Statistics

 

Source of image: https://www.york.ac.uk/depts/maths/histstat/lies.htm

It is only because People don’t UNDERSTAND statistics that is taken to be lies.

It is possible to use mathematics, and statistics is a branch of mathematics, to lie, e.g., 1+1=3, but the lie is very obvious.  It is only because people don’t understand the terms in mathematics or statistics that they think they are lies.  In the routine “Why a Duck”, it is only because Chico Marx doesn’t understand the terms ford or a viaduct, etc. that it is a comedy.  When Johnathan Swift called for the boiling of Irish children, he was intending it as satire, not as a cookbook.  When Archie Bunker sings “Those Were the Days”, we are supposed to laugh at him.  There is a difference between tactics and strategy, between a battle and a war, and between weather and climate. Just because they are similar does not mean they are the same.  If you think that there is no difference between a standard deviation and standard error, then like Lou Costello, you can expect someone like Bud Abbott to take advantage of you.           
https://www.youtube.com/watch?v=9udNrOh5DyA.

Standard deviation is σ.  Standard error is σ divided by the square root of n.  Yes, σ is a Greek letter.  This is a because much of our mathematics was developed by Greek philosophers.  In fact, Science used to be called Natural Philosophy to distinguish it from Spiritual Philosophy.  If you know the terms in philosophy, then you should also know the terms in science, mathematics, AND statistics.

N in the equation of standard error is the size, number of observations, in a distribution.  A distribution is just another name for a group.  The standard deviation multiplied by itself is the variance.  A standard normal distribution, such as those in Nature, has a standard deviation of, which also means that the variance is,  1.  During the COVID pandemic, the phrase “flatten the curve” became popular.  To a statistician that phrase is identical to “increase the variance”.  Its opposite would have been “steepen the curve”, “decrease the variance”.  Decreasing the variance has problems of its own. https://dbeagan.blogspot.com/2022/01/resiliency.html.

If the goal is to eliminate error, the response should be to INCREASE the size of the distribution, group.  It should not be to set the deviation to zero.  If the deviation is zero, then any value of n, including decreasing the size of the group, is possible.  Thus, claiming that to reduce error, deviation must be zero is absolutely compatible with exclusion.  However, IT IS NOT NORMAL.  Not only aren’t statistics lies, but we would also be better off if our politicians understood statistics.

 

 

Affirmative Action

 

Ac-Cent-Tchu-Ate the Positive

You got to ac-cent-tchu-ate the positive
E-lim-i-nate the negative
And latch on to the affirmative
Don't mess with Mr. In-between

Is Affirmative Action positive?

When my firm was preparing a sample of shippers for the Port Authority of New York and New Jersey, PANYNJ, to establish the behavior of shippers, at first there was a random sample of shippers based on their mailing address and size.  After the first sample was prepared, and obviously not every shipper was, nor was it expected to be, surveyed, as responsible survey designers we compared the sample to the general population of shippers.  It was found that very large shippers were underrepresented in the survey sample.  This was not unexpected.  Because they are a small subset of shippers, it was expected that the large shippers might have been missed in a random sample of any size.  An oversampling of large shippers was undertaken to ensure that the sample looked like the population of all shippers  to ensure that the sampling of behavior was consistent with the overall population of shippers.

When you come right down to it, isn’t this exactly what is being done in affirmative action programs.  The first sample of qualified candidates who would meet the original selection, sampling, procedure might result in a sample that is NOT consistent with the general population. If the goal is to have a sample that IS consistent with the general population, then affirmative action is appropriate.

No one claimed that in the shipper choice survey, that special treatment was being given to large shippers because they were being oversampled.  No one claimed that those small shippers who were not part of the original selection, were being discriminated against. In the same manner there is no discrimination against those in an affirmative action selection process who were NOT part of the original selection.  If the result of the original, is not consistent with the population that is intended, over sampling, affirmative action, of the targeted population is appropriate.

There is no judgment against the original sampling, selection plan.  In the Knights of Columbus, the membership is not expected to be Protestants.  The Ku Klux Klan is not expected to have BIPOC or LGBTQIA+ members.  The B'nai B'rith is not expected have Catholics in proportion to the general population.  But if a result is expected to be consistent with the general population, such as the civil service, police, Harvard University, the University of North Carolina, etc., then oversampling, affirmative action, is not only a good thing, it is the correct thing, accentuating the positive.

 

Mararthons

 

Go The Distance

And I won't look back, I can go the distance
And I'll stay on track, no I won't accept defeat
It's an uphill slope
But I won't loose hope, 'till I go the distance
And my journey is complete, oh yeah

Is going the distance winning? or an initiation?

