Enough

 

Too Marvelous For Words

You're just too marvelous, too marvelous for words
Like glorious, glamorous and that old standby amorous
It's all too wonderful, I'll never find the words
That say enough, tell enough, I mean they just aren't swell enough

How much is enough?

If there is a single absolute, then it is everywhere and is without error. A mathematician would say there is nowhere, 0, that the absolute is not, and the standard error of that absolute is 0. Taken together this would be 0±0. While this seems to be similar to the statement μ±σ, this does NOT mean that the mean, μ, of the absolute is 0 and the variance, σ² of the absolute is 0.

Instead, if the absolute is taken to be infinite series of repeating triangular waves, completely filling the range in which the absolute is defined, then the mean can be considered to be the phase of each wave, and the fact that opposing phases interfere with each other, 0=μ-μ, then this is true for every value of μ and not just μ=0. Similarly the standard error at a point n on the wave has a limit as n approaches infinity of zero, according to n→∞, σ/√n = 0. This is true for every value of σ, not just σ=0.

A group of n individuals can also operate as a single wave. To be consistent with the absolute, that single wave, the derivative of that wave, and the integral of that wave should have an amplitude related to the absolute. The amplitude, A, of  any wave is related to the variance of that wave according to the formula ½A²=σ². If the individuals are viewing the absolute from a hyperbolic surface, this is consistent with the individuals following a logistics, hyperbolic secant squared, distribution. From that hyperbolic surface, the absolute, an infinite series of triangle waves, would appear to have a variance of π/6, its derivative would have a variance of half of that, π/12, and its integral would have a variance of twice of that, π/3. While the period would vary accordingly, the mean/median/phase will repeat and can considered to be π/2 for the wave, its  derivative, and its integral.

However when viewed from a hyperbolic surface, the variance would appear to be 5/6 of the absolute. This makes the range variable, s, of the logistics distribution appear to be ½. From a hyperbolic surface the logistics distribution repeats but only on other imaginary surfaces. This means from the perspective of a real surface where the coefficient of the imaginary dimension is 0, the distribution will not appear to repeat. Also the logistics distribution is only consistent with values on the one of the sheets of the hyperbola ( e.g. only the positive portion of the wave.), the sheet which is being observed.

The limitation of 5/6 of the variance of the absolute is also referred to a Nash Equilibrium. When viewed from the perspective of the individual, it should be limited to 5/6 of the value of the absolute. Thus an individual’s contributions to the group should be on average 1/6, 16.7%, of the total, while each individual should try for no more than 83.3% of the total. If any individual tries to achieve 100% of the absolute, other individuals can also try to achieve 100% of the absolute and they will block each other. If a user also assumes that the median is also zero, this is a User Optimal and is not a stable equilibrium for a group. If an individual assumes that that the median is π/2 but the variance is that of the absolute then this is a System Optimal and it is also not a stable equilibrium for the group. Only the Nash Equilibrium, a mean/median of half of the absolute and a variance of 5/6 of the absolute, is stable for individuals forming a group. So if individuals set a goal of 5/6 of the variance of the absolute, what happens to the other 1/6?

It is suggested that 5/6, 83.3%, is why many building and engineering codes are set as between 80% and 85% of the maximum, and that taxation of individuals for the group should on average not exceed 16.7% of the Gross Domestic Product. (NOTE this does NOT mean that the effective rate for all individuals can not be higher than 16.7%, just than on average across all individuals in a group it should not exceed this value).  The current tax code appears to confuse marginal with effective rates, but has effective rates on average from the group close to this amount, although its median seems to be $0, not 50% of the absolute total.  A previous blog post proposed a Nash Equilibrium of tax brackets, https://dbeagan.blogspot.com/2024/08/laffer-curve.html, although the brackets cited in that post should obviously increase as the absolute total of the economy also increases. So in answer to what is enough, 5/6 of the total is enough.

Focus

 

Hit the Road Jack

Hit the road Jack and don't you come back
No more, no more, no more, no more
Hit the road Jack and don't you come back no more
What you say?
Hit the road Jack and don't you come back
No more, no more, no more, no more
Hit the road Jack and don't you come back no more

Should Travis Kelce hit the road just like Jack?

Popular wisdom is that all work and no play makes Jack a dull boy.  NFL players should NOT be dull.  That means that if their work is football, they better have other interests for play.  Rodney Harrison opinioned that Kelce Travis was not 100% focused on football. https://www.kansascity.com/sports/spt-columns-blogs/for-petes-sake/article292897164.html.

