Sowing the Seeds of Mathematics

The seeds were sown early.

I was sitting in Somerville's SCR, reading Steve Strogatz's "The Calculus of Friendship", when I suddenly recalled an old incident from 1st grade that I hadn't thought about in years.

I'm sure I'll get some of the details wrong, but here is what I remember (which unfortunately doesn't include many specifics): We were doing subtraction of numbers, and on occasion we were asked to subtract a larger number from a smaller one; e.g., writing down the answer to "3 - 5" would be a typical problem we had to solve. In such cases, the "correct" answer that we were expected to write down was "not defined" or "doesn't make sense" or whatever. That is, of course, bullshit---and unfortunately for my 1st grade teacher, I had encountered negative numbers somewhere and already knew it to be bullshit. (I wish I could remember the source. My best guess based on what I was reading at the time would be that I saw it in some magazine article about baseball. I certainly learned several other pieces of mathematics, such as decimals versus fractions, from baseball calculations before I ever saw anything like them in classrooms.) So on my assignment, I included negative answers at appropriate points. When these were marked with an 'X' to indicate that they were "wrong", I openly challenged my teacher (which all educators appreciate! :P ) and attempted to explain why it was correct. She made some comment along the lines of not being able to have -2 apples (I don't remember if it was apples or some other object, but my memory is suggesting "apples" as the likely example), and my counter-argument was the standard one of the concept of owing 2 apples. She would have none of that, and I have a vague memory of things escalating to the point that she had to call my parents (which, of course, they appreciated greatly). I also have vague memories of the other 1st grade teacher taking her side and my having to argue my point against both of them, but I'm not sure about that part either.

Anyway, I am confident about my memory that the argument was lengthy and public, and also about the fact that I was stubbornly insistent that I was right and my teacher was wrong (and, in particular, that I refused to concede the point---except that I did subsequently and grudgingly write their version of the "correct" answer on things just so I wouldn't lose points). I know that the argument escalated, but I'm not confident about the '2 on 1' bit with my arguing against both teachers and I'm also not confident that the argument reached the point that my parents had to be called about my bad behavior.

OK, so what seeds were sown here? I don't actually think it's horribly uncommon for somebody to encounter and then understand negative numbers on their own---it is an obvious concept, after all---and that's especially true when one considers the subset of people who choose subjects like mathematics (and other quantitative or scientific areas) as a career. The early signs that we really see here are my extreme stubbornness---and I can recount tons of other incidents that demonstrated when I was essentially (but not literally) arbitrarily young and the fact that I learned very early on that I could be right and my teachers could be wrong. (One could argue that I learned how to disrespect authority early on, but it was really more of a lesson to not assume that the authority was right by virtue of the fact that they were supposed to be the relative "expert" on the topic---or at least that they were supposed to know more than me.)

This was actually the second of four incidents I recalled in immediate succession---the difference is that the first, third, and fourth ones are ones that I have never forgotten, whereas I think the last time that I thought about this second one might well have been before I started college (or certainly not long after that). The first one involves my figuring out multiplication on my own in kindergarden, the third involves my father's $100.00 math challenge (when I was a very young age, but I can't precisely remember how old I was) from a problem he saw in the Los Angeles Times that he only gave me because he seriously underestimated me and didn't think I had a chance to get it right. (He was a bit shocked when he then had to keep his word and fork over the cash. I guess he could have gone back on what he said, but that wouldn't have looked good.) The fourth incident also occurred in 1st grade, and that was my refusal to say the pledge of allegiance because of the presence of the words 'under God'. That one also led to a public argument with my teacher, but I ultimately resolved that one by just opening and my mouth without saying anything at the relevant point (and lip-syncing during the rest of it) and hoping that the teacher just wouldn't notice. I didn't find out until I got to high school that it was actually illegal for the teacher to force me to say the pledge. (There were also a couple of incidents in high school about my refusal to say the pledge, but those were with fellow students rather than teachers.)

I guess the title of this post is a bit misleading (because this type of thing can be construed as mostly independent of mathematics), but this type of stubbornness and nature can be seen all the time these with my career choice---and this type of stubbornness is rather useful for scientific endeavors, behavior during seminars, etc.

Alright, I better get back to work. This post was a lot longer than I intended.

