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.

Choice VII

 

I’m a Man

If I had my choice of matter,
I'd would rather be with cats
All engrossed in mental chatter
Showing where your mind is at

If you believe in one God, then you believe in Choice.

Zoroastrianism believes in two competing absolutes, Good and Evil, that are constantly at war. It sounds an awful like today’s Hellfire and Brimstone evangelists.

The First of the Ten Commandment is that God is an absolute and is there is only one absolute. This means that Evil is NEVER equal to Good if God is Good. This is not only theological it is also mathematical. If there is an absolute, ∞, AND a complete opposite of that absolute, -∞, its zero is a relative zero between these two absolutes, (∞+-∞)/2=0. But if there is one absolute, then the multiplicative inverse of that absolute, 1/∞, is an absolute zero. That there is a difference between an absolute zero and a relative zero can be seen by setting these two zeros equal to each other. You end up with the absurdity that ∞²-∞²=2.

If there is only one God, then Evil can never be an equal to that absolute/God. To accept a relative zero, is to accept that there are at least two absolutes. If there is only one absolute, the choice is between that absolute and no absolute, not between Good and Evil, i.e., competing absolutes. If someone is telling you that the choice is between Good and Evil, then they are also telling you that they believe that there are at least two absolutes. And if there is only one absolute there must be one choice, that absolute or not that absolute. If someone is denying you that choice, then they are denying the existence of that absolute.

Certainty III

 

The Hello Song (the theme song to Animaniacs) 

There's a word in every language
A word that you should know
A word that means you're friendly
A word used high and low.
Though the way to say it varies
Most everywhere you go
Its meaning never changes
And that word is Hello 

Variance is just saying Hello 

What’s in a name? that which we call a rose 

By any other name would smell as sweet; 

Smart guy that William Shakespeare. He saw the problem that humans infer things because of a name. Take the Heisenberg Uncertainty Principle for instance. It could just as easily be called the Heisenberg Variance Principle, that for a particle at a location, x, the speed, δx, associated with that particle at that location is defined by the location and the standard deviation at that location. But because it is called the Uncertainty Principle, and God is Certain, it is assumed that God has No Variance, is Unvariant. 

Mathematically this is Determinism, 0 ± 0, versus Randomness, x ± σ. In trying to be God-like, humans assign a location of 0 and a Standard Deviation, σ, where variance is σ², of 0 to all things. However humans are not God, x<>0, and the correct equations should be 0 ± σ for God versus x<>0, x ± σ for everything else. In other words, we should try to  discover God’s variance and make that our own variance for all of our locations, if we want to be God-like.

The Middle

 

Stuck in the Middle

Clowns to the left of me
Jokers to the right
Here I am
Stuck in the middle with you.

But the middle is where you want to be.

The eternal debate always seems to be between the right vs left, whether that is monarchists vs. lower case r republicans; capitalists vs. communists; conservatives vs. liberals; libertarians vs. progressives; red vs. blue; etc. One side are User Optimalistsm, UO. The other side are System Optimalists, SO. But humans are individual users (UO) that form a society (SO). No side should win, or we have no society, and not thus no society to protect individuals from each other.

Mathematics/game theory provides the guidance that when individuals form a system they seek a Nash Equilibrium. Some users will achieve less than their own User Optimal, but all members of the System will be at Equilibrium,  will achieve the same value.

While this may sound like an unfamiliar concept, you probably have experienced it if ever you have driven in a lane drop in traffic, due to construction, work zones, accidents, etc. The System Optimal solution is for the lane which continues to move at capacity and for traffic to continue to operate in the lane that is being dropped for as long as possible until there is a safe gap to merge into the continuing lane. This is called a rolling merge. In fact few travelers have ever experienced a rolling merge. This is because an individual vehicle can always continue in the lane which is being dropped and then force its way to the head of the still moving lanes, because “don’t you know who they are.”  To prevent last-second lane jumpers, most other vehicles  move into the continuing lane at first notice. Also some vehicles will block the lane being dropped to block any attempts at lane jumping. This is neither a User Optimal free-for-all nor a System Optimal rolling merge, but somewhere in-between where individual Users function as if they were a System.

It is neither winner takes it all, nor everyone wins, but the team wins because some team members are willing to take one for the team. Neither extreme wins, but the middle wins.