It's A Wonderful Life II

 

Buffalo Girls

Buffalo gals, won't you come out tonight?
Come out tonight, Come out tonight?
Buffalo gals, won't you come out tonight,
And dance by the light of the moon.

Don’t we all want to lasso the moon!

45 years ago I married into a family from Tioga County, PA.  I spent many Fourth of Julys traveling from my in-laws home to see the see the Elmira Pioneers play baseball.  I shopped in downtown Elmira, Corning, and Horseheads.  While in college, I traveled to Cornell to root against Ken Dryden playing hockey against my college.  I toured most of the baseball stadiums in the New York-Penn League of baseball when it included the St. Catherine Stompers, the Welland Pirates, the Batavia Clippers, the Geneva Cubs, etc.  I am kicking myself now that I was so close but never visited Seneca Falls the inspiration for Bedford Falls,  especially after hearing the podcast, George Bailey Was Never Born.

My favorite movie of all time is still Casablanca.  My favorite Christmas movie fluctuates between Die Hard and White Christmas, depending on my mood.  But those are emotional decisions.  Intellectually, IMHO,  the most important movie of all time is It’s A Wonderful Life.

It is the movie cited most often by economists as being the best teaching tool.  https://www.npr.org/2023/01/10/1148144705/its-a-wonderful-life-bank-run-economics.

The movie intuited Nash Equilibriums before they were articulated by John Nash in 1951, where someone, e.g. George Bailey, blocks the bad impulses of some Users so that the rest of the Users can be equal.  Yes, the second act is a horror movie when George is not born and everyone can pursue their User Optimal. Yes, the first act is a horror movie where George has to accept something less than his own User Optimal to achieve a Nash Equilibrium for everyone.  But his is the price of achieving something approaching a System Equilibrium, and that seems better to him, and to everyone else, as is revealed in the final act.

The movie intuited that our reality is the exact opposite of what we would like it to be if you consider life to be complex. https://dbeagan.blogspot.com/2023/09/distribution-of-income-ii.html

I eagerly look forward to the new museum quarters being completed in downtown Seneca Falls.  My favorite  museum in the world is the Charles Shultz Museum in Santa Rosa, CA, and yes I have been, and am comparing it, to: the Louvre, the MFA in Boston, the Met in New York, the MOMA in Los Angeles, the Vatican Museum, the Rijksmuseum, the Getty Center, etc.  It is because the Schultz Museum loves its subject, and not merely its possessions.  And my goodness there is a great subject to love in It’s A Wonderful Life.

Rules

 

The Rules of the Road

So these are the ropes
The tricks of the trade
The rules of the road
You're one of the dopes
For whom they were made
The rules of the road

Let’s hear it for the rules!

A contest for dominance between only two players involves no rules.  Either player can lie, cheat, or steal to be dominant, win.  A contest with rules, especially rules enforced by referees, does not have to only be a contest of dominance.  If the losing player is not destroyed, can complete in future contests, either with the winner of that contest or some other player, then the result of that and many contests can also be one of certainty, in addition to dominance.

It might seem like a contest is only between two teams, contestants.  But if you look closely that is because the third team in the field/arena/court, the referees, are virtually invisible if they are doing their job correctly.  That does NOT however mean they are not there, and it does not mean that they are not important.

Players in such contests may “work” the refs to try to gain an advantage, but that is implicitly acknowledging that there are rules and referees.  A player who acts like there are no rules, or is not subject to rules,  and that there are no referees, may win every contest in which he competes but he will never achieve certainty.

In elections or other political contests, it might seem like you are competing for dominance. That may be a winning tactic, but it is a losing strategy.  A winning strategy is to compete in accordance with the rules to achieve certainty.  Learn and follow the rules.

Certainty II

 

You’re The Top

You're the Tower of Pisa
You're the smile on the Mona Lisa
I'm a worthless check, a total wreck, a flop
But if, baby, I'm the bottom, you're the top

But how many are on top!