(And, yes, I already was that much of a pain in the ass when I was in 1st grade. I suppose that that will surprise very few of the people who know me.)

Alternative Meanings for WTF?

One of my TAs for my nonlinear systems course sent me the following e-mail this evening:

Some students write 'what to show' at the beginning of questions as WTS, but there is one student in B8b who has abbreviated 'what to find' at the start of her questions as WTF. Or at least I hope that's what she meant!

Oh dear...

Gruesome Wiener Attacks

You don't believe me? Just take a look at this article. As if the Kansas City Royals needed more problems...

(Tip of the cap to Rob Neyer.)

Tales from the arXiv: Self-Propelled Hard Rods

This paper caught my attention because of its title:

\\
arXiv:1002.3831
Date: Fri, 19 Feb 2010 21:47:54 GMT (74kb)

Title: Nonequilibrium Statistical Mechanics of Self-propelled Hard Rods
Authors: Aparna Baskaran and M. Cristina Marchetti
Categories: cond-mat.stat-mech
\\
Using tools of nonequilibirum mechanics, we study a model of self-propelled
hard rods on a substrate in two dimensions to quantify the interplay of
self-propulsion and excluded-volume effects. We derive of a Smoluchowski
equation for the configurational probability density of self-propelled rods
that contains several modifications as compared to the familiar Smoluchowski
equation for thermal rods. As a side-product of our work, we also present a
purely dynamical derivation of the Onsager form of the mean field excluded
volume interaction among thermal hard rods.
\\ ( http://arxiv.org/abs/1002.3831 , 74kb)


Comment: Not necessary.

The World is Irrational

In his latest opinion article, Steve Strogatz writes about the fact that the world is irrational.

Also, his article links to this lovely exchange with a customer service representative, which unfortunately hits way too close to home. Just remember that units are important, and apparently that many people find both units and decimals to be confusing.

Update (2/23/10): Apparently, the comments written by readers of Strogatz's article, which I am told express profound disbelief and taking offense at his statement that 1 = .9999999999 (with the 9s repeating ad infinitum), are only supporting just how little people know about mathematics. (Disclaimer: I haven't read these reader comments; I was only told about them. I don't even want to look because it's just going to depress me. Hence, I am purposely qualifying my phrasing to indicate that I am taking somebody else's word for what these reader comments say.)

Depeche Mode concert

I went to the Depeche Mode concert last night; the last time I saw them in concert was in spring 2006 at Coachella. The time before that was in fall 2005. This was the third time I've seen them, which is the most I've seen any artist. There was some seriously cool stuff yesterday, although nothing quite on the level of the stripped-down version of "Shake the Disease" or the 100,000 people singing along to "Enjoy the Silence" at Coachella. The version they played of "Personal Jesus" to close the show was sweet---they started with a long acoustic introduction and then switched to the conventional version. There was also seriously cool stuff with "Policy of Truth" and (because of the audience!) "Home". They played "It's No Good", which pleased me greatly because I really wanted to hear that song live after they forwent it at the other two concerts. Sadly, they didn't play "Strangelove", even though that has often showed up among the encores during the current tour, and I am still waiting to hear that song (one of my all-time favorites) live. I've waited 23 years thus far, as I can handle waiting for a couple more years. I still haven't heard "People Are People" live yet either, though I have the sneaking suspicion that that is not one of the band's favorite songs. Here are the set lists from the current tour.

I got home from London at about 2:15. I was exhausted but exhilarated.

Other details: I went to the concert with Nick Jones and his partner Jane. Our seats were awesome, as we had the front row in our section, so we never actually had to stand up to see. Earlier in the day, I met up with Jit Kee, a classmate from Caltech and one of my best friends.

Now I've seen everything

In my tutorial that finished about 30 minutes ago, a student actually fell asleep while presenting a problem on the white board. He slid gradually down the board, hit his head on and de-attached the part that holds the markers, and proceeded to slide down onto the floor, where it took a couple of minutes to wake him up. (He seems to be alright, by the way. He's currently resting and the plan is to get him a taxi or something to take him home after he's rested up.)

This actually beats the time that Aaron Kuzin fell asleep in Phys 1 and was snoring really loudly for the entire lecture. (The prof was giving him dirty looks the entire lecture and those of us who were sitting near him couldn't stop giggling.)