If you have any interest in marathons, e.g. the Boston Marathon, can you tell me the winner of the most recent Marathon? I bet you can’t. But I bet that you will be able to tell me those who you know that completed that marathon, i.e. went the distance. That is because a marathon is not a single race. A marathon is an initiation, a rite, a ritual, as much as a Bar Mitzvah. The podium positions do not matter as much as knowing who completed the marathon, …went the distance. That is why there are thousands of entrants for a major marathon. There may be only one winner but winning is NOT the point. Going the distance, completing the marathon, is the point.

That is also why a baseball season is called a marathon, not a sprint. Moonlight Graham, in real life and in the movie Field of Dreams, or Roy Gleason of the 1963 Los Angles Dodgers, are considered to be major league players. Moonlight Graham had a single plate appearance and hit. In the movie his pain was eased because he became a marvelous doctor and saved the protagonist’s daughter. Roy Gleason played for the Dodgers and after a single plate appearance and hit, he was drafted and sent to Viet Nam where he was awarded the Purple Heart. They both went the distance and were initiated as major leaguers, even though they only stayed for the proverbial cup of coffee. They may not have been elected to Cooperstown, but they went the distance. Winning is not everything, playing the game the right way is. Fans didn’t follow the Cubs or Red Sox during their respective decades long droughts only because they expected to see a winner, although as a Red Sox fan the 2004 season was sweet! But I was in the stands before 2004 because I saw players who went the distance.

The playoffs are nice, and making the playoffs is exciting, but the playoffs are more important to the owner’s ego than to the hardcore fans. To borrow a phase, it is not whether you win or lose but how you play the game…. go the distance. Second place is not first loser. Second place, and every position including last place, still went the distance.

Truth II

 

Battle Hymn of the Republic

Mine eyes have seen the glory of the coming of the Lord;
He is trampling out the vintage where the grapes of wrath are stored;
He hath loosed the fateful lightning of His terrible swift sword
His truth is marching on.
Glory, glory, hallelujah!
Glory, glory, hallelujah!
Glory, glory, hallelujah!
His truth is marching on.

WHO can’t handle the truth?

"I believe that college actually erodes the best our country has to offer," Charlie Kirk, president of Turning Point USA, told Breitbart's Alana Mastrangelo, detailing his belief that college is "bankrupting our country," "brainwashing our youth," and is "a multi-trillion dollar enterprise that is designed to try to turn children against their parents." and ""The College Cartel" is no better than Mexican Drug Cartels"

Are you kidding me?  Charlie Kirk, who never graduated from college, has a warped idea of college. In 2015, Kirk told The Atlantic that he was taking part-time online classes at The King's College, and he was taking classes at Harper College, a community college near Chicago, but dropped out to pursue conservative activism.  He should ask for his money back.  The purpose of college is not to brainwash anyone.  It is to try and train students to discover the truth for themselves.

Sometimes you might be offended by what they discover to be the truth.  But your truth is NOT the only truth, no matter how “woke” it is. Can we all say sour grapes!

Little (?) League

 

Take Me out to the Ballgame

Take me out to the ball game,
Take me out with the crowd.
Buy me some peanuts and cracker jack,
I don't care if I never get back,
Let me root, root, root for the home team,
If they don't win it's a shame.
For it's one, two, three strikes, you're out,
At the old ball game.

Amen!

Thoughts while watching the joy in the faces of Little Leaguers when they lined up for autographs of the Red Sox and Oriole players, when Red Sox Manager Alex Cora spoke in Spanish to the team from Puerto Rico, and when watching the Red Sox and Oriole major leaguer players  joyfully slide down the hill on cardboard at Volunteer Field during yesterday’s Little League World Series game.

"They'll come to Iowa Williamsport, Pennsylvania for reasons they can't even fathom. They'll turn up your driveway, not knowing for sure why they're doing it. They'll arrive at your door as innocent as children, longing for the past.

"Of course, we won't mind if you look around," you'll say. "It's only twenty dollars per person." They'll pass over the money without even thinking about it. For it is money they have and peace they lack.

And they'll walk out to the bleachers, and sit in shirt-sleeves on a perfect afternoon. They'll find they have reserved seats somewhere along one of the baselines, where they sat when they were children and cheered their heroes. And they'll watch the game, and it'll be as if they'd dipped themselves in magic waters. The memories will be so thick, they'll have to brush them away from their faces.

People will come, Ray.

The one constant through all the years, Ray, has been baseball.

America has rolled by like an army of steamrollers. It's been erased like a blackboard, rebuilt, and erased again. But baseball has marked the time.

This field, this game -- it's a part of our past, Ray. It reminds us of all that once was good, and it could be again.

Ohhhhhhhh, people will come, Ray. People will most definitely come."

Thank you W.P. Kinsella for the novel, director Phillip Robinson for the movie, and James Earl Jones for the performance in that movie. Veni, Vidi, Vici.  Come, see, and get a victory for yourselves.

Currency

 

Garden Party

But it's all right now
I learned my lesson well
You see, you can't please everyone
So you got to please yourself

What lessons have you learned?