With apologies to Billboard,  it is not the Top 100.  With apologies to  AP sports polls, it is not the Top 25.  With apologies to David Letterman, it is not the Top 10.  It might be only the Top 3 that matters.

The top, first place, indicates dominance, but it does not indicate certainty.  Appearing on a top list can indicate certainty, but while more than a certain number increases visibility by appearing on the list, it does nothing to increase certainty. It is customary to rank things in order and to award the lowest number of points to the bottom of that list and the highest number of points to first place finishes. For example in a Top 5 list, 5 points for first place, 4 points for second place, and so on.  But the number of places in that list does not usefully increase certainty.  If there is a list of one, the certainty is only 25%.  If there is a list of two, there is a certainty of 50%.  If there is a list of the Top 3, there is a certainty of 75%.  If there is a Top 4 list, there is a certainty that the top is on that list of 100%.  If there is a list of the Top 5, there is a certainty that the top is on that list of 125%.  But anything more than 99.99999+% is also imaginary.  That means that the Top 3 list has the greatest certainty without being imaginary.  The number of podium appearances or the number of Olympic medals matter. Anything more is just window dressing. Good for public relations, but not certainty.

Medals

 

The Best

You're simply the best
Better than all the rest
Better than anyone
Anyone I've ever met

In the upcoming Olympics, which country is the best?

In the upcoming summer Olympics in Paris, during the opening ceremony there will be a parade of Nations of every athlete who participates in the Olympics.  During the closing ceremonies, the athlete participants are supposed to mingle without regard for country.  Between the Opening Ceremonies and the Closing ceremonies will be the events of the Olympics where medals will be awarded.  The closing ceremonies indicate that everyone gets a participation ribbon, but how should you count the medals by Nation during the events to determine which country is the best?

In each event, there are Gold, Silver, and Bronze medals awarded.  To be the Gold medalist in an event is to say that during that event you were the best.  But that does not mean that you are always the best, because that event can be viewed as a random event.  The gold medal indicates dominance on that day in that event, but it does not indicate certainty.  How can you indicate both?

In some countries only the number of Gold medals are considered.  I.e. each Gold medal is worth one point.  The country with the most points is considered the best.  But since the finish is random, that only indicates dominance, not certainty.  In some countries, each medal is awarded a point. Then the question becomes why stop at 3 medals for each event.  Why not award everyone who participates a medal.  Sounds like the political debate of woke vs. non-woke!

It is typical  in the United States, for each Bronze medal to be awarded one point, each Silver medal to be awarded 2 points, and each Gold medal to be awarded 3 points.  The points are totaled and the country with the most points is considered to be not only dominant but certain.

This is a Nash Equilibrium between the User Optimum of considering only Gold medals and the System Optimal of considering all medals as equal.  Is it perfect?  It does not consider Users who shop for a country which allows them the best chance to compete, nor does it consider a country which offers citizenship and/or rewards to athletes who have the best chance of winning.  But it considers the difference among medals, and awards no points to athletes who merely wish to compete with no expectation of winning, such as the Jamaican bobsled team. So arguably the US system is the best at determining the best country with dominance AND certainty.

Submission

 

Submission

Submission to the will, of Him who loves me still,
is surety of his love revealed.
My soul shall rise above this world in which I move;
I conquer only when I yield.

Words matter.  Who has the power when you are submitting?

Submission

the action or fact of accepting or yielding to a superior force or to the will or authority of another person.

Acceptance

the action or process of being received as adequate or suitable by another.

They sound the same but there is a significant difference between submission and acceptance. Submission is interior focused. You are submitting to an external force that is superior to yours.  Acceptance is externally focused. You are being received as adequate by a force that is external.

If you change and perceive that the external force is no longer superior to you, then you could no longer submit. If you are accepted by an external force and that force does not change, then you are still accepted even if you have changed.

If you submit to an absolute, then you can revoke that submission. If you are accepted by an absolute, then that acceptance will not be revoked. Presumably, the absolute understands how you might change and that was considered in the acceptance. While you might change, that absolute does not change.

