Saturday, July 02, 2005

Pi on You!

"A Japanese mental health counsellor has broken the world record for reciting pi, the ratio of the circumference of a circle to its diameter, from memory. Akira Haraguchi, 59, managed to recite the number's first 83,431 decimal places, almost doubling the previous record held by another Japanese." BBC News (July 2, 2005)

I suppose one might justifiably call this a useless recreation. Or does the exercise promote mental health?

But it's my job here to talk about evidence.

The mental health counselor's exercise is even more impressive than the feat of multiple games of blindfold chess played by some chess masters: the numbers that Mr. Haraguchi remembered conform to no order and do not make any (discernible) sense within some larger scheme or order.

How did Mr. Haraguchi do it? I don't know. (I suppose he practiced a lot. And no doubt he has a great deal of patience.) In any event, Mr. Haraguchi's success does suggest that we academics ought to take care before being seduced by the siren song of heuristics that supposedly simplify complex problems of evidence to levels that ordinary mortals can manage. (I'm all for strategies and mnemonic devices that make problems more memorable. See P. Tillers, Picturing Factual Inference in Legal Settings (2005). But I'm against strategies that wipe out important detail.)

Well, perhaps we don't really need Mr. Haraguchi's example to ward off such seduction. Have any trial lawyers or trial judges been seduced by the siren song of simple heuristics? (I regret that I was unable to sustain this alliteration to the end.) Where? When? How?

"In 1947 Miguel Najdorf broke the world record for blindfold chess by taking on 45 opponents simultaneously at Sao Paolo, Brazil. The display started at 8 pm on January 24, 1947 and finished at 7:30 pm on January 25. He won 39 games, drew 4 games, and only lost 2 games." Bill Wall, Blindfold Chess
  • Mmm ... [Tillers thinking] ... Do you suppose that extraordinarily powerful computers were somehow implanted within the skulls of Haraguchi and Najdorf?
  • Thursday, June 30, 2005

    The Logic of ... Investigation ... Inference ... This & That

    Some old riddles just refuse to go away. I was reminded of this on seeing the lovely NYTimes article by Dennis Overbye, The Remembrance of Things Future: The Mystery of Time (June 28, 2005). I have been interested for quite some time in ... well ... er ... the logic or ... well ... er ... the structure of fact investigation (and, also, of factual inference).

    Well, but which is it, Tillers: logic or structure?

    Well, that's the problem, you see. I'm not entirely sure which word I should use to characterize my subject: (i) logic or (ii) structure.

    "Logic" is a strong word -- perhaps too strong. "Structure" is a warm and flexible word -- perhaps too comfortable and flexible, too ... cheap and easy.

    There is a lot of awful talk around about the role of stories in proof and inference; it is said that (i) a good story has an actor (or that a story [good or bad] does not necessarily have an actor), (ii) a good story has a beginning, a middle, and an end (or not); (iii) a good story has a theme (or not necessarily); and (iv) so on.

    In response to such assertions (of either kind), one often wants to scream: Who or what sez so?!?

    The answer might be: well, (i) most people do; (ii) my intuition sez so; (iii) respectable thinkers think so; and (iv) so on.

    But -- one again (perhaps) wants to yell, "That's not good enough! Prove to me -- demonstrate -- that what you say is true -- and don't just tell me that you think it's true or that many people do ... and so on."

    But then the tables are turned on me: "Do you really think, Tillers, that logic alone can prove the importance of stories -- and of a specific kind of story?"

    My honest answer: "Well, I'm not sure it can. Granted, I can (and should) tell you that there is now a logic that goes by the name (sometimes) temporal logic. But I must 'fess up: I can't prove or demonstrate -- I am probably just intellectually and logically weak --, I can't prove that temporal logic (and all that it implies) tells us necessary things about human existence and (less grandiosely) about matters such as factual inference or fact investigation."

    Sensing the weakness of my "logical" position, but sensing (and believing) that some kind of "story" is a fundamental feature of human existence and (less grandiosely) of any rational argument about any question of fact, my instinct is to turn to "ontology" -- a theory of being, a theory of the way the world (the cosmos) is made -- and say, "You see, time and space are fundamental and unavoidable features of human existence and, thus, they must be part of any argument from evidence about what happened, is happening, or will happen in the world!"

    Well, this ontological turn is all well and good. The trouble is that the people who know a few things about the cosmos, the "space-time continuum," and all that sort of thing -- I mean modern physicists -- they would (if asked) almost invariably say, "Well, Tillers, you're wrong! You really don't understand our best understanding of nature, the world or cosmos in which human beings live and act. There is nothing in physics that shows that time runs only in one direction and that it cannot run backward. Au contraire! The direction of time means nothing for the kinds of puzzles physics works with!"

    I am left in despair.

    But now a ray of hope (see the NYTimes article): some physicists who are smart enough to be invited to take part in a conference at MIT say that physics must do better: it must develop an account of the kind of time that human beings experience - unidirectional time - and (perhaps) this new account must be one that acknowledges that for human beings time really does run only forward, and not backward.

    So I am reassured; my ontological intuition is not necessarily hogwash, not even in the eyes of (some) reputable physicists.

    But I am still left in a bit of a pickle, nicht wahr? For even if time runs forwards (for many purposes), accounts of how events are connected to each other can still vary a lot.

    But perhaps once the temporal character of existence (in some sense) is admitted, temporal logic can take over and drive us to some conclusions? I have some hope that this is the case -- although I strongly suspect that it will turn out to be the case that we will have to feed experience back into our logic -- now our temporal logic -- and the difficulty here (as always!) will be that our experience will fall short of a strict proof of telling us which variant of temporal logic best explains the world in which we live.

    Conclusion: You must forgive these sophomoric ruminations. But in my defense I say: problems such as this one -- the role of time in human existence -- are very old. If problems such as these do not plague us and weigh on us, it is usually only because we have decided that we just shall not dwell on them. Don't you agree?

    Wednesday, June 29, 2005

    Perhaps Narcissistic People Can Take Heart

    UK lawyers representing a youth who killed his parents sought to have the charges against the youth reduced on the ground that the youth had been afflicted with the malady of narcissistic personality disorder. See Guardian Unlimited (June 29, 2005). The strategy may have worked; the youth was allowed to plead guilty to manslaughter.