Truth V

 

The Three Bears

Just then, Goldilocks woke up
Broke up the party and beat it out there
Bye-bye, bye, bye, said the daddy bear
Goodbye, bye, said the mamma bear
Hey bubba-rebear, said the wee bear
So ends the story of the three bears

So, don't forget children, whatever you do
Don't go down to the woods tonight
Because the bears'll get ya!

Never mind about Goldilocks and the Three Bears, what about Absolute and The Three Zeroes.

In a previous blog post I proposed that there are three zeros: 1) absolute zero, 2) relative zero and 3) repeating zero. If one of the four cells in an outcome matrix is an absolute, then the other three cells must be zero if the entire outcome matrix is also to be absolute. Let’s assume the rows of the outcome matrix are wins and losses and the columns of the outcome matrix are true and false. Then if any of those four cells are absolute then the other three cells must be one of the three zeroes.

If Quadrant II (Quadrant numbering following standard mathematical  conventions: Top Right is Quadrant I, Top Left is Quadrant II, Bottom Left is Quadrant III, and Bottom Right is Quadrant IV) of the outcome matrix has true wins, then Quadrant I has false wins, Quadrant IV are has false losses, and Quadrant III has true losses. The outcome matrix is certain if all four cells sum to 100% and the outcome matrix is an absolute when any one of the four cells is 100%. If the absolute is a true win, then Quadrant III must also be a False Win and therefore an absolute zero; Quadrant IV must be a False Loss and a relative zero, and Quadrant I must be a True Loss and a repeating zero. An absolute win is identical with an absolute loss. However a win does not always have to be true. It is only true if the members of the group are also true. If there are N members of a group then if a group is going to function as an absolute, then N must be equal to three ( if N→∞ is 1, 100%, then Quadrant  is N/3 according to L’Hôpital’s Rule, the number of the group, N,  divided by the three outcomes: win , lass AND tie.)

If the outcome matrix is to be certain AND true, then Quadrant II must be N/3, and the sum of Quadrant II and Quadrant III must also be true. This mean the zero in Quadrant III has to be an absolute zero. The zero in Quadrant IV, a False Loss, and must be a relative zero since it is offset from an absolute zero. This means that the zero in Quadrant I, a False Win, must be a repeating zero. Thus there are four outcomes if an absolute is certain: Absolutely true; absolutely false; absolutely a win, and absolutely a loss. If the absolute must be certain and true , then there is only one matrix that satisfies this and as stated previously, Quadrant II must be N/3. If all cells of the outcome matrix must also be between zero and one, then non-negative values can be found for Quadrants I, III and IV that can satisfy the certainty of the outcome matrix if the members of the group are greater than 3. If the number in the group is 3, it IS consistent with the absolute. If N, the members of the group, is only 1 there are NO non-negative values of Quadrants I, III, and IV that can be found that are also true. If the number of members of a Group are 2 and Quadrant III is zero, then the group can be true OR false depending on the values for False Wins and False Losses. If the value of False Losses is between zero and 1/6 and the value of False Wins is also between zero and 1/6,  and the value of False Losses plus False Wins is equal to 1/3 then the group is true. 

To satisfy both conditions, if N=2, only Quadrant I=Quadrant IV=1/6 is possible. This means that the sum of values in Quadrant I and IV, which remember is only the stand-in for ties, is a normal distribution. Otherwise the win is ABnormal. If the percentage of True Wins is 2/3, 66 2/3%, and the sum of False Wins plus False Losses, i.e. Ties,  follow a normal distribution, then the maximum positive normal skew is 96%, the False Wins are 2% and the False Losses are also 2%. The minimum negative normal skew would be 46.53% and the False Wins and False Losses would be each 26.785%. However any value for False Wins less than 25%  is also certainly false. This means that 91% of the normally distributed values with a 2/3 in Quadrant II, true wins, are true and then 9% of the wins, the sum of Quadrant II and Quadrant I, are false.