The subject has the power. You submit. You are the subject. You are accepted. You are the object.

If you believe that God is an absolute, has the power, and is unchanging , then you don’t submit to God. You ask to be accepted by God and if you are worthy, then God accepts you.

Beware those "evangelicals" who have submitted to Jesus.  They are implictly saying that they believe that they can be more powerful than Jesus.  Trust only those that have asked to be, and were, accepted by Jesus.

Close Enough

 

The Long And Winding Road

The long and winding road
That leads to your door
Will never disappear
I've seen that road before
It always leads me here
Leads me to your door

How long are we taking about?

Pythagoras' Theorem is for a Euclidean, flat, surface.  The universe may be a hyperbolic surface.  This makes a difference for the solution of Pythagoras’ Theorem.  It does not really apply on spherical surfaces such as the earth, when the distances that are the sides of the triangle are large compared to the radius of the spherical surface (for example, the Earth).  On Earth, when the distances are small, the difference between the results of Pythagoras’ Theorem and the Great Circle Distance on the Earth is trivial. The same seems to be true for a hyperbolic universe.

For 1/3 of the size of the universe the difference between the hypotenuse on a hyperbolic surface of the universe and Pythagoras’ Theorem is less than 6%.  Since the size of the universe is approximately 14 billion light-years, until the sum of the squares of the distances exceeds 22 trillion billion miles the difference is less than 6%.  The distance from the Earth to the Sun is 93 million miles, 8.3 light-minutes, 1.6*10^-5 light-years.  The distance from our solar system to the Andomeda galaxy is 2.5 million light years, so we are talking about much more than intergalactic distances before there is an appreciable difference.  In fact for distances of a thousand miles on each side of a right triangle, the difference between a hypotenuse calculated with Pythagoras' Theorem and one for a hyperbolic surface is far less than 0.01%.  So don’t throw away Pythagoras' Theorem.  It is simpler and has very little error from the hyperbolic solution at most distances that you are likely to encounter.  So what is long to you, is insignificant to the universe.

Freedom of Speech

 

Everybody’s Talkin’

Everybody's talking' at me
I don't hear a word they're saying'
Only the echoes of my mind

Is it the public town square where the talking is taking place?

Does the First Amendment of the US Constitution  guarantee freedom of speech?  It does protect against government regulation.  Your right to speak in a private place, not a public place, is never an abridgement by the government.  In a private setting, your rights are subject to the owner of the space in which you are making that speech, not the government.  You are also free to exercise the right to speak, but you are not exempt from the consequences of that speech.  Libel, defamation, harassment, etc. can be judged a consequence of that speech.  The owner of the space in which that speech is made may be judged an accomplice and thus be liable for your speech.

The problem is that the space in which that speech is exercise is probably NOT a public space.  A town square is a public space, but a retail store is NOT a public space.  Most social media platforms (e.g. Facebook, X [formerly Twitter], Instagram, Tik Tok, etc.) are private companies/spaces, not public spaces. They may use public resources (e. g. air waves) in which case they may be subject to public regulation, but they are still private companies.  They can regulate your speech to protect their own interests. 

You are also only guaranteed the right to speak.  There is no guarantee that anyone will listen. Maybe you will hear only the echoes of your mind.

Privatization

 

Anything You Can Do

Anything you can do, I can do better,
I can do anything better than you

No, you can't
Yes, I can
No, you can't
Yes, I can!

Anything you can be
I can be greater, 
sooner or later
I'm greater than you

Can private companies do better than governments?

Before 1998,  for 18 years I was employed by governments.  Since 1998, I have been employed by a private firm selling its services to those governments.  Thus I am not asking whether there are services that governments can obtain from private companies or else I would be a hypocrite.  But when I offered those services, the action was ultimately taken by a federal, state, or local government.

