18 September 2009

Ways of knowing

I borrowed this title from here. Read the post of Jason Rosenhouse first.

I'd like to add one (out of dozens) of my personal experiences about what constitutes knowledge. (Most of them stem from religious faith, others from sheer idiocy. The first category I've encountered mostly in Texas. The second category is universal.)

Back in 1992, a professor, call him C, at the University of Texas came to my office and told me that the local "expert" in probability, Gary Wise (who is now in jail, despite the fact that he was a good Texas, bible-studying guy, but he managed, you see, to shoot the dean's car) referred him to me when C asked Gary something about Poisson processes. So C asks me the question, also referring to me as "the expert in Poisson processes". The question involved a rather trivial (well-understood) property of a Poisson process: Namely, if we consider two successive points of the Poisson process we know that their expected distance is the inverse of its rate, but if, in addition, we know that these points contain a specific observation time (12 o'clock, say), then their expected distance is twice the inverse of the rate.

There is nothing wrong with this. When we compute the expectation of a random variable, conditional on some information, we compute, in general, something very different from the expectation of the random variable.

Prof C asks me if the above property of the Poisson process is correct because he thought it was incorrect whereas the students in his class thought otherwise. I say, yes, of course. He replies, "I don't believe that!". "Well, let me give you a proof", I say. "I don't want a proof; this violates my sense of causality", says C. I could not, for the life of me, understand what he meant by "sense of causality". I explained to him that whereas a Poisson process may be used as a model of a random phenomenon in time, mathematically time plays no role as such. It could be space or whatever. Prof C went on giving a speech about the sky, the stars and god. I apologised and said that I will not go into these domains and that the only thing I can give him is a mathematical proof. He did not accept this. He repeated he needs no proof. Before leaving he said, "OK give me a reference". So I told him to look it up in Feller's book.

Several days later, C saw me at the corridor and shouted: "I believe it, I believe it! It's in Feller's book!" So, I asked if he has read the proof. "No, I haven't, but it's in Feller's book, so it's correct!"

For C, knowing was tantamount to seeing it written in a respectable book. For him, this is much better than a proof. I should not fail to mention that C is a born-again christian fundamentalist.


  1. Out of curiousity, what was C's discipline?

  2. Electrical Engineering. He used to 'teach' Probability to engineers. But his real forte was in 'bible studies'.



What measure theory is about

It's about counting, but when things get too large.
Put otherwise, it's about addition of positive numbers, but when these numbers are far too many.

The principle of dynamic programming

max_{x,y} [f(x) + g(x,y)] = max_x [f(x) + max_y g(x,y)]

The bottom line

Nuestras horas son minutos cuando esperamos saber y siglos cuando sabemos lo que se puede aprender.
(Our hours are minutes when we wait to learn and centuries when we know what is to be learnt.) --António Machado

Αγεωμέτρητος μηδείς εισίτω.
(Those who do not know geometry may not enter.) --Plato

Sapere Aude! Habe Muth, dich deines eigenen Verstandes zu bedienen!
(Dare to know! Have courage to use your own reason!) --Kant