Pro-Choice

 

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 God, then you must also believe in choice and in tolerance.

The exponential distribution is defined for the range of x>0.  It is convenient to translate from an origin of 0 to a new location, μ, and thus it becomes a range of x>μ at that new location.  It is also convenient to define x<µ as the mirror, negative of this exponential distribution.  Otherwise, when x is between 0 and µ, the probability density function and the cumulative distribution function will be undefined.

Thus a translated mirrored exponential equation also has a maximum value of 1 at the discontinuity of µ, and the combination has a Probability Density Function, PDF, and a Cummulative Density Function, CDF, of

x>μ,  PDF= λ e^{- (x-µ)} and CDF =  1-e^-λ(x-µ) 

and

x<μ, -PDF=- λ e^-λ(x-µ) and CDF = -1+e^-λ(x-µ).

While the mean of an exponential distribution is 1/λ and the median is 1/λ, the mean of the combined exponential and negative exponential distribution is 0, the median is 0 and the mode is equal to 0 but a value of 1 occurs at µ.  But this is NOT a normal distribution, becuase it is very skewed. 

The CDF of the combined exponential and negative exponential distribution appears similar to a hyperbolic tangent that has been translated to a new origin of (μ,0).  That hyperbolic tangent would have an amplitude, a, and a period, p, and thus be

a*(tanh(p*(x-µ))+C) with a constant, C, of 0, and a of 1.

which can also be expressed exponentially as

a*((e^-p*(x-µ)- e^p*(x-µ))/(e^-p*(x-µ)+ e^p*(x-µ))+C), with a constant, C,  of 0, and a of  1.

However if this is the CDF for the entire range of x, then its integral, PDF, would be 
p*sech²(p*(x‑µ)).  This is not very different than the logistics distribution, 1/(4*s)*sech²((x‑u)/(2*s)).
Its CDF is ½*tanh(((x-u)/(2*s))+ ½  which can also be expressed as an exponential as 
½*((e ^(x-µ)/2-e^-(x-µ)/2s)/(e^-(x-µ)/2s+ e^(x-µ)/2s)+ 1).  This normal CDF is a hyperbolic trigonometric function with an amplitude of ½, a period of 1/(2s) and a constant of 1. The hyperbolic tangent repeats every p/(2πi) which means that it only repeats in imagainary planes.  Because the variance, σ², for this distribution can be expressed as s²π²/3, this means that the period, p, can be expressed as √3/(2πσ).  This means that with the discontinuity, the variance must be 0, which means that the period is undefined, the amplitude must be 1, and the constant must be 0.  In other words, having no difference, the variance; no choice, the amplitude; and no God, the constant; is not normal.  Having choice, variance AND God is normal.

Independence

 

You’ll Be Back

You say the price of my love is a price you're not willing to pay
You cry in the tea which you hurled in the sea as you see me go by
Why so sad?
Remember we made an arrangement when you went away
Now you're making me mad.
Remember despite our estrangement, I'm your man

You'll be back
Soon you'll see
You'll remember you belong to me
You'll be back
Time will tell
You'll remember that I served you well
Oceans rise, empires fall
We have seen each other through it all
And when push comes to shove
I will send a fully armed battalion to remind you of my love

Was it only the taxes on Tea?

As we approach the July 4^th holiday, I am sure that most people will agree that  the phrase “No Taxation Without Representation” led to this day.  However what was not spoken and not acknowledged was the phrase “No Emancipation Without Representation” that was probably the impetus for the southern states joining in the rebellion again the King of England.  The northern states, particularly Massachusetts, as traders, were upset by the Intolerable Acts and the Tea Tax which gave the British East India Company an effective monopoly on the tea trade.  But the southern colonies did not have the type of trade that would prompt them to join with the northern trading colonies.  What prompted them to join in the rebellion? ( It is known as  the Revolution on this side of the Atlantic,  but the diffence between Rebellion and Revolution depends on the side that you support.)

The southern states were probably more upset by the 1772 case of Somerset v. Stewart. 

In that case, James Somerset, an enslaved African, was purchased by Charles Stewart, a customs officer when he was in Boston, Province of Massachusetts Bay, a British crown colony in North America.

