## Math, Logic, and Lawyers Daniel Henry Gottlieb --- October 9, 1995

This is a response to William H. Simon's article, "Merit and Affirmative Action" in the San Francisco Chronicle of June 16, 1995.

William H. Simon, a law professor at Stanford University, discerns a connection between Affirmative Action and other forms of selection imposed on job seekers or college applicants. He used his own case as an example of his idea.

The entrance exam for law schools replaced math problems with logic problems in 1970. He says "If the test had included the kind of math problems used in past years, I would have done poorly, but I'm fairly good at logic problems, and I got a good enough overall score to get into Harvard Law School".

I am a Mathematics professor, and when I read those words I was perplexed, because I didn't see how it was possible to be good at logic and yet poor at math at the same time. After some thought I may have found a solution to this puzzle. If I am right it may provide a good insight into the present problems of our legal system.

I think that the "logic problems" test the ability to recognize similarities and abstractions and principles, whereas the "math problems" test the ability to recognize the appropriate principle for the case at hand.

Consider the principle: `You can't add apples to oranges'.

If you believe this only refers to fruit, then Harvard Law is not for you. The "logic problems" test the ability to relate the principle to the statement that you can't add the elevation to the population, or Pesos to Dollars. The "math problems" test the ability to recognize that the principle applies if the problem were to find how many Pounds equals a Peso plus a Dollar, and does not apply if the problem were to add all the pieces of fruit on the table.

How does this play a role in our legal system? One legal principle which seems to be widely used is the following: In a sequence of actions the law is broken only if it is broken by at least one of those actions. The "logic problems" test whether you can understand this general principle and apply it to specific cases. The "math problems" test your ability to determine whether it is appropriate to apply this rule or not.

In the first Rodney King trial, the one whose verdict led to the riots, when the jury met to consider the case, they took a straw vote. They agreed that two of the officers on trial were indeed guilty of police brutality. But the judge had directed them to apply the following principle to their deliberation. They were to consider each of the sixty nine (?) blows, and then apply five tests to each. If a blow satisfied these five conditions, then the officer was guilty. If none of the blows satisfied the conditions, then he was innocent. Following this principle, the jury found the officers innocent on most of the charges.

If the judge had mathematical talent, he would have checked on where this principle leads to incorrect results. For example, suppose you had sixty nine numbers. Suppose the law is broken if the numbers add up to more than one. Apply the following method: `Consider each number. If it is less than one it did not break the law; if it is greater than one the law was broken. If none of the numbers broke the law, then the law was not broken'.

It is obvious that this method will give incorrect results.

This is a test of the principle in Arithmetic, not in the Law. So it is crystal clear that it is an inappropriate application of the principle since there are no gray areas in Arithmetic. But now that we know how the principle can be applied incorrectly, it is an easy matter to find an example in the Law: `Suppose Rodney King underwent Chinese Water Torture. You have to consider every drop and apply five tests to it...'.