Distributions

 

Patterns

And the light from a street lamp
Paints a pattern on my wall,
Like the pieces of a puzzle
Or a child's uneven scrawl

Finding the pattern,  (theory) can help you solve a puzzle.

Ruh-Roh.  Be warned.  This blog posting is especially nerdy.

Statistics is a descriptive science. It is NOT a predictive science. While statistics can help develop probabilistic models, Probability and Statistics alone can not develop models that predict with a  certainty. (see Pynchon’s  Gravity’s Rainbow or Stoppard’s Rosencrantz and Guildenstern Are Dead.)  It is possible to observe relationships that can assist in developing a theory, which is then used in predictive models, but first there has to be a theory. Observations can support a theory. But observations alone do not make a theory.

A normal statistical distribution has to allow the possibility of negative values. If the mean is significantly greater than zero, negative values are improbable BUT they are not impossible. For example, a normal distribution might have a mean of 100, a variance of 10, (the phrase “flatten the curve” that become popular during the COVID-19 pandemic would be translated to “increase the variance” by a statistician), a skew of 0, and a kurtosis of 0. If the kurtosis is 0, then the observed data has no outliers. If the skew is 0, then the function is uniform, and the mean is equal to the median which is equal to the mode. At a value of negative 100, this uniform normal probability function still says that -100 could be observed 2.2529*10^-262  % of the time. This is NOT zero. but it is a vanishingly small number and is often treated as if it WERE zero. 

There is a difference between a negative which is reported and a real negative. When you say it is  ‑10 degrees Fahrenheit outside, it does not mean that there is negative energy. Just that a value of zero on the Fahrenheit scale,  0 °F, was established as the freezing temperature of a solution of brine made from a mixture of water, ice, and ammonium chloride. The other limit established was a best estimate of the average human body temperature, which at the time the Fahrenheit scale was established was 96 °F. The Centigrade, or Celsius,  scale of temperatures defines values of 0 °C as the freezing point of water and of 100 °C  as the boiling point of water. At -40 degrees, the Fahrenheit and Celsius system are the same. However both systems are merely a translation of temperature from a temperature of absolute zero.

If negative numbers are not allowed, statistics suggests the use of an exponential distribution. While an exponential  distribution does not allow negative numbers, it is a smooth continuous function. That is a probability function of 1.5 will have a value, even if only integer values should be observed. It may be convenient to state the mean family size of as 3.14, and the median family size as 3.12, but families don’t come that way. Each family member will only be an integer value. The mode is most probably 3, and thus family size is  skewed, even if it is a very small skew.

A uniform normal distribution requires that the mean, median and mode are equal. In an exponential distribution the mode  is zero; the demand is equal to 1/λ, where λ is the coefficient of the exponential in the probability function of the distribution, λe^-λx; and the median is ln 2/λ , the mode is 0, and the skew is 2. A distribution that combines the features of a normal distribution with the features of an exponential distribution is an exponentially modified Gaussian (normal) distribution. Then the mode does not have to be equal to zero, and the median can be adjusted to be close to the mean without being the equal to the mean.

 

 

 

Gravity

 

Defying Gravity

It's time to try defying gravity
I think I'll try defying gravity
And you can't pull me down

Gravity follows spacetime. Is spacetime Euclidean ? Or is spacetime Non- Euclidean and  hyperbolic?

“According to Albert Einstein's general theory of relativity, gravity is no longer a force that acts on massive bodies, as viewed by Isaac Newton's universal gravitation. Instead, general relativity links gravity to the geometry of spacetime itself, and particularly to its curvature.

In classical physics, time proceeds constantly and independently for all objects. In relativity, spacetime is a four-dimensional continuum combining the familiar three dimensions of space with the dimension of time.

To account for gravity in relativity, the structure of this four-dimensional spacetime must be extended beyond the rules of classical geometry, where parallel lines never meet and the sum of a triangle’s angles is 180°. In general relativity, spacetime is not 'flat' but is curved by the presence of massive bodies."
  https://sci.esa.int/web/lisa-pathfinder/-/56434-spacetime-curvature

This is a bit of an exaggeration. Gravity IS a force, but it is an apparent, fictitious, or pseudo force. These fictitious forces  are familiar forces. Water in a bucket spinning overhead on a rope, appears to defy Gravity because of Centrifugal force. If a Centrifugal force were not acting on the water, it would slosh out of that spinning bucket. A motorcyclist in a Globe of Death seems to defy Gravity and rise on the walls because of Centrifugal force. Water in a drain spins in a clockwise direction in the Northern Hemisphere, but in a counterclockwise direction in the Southern Hemisphere, because of the Coriolis force.

Saying that Gravity is not a force, but is a fictitious force means that there is, with apologies to Paul Harvey, a Rest of The Story. Gravity is like a trick in stage magic. Understanding how it works can better understand how you were tricked. Like Humpty Dumpty told in Alice in Through the Looking Glass, understanding  Gravity means “which is to be master — that’s all.”  If you wish to master and  defy Gravity you have to understand Gravity.

