The Professor’s Beloved Equation

This was so beautiful! It couldn’t have been done anywhere else but Japan. The premise is that this math professor has Alzheimer’s, or at least a special form of it, such that his memory is only 80 minutes long. In the movie his memory was shown to have reset every day at the least, so every morning when his housekeeper arrives, the following conversation takes place:

“Konichiwa!”
“What’s your shoe size?”
“24 centimetres.”
“My, what a noble number… It’s the factorial of 4.”
“What is a factorial?”
“If you multiply all the whole numbers from 1 to 4, you get 24.”
“What’s your telephone number?”
“576-1455”
“Did you say 5,761,445? Why, that’s wonderful. That’s equivalent to the prime numbers up to one billion. In any event, come in.”

And then every day she came in after that, the same thing would repeat.

“What’s your shoe size?”
“24. The factorial of 4!”
“That’s wonderful. What a noble number…”

He meets her afresh every day, and while she goes about her daily chores he disrupts infuses her housekeeping experience with a good dose of math.

On the day one of the professor’s papers got accepted for publication in a journal:

“Do you often submit your papers to magazines?”
“Right.. I sent my proof to the Journal of Mathematics, Vol. 37 today. That’s good. ”
“Oh, no! I should’ve sent it express. Only first place takes a cash prize.”
“No, there’s no need to send it express. It’s important to arrive at the truth before anyone else, but it’s more important that the proof be beautiful. ”
“Are there such things as beautiful or ugly proofs?”
“Of course. In a truly correct proof, air-tight and compelling reasoning coexists without contradiction, with supple logic. Just as no one can prove why stars are beautiful, it’s difficult to express the beauty of mathematics.” He paused for a beat.
“What’s your birthday?”
“February 20th.”
“What a charming number!” The professor takes off his watch.
“220… Take a look at this. Back in college, I won the President’s award for my paper on Transcendental Number Theory.”
“Ah.. what a great honor..” the housekeeper tried to be relevant.
“No, that doesn’t matter. Can you read the number?”
“President’s Award No. 284. Does that mean you’re the 284th person to receive the honor?”
“I suppose. The question is 284 and 220. This is no time to be washing dishes. Come with me, quick!”

They walk over to the blackboard. The professor writes 220 and 284 on two ends.
“What do you think?”
“Well, I.. Both have 3 digits… How can I phrase this? At the meat counter at the supermarket, if there are two packets of ground beef, one 220g and one 284g, they seem the same to me. One quick glance, and they look similar. They’re both in the 200 range, and all the digits are even…”

“That’s a keen insight. Intuition is important. Grasp the numbers intuitively from your heart. Do you know what a divisor is?”
“Yes, I think so, I remember studying them.”
“Let’s write out all the divisors for 220 and 284, excepting themselves.”
220: 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110
284: 1, 2, 4, 71, 142,
“You can calculate all those divisors in your head?”
“I’m just using the same intuition you did. Onto the next step.”
1 + 2 + 4 + 5 + 10 + 11 + 22 + 44 + 55 + 110 = 284
1 + 2 + 4 + 71 + 142 = 220
“Will you behold, this beautiful chain of numbers. Add all the divisors for 284, and you get 220. Add all the divisors for 220, and you get 284. They’re amicable numbers.”
“Amicable numbers?”
“Mm. Such pairs are very rare. Even Fermat and Descartes only discovered one pair each. They’re numbers bound to each other by God’s design.”
“God’s design…”
“Mm. Isn’t it beautiful? Your birthday and the number engraved on my wristwatch are so perfectly intertwined.”

He gave everyone in his acquaintance names, mathematical names that represented their characteristics. To the housekeeper’s son, he gave the name “Root” (of course, pronounced “Root-oh” in Japanese)

“I can tell you’ve a wise heart in here. All right, you’re a Root. You accept any number that comes your way, rejecting none. A truly generous symbol, Root.”

