Certainty IV

 

Pistol Packing' Mama

We're a rough rooting tooting shooting trio
But you ought to see my sister Cleo
She's a terror make no error
But there am not no nicer terror
Here's what we tell her

Certainty is NOT its error, despite what I may have implied in an earlier post.

Absolute certainty is the ABSENCE of error. Therefore the formula for certainty should be the additive inverse of error, 100%- Standard Error%. If the formula for Standard Error is  σ/√N, then as N goes to infinity, the error goes to zero according to L’Hôpital’s rule, This is  regardless of the Standard Deviation, σ , or what engineers would call tolerance. If the tolerance is zero then the Standard Error is of course zero. But it also would be zero at infinity, the absolute, in any event. And the certainty would then be 100%.

If the certainty is NOT 100%, then that also can be used to compute the tolerance, the square root of the variance. If the certainty is perceived as 90.9% and N is two dimensions, space and time, then the tolerance is 100%-90.9%*√2=σ. Individuals acting as a group can be expected to follow a normal logistics, hyperbolic secant squared, distribution. In that case  the variance, σ², is equal to s²π²/3. If  the certainty is 90.9%, the variance is (100%-90.9%*√2)², thus 
s²=(100%-90.9%*√2)²*3/π² .  And in hyperbolic space this is
s=ln(0±sinh((1-.909*√2)*√3)/π)- cosh((1-.909*√2)*√3)/π)). This is approximately equal to 47.3%, On a hyperbolic surface the absolute value of the range variable, s, should be 50%, ½.

A series of 7 games would have a perceived certainty of 52.8%,(5/6)^7/2. A jury of 12 members would have a perceived variance of  36.9%, (5/6)^12/2. If there are 3 outcomes to a contest, then the theoretical outcome of the absolute should be 1/3, or 33.3% .  If there are two dimensions, then the chances of being one of those two dimensions is 50%, ½.  On the negative portion of hyperbolic space, you are able to perceive 5/6 of the absolute, and 1/6 on the positive portions. While on a flat surface, you could perceive 50% of an absolute on both the positive and negative portions. The fact that these are the traditional members on a jury and the traditional number of games in a series is not an accident. Those best approximate the rounded values of what can be perceived on a hyperbolic surface.

The fact that we can perceive only 5/6 of the absolute, means that we can never achieve the 100% certainty of the absolute, but society has tried to achieve as much of that 100% certainty as possible and thus settled on those numbers. If the surface being perceived was flat, then the size of juries should be  (1/2*2)/ln(1/3)= -1.09 and the number of games in a series would be only (1/3*2)/ln(1/3) =-0.369, of a single game, and these would be the negative of the expected number. If the surface was spherical, the percentage that could be perceived depends on the Radius of the sphere compared to the distance between the observer and the object being perceived.  On a flat surface, juries would consist of  a single member and there would be no need for any games to determine a winner.  That society has settled on different rounded values for the size of juries and the number of games in a series shows that they are being perceived as rounded values on the negative portion of a hyperbolic surface and this means they have a perceived variance of 5/6. This also means that the certainty can only approach, is not as good as, the absolute. That there is error is based on what can be perceived. If there is perception, there is no certainty.  If there is certainty, then there is no perception.  Only the absolute can perceive 100%, and the observer is NOT the absolute.

Fair

 

All in Love is Fair

But all is fair in love
I had to go away
A writer takes his pen
To write the words again
That all in love is fair

What is fair?

According to game theory, a fair game requires at least three players. one of which could be the referees enforcing the rules of the game. This creates a problem when there are only two players or one of the two players in a “fair” game cheats to achieve a false win. To avoid this a fair game should also be normal (false wins equal to false losses) and N, the number of potential players, should approach infinity. Even with these caveats, a fair normal game in two dimensions can only be certainly correct 91.29% of the time.

Any attempt to limit the number of players ( e.g. by voter suppression, discrimination, etc.) or by making any component of the game a zero-sum goes against the assumption that N is approaching infinity. (Currently the number of congressional seats and thus their electoral votes are fixed, a zero sum.)

Any attempt to award a win with only a plurality of votes and not a majority of votes also violates these criteria and this is why Rank Choice Voting is provided so that each voter has at least three choices. Only Alaska awards votes using Ranked Choice Voting.

In the US, electoral votes are supposed to be awarded on the basis of State (Senate) AND congressional districts. Only Maine and Nebraska currently award electoral votes in this manner, all other states award electoral votes by whole State only.

Making these changes (Eliminating voter suppression; eliminating zero-sum components; Ranked Choice Voting: and awarding electoral votes not by entire states)  does not change the fact that the elections can never be 100% certain in the two dimensional reality of space-time, but will ensure that each election is closer to being 91.29%, √(5/6)%, certain. Maybe they can’t be 100% certain, but they can be fair.

