Stephen Hawking died this morning. The Guardian published an excellent obituary written by Roger Penrose, giving a full picture of his scientific achievements as well as his personal struggles. Here I just wanted to say a few words about Hawking’s impact on my scientific career. Probably like many other people, I first got interested in physics from reading A Brief History of Time (which, in my case, I received as a gift when I was around 6 years old!), and up until the end of my undergraduate education, my main academic goal was to learn enough physics to understand everything in it (a goal that was only partially realized). Besides the science, I appreciated the book’s lucid discussion of philosophical issues like the role of mathematical models in science, and I think I still subscribe to something like Hawking’s positivist philosophy (which he called “model-dependent realism”). And although my current research is quite far from Hawking’s, his work still played a role in leading me to it: learning about a paper of Harlow and Hayden connecting computational complexity theory to Hawking’s problem of information loss in black holes was one of the things that convinced me to take quantum information seriously as fundamental physics, rather than “mere” engineering. Now that Hawking is gone, I hope there will be others to take up his mantle as not just a first-rate scientist but also a first-rate popularizer of science.
I recently discovered two very nice features of Aquamacs that make editing LaTeX documents very pleasant. Perhaps this post will convince those Mac uses among you who use inferior text editors such as Vim to switch.
- LaTeX-sensitive spelling correction: Aquamacs works with the standard Mac OS X spelling correction system, which uses the same dictionary across many applications. So words you add to the dictionary in Aquamacs should be available in other applications, and vice versa. What’s more, in Aquamacs, the spell-checker is set up to only check the text in your document, not the LaTeX code. To run the spell checker, type command-; to highlight misspelled words or command-: to open a window with suggested corrections.
- Inline previews: this is a feature of preview-latex, which I believe is part of AucTeX, the Emacs TeX package that Aquamacs uses. This feature is essentially what it says on the tin: all of your section headings, math, and included graphics are previewed inline in your buffer. This makes it much easier to read through your source file and find errors. Below are some screenshots of a document before and after previews are turned on:
Without previews:
With previews:
In order to turn on previews, you can use the commands in the preview menu, or just type C-c C-p C-d to turn on previews in the whole document. If you want to toggle previews at a point (e.g. so that you can edit a formula), move your cursor over the preview and type C-c C-p C-p to toggle the preview, or click with your middle mouse button (if you have one).One caveat: as of Aquamacs 2.1, there is a bug that causes preview mode to fail if you have Ghostscript 8.71 or above. To fix this, you can downgrade your Ghostscript (get the source from http://pages.cs.wisc.edu/~ghost/doc/GPL/gpl864.htm). To check what version of Ghostscript you have, just type gs in the Terminal and look at the output.
Greetings, gentle readers! The plan for this blog is to focus mostly on interesting things like physics, computer science, math, or other fields of science. But I don’t have any interesting to say on that at the moment, so here’s some recent “research” on Mathematical Theology. In particular, Marc Rasi and I seem to have proved a long-standing conjecture from the field of theology, namely the existence of God.
The proof uses the 
Of course, this whole argument is silly, but it does illustrate some interesting points. One is that beyond a certain point it seems rather silly to keep asking for a reason “why” things are the way they are, since that would lead to an infinite regress of explanations. The other is that anthropic considerations do matter – for instance, if it turned out that
Isotropic Bovines 