Root starts coming by the house everyday since the Professor cannot stand the idea of Root waiting at home alone for his mother while his mother prepares dinner for a complete stranger. After being thoroughly schooled in the beauty of numbers by the professor, Root goes on to become a math teacher, and teaches his students about the professor’s lifelong equation:

“Pi is the circle ratio, right? “i” is the square root of -1 and an imaginary number. Here we have pi, a number that continues to the ends of the universe, and the imaginary number “i” which never shows itself. What’s tricky, is “e”. “e” is also called the “Napier number,” after John Napier, the British mathematician. The Napier number is one of the constants so critical to math. For now, I’ll just tell you the conclusion. If you calculate this “e”, its value is 2.7182818284…. This is just like pi. It goes on and on and on forever. It’s an irrational number. From an infinite universe, pi drifts down to “e”, and shakes hands with the bashful “i”. They come together, and hold their breaths… none of them are connected. But, if a single human adds just one thing… the world is transformed.
root
The contradiction is resolved. Zero. In other words, the realm of nothingness embraces them.

Today, we celebrate this equation. When a single human added just one thing to my contradictory and irrational life.

Annunci

Soya bean milk

CH (Z’s college roommate) is back in Seattle! Which led to the soya bean milk** debacle today. For some time now the uwajimaya downtown has been rather lax about stocking the correct soya bean milk brand (with the yellow cap). Either they only have the large gallon-sized bottles which are a little difficult to finish, or they are out of stock altogether. An asian grocery. With no soy bean milk! So today we went to dinner in the ID with CH and parked at the Uwajimaya before heading to Fort St. George. While walking to the restaurant we walked through the supermarket and decided to check out how many bottles were left (we didn’t manage to get any last week). They come in gallon sized bottles (half gallons used to exist up until recently) and there were only 6 left. The boys were afraid that they’d be out when we got back from dinner, a very real possibility. So of course they decided to hide the soy bean milk among the regular milk, which is less popular. Only in an Asian supermarket. The regular gallon sized milk had blue caps so they arranged two gallons of soy milk in the middle of a bunch of bottles of regular milk. I don’t know why we always do unglam things. Further, the more people there are in our party, the more unglam the things we do. Like this soy milk hiding. Is it us who are inducing this unglam behaviour it or our friends who are like us? Not sure if I want to know the answer to that question.

Just the other day we picked up a scattered bunch of dried lavender just lying in the street. We were going to the Belle Epicurean for lunch (they have really good French sandwiches and feuilletes btw) and there was this van parked by the road with a bunch of lavender haphazardly scattered on the floor next to it. All dried and some broken stems but otherwise pretty intact and still smelt really good. The kind of thing you pay $14 at L’Occitane for. Well screw that, Z and I stopped, looked at each other, then got a paper bag from our car and filled it with the lavender and went merrily on our way.

3X2A0036
all artfully arranged and shit

 

After shopping at Uwajimaya we went to Daiso since CH needed a filter for his tub and we got sidetracked at the cashiers by the rows and rows of Japanese gummies! They both bought a pack of cuboidal kyoho grape flavoured gummies and I got a 5 pack of gumdrop shaped gummies. The difference (we sampled both in the car) is that the cube gummies are made with no gelatin, just glutinous rice flour so they are much softer than say gummy bears and lean more toward the consistency of mochi skin without being too bland. Very nice! Each packet only had 6 little cube-gummies though, all individually wrapped despite being sugar coated with no chance of coalescing into a giant gummy. There is no such thing as ‘Saving the Environment’ in Japan. My 5 pack in a chain (the kind you tear off) used both gelatin and pectin, but still managed to remain more pliable than typical gummy bears/circus peanuts (tts what Chris called them, if I remember correctly). I think it’s the use of glutinous rice flour/starch. Never really stopped to examine the ingredient list of Japanese sweets but they were both (yes, both these 28 year old men) so drawn by the shape of those gummies we had to try them all.

I love how my childhood follows me around like a ghost I cannot shed. Sophistication, so prized in adolescence, is now in short supply and shows no signs of returning.

** Asian soy milk is far and away better different from the artifically vanilla flavoured, overly sweet American version for the lactose intolerant. It is delicious hot, cold, sweet, salty (only in Taiwan), and especially with fried cruller dipped in. I don’t know what kind of magical sugar they use to flavour our soy milk but it is super amazing and Z and I can’t go without it. You’re meant to drink it on its own, like a latte.

Choice picks from Uncle Murakami

So for those who do not know, Haruki Murakami set up an online “Aunt Agony” column of sorts for fans, sorta like Reddit’s Ask me anything for famous people, but in Japanese.
murakami
The cover picture is gorgeous!

Here are some of his translated answers extracted mainly from WSJ Japan:

Asked by one fan on his thoughts about being called the frontrunner for the Nobel Prize in Literature, Mr. Murakami said it was “quite annoying.”

