Normal III

 

Nothin’ From Nothin’ Leaves Nothin’

Nothin' from nothin' leaves nothin'
You gotta have something' if you wanna be with me
Nothin' from nothin' leaves nothin'
You gotta have something' if you wanna be with me

What is normal?

A statistically normal distribution is one where the Median is equal to the Mean. However a normal distribution also requires that values less than zero, nothing, be allowed. In the real world less than nothing is not allowed. I mean an absolute. For example, a temperature can be below zero on the Fahrenheit scale, but it can not be below absolute zero. Therefore normal-like distributions such as the exponentially modified Gaussian (normal) distribution are used. In that distribution the Mean is close to, but not equal to, the Median. It also allows for a non-zero Skew which is not allowed in truly normal distributions. However there are still rules. An exponentially modified Gaussian distribution has a limit on the Skew of 0.31.

Another feature of a normal distribution is the 68/95/99.7 rule. That is one Standard Deviation from the Mean has 68% of the values; two Standard Deviations from the Mean have 95% of the values; and three Standard Deviations from the Mean have 99.7% of the values. If we assume that 99.7 % is close enough to 100%, it can be said that any modified normal distribution must have a Standard Deviation that is the Mean divided by three. If this is the Standard Deviation, then it is possible to estimate the Skew using Pearson’s Second Coefficient of the skew, and the Mean can not exceed 1.5 times the Median. If the Mean is more than 1.5 multiplied by the Median, then the group has to be considered as having more than one normal subgroup.

For example, LIS, the Luxembourg Income Study,  reports Mean and Median income. According to that data, the Mean US income in 2020 was $53,580 and the Median US income was $42,763 and unlike most counties the gap was increasing.  According to the Credit Suisse Wealth Databook, the US  Mean wealth was $ 505,421 and the Median wealth was $79,274.  These might be a lot of things, but they aren't normal or trending to normal.  However the mean life expectancy in the US in 2019 was 76.3 years while the median life expectancy was 78.8 years.  Life expectancy is probably one normal group. It is said that there are only two things that are certain in life: death and taxes.  Death may also be normal, but taxes may not be normal.

Gun Control II

 

What A Fool Believes

But what a fool believes he sees

No wise man has the power to reason away

What seems to be

Is always better than nothing

And nothing at all keeps sending him

Are Amercians being a fool on gun control?

Congratulations to President Biden for finally calling out Republicans.  I know that it was hard for him. Reaching across the aisle has always been an admirable quality of Joseph Biden. However gun control is an American issue, not just a bipartisan issue. An American issue requires a supermajority. It is not an issue for the Democratic majority. It is not an issue for the Republican minority, although they have learned to block any two player game. When the Democrats were a supermajority, they were able to pass the Affordable Care Act. When the Republicans were the majority, they passed nothing except tax cuts and stealing a seat on the Supreme Court. The party of Howard Baker, Everett Dirksen and John McCain has become the party of Kevin McCarthy, Mitch McConnell, and Donald Trump. This is not unprecedented. The bipartisanship that President Biden seeks is with the Progressive/Mugwump wing of the Republican Party. This wing was led in the past by Samuel “Mark Twain” Clemens and Teddy Roosevelt, who broke with the Republican Stalwarts. But trying to make bipartisan agreement with what you have today is a fool’s errand. You work with what you have, and we don’t have Bull Moose Republicans.

What is needed is to stop playing a two player game. Gun Control is NOT a bi-partisan issue. It is a multi-partisan issue , where the multi- is so large as to make it virtually indistinguishable from non-partisan. Stop playing a two person game. It never worked for Charlie Brown and Lucy in Peanuts and it won’t work here. My therapist said that I should write, which is why I blog. But if you are reading this then please read. https://dbeagan.blogspot.com/2022/05/filibuster-v.html, and https://dbeagan.blogspot.com/2021/05/tough-but-fair-beats-always-being-nasty.html

I thought that assault was against the law. Then aren’t assault rifles such as  AR-15s illegal and can be banned by the ATF. Laws aren’t necessary and might be foolish. Action is necessary.

Normal II

We're Not Gonna Take It

Hey hung up old Mr. Normal

Don't try to gain my trust!

'Cause you ain't gonna follow me any of those ways

Although you think you must

Is it Normal to accept no error?

Normal describes a group (a distribution) where the Mean is equal to the Median. If  everyone agrees, then the Mean will equal the Median. But normal is NOT limited to a Variance of  zero. A uniform normal distribution is the most stable distribution, and it has a Variance of one, not zero. (An aside. The big push for resiliency is because the push for just efficiency, making the Variance zero, is not always wise.  I apologize for linking to myself,  but this is what  I mean by efficiency vs. resiliency. https://dbeagan.blogspot.com/2022/01/resiliency.html)

If the Variance is zero, then everyone agrees. If the Variance is 1, then most people are not 100%, the same, but people are allowed to be different than the Mean. In a normal distribution, 68% of the observations are within one Standard Deviation of the mean.

