I hope you enjoyed your test this morning, and that you are by now persuaded that sqrt(3) is irrational. On Thursday we will start the next component of the class, which will deal with law. To keep the total work load for this week from becoming burdensome, I will keep the first assignment light. In particular:

[A] Prof. Kazdan several times has made the comment that mathematics is 'easier' than other subjects (like epidemiology, or law, or what not). What did he mean by this? Is the idea that the other subjects are 'applied' disciplines? If so, would he say the same thing about physics, or about applied mathematics? Would it make a difference if, instead of 'mathematics,' he had said 'proof in mathematics' (and 'proof in epidemiology' and 'proof in law')? Or was he perhaps joking? If so, does that make a difference to the value of his observation? Does it make you more or less likely to accept it as a proof?

Let's generalize a bit, and instead of 'proof' talk about 'standards of argument.' How do the standards of argument in mathematics differ from the standards in other disciplines X? (Pick your own values of X: e.g., philosophy, history, French literature, paleontology, marketing, veterinary medicine.) If mathematical proof is a matter of persuading an audience (recall the classroom discussion of the proof that every number is interesting), then how does it differ from rhetoric? Or is there something else going on? Is it possible to formulate a concept of a fully rigorous mathematical proof, entirely free of gaps or mistakes or unstated assumptions? (Note: the work of Euclid, or Euler, or Newton is full of such shortcomings, which often took years to notice, and then further years of intensive effort to correct.) Is a notion of fully rigorous proof possible in other disciplines X? Why or why not? Do some disciplines come closer to the ideal than others? Why?

There is nothing to write: just think about the questions, and come to class with something to say

[B] To help your thinking, and to prepare the transition to law, please read the attached article from the New Yorker. It reports the story of a man accused of murdering his family by arson; he was tried, convicted, and executed, but almost certainly on bogus scientific evidence. The article is not conceptually difficult, but raises important questions about legal proof, expert witnesses, objectivity of prosecutors, reliability of juries, the 'beyond a reasonable doubt' standard of proof, and much more. If you do not have time to read it, at least skim it so that you get the gist of the argument. The fact-checkers for the New Yorker, by the way, are famously careful and precise -- so you might ask yourself about the standards of proof expected for a literary magazine, and how they compare to the 'beyond a reasonable doubt' standard of proof as exhibited in this capital case.

[C] The next item is more difficult, but we will not discuss it in detail until next Tuesday. But here it is. It is the recent Supreme Court case of Scott v. Harris. It involves Mr. Harris, a young man (19 at the time) who was observed speeding in rural Georgia -- not outrageously, but about 15 miles over the limit. The police turned on their sirens; Harris, who was driving without a license, panicked, and sped away. The police gave chase. After a lengthy pursuit, Officer Scott finally rammed Harris from behind, causing a serious crash, and leaving Harris paralyzed from the neck down.

The case (opinion by Justice Scalia, solitary dissent by Justice Stevens -- the vote was 8-1) -- is short, and you should have no difficulty in following it. But for the non-law students, here are some points to observe.

1. Harris sued Officer Scott. He argued that Scott, in ramming his car at high speed, and in employing deadly force for what was in effect a speeding ticket, was acting unreasonably. (Specifically, that he violated the 4th Amendment of the US Constitution, which prohibits 'unreasonable searches and seizures.' Ramming is legally a seizure. Technical stuff: the law suit against a state police officer is authorized by a federal statute -- the famous '�1983' -- which is why this case is in federal rather than state court. Nothing for us turns on that fact.)

2. Some jargon. Initially the case would have been called 'Harris v. Scott'; the names are given in the order, 'Plaintiff v. Defendant.' But because Scott appealed, he now becomes the moving party (i.e. the person asking the court to do something), and the case, for this stage of the proceedings, becomes 'Scott v. Harris.' Scott is now called the petitioner, and Harris the respondent.

3. Observe that this is a civil action, not criminal. That is important. If it were criminal, Harris would have to prove his case to a jury 'beyond a reasonable doubt.' That would be almost impossible, given the facts in the case. But in a civil trial -- we shall talk a lot about this distinction -- the standard is much more relaxed: Harris must only persuade the jury that his case is 'more likely than not' to be true. ('More likely than not' is generally understood to mean p > 50%. The inequality is strict; can you see why? Can you think of real-life cases where you might have p = 50%?)

4. Scott argues that he has a 'qualified immunity' from suit. Basically, 'absolute immunity' means that you cannot be sued, whatever the circumstances. (For example, if you have diplomatic immunity, or if you are a judge and the losing party wants to sue you for bad judging.) 'Qualified immunity' means you are immune unless certain facts can be established. This bit of the legal doctrine is complicated, and has changed since the case was decided: the details do not matter to us. Basically (and simplifying slightly) for Scott to lose his immunity, Harris must show (1) that Scott violated his constitutional rights, and (2) that the right was clearly established (so that the violation was unreasonable: one can't expect police officers to know every latest shading of criminal procedure).

5. Scott asked the federal trial court (= the 'District Court') to grant him 'summary judgment' on the question of qualified immunity. That is, he asked the District Court judge to decide, as a matter of law, that he was immune. The judge rejected his motion. Scott therefore appealed to a second court, the Court of Appeals for the 11th Circuit. Scott's appeal is what is known as an 'interlocutory appeal.' That is (and in contrast to most appeals), it occurs before the case goes to trial -- so before a jury has a chance to decide on the factual issues. Can you see why the interlocutory appeal was granted?

6. Related question. In this situation, in evaluating a motion for summary judgment, the court must interpret the evidence in the light most favorable to the non-moving party, i.e. Harris. Can you see why this is the rule? The Court of Appeals (three judges), taking the facts to be as alleged in Harris's complaint, agreed with the trial judge.

7. Extremely important point. It is a fundamental rule of American law that decisions about matters of fact are to be decided by the jury. Only decisions about matters of law are for the judge. The question about whether Scott acted 'reasonably' is a factual matter: the basic idea is, let the jurors hear the testimony of both sides, and then render their verdict.

8. However, in very unusual cases -- this is one -- the court may conclude that no reasonable jury could reach a particular verdict. In that case, it grants the motion for 'summary judgment.' (There are other bits of jargon -- 'directed verdict,' 'judgment as a matter of law,' 'judgment notwithstanding the verdict' -- but they all come to the same thing. The court says that only highly unreasonable people could see the facts in any other way than the court, and it takes the decision away from the jury.) It is a very high standard -- in effect, you are saying that anybody who disagrees with your view of the facts is a bit crazy.

9. I note that one Justice of the U.S. Supreme Court -- Stevens -- viewed the factual matters differently than his colleagues. This may explain the tone of his dissent. The attitude of the four lower-court judges does not appear to be recorded.

10. Crucial to the decision was the existence of a video of the chase. It is available on YouTube. Here is the link.
    http://www.youtube.com/watch?v=qrVKSgRZ2GY You need not watch the entire thing; but please watch the first minute or so, and then the concluding two or three minutes. You should also look at the comments that viewers have appended to the video.

I look forward to seeing you on Thursday.

Best wishes,
Bill Ewald