An absolute appears consistent with groups with three Members, a trinity. A group with more than three members can always be true. A group with only 1 Member will always be false. Groups with two Members can be either true OR false. Groups with two Members (for example a two party system according to Duverger’s Law), which are normally distributed with a location parameter of 2/3 and a range parameter equal to ½ are true 91% of the time, including all those that are positively skewed, but are false 9% of the time, including the maximum negative normal skew.

A normal win in a real election with two group (e.g. parties) indicates that the win is true 91% of the time. If the distribution of False Wins and False Losses (whose sum is ties) are normally distributed, it  will be false 9% of the time including some negatively skewed normal distributions. The maximum positive skewed normal distribution for a group of two has a win certainty of 98%, and a truth certainty of 96%, Those are almost identical to the absolute value of 100%.

Things that are assumed in making wins true.

1 The members of the group should approach the absolute, i.e., N→∞. All measures that decrease N, such as voter suppression, reduce the chances of the win being true.

2.  Ties have to be allowed. Zero-sum games assume than a contest will always result in a win and that all other outcomes are a loss. Thus contests that include a fixed sum, such as fixing the size of the House at 435 seats, the number of Supreme Court justices at 9, or fixing the currency to a commodity standard, should not be allowed. It is noted that if rather than the current method of allocating Congressional House seats, a method which apportions one seat to the smallest state by population and all other seats based on the ratio to that state, currently Wyoming. This is why the popular name for this rule is the “Wyoming” rule.

3.  There must be three choices accommodating the three outcomes of win, loss, and tie. Since Duverger’s Law says that in the current single representative for a district system used in the United States will tend to two parties (groups) , this can be satisfied if each of the two parties nominates two candidates in each election. Otherwise voting might only indicates opposition to a candidate, not voting for a candidate.

4. Rank Choice Voting, as currently used in Alaska, should be included in all elections where the winner is by plurality rather than majority. In the 2024 Presidential election, at least the state votes in Michigan (Trump 49.7%) and Wisconsin ( Trump 49.6%) were by less than a 50% majority. It is not know what the results were in the congressional districts.

5. The electoral college is intended to elect a President based on the people’s choice AND the state’s choice. Thus awarding electoral votes should be done by Congressional District AND by states, as is the case currently only in Nebraska and Maine. It is not commonly reported what the people’s portion of electoral college vote would have been in all other states if they were awarded by Congressional House District. 

Even if all of these measures were in effect, it is noted that a normal election with two major parties is only absolutely true in 91% of all cases, based on statistics and game theory. Knowing the difference in the three zeroes makes it possible to solve for truth even when some of the Quadrants are NOT zero.  And it in reality, where there are both, 2, sides then not being normal is not being truthful.

Winning

 

I’m A Loser

What have I done to deserve such a fate?
I realize I have left it too late
And so it's true pride comes before a fall
I'm telling you so that you won't lose all

I'm a loser
And I lost someone who's near to me
I'm a loser
And I'm not what I appear to be 

What does it mean to “lose” an election.

Our constitution is based on the fact that “We the People” are the sovereign, the absolute. The people elect those who will execute sovereignty as the representative of themselves. The winner of an election is certain, but while the absolute can be true, a “win” only demonstrates dominance. It does not, and can not, indicate truth.

Am outcome matrix/table will demonstrate this fact. An outcome matrix has FOUR cells. The certainty is the value of the ENTIRE matrix. But there are THREE outcomes in any game, Win, Loss, AND Tie. In order to fit these three outcomes into a four cell outcome matrix, it is useful to treat the sum of false wins and false losses as a tie. That means that an absolute loss is just as certain as an absolute win. Win and losses, or true and false, are only the row, or the column. marginals of the outcome matrix, table, not the entire table. An outcome matrix with a certainty of 100%, can be certainly true, or certainly false. The outcome matrix would reflect the absolute if the value of ANY of the four cells in that outcome matrix are 100%, but it will always reflect certainty if the TOTAL of all of the cells is 100%.  Winning is only two of three outcomes.  A win will be the sum of  true wins and false wins.  Winning an election is no different.  It might be a win, and that win might be real and certain but not be true. The win would be real if all of the cells of the outcome matrix are greater than zero, but that win might not be true.

