Dominance or Certainty

 

Winner Takes It All

The winner takes it all (takes it all)
The loser has to fall (has to fall)
It's simple and it's plain (it's so plain)
Why should I complain? (Why complain?)

So Wall Street which is it? Dominance? or Certainty?

The Wall Street stock market is all about winners and losers, by dominance. But the stock market also hates uncertainty. You can’t have certainty in a contest with only two parties which will be decided by dominance.

The stock market is not certain,which is why there are Index funds and why a random walk of the stock market does better than day trading. Collectively you can achieve certainty. Individually you might achieve dominance but that is at the expense of allowing uncertainty. A contest where there are only two outcomes and two players can be 100% dominant, but that outcome is purely by luck, a random occurrence if the game is fair and the parties are equal. In this case the certainty that the dominant winner is the certain winner is the value of that outcome, 100%, multiplied the reciprocal of the probability of that outcome, which is 50%. Thus even though the dominance of the winner has been established, the certainty is only 50%.

The difference between certainty and dominance can best be seen in the jury system. A 7-5 jury vote indicates 100% dominance, but it is only 80.66% certain.  A 12-0 finding of Guilty, or Not Guilty,  remains 100% dominant, but the certainty has increased to 99.98 %.

Thus for a single stock transaction, you can be dominant or certain, but being dominant does not mean being certain. However being certain does mean being dominant.

Zero

 

Transcendental Meditation

Transcendental meditation
Transcendental meditation
Can emancipate the man
And get you feeling grand
It's good

Is zero transcendental?

In mathematics, a transcendental number is a real or complex number that is not algebraic – that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best-known transcendental numbers are π and e.

https://en.wikipedia.org/wiki/Transcendental_number

While π and e might be the best known transcendental numbers, it is noted that hyperbolic trigonometric functions, which are expressed as functions of powers of e,  which is itself a transcendental number, are transcendental functions.  These hyperbolic trigonometric functions are also periodic in i*π,  i.e. repeat on the imaginary axis with a frequency of multiples of π[1], another transcendental number.   

Euler’s formula, e^ix=cos(x)* sin(x)*i, is also the coordinate transformation of a complex number from polar coordinates to rectangular, Cartesian, coordinates with a real and an imaginary axis, where the polar radius is 1.   It includes the rotation of the imaginary axis by an angle of x.  Sin(π)=0 means that the coefficient of the imaginary axis is zero.  Does that mean that there is NO imaginary axis?  That depends on whether that zero is absolute or relative. 

Absolute zero is the absence of the absolute, i.e. a temperature of absolute zero means that there is an absence of temperature.  By contrast, zero on the Centigrade scale does not mean that there is no temperature, just that the temperature is relative to a zero point on the scale, which in the case of the Centigrade scale is the freezing point of water.  IOW, negative numbers are allowed on a relative scale.

Transcendental functions are not expressible as a finite combination of the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extracting a root. Examples include the functions sin(x), cos(x), cosh(x), sinh(x), e^x, ln(x), etc., and any functions containing them. Special transcendental functions are the reflection of sin(x), which is sin(‑x) and is equal to sin(x) and the reflection of cosh(x), which is cosh(-x) and is also identical to cosh(x). This is not true of cos(x), tan(x), sinh(x), tanh(x), e^x, ln(x) and other transcendental functions.  They are not self-reflective, reflections of themselves.

Because cos(x) is transcendental but not self-reflective this means that Euler’s formula is also transcendental but not self-reflective. In that equation x can take on any value between -∞ and ∞.  Because Euler’s Formula is a combination of a self-reflective sin(x) and a non-self-reflective cos(x), but trigonometric functions are repeating, there are many solutions with a zero coefficient of the imaginary axis, i.e. a rotation of the imaginary axis of zero: even multiples of π, including zero, which have values of cos =1 as the coefficient of the real axis; and odd multiples of π which have values of cos=  -1 as the coefficient of the real axis. Since in this case zero is not merely the absence of an absolute, and is in fact multiple numbers, it must be a relative zero, not an absolute zero. An absolute zero is the absence of a transcendental .  A relative zero is not.

So is zero transcendental?  That depends on if that zero is absolute or relative.

---

[1] Cosh, sinh, and related functions, repeat with a period of 2*π*i.  Tanh and related functions repeat with a period of π*i. 

Absolutely IV

 

With A Little Help From My Friends

Would you believe in a love at first sight?
I'm certain it happens all the time, yeah
What do you see when you turn out the light?
I can't tell you, but it sure feels like mine.

How certain are you that it happens all the time?

A random equation has two parameters: 1) its location, mean/median/mode, and 2) its scale, variance, uncertainty. The adage is that nothing is certain except death and taxes. Given that you can cheat on taxes, but you can’t cheat death, I would suggest that only death is certain, and thus life is uncertain, i.e. has a variance.

An exponential distribution also has a variance but is defined only for positive numbers. This restriction is identical to saying that its location is zero. It still has a scale parameter, a variance, that is given as λ. It is suggested that the exponential distribution is a distribution of the absolute. It can be coordinate transformed by translation to any location, µ, as long as µ>0 and then its Probability Density Function, PDF, becomes

λ*e^-λ*(x-µ)

and its Cumulative Distribution Function, CDF, becomes

1-e^-λ*(x-µ)

The median of an exponential distribution is generally given as ln 2/λ, but this is when the location is zero. With the translation of the location, the median is ln 2/λ+µ. The mean is 1/λ+µ.