It isn’t like there’s an official shortlist, it’s just private bookmakers coming up with these odds. It’s not as if this were a horse race,” he replied

Another fan asked the author how people can improve their writing skills.

Writing talent is similar to the art of chatting up a girl. You can improve to a certain degree through practice, but basically you are either born with it or you aren’t,” he wrote.

He also revealed in a separate post that he seldom reads his own work because it is too embarrassing.

In opening the website, the author said he is open to a variety of comments and questions including queries about cats, creatures that are a frequent motif in his work. One fan asked Mr. Murakami if he had any idea where her pet cat, missing for years, had gone.

Cats tend to disappear. Take good care of them while they are around,” Mr. Murakami replied.

In one of his responses since then, he took up the theme of the afterlife with a 34-year-old female fan. After dying, Mr. Murakami said he simply hopes to rest in peace.

I don’t want heaven or hell, or hostess bars,” he wrote. “I don’t want to be disturbed by anyone, and would like to simply sleep in peace. I might want to eat some oyster fries every once in a while, though.

On same-sex marriages, Mr. Murakami said he had many gay friends who recently tied the knot in the United States.

Everyone looked very happy about getting married. That delighted me. Therefore, I am in favor of same-sex marriage,” he said.

In another response, the writer said Natsume Soseki’s “Sanshiro” was one of his all-time favorite books, while “The Goldfinch,” a 2013 novel by Donna Tartt, was one of his more recent preferred reads.

One fan said she couldn’t picture Mr. Murakami using a smartphone. The author replied that he was a hardcore fan of Apple Inc.’s products.

I have used a Mac since 1991,” as well as an iPhone, iPad and iPod, he wrote, adding that he has spent a fortune on Apple products.

The period when Steve Jobs was away from the company he described as “the dark ages,” saying it still made him feel gloomy thinking about that time.

And what does Mr. Murakami listen to on his iPod? The author wrote that he likes hip-hop acts, such as the Black Eyed Peas and the Gorillaz.

Q: Hi, Mr. Murakami!
I am really a big fan of yours.
I just want to ask how do you come up with your ideas in writing a story?  And where do you get inspiration from?

A:Honestly, I don’t trust inspiration. Inspiration is just an accumulation of your usual small memories. Trust your memories.

In response to a question from a 17-year-old female fan on how to lose weight, Mr. Murakami said that there are only three ways to achieve the goal. “There is no need to read any manual on diet. It’s very simple,” he wrote, explaining that one has to eat less, exercise often or fall in love. “The final option is very effective,” he wrote.

One male student asked Mr. Murakami about the process of falling in love, in English.

Basically it’s an accidental collision. It is unpredictable and inescapable. So, always fasten your seatbelt,” the author replied.

A 26-year-old female fan asked for advice on how to carry fewer items in her bag, to which Mr. Murakami answered that he had a similar problem.

Mr. Murakami said he carries books, an iPod, swimming suit in case he has the sudden urge to swim, an Amazon Kindle book reader, glasses, tooth brush, a Red Sox cap, and an appointment book among other items. I would like to travel light if only it were possible, he said.

Q: Dear Haruki-san, I have a question that whether you have ever thought about that your work has such a big influence abroad? When you conduct your work, have you ever thought about meeting the needs of foreign readers?

A:Honestly, I don’t think about the readers, either domestic or foreign, when I write. I have no idea what kind of people are reading my novels. Stories come to me and I grasp it and write it down. That is all. It is just like catching exotic birds or butterflies in the deep woods. I have no time to think about the readers. I am too busy catching stories. If I lose sight of them once, they would be gone in an instant, and probably for good.
****

I wish everything I said were that quotable. I love all the little illustrations on his site! They are so Japanese. We’re in midterm week and I just submitted my algebra midterm just now. Couldn’t solve a part of the last problem :(
Going to be really busy completing the two homeworks due Monday and preparing for the complex midterm on Wednesday. Nobody has time to think about Valentine’s day and anniversaries and stuff with school going on. I guess graduate students are less lonely than the average person who has time to slouch around and moan about being alone. I haven’t decided if that’s a good thing or a bad thing.

