## Intel STS: Liveblogging day 2 March 12, 2010

Posted by Akhil Mathew in General.
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I’m going to try liveblogging (insofar as possible) a science fair.  [9:24- It’s now pretty clear that what I’m doing is more like deadblogging.  Still, it’s better than nothing, I suppose.]

(9:45) So I’m at the 2010 Intel Science Talent Search in Washington, D.C.  Presumably many of the folk that come across this blog will have heard of it; it’s a science competition for high school seniors.  There are seven people from RSI here this year.  I’ve also met many interesting people among the other finalists for the first time, all of whom seem to be rather beastly.  Everybody arrived yesterday–I took the train–but nothing competitive actually happened.  Today, we will be judged by a panel of ten or eleven scientists and mathematicians who are going to ask us general questions about science in general, and not our projects.  My first interview is in about half an hour, so I’m basically procrastinating by writing this entry, if there was anything that I could do to prepare :-).

In any case, it was pretty cool to find that I’m in a room that has a TV in the bathroom.  The hotel is ridiculously fancy.

After this, I’m going to go back to random Wikipedia surfing about diverse scientific topics.   They told us this morning that the judges want to see the scientific process rather than technical knowledge–perhaps this is a license for me to babble?  I’ve always enjoyed idle pontification.  In any case, I promise more later after my judging interview.

(11:31) OK, phew.  My judging interview (and recounts thereof to many fellow finalists) is now complete.  I don’t know if I’m allowed to say who the judges were, but two were doctors and one a mathematician.  The doctor went first and asked me to explain why when one flies (at 35000 ft) 80% of the atmosphere (by mass) is below you.  Uhhh….I was confused.  I’m not really all that solid on physics (took AP Physics B freshman year, haven’t thought about the subject since with any success).  Anyway, I have to figure out the problem by Sunday, where he’s going to ask me it again.  Next the mathematician said that she was going to ask me LOTS of questions about my project (hopefully a good thing).  She then asked me to explain why representation theory was interesting to her two nonmathematical colleagues.  So, I started babbling at full speed.  I started with the remarks that “representation theory is how algebraic objects act on vector spaces” and mentioned how it reveals information about the objects themselves (mentioning Burnside’s $p^aq^b$ theorem).  She asked me to go back to what I said, and I said that the tools of linear algebra are much easier than studying complicated algebraic objects directly.  I said that the classification of finite simple groups was something like 10000 pages in length.  I then started to say that group representations were useful in chemistry and Lie groups and Lie algebras in theoretical physcis (but freely confessed my ignorance of said subjects).  I said that the representation theory of Lie algebras was interesting itself, which is where I was cut off.  I was posed some fairly simple combinatorial problem about  The next person asked me about stem cells. I told her that I knew about stem cells but couldn’t tell her the difference between adult and embryonic stem cells.  Anyway, I was next questioned about the ethical and scientific issues in transporting stem cells from her to me.  I suggested that there were potential incompatibilities (like blood types).  Our time soon ended and she concluded by saying that I was on the right track.  Probably not horrible, for a math person at least.

I then had my picture taken.  All the finalists have to do this today.  My next interview’s after lunch.

(3:11) I just got back from my second judging interview.  The interviewers included a distinguished astronomer, who went first; she opened with a question about what latitude and longitude was.  I said that they were a system of coordinates on a sphere minus the two poles.  I said something about their being an injective immersion, which may or may not have piqued their interest (none of them was a mathematician).  She then asked why astronomers would use them, to which i replied something about “objects being spherical.”  Next, she asked me to tell me what I knew about the universe—which has to be by far the broadest question I have received all day.  I babbled mildly about the four main forces and that they could be described by mathematical laws, sand omething about the age of the universe and its expansion.  This is all very rudimentary, but I don’t know anything about astronomy.  The next interviewer asked me why France would launch satellites from New Guinea; I suggested it was closer to the equator, but didn’t realize that the explanation for that was simply that the earth’s rotation provided additional speed.  (Whoops.)  I was then asked how one might determine whether switchgrass was an efficient fuel (including environmental concerns); I suggested that would one have to compute the total expenditure (i.e. of the land deforested, inputs of irrigation, fertilizer, fermentation, etc.) and compare the obtained energy per unit cost to the analog for, say, coal.  My questioner pointed out that I should have determined the energy inputs of the tractor and taken them into accouont.  Finally, he asked me the following math problem that I embarrassingly failed at: given 248 arm-wrestlers, how many matches would it take to determine the best one?  I said something like $\mathrm{log}_2(248)$ given that an elimination  process was optimal.  This is wildly wrong, of course, because there are roughly $\mathrm{log}_2$ levels, each of which (except the last) contains omre than 1 match.  So he said there was a trivial solution and asked me to work out how many matches would be necessary.  After a short computation I arrived at…247.  Which is utterly trivial, because there must be one loser per match, and 247 losers.  The judges laughed and said they had enjoyed the time; I am not sure whether that was necessarily a good thing.

(9:24) I’ve now had my third judging interview and a very enjoyable dinner.  The first person at the third judging interview started by immediately asking me the probability that a function $f: A \to A$ where $A$ has cardinality $n$ has no fixed points.  The answer is (rather trivially) $(n-1)^n$, but for some reason it didn’t occur to me over several minutes as I babbled about inclusion-exclusion and inductive proofs.  Next the same judge asked me the same for $f: [0,1] \to [0,1]$ continuous, which is an easy application of the intermediate value theorem; it’s also a special (and relatively easy) proof of the Brouwer fixed point theorem.  He asked me whether the same was true for the circle; I said no, a rotation would do the trick.  He asked whether it was true for $D^2$ (unit disk in $\mathbb{R}^2$); I replied that it was the Brouwer theorem, which he then asked me to prove (in that case).  I gave the usual proof using singular homology (which he said was allowed); I actually sort of half-alternated between talking about the fundamental group and that.  (If you haven’t seen it, cf. any book on algebraic topology.)

The next judge then told me that the chair he pointed to in the back of the room was magical and could take me 1 million years in the past.  I could take three things wit h me, and I had to decide.  I said that I’d take a weapon to defend myself, fertilizer to help grow food, and textbooks to entertain myself (I really couldn’t resist the last part).

The third judge in the panel asked me about gases.  He inquired about what would happen if a box of gas had its volume changed (temperature kept constant); I remembered enough basic chemistry from sophomore year to explain the ideal gas law.  He asked me about the deviations from the ideal gas law.  I said that they were caused by van der Waals forces and other intermolecular attractions, though I couldn’t remember enough to say it well.  The 15 minutes were up, but they said it was a good interview.  Dropping algebraic topology references was probably a good idea, though the brain-freeze on a baby problem was embarrassing.

I next went to dinner, which included the other 39 finalists, the judges, various SSP people, and a couple of Intel alumni who had distinguished themselves.  One of them was Roger Tsien, who said that his obsession with producing pretty colors in chemistry experiments was part of his motivation to study fluorescent proteins.  Tsien gave an amusing recount of his life story and major discoveries.  The other was an aerospace engineer from MIT  who told us that each of the finalists get an asteroid named after him or her.

I’ve got one more (nonmathematical) interview tomorrow.   On Sunday, we’re actually going to talk to the judges about our projects.

(10:38) A conversation with David Liu just made me realize that I omitted a part of the third judging interview.  In particular, a doctor asked me to name a letter from A-Z (which, upon asking, was inclusive of the endpoints).  I picked “A” and was asked what the adaptations of aardvarks are; I said something about their fur and warm-bloodedness.