What Does Equality Mean?

Lincoln's Gettysburg Address was 270 words in length. It opens with some fancy wording about how long it's been since the Founding, and then it says what this nation is about. Lincoln says that this is "a new nation, conceived in Liberty, and dedicated to the proposition that all men are created equal."

I love how clear the language is. And yet, what does he mean exactly by equal?

Does it mean that everybody in a classroom should receive the same grade? Does it mean that everybody should have the same job, and work the same hours? Does it mean that everybody's mathematical skills should be equal? Does it mean that it's unfair that I can't sing like Sinatra, play baseball like A-Rod, box like Mike Tyson, tell jokes like Steven Wright, write novels like Jane Austen, or be as wealthy as Paris Hilton?

If equality means "the same as," then it should mean that everyone should be identical in every way, and have the exact same quality of life.

Darwin, who was born on Lincoln's birthday, tells us instead that it is incremental advantages (in-equality) that are the driving force in evolution. That evolutionary success (ability to successfully mate and pass on genes) is due to very slight advantages which confer success. Perhaps it's slightly better looks, or slightly better social skills, or perhaps the ability to make a partner laugh, or perhaps it's just simply rudimentary health (depending on the context, whether one is a lumberjack, or whether one is in a Parisian drawing room, different skills would amount to different advantages), or perhaps it's the ability to understand and follow mathematics.

Are Darwin and Lincoln polar opposites: one believing that life is fundamentally a matter of equality, and the other, believing that life is fundamentally a matter of inequality?

Is there some way to reconcile the two?

In the most recent issue of Reader's Digest, there is an article about Malcolm Gladwell. Gladwell's published a recent book entitled: OUTLIERS: THE STORY OF SUCCESS (Little, Brown). Gladwell argues that it isn't IQ as much as experience in a field that gives an advantage. He says that Bill Gates spent thousands of hours computing at a time when no one else had that experience. The Beatles spent thousands of hours playing in Hamburg when no one else had that kind of time spent in live performance. "Success is the steady accumulation of advantages."

Moreover, success can come late. He notes that Paul Cezanne had his first one-man show at 56.

Hard work, finding meaning in your work, and having a lot of experience in an area from childhood on up, can give a kid a slight advantage that might eventuate in a Tiger Woods, or an Alfred Hitchcock.

Should everyone be equal to a Paul Cezanne or a Tiger Woods? Part of the fun of sports or arts is that some are so spectacular, while most aren't. Should everyone nevertheless be the same? Is that the kind of equality we want?

It seems to me that a growing number of people think that that's what equality means.

I've been reading a book called Women in Mathematics (MIT Press, 1975), by Lynn Osen. In the last chapter she makes such an argument.

Osen is dismayed that in the aftermath of the Sputnik scare in which the Russians threatened to gain an incremental advantage on the US in space, that the huge push toward mathematics and science did not eventuate in more female scientists. But she laments, "the resulting curricula changes have appealed more to males than to females. It is a problem that was not caused by educators and educators by themselves cannot solve it. But if the ideological goal of achieving TRUE EQUALITY [my emphasis] is to be realized, then women and interested educators must discuss and define concrete programs aimed at effecting change at all levels of education, attracting more women to this field of study, researching and understanding the psychological dynamics underlying the difficulties women encounter in this field, and offering compensatory training where necessary" (168).

Osen however also notes that there are of course important women mathematicians, and always have been. But there is a single advantage that these women almost invariably had. "For many of the women mentioned in these biographies, it was the early support of an intelligent and mathematically educated father that made the crucial difference in the socialization process" (165).

Certainly the state cannot afford to provide a substitute parent for all of us who lacked a "mathematically educated father" in order to produce pure equality in the creation of math genius.

Math genius, sports genius, computer genius, dance genius, athletic genius generally, literary genius, is often a matter of slight incremental advantages, probably largely caused by an influential and talented parent. Communities full of one-parent homes, or homes with stressed out fathers and mothers barely scraping by, with little or no education, and next to no higher abilities, certainly confer a disadvantage upon the children.

What's to be done about it?

One answer might be to kill all talented parents, or else take the children from such homes and place them in poor environments, and seclude them as much as possible from any kind of mental stimulation, so that other kids from disadvantaged homes will not be left behind. One could forbid the children from ever seeing their parents, and perhaps even place them in blinders, and scream at them a lot every time they go near a book.

On the other hand, schools can be built for the disadvantaged, teaching salaries raised, money can be thrown at the problem, but it seems to come down to parents, which is an evolutionary issue, in which each parent is always trying to confer an advantage on their own offspring. I admit I'm somewhat behind in math. And yet there may be time to run back through life and pick up the topic, and spring forward, algebra textbook in hand, so as to inspire my children with the fun and beauty of it, and thus give my own kids a fighting chance.

All men may be created equal, in Lincoln's wording, but there will always be various kinds of inequality as we compare across families. Some parents are more devoted than others. Some better educated, some better financed, some revealing a harder work ethic, some a less. Lincoln had part of the equation right. Darwin had another part.

Sophie Germain was a Frenchwoman "best known for her work in the theory of numbers. Here she demonstrated the impossibility of solving Fermat's last theorem if x, y, and z are not divisible by an odd prime n" (91). She was wealthy and her early childhood was spent during the years of the French terror, in which Liberty, Equality and Fraternity were the cries of the people, and people like Sophie often went to the guillotine. She spent years hiding, with nothing to do but work on mathematics. Her father had an enormous library of mathematical volumes, with which she had total liberty of accesss. She later corresponded with Gauss, and others, but her education was stymied by a system that didn't admit women. She did most of her mathematical work all alone, sometimes corresponding under male pseudonyms. She lacked the formal education to tackle the most difficult problems, and yet managed to overcome many hurdles. She had some advantages in terms of her status, and the fact of her father's library. What if she had been given better circumstances? Would she have been equal to Gauss?