Outcomes II

 

Paint it Black

I see a red door
And I want it painted black
No colors anymore
I want them to turn black.

If you only see things in Black and White, you can be missing quite a lot.

Black and White might seem like two  dimensions.  It is not. It is only one dimension,  choice, and black is not making that choice and white is making that choice.  But Black is only the choice of one outcome.  If you look at multiple choices, then the most probable choice is 50% Black and 50% White, in other words gray.  If various shades of gray were allowed, for example 50 as in the popular book series, then only one of those 50 is 100% black and one of those 50 is 100% white.

Microsoft Word allows for three colors, dimensions: Red, Green, and Blue. It allows for 256 graduations within these colors.  This allows for 256³ gradations within these three dimensions, or 16,777,216 colors.  And the most common color is still grey. It does not take many dimensions and many gradations within those dimensions to give rise to many, many possible outcomes.

Outcomes

 

Impossible

But the world is full of zanies and fools
Who don't believe in sensible rules
And won't believe what sensible people say
And because these daft and dewy eyed dopes keep building up impossible hopes
Impossible things are happening every day\

There is a difference between impossible and improbable.

Improbable means that there is only one outcome, or a few outcomes, out of the myriad of outcomes that could happen.  Impossible means that there is NO  outcome.  The problem is when the number of outcomes gets very large, or the popular wisdom rules out certain outcomes as impossible, people confuse impossible with improbable.

Automatic sliding doors that detect the approach of a person who wishes to use that door, did not exist at the time of the production of the original Star Trek TV series.  To appear futuristic, the doors on the StarShip Enterprise appeared to open automatically.  In reality, this was a practical visual special effect where an off-screen stagehand pulled the door open when an actor approached.  Automatic door opening was an improbable outcome in 1966, not an impossible outcome.  Now most retail stores have automatic doors, sliding or folding, and what seemed improbable in 1966, has become so possible that it is common place.  Before 1969, a man walking on the moon might have seemed an impossible outcome, but now we know that it was merely an improbable outcome.

Impossible things can never happen.  But many improbable things are often incorrectly characterized as impossible.

Reality

 

Compared to What

Slaughterhouse is killin' hogs
Twisted children killin' frogs
Poor dumb rednecks rollin' logs
Tired old lady kissin' dogs
I hate the human love of that stinking mutt (I can't use it!)
Try to make it real, compared to what? C'mon baby now!

Making it real might be accepting that reality is hyperbolic.

If the shape is always flat, then Euclidean geometry would apply in all places. It does appear to apply locally but fails to produce reasonable results when traversing the globe, when the distance between two points is significant compared to the radius of the spherical Earth. When the distance is large, spherical non-Euclidean geometry, not Euclidean geometry, applies and its Great Circle distance is used, rather than the shortest distance between two points in flat space.

Similarly if the universe is flat, then Euclidean geometry would apply in all places. As above, it does appear to apply locally but, given the above, it is reasonable to question if  it applies globally. If the universe is hyperbolic, rather than flat, then non-Euclidean geometry, i.e. hyperbolic trigonometric functions, should apply and not the shortest distance between two points in Euclidean geometry.

If only the shortest distance were involved, this would not be as significant. However this is really the relationship between numbers, where any number, c, can be defined by two other numbers, a and b.

c = a * b

c = a + b

While these relationships are true in any geometry, the relationship between the sum of squares depends on the geometric system being used.

c² = a² + b²

has different solutions depending on the geometric system.

·        In a flat Euclidean space, the solution is 

        c=√(a²+b²), 

      but this only has answers for c in the real plane if a²+b² is greater than zero. If it is less than zero, i.e. negative, then the solution for c is a complex number which requires the use of imaginary numbers.

·        In a spherical non-Euclidean space, the solution is 

      c=1/R*cos^-1(cos(a/R) *cos (b/R)) 

      but this also assumes that this solution is on a sphere which is a closed space which has a Radius, R.

·        In hyperbolic non-Euclidean space, the solution is

      c=cosh^-1(½*cosh(a+b)+½*cosh(a-b)),   

      which is on an open hyperbolic plane with no fixed Radius, R.

