Dr. Suess vs Mother Goose

 

Teach Your Children

Teach your children well
Their father's hell did slowly go by
Feed them on your dreams
The one they pick's the one you'll know by

All you really need to know you learned in Kindergarten.

As children we learned from Doctor Suess, not Mother Goose and maybe that is the issue.  To be fair the Little Red Hen was written by Mary Mapes Dodge, not Mother Goose.  But the lesson of the Little Red Hen, like much of Mother Goose, is that if you don’t work you will get no benefit.  However the Little Red Hen did not ask why no one else in her group would help her.  She ignored that her growing of the wheat depended on the weather being good, there being enough rain, there being no pests, etc. IOW, luck.  And when she ate the bread, it was not clear than she could actually eat all of the Bread instead of sharing it.

Doctor Suess instead taught us that 

“A person’s a person no matter how small."

“Maybe Christmas, the Grinch thought, doesn’t come from a store.” 

“Why fit in when you are born to stand out”. 

“Unless some like you cares a whole awful lot.  Nothing is going to get better. It’s not”.  

Thank you, children, for listening, and not giving up on the dream.

Business

 

Taking Care of Business

And I'll be taking care of business (every day)
Taking care of business (every way)
I've been taking care of business (it's all mine)
Taking care of business and working overtime, work out

Is the Business of America, Business?

The business of a business is to make money, to seek the user equilibrium of their business. The business of America is America, not business, to ensure that a system equilibrium is reached and to ensure that each individual, including businesses, have the resources available to be able to do business. This may mean spending money on the group rather than making money on every transaction.

In order to do business, those businesses have to access to goods. Goods are classified in two dimensions by economists: rival (priced) and exclusive (only one person can use that good), not just one dimension as private and public property. There are private goods, and those are priced and exclusive, using a good prevents another from simultaneously using that good. Government, the group, has a role in ensuring that private priced and exclusive goods are not taken without compensation. That is why there are crimes against stealing and a police force to deter that theft. There are Public Goods and those are unpriced and nonexclusive. Government has a role in ensuring that everyone has access to those goods. Individuals can not demand access fees from others to public goods.

It gets more complicated for Common Resources, which are unpriced but exclusive. These are not necessarily free or unlimited. Businesses may not be able to function unless these resources continue to exist. An educated workforce is one example. Each business may depend on, take advantage of, but not pay for, the education of the workers that it employs. But that education has a cost which is covered by the government with no expectation that it will make a profit, or even cover those expenses.

It also gets more complicated for Club Goods, also called Public Monopolies, which are priced but nonexclusive. While they are priced, using that good does not prevent others from also using that good.  Unless they are protected in some fashion, those goods may not be produced. Government may license those goods, for example a cable TV system, or may issue copyright or patent protections to ensure that these goods are not copied without compensation. The government may not receive a profit or even cover the expenses for the license, copyrights, or patents.

Why is this an issue? The Constitution says that a Postal Service will be provided to ensure the free exchange of ideas among all of its citizens. It may not be profitable to make this service available to citizens living in rural areas. But we currently have a businessman in charge of the United States Postal SERVICE (emphasis puposefully added), who is discounting or curtailing rural service that does not make a profit. Duh,…. it is called service because it is NOT always expected to make a profit or even cover its costs. But that does not mean that it is not essential. No one is saying that a service should be provided at any cost, but a small loss does not mean that the service ( there is that work again) is not essential. And that is the difference between America and a business, America seeks a system equilibrium, an a buisness seeks an individual user equilibrium. Taking care of business means respecting and cherishing that difference.  In other words, viva la difference.

Packing SCOTUS?

 

Midnight Rider

And I've gone by the point of caring,
Some old bed I'll soon be sharing,
And I've got one more silver dollar,
But I'm not gonna let 'me catch me, no
Not gonna let 'me catch the Midnight Rider.

Should the Supreme Court ride again?

The United States currently has 12 Circuit Courts of Appeal.  So why are they called Circuits?  At the time of the country’s founding, travelling was difficult, and it made more sense for judges to travel to the trial, rather than having the trial come to the judge.  The judges instead would thus "ride" a circuit from trial to trial.

