Joel's Blog Archive

I'll bet this messes with your head re: [dear_raed.blogspot.com]

by Joel Aufrecht 12:23 PM, 12 Feb 2004

A couple of months after the war ended the US army started blowing up UXO’s (unexploded ordinance – it took me forever to figure out what those three letters meant). They issued a warning saying that explosions on the top or half hour were controlled explosions. Just so that we wouldn’t freak out. Almost half a year later I still look at my watch every time I hear an explosion. I noticed my cousin does the same thing.

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Baseball's Hilbert Problems re: [premium.baseballprospectus.com]

by Joel Aufrecht 12:16 PM, 12 Feb 2004

In 1900, a mathematician named David Hilbert addressed the International Congress of Mathematicians in Paris and delivered what was to become history's most influential speech about mathematics. Hilbert outlined 23 major problems to be studied in the coming century. In doing so he expressed optimism about the field, sharing his feeling that unsolved problems were a sign of vitality, encouraging more people to do more research.
...
By putting forth our own "Hilbert problems" for baseball analysts of the future, Baseball Prospectus is outlining our philosophy for how and why this kind of work ought to be done--our attempt to provide inspiration and guidance to the baseball community at large.

Hilbert Problem in Math	"Hilbert Problem" in baseball
3. The equality of two volumes of two tetrahedra of equal bases and equal altitudes. In two letters to Gerling, Gauss5 expresses his regret that certain theorems of solid geometry depend upon the method of exhaustion, i. e., in modern phraseology, upon the axiom of continuity (or upon the axiom of Archimedes). Gauss mentions in particular the theorem of Euclid, that triangular pyramids of equal altitudes are to each other as their bases. Now the analogous problem in the plane has been solved.6 Gerling also succeeded in proving the equality of volume of symmetrical polyhedra by dividing them into congruent parts. Nevertheless, it seems to me probable that a general proof of this kind for the theorem of Euclid just mentioned is impossible, and it should be our task to give a rigorous proof of its impossibility.	3) Measuring the catcher's role in run prevention. In Baseball Prospectus 1999, Keith Woolner presented a compelling case that catchers do not have a noticeable effect on a pitcher's performance. If there is no "game-calling" effect, what impact does a catcher have? Is it primarily controlling the running game? If so, how much of that is attributable to the pitching staff? Is it in preventing wild pitches and passed balls, thus giving the pitcher more confidence to keep the ball low? What about reading a pitcher's physical state and helping to keep his pitch count low?
10. Determination of the solvability of a diophantine equation Given a diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: to devise a process according to which it can be determined by a finite number of operations whether the equation is solvable in rational integers.	10) Projecting minor league pitchers accurately. One of the holy grails of sabermetrics is creating useful projections of major league pitcher performance based on minor league performance. While strikeout-to-walk ratios and other means of assessment can give us rough guides to good and bad young pitchers, we're nowhere near the level of certainty we want to achieve. ...
17. Expression of definite forms by squares A rational integral function or form in any number of variables with real coefficient such that it becomes negative for no real values of these variables, is said to be definite. The system of all definite forms is invariant with respect to the operations of addition and multiplication, but the quotient of two definite forms—in case it should be an integral function of the variables—is also a definite form. The square of any form is evidently always a definite form. But since, as I have shown,37 not every definite form can be compounded by addition from squares of forms, the question arises—which I have answered affirmatively for ternary forms38—whether every definite form may not be expressed as a quotient of sums of squares of forms....	17) Determining the value of draft picks, Rule 5 picks, player-to-be-named-later arrangements, and other non-specific forms of compensation in transactions. The more esoteric forms of compensation in trades are usually ignored, but they must have some real value if teams continue to exchange talent for them. What does a team give up when it signs a Type A free agent? How much is that draft pick worth? Is a typical Rule 5 pick worth the $50,000 and the roster spot? Are teams taking full advantage of the Rule 5 draft? What kinds of PTBNL deals make sense for both teams?

Selected Hilbert problems from Mathematical Problems, Lecture delivered before the International Congress of Mathematicians at Paris in 1900. By Professor David Hilbert

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New feature: List of songs not in 4/4 re: [aufrecht.org]

by Joel Aufrecht 12:02 PM, 12 Feb 2004

I've added a new feature to the site, a compendium of songs (mostly pop, jazz, and country) which are not in 4/4 time. Please use this list for those purposes which you see fit.

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