This relationship does not merely impact the shortest distance between two points. It impacts every solution that involves the square of two numbers. For example, the Lorentz transform, used in time and length dilation, and mass expansion, which varies based on the ratio of the velocity to the speed of light, in flat Euclidean space is √ (1-(v/c)²), which requires the use of imaginary number if v/c is greater than zero. However if globally space is  non-Euclidean and hyperbolic, then the Lorentz transform is 1+ln(cosh(v/c)±sinh(v/c)), and does not imply the use of imaginary numbers when v/c is greater than zero. It simply becomes undefined ( the natural logarithm of a negative number is undefined). It is suggested that all physical equations, for example those in electrical engineering involving alternating current,  which involve the square of two values should not use the Euclidean solution, but should use the hyperbolic solution. This will prevent the creation of imaginary or complex number solutions which are only a result of assuming that space is flat.

Further, if the universe, space, is hyperbolic, as proposed by Mabkhout [1], the implication is that dark energy and dark matter, are not needed to deal with  cosmic inflation and expansion, the size of the observable universe is consistent with its age, and the Planck length is consistent with the Planck energy, etc..

Additionally if the universe is random and hyperbolic, it must be tolerant and there is no rationale for superstition, scapegoating, or intolerance which are only an attempt to find deterministic reasons for random events.

[1]        Mabkhout, S.A., 2012. The infinite distance horizon and the hyperbolic inflation in the hyperbolic universe. Phys. Essays, 25(1), p.112. https://www.researchgate.net/profile/Salah-Mabkhout/publication/302521692_The_Infinite_Distance_Horizon_and_the_Hyperbolic_Inflation_in_the_Hyperbolic_Universe/links/5730e0cf08ae6cca19a1f675/The-Infinite-Distance-Horizon-and-the-Hyperbolic-Inflation-in-the-Hyperbolic-Universe.pdf

Storytelling

 

As Time Goes By

It's still the same old story
A fight for love and glory
A case of do or die
The world will always welcome lovers
As time goes by

What makes a good story?

My forecasting career has been about finding the most likely outcome/maximum entropy, that is the mesostate, outcome, that has the greatest number of microstates, possibilities.  Storytelling is about finding an improbable but desirable outcome and ensuring that that is believable, possible.  My career has been about finding the stories of Dog Bites Man, Goliath Beats David, etc.  But those stories do not fascinate us.  The improbable stories with an  outcome that we believe fascinates us, e.g. Man Bites Dog, David Beats Goliath.  I.e. a mesostate that is not the most probable but is fascinating. 

A billionaire winning a billion dollar lottery, improbable, but not very fascinating.  A pauper losing a million dollar lottery, probable, but not very fascinating.  A pauper winning a billion dollar lottery, improbable AND fascinating.

Goliath beating everyone, including David, probable, but not very interesting.  David beating Goliath, improbable AND interesting.

A good story is about getting from the beginning: David versus Goliath, a pauper and a billion dollar lottery, etc. believably through a middle, to that improbable but desirable, fascinating, interesting outcome or ending.

Forecasting is using believability to get to the most probable outcome

Storytelling is using believability to get to an IMprobable, desirable, and fascinating, outcome.

A problem is that the skills for convincing us about the believability can be misused to produce an outcome that we don’t desire, but is desired by the forecaster or storyteller.  The Boy Can Cry Wolf when there is No Wolf just to get attention for the Boy. Then we don’t believe or trust him when The Boy Cries Wolf and there really is a Wolf.

Just like you can appreciate a good forecast, you can appreciate a good story, but make sure it is believable and that its outcome is one that you desire. Not every good story is true.

Loaded Dice

 

Democracy

It's coming from the sorrow in the street
The holy places where the races meet
From the homicidal bitchin'
That goes down in every kitchen
To determine who will serve and who will eat
From the wells of disappointment
Where the women kneel to pray
For the grace of God in the desert here
And the desert far away:
Democracy is coming to the USA

Believe in democracy , even when it can’t determine.

The belief in a deterministic universe, Determinism, as opposed to a random universe, Free Will, is IMHO at the heart of the problems that we have currently in society.  If you believe in determinism, that everything  happens for a reason, then you may look for that reason. That can make you believe in conspiracies, like “the COVID vaccine kills people”, or to scapegoating certain people, like “the Jews did it.” However, if there is no reason and the world is random and stuff just happens, then those conspiracies are silly and the scapegoating is incorrect.

