Inequality II

  

I Have A Dream

Now is the time to make real the promises of democracy. Now is the time to rise from the dark and desolate valley of segregation to the sunlit path of racial justice. Now is the time to lift our nation from the quicksands of racial injustice to the solid rock of brotherhood. Now is the time to make justice a reality for all of God's children.

It would be fatal for the nation to overlook the urgency of the moment. This sweltering summer of the Negro's legitimate discontent will not pass until there is an invigorating autumn of freedom and equality.

It is not only morally true, it is mathematically true.

If the absolute is perceived to be in flat space, its variance is 1.41, which is the rounded value of the square root of 2 . If it is curved hyperbolic space and the imaginary axis is considered, the variance is 1.47, or ~1.5.  According to wave theory the amplitude squared should be twice the variance, which makes it approximately 3.  100% of the absolute should be within 3 times its standard deviation, σ. If a function is confined to only one value of the imaginary axis, i.e. the coefficient of the imaginary axis is 0, the perceived variance is limited to this reality, then 100% of the absolute should exist with 3 times the standard deviation divided by ~1.5, or 2 times the standard deviation. This is equal to 5/6 σ².

Additionally for a value of s=½, the range parameter of a logistic or hyperbolic secant squared distribution, the Probability Density Function, PDF, of this normal distribution must be 50% at the mean/median/mode, μ. For any value of s, to be a normal distribution, the mean must be less than 1.44 times the value of the median.  This requires that for a system of n individuals to act as if they were a normal absolute, the mean of the system should be no more than 1.44 times the median of the system.

If the observed mean is more than ~1.5 times the median, then it is suggested that the distribution is NOT normal in that therefor some of the n individuals in the system will have more than 100% of the absolute.    To prevent this merely requires that at equilibrium, no individual should have more than 5/6 of the variance, σ², which is equal to μ+2σ, or the system is abnormal and is NOT acting as the absolute.

In 2022, the report of the distribution of wealth by country according to the Global Wealth Databook published by USB, formerly by Credit Suisse, shows that in most countries the mean wealth was fairly stable in the past but has become more inequitable over time.  https://dbeagan.blogspot.com/2024/02/distribution-of-wealth-iii.html 

In the United States the distribution of mean to median wealth was 4.7 in 2000 and increased to 5.1 in 2022. This increase in wealth has largely come because the US tax code has increased the discretionary income available to the highest percentage, This means that more of that discretionary income could be saved and invested.  The tax code changed in 1981 so it is hardly surprising that the inequality  has been increasing since that time. Not going back!