Serenity

 

Mblem

Lord give mе serenity to accept the things I can't change
And the courage to change the things I can, yeah
And if in life on my journey if I should stumble and fall
Make me wiser than the man I already am, yeah, yeah

This I pray.

Yet another threesome. This time it is serenity, courage, and wisdom.  I guess it really is true that good things come in threes. 

Among the things I can’t change are uncertainty, randomness.  I might not like that things can be random and uncertain, but I need the serenity, courage, and wisdom to accept that uncertainty. 

Stories

 

Camelot (reprise)

Ask every person if he's heard the story,
And tell it strong and clear if he has not,
That once there was a fleeting wisp of glory
Called Camelot.
Camelot! Camelot!
Now say it out with pride and joy!

What is important is the story!

My heroes are Shakespeare, Shaw, Bob Dylan, Cole Porter, Joni Micthell, Picasso, Frank Capra, among many, many others. I wish that I could tell stories like they do with words, songs, or pictures. But that is not how I roll. My stories use numbers and variables, mathematics, but they are stories nonetheless. And I would like to believe that those stories are important and add to the glory too!

Stories are important because they require imagination. And while we live in a real world where the coefficient of imagination is zero, that does NOT mean that imagination does not exist. If it does exist and has to be considered, then the implications are tremendous.

Imagination might be why randomness, entropy, gravity, etc. exist in the first place. We ignore imagination at our peril. It is convenient to pretend that the square of any number, x², should be solved by simply taking its square root, but the square root is only real if imagination is NOT considered. Take the variance, σ², for example. It is often assumed that the Standard Deviation, SD, is the square root of the variance. But this is strictly only true for flat, Euclidean, surfaces. In the surface is flat, then the variance is σ²= (SD)² +0²*i does indeed have the solution, SD=√σ², but is only because on a flat surface cos(σ)=cos(SD)*cos(0). On a hyperbolic surface it should be cosh(σ)=cosh(SD)*cosh(0). This does NOT become a single value but two values, σ=ln(cosh(SD)±sinh(SD)). When sinh(SD) is very small, that term  can be ignored and then the mid point of this range approximates SD = √σ². It is appropriate to think of the term cosh(SD) as the location, µ, parameter in a random equation where the range parameter, the standard devation , σ, sinh(SD) is the other parameter.

The problem is that no number is exact. There is always a Standard Error term, SE. The definition of SE is SD/√n, where n is the size of the sample population. If there is growth, a value that is outside those values range, then a Growth Factor, GF, has to be applied to the values to include that growth, GF*(x-SE)<y<GF*(x+SE). X is the average, mean, value of a series of numbers, corresponding to the sample population, (∑x_i)/n. If n, the sample size of the population has not changed, then the Growth Factor should only be applied to every value of x_i.  If the Growth Factor is also applied to SE, and if the sample population has not changed, then it has to be applied  to the SD. This new SD may now have become so large that the uncertainty of the range can no longer be ignored. Otherwise, to keep the Standard Error the same, the size of the population has to be decreased.

Sounds like the “rINO, republicans IN Name Only” response to growth, decreasing the size of the population? The problem is that if the size of the population is decreased, then the location term, µ, has to decreased by even more because it is divided by n not √n. So you get into a mathematical death spiral. In order to accommodate growth, without increasing error, you have to constantly decrease the size of the population.

Mathematics is a harsh mistress, and imagination is ignored at all of our peril. That is my story, and I am sticking to it!

 

 

The Middle II

 

You Do Something to Me

You do something to me
Something that simply mystifies me
Tell me, why should it be
You have the power to hypnotize me?

We are in the middle of a battle between “Do Something” versus “Destroy Everything”

Progressive Democrats such as Alexandria Ocasio-Cortez, Bernie Sanders, Elizabeth Warren  seem to be believers in “Do Something”.  The Freedom Caucus and their allies such as Matt Gaetz, Majorie Taylor Greene and Ted Cruz seem to be believers in “Destroy Everything”.  It is up to the moderate and conservative Democrats, and the remaining liberal and moderate Republicans (who are believers in our constitutional republic and are not “republicans In Name Only” ) to ensure that some things that have been done will be destroyed, but not everything that has been done will be destroyed. 