As travel became easier, the practice of riding a circuit was discontinued, but the word remained.  Why does this matter for the Supreme Court?  At the time of the Supreme Court’s founding, each Supreme Court Justice was responsible for a circuit.  There are 12 Circuits of Appeals Courts in the United States, so there must be 12 Justices on the Supreme Court?  Oh, there are currently only 9 Justices?  Then adding three Justices would be returning to normal, not court packing.  The idea that there should be Circuits, is because while there could be an opinion within a Circuit, which is typically several states, it is the opinion of the entire United States that should be the opinion of the Supreme Court.

The Justices of the Supreme Court are individuals, not an absolute.  So how can we ensure that they have the certainty of an absolute?  The answer is in the very jury system overseen by the judiciary.  There are twelve members of a jury in a criminal case.  Those cases are decided by unanimous decisions, i.e. 12-0 of the jury, not by dominate decisions, i.e. 7-5. 

There is a reason for that.  There are 4,096 possible votes of a jury, only two of which are unanimous decisions: Unanimously Guilty; or Unanimously Not Guilty. The certainty of a Unanimous Guilty decision by a jury is thus not 100% but it is 99.98%.  But as could be imagined a lone hold-out juror might extract concessions from the rest of the jury and the decision could then be biased, not certain.  That is why a unanimous decision is not required in a civil case.  The decision is less certain, but also with less of a possibility of a hung jury, or a decision which reflects the lowest common denominator of the entire jury.

A twelve-member court has a mean of 6.5 and a variance of all of their votes of 4.  A 6-6 decision reflects no more than chance, 0% dominance but 77% certainty.  A 7-5 decision  reflects 100% dominance but only a certainty of 80.6%.  A decision that is 9-3, still reflects 100% dominance but its certainty has increased to 94.6%.

For reasons cited in a previous blog post,  https://dbeagan.blogspot.com/2023/05/judicicary.html, which discussed only increasing the size of the Supreme Court’s bench to 10 members, a sixteen-year term, staggered among the Justices, is recommended, but the first terms of the three new Justices could be adjusted such that they have terms that expire, assuming their appointment in 2025, respectively, in 2045, 2047, and 2049.  The sitting Justices’ terms would then begin to expire in 2027 with one term expiring in that year and every subsequent 2 years based on the seniority of the sitting Justices. Thus the last sitting Justice’s term would expire in 2043, assuming that the terms of the three new Justices begin in 2025. Upon the death, or resignation, before the end of that term the President would be expected to nominate and the Senate to confirm the nomination of a Justice to complete the unexpired term.  A president, serving one four-year term could thus nominate only 2 Justices  serving full terms. A president serving two one-year terms, could thus only nominate 4 Justices serving full terms.  Even in the event of a vice president being promted into more than 3 years of the term of his President, and then subsequently beginning elected to two of his own four-year terms would only get to nominate 6 of the 12 Justices serving full terms. That nomination could be of the Justice whose term is expiring.  Yes, that would mean that individual could conceivably  serve 32 years, but life expectancy and interest is expected to cut that short, such that a two term limit for justices seems superfulous.

The number of Supreme Court Justices would then be consistent with the number of Circuit Courts of the United States, even if those Justices would not be required to "ride" those Circuits.  The decisions of the Supreme Court would be required to be 9-3 which represents both the certainty of one standard deviation, the square root of variance, from the mean, AND dominance.

Distribution of Income II

 

It’s A Wonderful World

I hear babies cry
I watch them grow
They'll learn much more
Than I'll ever know
And I think to myself
What a wonderful world
Yes, I think to myself
What a wonderful world

If we knew how to treat growth, it could be a Wonderful World

In the movie It’s a Wonderful Life, George Bailey, played by Jimmy Stewart, gets to see the nightmare of Pottersville which replaces his beloved Bedford Falls.  Pottersville is a horrible place where people only look out for themselves, instead of looking out for each other.  The world seems to be living that movie, but I am afraid that we are living in Pottersville.

When dealing with growth you can either increase the variance within, or increase the median of, the group.  In today’s United States, we seem to have chosen the path of living in Pottersville by only increasing the variance, not increasing the median.  The relationship to an absolute is defined by an exponential distribution.  The relationship to others in a group is NOT defined by an exponential distribution.  It is defined by a normal logistics distribution, whose cumulative distribution function is a form of a hyperbolic tangent.  The mistake is by treating each other like absolutes, instead of like individuals, it squanders that growth, which effects even those who seem to have benefited from that growth.

