Before all the recent airport troubles, I took a trip to Maine using JetBlue's new JFK -> Portland route. For the second time I accidentally brought a leatherman multitool with a knife in it in my carry-on bag and it went undetected on the way out, then was found and had to be confiscated on the way back. The last time I did this was on a business trip to Newport Beach, CA. Both times the security people explained my options to me, although they were more thorough this time--I could put it in a checked bag (but I didn't have another one I was willing to check), I could leave it with someone who wasn't traveling and was still waiting for me (didn't have anyone), I could mail it to myself (but the store at which I can do that was already closed), or I can surrender it to the US Government and it will be "destroyed." They were much nicer this time--at John Wayne airport in CA they told me after measuring the blade that it was "damn near a misdemeanor" and that they "really frown on this sort of thing." They seemed to think I was trying to see what I could get away with for fun. At Portland they simply explained the options, I made no argument since I knew what was coming, and he said "cool."

More remarkably, I managed to bring my Espion S digital camera that's disguised as a Zippo lighter in my pocket on the way out without even thinking about the security implications. In most circumstances this is a device that's suspicious disguised as one that isn't, but at an airport it suddenly becomes an innocent object disguised as contraband. I stupidly walked through the metal detector with it still in my pocket and set it off. When I reached in my pocket I thought, crap, but decided the best thing to do was take the camera and the lighter case apart and put it through the X-ray machine that way. The screener on the other side looked it over for a bit, and said "Originally I thought you had already had a lighter confiscated, because we let people keep the cases and just take the inner parts." He also said "Thanks for taking it out and apart like this, otherwise we would've had to do a bag search. Evidently you've been through this before." Uh, right, yeah, I said.

On the way back I thought about putting the camera in a checked bag, but I didn't want to take the chance that it would be seen as suspicious by an agent at the checked baggage X-rays while I was on my way to the plane, and be confiscated without my knowing until I got home. So I carried it through again. The camera was taken off the X-ray conveyor belt and 5 or 6 screeners gathered around to look at it. Maya couldn't believe what a troublemaker I was. When my leatherman was found, it fortunately didn't seem to create any compounded suspicion in the screeners, but it did distract me so much that I started walking to the gate while they still had the camera, and they had to page me back on the PA. When I went back the screener who had the camera was very nice; he asked me where I got it, and said it was totally fine but that I shouldn't be surprised if it causes delays next time, due to looking like a lighter. Yep.

But now to get to the actual point of this entry, by now a subject of some debate in this household, which debate I will present here. While boarding a plane, I often hear flight attendants on the PA announce "We have a very full flight today..." And other times, such as on the flight back from Portland, they say "We have a full flight today." When they say it in the latter way, I interpret it as meaning that all the seats on the plane are reserved. When they say it with 'very', and this is where you may disagree, it means to me that almost all the seats are taken.

What's happening here, assuming I interpret the 'very' form correctly, is that there are two different meanings of full--one absolute, and one relative. For example, the word 'unique' has the first definition:
1 Being the only one of its kind.
But definition 3b, now much more common in American usage, is:
3b Informal. Unusual; extraordinary.

It's my contention that the same thing is happening to 'full' in this case. My reason for saying so is that clearly 'very' does not make sense as an intensifier if 'full' is being said in the absolute way, because practically speaking, the airline would never intentionally let more passengers on board than there are seats. It is possible that by "very full" they mean the same as "[absolutely] full", that all the seats are taken. But since I sometimes hear them say it as simply "full," it does seem that at least some of the time they just say that to mean all the seats are taken. The only meaning that remains is that not quite all the seats are full. I don't remember looking around on any specific flights when this was said, but I believe this is the meaning usually intended by "very full." If this is true, we can then say that "very full" means the same thing as "not full," even though it's really two different meanings of 'full.' But I do accept the possibility that sometimes they mean "absolutely full" when they say "very full." Does anyone have anecdotal evidence one way or the other? My next air travel is planned for early September, so I'll have my eyes and ears open.

I really need to get a good introductory book on mathematical topology. Ideally one for laymen like "A Brief History of Time" did for physics, but I don't know if such a thing exists. Every time there's a story in the news about an advance in this field, it makes no sense at all to me. For example, the recent stories about the proof of the Poincare conjecture, and the subsequent refusal of the Fields Medal. From the first Times article about it:

To a topologist, a sphere, a cigar and a rabbit�s head are all the same because they can be deformed into one another. Likewise, a coffee mug and a doughnut are also the same because each has one hole, but they are not equivalent to a sphere.