Gravity is the observation that particles will follow the shortest geodesic in spacetime.  When spacetime is curved, as it is required to be by General Relativity, then what appears to the path of a particle may be because spacetime is curved.  In Euclidean , what is called classical geometry in the quote above,  this apparent deviation from a straight line is attributed to Gravity.  If spacetime is curved, Non-Euclidean, and hyperbolic where the angles in triangles sum to less than 180 degrees, then Gravity can be a fictitious force.

If Gravity is a fictitious force, then efforts to include Gravity in a Unified Field Theory may be misplaced.  If Gravity is a fictitious force then efforts to develop a theory of Quantum Gravity may be as silly as trying to develop a theory of Quantum Centrifugal Force.

Republicans IV

 

Satisfaction

When I'm watchin' my TV
And a man comes on and tells me
How white my shirts can be
But, he can't be a man 'cause he doesn't smoke
The same cigarettes as me

What kind of a man is a Republican?

·       “McConnell during a recent GOP lunch implored his caucus to reject Ketanji Brown Jackson's SCOTUS nomination.

·       He reportedly praised Judiciary Republicans for scrutinizing the judge's sentencing history, per The Hill.

·       Sen. Susan Collins is currently the only Republican who plans to vote for Jackson's confirmation.

Senate Minority Leader Mitch McConnell is pressing his GOP caucus to vote against confirming Ketanji Brown Jackson to the Supreme Court, according to The Hill.” https://news.yahoo.com/mcconnell-pressing-gop-senators-oppose-161708443.html

Let me get this straight. 

·       You can’t be a Republican if you vote to approve the nomination of Ketanji Brown Jackson. 

But

·       You can be a Republican if you say Republicans have sex orgies and consume bumps of cocaine. 

·       You can be a Republican if you say that the Capitol Riot of January 6, 2010 was “legitimate political discourse”. 

·       You can be a Republican if you say that “there were fine people on both sides” in the Charlottesville March of August of 2017.

·       You can be a Republican if you say that Jewish Space Lasers started California wildfires

·       You can be a Republican if you  post an animated video that depicts the killing of a Democratic congresswoman and attacking Joe Biden.

I guess being a Republican doesn’t mean the same thing to Senator McConnell, that it does to me.  He probably doesn’t “smoke the same cigarettes as me” either.

Voting Restrictions

 

Snoopy For President

All the politicians, they swore he couldn't win
But Snoopy only shook his head and flashed his famous grin
He jumped into his faithful friend, the Sopwith Camel plane
And bounced around the countryside from Washington to Maine

You can try as hard as you can, but you are NEVER going to demonize Snoopy.

The United States has a first across the line, single representative per district, voting system. This means that there will generally be two parties according to Duverger’s Law. If one of the candidates receives a plurality of those voting, they will be elected. Thus in campaigning a viable winning strategy is to keep those who would vote for your opponent from voting. This means that the winner of the elections may not be a majority of all eligible voters (including those who were eligible but did not vote).

Whether the voters for one’s opponent are kept from voting by restrictions ( e.g. poll taxes, literacy tests, voter IDs, voting during working hours, restrictions on mail in voting, etc.) or by demonizing /throwing mud at, an opponent, does not matter. The important thing for a candidate is that they do not vote.

One way that has been proposed to deal with this is ranked choice voting. This is not an exotic system. A form of ranked choice voting is how national polls for the top college basketball or football team works. As proposed, a majority is required for elections. If a majority is not achieved, any votes for the last place candidate are eliminated and those votes are shifted to the next highest ranked candidate. ( I.e. if a candidate is eliminated, their second-place vote become first place votes for the remaining candidates.) Ranked choice voting requires that there be more than two candidates. An alternative is collegiate sporting polls where every vote is retained, but first place votes are scored more than second place votes, second place votes are scored more than third place votes, etc. The total score is tallied to determine the winner. But according to Duverger’s Law, if only two parties will nominate candidates, regardless of whether the traditional, or the sports poll method is chosen, ranked choice will not change the result.

If a ranked choice voting system exists, there is still the temptation to demonize other candidates so that they become a lower ranked choice of any voter.

Australia has a mandatory voting law, but it also has ranked choice voting and has a multiple representative per district voting system. While every voter in Australia will cast a ballot, candidates still have an incentive to demonize their opponents so that they appear lower as ranked choices on ballots.

Rather than promote ranked choice voting in the United States when there will typically only be two candidates and ranked choice voting will not change the result, or opposing voter restrictions, given only two candidates in most elections,  mandatory voting, and not opposing voter restrictions, could eliminate the incentives to demonize an opponent in an election.

Idleness or Opportunity to Think

The Fool On The Hill

Day after day, alone on a hill
The man with the foolish grin is keeping perfectly still
But nobody wants to know him
They can see that he's just a fool
And he never gives an answer

But the fool on the hill
Sees the sun going down
And the eyes in his head
See the world spinning 'round

What happens when you have the time to see the world spinning round?

