Today, The University of Houston's College of Engineering
presents this series about the machines that make our civilization
run, and the people whose ingenuity created them.

Max Lorenz was a doctoral student at the
University of Wisconsin in 1905, when he published a paper titled:
*Methods of measuring the concentration of wealth*. He included
a graph that summed the income against the population from poorest
to richest.

If everyone in a country had the same income, the line would be straight.
Great disparities between rich and poor give a deeply concave line.
It was a neat way to show the pattern of income. Lorenz's curve certainly
didn't bring in all the factors. But it drew attention to a terribly
important issue by displaying it in an obvious way. And it raised all
kinds of questions.

For example, is perfect equality of income desirable? Lorenz curves for
the old communist countries were very straight. Those countries regulated
wages, but they made some people wealthy by providing privileges. Lorenz
curves didn't show that grim back-story.

On the one hand, when we have incentives for doing more and doing better,
income cannot stay uniform. But a subtle mathematical catch arises. It's
this: A society that offers great access to opportunity tends toward greater
equality of income. More people will find more ways to create and share wealth.

That might seem counter-intuitive -- the fact that true equality of income
is not a product of leveling by the state. It's a product of human enterprise.
Access means that a Horatio Alger child need not stay poor. And yet ... well,
things are never really quite what they seem.

Let's look at equality of income in real countries: One common measure is the
ratio of earnings of the top and bottom ten percent of the people. In the US
and Uganda, that ratio is sixteen. In Canada and Switzerland it's only nine.
American incomes are very unequal and they've been getting steadily worse for
over forty years.

So, back to mathematics: The math tells us that, when it's a simple matter of
having access for our potential, incomes tend to equalize. When artificial
factors keep high incomes high, and low incomes low, we are in trouble.

As I write in 2011, Democrats and Republicans both claim to know how to fix our
poor economic situation. Yet inequality has steadily risen under both parties.
So maybe I should add my own silver bullet to the many silver bullets flying
about us today.

If economic woes and inequality of income are wed, let's find means for reducing
inequality. It's both the problem and the main symptom. The gap between our rich
and our poor now matches countries like Mali, Cambodia, and Nigeria.

We are a smart, energetic, creative people. We can invent our way out of this
situation just as we've invented better health and better transportation. Find a
way to get problem solving out of the political arena and I promise you. We can
lick this one as well.

I'm John Lienhard, at the University of Houston, where we are interested in the
way inventive minds work.

(Theme music)

I've developed the math behind the idea of access, with two coauthors, in two places:
Paul L. Meyer and I created the mathematical tool in this paper:
L. Berkley Davis, Jr. and I applied these ideas to income distribution in this paper:
Once one has plotted a Lorenz curve, one may evaluate it by dividing the area under
the perfect-equality, straight-line curve by the area under the actual curve.
Subtract that ratio from 1 and the result is called a *Gini Coefficient*.
A Gini Coefficient of 1 is perfect inequality. A Gini Coefficient of zero is
perfect equality. Gini Coefficients for the US and Senegal are 0.41. For Canada
and France, they're 0.33. For Denmark and Japan, they're 0.25.

See also the Wikipedia pages for
Lorenz Curve,
Gini Coefficient,
Economic Inequality,
List of Countries by Income Inequality,
and Income Inequality Metrics.

This episode was first aired on September 26, 2011