²+b²)), if reality is one solution. This is no different than electrical engineering where some solutions have real and imaginary components, and the imaginary component is ignored. The single solution merely says that the real solution has the opposite sign of the imaginary solution, and that the imaginary solution is being ignored.

A rebound in flat space is symmetrical because a straight line is symmetrical about that discontinuity. Hyperbolic motions are NOT symmetrical as real numbers. They are almost linear on one side of the discontinuity and almost parabolic on the other side of the discontinuity. If there is a linear motion on one side of a discontinuity and that discontinuity is NOT a surface and the motion is parabolic on the other side of the discontinuity, this probably is an indication that the motion is hyperbolic, NOT a highly skewed parabola. A parabola requires an imaginary solution if that motion passes through, is rotated by 180º or π. It is suggested that is more reasonable to assume that this discontinuity is because the observable behavior continues as unobservable behavior than it is to assume the behavior has become imaginary.