Monopoly as a board game, is indeed the board game that your little sister is most likely to upend in frustration, but it was originally intended as an economics instruction game. Monopoly is derived from The Landlord's Game, created by Lizzie Magie in the United States in 1903 as a way to demonstrate that an economy that rewards individuals is better than one where monopolies hold all the wealth and to promote the Henry George's economic theories on taxation. And despite its current use as primarily an entertainment game, it is actually serving its original function.

One of the lessons that Monopoly imparts comes from a strict interpretation of the printed rules versus the “House” rules as they are often played. (For example, in the printed rules, fines are NOT placed in the center of the board and given to the player who lands on the “Free Parking” space, but this is often the case in “House” rules.)  Strictly according to the printed rules, there is the opportunity to create a housing shortage. This happens when a player, such as your annoying little brother, buys all of the houses and refuses to turn them into hotels. Thus, when you want to buy a house, the bank has nothing to sell you.

Cornering the market on a commodity is bad for the game, or the economy. My father worked for Gorham Silver and that business was ruined when the Hunt brothers tried to corner the market on silver in the late 1980s. The Hunt brothers intended to make a large profit by forcing anyone, such as Gorham, to have to come to them if they wanted to continue using silver. In reality what they did is to drive up the price of silver for everyone and lose a tremendous amount of money for themselves  in the process.

But back to Monopoly. It is considered a dirty tactic to create a housing shortage. It creates an impasse in the game. But the actual rules say that it is allowed. The “House” rules find a way to create more houses so that there is no shortage. This may involve forcing your little brother to turn his houses into hotels, or using chits for houses. There is a lesson here.

When the currency is a commodity, it is possible to corner the market on that commodity/currency. We do not currently have bank runs or a collapse of the economy but this is what happens when a commodity/currency becomes concentrated in the hand of a few and the economy tries to respond. The alternative is a fiat currency, which is what the US dollar has been since the 1930s. But there is a problem when those issuing the chits, fiat, get carried away such as the Confederacy, Weimar Germany, or post Hugo Chavez’s Venezuela. Having too much currency is just as bad as having a shortage of currency. The Confederacy and Weimar Germany actually printed too much currency. Hugo Chavez’s Venezuela did it unintentionally by price controls such that there became a surplus of currency because you could earn currency but not spend it

The strict rules can often bring a game to an impasse. The “House” is NOT interested in the outcome of the game, but the continuation of that game. The "House", the group, can, and should, change those rules that cause an impasse. But it should be careful in how it does that. Its intention should only be to continue the game, not to change its random outcome.

Newton

 

Good Advice

Sir Isaac Newton came around to my house one day
His face was all sunburned and red
He said he didn't want to sleep in the shade of a tree,
Because an apple might fall on his head
I said, "Sir Isaac, you dumbbell, take my advice
Go right back there and sleep beneath that tree
And if you let that rotten apple fall down on your head,
Why you'll discover gravity"

Maybe Newton only APPEARED to discover gravity!

Newton’s Laws of Motion are:

Law 1. A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.

Law 2. When a body is acted upon by a force, the time rate of change of its momentum equals the force.

Law 3. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

These laws describe the motion in a flat, Euclidean, spacetime.  If the universe is hyperbolic, and Einstein’s General Relativity is considered, it should be :

Law 1. A body remains at rest, or in motion at a constant speed in a straight line along a geodesic in spacetime, unless acted upon by a force.

Law 2. When a body is acted upon by a force, the time rate of change of its momentum equals the force.  If a body moves along a geodesic to decrease its energy, it may appear in a Euclidean frame of reference that a force has changed that body's momentum.

Law 3. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.

This has an implication on the Lorentz Factor that governs time dilation, T=T₀*γ; length contraction, L=L₀/ γ ; and rest mass, M=M₀*γ.  The Lorentz Factor is typically given as

γ=1/sqrt(1-(v/c)² ).

where 

sqrt    = the square root operation;

v        = velocity, and

c        = the speed of light.   

This has the problem that there is a discontinuity, it is undefined, at a v/c of 1.

In hyperbolic spacetime, this factor would be

γ=1_ln(cosh(v/c)±sinh(v/c))

where 

ln    = the natural logarithm function, a logarithm with  a base of e

This does not have a discontinuity of 1 at a v/c of 1.  At a v/c of 1, the factor is zero. 

It also means that Gravity is NOT a force in hyperbolic spacetime.  It is an apparent force, unlike the other fundamental forces:

• The strong nuclear force: the force responsible for holding quarks together to form hadrons, and holding neutrons and also protons together to form atomic nuclei. The exchange particle that mediates this force is the gluon.
• The electromagnetic force: the familiar force that acts on electrically charged particles. The photon is the exchange particle for this force.
• The weak nuclear force: a short-range force responsible for some forms of radioactivity, that acts on electrons, neutrinos, and quarks. The W and Z bosons are the exchange particles for this force.

