[Alexandre] Grothendieck had a mathematical style all his own.... [I]t seemed completely different and new. But it is hard to articulate what the difference was....Strange, how minds work. I think there is a similar divergence of minds in law and in politics, but it's so nicely clear in that contrast of the mathematical minds, Ramanujan and Grothendieck.
Although Grothendieck approached problems from a very general point of view, he did so not for generality’s sake but because he was able to use generality in a very fruitful way....
One striking characteristic of Grothendieck’s mode of thinking is that it seemed to rely so little on examples. This can be seen in the legend of the so-called “Grothendieck prime”. In a mathematical conversation, someone suggested toGrothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.”
But Grothendieck must have known that 57 is not prime, right? Absolutely not, said David Mumford of Brown University. “He doesn’t think concretely.” Consider by contrast the Indian mathematician Ramanujan, who was intimately familiar with properties of many numbers, some of them huge. That way of thinking represents a world antipodal to that of Grothendieck. “He really never worked on examples,” Mumford observed. “I only understand things through examples and then gradually make them more abstract. I don’t think it helped Grothendieck in the least to look at an example. He really got control of the situation by thinking of it in absolutely the most abstract possible way. It’s just very strange. That’s the way his mind worked."
Lacking the subtle joy of living in a prime number year, I have the opportunity to see my life in segments, in this case, 3 segments of 19. (19 segments of 3 is not interesting.) The story of my life does, in fact, divide neatly into 19-year segments, not that I'm going to reveal why the first 2 19-year points look significant from the vantage point of the third. But will the fourth 19-year segment be different from the third? Will I have all 19 years? 19 beyond that? 19 beyond that? 19 beyond that? Surely, not 19 beyond that.
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44 comments:
That prime number stuff is cute, but the big questions: are you happy and are you healthy?
Tom Faranda 56 & 1/2, 2 years post-chemotherapy
It might be cool to blog about the 19 year transition points...19, 38, and now!
I'll be 57 later this year. It makes a good name for a steak sauce although I prefer is on meatloaf.
Well, I heard Rush Limbaugh yesterday and it is apparently his birthday and he is 57 as well. So ask Rush what he thinks of your mutual birthday on open line Friday.
57
VARIETIES.
HAVE YOU TRIED THEM ALL
YET?
I HOPE SO...
ALL THE BEST!
did dadv. give enough of a hint?
I have an old pickle pin around here somewhere:
http://en.wikipedia.org/wiki/Heinz_57
This day in History:
1773
The first public museum in the U.S. was established in Charleston, S.C.
1896
H. L. Smith took the first X-ray photograph. It was a hand with a bullet in it.
1915
The U.S. House of Representatives rejected a proposal to give women the right to vote.
1932
Hattie W. Caraway, a democrat from Arkansas became the first woman to be elected to the U.S. Senate.
1964
One month after Zanzibar became independent, the ruling Zanzibar Nationalist Party was overthrown in a violent coup.
1991
A divided Congress gave President Bush the go-ahead on the Persian Gulf War.
1998
Nineteen European countries signed an agreement banning human cloning.
The trick in remembering how old you are is in remembering what year you were born in.
Then it can be worked out at leisure.
One word:
Heinz
You now know everything you need to know about the flavor of the year.
My father's social security number was prime. He asked me to check it on a computer.
Though he would only have to have checked with all the primes up to 12000.
Happy Birthday!
A trick to remember:
If you add up the numerals in a number and they are divisible by three, 5+7=12/3=4 then the number is divisible by three.
If the numerals add up to 9 then it's both divisible by 3 and 9
09, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108...
Did rhhardin disclose his father's ss#?
Happy Birthday Ann!
Interesting that Ann & Rush were born on the same day...two great communicators and both well-known too.
One has an advanced degree and one is a college dropout I believe.
Both are precise regarding words. Ann is cagey about some of her own stances while Rush leaves you no doubt about his.
Actually and obviously, today marks the passing of your 57th year and the beginning of your 58th. I wish you all the best in the coming year but tend to think 2011, beginning on 3 February 2011, will be even more significant as it will be a return (in the Chinese zodiac) to your Metal Rabbit birth year for the first time since 1951.
from Wikipedia the free encyclopedia:
The average Rabbit person emphasizes the importance of small details. They pay attention to everything from color, design and furniture to food and conversation. And only when they are sure that everything has been arranged as they wish can these people relax and have fun.
People born in the year of the Rabbit often lead a conservative lifestyle where one of the most important things is their security. This quality has a negative side also: opting for safety over risk, they may miss good opportunities. These people are not frivolous or irresponsible, for when they truly believe in something, they are serious, persevering and capable.
Calm as they are, it is not easy to provoke Rabbit people. They are sentimental and compassionate. They can be moved by the personal problems you share with them
Happy birthday, Ann!
I hope there's all kinds of wonderfully interesting things about 57 for you.
Happy Birthday, Ann!
Ramanujan, who was intimately familiar with properties of many numbers, some of them huge.
Indeed. When Ramanujan was in the hospital he was visited by the mathmatician G.H. Hardy. Trying to make conservation, Hardy remarked how boring the taxi cab's number – 1729 – had been. Ramanujan looked him at said: "No, it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."
[1729 = 1^3 + 12^3 = 9^3 + 10^3]
57 is only 39 in hexadecimal. Next year you'll be 3A.
The social security crisis can be solved by changing the base of the number system to 16.
Might as well go metric at the same time.
Is each third distinguished by its first birthday being in a different city (indeed, university in one capacity or another)? At 19, presumably U-Mich, at 38, UW, and at 57, Brooklyn?
rhhardin said...