Perceptions V

 

Big Boss Man

Well, I'm gonna get me a boss man, one gonna treat me right
Work hard in the day time, rest easy at night
Big boss man, can't you hear me when I call?
Well, you ain't so big, you're just tall, that's all

You ain’t better, you’re just bigger, that’s all.

“All that glitters is not gold” and “All that is gold does not glitter”. And just because something is bigger does not mean that it is better. Toddlers are often asked to choose between a nickel and a dime. If a toddler does not understand the value of each coin, that toddler might pick the nickel because it is bigger.

Similarly in viewing laminar/uncongested/orderly flow versus turbulent/chaotic/congested flow, the chaotic flow may appear to be bigger but that does NOT mean that it is better. It may appear that the chaotic range is 5 times the size of the orderly range, but that does NOT mean that order is 1/6 the value of chaos. In fact there are three outcomes, win, loss and TIE and that does not change. If you are perceiving more of the observable outcomes, then you should be perceiving less of the unobservable outcomes ( if you could indeed perceive them). The two dimensional odds of a win or a loss are only 50% because in a two dimensional space 50% of the surface can be perceived. But that 50% is 2/3 of the outcomes. If orderly range is 5 times the size of chaotic range, that may only be because while the dimensions are two and the surface is hyperbolic, not flat. What is being perceived as 5/6 would continue to be 2./3 on a flat surface. So the fact that the orderly observable is 5 times the size of the flat domain may only indicate that it is being perceived as 5 times the size, not that it IS 5 times the size.

In fact the unobservable ties, if they could be observed, would be perceived as 20% when they should be 33 1/3%. Thus while the observable percentage is larger, the unobservable percentage is smaller. If the mirrored but observable ties are larger, regardless of the perception that the total with unobservable wins and losses should also be larger. The median percentage of observable is .5, but it would be perceived as .6. If this is half of a half a period, then the full half period would be perceived as 120% of the actual half period. It is not bigger; it is merely PERCEIVED as being bigger. If the surface is curved, then the objects in the mirror may appear larger (or smaller) than they actually are. While passenger side view mirrors on automobile often come with this warning, it would be wise to remember this for any curved surface. Don’t ever confuse perceptions with an absolute. Don’t ever confuse bigger with better. Choose the gold not the glitter.

Ties III

 

Step To The Rear

Will everyone here kindly step to the rear
And let a winner lead the way
Here's where we separate
The notes from the noise
The men from the boys
The rose from the poison ivy.

But what about Ties!

The outcome of every game is NOT win or lose. It is win, lose, OR TIE. Because humans do not like ties, the rules of most games may employ elaborate methods to break ties: overtime, extra innings, shoot outs, sudden death, winning by an advantage, etc.  To entice players into fair games that could end in a tie even when one player has a clear advantage over the other player, handicaps, ratings, point spreads, etc. are maintained by an impartial overseer. 

All of this is to say that ties are statistically probable and are important. But what if we could not see those ties? What if in reality wins and losses were observable but ties were not observable? What if what is perceived as ties are only the observable portion of a mirror of the original game. But a mirror game does not have to begin at the same point. Its mirror ties only have to be equal to the observable games wins and losses. That then means that the unobservable wins and losses of that mirror game also have to be equal to the ties of the observable game. If wins and losses are equally probable as ties, then this is an inevitable outcome. If wins, loses, and ties are all equally likely then each should occur 33 and 1/3% of the time. That means the unobserved ties should be equal to the total of observable wins and losses. And if the observable wins and losses are equal to the observable but mirror ties, then the mirror game has to be twice the size of the original game. And the dividing line between observable wins and losses and observable but mirror ties should occur at 2/3, 66 2/3 % of the total outcomes. This also means that the intersection point of the original game and its mirror must occur exactly at 50% of all games. If it occurs at a different point, for the observer to perceive observable wins and losses to be equal to the observable mirror ties then it may be necessary for a different surface than the normal Euclidean surface to be used.

There are three surface types as indicated by their curvature: Spherical, Flat (Euclidean); and Hyperbolic. The limit of an outcome on a spherical surface is the same as the outcome on a flat surface if the size of the Radius of the Sphere is large enough. This is because of the identity 1=cos²+sin². However the limit on a hyperbolic surface will NOT be the same as that of a flat surface because of the identity 1=cosh²-sinh². Thus if the starting points of the mirrored game and the original game are not identical, their intersection will not occur at the median of each,  and if the area above the intersection appears smaller, then it is most probably a hyperbolic surface. 

If the surface is flat then the observable perception of a 3-D object on that surface is 50%. And thus 50% is unobservable. You can infer the characteristics of the unboreable portion of the object, but you can NOT observe them. On a hyperbolic surface, the perception would be different. Thus while on a spherical or flat surface the perception might be that the original game is twice the size of the original game. If the intersection is NOT at 50%, the mirror of the original game would be perceived as 5/6 of the original game, (or its additive, and symmetric, inverse 1/6), not 2/3, (or 1/3). The fact that there are observable ties that are a mirror of unobservable wins and losses must lead to the conclusion that the intersection is occurring on a hyperbolic surface and the intersection is perceived to be at 5/6, not 2/3. This is only because it is also being perceived from hyperbolic surface. This has an implication on behavior that will be explored in the next blog post.