Living Bum RPG

I shit you not. This is a real role-playing game. Though the content seems rather insensitive, it seems that many of the proceeds are going to help the homeless, so I am intrigued by this.

(Tip of the cap to Louis Wang.)

See Also: RECURSION

Here is the latest entry in my photoblog.

Reducing the Eurocracy for Research Funding in Europe

Well, at least we can try. Here is a petition to sign whose goal is to do that. Assuming that you believe in reducing the amount of red tape to try to get research funding in Europe, please sign this petition.

It's a Rankmaniac, Rankmaniac (on the Floor).

Apparently, some Techers will benefit from some sort of "Googlebombing" competition (I'm not sure if it's a Google competition) based on how many people link to their entry.

That's the purpose of this blog entry. Booyah!

Their entry is meh, in my opinion.

Blast from the Past: 2007/2010 edition

I only read this blog post 2.5 years or so after it was written. I guess it's not too insulting (and the insults seem to be implied rather than stated anyway), and the only form of disagreement I can really offer would be to nitpick at details (which doesn't seem worthwhile, given that this was written so long ago). The main detail at which I can reasonably nitpick would be to point out that multiple close friends of mine were still at Caltech in 2003, which completely justified my continuing to visit!

Don't sing "My Way" at Karaoke Bars in the Philippines

It might not be as dangerous as playing "Tarzan Boy" at Caltech, or as dangerous as playing "The Ride" at Caltech, or even as dangerous as playing "Hotel California" in the Caltech Coffeehouse (well, at least with certain people behind the counter), but apparently singing Frank Sinatra's "My Way" can lead to life-threatening situations at karaoke bars in the Philippines.

(This link is courtesy of the new mini-AIR mailing.)

Best. Fan letter. Ever.

Twins reliever Pat Neshek posted an "awesome" fan letter on his blog (with the name of the "fan" deleted, of course). Here is a link to an article about this beauty. (I am linking to this article instead of to Neshek's blog because I couldn't figure out a way to link to that entry specifically. I don't think he's organized his web page to make that possible. And he also seems to be unaware of the fact that Google uses links very fundamentally in their search algorithm.)

(Tip of the cap to Rob Neyer.)

Second-Hand Obesity

You don't believe that this exists? Well, Kevin Smith just got kicked off of a flight for it.

The Enemy of my Enemy

Here is the third article in Steve Strogatz's mathematics series in The New York Times.

We actually went through Frank Harary's social balance proof in our networks journal club a couple of years ago.

Also, I was wondering how many articles in the series that it would take for Strogatz to get into networks. I suppose that's kind of like answering how many licks it takes to get the chewy center of a Tootsie Pop? (I hope somebody else remembers that.)

Social Awkwardness is a Scarlet Letter

I wished I lived in a world in which social awkwardness didn't result in quite so prominent a scarlet letter. I was in G & D's (a local ice cream place) and overheard a rather demoralizing conversation: The people at the next table were talking about socially awkward people as if we were a lower form of life---apparently, we're less nice, feel less, etc. than other people. I know I can dismiss them as a bunch of idiots, but I felt like utter shit after listening to that and I do believe that most people look down on me to some extent because of my social awkwardness. (One of the reasons I feel bad when I hear that stuff is my belief that so many people believe it to at least some extent.)

Obviously, I have been able to find people who aren't that way, but one of these days I would like to believe that the number of such people isn't so small. I go out of my way to find people who I feel are egalitarian in this respect, and that's one of the reasons that I have a lot of difficulty finding friends. Simply, this is a very hard search problem. (Though, again, I have obviously found some of these special people!)

One can get better at social skills---but only to a point. (And indeed I am better now than I used to be.) In the same way, one can get better at doing contour integrals---but only to a point. In each case, there is some level of natural ability involved, and I wouldn't dream of looking down on people if they had trouble with contour integrals.

"The Condensed Matter Song"

"The Condensed Matter Song"

By Mason A. Porter, Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford

(parody of the "Matter-Patter Trio" by Gilbert and Sullivan)



I'm having lots of trouble with this awful calculation –
So I shall go back to my lab for some Bose-Einstein condensation.
And see if better vortex lattices cannot attract my senses,
And with some extra stirring I shall find the consequences.
Oh but in my complex conjugate I did forget the dagger,
And now that I get vortices I have regained my swagger,
And a word or two of compliment my vanity would flatter,
But I won't get tenure anyway, because it's really condensed matter!