Okay, certainly a strange way of looking at things, but so far I'm with you.

In effect, what Poincaré suggested was that anything without holes has to be a sphere. The one qualification was that this "anything" had to be what mathematicians call compact, or closed, meaning that it has a finite extent.

Alright...

In the case of two dimensions, like the surface of a sphere or a doughnut, it is easy to see what Poincaré was talking about: imagine a rubber band stretched around an apple or a doughnut; on the apple, the rubber band can be shrunk without limit, but on the doughnut it is stopped by the hole.

When did we start talking about being able to shrink things without limit? And how do spheres and doughnuts exist in two dimensions? Or is it just the rubber band that's in two dimensions?

With three dimensions, it is harder to discern the overall shape of something; we cannot see where the holes might be.

What? Now I'm picturing a mathematician bent over an apple or a sponge, turning it over and over in his hands, shouting "Damn this conjecture! Where are the holes?" But evidently since we were talking about an apple as being two dimensional before, we're now really talking about four-dimensional objects:

...when we envision the surface of a sphere or an apple, we are really seeing a two-dimensional object embedded in three dimensions.

And at this point I've pretty much checked out. Now I admit this may be an issue of the mainstream press's understanding and reporting of science as much as anything else. It's probable that a topologist would pick this account apart the way the guys at Language Log do any article that contains a single sentence or more that appears to make a claim related to linguistics. But I wouldn't have any chance at understanding the primary sources, the academic papers, so this is pretty much what I'm stuck with, unless anyone can show me a topology version of Language Log.

For quite a while I periodically puzzled over the Four Color Map problem, which stated (as I had heard it) that you never need more than four colors to have a map with no adjacent territories having the same color. I couldn't understand whether this referred to maps of the real world, or abstract maps with any conceivable layout of territories. Of course it would be odd for mathematicians to be concerned with the real world, but I couldn't see how it could be true in the abstract, because I assumed the real-world rule held that territories can be non-contiguous (imagine how many colors you would need on a world map that shaded embassies as part of the countries they represent). Finally a coworker informed me that they have to be contiguous, and that they have to share a side, not just a point. I then spent much of a day drawing shapes, trying unsuccessfully to find a counterexample, then being amazed when I realized it was true.

The New Yorker has an article on the web about the Perelman affair, and it includes in the 13th paragraph a similar but much better explanation of basic topology concepts than the Times article I criticized in the previous entry. In fact the similarity of the description, using the same examples of bagels or donuts and coffee cups and rubber bands, makes me think that both came from the same source, perhaps a textbook, or a sheet that's passed around by journalists who have to write about difficult topics, and the author of the Times article tried to compress it a bit too much, or just not very well. The New Yorker sometimes makes unintentionally humorous statements about technology, such as the sentence "There were at least a hundred billion numbers in the shopping bags" referring to bags full of CDs in the Unicorn Tapestries article. But often they do a very impressive job with technical descriptions that are clear to technically oriented readers without alienating the non-technical ones.

On the L train last week there was a young woman who had earrings with a name spelled out in metal across a circle. When I looked at them for a few seconds I was quite surprised at the name's spelling: Regecca. Immediately I wondered if that was really her name, or if it was a mistake and her name was Rebecca. But if it was a mistake, why would she wear them? And if it wasn't a mistake, how the hell did she get earrings with that name on them? They looked like very typical, fake golden, stamped out, mass-produced earrings.

Googling produces 1,290 results, many of which are random lists of words or obvious misspellings like Regecca Romijn. One result is in the backstory of a character on a Dungeons & Dragons website. In the first 40 results there are 6 that appeared to be names of real people. There's also this doll named Regecca, which perhaps indicates that it was slightly less rare in Victorian Britain (now that I've repeated it to myself enough times it is starting to sound rather aristocratic). I wasn't able to find it in any national name databases; the ones I checked only include the 1000 most popular names.

So the most likely explanations I can see, in descending order of likelihood, are that a) the earrings were custom-made, despite not looking it... Well, that's really the only explanation I can imagine. The chance that they were either mass-produced on purpose or as a mistake but then still sold somewhere, and that this woman then obtained them either because they matched her name or despite the fact they didn't, seems vanishingly small. Any other possibilities?