This week’s “Ask a ScienceBlogger” is an interesting one, but *very* tricky to answer.
The question was proposed by fellow SBer [Dave Munger:][munger] **”What’s a time in your
career when you were criticized extremely harshly by someone you respect? Did it help you or
set your career back?”**
I have to tread carefully while answering this one. It’s a good question, but it involves people who *could* be reading the blog.
Overall, I’ve been remarkably lucky in my career. For the most part, I’ve had excellent
mentors who’ve been kind and helpful, and I’ve done my best to listen to them, and not
screw things up badly enough for them to really tear into me. But no one in a research career can escape complete unscathed. So I’ve got my own war stories of the ways that I’ve been shredded. And the effect/outcome has varied enormously.
GM/BM has been pretty slow overall this week, both in new posts and in my responses to comments on previous posts. It was both bigtime deadline week on my project at work; and a very bad week for family health issues.
My dad, who I’ve mentioned on this blog a lot of times because of the fact that he’s the one who
got me started on math and geekery, has had some serious medical trouble lately, and he wound up
in the hospital this week with gangrene and a related blood infection. So I’ve been running to NJ to see him and help my mom, and back to NY to my own family and work. That hasn’t left much time for blogging, and
the time I’ve had, I’ve been rather distracted.
In particular, I really shouldn’t have posted part two of the sheaves posts. I’d just started writing it when I got the news about my dad, and I tried to just finish it up quickly so I could post it, and not leave part one hanging without part two. Unfortunately, the result showed how distracted I was. It’s definitely not up to the kind of quality that I aim for. When I have time, I’ll rewrite that one so that it actually makes sense.
Things should, most likely, be back to normal by next week. In the meantime, thanks for all of the votes in the blog awards! Last I checked, GM/BM was in *fourth place*! Coming in fourth in a group of people like
that is simple amazing.
Following in the footsteps of [orac](http://scienceblogs.com/insolence) and [PZ](http://www.scienceblogs.com/pharyngula) among others of my fellow SBers, I’ve taken the survey to find out which historical lunatic I am. And I must say, I’m pleased with the results! Which Historical Lunatic Are You? From the fecund loins of Rum and Monkey.
I’ve actually had a fondness for Emperor Norton since I first learned of him by way of Neil Gaiman’s Sandman comic. He was a silly, nutty old guy, but remarkable for his good nature, humor, and general goofy eccentricity. Something about his particular kind of nuttiness actually made me feel an affinity for him.
So just call me the Math Geek Emperor of ScienceBlogs from now on!
Don’t forgot: GM/BM is a finalist in the weblog competition for best science blog. I’ve got no chance of winning, but there’s a slim chance that I could make third or fourth. You can vote once per day.
Continuing from where we left off yesterday…
Yesterday, I managed to describe what a *presheaf* was. Today, I’m going to continue on that line, and get to what a full sheaf is.
A sheaf is a presheaf with two additional properties. The more interesting of those two properties is something called the *gluing axiom*. Remember when I was talking about manifolds, and described how you could describe manifolds by [*gluing*][glue] other manifolds together? The gluing axiom is the formal underpinnings of that gluing operation: it’s the one that justifies *why* gluing manifolds together works.
Suppose we’ve got a topological space. So far, in our discussion of topology, we’ve tended to focus either very narrowly on local properties of **T** (as in manifolds, where locally, the space appears euclidean), or on global properties of **T**. We haven’t done much to *connect* those two views. How do we get from local properties to global properties?
One of the tools for doing that is a sheaf (plural “sheaves”). A sheaf is a very general kind of structure that provides ways of mapping or relating local information about a topological space to global information about that space. There are many different kinds of sheaves; rather than being exhaustive, I’ll pretty much stick to a simple sheaf of functions on the topological space. Sheaves show up *all over* the place, in everything from abstract algebra to algebraic geometry to number theory to analysis to differential calculus – pretty much every major abstract area of mathematics uses sheaves.
While there’s nothing mathematical about this bit of silly woo, I couldn’t resist mocking it. There’s a Japanese inventor who claims to have created a device that instantly ages wine through a magical homeopathic-sounding process of magically restructuring water molecules.
For why I can’t resist… Well, you see, I’m a
bit of a wine nut, and I’m particularly passionate about one very special wine: vintage Port. The problem with vintage Port is that it’s pretty close to undrinkable when it’s young; it needs to sit and age for at least a decade; 20 to 30 years is better for a really good one. Buying it aged for that long is very expensive (I’ve paid as much as $210 for a particularly good bottle of 1970 port that I used for my Y2K New Years Eve party); and waiting for it to age in the basement is both frustrating and tricky. (If it gets too warm, it can be ruined; if it gets too damp, the cork can rot and ruin it; if it gets too dry, the cork can shrink and ruin it.) So anything that could *really* accelerate the ageing process without wrecking the wine is something that I would really love to see.