If you want to approach the absolute,  then you want to make the Standard Deviation (the square root of the Variance) as small as possible. That is what science is all about. You make lots of observations with a decreasing  Standard Deviation until you approach the absolute. The gold standard in most science is 3 Sigma, 3 Standard Deviations, 99.7%. In particle physics, e.g. the weight of an electron, it is 5 Sigma, 99.99994%.

But once you have established an absolute, then there is by definition no error, and the Variance is zero. But you DON’T start by assuming that the Variance is zero. Error is the Standard Deviation divided by the square root of sample size. If you wish to reduce error, then you don’t automatically assume that the Variance is 0, instead you increase the sample size ( the size of the group). Once you are absolutely correct, the sample size will be irrelevant, the Variance will be zero, and increasing the size of the group won’t change that result. But if there is the possibility that you are wrong, then the way to reduce error, approach an absolute, is to increase the sample size of the group.

It is abnormal to say that the Variance IS zero. If things are normal, then the Variance might be greater than 0 and you better increase the group size if you want to reduce error.

Once upon a time, there was no separation between natural (science) and spiritual philosophy. The separation appears to have been a mistake.  Science can inform the spiritual and vice versa.

Deviation

 

Knocking on Heaven’s Door

Mama, put my guns in the ground
I can't shoot 'em anymore
That long black cloud is comin' down
I feel I'm knockin' on heaven's door

Who is knockin’ on heaven’s door?

One day three men die and go to heaven.  “Religion?" God's secretary asked the first man. "Jewish," the man replied. "Okay, go to room 23, but be very quiet when you go past room 8," the secretary said. "Religion?" he asked the second man. "Muslim." "Go to room 10, but be very quiet when you go past room 8." "Religion?" he asked the third man. "Agnostic." "Go to room 71, but be very quiet when you go past room 8." "Why must I be quiet when I go past room 8?" the man asked. The secretary replied, "Oh, the Catholics are in room 8, and they think that they are they only ones here."

I heard this joke from a Catholic Priest.  It pokes fun at the conceit that only Catholics can go to heaven.  There is nothing in the Catholic faith that teaches this. To enter heaven, a good relationship with God is required.  God is an absolute and without error.  So to be close to God is to reduce error. 

What does mathematics teach us about error.  Error is defined as the square root of the variance divided by the square root of the sample size.  If you wish to have no error, then you can either set the variance to zero or increase the sample size.  Since error probably exists in each member of the sample, an error in one direction will be canceled out by an error  in the other direction.  The larger the sample, the more likely will be this cancellation.

Unfortunately some people think that the way only way  eliminate  error is to set the  variance to zero.  The standard deviation is the square root of the variance.  If the variance is zero then, by definition, the deviation also has to be zero.  So in an attempt to be closer to God, some people will allow no deviation.  If there is  no variance, then you aren’t  just closer, you are identical to God.  Thus accepting no variance is the height of hubris and is in fact the belief that you are God.  Isn’t that what we are taught is  why Satan was cast out of heaven.  Rather than a belief that no deviation is the only way to get into heaven, allowing no deviation seems to be the way to get cast out of heaven. Or to put it another way, “Judge not, lest you be judged.”

Gun Control

 

Happiness Is A Warm Gun

Happiness is a warm gun (bang, bang, shoot, shoot)
Happiness is a warm gun, momma (bang, bang, shoot, shoot)

Maybe we shouldn’t be so happy.

It is once again time for the National Rifle Association, NRA, to offer thoughts and prayers and to remind everyone that guns don’t kill people, people kill people. Don’t tell them that it is people with guns that are killing people. They will point to the gun ownership rate in Switzerland which is comparable to the gun ownership rate in the United States and say that since murder rates are so much higher in the United States than in Switzerland, they will tell you that mental illness, unlocked doors, unarmed victims, or some other nonsense must be the cause. What they won’t tell you is why gun ownership in Switzerland is so high.

Every Swiss citizen is part of the army, i.e. the state’s militia. They are first conscripted into active duty and after honorable service are discharged with their rifle. That service rifle is to be used in the event that the militia, and remember they are still part of the militia, ever requires their service. Their gun is supposed to be only used in service of the state’s militia. It is not a weapon to be used against other citizens. If you are discharged from the militia, say because you are mentally unstable, then you do not have a gun. In the United States we still have state's militia. A state’s militia is just now known as its National Guard.

The full text of the Second Amendment to the US Constitution, which the NRA loves to hide behind, is “A well regulated Militia, being necessary to the security of a free State, the right of the people to keep and bear Arms, shall not be infringed. ( emphasis added). The late Justice Antonin Scalia, whose seat Justice Neil ”Not Merrick Garland” Gorsuch now fills, wrote the majority opinion in District of Columbia et al. v. Heller. In that opinion, he invented a right to self defense UNRELATED TO MEMERSHIP IN A MILITIA to justify the opinion that, even non-militia members should be able to own guns. Justice Scalia was supposedly an originalist. Uh, that is NOT what the original text says. If you are not a member of the militia then you have no right to bear arms. Unless the militia has said that it will require its members to provide their own guns, it does not appear that the Second Amendment protects even gun ownership by militia members. I do not believe that Salvador Ramos, the shooter in Uvalde; Payton S. Gendron, the shooter in Buffalo; Stephen Paddock, the shooter at the Las Vegas Music Festival; Adam Lanza, the shooter at Sandy Hook; Nikolas Cruz, the shooter at Stoneman Douglas High School; or ANY of the shooters in the tragic mass shootings were members of a state’s militia. Even if the Constitution did somehow protect gun ownership unrelated to a militia, which again is NOT in the text, only if you are stupid or a liar would say that those shootings were in self defense. It is up to the voting public to decide whether the NRA and its supporters are stupid or liars. Remember when you vote.