The United States economy, stated in 2021 inflation adjusted dollars, has grown from an annual income of $3.5 trillion in 1968 to $15 trillion in 2021.  However by insisting that the median of the group (which again should considered to be individuals, not an absolute) be zero, ( $0 at 0%, which is in fact 50% of the group) the distribution of total income, and the amount of total income that could spur future growth, is concentrated in only a few.  However if just a fraction of that growth had been used to increase the median of the group, which amounts to a median public expenditure of $142,000 per household, which is called Universal Basic Income, UBI, in the figure below, the distribution of income to the top 5% would be the same, but the distribution of income to the group would increase dramatically.  If ALL of the growth in taxes had been used to increase the median of the group, which would be the ideal, then every income group would benefit.  This would amount to a public expenditure of $367,000 per household, but that is only 2.15% of the total growth in taxes, if taxes were at a median of 20% of the total growth.

Growth of the group should be used to benefit the group, not just a few in the group.  If the response is only to increase the variance of the group, then the group suffers, which means that even upper income households of the group suffer.  Let’s instead live in a Wonderful World.

Income

 

Happiness Is

Happiness is having a sister.
Sharing a sandwich.
Getting along.
Happiness is singing together when day is through,
And happiness is those who sing with you.
Happiness is morning and evening,
Daytime and nighttime too.
For happiness is anyone and anything at all
That’s loved by you.

According to Mr. Micawber, happiness is income greater than expenditures.

Is income an absolute? If income can be negative then income is relative, NOT an absolute. 

Can there be negative income?  If you ask an accountant, then everything is either a credit or a debit.  The sum of credits over a period of time is your income.  The sum of debits over a period of time are your expenses.  The sum of your credits at any point in time are your assets.  The sum of your debits at any point in time are your liabilities.  The difference between your assets and your liabilities is your net worth.  If your net worth is positive, then you are said to be wealthy. If your net worth is negative then you are said to be in debt and possibly bankrupt.

On these definitions alone, because credits and debits are aways positive, it would seem reasonable that income should always be positive.  However there are loans which are treated like income but are actually debits.  And you can pay for debits with previous assets, such that your change in net worth in a period is negative.  So while income may always be positive, mathematically it is convenient to treat it as if it can also be negative.

So why does this matter?  If you act like income must always be positive you might treat it as an absolute.  In this case, the distribution of income should follow an exponential distribution which has an absolute value at zero.  If instead, income can be negative, then the distribution of income should follow a hyperbolic tangent.  The Cumulative Distribution Function for an exponential distribution is 1-e^-λ*x, but this should really be 1 - e^-λ*(x-µ), where µ is equal to zero.  By contrast the formula for a hyperbolic tangent is tanh((x-µ)*b), where in this case b is a function of the variance, σ².   The value µ is not only the translation along the income axis, but also a parameter defining a random distribution of an individual in a group. 

The US Census reports on the distribution of incomes.  Using the distribution of incomes, adjusted for inflation, the limit of the decile percentage, and the top 5% are shown as reported in the figure below. Both an exponential distribution and a hyperbolic tangent fit the distribution of income very well.  However if you treat the amount of public investment at 0% as not confined to zero, but you keep the same variance from 1968, then you end up with a completely different distribution of income.  I am calling this amount Universal Basic Income, UBI, but this income does not have to be in cash.  It can also be in the form of public education, public healthcare, public childcare, public housing, etc. that are available to any one with little or no income. 

Fitting an exponential distribution in 1968 implies a basic public expenditure of $12,327 dollar per household, while fitting to a hyperbolic tangent implies a basic public expenditure of $6,480 per household.  However in 2021, the exponential distribution implies a basic public expenditure of $14,770, while the hyperbolic tangent implies a basic public expenditure of minus $1,298 per household.  The fit to the exponential distribution was achieved by allowing the value of µ to be as close to zero as possible but allowing the variance to more than double.  ( Ironically, mathematically the square root of the variance is called the standard deviation.  Those in favor of the 2021 existing distribution of income, which requires an INCREASE in variance, also want a DECREASE in deviation). If there is no change in the variance from 1968, then the basic public expenditures, Universal Basic Income, µ, might be $58,937.  At this amount, the distribution of income is almost equal for those in the top 80% . The mean income increases for those households under 80% and the mean income decreases for those over 80%. This UBI sounds like a lot, but the economy and the number of households have both increased from 1968.  If the tax revenues average 20% of household income (the median, NOT the mean) then that amount is only 0.345% of the increase in tax revenues. 