There are two links for this. First, [a short NYT piece](http://www.nytimes.com/2006/12/10/magazine/10section4.t-8.html?_r=2&oref=login&oref=slogin):
>As liquor ages, Tanaka explains, the water molecules slowly rearrange themselves more closely around
>the alcohol molecules, giving the alcohol its distinctive mature taste. Tanaka puts that process into
>overdrive. He pours the wine into a 70-pound container outfitted with an electrolysis chamber. A
>few-second electrical zap gives the wine a slight charge, which breaks up the water molecules and
>allows them to blend more completely with the alcohol. Voilà: Instantly-aged pinot noir, “smoother and
>more mellow than before,” Tanaka’s American partner, Edward Alexander, claims.
Pure bullshit. In wine, what you’re going for in the aging process is breaking down tannins. Tannins are
a compound that come primarily from the skins in red wines. When you drink a young red wine, and there’s a bitterish bite, and a sensation that the wine is drying your mouth, that’s coming from the tannins. Over time, some the tannins are decomposed, and settle out of the wine as sediments in the bottle. The end result is that there’s less of the hard biting tannin, and you can taste the wine. The big tradeoff is that the parts of the grape that give a red wine the most flavor are the same parts that contribute the tannins. So most good red wines are very tannic when young, and they need to be
aged for a while to allow enough of the tannins to break and settle.
As always, though, there’s some tradeoff. The organic chemicals that can give wine a fruity flavor
also break down as the wine ages. So if you like the fruity flavor of a wine like a good red Zinfandel (note the **red** in that statement!), you have to drink it young. The usual trick for that is to open the wine, and “let it breathe” – that is, let it sit open to the air for a while. The oxidation process that happens when you expose wine to air will start to break down the tannins, so that the wine will be less harsh.
None of this is magic; none of it has anything to do with any homeopathy-like woo about clustering water molecules around alchohol. It’s relatively simple organic chemistry.
So guess what these guys have done? They’ve invented a machine that bubbles the wine through a bunch of hoses with some air and passes electricity through it. The important part is “bubbles through a bunch of hoses with some air”. They’re just doing a quicker version of the “letting it breathe” thing, and attaching some silly woo to explain why you need their fancy expensive machine to do it.
Anyway – here’s the *real* prize. They did a [promotional *cartoon* about their gadget,][cartoon] complete with
woo-babble about charging water with “positive electricity” and wine (I think they meant alchohol) with “negative electricity” in order to make the water be attracted to and cluster around the alchohol.
In my last topology post, I started talking about the fundamental group of a topological space. What makes the fundamental group interesting is that it tells you interesting things about the structure
of the space in terms of paths that circle around and end where they started. For example, if you’re looking at a basic torus, you can go in loops staying in a euclidean-looking region; you can loop around the donut hole, or you can loop around the donut-body.
Of course, in the comments, an astute reader (John Armstrong) leapt ahead of me, and mentioned the fundamental group*oid* of a topological space, and its connection with category theory. That’s
supposed to be the topic of this post.
This was posted on slashdot, and forwarded to me by several readers. It’s worth listening to the first few minutes to get an idea of just how pathetically inummerate many people are. It might also help convince you to stay the hell away from *any* service provided by Verizon; my experience with them suggests that this is absolutely typical.
The basic story is that the guy who recorded this took a trip to Canada. Before he left, he checked with Verizon about how much it would cost him to use his cellphone for internet access during his trip, and was told that it cost 0.002 *cents* per kilobyte. But when the bill arrived, they charged him 0.002 *dollars* per kilobyte – 100 times the quoted rate. He then embarked on an odyssey of stupidity, trying to get someone at Verizon to acknowledge the fact that there is a *difference* between 0.002 dollars, and 0.002 cents.
[Go. Listen. Be amazed.][verizon]
So, Goodmath/Badmath was nominated for a weblog award for the best science blog. I was actually planning on ignoring it for two reasons. First, Pharyngula was nominated in the same category, and there is absolutely no way that I can *hope* to complete with PZ. And second, the Weblogs are kind of goofy, with very strange voting rules (for example, you’re allowed to vote once per day).
But people keep emailing me and asking why I haven’t said anything. So, if you feel like voting for this
blog, please do. Maybe I’ll manage to come in third or fourth 🙂
And many thanks to the folks who nominated me. It’s really nice to know that people have such a positive opinion of my blog. It’s incredibly flattering to be nominated alongside people like PZ and Phil.