First day of Winter Quarter

And the homework has hit like a full cannon. Algebra is due on Friday, Manifolds due on Monday… and I’m still in denial. I think I cook more when school is in session to try to avoid doing work. Just today I made Vietnamese banh tet – small bananas wrapped in sticky rice steamed in banana leaves. And a brussels sprout gratin – to finish up the leftover brussels sprouts from the branch I got from Trader Joes during, get this, Thanksgiving. So apparently brussels sprouts can last > 1 month in the crisper. Good to know. I have no real experience cooking them except at thanksgiving where I sauteed them with bacon and then doused it in heavy cream before gratinating it with shredded gruyere and parmesan on top. Toasted a hunk of cheesy garlic bread I prepared eons ago and froze, and heated up a satchet of soup from Whole Foods which tasted horrible even though the packaging looked so nice. Well now I know.

After dinner, we headed to the Crest to catch Gone Girl, which is now out for only $4 a ticket! It was morbid and horrifying, but also a really, really good movie. Reese Witherspoon was one of the producers. When her name came up on the screen you could hear everyone around us whispering “Hey, Reese Witherspoon is one of the producers.” It’s really obvious because they have to whisper ‘Reese’ and suddenly the whole room is filled with hisses.

If you haven’t watched it, you should. It totally screws with your mind. Like inception, but without all the geeky stuff. A plain psychological thriller. Like the Page Turner. There’s a bit that’s really gory, but I just kinda shut my eyes for that. Rosamund Pike is PERFECT for the role, I can’t emphasize how perfect she was. Ben Affleck was also really good as the always-one-step-behind cliche of a professor but Pike plays the perfect writer, who’s got the whole world hanging on every last development of her story, which instead of writing a book about, she orchestrates in real life. It’s pretty Woody Allen-y. I didn’t like the casting of Neil Patrick Harris though, he strikes me as somebody waay too slick to be caught up in the protagonist’s lies. Modern film crit had better come up with more terms for key characters in movies, since there’s going to be a whole lot more of the protagonist-who’s-actually-the-antagonist-who’s-actually-the-protagonist-hah-gotcha-again-didn’t-I-she’s-actually-the-antagonist. Actually they probably already have a term for it but I’m too lazy to google it I’ve got some complex analysis reading to do. A mathematician would call it the protagonist with order n, i.e. the protagonist who plays with the audience’s feelings n times (protagonist squared = antagonist, etc. etc.) before reverting to his identity as the protagonist that everyone loves and sympathizes with in the end. If who the audience thought was the protagonist turns out to be the antagonist (does not achieve identity) as in so many Agatha Christie books, then the cast/character list would be said to be non-cyclic and that protagonist is described to have infinite order.

What I absolutely adore about the Crest is how everything has the human touch. Right before the movie this guy comes up to the front, welcomes you, tells you that the previews will start in the few minutes, and politely requests that you silence your phones. And when the movie is done and you stream out, the guys at the popcorn bar ask you how the movie went and say they want to catch it too. It must be really fun working that popcorn bar – you can decide which movies to watch based on the crowd’s reaction at the end of every movie. And not just the crowd’s reaction, but also the dressing and the general vibe of person each movie attracts; you can decide if you identify with that or not. I’ve heard that they do the best popcorn in town too – you can smell it, that buttery aroma wafting all about the lobby – but it’s pretty pricey, so we haven’t tried it yet. I’m also not a super big fan of salty popcorn (in Sg you have the option between sweet and salty, and the sweet popcorn there is crunchy because it’s usually coated with a thin layer of caramel), but I think they just might change my mind.

Hmmm

got this cute email from the dept chair:

Graduate Programs is pleased to announce its Spring 2014 Rankings of the Top Mathematics Graduate Programs according to students, enumerating the best graduate programs in the country in a variety of fields based solely on ratings and reviews from current or recent graduate students posted on graduateprograms.com.

Program rankings, compiled using data gathered between September 1, 2012 and September 30, 2014, encompass reviews posted by more than 70,000 students participating in over 1,600 graduate programs nationwide. Ratings are based on a 10 star system (with 1 being the worst and 10 being the best).

For a copy of our Top 25 Rankings Badge & Seal, please click on the link.

For specific rankings for Engineering, please click on Mathematics Rankings.