Stewart brought Somerset with him when he returned to England in 1769, but in October 1771 Somerset escaped. After he was recaptured in November, Stewart had him imprisoned on the ship Ann and Mary (under Captain John Knowles), bound for the British colony of Jamaica. He directed that Somerset be sold to a plantation for labor. Somerset's three godparents from his baptism as a Christian in England, John Marlow, Thomas Walking and Elizabeth Cade, made an application on 3 December before the Court of King's Bench for a writ of habeas corpus. Captain Knowles on 9 December produced Somerset before the Court of King's Bench, which had to determine whether his imprisonment was lawful. https://en.wikipedia.org/wiki/Somerset_v_Stewart

Lord Mansfield, the Chief Justice of England, ruled

“The state of slavery is of such a nature that it is incapable of being introduced on any reasons, moral or political, but only by positive law, which preserves its force long after the reasons, occasions, and time itself from whence it was created, is erased from memory. It is so odious, that nothing can be suffered to support it, but positive law. Whatever inconveniences, therefore, may follow from the decision, I cannot say this case is allowed or approved by the law of England; and therefore the black must be discharged.”

The Town in Massachusetts in which I live was named for Lord Mansfield.  On this July 4^th let us remember that Independence was just as much about No Emancipation, as it was about No Taxes, without Representation. 

Branding

 

Branded (TV Theme Song)

Branded!
Marked with a coward's shame.
What do you do when you're branded,
Will you fight for your name?

So is branding a bad thing?

Branding is supposed to indicate the ability to trust.  A trademark is intended to ensure that you can trust the goods.  A trademark is meant to ensure that you can trust the seller, the provider of the products or service.  In the context of the theme song, branding is intended to indicate that you can NOT trust the individual. In this context a brand is similar to the Scarlet Letter A for Adultery or the Mark of Cain. Thus branding can be good or bad, depending on the purpose of the brand.  The brand itself is supposed to indicate truth, but the branding can itself be a lie.

Macy’s must be especially proud of its TV commercial from 2007, https://www.youtube.com/watch?v=fHNCqPxe2WA which features the branding of convicted felon Martha Stewart, indicted Donald Trump, and, while Calvin Klein is played by Lost’s Josh Holloway, Brooke Shield has claimed to being sexually exploited while doing Calvin Klein ads.  These are instances were maybe the branding was not being truthful.  Branding is a good thing when it is truthful, but it can be a bad thing when the branding is used instead to tell a lie.  Just because someone tells you that you can trust them, it does not mean that you can always trust them.  Branding is telling you the nature of that product and person.  It is up to you to determine whether the branding is telling you the truth.

Choice IV

 

Both Sides Now

I've looked at life from both sides now
From win and lose and still somehow
It's life's illusions I recall
I really don't know life at all

Choice is seeing both sides now.

A real number can be expressed as the sum of a series of n real numbers x₁, x₂, …x_k or ∑f_ix_i , summed from =1 to k where the index i is the i^th grouped observation, f_i is the frequency of that observation. E.g. if there are 3 observations of 2, this makes 3 the frequency of the group of observations that is 2; k is the number of groups; and, n is the number of observations, n =∑f_i , summed from =1 to k where the index i is the i^th grouped observation.

If k is a set of sequential integers, then k is also the choices. For a 6-sided die where each side is numbered from 1 to 6, the choices are thus 1 through 6. This is also true for any n‑sided die. A coin can be thought of as a two-sided die. Instead of numbering the sides as 1 and 2, often in a coin flip to simulate a one-sided die, it is customary to designate one side of the coin as a win, 1, and the other side of the coin as a loss, 0. However however this is a relative scaling not an absolute scaling. Topologically, a one-sided die is possible, i.e. a mobius strip. Its average outcome is 50% of 1, 0.5, although the outcomes can only be 100% of 1 or 100% of 0. The median is also 0.5. But the mode, the most common value, is split equally between 1 and 0.  Therefore a single event is not “normal”. The mode can only ever be the same case as the outcomes, but the median and median do not have to be the same case as the outcomes. However if a one-sided die is flipped an infinite number of times, that event is repeated an infinite number of times. Infinity is part of every case and at infinity, even if the choice, group, is only 1, the mean is therefore equal to the median is equal to the mode.

An analogy can be made between the logistics distribution, the hyperbolic secant squared distribution,  i.e. a normal distribution,

(1/4s)*sech²((x-μ)/2s) =PDF(x:μ,s)

and momentum. The integral of the logistics distribution is

½ * tanh((x-μ)/2s)+½=CDF(x:μ,s)

which is, by analogy, energy.