But there are services that are offered exclusively by governments, like armies, postal delivery, prisons, law enforcement, fire fighting, education, libraries, etc.  Should those services be offered by private companies?   It certainly seems like they are cheaper than government in many cases.  When I was in government service between 1992 and 1998, I served in an administration that was convinced that anything a government did, a private company could do better. IOW, all government services should be privatized.  This included road construction and road upkeep, which was my government department.  The government functions seemed to devolve to just purchasing these services.

But the USDOT took the step of saying, not with our money you don’t.  They took action to decertify our state transportation department because they felt that the procurement officers were no longer capable of telling whether their federal standards were being followed or we were simply being lied to by those private companies.  If those private companies were cheaper because they were smarter, then the government should of course pay to become smarter.  But if those private companies were ignoring acceptable standards, or paying their employees or contractors below fair compensation, or ignoring laws, didn’t this merely make the government complicit in those actions.  And there is that little thing called profit.  Public governments do not have to make a profit, private companies do.

Public governments also must offer services to all of its citizens, and not arbitrarily turn away anyone. Private companies can decide to not ever offer services to anyone, or only offer services under certain conditions. Like not delivering on weekends, or cutting hours.  Private armies can hire criminals.  Are those actions that governments should emulate?  They should be better, not just cheaper!

Winning?

 

Marianne

All day, all night, Marianne
Down by the seaside siftin' sand
Even little children love Marianne
Down by the seaside siftin' sand

My maternal Grandmother’s name was  Marjanna.  My sister is named Marianne.  This post is of course dedicated to them.

The icon of the French Republic is Marianne.  The comparable in the United States would be Lady Liberty.  The Motto of the French Republic is Liberté! Égalité! Fraternité!

Those who believe primarily in Liberté, Liberty, are perhaps User Optimalists.  They believe that their own Optimal is paramount.  They believe in Winning.  They think that Winning is not the thing, it is the only thing.  They believe that a Tie is like kissing your sister and that second place is first loser.  At its worst this means winning at all costs including lying, cheating, and stealing.  Because of their beliefs it is difficult to find anyone to play with them.

Those who believe primarily in Égalité, Equality, are perhaps System Optimalists.  They believe that the Optimal of the system is paramount to their own Optimal.  They think everyone should get the benefits of winning, that everyone should get a participation ribbon, that everyone should take one for the team, and that no score should be kept.  They believe that a tie should have the same value as winning.  At its worst this places no value on winning.  Because of their beliefs, System Optimalists have no incentive to produce anything if it only can be taken from them and besides, they don’t like playing anyway.

Those who believe primarily in Fraternité, Fraternity, believe in the strength of brotherhood, safety in numbers, that the whole is greater than the sum of its parts.  At its worst, they will give trust to other members of their fraternity which is not warranted, and fear anyone not in their fraternity. Because of their beliefs they are likely to want to produce value and oppose zero-sum games for at least for their own members.

Society needs all of those people. Society wants everyone to play; to produce, not only for themselves but for others.  It does so by instituting rules, which in game theory would be payout matrices.

User Optimalists would be happy with a payoff matrix, which in a classic game of two choices where you are rewarded for being different and penalized for being the same, of

		Player One
		Odd	Even
Player Two	Odd	-1	1
	Even	1	-1

System Optimalists would be happy with a payoff matrix where you were rewarded for being the same and penalized for being different, e. g.:

		Player One
		Odd	Even
Player Two	Odd	1	-1
	Even	-1	1

The problem is that while these matrices are fine for zero-sum Games, believers in Fraternity want something more than a zero-sum game, where only members of their own group can be a player, such as

		Player One
		Odd	Even
Player Two	Odd	1	1
	Even	1	1

None of these payout matrices is acceptable to all three groups.  A compromise is proposed where one choice is the preferred choice (in the example below, Odd).  It has the advantage of awarding the most points for a Win, less for a Tie, but still valuing a Tie more than a Loss, and is not a zero-sum matrix. It is  

		Player One
		Odd	Even
Player Two	Odd	0	1
	Even	2	1

But there is an interesting and simple winning strategy with this payout matrix.  A player always plays the non-preferred option in the first game.  If his opponent also chooses the non-preferred option, then that player gains a point. But if his opponent plays the preferred option, he gains no points and his opponent gains two points.  On every subsequent game with the same opponent, that player opts for whatever that opponent played in the prior game.  In this manner, if his opponent plays the preferred option again, then both players are blocked and get no points.  Let’s call this the “Tit for Tat” strategy. 