The difficulty of including gravity in a unified field theory, and the inability to discover a graviton as the exchange particle, is proposed to be a consequence of the hyperbolic shape of the universe, spacetime.

Newton Law of Gravity, which is from a Euclidean frame of reference, states that the force of gravity is

F=G*(M₁*M₂)/(d₁₂ )²

where:

F             = The force of gravity,

M₁            = Mass one,

M₂            = Mass two,

d₁₂            = The distance between mass one and mass two, and

G            = The Gravitational constant, 6.6743 × 10^-11 m³ kg^-1 s^-2.

From a hyperbolic, non-Euclidean, frame of reference there is no force, and the movement of the two masses to a center of mass is a consequence of entropy maximization and the objects moving from their initial positions to their center of mass along a geodesic.

 

F'=G*M₁*M₂*exp (-1/2*d₁₂ )

where:

F’            = The apparent force of gravity,

exp         = the exponential function,

M₁            = Mass one,

M₂            = Mass two,

d₁₂            = The distance between Mass one and Mass two, and

G            = The Gravitational constant, 6.6743 × 10^-11 m³ kg^-1 s^-2.

Growth II

 

What Do I Know?

No university, no degree, but lord knows
Everybody's talking 'bout exponential growth
And the stock market crashing in their portfolios
While I'll be sitting here with a song I wrote
Sing, love could change the world in a moment
But what do I know?
You probably know more than you think!

Any exponential growth function can be expressed as a compound growth function. Compound growth functions have a constant and continuous growth. Exponential growth functions have a continuous but not constant growth. However any compound growth rate can be expressed as an exponential function.

If the growth rate, in demand, is 10% per period, then the compound growth formula would be

Future value=Present value*(100%+10%)^x

where x is the number of time periods from the present to the future.

At infinity, this will have a value of infinity. But this assumes that the time periods are also infinite. It is possible for the Future value to consume all of available supply before an infinite time unless the growth in supply is also 10% per year. If it is less than 10% then the future value in demand will exceed the future value in supply long before an infinite number of time periods have been reached. In other words, in compound growth you will approach infinity in a finite period. In exponential growth you will only approach infinity only after an infinite period.

The rich have a disparaging comment about the poor that they are poor because they live off principal instead of living off interest. Doh, if the present value, principal, is zero then it makes no difference what the interest rate is, the future value will always be zero. The ideal is to have enough principal that you CAN live off the interest. But if your living expenses are higher than the interest on your principal then your principal gets reduced and the next Future value will be smaller because the Present value in that next time period is also smaller.

An exponential growth can be made from this compound growth

Present value*(100%+10%)^x=Present value*exp(λx)

 if

λ=ln (110%)

In fact any compound growth rate, r%, can be made into an exponential growth if

λ=ln (100%+r%)

If λ is negative, less than zero, this is said to be a decay function, for example a radioactive element decay function, and λ can be converted into a half-life. Long half-lives are stable, good, and short half-lives are radioactive, unstable, bad. When λ is positive, greater than zero, this is said to be a growth function. But λ can still be converted into a time, say a doubling period. But while this will be the inverse, the qualifications are still valid. A long doubling period is good and a short doubling period is bad. Short doubling periods have lots of energy but expire soon. Long doubling periods have less energy but they last longer.

Given that, what should the best growth rate be? The question should be what is the growth rate of a market? The best is arguably an example of the Lake Wobegon effect ( “all the children are above average”) or the Yogi Bear effect (“smarter than the average bear”). If the population is normal, then the maximum, "best", of the crowd should be twice the average of the crowd ( e.g. the Z-score of 99.9% is approximately 2.)

Sustainable growth should thus be twice the growth of the market ( yes a  firm could grow by 10% if the market only grows by 2%, but eventually that firm will have 100% market share.)   The maximum sustainable growth  should not exceed twice the growth of a market. Twice is only sustainable if the average  IS the maximum ( which is only true when the standard deviation is zero, but then that is no longer normal.)

Should that firm enter other markets? Absolutely, but that growth still should not exceed 2 times the growth in its combined markets ( the original market plus the new market). If the best growth rate is compared to the revenue from the original market, the growth in  revenue will appear to be greater than the growth in the original market. But this is only because of the choice of the dominator in that growth rate.

This also defines the size of the new market. If a firm wishes a growth rate, r, that is more than twice the growth of its market, it should pursue new markets whose value, V, is larger than its current market according to.

Proposed Growth Rate=

2*(V_{Old Market}*r_{Old Market} +V_{New Market}*r_{New Market} )/(V_{Old Market)} +V_{New Market})

This also explains why you should pursue new markets.  If your old market is buggy whips and you don't go after any new markets, then the best growth rate you can expect have is twice the growth rate of the old market. Having 100% of the buggy whip market will still mean a growth rate of 0% since the buggy whip market is not growing.