Forgiveness

 

Oops I Did It Again

You see my problem is this
I'm dreaming away
Wishing that heroes, they truly exist
I cry, watching the days
Can't you see I'm a fool in so many ways
But to lose all my senses
That is just so typically me
Oh baby, oh

Oops, I did it again
I played with your heart, got lost in the game
Oh baby, baby
Oops, you think I'm in love
That I'm sent from above
I'm not that innocent

To err is human. To forgive is divine.

If this wisdom is true then the opposite is also true: “To NOT err is INHUMAN, to NOT forgive is DEMONIC”.  Sound like anyone we know DJT?

The original saying is a example of exponential behavior.  An absolute will be true AND forgiving.  Humans can aspire to approach the absolute, but never attain the absolute. This means we will err in our attempt to attain the truth, but we should also aspire to forgive any mistakes ( “And forgive us our trespasses, as we forgive those who trespass against us", according to the Lord’s  Prayer.)  We are not that innocent.

Perceptions

 

My Hero, Zero!

How wonderful you are, why we could never reach a star
Without you, Zero, my hero, how wonderful you are
What's so wonderful about a zero? It's nothing, isn't it?
Sure, it represents nothing alone

But place a zero after one, and you've got yourself a ten
See how important that is?
When you run out of digits, you can start all over again
See how convenient that is?
That's why with only ten digits including zero
You can count as high as you could ever go
Forever, towards infinity
No one ever gets there, but you could try

Zero IS also my hero, but what kind of zero.

There are three kinds of zero: 1) absolute zero, 2) relative zero, and 3) repeating zero. Mathematically this can be expressed as

1.      0<x<∞, absolute zero;

2.      -∞<x<∞, relative zero; and

3.      (n-1)*π*∞<x<n*π*∞, repeating zero.

It is confusing because absolute zero is often expressed using a relative scale, but that does NOT make it a relative zero. Absolute zero occurs a temperature of 0º on the Kelvin scale. But temperature is more often reported using the Celsius or Fahrenheit scale, where e.g., 0º Celsius is the  boiling point of water. -4000º on the Celsius scale is undefined because absolute zero occurs at ‑453º Celsius. Nothing exists below absolute zero.

By contrast a relative zero is only a reference point and infinity exists before that reference point as well as after that reference point. For example time is a relative zero where the reference point can be the birth of Christ, the Common Era, the founding of Rome, the start of the Exodus, the Big Bang, etc.

A repeating zero is a recognition that zero may occur an infinite number of times for example as in wave functions. It will pass through zero an infinite number of times, periodically.

Not only are there three kinds of zero, but each also appears to correspond to a dimension. Space is an absolute zero. There is no such thing as negative space. There are three components of space: length, width, and height, but as Minkowski showed, it is useful to combine them into a single dimension of space. Time appears to be a relative zero with the reference event being now. There is an infinite amount time before that event, the past, and an infinite amount of time after that event, the future.

Space and time are often taken together as space-time. This defines reality and light is assumed to travel on a flat, Euclidean, surface which defines a light cone. However, it is only an assumption that spacetime is flat, Euclidean. The Earth's surface is spherical and is only perceived as flat because the radius of the surface of the Earth is so large. Similarly if the universe were hyperbolic, curved, then light would travel on that hyperbolic surface, and while there is an infinite amount of space-time in which light can travel, the range of that space-time can repeat cyclically according to a hyperbolic function. If light travels on that hyperbolic surface, it might be more useful to speak not of inverted light cones, but two sheets of a hyperboloid where the separation between the two sheets is zero.

