Paige by Paige (2.1)

Defining "random" - Part I

[This is part of a long series which started October 9, 2021. The beginning point is at this link. You have joined us starting Chapter 2 of Paige Harden’s book]

On Page 34 we find:

“Selecting a partner for reproduction is never random…”

Perhaps, but how about selecting a partner for not reproducing? A hundred years ago a random nitwit walked into a drug store to find a gorgeous leggy brunette working behind the counter. She looked at him, sighed internally, and said to herself “He’s the best of a bad lot so I guess he will have to do.”  A short while later (as short as I could make it) and married, we decided that we had survived, as children ourselves, all the randomness we could stand. Not wishing to compound those mistakes, we made the conscious decision to not reproduce. It was at that moment that Nature met Nurture. We made a conscious decision to travel away from the biological forces. That decision made us, in statistical terms, “outliers,” far from the average. We, therefore, find ourselves in the “tails” of the distribution, specifically in this case, the left tail below.

Much of Paige’s Chapter Two is concerned with the normal distribution, containing only brief mention of extreme values (out in the tails as we say). That is fine, she says she is covering “the basics” which is to be expected in a second chapter. Since I have read the ending and know where Paige is going, we need to establish how wrong it can be to carelessly borrow theories and methodology from the hard sciences (biology) and apply them to social science (economics). Let me explain why I am unmoved by a comparison of genome outliers to financial outliers.  Imagine you are in a crowded football stadium. Of 60,000 fans there is some average adult height, say, 69 inches. There is also an average annual income, about $35,000 per person. Now, ask yourself two questions: What are the chances you could locate someone in the stands who is six times the average height? What are the chances you could find someone who earns six times the national average income?

Thus, “tail behavior” in economics arises, in part, from making choices. Not all your choices are good ones, not all your wishes are granted. Stuff happens. What we debate with Paige is how much those who made sound choices or had good fortune must pay to those who made bad choices or had bad luck.

It is easy (for me) to believe that most of the randomness in Nature occurs prior to birth. Once born, your nature becomes my nurture and vice-versa. Out in the world, mixing together, competing for resources, making decisions, some good, some bad, we constantly fiddle with the randomness. More about this in Chapter 4.

On page 36 Paige provides:

“Fisher showed that Mendelian inheritance will result in a bell curve distribution of outcomes, so long as the outcome in question is influenced by many different ‘Mendelian factors’…” (emphasis mine)

So, what is your point, Paige? Your “so long as…” is an assumption that permits you to use the normal distribution (bell curve) to describe the world. What follows is just a numerical representation of the Galton board Paige offers in Figure 2.2 on page 37. Permit me to demonstrate how trivial it is to simulate “…many different ‘Mendelian factors’…” or any other kinds of factors. Keep in mind as you read this that my being able to simulate may be trivial but your living through these factors is not.

Richard von Mises (p. 107 of Probability, Statistics and Truth) describes forming long numbers composed of only 1’s and 0’s. Beginning with numbers 100 digits long, here is one such number

Fascinating. For some real fun, do this repeatedly, making a thousand of these long numbers. About 25% of those long numbers will contain 49, 50, or 51 zeroes. Naturally, for each of those that must mean there are 51, 50 or 49 ones. Increase the size of each of the long numbers to 1000 digits (displaying them in a single line here would make them microscopic so you need to let your imagination carry you the rest of the way). Make a bunch of those, too. About 49% of them will have between 490 and 510 zeroes. Now increase the size to numbers 10,000 digits long.  The proportion having between 4900 to 5100 zeroes becomes an astounding 95%. Graphically, here is what these three look like.

This bit of wizardry with just numbers composed of only 1 and 0, makes an important point about the famous normal distribution, upon which the bell curve is based. You can analogize to games of chance by imagining that each long number is a sequence of tosses of a fair coin (1=heads; 0=tails), but you need not. With no reference to games, probability, the genome, human beings of any color or any of the contexts in which we usually find randomness, just by writing down 1’s and 0’s randomly, we get this result. This makes the normal distribution, while an important mathematical concept in probability theory, little more than a counting algorithm in real life. I submit that the implicit law of large numbers at work here is manifest mostly in the trillions of cells and genetic elements of the human body. Once the baby is delivered, that genie is out of the bottle, as it were. Nurture has begun, and the pure randomness of Nature at birth begins a slow fade into the background.

Here is another important point lost on many social engineers. Probabilities may be multiplied together to get what is called a proper joint probability ONLY when events are independent. Thus, it is appropriate to compute, for tossing a fair coin, the probability of two heads in a row as

because the second toss is not influenced in any way by the first toss. The coin has no “memory.” Not true in most of life. Things are connected. People couple up, have children, uncouple, leaving all of them connected forever. Then they do it again. True independence is extremely rare. And yet it is used as the basis for a lot of the social engineering that passes as science. This, because the convenient assumption of normality, as often used and not always correctly, implies independence! When you start with a wrong assumption, what is the likely outcome?

From Page 43

“Results like these also raise a host of moral and political questions: Does this mean that differences in wealth are innate or inevitable? That social and economic policies designed to increase equality or redistribute wealth are doomed to failure?”

Actually, there are answers to those questions and the answers are the same. For the first question: “Yes,” in an economy based on enlightened self-interest (aka “The Invisible Hand”) property rights gravitate to the highest bidder. The simple reason is that the highest bidder can use property in the most efficient way. This is Nurture in the form of human survival. To the second question: Also “Yes,” all efforts to interfere in or meddle with the natural order of wealth accumulation is just an expensive, temporary frustration. Strong laws of equilibrium tell us that the most efficient will, in the end, produce the most desirable allocation of resources. Nature will struggle in the direction of that outcome no matter what man does. The laws of man are things Nature gives humans to play with while waiting for the Universe to act.

From Page 44

“Like any program of research, research on how the genetic lottery shapes our lives has flaws and holes. It makes simplifying assumptions that can’t possibly be true; it grapples with incomplete data.”

Applause to Paige, again, for her candor. This is one reason the words “Hello, I am from the government, and I am here to help…” are so chilling. The costly baggage attached to that “help” disturbs the natural healthy randomness of Nature.

A buffet of unintended consequences follows.