Don't Dwell in the Past

 

Dog Days Are Over

Run fast for your mother, run fast for your father
Run for your children, for your sisters and brothers
Leave all your love and your longing behind
You can't carry it with you if you want to survive
The dog days are over
The dog days are done
Can you hear the horses?
'Cause here they come

The worst is behind you.

The dog days or dog days of summer are the hot, sultry days of summer. They were historically the period following the rising of the star system Sirius (known as the "Dog Star"), which was connected with heat, drought, sudden thunderstorms, lethargy, fever, mad dogs, and bad luck. They are now taken to be the hottest, most uncomfortable part of summer. If you have survived those days, then cooler, better days are ahead. The dog days will come again next year, but the important thing to remember is that you have survived. Do things in the days to come that ensure that you will survive the dog days next year. You have a whole year to get ready.

Competition

 

All I Really Want To Do

Now I ain't lookin' to compete with you
Beat on, cheat on, mistreat you
Simplify you, classify you
Deny, defy, mystify you
All I really want to do
Is baby, be friends with you
Baby, be friends with you

Reality is NOT a competition.  No wagering please!

Reality is random.  Fair betting requires random events.  Therefore there should be betting on reality, correct?  Not exactly.  There is betting by individuals, but collectively there should be no betting.  Betting requires a zero sum game: i.e. winners AND losers.  Reality is NOT a zero sum game, there is expected to be at least a change, and hopefully growth, from the current reality. So betting individually may make sense, but betting collectively does not make sense.  If there is change, and again hopefully growth, it should be shared by both winners AND losers, because in a fair game, the winners in the past could be losers in the current contest.

If the total value of a system increases, then the median should increase.  However it is possible that the increase could go only to the current winners, or a subset of the current winners. In this case, the mean might increase while the median decreases, or stays the same.  The problem is that popular wisdom is that the average is the mean, because that is easiest to compute, i.e. system total divided by individuals in the system. Actually, average is the centrality of the normal, which is by definition the median, where half of the individuals have more than the median and half have less than the median. If the mean is the median, as it is in normal distributions, that popular wisdom isn’t a problem.  But if there is a gap between the mean and the median, it indicates that the situation is NOT normal.  If the gap between the median and the mean is increasing, this also indicates that the situation is becoming more ABnormal.

I wish I could say that the gap has been decreasing, but based on US Census reports, the gap has been increasing. 

This is not only because people have confused the mean and the median  https://dbeagan.blogspot.com/2018/08/wonderful-world-dont-know-much-about.html , inflation has masked the impact, and the tax code has exacerbated the effect, https://dbeagan.blogspot.com/2020/06/taxman.html.

Competition should be between groups, not between individuals within groups. Let’s not compete. Let’s be friends.

 

Art v. Science

 

It’s So Easy

People tell me love's for fools.
So, here I go, breaking all the rules.
It seems so easy (Seems so easy, seems so easy)
Oh so doggone easy (Doggone easy, doggone easy)

Breaking rules isn’t easy, but it is necessary.

“Art is in the eye of the beholder”.  “There are rules”.  And this describes the apparent conflict between the arts and the sciences.  Artists are individuals, breakers of rules.  Scientists are also individuals, discoverers of rules.  Those of you who are old enough to remember the classic TV show The Prisoner with Patrick McGoohan, playing Number 6, might remember the phrase.  “I am not a number.  I am a free man.”  Those of you who also remember the finale will remember that the elusive Number One was shown also to be Patrick McGoohan.  The finale seemed to imply that I am a free man because I am a number.  The problem is that man is an individual animal, but man is also a group animal, a member of a group.

The phrase is “All for One, and One for All”.  In an ideal world, All, the group, supports the individual, One and the individual, One, supports the group, All.  Or as I learned in Cub Scouts, “The Cub Scout helps the Pack go. The Pack helps the Cub Scout grow”.  A group, such as the United States in its Constitution, “Promote(s) the Progress of Science and useful Arts.”  It does so by promoting those who discover new rules and those who break old rules. To do so you don’t force old rules on individuals because those rules might be wrong or incomplete.  You also don’t prevent individuals from breaking old rules, again because those rules might be wrong or incomplete.  There should be no conflict between arts and sciences. They both have the same end goal, the making of new rules, that improve on, and may replace, old rules.

