A fascinating `Nova' on math; capital-punishment documentary

If a ``Nova'' is a public television series, what do you call an especially spectacular number in that series? A ``Super Nova''?

While that little riddle might not hold up to the rigors of mathematical thought, the program that inspired it certainly lives up to the name. A Mathematical Mystery Tour (PBS, Tuesday, March 5, 8-9 p.m., check local listings) spins out enough mysteries and theories, as it explores the infinitely detailed field of mathematics, to keep you fascinated and occasionally awe-struck.

The program counterpoints reconstructed history with interviews of such internationally acclaimed mathematicians as Jean Dieudonne, of France, Sir Michael Atiyah, of England, and historian Greg Moore, of Canada. It elaborates some of the more abstruse problems that have beset mathematicians over the centuries. It also traces the development of mathematical thought in human history.

If all of this strikes you as a trifle dry, consider the following paradox:

A librarian is asked to make a catalog of every book in her library. At the end, she wonders if she should include the catalog she has just made (which, after all, is a book in her library) in her own catalog. She decides not to and sends her catalog to the national library. The national librarian is then given the task of cataloging all local catalogs into two masters: one of those that do include themselves, and one of those that don't. At the end of compiling his catalog of those that don't, he wonders: Should I include my master catalog? If he doesn't, the catalog will be incomplete (since his master will be a catalog that does not include itself), and if he does, it will be in error (since he will be including a catalog that does include itself in the catalog of those that do not).

That puzzle, advanced by Bertrand Russell, convinced a mathematician that his lifework on number sets had been totally wasted.

Such stories as this, and that of the French student who laid out the seeds of an important branch of mathematical study on the eve of a duel in which he was killed, crop up now and then in ``A Mathematical Mystery Tour''; but the main order of business here is to bring into view mathematical questions that, by their very existence, stretch the bounds of our thinking.

Platonists, for instance, accept Plato's theory that mathematical concepts have empirical reality outside the human mind, that they are discoveries, instead of commonly accepted principles. To hear them discuss a mathematical theory is little different from listening to astronomers recount their observations of dark stars and twin moons.

The cosmic nature of mathematics is made all the more impressive because it deals purely in thought. And the mathematical cosmos is really this program's subject. Though easily as far reaching in its visions as any episode of Carl Sagan's ``Cosmos,'' this little film may not make us grasp the phenomena it presents. But at least it brings them into view, like supernovas, and lets us peer into their mysterious depths. PBS documentary

Death and the Mistress of Delay (PBS, Monday, March 4, 10:30-11 p.m., check local listings) has us peering into something infinitely smaller and more sordid: a tiny prison cell on ``death row'' in Florida. The cell may be inhabited by any of the inmates awaiting execution in that state, which has the highest death-row population of any state in the Union.

The current occupant doesn't concern the program so much as the tug of war between a local group called LOVE (League of Victims and Empathizers), which wants the inmate killed, and Sharlette Holdman, ``the Mistress of Delay,'' as Newsweek magazine dubbed her, who has probably saved the lives of dozens of inmates.

This program explores questions of victims' rights and the ultimate form of social revenge: capital punishment. It probes the anger and outrage of parents whose daughter was killed, over the fact that her killer is still alive.

At the same time, it follows Miss Holdman's line of reasoning that indigent death-row inmates -- almost all of them are indigent, she contends -- are not allowed free attorneys on federal appeal and that many die for that simple reason. The Florida Clearinghouse of Criminal Justice, which she heads, works to get attorneys for these inmates.

The program does not begin to hide its own anti-capital-punishment sentiments. Balance is not one of its long suits. ``What is justice?'' it asks in the end: ``Death or delay? And is the ultimate penalty worth the price?'' Well, it answers its own question pretty frankly, according to its own judgments.

Still, if it fails as balanced journalism, ``Death and the Mistress of Delay'' succeeds mightily on one account -- bringing before us the naked reality of death by execution, so that the public, which seems to favor capital punishment, may evaluate the price for itself.