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.

Priceless

 

Ain't Got You

I got a house full of Rembrandt and priceless art    
And all the little girls they want to tear me apart   
When I walk down the street people stop and stare
Well you'd think I might be thrilled but baby I don't care   
'Cause I got more good luck honey than old King Farouk    
But the only thing I ain't got baby I ain't got you

What do you do when things are priceless?

“There are some things that money can’t buy, For everything else there is MasterCard.” So went an advertising campaign in the late 1990s. Economics is about allocating scarce resources.  The most familiar, but not the only way, of allocating resources is setting a price.  So what do you do about setting a price for something that is priceless?  There is also the problem that what is priceless to me, might not be priceless to you. To me, being able to attend the Red Sox 2004 Duck Boat Parade, priceless. To my brother, who is not a Red Sox fan, worthless. There is also the recent brouhaha about $5000 tickets to Bruce Springsteen concerts. ( and the lyrics listed above are from a Bruce Springsteen song). Fortunately, the Boss is not charging $5000 a ticket or the anger would be directed at him.  Instead the ire is directed at Ticketmaster. Their defense is that they are merely charging surge pricing, the same as airlines and hotels.

This assumes that pricing is the only way that a scare resource can be allocated.  It is not. My wife is a runner, I am a sitter, but an example from the running world is instructive.  Marathon bibs are a scarce resource. More people want those scarce bibs than there are bibs available.  The bibs could be auctioned, but that would incur ill will from those runners who can’t afford the price.  Most marathon organizers do not even want the money that could potentially be raised from an auction ( it is not that they want no money, it is just that they don’t want that much money).  Additionally if bibs were offered only to the highest bidders, eventually the losers would eventually not even bother to bid on the bibs and at some point in the future, there might not even be enough runners to keep the race going.  Also some of the runners are so desirable (elite) they should get bibs, even if they do not can’t afford/won’t pay that auction price.  But awarding the bibs on merit, say a qualifying time, is hard to manage and is also discouraging to those who can’t make the time but are willing to bid high on the price.  The bibs could be  awarded randomly ( and this is not a technological challenge.  When I went to a Rolling Stones concert in 1972 at the old Boston Garden, yes THAT concert, the tickets were allocated by a mail-in lottery. )

The most successful marathons allocate bibs on a combination of all of these approaches:

·       Auction ( where the bibs are actually awarded to charities who manage and get the proceeds from any auction);

·       Merit ( which does not have to be say qualifying times to get the elite runners.  It can also be volunteering at events, or as Pearl Jam offers tickets, membership in its fan club) ; and

·       Random  ( and by that, I mean truly random, and not the rope drop, or line sitter, or online multi-screen hacking and bot infected  “lotteries”)

Then you can allocate the scarce resources without having to set a price on something that to someone is priceless.

Intellectual Property II

 

Woodstock

By the time we got to Woodstock
We were half a million strong
And everywhere was a song
And a celebration

Should the music be free?

In 1969, I was at the Newport Jazz Festival that was cancelled mid-performance because the fences were stormed.  Consequently, I did not go to Woodstock because I made the false prediction that it would also be cancelled mid-performance.  To show how good my instincts are, I also attended the Newport Jazz festival in 1971, the one that was cancelled mid-performance while Dionne Warwick was singing “What the World Needs Now” and the fences were stormed.

The problem is not that music should be free, as at Woodstock, or cancelled, as at the Newport Jazz Festivals.  One of the first things that the US Congress passed in 1790 was the copyright protection act.  If you do not protect Intellectual Property, like music, and the performers and copyright holders are not paid for their Intellectual Property then they have no incentive to create or perform.  You might wish their work was free, but I bet they don’t.  If wishes were horses, beggars would ride.

Both the Newport Jazz  Festivals and Woodstock were problems in that the expected and protected attendance did not match the actual attendance.  Newport cancelled.  Woodstock 1 gave up.  Once festivals figured out how many people would attend and figured out a way to collect admission fees from the attendees, which the festival, the attendees, and the performers all thought was fair, and like Bonnaroo, Woodstock 2 and 3,  Burning Man , Coachella, etc., etc. festivals happened.  Music, like all Intellectual Property,  isn’t free, and if the system is fair, then everyone will agree that it should not be free.