The derivative, rate of change, of the logistics distribution, is then

-(1/4s)*(½)*(1/2s)*(sech²((x-μ)/2s))²

^or

- PDF²(x:μ,s)

which is, by analogy, force. It is also the negative of the square of the randomness, PDF.

Then Newton’s Three Laws can be re-written as

Law 1. A random normal event will stay random unless acted upon by a force.

Law 2. When a random normal event is acted upon by a force, the time rate of change of its randomness equals the force.

Law 3. If two random normal events exert forces on each other, these forces have the same magnitude but opposite directions.

This has some implications. The variance of a logistics equation is s²π²/3, which means that if s>0 then variance is also greater than zero. If there is a single choice, then s=0.5, and if the mean, μ, is set equal to zero, then the  Probability Density Function, PDF(x:0,0.5),  is

1⁄2 *sech² (x) 

The energy, which is also the Cumulative Distribution Function, CDF(x:0,0.5),  of this distribution is

1⁄2 * tanh(x)+1⁄2

And the force that changes randomness is

-1/4 * sech⁴ (x)

A random event produces energy.  If the total energy must be zero, then it must be balanced by a force that causes a loss of energy ( e.g. entropy).

If there is no choice, s=0, then the PDF is not normal, it is undefined; its energy is undefined; and its entropy is also undefined. It is common to talk of a standard normal distribution as having a variance of 1. If that is true then s= √3/π=0.551329, which means that there must be 2 times that in choice. But choice must also be an integer. If there is one choice, then s must be =0.5 and the variance must be  0.822467, not zero or 1.

Supreme Court IV

 It's A Lovely Day Today

And beside I'm certain if you knew me
You'd find I'm very good company
Won't you kindly let me stay? 

Shouldn't justice also be about certainty?

Opinions of the Supreme Court are not constitutionally required to be decided by a majority. The Supreme Court is asked to render an opinion and each justice may issue concurring or dissenting opinions. But we are so used to hearing about the actual vote of the court that we have become have been become used to thinking that dominance, a simple majority is required. In fact it was not until the 1940s under Chief Justice Harlan Stone, that an actual tally of the vote of the justices on each opinion of SCOTUS was released to the public. An opinion of the SCOTUS with no dissenting opinions could have been a unanimous vote of the justices or could have been a simple majority where none of the dissenting justices felt compelled to issue a dissenting opinion. Dissenting opinions are important. Dissenting opinions may contain arguments that form the basis of majority opinions in future cases. Justice John Harlan became so famous for his dissenting opinions that he became known as “The Great Dissenter.”  Even the infamous Dred Scott decision had a majority opinion and 2 dissenting opinions, which meant that the decision could have been anywhere from 5-4 to 7-2.

That the opinion of the Supreme Court should be decided unanimously has been proposed by others[1]. But a unanimous requirement places tremendous power in a lone dissenter. A unanimous decision may reflect the lowest position of the majority that was acceptable to that lone member. This may actually reflect less certainty than the current simple majority decisions, but a court case that has reached the Supreme Court is one where there have been questions about its certainty during the appeals process.

The judicial system is supposed to reflect certainty, not dominance. A case that has been decided by a single judge might be certain, but it also may only reflect the dominance of that judge. A 5‑4 opinion is dominant, but it is also obviously not certain. Is it possible to achieve certainty during the process? I believe that the answer is a resounding yes. It is possible to say a decision reflects certainty rather than dominance, and that belief is based on the Constitution and is consistent with statistics.

The most important decisions of the nation Constitutionally (e.g. overriding a veto, declaring war, approving amendments to the constitution, etc.) require a two-thirds vote of the Congress. An amendment to the Constitution requires ratification by three-fourths of the states after approval by Congress and the President. Statistics would agree that in a normal distribution 68 percent of all of the opinion of group will occur by the mean plus one standard deviation, while a simple majority only requires one member more than the mean. It is not possible to achieve a unanimous decision in a normal distribution. Even in particle physics, the most that certainty is generally expected is the mean plus 5 standard deviations, i.e. not 100% but 99.99994%. It is the responsibility of the Chief Justice to decide whether an opinion shall be issued, is certain.