Travis, like Jack, should NOT be 100% focused on football.  If he is not performing as hoped, that should be attributed only to football and NOT to how focused he is on football.  It is expected, and hoped, that he, like Jack, has interests other than work, football. LOL! I wonder what childless cat lady  interest Rodney is afraid is distracting him?  Swifties unite!

Perception

 

If They Could See Her Through My Eyes

Yet when we're walking together
They sneer if I'm holding her hand
But if they could see her through my eyes
Maybe they'd all understand

Let’s not forget that there is a difference between your and my eyes.

Perception, what you see through your eyes, is important.

If you think that you are the only thing that matters, the surface of the Earth may appear flat. You would be wrong, the earth is a sphere, NOT flat, and you can circumnavigate that sphere, globe.

If you think that you are the center of the universe, then the sun may appear to  revolve around you. You be wrong, the Earth revolves around the sun, and this has been known since Copernicus. 

If you may think that everyone sees the same stars as you, you would be wrong. Many of the stars visible in Perth, Australia are different from those visible in New York City.

Thus it is not surprising that our human perception of the absolute may NOT be the absolute’s perception of itself.  Einstein showed that perspective matters when viewing an absolute.  That is the basis of his Theory of Relativity which deals which different frames of reference by observers of the absolute speed of light.

However Einstein solved his equations assuming that space was Euclidean, flat.  If space is instead hyperbolic, that also makes a difference. What may be assumed to have imaginary solutions, for faster than light speeds, might instead only be a difference in perception. Instead, two solutions with NO imaginary solutions, may only be different solutions on sheets of the same surface. (A hyperbolic surface has two sheets, with opposite signs).

On a flat space, transformation of a complex number from polar coordinates, r*e^ix, to complex coordinates is r*cos(x) + r*sin(x)*i, where r is r=cos^-1(cos(cos²(x) * cos(sin²(x))) which because of the circular identity cos²+sin²=1 is identical to r=√(r²*(cos²(x)+sin²(x))) or r=r.  But this does not consider that r² can be either (r)² or (-r)². By contrast on a hyperbolic surface, the solution  is always                     r=cosh^-1(cosh(r*cos(x))*cosh(r*sin(x))). Because of:

1) the hyperbolic identity, cosh²-sinh²=1, 

2) the inverse of the function cosh, cosh^‑1(u),  which has two solutions, ln(u±√(u²-1)), and

 3) the sin(0) is equal to 0, 

if the coefficient of the imaginary axis is 0,  then the solution is

r=ln(cosh(√(a²+b²)) ± sinh(√(a²+b²))), where √(a²+b²) is the real coefficient, r.

If the absolute is an infinite number of triangular waves, just one of its waves might be perceived by an observer on a hyperbolic surface as a normal logistics distribution with s=.5 and μ=π/2 and there would be no solution on the other hyperbolic sheet which is only the negative (e.g. π to 2π ) portion of that wave which can not be perceived. This means that Pythagoras’ Theorem, which is also the CDF of a triangular wave from 0 to π, is only a matter of perception, as are hypotenuse of any triangle. Thus a logistic distribution, and all sum of squares, may only be the perception of a single wave of the absolute as a logistics distribution from an observer on one sheet of a surface with two hyperbolic sheets.

PDF of Triangular wave versus Logistics Distribution on hyperbolic surface.

CDF of Triangular wave versus Logistics Distribution on a hyperbolic surface.

The absolute may feature straight lines and sharp corners, discontinuities, but from the perspective of an observer on a hyperbolic surface, these might look like curved lines and smooth corners.  Know your place.

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 is 1/3 of the total. The total is thus always 1/3+1/3+1/3. 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 ideological purity and refuses membership to those who would work with the other party, the total will not change. In fact the excluded members may join with the other party. 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 tests to 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 no-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, and those who were anti-slavery but low-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 John McCain 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 by JD Vance, Ron Desantis, or even Donald Trump, Jr. are widely deplored, and yet those same policies espoused by Donald Trump, Sr. are admired by many of those same people.  He concluded that it is the personality, not the policies, that are being endorsed. And since personalities have a limited lifespan, one has to ask when Donald Trump, Sr. 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 odd repeats of n*πi and are negative during the next following even repeat of n*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  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 universally 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.