Monkeypox

 

Hello Muddah, Hello Fadduh (A Letter from Camp)

Wait a minute, it stopped hailing,
Guys are swimming, gals are sailing.
Playing baseball, gee that's betta,
Mudda, Fadda, kindly disregard this letter!

Patience you must have, my young padawan.

If your time period is truly short, like the one day in this song, you can have a quite different impression than if you look at a longer time period. There is a difference between weather and climate; between revolution  and evolution; between winning a battle, tactics, and winning a war, strategy; etc. Confusing these is NOT good. There is also a difference between risk and likelihood. Risk is the product of likelihood AND consequences. If the consequences are low then the risk is probably acceptable, regardless of the likelihood. If the consequences are high, then the risk can be unacceptable even when the likelihood is low.

This came up during a conversation on the risk of monkeypox if you have already been vaccinated against smallpox. Smallpox was eliminated and the vaccination against smallpox stopped in 1972. The LIKELIHOOD  of getting monkeypox if you have been vaccinated against smallpox is 15%. The likelihood of successfully filling an inside straight in poker is about 8% so if you think that 15% is acceptable, can we play poker please???

The CONSEQUENCES of getting monkeypox are considerable, so that the risk of getting monkeypox might be unacceptable even if the likelihood of getting monkeypox is low. Don’t be confused.

Hyperspace?

 It Ain't Necessarily So

It ain't necessarily so

It ain't necessarily so

They tell all your children

The devil he's a villain

It ain't necessarily so

Believing only what you can see locally is wrong

Pythagoras’ theorem is that any number can be expressed by two smaller numbers according to the relationship c²=a²+b². This was originally solved in Euclidean geometry, space with a curvature of zero, as the hypotenuse of a triangle. The relationship is true for a triangle in any geometry, including non Euclidean. It is just that under other geometries, the formula for the hypotenuse of a triangle is different because the sum of the angles in a triangle will be different. If the sum of the angles in a triangle is greater than 180 degrees, the curvature is positive and the non-Euclidean geometry is spherical. If the sum of the angles in a triangle is equal to 180 degrees, the curvature is 0, flat, and the geometry is Euclidean. If the sum of the angles in a triangle is less than 180 degrees, the curvature is negative and the non-Euclidean geometry is hyperbolic.

In Euclidean space, with a curvature of zero, the formula for a hypotenuse is

c=sqrt(a²+b²)

But this is only the formula in Euclidean space. The Flat Earth fallacy is because while locally space is Euclidean, the Earth is a large sphere, with a radius R, has positive curvature, and the formula for a hypotenuse which is its Great Circle Distance is

cos (c/R)=cos(a/R)*cos (b/R)

When the radius of the sphere is exceptionally large compared to c, a, and b, this is virtually indistinguishable from the formula in Euclidean space, i.e. locally space is Euclidean but over the entire surface of the Earth the geometry is spherical.

If the curvature is negative, hyperbolic, the formula is

c=ln(cosh(a)cosh(b)±sinh(a)sinh(b))

Mabkhout[1] proposed that the universe is globally hyperbolic and locally flat. If Einstein’s equations are solved for globally flat space, then dark matter and dark energy must be invoked in order  to be consistent with cosmic inflation immediately after the Big Bang;  to solve the paradox of rotating galaxies; to solve for the apparent difference in the size and the age of the observable universe; and to result in an expanding universe. If the universe is globally hyperbolic, then all of these issues can be resolved without invoking unseen dark energy or matter. Additionally gravity may be only an apparent force and the time dilation, length contraction, relativistic mass transform would not be the Lorentz transform, but would be

γ=1+ln(cosh(v/c)±sinh(v/c))

Just because something is true locally, it is not necessarily so that it is true globally.

 

 

---

[1] Mabkhout, Salah A. "The infinite distance horizon and the hyperbolic inflation in the hyperbolic universe." Phys. Essays 25.1 (2012): 112.

Marginal Tax Rate vs Effective Tax Rate

 

Slow Hand

You want a man with a slow hand
You want a lover with an easy touch
You want somebody who will spend some time
Not come and go in a heated rush

Slow and steady wins the race.

I got especially upset when I heard one of my favorite podcasts, Planet Money Indicator, repeat the falsehood that the tax rate once was as high as 91%. I know that I took macroeconomics more than 50 years ago, but it was math then and it should still be math. Saying the tax rate is 91% is confusing speed with acceleration. The marginal tax rate, second derivative or the rate of change of change for the math geeks in the crowd, might be 91%, but the effective tax rate, the first derivative, the rate of change, was no where near this. Talking Barbie might be right, Math is Hard, but just because it is hard doesn’t mean that it is not true.