Normal III

 

A Wonderful Guy

I'm as corny as Kansas in August,
I'm as normal as blueberry pie.
No more a smart little girl with no heart,
I have found me a wonderful guy!

One Blueberry Pie distribution coming right up!

In a normal distribution, the mean is equal to the median. (Or as Donald Trump Junior so famously put it “That’s how math works”).  However the mean is not always equal to the median in many distributions.  This is often only because the negative numbers are not reported because of where the y-axis is being set.  For example saying that temperatures are 40 below zero is only because the temperature is being measured on a relative scale, not on an absolute scale.  If an absolute scale had been used, then the median should be equal to the mean for a normal distribution.  Stating the median and the mean with a with a relative rather than an absolute zero, allows the calculation of the variance, if negative values had been allowed

NAR, the National Association of Realtors, has reported the mean ($639,000) and median ($396,500) prices for existing home sales.  Since the mean is not equal to the median this is hardly normal. It is suggested that this might be because negative sales prices are obviously not reported.  But if they could be reported, then if this was a normal distribution then no values would be observed for the mean minus 3 times the square root of the variance.  This requires that the variance must be the mean²/9=45.37 million.  It has already been reported that 50% of the homes sell for less than $396,500. If this were also a normal distribution, then 68% of the existing homes should sell for less than $852,000;  95% of the existing homes should sell for less than $1,065,000 and 100% of the existing homes should sell for less than  $1,278,000.  If there are existing homes selling for more than $1.3 million, then that also indicates that the existing home sales prices are not normal.

Pro-Choice II

 

My Way

And now the end is here
And so I face that final curtain
My friend I'll make it clear
I'll state my case, of which I'm certain
I've lived a life that's full
I traveled each and every highway
And more, much more
I did it, I did it my way

Yes, but did you also let me do it my way, or did you insist that I do it your way?

Those who are Pro-Life think they are going to heaven.  If they are Pro-Life but also Anti-Choice, then I am afraid that they have violated the First of the Ten Judeo-Christian Commandments, “I am the Lord thy God . Thou shalt have no other gods before me.”  By being Anti-Choice, they have confused a discontinuity with the absolute.  They are saying that Good is equal to Evil, that they have chosen Good, and everyone else should have no choice/should also choose Good.  Unfortunately the math does not work that way.

An exponential distribution has a discontinuity.  Traditionally this is zero, but it can be shifted to any discontinuity, µ.  While the exponential distribution is not defined before that discontinuity, it can be reflected at that discontinuity. This is implicitly saying that if the distribution at the discountinuity has a value of 144%, ln(2)%, certainty, then there is a pseudo mean, because of the discontinuity, at µ+1/λ.  That is interesting but if you smooth out the discontinuity to a normal distribution, and say that at most you can be 100% certain, then a factoring of a normal distribution is appropriate. But by saying it must be 100% certain, you are also saying that there is a Cumulative Distribution Function, CDF, of that factoring, which has almost the shape as the CDF of the exponential distribution with a discontinuity.  But the problem is that before the discontinuity, the exponential distribution implies a negative absolute while the factored continuous normal distribution has only one absolute. 

If you say that there is a choice, then you should only have a 50% chance of making that choice at the discontinuity. However by also saying that choices made before the discontinuity should not be considered, are treated as if they are zero, the Cumulative Distribution Function is of course substantially lower, and it takes until well after the discontinuity to reach 100%.  If you are Pro-Life AND Pro-Choice, then your CDF will reach 100% much sooner. If you are Anti-Choice, then you are also saying that there are two absolutes, not one.

So if someone is Pro-Life AND Pro-Choice, then they are keeping the Commandments, not breaking them.

The Unethical Justice Alito

 

Waiting for the Robert E. Lee.