The problem is that we may believe in an absolute, e.g. God, and that absolute should know what will happen, have omniscience, have absolute knowledge.  But this creates a paradox if the absolute knows the outcome of random events, then how can they be random.  To use Einstein’s complaint about the randomness of quantum mechanics, "God does not play dice with the universe".  The paradox is that we play dice, and dice IS random.  A possible answer is that God does play dice with the universe, it is random, but he plays with loaded dice,  i.e. knows the outcome of random events.  Since we are not absolute, we can appreciate this fact, even if we can’t understand it, and thus we play without knowing the outcome.  Casablanca is my favorite movie. I have no problem thinking of God as Rick Blaine.  God should be flattered. Rick did a beautiful thing.  
https://www.youtube.com/watch?v=xD_bKVAZJBw

Choice

 

Uncle John’s Band

I live in a silver mine and I call it beggar's tomb
I got me a violin and I beg you call the tune
Anybody's choice, I can hear your voice
Wo, oh, what I want to know, how does the song go

What is choice?

Choice is inherently random. You can choose or not choose. That is what choice is all about. A popular example of random events in the United States is Las Vegas casinos. Those casinos feature games of chance. But there are odds dictating the payouts on its games of chance. Statisticians help the house set those odds, to ensure that the game is random, but there are still ways to make sure that the house has an advantage in the payout.

The steps in setting the payout, without ensuring that the house gets a cut, is to first find the odds of each outcome and make sure that the payout is consistent with those odds. Thus in a game of roulette, with no zero or double zero slot, the odds of the roulette ball landing in an odd slot are 50% and the odds of landing in an even slot is 50%. If there is one zero slot and that slot is defined as neither odd nor even, then the odds drop to 18/37 odd, 18/37 even and 1/37 zero. If the payout is still 18/36 for odds or evens, then the house makes money on every bet because there are 37 outcomes, not 36. That is why in Blackjack, the House wins on ties. That is why in sports betting, the bookie doesn't pay on pushes.

If the odds are not set in advance but by the bettors, parimutuel betting, then first the house cut is taken off the total amount bet, and the amount bet on each outcome dictates how the remainder is allocated for each outcome. 

Whenever you see the word choice, whether, as in my field of travel demand forecasting, it is destination choice, mode choice, route choice; the method includes a pseudo random number generator; or is based on maximum entropy or maximum likelihood; it is setting the odds of a random event. Forecasting under these circumstances is trying to set the odds. Forecasters may not always dress like racetrack touts in a Damon Runyon story, but the similarity should never be forgotten

Enabling

 

Stand by Your Man

Stand by your man
And show the world you love him
Keep giving all the love you can
Stand by your man

It is possible to love him, but not like his behavior.

People have a hard time separating the artist from his work of art, the creator from his creations. This is the basis for the popular wisdom, and why it also so hard, to love the sinner but hate the sin. Ty Cobb and Pete Rose were wonderful baseball players, but deeply flawed human beings.

And people have a hard time separating exceptional behavior in one field from poor behavior in another field. This is the basis for the “Peter Principle,” where people are promoted into situations  for which they are not suited because it mistakenly assumed, for example, that a good salesman will make a great manager of other salesmen. Ted Williams was a Hall of Fame baseball player, but a lousy manager of other baseball players.

So how do you know if you are loving, not resisting, the bad behavior and not rewarding, enabling, the bad behavior? Are you making excuses for the bad behavior? Are you ignoring your needs to deal with that bad behavior? Are you taking on more responsibilities to deal with that bad behavior?Are you lending financial support to further that bad behavior? Are you resenting that bad behavior? Are you afraid that if you don’t accept the bad behavior, you will not receive love in return? Are you perpetuating this enabling because this is what you learned from others?

To deal with this bad behavior you first have to admit this is bad behavior. You have to set and stick to strict boundaries that you will not accept this bad behavior. You have to learn how to say no.

Because just as people are not their good behavior, people are not their bad behavior. Stand by and love your man, but this does not mean liking his bad behavior.