A normal logistics distribution has both a location and a scale parameter. Its CDF is

½*tanh((x-µ)/(2s))+½.

For the median of the two distributions to be equal requires that s = (ln 2)/λ and that µ>0.

When the location of a logistics distribution is zero, then its upper half, above its median, looks like an exponential distribution with a location of zero. This is hardly surprising. The exponential distribution is also the equation of radioactive decay. Its scale parameter, λ, is then known as a half-life.

There is no need as Grushka (Grushka, 1972) and Reyes (Reyes, Venegas, & Gómez, 2018) wo each have proposed to combine an exponential with a normal (e.g. Gaussian or logistics) distribution.  An exponential distribution is only the upper half of a normal logistic distribution with a location of zero. That does not mean that a logistics distribution is an absolute. An exponential distribution, an absolute, is half of a random normal logistics distribution, life.  Of this I'm certain.

References

Grushka, E. (1972). Characteristics of Exponentially Modifed Gaussian Peaks in Chromatograhy. Analytical Chemistry Vol 44, pp. 1733-1738.

Reyes, J., Venegas, O., & Gómez, H. W. (2018). Exponentially-modified logistic distribution with application to mining and nutrition data. Appl. Math 12.6, 1109-1116.

 

Impossible

 

Impossible / It’s Possible

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!

Did you mean Improbable?

When I was growing up, many of my neighbors and relatives worked for the then headquarters of the Naval Construction Battalion of Engineers, "SeaBees", at Quonset Point Naval Air Station.  The motto of the SeaBees is “Can Do” and the phrase "With willing hearts and skillful hands, the difficult we do at once, the impossible takes a bit longer" is often associated with them.

I always wanted to be a Seabee, but I had to settle for being just an engineer.  As an engineer I may be willing, but I know engineers can’t ever do the impossible, just the improbable.  But often what is called impossible is merely improbable.  So ask an engineer.  He may be just the zany fool you need!.

Safe Schools

                                                                 Ever True to Brown

We are ever true to Brown,
For we love our college dear,
And wherever we may go,
We are ready with a cheer,
And the people always say,
That you can’t outshine Brown Bears,
With their Rah! Rah! Rah! and their Ki! Yi! Yi!
And their B-R-O-W-N.

Go Bears!

I graduated from Brown University in 1973.  While I am proud to be a Brown Alum, this was not my first, or even my second, choice of school.

My first choice was the US Naval Academy.  I thought that my godfather having the rank of Navy Captain and my being a Merit Scholar made me a shoo in.  But I failed the medical exam because of my eyesight.  ( I CAN see a battleship!  I immediately went to my draft board physical and was found to be 1-A before I got a student deferment.  Apparently I see good enough to be a grunt, just not to be a naval officer!)  My second choice was MIT, but I was rejected there. Which made Brown my "safe" school.

Art

 

A Secretary Is Not a Toy

That a secretary is not a toy
No, my boy
Not a toy to fondle and dandle
And playfully handle
In search of some puerile joy
No, a secretary is not
Definitely not
A toy

And an artist is NOT his work of art.

The worst blowout in College Football happened in 1916 when Georgia Tech beat Cumberland College by a score of 222-0.  Apparently the football coach of Georgia Tech, who was also its baseball coach, wanted to enact vengeance because of a baseball loss to Cumberland College of 22-0.  Cumberland College had disbanded its football team and tried to get out of the game.  The Georgia Tech coach refused and the game was to be played as scheduled.  A ragtag football team was assembled from the student body for just this game.  Georgia Tech scored on every possession in the inevitable slaughter.  The vengeful football coach of Georgia Tech?  John Heisman. Yes, the same coach whose name is honored in the Heisman trophy.

Sticking with a college football theme,  Pop Warner was the coach at the Carlise Indian School where he was not above cheating to win his games against other college football teams.  In fact many of his efforts to bend the rules of his day were adopted to become the regulations of what we know today as football.

It isn’t only college football.  Vincent Van Gogh was a madman who cut off his own ear.  Thomas Jefferson owned slaves when he wrote the Declaration of Independence.  Kevin Spacey won an Oscar for his performance in American Beauty before his sexual assault scandals.  Bill Cosby was America’s Dad before his own scandals. Has anyone seen the movies The Imitation Game or A Beautiful Mind?

All humans, including artists, are flawed beings.  The Bard was being ironic when he wrote “I come to bury Caesar, not to praise him. The evil that men do lives after them; The good is oft interred with their bones”.  Often it is the good that lives after them and the evil that is buried with their bones.  What endures is art.  The art may be judged as good or great, even if the artist is flawed.  You might expect great art from certain artists, but that does not make those artists without flaws.  The art may be great, but the artist, as a human, can be not so great. Don't confuse the two. "Love the sinner, but hate the sin" works both ways. You can "Love the art, but hate the artist".

Absolutely III

 

Let’s Call the Whole Thing Off

So if you like pajamas (I like pyjahmas)
I'll wear pajamas (you got pajamas)
For we know, we need each other
So we better call the calling off, off
Let's call the whole thing off
Let's call the whole thing off (yes)

You saying ee-ther and I saying eye-ther is not a very big difference!

At infinity, the absolute, differences do not exist.  The absolute is accepted as being two things at one time: odd and even, male and female, red and black, less filling and tastes great, liberal and conservative, Democrat and Republican, etc.  So if we are to try and emulate the absolute, shouldn’t we accept that our differences do not matter, we are all the same and we need each other.  Let's call the calling off, off.