Way down on the levy in old Alabamy
There's Daddy and Mammy
There's Ephraim and Sammy
On a moonlight night you can find them all
While they are waiting,
The banjos are syncopating

Stop the music “Strip Search” Sammy! Your waiting is over!

You just knew that Justice “Strip Search Sammy” Alito could not let Justice “Long Dong Silver” Thomas get all of the headlines as the villain of the Supreme Court. “Strip Search Sammy” just wrote an editorial in the Wall Street Journal that it was unconstitutional for Congress to impose a code of ethics on the Supreme Court. Let’s give you a civics lesson “Strip Search.”  The Constitution, as in says in the very opening  line, is the document of “We The People.”  The Congress is the elected representatives of “We The People", whose job is to enact laws. The Supreme Court only offers opinions on those laws as to whether Congress acted against the stated protections, not of the Supreme Court, but of “We The People.’  If Congress says the Supreme Court should be 

1. ethical, or 
2. have terms limits because its justices are not immortal, or 
3. should decide cases not by domination but by certainty, or 
4. decide that there should be ten rather than the current nine members of the Supreme Court, as has been the case in the past, 

AND that law does not require an action that is specifically prohibited by the Constitution,  (And let’s save you the trouble, “Strip Search”.  Just as the Constitution did not mention a right to an abortion,  it also does NOT prohibit ethical standards), then who are you to speak.  Put down the shovel, Sammy. You are in a deep enough hole right now. Your waiting is over. The People are coming for you.

Pythagoras

 

Supercalifragilisticexpialidocious

He traveled all around the world and everywhere he went
He'd use his word and all would say there goes a clever gent
When dukes or Maharajas pass the time of day with me
I say me special word and then they ask me out to tea (woo)

But if you say HYPERBOLICfragilisticexpialidocious, then you might be even smarter!

e^ix=cos(x)+isin(x), where cosh(x) is the hyperbolic version of the trigonometric cosine, cos(x), is Euler’s Formula, where i is  the imaginary number, √-1, which is called j by electrical engineers.  This can be restated as y=f(x)=ln(cos(x)+i*sin(x))/i, and which implies cos(x)=e^ix - isin(x). If f(x) is coordinate transformed by rotating by 90° it becomes x=f(y)=ln(cos(y)+i*sin(y))/i. This can restated as y=g(x) where g(x)=sin(90°)f(x).  But this also means that cosh(ix)= cos(y) + isin(y). Any cosine can also restated as √(1-sin²). This means that cosh(ix)=cos(x)+isin(x) therefore becomes cosh(ix)=√(1 - sin²(x))+isin(x) and also cosh(ix)=√(1-sin²(y)+2isin(y)). If only the real components of the complex numbers are used, this means that the rotation of Euler’s Formula by 90° is true only if y and x are identical and zero.

Pythagoras’ Theorem, c=√(a²+b²), is true because cos²(x)+sin²(x)=1, which is also the formula for a circle.  By contrast, cosh²(x)-sinh²(x)=1 is the formula for a hyperbola.  Pythagoras’ Theorem is only true for a flat surface.  If the surface is spherical, whose sphere has a radius R, then the formula for the hypotenuse, c, of a right triangle whose other sides are a and b is cos(c/R)=cos(a/R)cos(b/R).  If this is expressed as a series, then as R approaches infinity, the series becomes c=√(a²+b²). For a hyperbolic surface, the formula for a hypotenuse is cosh(c)=cosh(a)cosh(b), but if the coefficient of the imaginary number is zero, or only the real portion is used, then this also becomes Pythagoras’ Theorem. 

For a finite spherical surface, as R, the radius of the sphere, becomes very large compared to a or b, this becomes Pythagoras’ Theorem.  On a infinte surface, it also becomes Pythagoras’ Theorem but we appaer t only use the ral portionof the solution. Using only the real portion of a complex solution is precisely how electrical engineers treat the imaginary portion when their solution is a complex number. And now you know the rest of the story. If you use only Pythagoras' Theorem, then apparently you have no imagination!  If you have an imagination then you are HYPERBOLICfragilisticexpialidocious!