Semantic Compositions

How long is thirty minutes?

Radagast has put up a worthwhile summary of an article from the Journal of the American Medical Association supporting the idea that some exercise is better than none, even you don't make the mythical 30 minutes five days a week (I seem to recall reading three times a week in the past, but his link goes right to an official U.S. Government source, so who is SC to argue?). The study demonstrates -- at least in the case of postmenopausal, overweight women -- that even getting half as much exercise as is allegedly necessary has significant health benefits. So go get on an exercise bike while you read the rest of this post.

Now, the study doesn't actually measure things in terms of "minutes per week", except incidentally (not that the figures weren't tracked, but that's not how exercise regimens were prescribed). As you can see in the graphs Radagast put up, the groups in the study were segmented by the number of calories per kilogram per week that each person was assigned to burn. So a person weighing 170 pounds (77 kilos) would have to do 308 calories worth of exercise if they were in the 4 kcal/kg group, 616 in the 8 kcal/kg group, and so on. Keeping in mind that the 8 kcal/kg group is the one corresponding to 100% of the recommended weekly exercise, that means that our hypothetical 170 pound person would have to work out at a rate of 246 kilocalories per hour if they were to exercise for 30 minutes 5 times per week. That's not an especially hard workout. And frankly, even if you cut it to 3 times per week, that only gets you to 412 kilocalories per hour, a rate which only moderately impairs SC's ability to simultaneously carry on a phone conversation. On the other hand, who said you should be able to talk on the phone while working out?

That brings us to the point about language here. Before writing this post, your host discussed with Radagast the problem of specifying just how hard the workouts are. The phrasing of exercise requirements in units of time obscures the fundamental issue about how many calories one actually is burning, a number which is admittedly hard to measure directly (that's a point Radagast encouraged your host to make). SC has used numerous exercise bikes from different manufacturers, which vary by as much as 20-30% in their estimates of caloric expenditure for what feel like subjectively similar intensities. So the number you get from the equipment may not actually be all that useful as a guide, and telling people to work out for a certain amount of time might be about the best you can hope for. On the other hand, it's also painfully clear from SC's daily trips to his gym that his idea of a 30 minute workout is very different from many other people's. It's not uncommon for your host to brutalize himself at rates that his preferred bike estimates at 700+ kilocalories per hour, only to look down the aisle and see other people merrily plugging away at the lowest setting the bike has to offer while yapping on their cell phones or reading a book.

This problem of specifying amounts of exercise in terms of time reminds SC of another of his great pet peeves about indirect measurement in English. If someone tells you that a hotel is "15 minutes" from an airport, you have no way of being sure if they're adjusting appropriately for local traffic conditions. 15 minutes might be 15 miles in Flagstaff,  5 miles in Las Vegas, and about 1.5 miles in Los Angeles. It is your host's opinion (unsupported by anything beyond subjective impression) that people often implicitly use an estimate of 60 miles per hour when making such statements, since that neatly converts into 1 minute per mile.

None of this is to say that the scientists involved set out to be misleading when they reduce their exercise recommendations to units of time. As we've discussed, it's hard to be sure of exactly how hard a workout you're doing, and it certainly isn't reasonable to expect every gym to have a physiologist on staff to take accurate measurements of your oxygen uptake levels. But the fact that calorie burning is hard to measure directly doesn't mean that it's hard to figure out whether or not you're doing a serious workout. The next time you tell yourself that 30 minutes ought to be enough, ask yourself just one question -- are they 30 minutes worthy of the name?

Megatron's language acquisition problem

Last night, SC went to see the new Transformers movie, which he had been waiting for nervously ever since the trailers first came out last year. The nervous part came mostly from the involvement of Michael Bay, who has somewhat less than a stellar reputation for story and character development, albeit a great reputation for explosions. He lived up (or down) to many of these expectations, but in a surprisingly pleasant way, and your host has no patience for all of the "he's ruined my childhood" laments to come out of some of the more obssessive fans of the original series (although SC confesses to having feared such things going iin). If you doubt the obsessive nature of the fans involved, have a look at the Wikipedia entry for the movie, and ask yourself, "Why does this article have so many more references than Wikipedia's entries on quantum mechanics, the Protestant Reformation, and the Battle of Hastings? Combined? Times 10?"

Rather than providing a spoiler-laden review, though -- which is not to say that spoilers don't follow, and you've been warned -- SC wishes to focus on a language acquisition issue which is never properly addressed in the movie -- and the movie does address language acquisition, as Optimus Prime is asked how the Autobots (incidentally, given a retconned etymology) learned English. His reply, "From the World Wide Web". While no explicit learning mechanism is provided, it's fair to assume that robots that have already mastered interstellar flight and the ability to reconfigure their bodies to imitate any object they happen to scan have long since figured out grammar induction from unlabeled data (and maybe they happened across the Penn Treebank during their studies).

No, the real problem comes with the question of specifically how Megatron learned English. It's no great spoiler to mention that unlike all of the other Transformers, he's been kept on ice -- literally -- all the way up until he is freed to take place in a climactic battle near the end of the film. And yet, moments after being thawed out, he is able to announce "I am Megatron!", which requires at least some knowledge of English (shortly afterward, he utters something less corny, and considerably more classic to fans of the original series, which SC will only note demonstrates that he's aware of time expressions as well).

Here's what we know:

1) The movie subscribes to the modularity of mind, as demonstrated by the fact that Megatron's navigation systems are able to be woken up without activating the rest of him.
2) He has been around humans speaking language (they've been studying him daily for 70 years), but this does not preclude arguments about poverty of the stimulus, because the humans were all grown adults, who presumably rarely if ever critiqued each others' language use. (SC does not buy into POTS himself, but it's unarguable that Megatron has been receiving only a very specialized sort of linguistic input.)
3) He has almost certainly not been plugged into any sort of network connection (no definitive statement is offered, but great measures are taken to keep him frozen and unpowered), and so even if his language module was adequately powered and functioning, he did not have access to a text corpus like the Autobots did.

All of this would seem to indicate that it is impossible for Megatron to speak English, at least immediately on waking up. And yet he does. There is one remaining possibility that explains this. The other Decepticons are shown communicating in a language we are given to understand is Cybertronian (although not explicitly labeled as such), and they are also clearly able to communicate with each other by radio (such a discussion is shown in the movie). It is entirely possible that one of them, after establishing the needed radio connection to Megatron, simply uploaded the needed configuration parameters (thanks, Chomsky, now look what you're responsible for) for his language module to him, although why they would expect him to care about communicating with humans is a mystery with no obvious answer of its own.

Of course, thinking about such things loses what makes the movie so much fun: giant robots beating the crap out of each other and destroying much of downtown Los Angeles in the process. SC is eternally grateful to Michael Bay for that glorious sequence, which was far more plausible (and desirable) than the similar (but thoroughly ludicrous and unfortunate) destruction of downtown San Diego by dinosaurs in the second Jurassic Park movie. Now, let's get started on the really important details, Mr. Bay. Where's Laserbeak? And Frenzy isn't a boombox. And Devastator isn't a tank...