Category Archives: Review

Review of “Shtetl-Optimized” – the blog of Scott Aaronson.

Shtetl-Optimized, as I’ve mentioned elsewhere, is the blog of Scott Aaronson. And, as I’ve just linked to his wiki page, I don’t feel especially inclined to say much about his biography. Aaronson’s field of research is quantum computation; an exciting new field with possibilities. It lies at the intersection of mathematics, physics, computer science, and electrical engineering.

I have found Shtetl-Optimized to be well-written and informative. His latest post, dated March 22nd, is about Tegmark, his book Our Mathematical Universe, and Tegmark’s idea of the Mathematical Universe Hypothesis. Aaronson’s writing is lively and witty, you’ll find. He writes about both the human-ness of Tegmark’s writing, as well as his disagreement with Tegmark’s fundamental thesis, which is that the universe is not just mathematical, but is itself the mathematics. One of Aaronson’s reasons for finding the Mathematical Universe Hypothesis (MUH) unconvincing is that it is not impressive science – defined as when elegant mathematics lines up with facts as we have experienced them. I think this is exactly right. It does seem unlikely, as well, that anyone could ever devise experiments to test the MUH. This is my issue with all multiverse theories: while theories are definitely a part of science, and important (theories are the goal, after all!), experiment is the life-blood. A theory without experiment exists only in men’s minds, and has dubious predictive power.

Shtetl-Optimized is probably not for the layman, however, as he has no hesitation in getting “technical”. If you are interested in popular science, this blog would stretch you. Perhaps that is what you’re seeking, and if so, you’ve found a good place. It’s like classical music: you get out of this blog what you put into it.

What shall this blog be about? (I)

It seems to me that great mathematical writing is rare, and to be celebrated. It follows that pointing out great mathematical writing, as well as poor mathematical writing, could be a very useful function of this blog. So I propose this as one feature of the blog.

We can review books, blogs, articles, etc. Any mathematics in print is fair game. What should be the criteria by which we judge mathematics to be well-written or not? To some extent, the rules of basic English should apply. We should see punctuated equations, as per N. David Mermin, correct grammar and syntax, and consistent formatting. In addition to these low-level necessities, we should see careful definitions, a concern for the reader, a lively, interesting, engaging style, as well as clarity of expression.

One aspect of mathematical writing not often brought to the fore is the difference between research and scholarship, as mentioned in Morris Kline’s book Why the Professor Can’t Teach, to which I linked above. Research is coming up with new mathematical theorems, procedures, etc. Scholarship is organizing, codifying, and clarifying existing research. One quote from Kline’s book (which I quote loosely) is that “One good scholarly paper is worth a hundred research papers.” Having attempted to read a number of research papers, I can definitely say that the vast majority of them are exceptionally poorly written, tending to be esoteric for the sake of being esoteric, and are generally useless except for the ultra-specialist.

It was V. I. Arnold who wrote the following:

It is almost impossible for me to read contemporary mathematicians who, instead of saying “Petya washed his hands,” write simply: There is a $t_1 <0$ such that the image of $t_1$ under the natural mapping $t_1 \mapsto \x{Petya}(t_1)$ belongs the set of dirty hands, and a $t_{2}, t_{1}<t_{2}\le 0,$ such that the image of $t_2$ under the above-mentioned mapping belongs to the complement of the set defined in the preceding sentence.

This is exactly right. It is this sort of obfuscated “mathematicalese” that I would combat, and I would welcome fellow fighters in this regard.