Gravity II

 

Little Green Apples

God didn't make little green apples
And it don't rain in Indianapolis in the summertime
And there's no such thing as Doctor Seuss
Or Disneyland, and Mother Goose, no nursery rhyme.

What does a falling apple tell us about gravity?

Space-time tells mass-energy how to move. Mass-energy tells space-time how to curve. If space‑time did not curve, then we would live in a Euclidean world. In most applications, the curvature is so small that we tend to approximate spacetime as flat, i.e. our approximate Frame of Reference is Euclidean. But the curvature is there nonetheless, which makes the absolute Frame of Reference non-Euclidean.

If space-time is curved, then the question is that curvature positive, i.e. spherical, or negative, i.e. hyperbolic. If the curvature is positive and the radius of the sphere is exceptionally large compared to a typical distance, then space-time can be treated as virtually flat. If the curvature is negative, its radius is NOT a factor.

Mass-energy should move along the shortest path in space-time. That is what Newton’s First Law says: “An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.”  The shortest path in in the same direction in spacetime is the hypotenuse between two points, i.e. a geodesic. If space‑time is curved hyperbolically, and the curve of space-time determines the geodesic over which mass-energy will move, then gravity is an apparent force, like Centrifugal Force or the Coriolis Force. If there are two objects, then the geodesic between those two objects is the distance in space-time between those two objects. If spacetime is curved, then the object with less mass‑energy will move towards the object with more mass‑energy. Thus what we interpret as gravity, is because we interpret that movement as Euclidean and it is really an apparent force if spacetime has a hyperbolic curvature. If two objects have exactly the same mass-energy, if both objects are not moving, then they should  NOT move towards each other.[1]

Consider Newton’s apocryphal apple falling from a tree. How might that be interpreted in hyperbolic, non-Euclidean space-time? In Euclidean space-time, the apple moves from the tree to the surface of the Earth. It would keep moving towards the center of the Earth, but the Pauli Exclusion principle, that two objects can not occupy the same space at the same time, says it can not pass through the surface of the Earth. In non-Euclidean space-time, the apple and the Earth are both moving,  e.g. the Earth is moving around the Sun, etc. It is just that both are moving at the same speed and in the same direction. Thus to an observer in our Euclidean frame of reference on the Earth, it only appears that the apple is not moving before it falls. Since the apple is much smaller than the earth, it should fall towards the earth. The path that it follows is the geodesic in space‑time. What appears to be an attraction between the two objects is merely the smaller object moving according to the curvature of space-time.

The difference between a Euclidean geodesic and a non-Euclidean, hyperbolic, geodesic is that the hyperbolic, non-Euclidean, geodesic will follow an exponential formula. In my field of Travel Demand Forecasting, trips are distributed according to the “Gravity” Model. It was called this because the impedance between the production of a trip and the attraction of a trip seemed to follow Newton’s Law of Gravity. A. G. Wilson later showed that this is because the trips actually randomly followed an  exponential function that looked like the gravity function. I was working at the Boston Metropolitan Planning Organization when I presented this ( I am amazed now that I was not thrown out for being particularly nerdy) and my favorite comment was by a manager who said that he had a tough time believing that people made trips like apples, but he had no problem believing that people made trips randomly. It appears that even Newton’s apples don’t behave like apples, but instead follow a similar exponential function. If gravity is an apparent force, then trying to find a Quantum Theory of Gravity may make no more sense than trying to find a Quantum Theory of Centrifugal Force. Gravity as a force may not fit into a Unified Field Theory because Gravity is not a real force, it is only an a apparent force.

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[1] Assuming those objects both have the same charge, etc. If they have opposite electrical charges, then the electromagnetic force will attract them, which IS an application of a force.

Love of Country

 

Tobacco Road

Bring that dynamite and a crane
Blow it up, start all over again.
Build a town, be proud to show.
Give the name Tobacco Road.

Could you blow up your home?

Once upon a time the phrase yelled at protesters was “My Country, Right or Wrong” . Their response to that was “My Country, Right or Wrong.  If it’s Right, Keep it Right. If it’s Wrong, Make it Right.”

The cry now seems to be “My Country is Wrong. Let’s tear it down and start all over again”.  What is left unsaid is what is wrong, and who gets to decide how it is run when it starts over.    The sense of dread, self-hate, and despair about the state of our country seems to be the major commonality of those perpetrating  mass, including school, shootings. Who do you think loves, is proud of, their county? The person who tries to make it right? or the person who tries to tear it down?