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.