That the distribution of incomes does not follow an exponential distribution is apparent from the difference between the mean and median incomes.  Under a true exponential distribution, the mean would be equal to the median.  That it is not, and in fact the gap between the mean and the median is growing, shows that income is not an absolute and should NOT be distributed according to an exponential distribution.  

The slope of a hyperbolic tangent is the hyperbolic secant squared. In 1968 and 2021, the slope of a hyperbolic tangent looked very much like an exponential distribution, but that does not mean that income is an absolute.  As a group it should follow a random distribution. A way to increase the distribution of the group is to maintain the variance while increasing the “income” at zero percent.

Universal Basic Income

 

Suzanne

And Jesus was a sailor
When He walked upon the water
And He spent a long time watching
From His lonely wooden tower
And when He knew for certain
Only drowning men could see Him
He said, "All men will be sailors then
Until the sea shall free them

Sailors should know about tides and boats.

A rising tide raises all boats.  Donald J. Trump Junior famously said of averages that “I would imagine that 50% are below average, that's how math works.” I know that he is a graduate of the Wharton School, but also I took classes at the Wharton School when I attended UPenn’s Towne School of Engineering.  Let’s give DJTJ the benefit of the doubt that he was merely drunk in class when averages were taught, and not merely grifting again, but he is confusing the mean with the median.  The average is the centrality of the normal, which is the median.  In normal distributions, the mean and the median are equal, but when distributions are not normal they do not have to be the same.  Taking advantage of those who confuse the two is NOT a nice thing. https://dbeagan.blogspot.com/2018/08/wonderful-world-dont-know-much-about.html

A rising tide rises all boats means that as the tide, median, increases, then every boat should rise by the same amount.  Not that a few boats should rise by more than the tide and many more boats should be sunk, but that is actually what has happened.  Let’s be kind and say that it was by accident and not design.

The distribution of income is reported by the US Census Bureau.  The distribution of that income in 1968, in 2021 dollars, fits a hyperbolic tangent.  It also fits a hyperbolic tangent in 2021. That is not suprising since a statistical distribution should fit a hyperbolic tangent.  But the distribution in 1968 had a de facto Universal Basic Income, UBI, of almost $10.5 thousand.  The distribution in 2021 also fits a de facto Universal Basic Income, but it is negative $1.2 thousand. The number of households and income grew from 1968 to 2021.  If all of that increase in income was applied to everyone, then the distribution would stay the same, but the distribution was actually shifted towards higher incomes.  But by insisting that policies that should ensure that there is NO Universal Basic Income, and the distribution of income at zero percent should be as close to zero as possible, while the incomes for the top 20% are remarkedly similar, the incomes for the remaining percents are severely decreased.  By sinking all of those boats you might make the upper income yachts raise higher, but if you had just distributed income normally, then the end result would have been the same. 

And the amount of Universal Basic Income is not enormous. If  income tax is 20% of the total income and 0.4 % of the increase in taxes between 1968 and 2021 was shared among the total households in 2021, it would amount to $68 thousand per household.  And THAT is how math really works.

Destruction

 

Turn, Turn, Turn

A time to build up, a time to break down
A time to dance, a time to mourn
A time to cast away stones
A time to gather stones together
To everything turn, turn, turn
There is a season turn, turn, turn
And a time to every purpose under Heaven 

What time is it now? 

In the Hindu mythology, the trinity of the highest gods are:  

·        Brahma, the Creator ;

·        Vishnu, the Preserver, and

·        Shiva, the Destroyer.

Hindu mythology acknowledges that creation of the new will not occur unless there is destruction of that which has been created but found wanting.  But you can’t destroy everything or the end result would be nothing.  Thus Vishnu’s role is to decide what of creation will be preserved and what of creation will be destroyed.

