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.

 

 

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[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.