Last night, there was a terrible thunderstorm in Chicago; I’ve never seen so many trees on the road! I was supposed to land at Midway at 7:30pm last night, but we were diverted to Indianapolis, so I didn’t land in Chicago until 2:00am, and then I waited until 3:00am to get a taxi, so I didn’t get home until almost 4:00am. Crazy!

My house lost power last night, and today some places are still without power. In particular, Co-Op Market’s 53th street store was closed, merely displaying a sign “Closed No Power Mgmt.” Considering that their 47th street store shut down, and that their 55th still (?) lacks price scanners, I can only expect that this power outage is the final blow to Co-Op.

In contrast, the also-powerless-but-superior Hyde Park Produce Market was using a generator to power their cash registers (and to provide one very bright light in an otherwise dark store).

My cell phone still works, even after being dropped into water.

I’ve spent a lot of time constructing languages (Kisonef and Naedari being my favorites); in a similar vein, I also tried to create a language that an alien civilization would be able to understand. I had hoped to put a message written in my universal language in a conspicuous place (say, on a college campus), just to test if what I made really was understandable, even to humans!

But I never got around to that, and plenty of other people have done exactly that. This is related to the following question: state and prove a theorem in such a way that an alien would be able to follow your proof.

But whoa! I found out that Freudenthal (the mathematician) did the same thing: he created LINCOS. Bizarre. I also enjoyed looking at this image that we sent into space and trying to imagine what the aliens must think of people who write with such strange characters.

I’m fond of the Pineapple Sauce Pancake graph: the vertices are English words, and there is an edge from $a$ to $b$ if $ab$ is also an English word (e.g., “pan” and “cake” are English words, and there is an edge from “pan” to “cake” because “pancake” is also an English word).

To play around with this, I wrote a Javascript program, complete with a Web 2.0 logo–which reminds me, I wonder if there is an interpreter for the programming language logo, written in Javascript?

Anyway, what I really wanted to do was to make a wall-sized picture of the Pineapple Graph, but Graphviz isn’t quite able to handle it, but maybe with some tweaking, I’d be able to produce a beautiful poster.

There are some questions about outer space that I would like to be able to answer. Some nice survey articles look to be:

Bestvina, Mladen. The topology of $\rm Out(F_n)$. 2002. 373–384. MR.

and also:

Vogtmann, Karen. Automorphisms of free groups and outer space. Geom. Dedicata 2002. 1–31. MR.

Here is a ridiculously simple question I have wondered about: given $A, B \subset F_n$, say with $[F_n : A] = [F_n : B]$, how can I tell if $A$ and $B$ are conjugate? I suspect I’m being stupid here.

In light of my recent comments on LINCOS and communiating with extraterristrials, I found an article:

Ruelle, David. Conversations on mathematics with a visitor from outer space. 2000. 251–259. MR.

Putnam also makes use of the idea of mathematicians from other planets, to more philosophical ends.

Today in Geometry/Topology seminar, quasihomomorphisms $\Z \to \Z$ were discussed, i.e., the set of maps $f : \Z \to \Z$ such that $| f(a+b) - f(a) - f(b) |$ is uniformly bounded, modulo the relation of being a bounded distance apart. These come up when defining rotation and translation numbers, for instance.

Anyway, Uri Bader mentioned that these quasihomomorphisms form a field, isomorphic to $\R$, under pointwise addition and composition. I hadn’t realized that this is a general construction. Given a finitely generated group (with fixed generating set, so we have the word metric $d$ on the group), I can define a quasihomomorphism $f : G \to G$ by demanding $d(f(ab),f(a)f(b))$ be uniformly bounded, and where two quasihomomorphisms $f, g$ are equivalent if $d(f(a),g(a))$ is uniformly bounded. Let’s call the resulting object $\hat{G}$ for now.

What can be said about $\hat{G}$? For instance, what is $\hat{F_2}$?

I wonder if anyone knows about alphabet songs in other languages? I’d be particularly interested in knowing about Greek and Hebrew alphabet songs, and a bit about the history of such things. It seems like these songs must be used primarily to teach the lexicographic ordering of the letters; I suppose the Latin alphabet is ordered in keeping with the Greek alphabet, and so forth, but why did the early alphabets get placed in the order that they did? Saying “numeric value”just begs the question (after all, then why those values?).

It also seems a bit odd that Twinkle Twinkle Little Star is song for the alphabet. It also seems like the alphabet song should be related to the zed/zee distinction.

And not too surprisingly, Wikipedia has an article about the Alphabet Songsong). Wikipedia knows too much (although they are still missing an article about superrigidity!).