It is probably no accident that 1/3 of all Americans are backers of the Jan 6^th, 2021 insurrection, whether by explicitly by backing the insurrection or implicitly by saying that it was not an insurrection.  It is probable that 1/3 of all Americans support all things progressive, and are the libs that MAGA wants to own. It is up to the remaining 1/3 of all Americans to decide which of the progressive actions they wish to support and which they want to destroy. 

The problem is that in a single representative per district system of governance, such as the one in the United States, there will most likely be a two party system.  If one party is captured by the destroyers and will only nominate destroyers as candidates, then the preservers may be forced to choose the candidate of the creators or else they will have nothing left to preserve. 

Mirror, Mirror

The Man in the Mirror

I'm starting with the man in the mirror
I'm asking him to change his ways
And no message could've been any clearer
If they wanna make the world a better place
Take a look at yourself and then make a change.

We are, of course, the man in the mirror.

Reality as a complex number is re^iθ, where r is the real part and θ is the angle of rotation of the imaginary axis.  This can also be stated as a+bi.  As was suggested in a recent blog post, https://dbeagan.blogspot.com/2023/08/complexity.html,  reality must be -ln(0.5)/λ , where λ is the decay coefficient of an exponential distribution.  It was also noted that 1/λ is the mean and median of that exponential distribution.  It was suggested that this apparent paradox could be resolved if 1/λ is only the real part of the complex number that is -ln(0.5)/λ.  However that leads to an undefined number where the rotation of the imaginary axis is ln(-ln(.5)) . The solution to this paradox is in another blog post, https://dbeagan.blogspot.com/2023/09/reality-ii.html, that reality (as a complex number) is equal to -reality(as a real number) +0i. If the real part of a complex number is -1/λ then the rotation of the imagainary axis is 1 radian, and since one radian is π it is 180 degrees.

This means that our reality is the mirror universe, a reflection of complex reality.  Thus that OG Star Trek Episode, “Mirror, Mirror” is correct except that we are living in the reality of the Imperial Star Ship Enterprise, of the Terran Empire, not Starfleet. The reality where Spock has a goatee.  The one in which McCoy says that he is “A doctor, not an engineer” and Mr. Scott replies that “Now you’re an engineer”.  IOW, it takes an engineer to find a solution.

Time Travel

 

Back In Time

Don't bet your future
On one roll of the dice
Better remember
Lightning never strikes twice
Please don't drive at eighty-eight
Don't want to be late again

Are there rules for time travel?

Time travel has fascinated storytellers for a very long time.  And IMHO time travel is possible, but you can’t change much about the past, so you may not want to time travel.

If the future has not been written, that is because there are choices that have yet to be made in the future, but choices have already been made in the past.  Just as there is a probability cone of future events that becomes wider as the time from that event increases, there is also a past in which those choices have already been made, so for the same distance in the past from that event, the probability cone is much narrower, and you are confined to visit only the past which could lead to the current choices.  Thus you can’t travel back in time and assassinate Hitler before WWII or prevent him from being born, because you come from a reality where Hitler was born and started WWII.  You can visit Hitler, but your actions can’t change the present from which you started.  You can’t also guarantee a win in tomorrow’s lottery because that has not yet happened. 

This sounds a lot like the time travel rules that existed in Superman comic books from 1949 to 1984.  Superman could visit the past, but he could not change the past.  Superman writers followed those rules because otherwise if Superman could travel to the past then why wouldn’t Superman change the past.  You also can not get to a past that is not in your past.  The South winning the Civil War might be one of the Multiverses, but we can not travel from our reality to a past where the South won the Civil War because the South did not win the Civil War in our reality. We can only visit what has happened, not what might have happened. 1.21 Giga Watts!!! What was I thinking?

Patriotism

 

Tell Her No

Tell her no no no no-no-no-no
No no no no no-no-no-no
(Don't let her down from your arms)
No no no no no (Oh, oh, oh, oh)
Don't hurt me now for her love belongs to me

“No” might be a complete sentence, but the phrase is “No taxation without representation”

The complete phrase uttered by the Founding Fathers/American Revolutionaries was not “No Taxation”.  It was “No Taxation WITHOUT Representation".  You might be opposed to taxes, but please remember to say the complete phrase.  The American Revolution was not fought over taxation, it was fought over representation.  When you are saying “No Taxation Without Representation” you are explicitly in favor of taxation, but not without having representation to decide what those taxes should be, the amount of those taxes, and how the revenue raised from those taxes is to be spent.  No taxation at all, or cheating on taxes, is not consistent with this phrase and is un-American.

