Douglas Bruce finds himself one day riding the subway in New York without knowing where he is going. In fact, he doesn’t know where he is, he doesn’t recognize any of the buildings. Panic sets in once he realizes he doesn’t know where he took the train, or even his own name. Doug suffers total amnesia, a rare condition in which one forgets everything about one’s life. Well, this is not exactly true: He knows how to talk, and when in the hospital someone asks him to sign, he remembers his signature. This strange and fascinating condition is explored in this documentary that uses footage shot by Doug himself and directed by his (former) friend Rupert Murray.

I found the documentary quite interesting, but I also found it wanting in several respects. Part of it may be due to the simple fact that we still know very little about how memory works, so surprisingly little time is devoted to hard data, to what may be happening—as for why it is happening, nobody knows. Some hypotheses are mentioned, and as the story progresses we get some clues. But part of the problem with the story I think is due to what I perceive as a shortcoming of the director: There are questions that do not get asked, some that beg to be asked, and why they are not seems to be because everybody is so fascinated by what is happening that they assume that filming it is enough. Part of it I think is due to the friendship between Doug and Mr. Murray. Mr. Murray seems to go out of his way to make Doug feel comfortable, while obviously the subject matter may make him uncomfortable. So, at the end of the day, I find the final product a bit awkward. There are a few extras in the DVD that leave me feeling the same (at least there is consistency); I missed (being in Vienna) the controversy on the veracity of the story, so the short section addressing it didn’t mean much to me. There is a long section explaining how a sequence was shot. I found it very curious that the director put so much thought into the visual look of the final product instead of trying to add a bit more substance to it.

I like explorations of memory, and mental problems intrigue me to no end. So this was a good movie overall. It complements well other documentaries in similar subjects, like anterograde amnesia, the disease that Memento popularized. I had the fortune of watching in 2004 an excellent documentary by Koreeda Hirokazu about one such case in Japan, Without memory.

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I learned of this problem through Su Gao, who heard of it years ago while a post-doc at Caltech. David Gale introduced this game in the 70s, I believe. I am only aware of two references in print: Richard K. Guy. Unsolved problems in combinatorial games. In Games of No Chance, (R. J. Nowakowski ed.) MSRI Publications 29, Cambridge University Press, 1996, pp. […]

Let $C$ be the standard Cantor middle-third set. As a consequence of the Baire category theorem, there are numbers $r$ such that $C+r$ consists solely of irrational numbers, see here. What would be an explicit example of a number $r$ with this property? Short of an explicit example, are there any references addressing this question? A natural approach would […]

Suppose $M$ is an inner model (of $\mathsf{ZF}$) with the same reals as $V$, and let $A\subseteq \mathbb R$ be a set of reals in $M$. Suppose further that $A$ is determined in $M$. Under these assumptions, $A$ is also determined in $V$. The point is that since winning strategies are coded by reals, and any possible run of the game for $A$ is coded by a real, […]

Yes. This is obvious if there are no such cardinals. (I assume that the natural numbers of the universe of sets are the true natural numbers. Otherwise, the answer is no, and there is not much else to do.) Assume now that there are such cardinals, and that "large cardinal axiom" is something reasonable (so, provably in $\mathsf{ZFC}$, the relevant […]

Please send an email to mathrev@ams.org, explaining the issue. (This is our all-purpose email address; any mistakes you discover, not just regarding references, you can let us know there.) Give us some time, I promise we'll get to it. However, if it seems as if the request somehow fell through the cracks, you can always contact one of your friendly edit […]

Consider any club subset of $\kappa $. Check that it has order type $\kappa>\lambda $, and that its $\lambda $th element (in its increasing enumeration) has cofinality $\lambda $.

A very nice introduction to this area is MR0891258(88g:03084). Simpson, Stephen G. Unprovable theorems and fast-growing functions. In Logic and combinatorics (Arcata, Calif., 1985), 359–394, Contemp. Math., 65, Amer. Math. Soc., Providence, RI, 1987. Simpson describes the paper as inspired by the question of whether there could be "a comprehensive, self […]

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I'm posting an answer based on Asaf's comments. The following reference addresses this question to some extent: MR0525577 (80g:01021). Dauben, Joseph Warren. Georg Cantor. His mathematics and philosophy of the infinite. Harvard University Press, Cambridge, Mass.-London, 1979. xii+404 pp. ISBN: 0-674-34871-0. Reprinted: Princeton University Press, P […]