Because atomic physics is really condensed matter,
condensed matter, condensed matter,
Yes it's really condensed matter,
condensed matter, condensed matter,

Yes it's really condensed matter,
It is really condensed matter,

BECs are condensed matter, condensed matter, condensed matter!

matter, condensed matter, condensed matter,
condensed matter, condensed matter, ...


It may be a little tired and perhaps generally silly
And that energy landscape seems to me complex and hilly;
Though with it I want to grapple with a biological question,
But I know not what, so do you have a suggestion?
I shall then submit a paper to Physics Review Letters,
With excellent predictions to be tested when technology is better,
But right now I wish that landscape would be flatter,
And I don't actually know biology, so I study condensed matter!

Yes I study condensed matter,
condensed matter, condensed matter,
Biology is really condensed matter,
condensed matter, condensed matter,

Yes it's really condensed matter,
It is really condensed matter,

Biology is condensed matter, condensed matter, condensed matter!

matter, condensed matter, condensed matter,
condensed matter, condensed matter, ...


If I had been so lucky I would have studied complex systems
But unless I find a power law surely nobody will listen –
I was given good advice when my mentor saw me erring
That to study networks and call it "physics" would be ever so daring,
And then with real data I would truly get to fiddle,
And publish papers in Nature and Science that aren't worth a piddle.
That particularly vapid, unintelligible patter
Is very sexy nowadays, but we all know it's really condensed matter!

Yes it's really condensed matter,
condensed matter, condensed matter,
Complex systems is really condensed matter,
condensed matter, condensed matter,


All this rapid-publication, unintelligible patter
Is presented at the March Meeting, so it must be condensed matter,
Yes this rapid-publication, unintelligible patter
Is all part of the subject that we call condensed matter,
matter, condensed matter, condensed matter,
matter, condensed matter, condensed matter!



(OK, so I'm probably being a little harsh here and I'm definitely biting the hand that feeds me. But I couldn't resist doing this...)

The Curious Case of Batman and Robin

This demotivational poster is a big win. (It's also highly appropriate for Valentine's Day.)

The Big Hurt has officially retired.

Frank Thomas (aka "The Big Hurt") has officially retired. Next stop: Cooperstown. (Thomas last played in 2008 but hadn't officially retired.)

Just take a look at his hitting stats. The man could hit, especially in his prime.

One of the articles I was reading earlier today when the news leaked (but the press conference hadn't occurred yet) wrote something to the effect that Thomas "will get strong consideration for the Hall of Fame" (the quote is approximate, but the tone is accurate). Um, excuse me. Thomas is a mortal lock for the Hall (as long as PED-type rumors don't surface, and they haven't yet). The idea that he is in any way borderline is frankly absurd (pun intended).

Ernie Harwell wins Vin Scully Award

I didn't even know that there was a Vin Scully Award, but there is one, and Ernie Harwell has won it. This award, which is a lifetime achievement award in sports broadcasting, is richly deserved. (And it's also fitting that it's named after Vin Scully---not that I'm biased or anything...)

Celebrating Number 34

Yesterday was my 34th birthday (with 10:50 pm UK time the time where things turned over, according to my birth certificate), so I had a bunch of friends over to celebrate. We played some games, ate some cake, and generally hung out. The main party started at 7pm, and just before that I went out to dinner with my best friend among the locals.

Now it's very quickly back to the old grind, starting with marking quantum mechanics homework tonight. (My students who are taking this have told me that this is the hardest problem sheet they've seen in the 1.5 years that they've been here. I hope I'm not going to have to do all of these problems from scratch tonight---I'd greatly prefer a calmer marking period where I can wing things. We shall see.)

Strange Googling

This google search for future of those born on 10th February, 1976 has one of my web pages in the top spot. This is two spots ahead of a web page about Celine Dion on Oprah, because apparently in celebration of my 34th birthday tomorrow Celine Dion is apparently going to appear on Oprah. Let me just say that this is not what I wanted for a birthday present. Sheesh.

Update (right after original post): Except that now when I try the link to the search, my web page comes up 2nd instead of 1st. I'm not sure which parameter got changed, and I'm going to finish reading Salvatore killing off some major characters instead (just a few pages left). Given that I don't think any of you read his book's anymore, I don't feel too guilty about that spoiler.