 

 

 

 

Perceptions IV

 

You’ve Got to Hide Your Love ( Beach Boys version)

Hey! Somebody hid my teeth away
(Just call that number...)
Hey! Somebody hid my teeth away
(Everly Brothers.)
(Hey!)
(What's the best Everly Brothers song? Besides, ah...)
(Go.)
("Bird Dog.")
(Who's gonna fool with it?)
(You're gonna fool with it. You and me.)
(You shouldn't fool with an Everly Brothers song--you should do it right.)

You shouldn’t fool with ANYthing, just do it right!

Trying to make inferences from existing trends is good. But remember they are only inferences. Don’t expect those inferences to be perfect, and be prepared to change them and NOT fall in love with your inferences.  Not only your inferences, but the inferences that others make should also be questioned. What seems to be consistent with your inferences might only be a foolish consistency and remember what Emerson said about foolish consistencies.

For example the trend inferred of perceiving the absolute. The absolute  will be perceived from a frame of reference. Our frame of reference is not absolute so we can’t expect our perception of the absolute to be absolutely correct. Just because someone else’s perception seems to be close to ours, that does not confirm ours.

Our perception of the absolute can be a System Perspective, that the perceived slope of the absolute is all that is important. It can also be a User Perspective, that the starting point of the absolute is all that is important. It can be that  the perceived starting point AND the perceived slope are both important. Thus is called a Nash Equilibrium after mathematician John Nash.

The perception of the only the slope which is the System Optimal, SO, parameter trended to the perceived starting point is close to the User Optimal, UO,  parameters. The parameters of the Nash Equilibrium, NE, are not close to either those of the SO or UO. But the parameters of the Nash Equilibrium match better to the perception of the absolute than either that of the System or User Optimals.

The blue dots and lines are User Optimals, UO. The red dots and lines are the System Optimals, SO. The brown dots and lines are Nash Equilibriums, NE. Despite the fact that the UO and SO parameters are close together at the left side of this graph, the parameters of the Nash Equilibrium are closer to  both the perceptions of the absolute at both the Left, and Right sides of the graph, despite being farther away from the trend of either UO or SO parameters. It is more important to be consistent with the perception of the absolute than it is to be consistent with the perception of others. Don’t be fooled.

 

It's a secret

 

Give a Little Whistle

Take the strait and narrow path
And if you start to slide
Give a little whistle
Give a little whistle
And always let your conscience be your guide.

And doesn’t voting your conscience mean a secret ballot?

To eliminate bullying, and/or voter intimidation, votes by ballot are secret. There is a reason for this secrecy. Then voters can NOT be subject to retaliation on how they voted in their ballot.

The same is true for voting by senators and representatives of the people. But each of their votes is public and potentially subject to retaliation. Shouldn’t their votes of conscience also be secret? This includes votes to impeach a sitting candidate or approve a nominated candidate. Votes to  override an executive veto are already by  2/3 of both houses of Congress. Shouldn’t those votes also be secret? Votes to override a judicial action may involve a constitutional amendment which already requires more than a simple majority of states and Congress. Shouldn’t these votes also be secret. Declaring war, entering into treaties,  as well as any action that already requires a 2/3 vote should arguably be by secret vote. This also includes the ending of debate and the advancing of proposed bills to a policy vote. 

Matters of simple policy are by simple majority and there is no reason that they can not be public votes. But votes of conscience should be different. This does not require a complicated process. Elections by all of the voters are already by secret ballot. Secret votes by their representatives can be by black and white balls (hence the term blackballed). Making votes secret is merely a way to ensure that bullying and retaliation don’t interfere with your conscience being your guide.

Perceptions III

 

If You Could See Her

Yet when we're walking together
They sneer if I'm holding her hand
But if they could see her through my eyes
Maybe they'd all understand

I understand your objection
I grant you the problem's not small
But if you could see her through my eyes
She wouldn't look Jewish at all!

Misperception is deadly.

As individuals we can only perceive the absolute from a surface. If that surface is hyperbolic, while the absolute is zero at absolute zero, to an individual on that hyperbolic surface, the absolute would be perceived as a normal logistic, sech squared, distribution. That means that while there is an absolute zero, it is perceived as having a value of 2%. That 2% is because of the Standard Deviation, what an  engineer would call tolerance, of the absolute. Therefore what is absolute zero to the absolute is 2% to an individual observing that absolute from a hyperbolic surface.

If life begins at birth, is absolute zero, from the perspective of the absolute it has no value, but it is perceived by an individual on a hyperbolic surface as having a value of 2%. This leads to the individual to perceive that life before birth, before an absolute zero, must also have a value. It is possible therefore that the belief in fetal personhood is only because of this misperception.