But if his opponent plays the preferred option in another game with another player, and that other player also plays the preferred option, then neither player gets any points.  Let’s call always playing the preferred option, the “Always Go For The Win” strategy. 

If person following the “Tit for Tat” strategy continues this strategy with another player who also plays the non-preferred option on his first move, they both get a point. But the “Tit for Tat” strategy gets no points in every game against players following the “Always Go For The Win” strategy.

After a large number of games have been played, players following the “Tit for Tat” strategy have the most points.  Those players may have won no games.  The “Always Go For The Win” strategy, wins more games, wins no games against those also follwing an "Always Go For The Win" stagegy, but it does not have more points. This has been tested repeatedly. https://dbeagan.blogspot.com/2021/05/tough-but-fair-beats-always-being-nasty.html

This payout matrix not only satisfies Liberty, Equality, and Fraternity, but society as a whole wins!

Journalists

 

A Day In The Life

I read the news today, oh boy
About a lucky man who made the grade
And though the news was rather sad
Well, I just had to laugh
I saw the photograph

Good or bad, we count on journalists to tell us the news.

“who disguised as Clark Kent, mild-mannered reporter for a great metropolitan newspaper, fights a never-ending battle for Truth, Justice, and the American Way. “  BTW Superman, whose Kryptonian name was Kal-El, was created by two Jews and is a thinly veiled retelling of the Moses story with a spaceship subbing for a basket in the bulrushes.

Journalists are supposed to be interested in the Truth, certainty, not merely in who wins, dominance.  Journalists are supposed to speak truth to power, not present both sides.

It is hardly surprising that 1/3 of the people support Trump.  The minimum number of players according to Game Theory is three.  ( yes, it may look like there are only two teams on the field, but have you forgotten about the refs?)  So 1/3 choosing Trump, and 1/3 choosing Biden, means that the battle for dominance is for the middle third.  

As a traffic engineer, I ask you to think about what happens when you encounter a “Lane Drop Ahead” sign.  The System Optimal solution would be to use the lane drop as long as possible and then seek a safe gap to merge into the continuing lane, a "rolling merge".  The User Optimal solution is to drive until the end of that lane being dropped and then force yourself into the continuing lane, regardless of others in that lane.

What happens is that neither the System Optimal or the worse case User Optimal solution is chosen by most cars.  Instead cars get into the moving lane as soon as possible and someone if necessary, usually a semi-tractor trailer truck,  blocks the lane which is being dropped.  This is called a Nash Equilibrium after John Nash, the subject of the movie A Beautiful Mind. https://www.youtube.com/watch?v=-6eK0yiw9t0&t=11s .  Only in this case, semis are blocking the lane, not the Blonde.

The 1/3^rd who want their User Optimal try to convince the middle to let everyone choose their own User Optimal.  That can include lying if necessary, in order to win a majority of that middle 1/3^rd.  But if the middle 1/3^rd knows that those are lies, then expect a Nash Equilibrium instead. But we are counting on journalists to tell them that they are lies.  “Everyone is entitled to their own opinion but they are not entitled to their own facts”.  Please journalists, fight for the Truth, Justice and the American Way. Be our Supermen.

Art

 

ARTPOP

A hybrid can withstand these things
My heart can beat with bricks and strings
My ARTPOP could mean anything

Is Art a hybrid, that is a combination?