"The social security crisis can be solved by changing the base of the number system to 16."
I think we should just assign everyone their own IPv6 subnet and use the network address of that as their unique ID. Think about it - no more anonymous commenters.
I was born in 1957.
Happy Birthday Ann.
So AI starts up next week, will up enrage the ADS crowd by blooging about it? It's on a short TiVo lease with me after last year.
Happy Birthday, Ann!
Happy Birthday!
Here's hoping that the next 19 years are chock full of bloggy goodness.
I'm nearing the end of my fourth 19 years, and regretting all I haven't done. Have you a list of the undone things that are important to you?
You hit your prime at 59, so for now you'll just have to catch up.
I think it's because both "5" and "7" are prime, people would naturally and subconsciously assume that the two put together as 57 would be an ultimately prime number. I suppose this is not the case.
Happy Birthday, Ann! Thank you again (I've said it before) for providing a cool place for all of us here to hang out. You're by far my favorite blogger.
Re: the divergences in the ways our minds work, particularly with respect to law and politics: my mode of thinking clearly falls within the Grothendieck model, which starts from philosophy and abstraction, which starts from philosophy and abstraction. By contrast, I'm often humbled by the commenters here who are clearly attracted enough to concrete examples in the realm of law and politics to be able to summon so many of them forth in argument. The distinction isn't completely absolute, at least in my case: after all, my political thinking got its original impetus from the very concrete and presumably valid example of my own direct personal experiences with law and government. In any event, I like the way Mumford pointed to how different Grothendieck's mode of thinking was from his own without claiming that Grothendieck's mode was necessarily inferior.
rhhardin: The social security crisis can be solved by changing the base of the number system to 16.
Might as well go metric at the same time.
Change our system of numbering to base 16 and change our system of measurement to base 10? What's that supposed to accomplish, besides messing everybody up?
"Here's hoping that the next 19 years are chock full of bloggy goodness."
I wonder how long one can keep blogging.
Sometimes, I imagine myself finding out I have some terrible disease and blogging through to the end (even if it involves losing my mind).
My 4-year blog anniversary is Monday. 4 years, with not one day missed, and averaging more than 7 posts a day.
It's also true that if you've reached the conclusion, as I have, that "there is, and can be, correctly speaking, no law but natural law," what such-and-such Supreme Court Justice has said about the constitutionality of such-and-such legislation must necessarily become a tad less interesting. A common reaction to thoughts (reflecting lack of engagement with politics "in the real world") such as these is "well, you're making yourself irrelevant and 'a wallflower in the ballroom of progress'." But sadly, unless you have gazillions of dollars at your command or otherwise have real access to the heartstrings of federal political power, you, despite your extensive knowledge of politics in the real world, are just about as irrelevant as I am in the eyes of the federal government. What does your one vote, however informed it may be, among thousands and thousands of other (informed and uninformed) votes, for a "representative" among a very limited number of similar choices, who if elected may or may not carry out your wishes, get you? Now, if most government was carried on at the very local level, as it should be, then we could get some real democracy going. But as things now stand, local politics is as uninteresting to me as national politics, because most of the really important and interesting matters have been preempted by the federal government and thus taken out of the hands of local government and therefore out of the hands of "the people."
Happy birthday! Thanks for the many thought-provoking posts and the photos. And for maintaining a salon where many points of view can be aired.
Sometimes, I imagine myself finding out I have some terrible disease and blogging through to the end (even if it involves losing my mind).
There would be a certain karmic justice in that, seeing as how you've driven so many others mad.
And they would be able to gloat, as they did with Reagan, "See! We knew it all along!"
Happy Birthday, and welcome to 57. I joined about 3 months ago. I always knew we were close in age, but never quite that close. Good luck.
Happy birthday, Ann.
Did rhhardin disclose his father's ss#?
I think rhhardin's father's SSN is safe. I doubt that the SSN is really between 11,999 squared and 12,000 squared, but even if it is, there are 1,231 prime numbers between those two numbers. It's more likely that when rhhardin says he only needed to check the prime numbers up to 12,000, he meant that the maximum prime number he needed to check was between 11,000 and 12,000, and there are 1,230,137 prime numbers between 11,000 squared and 12,000 squared.
Thanks, RHodnett. That's just the kind of answer I was looking for. I'm just going to assume it's correct, because why would you write that if you weren't the sort of person who knows things like that?
Well, thanks, Ann, but I certainly don't know things like that. I got curious and wrote a simple program to figure out the answer. I'm pretty sure the program is correct, though. (Gulps and crosses fingers.)
Happy birthday!!!
Alas, it was "57 varieties" that came into my mind unbidden. Advertising works!
You still have your second Saturn return to look forward to!
The first thing we do is look back on your first Saturn Return, which occurred when you were 28-30 years old. We identify the main issues and reflect on events that took place near that time.
If you took action, chances are you will be building on the outworkings of that decision successfully in the second Return.
If, on the other hand, you failed to seize the opportunity ... you will be getting another chance in some subtle way that you will have to recognize during your second Saturn Return.
(No link because she's selling "Saturn Return Readings.")
http://www.youtube.com/watch?v=PFd6YLKVjek
http://www.youtube.com/watch?v=Pg4Pjd6GbYQ
Hippo birdie.
Two ewes.
Time marches on.
For 57 or more people, the probability is more than 99% that two of them will share the same birthday. I have a friend who works in Antarctica. He is convinced that the number 57 is unduly represented in movies. He actually asked James Cameron about it and was told that he and his fellow Antarcticans had too much time on their hands.
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