Reality II

 

Imagination

There is no life I know
To compare with pure imagination
Living there, you'll be free
If you truly wish to be

Imagination may be the key to the multiverse!

Is there a multiverse?  If there is, it must be a complex number, the sum of a real number and an imaginary number.  Euler’s Formula is e^ix=cos(x)+isin(x), in other words a complex number.  This also means that as complex numbers, cos(x)=e^ix-isin(x), and sin(x)=(e^ix-cos(x))/ i,

These can also be used to find values of cos²(x) and sin²(x) as complex numbers.

cos²(x)=(e^ix-isin(x))²= (e^ix)²-2isin(x)e^ix+sin²(x)

and

sin²(x)=((e^ix-cos(x))/i)²= -(e^ix)²+2isin(x)e^ix-cos²(x)

Using Euler’s Formula, these can be restated as

cos²(x)= (e^ix)² -2isin(x)*( cos(x)+isin(x))+sin²(x)

or

cos²(x)= (e^ix)² +sin²(x)- 2isin(x)cos(x)

and

sin²(x)= -(e^ix)² +2isin(x)*( cos(x)+isin(x)) -cos²(x))

or

sin²(x)= -(e^ix)² -cos²(x)+2sin²(x)+2*isin(x)cos(x)

Therefore the formula for a circle, 1=cos²(x)+sin²(x), as a complex number is  

-(cos²(x)+sin²(x)) +bi,

where b can be any real number.

The formula for a hyperbola, 1=cos²(x)-sin²(x), as a complex number is

(cos²(x)-sin²(x) )+ sin(x)(-4cos(x))i+ 2*(e^ix)²

The formula for a circle, cos²(x)+sin²(x)=1 is a real number.  But if it were expressed as a complex number, then the coefficient of its real component is a 90° rotation of that complex number with any imaginary coefficient.  The formula for a hyperbola, cos²(x)-sin²(x)=1, is a complex number, but it is also the coefficient of its real component,  plus the coefficient of the imaginary number which is the rotation by the angle of x of -4 multiplied by cos(x), plus 2 multiplied by the square of Euler’s formula.  If you apply the value for the square of Euler’s formula, then the imaginary coefficient becomes a coefficient of zero. 

                                                (cos²(x)-sin²(x) ) + 2cos²(x) - sin²(x)+0i

The Euclidean, flat, surface is the transition between a circle and a hyperbola.  Pythagoras’ formula relies on the formula for a circle, but saying that the imaginary coefficient is zero does not mean that there is no imaginary coefficient. Evidence of absence is not absence of evidence. There is a big difference between a relative zero and an absolute zero.

IMHO the problem, is that the x property describes a vector relationship to an absolute.  A vector has both a magnitude AND a direction, BUT that magnitude is never negative and the direction always points away from the absolute.  Analyzing its magnitude as a scalar does not change those facts. You can have a magnitude of an equal amount in the opposite direction, but this is NOT a negative magnitude in the same direction. You have only appeared to create an new absolute, but you have not created a new absolute. You have only reflected the old absolute.

The relationship to the absolute can be rotated around absolute zero to create a solid which has dimensions of time, space and imagination.  But that rotation does not change the relationship to the absolute.  There can be the perception that there is negative space, etc., but this is only because of the 2π rotation around the absolute to create an imaginary axis.  The relationship of space, time, and imagination is still with respect to the absolute.

Euler’s Formula describes a complex relationship including an imaginary relationship, ix, not a real relationship. Pythagoras’s Theorem is a real number, but it is also a rotation of the real part of a complex number, which has an imaginary coefficient of zero.  

IOW, Reality as a complex number is then -Reality +0i.  If the Multiverse is a complex number which has the current universe as its real component, it must be Reality + bi.  Thus the Multiverse excluding our current universe is (b+0)*i.