Soon after Isaac Newton had obtained his BA degree in August 1665, Cambridge University temporarily closed as a precaution against the Great Plague. Although he had been undistinguished as a Cambridge student, Newton's private studies at his home over the subsequent two years saw the development of his theories on calculus, optics, and the law of gravitation. https://en.wikipedia.org/wiki/Isaac_Newton

More than 400 years ago, as epidemics raged in London, forcing theaters and other public places to shutter, William Shakespeare was busy crafting stories of kings going mad and thanes coveting power. He was, scholars believe, in the midst of an astonishingly potent creative period, one that produced some of the most extraordinary tragedies ever written — “King Lear” and “Macbeth” among them. https://www.washingtonpost.com/entertainment/theater_dance/great-artistic-works-during-plagues/2020/11/05/6575cac2-1d29-11eb-90dd-abd0f7086a91_story.html

After finishing his studies in 1900, Einstein could not get accepted anywhere for a teaching post. Eventually he was offered a job by his friend’s father at a Swiss patent office in 1902, where Einstein’s task was to look through inventions, check their originality, and write clear patents to protect the inventors’ new ideas. His job lasted from 1902 to 1909, during which time Einstein published his four Annus Mirabilis (miracle year) 1905 papers. Einstein described the patent office as his ‘worldly cloister’, where he ‘hatched [his] most beautiful ideas’. https://oxsci.org/einstein-at-the-patent-office/

The COVID-19 lockdown is NOT the first lockdown in recorded history.  Periods of boredom in meaningless jobs provide lots of opportunity to do other things, such as seeing the world spinning round.  If history is an example, we can look forward to what may result.

Passing

 

The Great Pretender

Oh-oh, yes, I'm the great pretender
Adrift in a world of my own
I've played the game but to my real shame
You've left me to grieve all alone

What is the price of pretending?

The United States  is unfortunately a caste, class-based, society. There are the best schools, the best neighborhoods, the A-list, first class travel, etc. If people have certain characteristics they might be treated as if they are in a higher class.  For example a white male who graduated from two Ivy League schools might be considered to be a male WASP. At least in my own case that assumption would be wrong. I am a male and white but I am also an Irish‑Polish Catholic from a working class, union family.  My family has members with different genders, different sexual orientations, disabilities, and have, including especially me, mental health issues. But my last name is Beagan, and while Ronald Reagan was President I answered to BAY-gan and was assumed to think and act like Ronald Reagan, even though I pronounce it BEE-gan and I don’t think like former President Reagan. I should have corrected the pronunciation. But then I should have also objected to the accompanying disparaging comments and jokes about religion, nationality, gender, unions, income, sexual orientation, disabilities, mental health, etc, but I did not.

Those who have a different sexual orientation can talk about the cost that comes from being in the closet. Those light-skinned blacks who are passing for white, pay the cost of knowing that their identity could be uncovered. Not to put myself in the same category, but I have played the price of being in the closet, passing, pretending I was in another class. If I believe that there should be no classes, and that no one is better than another, then I should act as if there are no classes, and not accept the benefits that come from being incorrectly perceived to be in an “higher” class.

Will Smith

I’m A Man

Who imagine I'm not human
And my heart is made of stone
I never had no problems
And my toilet's trimmed with chrome

Being a man does  not mean making the first slap.

The Will Smith-Chris Rock spat is being viewed by many lenses.  I would like to suggest viewing it as an example of vigilantism.  Was Chris Rock’s joke about Jada Pinkett Smith hurtful and wrong.  She has a shaven head not because she is auditioning for GI Jane, or any stylistic choice,  but because she has publicly said that she has alopecia, hair loss.  If Donald Trump’s mocking of a disabled journalist was despicable, and it was, then this “joke’ by Chris Rock was not very funny either.  Chris Rock should not even have been making such a “joke”.  It was not in his prepared and approved remarks.  He was after all, there to present an award for Best Documentary on behalf of the Academy of Motion Pictures.  None of the documentaries nominated were about Jada Pinkett Smith, Will Smith, GI Jane, or alopecia, so, IMHO, the ”joke” was not only NOT funny, it was inappropriate.

However Will Smith escalated Chris Rock’s offensive behavior and took it on himself.  He was in a position to reach the stage only because the stars had been given a special section in the Dolby Theater, supposedly because of COVID, and not because they need and deserve special treatment.  Chris Rock’s offense was against the Academy.  Any action should have been taken by the Academy.  Will Smith acted as a vigilante.  Whether it  is “playing the dozens”, “your mama”, or "pistols at dawn", a feud to protect one’s honor, or the honor of one's loved ones, is still a feud.   The Power of the Dog was about the dangers of toxic masculinity and revenge.  A picture released this year was the Last Duel. Might does not make right, i.e. trial by combat, whether that might is a slap, jousting, a sword, a gun, or anthrax-tainted rawhide.  The tribe decides what is right.  Taking justice into one’s own hands, makes you a vigilante, and does not prove your love.  Two wrongs never make a right.

If the special seating was due to COVID safety concerns, let us hope that the Academy will end it when the Pandemic ends.  No one should be treated so specially  that they think that their pride is more important than the group's pride.