Neither of the two opposing sides should win.  It is that middle that should win because the middle is most of us.

Certainty IV

 

Michael Row the Boat Ashore

Jordan's river is chilly and cold, hallelujah
Chills the body but not the soul, hallelujah

Michael row the boat ashore, hallelujah
Michael row the boat ashore, hallelujah
Sister help to trim the sail, hallelujah
Sister help to trim the sail, hallelujah

What position in Heaven is the Archangel Michael?

In a previous blog post I claimed that the Top is one of the Top Three. IWAS WRONG!!!!. While it is easy to compute dominance, it is the winner, first place, it is harder to calculate certainty, the best. The problem is that in any contest it could be determined by pure luck and the best could finish second. The Trinitarian in me made the mistake of thinking that the Top Three in Heaven were obviously the Father, Son, and Holy Ghost Spirit, which makes the Archangel Michael, the Head of the Heavenly Host, number four. The problem is that while it is true that they are the Top Thee, a contest can not include the absolute. So what is the certainty of the best being in the Top X finishers, excluding the absolute.

This is a statistics problem. If points are awarded to finishers based on the inverse of the number of places receiving points e.g., if 10 places receive points, then 10 points for a first-place finish, 9 points for second place, etc. What I forgot to  consider previously is that any finisher can only finish, get points, once, e.g., you can’t get points for first AND second place ....unless you are the absolute and the Pauli Exclusion principle doesn’t apply. Thus you know the total points which can be awarded (the sum of the number of places getting points) divided into the number of points awarded for a mean-finish. The certainty is 100% minus this number.

While it is true that if only the first place is awarded points, that first space is 100% dominant, but the certainty of its being the best is only 50%, no better than luck. The certainty increases if points are awarded to the first two places, such that the certainty that the best is in that Top 2 has increased to 67%. It is 75% certain that the best is in the Top 3. The number of places that receive points increases the certainty that the best is among those receiving points, but that increase is at a decreasing rate as shown below for the top 20 places.

There is of course a limit, and that limit is 100% certainty that the best is among the places receiving points, as the number of places being awarded points approaches infinity. However there always has to be more contestants in the contest than those receiving points so absolute certainty can never be achieved. So while the Top Three in Heaven may have certainty because they are an absolute, and Michael may be the best of the angels, but the certainty that he finishes in the money, gets a medal, etc. in any contest of the angels has no more than 75% certainty as long as 4 or more angels compete.

L'Chaim

 

To Life

May all your futures be pleasant ones
Not like our present ones
Drink, l'chaim, to life
To life, l'chaim
L'chaim, l'chaim, to life
It takes a wedding to make us say
Let's live another day
Drink, l'chaim, to life

Life appears to be reality plus imagination.

Euler’s Formula is e^ix=cos(x)+sin(x)i.  But this is true only on a Euclidean flat surface.

It is not true on a hyperbolic surface. On a  hyperbolic surface, Euler’s Formula is true when x=0, but it is not true when x=π.  Euler’s  Formula is true because it is the transformation of a complex number in polar coordinates to a complex number in Cartesian, rectangular, coordinates, when the real radius, r, is equal to 1. However coordinate transformation requires the use of a triangle.   A triangle behaves differently on flat and hyperbolic surfaces.  If that coordinate transformation is of a complex number with both a real and an imaginary axis, then it is re^ix=rcos(x)+rsin(x)i.  It is true that x=tan^‑1(rsin(x)/rcos(x)) on all surfaces.  However r²=(rcos(x))²+(rsin(x))² only is r=√((rcos(x))²+v(rsin(x))²) on a flat space.  On hyperbolic surfaces, if x=0, then this also appears to be correct, but for x=π, if the coefficient of the imaginary axis is not ignored, then this leads to r=cosh^‑1(cosh(rcos(x))*cosh(rsin(x))),  and for x=π, it leads to r=-r.  This is only true if the coefficient of the real axis, the radius, is always equal to 0.  Euler’s Formula works because of the trigonometric identity cos²+sin²=1.  However the hyperbolic trigonometric identity is cosh²‑sinh²=1.  On a hyperbolic surface, it is proposed that Euler’s formula should be restated as e^ix=cosh(x)-isinh(x).  In this case, you can take advantage of the fact that cosh(x) is symmetric about the zero axis, i.e. cosh(x)=cosh(-x), while in flat space it is sin(x) that is symmetric, i.e. sin(x)=sin(-x).  With the restatement of Euler’s Formula, r=ln(0±sinh(cosh(x))), and for x=π, r can be any value and is not limited to only zero.