If the median, what a statistician would say is normal, tax rate is 20%, then for any normal tax rate, the highest tax rate should be about twice that amount and the lowest tax rate should be about half that amount. If the median tax rate is 20%, then the highest effective tax rate should be 40% and the lowest effective tax rate should be 0%. But the highest marginal tax rate is not constrained to be 40%. It can be as high as 100% if the size of the brackets (increments) are equal and infinite. Math is hard, and it is useful to approximate a complex function such as a tax rate by a series of increments, brackets. The increments should be as small as possible for the approximation to be useful, but they still must be equal.

If the number of brackets is infinite, for a progressive tax rate, which has a first derivative of x% then the second derivative of the highest tax bracket can be 100%. The smaller the number of brackets, the lower that the second derivative appears to be.

Lowering of the marginal tax rate, should have been accompanied by dividing the intervals to highest income bracket into equal amounts.  If the size of the brackets are not equal,  the math is such that the approximation will not work.

I don’t want to know the highest marginal tax rate. I want equal tax brackets. The highest effective tax rate should be twice the median tax rate. The size of the brackets should be equal. When Maverick said in Top Gun, “I feel the need for speed,” he did not mean “I feel the need for acceleration.” The human body does not have a constraint on its maximum speed, but it does have a constraint on its maximum acceleration, G- force. Don’t confuse speed with acceleration… you want a slow hand.

Independent Legislative Authority

 

Sitting on Top of the World

"Glory Hallelujah," I just phoned the Parson
"Hey, Par get ready to call"
Just like Humpty Dumpty, I'm going to fall
I'm sitting on top of the world
Just rolling along, Just rolling along

Are you like Humpty Dumpty?

In the book Through the Looking Glass, when Alice meets Humpty Dumpty she has the following exchange:

'When I use a word,' Humpty Dumpty said, in rather a scornful tone, 'it means just what I choose it to mean — neither more nor less.'

'The question is,' said Alice, 'whether you can make words mean so many different things.'

'The question is,' said Humpty Dumpty, 'which is to be master — that's all.'

The US Constitution reads ” Each State shall appoint, in such Manner as the Legislature thereof may direct, a Number of Electors, equal to the whole Number of Senators and Representatives to which the State may be entitled in the Congress: but no Senator or Representative, or Person holding an Office of Trust or Profit under the United States, shall be appointed an Elector.”

The independent legislative authority theory hinges on what is meant by legislature.  If is narrowly defined as the body that makes laws in states and excludes the courts, the governor, the constitution of the state, the voters of the state, etc. then the position of independent legislative authority is correct. If the term is meant to include all of the legal bodies of the government of a state, then the independent legislative authority is wrong. And unfortunately this Supreme Court will try this case and three sitting justices — Clar­ence Thomas, Samuel Alito, and Neil Gorsuch —have already endorsed a narrow reading  and the full court gets to decide on the meaning of the word legislature. And whether by that single word whether they are masters, like Humpty Dumpty,  instead of our servants.

Local is Not Global

 

I’m Old Fashioned

I am not such a clever one
About the latest fads
I admit I was never one
Adored by local lads
Not that I ever try to be a saint
I'm the type that they classify as quaint

Maybe being adored by locals is not all it’s cracked up to be?

A phrase in the environmental movement is to “Think global, Act local.”  It acknowledges that our local actions  have a global impact. This has been true throughout history.  Recognizing that there is a difference between local and global has changed our way of thinking.

The Earth is flat.

It appears to be flat, Euclidean, to a local observer. The problem is that a local observer is very, very small compared to the size of the Earth. There was evidence that was inconsistent with a flat Earth. The shadow cast by a stick at noon became longer the father north you travelled. The mast of ships appeared over the horizon before the whole ship could be seen. The ocean did not fall off the edge of a flat earth, etc. These could all be addressed if it were recognized that the Earth was a sphere,  not flat. When you do large scale navigation you use non-Euclidean spherical  geometry to find the Great Circle Distance based on the surface as a sphere, where the sides of a triangle are very large compared to the radius of the Erath and the angles of a triangle do NOT sum to 180 degrees.

The Sun revolves around the earth.

To a local observer on Earth, it appears that the Moon and the Sun revolve around the Earth. But this geocentric model causes all sorts of problems requiring the “retrograde” movement of planets. All of these “retrograde” movements disappear if it is recognized that the Earth actually resolves around the Sun. Deep space voyages and astronomy rather than astrology are made possible by recognizing that we actually have a heliocentric earth.

My frame of refence is the correct and only frame of reference.

Is the local observer's the only valid frame of refence? Einstein showed that ALL frames of reference are possible and valid. Tying to reconcile an absolute, like the speed of light, with only one frame of reference resulted in trying to accommodate the aether though which light travelled. Einstein’s Theory of Relativity resolved this and many other seeming paradoxes such as the precession of Mercury, black holes, the apparent movement of stars during eclipses, and resulted in among things including atomic energy.

The universe is flat, Euclidean.

