I came across a videotaped lecture by Itamar Pitowsky given at PITP some years ago on the question of probability in physics that we discussed in two earlier posts on randomness in nature (I, II). There are links below to the presentation slides, and to a video of the lecture.
A little over a week ago on Thursday, Itamar, Oron Shagrir, and I sat at our little CS cafeteria and discussed this very same issue. What does probability mean? Does it just represent human uncertainty? Is it just an emerging mathematical concept which is convenient for modeling? Do matters change when we move from classical to quantum mechanics? When we move to quantum physics the notion of probability itself changes for sure, but is there a change in the interpretation of what probability is? A few people passed by and listened, and it felt like this was a direct continuation of conversations we had while we (Itamar and I; Oron is much younger) were students in the early 70s. This was our last meeting and Itamar’s deep voice and good smile are still with me.
In spite of his illness of many years Itamar looked in good shape. A day later, on Friday, he met with a graduate student working on connections between philosophy and computer science. Yet another exciting new frontier. Last Wednesday Itamar passed away from sudden complications related to his illness.
Itamar was a great guy; he was great in science and great in the humanities, and he had an immense human wisdom and a modest, level-headed way of expressing it. I will greatly miss him.
Here is a link to a Condolence page for Itamar Pitowsky
|Probability in physics:
where does it come from?
Dept. of Philosophy, The Hebrew University of Jerusalem
The application of probability theory to physics began in the 19th century with Maxwell’s and Boltzmann’s explanation of the properties of gases in terms of the motion of their constituent molecules. Now the term probability is not a part of the (classical) theory of particle motion; so what does it mean, and where does it come from? Boltzmann thought to reduce the meaning of probability in physics to that of relative frequency. Thus, eg., we never find a container of gas in normal circumstances (equilibrium) with all of its molecules on the right hand side. Now, suppose we could prove this from the principles of mechanics- that a dynamical system with a huge number of particles almost never gets into a state with all its particles on one side. Then, to say that such an event has a vanishing probability would simply mean (and not only imply) that it is very rare.I shall explain Boltzmann’s program and assumptions in some detail, and why, in spite of its intuitive appeal, it ultimately fails. We shall also discuss why quantum mechanics with its “built in” concept of probability does not help much, and review some alternatives, as time permits.
For more information about Itamar Pitowsky, visit his web site. See his presentation slides.
Additional resources for this talk: video.
(Here is the original link to the PIPS lecture) My post entitled Amazing possibilities about various fundamental limitations stated by many great minds that turned out to be wrong, was largely based on examples provided by Itamar.
Many people do not regard mathematics as a science since it does not directly probe our physical reality; some mathematicians even like to think about mathematics as being closer to art, music or literature. But is there really a big difference between exploring the physical reality and exploring the logical/mathematical reality?
It is perhaps too early to have an open discussion thread on this blog but let me try anyway. What do you think? Is mathematics a science?
(This post was influenced by a recent post on Peter Woit’s blog where he referred to an article by Robert Matthews entitled: “Do we need to change the definition of Science?”)
Updates: (June 18; June 30 ) A related very successful discussion titled “What is Purity” is taking place Continue reading