So not just for zero, but for non-zero values of the radius of reality, if we live on a hyperbolic surface, life may be -r+0*i.  It has a coefficient of zero for imagination, but it is imagination nonetheless.

I Don't Know

 

Maybe

Maybe they're strict
As straight as a line
Don't really care
As long as they're mine
So maybe now this prayer's
The last one of its kind
Won't you please come get your "baby"
Won't you please come get your "baby"
Maybe

Yes or no can’t be the only answers. Sometimes the right answer is maybe.

Yes or no; true or false questions should not be allowed. Otherwise this can lead to “Have you stopped beating your wife?” questions. If you answer yes, you seem to be admitting that once beat your wife but have now stopped. If you answer no you seem to be admitting that you still beat your wife. But if you have never beat your wife, neither answer is correct. That is why I don’t know; it depends; it’s complicated; it’s not that simple; tentatively; maybe; or some third choice has to be offered along with yes  and no for the answer to have any meaning.

John F Kennedy said that “ Let us not seek the Republican answer or the Democratic answer but the right answer.”  He understood that the right answer, might be a third choice. Harry Truman asked for one-handed economists because he was tired of economists who appeared to have three hands: on the one-hand; on the other hand; on the third hand. A simple yes or no  answer might be what you want to hear from your experts, but it may NOT be the correct answer. On the Car Talk radio show, the new puzzler was in the third half of the show. Tom and Ray Magliozzi, Click and Clack, the Tappet Brothers, were only trying to be funny but they spoke a great truth. The answer may be in the third half of the show.

Three

 

The Power of Love

You don't need money, don't take fame
Don't need no credit card to ride this train
It's strong and it's sudden and it's cruel sometimes
But it might just save your life
That's the power of love
That's the power of love

But what about the power of three.

I have posted previously about the power of three, a trinity. Some additional points:

·    Only the first three numerals have special suffixes, 1^st, 2^nd , and 3^rd , while all other ordinal numbers that are not numbers times powers of 10 plus those numbers, e.g., not 21^st, 201^st, 2001^st, etc. all share the same suffix, 4^th, 5^th, 6^th, 7^th, 8^th, 9^th, 10^th.

·     There are three fates, three Norns, three witches in Macbeth, three bears, three musketeers, etc.

·     In the TV series Charmed, the women stars wield the Power of Three.

·        Pro and con opinions are not very insightful. Add a third opinion and it can become very profound.

·    Toastermasters trains it speakers to offer three facts in every speech, claiming that the human brain responds best to three facts

·     The three basic laws of Alegra, can all be defined with only three variables: 

Commutative, a+b=c=b+a;

Associative, a+(b+c)=(a+b)+c;

Distributive, a*(b+c)=a*c+b*c

·     In game theory, a fair game must have at least three players. In two-player games with rules, the rules are by definition the third player.

·     Most plays, stories, etc., consist of three acts: a beginning, a middle and an ending.

·     A shape with three sides, a triangle, is always stable. A shape with less than three sides is not stable. A shape with more than three sides may not be stable.

·     A sentence has three basic parts: a subject, an object, and a verb.

·     An economic transaction requires three things: a seller, a buyer, and something to be exchanged.

·    There are three dimensions : space, time and imagination.  Space can be further divided into three parts: x, length; y, width; and z, height.  Time can be further divided into three parts: past, present, and future.Imagiantion can also be divided tinto three parts, postive day dreams, negativve nightmares and neutral reality.