A local observer may assume that because his frame of refence is flat, Euclidean, that the universe is flat. However if the universe is Euclidean, then it requires dark matter and dark energy to resolve: cosmic inflation, the rotation of Galaxies, discontinuities, etc. that are either paradoxes or complications to try and resolve those paradoxes. If the universe is hyperbolic, has negative curvature as opposed to positive, spherical, curvature, these paradoxes may be resolved without the need for complications. It may also suggest that gravity is an apparent force, unlike the other three intrinsic forces. The movement that is observed in a Euclidean frame of refence might appear to be the force of gravity but it might actually be just particles minimizing their energy, which is equivalent to maximizing their entropy.

If you think globally and act locally, the Earth is spherical,  the sun resolves around the earth, and there is more than one frame of reference to an absolute. What else might recognizing that the universe might be locally flat and globally hyperbolic entail.

One Small Step

 

Blame It On The Bossa Nova.

Blame it on the bossa nova with its magic spell
Blame it on the bossa nova that he did so well
Oh, it all began with just one little dance
But soon it ended up a big romance
Blame it on the bossa nova
The dance of love

One small thing can be to blame for a whole chain of events.

If during my Freshman year at Brown University, the Kent State shootings had not occurred and the college had shut not have shut down, then I might have changed my major from Engineering to Quantum Physics.

If I had not taken an Electrical Engineering course,  then when I saw a plot of reliability, I would not have said that it looks like the response of  Resistor-Capacity, RC, circuit..

If the Atlanta Regional Commission, ARC, had not asked  Cambridge Systematics, the firm at which I work, to comment on its Volume Delay Functions, VDF, that varied by Time of Day, TOD, and the response had not been that vehicles should have the same VDF all day, then it might not have occurred to me that maybe the VDF was the reliability of the drivers, which could vary by TOD,  AND the time of the vehicles. Then both parties could be correct.

If COVID-19  had not confined me to home, then I might not have time to research an alternative to the speed-volume curve for vehicles that could be combined with reliability .

If my engineering courses had not included Fluid Mechanics, then it might not have occurred to me that the speed-volume vehicle flow in traffic looked like fluid flow in pipes.

If that proposal had not been reviewed and rejected, and one of the rejections said snidely that people in vehicles don’t behave like water, then I might not have been gotten mad enough to try and prove them wrong.

If I had not gotten mad, then I might not have started looking at other instances that looked like flow in a pipe, with separate stable and chaotic domains, which led me to cosmology and the proposal that space, the universe, was hyperbolic.

If I had not tried to understand  the articles on a hyperbolic universe, then I would not have learned about Minkowski Space. I had learned about  Lorentz Transforms before, in Quantum Mechanics, but it had been to flat Euclidean Space not hyperbolic non-Euclidean Space.

If I had not watched YouTube videos on Minkowski space, then I would not have leaned the concepts of invariant spacetime intervals, or that the  transition from Minkowski to Euclidean space was a Lorentz Transform, and I would not have proposed an alternative transform from Minkowski Space to hyperbolic space.

If I had not watched those YouTube videos and learned that the worldline of an event in Minkowski space which was the transform of a trajectory in the universe,  then I would not have thought about the quantum entanglement dilemma. While events with the same trajectory are the same in space, events with the same worldline are the same in Minkowski space. Thus spooky action at a distance, quantum entanglement when particles are separated by a distance, might be nothing more than the same particles having the same worldline, even when they are separated by a spatial distance.

If I had not had a career in traffic engineering, then I would not have known about Entropy Maximization and proposed that Entropy Maximization in hyperbolic space might be responsible for what appeared to be gravity in a flat Euclidean  space.

So if I am correct that... space is hyperbolic, the transform between Minkowski and hyperbolic space is NOT the Lorentz Transform, and gravity is apparent not fundamental, …blame it on the shootings at Kent State.

Brittney Griner

 

No Peace, No Justice

No peace, no justice
No peace, no justice
Were we provoked or were we just bored? 

In Russia, there is no Peace and no Justice. 

Brittney Griner has just been sentenced to 9 years in prison by a court in the Russian Federation because her  airline luggage contained vape cartridges which contained cannabis oil. Those vape cartridges were medically prescribed to deal with the pain from her sports injuries. She was only in the Russian Federation to play sports, basketball, during the WNBA off season. Did she violate Russian Law? Apparently? But was Justice administered? Absolutely not! 

A classic line from the Untold Legend of the Batman tells why  Bruce Wayne became the  Batman. While Bruce was in law school, his course was discussing a  case where a man went to jail. Bruce complained that it was not justice to which his Law Professor responded “ Is it Justice? No. It's the Law.” This was also the title of an old episode of the Naked City. 

What Brittney Griner received was the Law, not Justice. What Putin's Russia has given Ukraine is War, not Peace. Which only goes to prove that the old Civil Rights chant is correct. “No Peace, No Justice.”  

Error II

 

Somebody To Love

When the truth is found to be lies
And all the joy within you dies
Don't you want somebody to love
Don't you need somebody to love
Wouldn't you love somebody to love
You better find somebody to love

Can you handle the Truth?