To ensure that Supreme Court opinions reflect certainty for the Nation, rather than merely dominance within the Nation, it is proposed that an opinion of the SCOTUS NOT be issued if there is merely a simple majority of Justices supporting that opinion, but rather that a two-thirds super-majority of the Justices supporting that opinion be required. Given the current nine members of the Supreme Court that means that an opinion would be determined to be certain, and not merely dominant if there is a 6-3 vote. (a 6-3 vote is two-thirds, 66.7%  of the members. Ideally, according to statistics a 7-2 vote would be better in that it reflects more than 68% of the members.)

To make it clear that dominant opinions are never acceptable, it is recommended that one justice be added to the Supreme Court such that a split vote is a possible outcome where there would be NO dominance. In this case a 7-3 vote would satisfy the strict certainty of a normal distribution.

 

---

[1] Orentlicher, David. (2022). Judicial Consensus: Why the Supreme Court Should Decide Its Cases Unanimously. Conn. L. Rev., 54, 303. Accessed on June 19, 2023, at      
https://scholars.law.unlv.edu/facpub/1362/

 

Dominate?

 

The Perfect Nanny

If you won't scold and dominate us
We will never give you cause to hate us
We won't hide your spectacles
So you can't see
Put toads in your bed
Or pepper in your tea
Hurry, Nanny!
Many thanks
Sincerely,
Jane and Michael Banks

What is with this whole dominate business anyway?

Genesis 1:26: “And God said, Let us make man in our image, after our likeness and let them have dominion over fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepth upon the earth.”

If the Bible is the inspired word of God, then the Bible was not written in English. It was translated into English. Unless God also inspired the translators, it is possible that only the original Aramaic, ancient Hebrew, was the inspired word of God. Things do get Lost in Translation. I am reminded of my Serbian landlord in New York City who once told me he was going to the store to get a bag of “Chips of Potatoes,” instead of “Potato Chips.”  Did God really say that he gave dominion to man?

The Hebrew word was probably yiredu which was translated from the root word radah which means dominion, (to subdue, to rule over), rather than the root word yarad (to lower oneself). Christians believe that God is a good sovereign, the ruler of ALL of the universe. God apparently believes in System Optimal decisions ( That whole lay down your life jazz!) and not User Optimal decisions ( What’s in it for me?). Since there is the possibly that a man as the sovereign will choose User Optimal decisions, a wise System Optimalist would retain dominion, sovereignty, and merely pass stewardship ( lowering oneself) to man. Which puts a whole different wrinkle on contests. Are contests to achieve dominance, or to achieve truth, where God is Truth. This means that outcomes that only achieve dominance by choosing the opposite of Truth are not desirable outcomes. The Bible probably should have been translated as.

Genesis 1:26: “And God said, Let us make man in our image, after our likeness and let them have stewardship over fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth, and over every creeping thing that creepth upon the earth.”

Corporations

 

People

People
People who need people
Are the luckiest people in the world

Are Corporations People?

The SCOTUS is again facing the issue of whether Corporations are People. They faced it before in the infamous Citizens United v. FEC opinion. They are facing the question again in Moore v. the United States Of America. The Moores are arguing that they owe no taxes on foreign income because they did not realize this income. They have lost in every court decision so far, but the fear is that if decided in their favor that any corporate taxes on foreign income will also be rescinded.

Even if the Moores do unexpectedly win, Corporations are not People,  They are not enumerated as such in the US Census required by the Constitution. Yes, corporations are groups of people BUT they are special entities of the state created to ensure that the assets of the corporate officers or shareholders of the corporation are not confused with the personal assets of the corporate officers or shareholders.  That is what limited liability is all about. So the government AND the members of the corporation, have already decided that they are not merely groups of people. Any decisions affecting People should have no bearing on Corporate taxes because Corporations are NOT People.

In which case, Citizens United was wrongly decided by SCOTUS. If free speech is a constitutionally protected asset of the People, and the assets of the shareholders are NOT the assets of the corporation, then the asset of free speech was not transferred to the corporation. You can not have it two ways. Corporations can not be groups of people, when it comes to free speech, but not groups of people when it comes to liability. If corporations are protected from liability, then regulations that restrict the free speech of corporations are not in violation of the Constitution. Besides since there are no corporations on Death Row in prisons, even Texas seems to agree that they are not People, since they are not trying to execute them.