The Top 25 Mathematics Grad Programs are listed below:

1 Harvard University
2 Columbia University NY
3 University of Washington Seattle
4 Princeton University
5 The University of Texas at Austin
6 Brown University
7 University of Louisville
8 Texas A&M University
9 Cornell University
10 Louisiana State University
11 Massachusetts Institute of Technology
12 University of Maryland College Park
13 University of Delaware
14 Oregon State University
15 Rutgers University-New Brunswick
16 University of Michigan-Ann Arbor
17 University of Central Florida
18 Texas Tech University
19 California State University Long Beach
20 University of Wisconsin-Madison
21 Arizona State University
22 The University of Chicago
23 Northwestern University
24 University of California-Berkeley
25 The Ohio State University

sketchy, right? Then it got even sketchier when it announced its methodology:

METHODOLOGY
Graduateprograms.com reaches current and recent graduate students through scholarship entries as well as social media platforms.

Graduateprograms.com assigns 15 ranking categories to each graduate program at each graduate school. Rankings cover a variety of student topics such as academic competitiveness, career support, financial aid and quality of network

I feel tempted to reply and tell him this ranking only tells you which school’s math grad students are on facebook the most. But I think it’s a pretty worthwhile survey – especially if you were a graduate student interested in quality of life and education over things like reputation, then hearing from current students would be most helpful.

Swamped

School has started and we’re right in the thick of things. 3 (hard) problem sets a week, I’m amazed I’m keeping up at all after 2 years of slacking my ass off. I’m not doing it well of course, just well enough to keep my head above the water.

I like the teachers at U* a lot. They’re really funny and/or personable, apart from the one who keeps nagging us to keep up with the homework like a grandfather. I know he means well but it makes me feel like rebelling haha. Also I think they are a lot clearer in their exposition than the teachers I had at C*.

Our algebra prof has started offering money for every typo students spot in his notes! $1 a typo. J asked at the end of the class “So when you said you were offering money, you mean… cash, right?”
S: “That’s right! This is it guys, this is your chance to make millions from the comfort of your own home!”
J: “So on Monday, bring cash.”
People have been hunting for typos like clam-diggers and today he shelled out 6 bucks to two different students :P

And the topo prof is also really cute. He’s got a really weird style going on with lots of striped shirts and squeaky heeled shoes, which made me think he was 30+, but it turns out he’s nearly as old as our dads and got his PhD in the 80s :S Last week he closed the door after the lesson started and this student who was late knocked on the door, and he opened it, and was like “Does it not open?” The student said he tried opening the door but it wouldn’t open. Someone else piped out that that’s not possible since undergrads walk into our classroom mistakenly all the time (we have a fixed classroom for all the core grad classes) , so I told him “Why don’t you go out and try it?” He said “Do you want to try it? I would but I’m just worried that if I go out nobody will let me back in.” lol which was so endearing (and also exactly what I was thinking).

Today he was running through the schedule at the end of class. “So, I’ve pretty much said everything I want to say on this chapter and on Friday we’ll start on simplicial complexes… Your homework is also due then, so remember to turn it in… And then on Monday we’ll have the midterm.” And he just stopped there and started packing up his notes. There was a stunned silence in the class where everybody thought oh, did I miss something? Maybe I didn’t pay attention when he announced it. One student finally ventured to ask “Wait, what?” I swear my heart literally stopped beating. And then he burst out laughing and said “That was a joke guys” and all of us were like wth kind of joke is that haha.

ok I gotta go bust my ass for the algebra problem set, so I have time tomorrow to do the topo one, and then we can all start breathing on friday afternoon when the week is over. Pumpkin carving with ggy on saturday! I’m making a lasagna and perhaps matcha creme brulee.

Grad sch vs. A Real Job

Cons of going to grad school

  • Less free time
  • Subject material more technical
  • More deadlines
  • More stress
  • Need for original research
  • Late nights due to procrastination. When work at my office job is procrastinated, one can just do it the next day AT work
  • Less money for expenses in local bank i.e. can’t shop as much as before

 

Pros of going to grad school

  • Only go to school 3 times a week
  • Can do work in pajamas. Can also go to the office in pajamas.
  • Can wake up later
  • Shorter and more comfortable commute to work
  • Still get salary in Sg without doing work in Sg
  • Can do random stuff like write this post in the middle of the “working day” without guilt or anyone peering behind your back.

I think I prefer being here! It is kind of fun attending math classes again. The level of difficulty is drastically different here than at cornell, where everyone is sort of assumed to read on their own and have excellent foundations and to be really smart so some professors demand a lot and/or go really fast. My foundations aren’t that great so it’s nice to go for all these relaxing lectures hahah where even if I don’t give a 100% of my attention I can still get by and it doesn’t really compromise my learning.