What I've discovered is that in art, as in music, there's a lot of truth—and then there's a lie. The artist is essentially creating his work to make this lie a truth, but then he slides it in amongst all the others. The tiny little lie is the moment I live for, my moment. It's the moment the audience falls in love. -  Lady Gaga

Far be it from me to disagree with Mother Monster, because I don’t, but Art is Truth.  And Lies are the absence of Truth.  Truth is a combination of Reality and Imagination.  Lady Gaga has Imagination.  She does not tell Lies.  I think what Lady Gaga meant to say is:

What I've discovered is that in art, as in music, there's a lot of reality—and then there's imagination. The artist is essentially creating his work to make this combination a truth, by sliding his imagination in amongst all the reality. The imagination is the moment I live for, my moment. It's the moment the audience falls in love.

Election Slogan

 

Save The Country

We could build the dream with love
And I got fury in my soul
Fury's gonna take me to the glory goal
In my mind I can't study war no more
Save the people! Save the children! Save the country!
Save the country! Save the country! Save the country!

Save the Country!

The Biden Campaign has seems to have decided on “Save Democracy” as its slogan.  That sounds like it is favoring the Democratic Party.  Should it be “Save the Republic”?

Republic, form of government in which a state is ruled by representatives of the citizen body. Modern republics are founded on the idea that sovereignty rests with the people, though who is included and excluded from the category of the people has varied across history. Because citizens do not govern the state themselves but through representatives, republics may be distinguished from direct democracy, though modern representative democracies are by and large republics.

https://www.britannica.com/topic/republic-government

The Biden election is being opposed by "republicans In Name Only", rINOs, who are afraid that the people will not choose as those rINOs have chosen. They do not want representatives of the people but representatives of only themselves.  When Benjamin Franklin was asked what form of government the Constitutional Convention had given, he is supposed to have said “A republic, if you can keep it”.  This appears to be an election that will decide whether we can keep it.

Dominance or Certainty

 

Winner Takes It All

The winner takes it all (takes it all)
The loser has to fall (has to fall)
It's simple and it's plain (it's so plain)
Why should I complain? (Why complain?)

So Wall Street which is it? Dominance? or Certainty?

The Wall Street stock market is all about winners and losers, by dominance. But the stock market also hates uncertainty. You can’t have certainty in a contest with only two parties which will be decided by dominance.

The stock market is not certain,which is why there are Index funds and why a random walk of the stock market does better than day trading. Collectively you can achieve certainty. Individually you might achieve dominance but that is at the expense of allowing uncertainty. A contest where there are only two outcomes and two players can be 100% dominant, but that outcome is purely by luck, a random occurrence if the game is fair and the parties are equal. In this case the certainty that the dominant winner is the certain winner is the value of that outcome, 100%, multiplied the reciprocal of the probability of that outcome, which is 50%. Thus even though the dominance of the winner has been established, the certainty is only 50%.

The difference between certainty and dominance can best be seen in the jury system. A 7-5 jury vote indicates 100% dominance, but it is only 80.66% certain.  A 12-0 finding of Guilty, or Not Guilty,  remains 100% dominant, but the certainty has increased to 99.98 %.

Thus for a single stock transaction, you can be dominant or certain, but being dominant does not mean being certain. However being certain does mean being dominant.

Zero

 

Transcendental Meditation

Transcendental meditation
Transcendental meditation
Can emancipate the man
And get you feeling grand
It's good

Is zero transcendental?

In mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best-known transcendental numbers are π and e.

https://en.wikipedia.org/wiki/Transcendental_number

While π and e might be the best known transcendental numbers, it is noted that hyperbolic trigonometric functions, which are expressed as functions of powers of e,  which is itself a transcendental number, are transcendental functions.  These hyperbolic trigonometric functions are also periodic in i*π,  i.e. repeat on the imaginary axis with a frequency of multiples of π[1], another transcendental number.   

Euler’s formula, e^ix=cos(x)* sin(x)*i, is also the coordinate transformation of a complex number from polar coordinates to rectangular, Cartesian, coordinates with a real and an imaginary axis, where the polar radius is 1.   It includes the rotation of the imaginary axis by an angle of x.  Sin(π)=0 means that the coefficient of the imaginary axis is zero.  Does that mean that there is NO imaginary axis?  That depends on whether that zero is absolute or relative. 