An absolute might then be represented as an infinite series of overlapping triangular waves.  Each wave would have a sharp transition point at its apex.  However to an observer on a hyperbolic surface that wave, and its discontinuity, would be perceived as almost smooth and would repeat infinitely with each period of that wave, even if the observer could  perceive only the period in which the observer was located. The sharp discontinuity at each half period would be perceived of as a single discontinuity.  If the variance of the wave is perceived as 5/6 of the true variance, then the mean/median/mode/location of that wave might then be assumed to be 6/5 of the true mean/median/mode/mode location of that discontinuity in order to correct for this perception.  Setting only the location, i.e. a User Optimal, or only the variance, i.e. a System Optimal, is inferior to setting, and correcting the perceptions, of both the location and the variance, i.e. a Nash Equilibrium. 

Zero is still my hero, but that includes all three kinds of zero!

Merry Christmas

 

Charlie Brown

Charlie Brown, Charlie Brown
He's a clown, that Charlie Brown
He's gonna get caught, just you wait and see
(Why's everybody always pickin' on me?)

And that's what Christmas is all about, Charlie Brown.

https://youtu.be/eff0cqYefYY?si=66oMxhWo_UeYtH7f

Merry Christmas. Happy Hanukkah.  Blessed Diwali.  Happy Kwanzaa.  Happy Saturnalia.  Etc.  The meaning of all of these holidays is a belief in "Peace on earth, good will to ALL men", NOT just those men who are celebrating with you.

The Future III

 

Restless Farewell

But to remain as friends
You need the time to make amends
And stay behind
And since my feet are now fast
And point away from the past
I'll bid farewell and be down the line

MAGA? How about pointing AWAY from the past.

The lyric above is by 2016 Nobel Laurate Bob Dylan. The past is the choices that have already been made. The future is the choices that have yet to be made. The ratio of choices to be made in the future to the choices already made in the past is enormous, which means that the future is bigger than the past. But the fact that the past appears bigger than the future does not mean that you should choose the past, any more than the larger nickel is worth more than the smaller  dime. Despite what a toddler may think, a dime is worth more than a nickel.  If your feet are going to be fast, you can acknowledge the past, but remember that your feet point away from the past. And anyway you can’t revisit the past and change the choices that have been made. That is why Make America Great Again, MAGA, is so wrong headed. America has Always been GREAT  To embrace the future of America is to make it greater, not to only relive its past.

You can acknowledge the past and learn from it, but you can’t relive it. History does not repeat, but it sure does rhyme. Those who do not learn from the past are doomed to repeat it.

True or False?

 

The Hallelujah Chorus

King of Kings
For ever and ever
Hallelujah! Hallelujah!
And Lord of Lords
For ever and ever
Hallelujah! Hallelujah! 

For ever is an INFINITE amount of time. 

In a recent blog post https://dbeagan.blogspot.com/2024/12/intentions.html. I discussed payout tables, matrices. It is also possible to define these payout matrices using an equation of N replacing x.  In this case the payout matrix might be 

The certainty is 100% if the sum of C₁+C₂+C₃+C₄ is equal to 0. As N approaches infinity then ∞/(σ*N) also approaches 1 and the marginal of the true column of the matrix is greater the marginal of false column if  -1+C₁+C₃> C₂+C₄.  As N approaches 0 then ∞/(σ*N) also approaches 0 , and the marginal of the true column is greater than marginal of the false column if  1+C₁+C₃<C₂+C₄. 

For the payout matrix to be true, C₃ must be equal to 0.  For the payout matrix to be normal, C₂ must be equal to C₄.  A normal AND true matrix has a solution of C₁=2/3,  C₃ =0, and C₂=C₄=-1/3.  There is NO normal distribution of N that is false.  For an absolute, infinity, the payout matrices have to be  

absolutely true,  dominantly true, dominantly false,  and 

absolutely false.

Only the first two matrices are always true.  It is acceptable to have a payout matrix that is certain and true, but it should not be acceptable to have a payout matrix that is certain and false.  Similarly it is possible to have a payout matrix where N follows a normal distribution, and while it is possible to have a payout matrix that is false, the N members of that group would have to follow an ABnormal distribution. As stated previously, as N approaches INFINITY that ABnormal matrix would also have to be false.

,