Truth is  the absence of error. Lies, the opposite of truth must therefore be error. The mathematical formula for error is σ/√n, the standard deviation divided by the square root of the size of the sample. If the goal is no error it might seem like the easy way to achieve that goal is to have zero standard deviation. The other harder way, is to increase the size of the sample group, n. However, statistically a uniform normal distribution has a variance of 1, not zero. Therefore you can not be normal if the standard deviation is zero. If you are normal, and wish to reduce error, you should increase the size of the group. If you are normal, then you would not still not achieve zero error unless the size of the group increased to infinity, but increasing the group is a way to normally reduce error, i.e. be closer to the truth.

Measures to decrease the size of your group, such as by restricting immigration, by racial or religious discrimination are NOT normal. If you are not normal, unless you decrease the size of your group to zero, there will still be error. There will be no error with respect to A truth, but this does not mean that there is not error with respect to THE truth.

If the variance, the square of the standard deviation, is equal to 1, is a standard normal distribution, the better way to reduce error is to increase n, the size of the group. It will reduce error and will arrive at A truth. The hope is that this truth will also be THE absolute truth.

Growth

 

I’ve Got The Power

I've got the power (Power, power)
(You could break my heart, you could break my heart apart)
(You could break my heart, you could break my heart apart)
I've got the power (Power, power)
(Oh-oh-oh-oh)
I've got the power (Power, power)

You don’t WANT the power! You need an exponential.

Thinking about the future, forecasting/planning, has a long history in ….history. The simplest approach to forecasting, is to assume that it is like the past. This can take the form of trend analysis, but it is also why forecasting models are VALIDATED, based on historical data, to ensure that the present is consistent with the past, and those models are “backcast” to see how well a model “predicts” the past.

The simplest form of forecasting is to assume that there is a straight line from the past to the present to the future, where a simple Annual Growth Rate, AGR is used.

Future=Present+(AGR)*Years_{(from present to future)}

This does not acknowledge the fact that the years between the present and the future should also be considered, i.e. that compounding should occur. One of the songs in Mary Poppins, “Fidelity Fiduciary Bank” https://www.youtube.com/watch?v=XxyB29bDbBA goes into the glories of compounding. When loans or investments are made, it is typical to state a Compound Annual Growth Rate, often abbreviated as a CAGR. Compounding can be decibed mathematically as a power function.

Future=Present *(100%+CAGR)^years_{from present to future}

which can be restated as a power function of the form, y=a*b^x, where y is the future, a is the present, 100% + CAGR is the base, b, and the x is the number of periods, years, which have elapsed between the present and the future. This also means that it is possible to calculate a CAGR if you have a present value, a future value, and the number of years, periods, between these values.

CAGR=(Future/Present) ^(1⁄(years _{from present to future}⁾⁾ -100%

This assumes that the rate of growth is constant. An alternative function to growth is an exponential function which only requires that the growth be continuous, NOT continuous and constant. E.g. it is quite easy to grow in the early years, but very hard to grow in the future years.

Future=Present*exp (λ*years _{from present to future} )

The base in this case, exp(x), is the function of the special irrational number, e, the Euler number. This  can also be written as a power function, y=a*e^x, where y is the future, a is the present, e is the Euler number, and x is λ times the period, years, from the present to the future. In the special case when λ=1 and CAGR=e-100%, the power and exponential functions are identical.

This equation might be more familiar as a decay function when λ is less than 1, which if the future is considered to be event 1 and the present is event 2, is equivalent to saying the elapsed years between event 1 and event 2 are negative, i.e. the future occurs after the present. A half-life is given to the term  in a radioactive decay function and is proposed as the name given to λ, even when the elapsed time is positive, growing and not decaying. The “half-life” can be simply computed as

λ=ln (Future/Present)/years _{from present to future}

Exponential growth is an outcome of maximizing entropy. Maximizing entropy is implicit in many of the tools that Cambridge Systematics, the firm at which I work, uses: e. g.

·       Frataring;

·       Trip Distribution ( i.e. A.G. Wilson’s Gravity Model);

·       Mode Choice ( e.g. logit models);

·       ODME ( a digression ODME is the trade name given by Caliper. The generic name is Maximum Entropy Matrix Estimation);

·       Stochastic assignment (i.e. use of a logit equation to select among efficient paths);

·       bridge deck and pavement deterioration;

·       capacity investment decisions;

·       reliability.

Cambridge Systematics’ motto is “Think Forward” where those two words are separated by a stylized CS. (another digression. I have always translated this as “Thinking Ahead” inside of a diamond safety warning sign). If Cambridge Systematics is thinking ahead, I hope in the future we consistently always do it as an exponential rather than as a power function. Do not use a CAGR. Compute the half life. Growth is not constant, it must be resilient. That is why Ponzi schemes do not work.