Absolute zero is the absence of the absolute, i.e. a temperature of absolute zero means that there is an absence of temperature.  By contrast, zero on the Centigrade scale does not mean that there is no temperature, just that the temperature is relative to a zero point on the scale, which in the case of the Centigrade scale is the freezing point of water.  IOW, negative numbers are allowed on a relative scale.

Transcendental functions are not expressible as a finite combination of the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extracting a root. Examples include the functions sin(x), cos(x), cosh(x), sinh(x), e^x, ln(x), etc., and any functions containing them. Special transcendental functions are the reflection of sin(x), which is sin(‑x) and is equal to sin(x) and the reflection of cosh(x), which is cosh(-x) and is also identical to cosh(x). This is not true of cos(x), tan(x), sinh(x), tanh(x), e^x, ln(x) and other transcendental functions.  They are not self-reflective, reflections of themselves.

Because cos(x) is transcendental but not self-reflective this means that Euler’s formula is also transcendental but not self-reflective. In that equation x can take on any value between -∞ and ∞.  Because Euler’s Formula is a combination of a self-reflective sin(x) and a non-self-reflective cos(x), but trigonometric functions are repeating, there are many solutions with a zero coefficient of the imaginary axis, i.e. a rotation of the imaginary axis of zero: even multiples of π, including zero, which have values of cos =1 as the coefficient of the real axis; and odd multiples of π which have values of cos=  -1 as the coefficient of the real axis. Since in this case zero is not merely the absence of an absolute, and is in fact multiple numbers, it must be a relative zero, not an absolute zero. An absolute zero is the absence of a transcendental .  A relative zero is not.

So is zero transcendental?  That depends on if that zero is absolute or relative.

---

[1] Cosh, sinh, and related functions, repeat with a period of 2*π*i.  Tanh and related functions repeat with a period of π*i. 

Absolutely IV

 

With A Little Help From My Friends

Would you believe in a love at first sight?
I'm certain it happens all the time, yeah
What do you see when you turn out the light?
I can't tell you, but it sure feels like mine.

How certain are you that it happens all the time?

A random equation has two parameters: 1) its location, mean/median/mode, and 2) its scale, variance, uncertainty. The adage is that nothing is certain except death and taxes. Given that you can cheat on taxes, but you can’t cheat death, I would suggest that only death is certain, and thus life is uncertain, i.e. has a variance.

An exponential distribution also has a variance but is defined only for positive numbers. This restriction is identical to saying that its location is zero. It still has a scale parameter, a variance, that is given as λ. It is suggested that the exponential distribution is a distribution of the absolute. It can be coordinate transformed by translation to any location, µ, as long as µ>0 and then its Probability Density Function, PDF, becomes

λ*e^-λ*(x-µ)

and its Cumulative Distribution Function, CDF, becomes

1-e^-λ*(x-µ)

The median of an exponential distribution is generally given as ln 2/λ, but this is when the location is zero. With the translation of the location, the median is ln 2/λ+µ. The mean is 1/λ+µ.

A normal logistics distribution has both a location and a scale parameter. Its CDF is

½*tanh((x-µ)/(2s))+½.

For the median of the two distributions to be equal requires that s = (ln 2)/λ and that µ>0.

When the location of a logistics distribution is zero, then its upper half, above its median, looks like an exponential distribution with a location of zero. This is hardly surprising. The exponential distribution is also the equation of radioactive decay. Its scale parameter, λ, is then known as a half-life.

There is no need as Grushka (Grushka, 1972) and Reyes (Reyes, Venegas, & Gómez, 2018) wo each have proposed to combine an exponential with a normal (e.g. Gaussian or logistics) distribution.  An exponential distribution is only the upper half of a normal logistic distribution with a location of zero. That does not mean that a logistics distribution is an absolute. An exponential distribution, an absolute, is half of a random normal logistics distribution, life.  Of this I'm certain.