3rd Annual Conference of the Oxford student chapter of the Society for Industrial and Applied Mathematics

We hosted a spiffy conference today.

Here are some pictures that I took. Kit Yates took even more pictures than I did, and I'm sure that they will be posted shortly.

Rock Groups

Here is Steve Strogatz's second article (of 15 total) in his current New York Times series. As I mentioned in the last blog entry, he's starting from the mathematical ground up. (I'm looking forward to the more advanced topics, but it's already neat to see how he's writing about the fundamental stuff.)

Lawful Neutral

I approve of this poster! If it existed in real life, I expect that this poster would tie the room together.

I come from the land down under.

Apparently, the song "Down Under" by Men at Work (a really awesome song, by the way) copied a bit from an Australian nursery rhyme.

Tales from the arXiv: Mastication of Fish Sausage

Not only is this abstract "awesome", but I think that the authors might have an Ig Nobel prize in their future... In particular, I'd like to point out the last sentence: In order to explain this structure, we propose a mastication model for fish sausage based on stochastic processes.

\\
arXiv:1002.0404 (*cross-listing*)
Date: Tue, 2 Feb 2010 07:17:47 GMT (878kb)

Title: Fragmentation of a viscoelastic food by human mastication
Authors: Naoki Kobayashi, Kaoru Kohyama, Kouichi Shiozawa
Categories: physics.data-an cond-mat.stat-mech physics.bio-ph
Comments: JPSJ3, 4 pages, 8 figures
\\
Fragment-size distributions have been studied experimentally in masticated viscoelastic food (fish sausage).The mastication experiment in seven subjects was examined. We classified the obtained results into two groups, namely, a single lognormal distribution group and a lognormal distribution with exponential tail group. The facts suggest that the individual variability might affect the fragmentation pattern when the food sample has a much more complicated physical property. In particular, the latter result (lognormal distribution with exponential tail) indicates that the fragmentation pattern by human mastication for fish sausage is different from the fragmentation pattern for raw carrot shown in our previous study. The excellent data fitting by the lognormal distribution with exponential tail implies that the fragmentation process has a size-segregation-structure between large and small parts.In order
to explain this structure, we propose a mastication model for fish sausage based on stochastic processes.
\\ ( http://arxiv.org/abs/1002.0404 , 878kb)

Oscar Nominations

Here are the 2010 Oscar nominations.

The main one I care about is Christoph Waltz winning the Best Supporting Actor award for his role in Inglourious Bastereds. (He was awesome!) I also really want Coraline to win the award for Best Animated Feature. Also, if A Serious Man wins for Best Picture, I'm going to be really annoyed. (I'll be somewhat annoyed if it wins the award for Best Screenplay.) I found that movie to be woefully disappointing. It had a few moments, but that's all it had.

Given my awful track record and other things I want to do (besides write an interminably long blog entry), I'm not going to bother actually predicting the award winners.

Look at all these Rumors

Somebody apparently started a false rumor that the seminar speaker that I am hosting on Thursday wasn't going to come. (I'm partly wondering what's going on, partly wondering whether somebody is trying to screw with me, and partly amused if somebody is indeed trying to screw with me this way.) Anyway, members of OCIAM and whoever else wants to come will most certainly be hearing about the FPU problem this Thursday.

The game is afoot.

Killed off in chapter 1?

I have heard rumors that a literary mathematician who is named after me is slated to be killed off in chapter 1 of a book. Granted, the rumor is now several years old, and this could easily change. Tom Hanks should clearly play him in the movie version.

Broadcaster Jon Miller joins Hall of Fame

Broadcaster Jon Miller, who is most famous for his play-by-play work on ESPN's Sunday Night Baseball, has won the Ford C. Frick Award and has thereby earned a spot in the broadcaster's wing of baseball's Hall of Fame. About time.

Monday Catblogging

Here is a picture of Pogo trying to keep warm.

One Fish, Two Fish, Red Fish, Blue Fish

OK, so that only makes four fish, but in this New York Times article by Steve Strogatz, one gets all the way up to 12 (count 'em) fish. Steve is writing a series of opinion pieces in the New York Times where he will take mathematics all the way from preschool to graduate school. This is the first article in the series.