I Was Told There Would Be No Math

image014There are two mathematical concepts that almost everybody intuitively knows – even if you attended public schools anytime within the past 30 years or so. The first is called the Law of Large Numbers, a mathematical rule that states that “as the number of trials of a chance experiment increase, the experimental probability of an event becomes closer to the true probability of that event.” The Law of Large Numbers is often confused for the Law of Averages which is not actually al law at all. The false “Law of Averages” is also known as the Gamblers Fallacy, and is not a mathematical phenomenon, rather it is a psychological trick people play on themselves to convince themselves that favorable outcomes are about to occur, using past behavior to influence their reasoning. It is a misapplication of the Law of Large Numbers, where people try to apply long-run probabilities to short-run events.

The second concept is called the Central Limit Theorem (CLT) which roughly states that the distribution of the sum (or average) of a large number of independent, identically distributed variables will be approximately normal, regardless of the underlying distribution. That is to say that large groups of numbers tend to be normally distributed around a mean. The CLT and the law of large numbers are the two fundamental theorems of probability.

Given the fact that almost all of us have taken math classes that seemed to be worthless at the time but our teachers told us we would use – my personal scourge was my high school Advanced Math/Calculus teacher, Mary V. Golding – I am here to inform you that sadly for us who didn’t pay as much attention as we should have – they were right. What Mary V. knew that has taken me years of mathematical hard knocks to learn is that mathematical laws are exactly like the law of gravity – they always apply – it doesn’t matter if you believe them or understand them, they still apply.

I’ve been thinking a lot about the progressive Democrat assertion that economic equality is a destructive force. Given the mileage that #feelthebern got from this idea and the chance of a Hildebeast/Fauxcohontas Democrat ticket, we are likely to be hearing about “inequality” on many different levels for a long, long time. Even if some broadly and malleably defined “inequality” is a culture killer, the solution to such a condition is important and to understand the correct solution, one must also understand the cause.

The three Democrat Stooges – Bernie, Hillary and Liz – want to take from the top and give to the bottom because they theorize the curve is skewed toward the rich. Taking a simplistic view, if we do the math (according to the two concepts explained above), that will work. If we assume that we are successful in shifting enough wealth to the bottom, they propose the distribution will trend closer to the symmetry of a normal distribution (a bell-shaped curve where the right and left halves are mirror images of each other).

I disagree because this view is too simplistic. There is another way that inequality expresses itself and that is through a bi-modal bimodal_distributiondistribution. A bimodal distribution is when a large group of numbers have two peaks, essentially two distinct normal distributions shoved together around two different means (there also can be multi-modal distributions but for simplicity’s sake, let’s work with just two peaks). I do think that inequality, as expressed by the distance between these two means (the peaks) is a problem and I know that the Democrats’ simplistic solution will not cure the problem because it does not address the root cause.

The Democrats believe that the problem causing the skew is that the rich are getting richer and leaving the poor behind and while that may be true, that is an observation not an explanation. What I have learned from my limited study of history and great civilizations is that what begins as a skewed curve that increases wealth for all (the entire curve moves to the right) sometimes becomes a bimodal distribution as the number of producers creating wealth shrink in comparison to the number of non-producers who come to depend on distributions from the wealth of those producers. As the number of producers shrink and non-producers increase, the producers become far more visible and much easier targets for the non-producers to blame and by extension, to attack.

It isn’t always the mean of the “rich” distribution that moves away from the “poor” distribution – I have noticed that in declining socioeconomic systems, it is often the “poor” distribution that stops moving (sometimes actually regressing) as the “rich” continue to push to the right. That stop/regression is responsible for the gap, not simply the rich getting richer. As a result, the simplistic solution if wealth redistribution will not create a normal distribution without reducing the mean for all of the system, harming all.

The real answer is that policies must be enacted not only to free the “rich” to keep getting richer but to encourage the “poor” distribution to catch up. The distributions must be merged by the left joining the right, not bringing the right down to the left. If the producers have a moral obligation to be the support columns for a socioeconomic system, the non-producers must also bear the responsibility to become producers. The true danger isn’t inequality within a single distribution, rather it is creating two separate distributions which drift apart with an insurmountable distance between their respective means.

Capitalism has proven it can close the gap between the curves and benefit all with increasing standards of living, collectivism can close the gap by equally sharing decline and misery with all. It is our choice to make.


3 thoughts on “I Was Told There Would Be No Math

  1. Very interesting analysis, but a little too much pure math for a simpleton such as myself.
    The way that I see it, the problem with redistributive policies is that they will eventually make everyone poorer, because actual wealth (as opposed to money) will be consumed faster than it is produced. What’s happening in Venezuela is a classic example of where this has to lead.
    Being an old sailor, I mhm made a more physical analogy a few years ago.

  2. Yeah. They told me the same thing when I signed up for my Quantum Chromodynamics seminar. I showed up with the 64 color crayola caryon box all set……. WTF !! ?

  3. ” Capitalism has proven it can close the gap between the curves and benefit all with increasing standards of living, collectivism can close the gap by equally sharing decline and misery with all. It is our choice to make.”

    Perfect summation !
    I would add this : Both Capitalism and collectivism lead to Elites….winners. But in collectivism you have no chance of becoming an elite by your own efforts exclusive of being favored by the collectivist elite. In short you have no no Choice.

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