References

Grushka, E. (1972). Characteristics of Exponentially Modifed Gaussian Peaks in Chromatograhy. Analytical Chemistry Vol 44, pp. 1733-1738.

Reyes, J., Venegas, O., & Gómez, H. W. (2018). Exponentially-modified logistic distribution with application to mining and nutrition data. Appl. Math 12.6, 1109-1116.

 

Impossible

 

Impossible / It’s Possible

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!

Did you mean Improbable?

When I was growing up, many of my neighbors and relatives worked for the then headquarters of the Naval Construction Battalion of Engineers, "SeaBees", at Quonset Point Naval Air Station.  The motto of the SeaBees is “Can Do” and the phrase "With willing hearts and skillful hands, the difficult we do at once, the impossible takes a bit longer" is often associated with them.

I always wanted to be a Seabee, but I had to settle for being just an engineer.  As an engineer I may be willing, but I know engineers can’t ever do the impossible, just the improbable.  But often what is called impossible is merely improbable.  So ask an engineer.  He may be just the zany fool you need!.

Safe Schools

                                                                 Ever True to Brown

We are ever true to Brown,
For we love our college dear,
And wherever we may go,
We are ready with a cheer,
And the people always say,
That you can’t outshine Brown Bears,
With their Rah! Rah! Rah! and their Ki! Yi! Yi!
And their B-R-O-W-N.

Go Bears!

I graduated from Brown University in 1973.  While I am proud to be a Brown Alum, this was not my first, or even my second, choice of school.

My first choice was the US Naval Academy.  I thought that my godfather having the rank of Navy Captain and my being a Merit Scholar made me a shoo in.  But I failed the medical exam because of my eyesight.  ( I CAN see a battleship!  I immediately went to my draft board physical and was found to be 1-A before I got a student deferment.  Apparently I see good enough to be a grunt, just not to be a naval officer!)  My second choice was MIT, but I was rejected there. Which made Brown my "safe" school.

Art

 

A Secretary Is Not a Toy

That a secretary is not a toy
No, my boy
Not a toy to fondle and dandle
And playfully handle
In search of some puerile joy
No, a secretary is not
Definitely not
A toy

And an artist is NOT his work of art.

The worst blowout in College Football happened in 1916 when Georgia Tech beat Cumberland College by a score of 222-0.  Apparently the football coach of Georgia Tech, who was also its baseball coach, wanted to enact vengeance because of a baseball loss to Cumberland College of 22-0.  Cumberland College had disbanded its football team and tried to get out of the game.  The Georgia Tech coach refused and the game was to be played as scheduled.  A ragtag football team was assembled from the student body for just this game.  Georgia Tech scored on every possession in the inevitable slaughter.  The vengeful football coach of Georgia Tech?  John Heisman. Yes, the same coach whose name is honored in the Heisman trophy.

Sticking with a college football theme,  Pop Warner was the coach at the Carlise Indian School where he was not above cheating to win his games against other college football teams.  In fact many of his efforts to bend the rules of his day were adopted to become the regulations of what we know today as football.

It isn’t only college football.  Vincent Van Gogh was a madman who cut off his own ear.  Thomas Jefferson owned slaves when he wrote the Declaration of Independence.  Kevin Spacey won an Oscar for his performance in American Beauty before his sexual assault scandals.  Bill Cosby was America’s Dad before his own scandals. Has anyone seen the movies The Imitation Game or A Beautiful Mind?

All humans, including artists, are flawed beings.  The Bard was being ironic when he wrote “I come to bury Caesar, not to praise him. The evil that men do lives after them; The good is oft interred with their bones”.  Often it is the good that lives after them and the evil that is buried with their bones.  What endures is art.  The art may be judged as good or great, even if the artist is flawed.  You might expect great art from certain artists, but that does not make those artists without flaws.  The art may be great, but the artist, as a human, can be not so great. Don't confuse the two. "Love the sinner, but hate the sin" works both ways. You can "Love the art, but hate the artist".