Dawkins isn't GodThe reviewer can't expect a biologist to know more about number theory than Hardy!
Dawkins isn't God
Very interesting article. As Thompson notes in that article, Dostoevsky uses mathematics mainly as a symbol for materialism, and but does not explore the actual ideas from mathematics like non-Euclidean geometry. I find this to be a pretty typical stance toward mathematics in literary cricles -- that math (and science) is the opposite of the ineffable human spirit. For example, this is how mathematics is used in Zamyatin's We. I don't think this is merely the result of writers trying to defend their field from the encroaching influence of math and science. Many readers probably find a ring of truth in the idea that the authority of mathematics robs us of an important aspect of life that humanistic pursuits like literature and religion provide. Maybe it is just the result of a broken education system, as Paul Lockhart argues in this article, or maybe there is something to it.Originally Posted by mal4mac
As a side note, sometimes I see the discovery of non-Euclidean geometry depicted as some kind of defeat of Euclid. But it actually is strong evidence of Euclid's remarkable insight. People suspected for almost two thousand years that Euclid's fifth axiom could be deduced from the other four axioms, that is, they suspected that Euclid could have been smarter about his system and left out the fifth axiom. The discovery of non-Euclidean geometries proved that the fifth axiom was indeed independent of the others and that Euclid was correct to see it as indispensible. Moreover, it showed that this insight was not at all obvious, having taken more than a millenium to prove.
P.S. Happy belated pi-day!
Optima dies ... prima fugit
Mathematicians, thinking as mathematicians, can't conceive of black holes because they are part of the physical universe. Only physicists/astronomers can conceive of black holes. If a mathematician conceives of a black hole he is moonlighting as an astronomer...
Using Newton's Laws, in the late 1790s, John Michell of England and Pierre LaPlace of France independently suggested the existence of an "invisible star." Michell and LaPlace calculated the mass and size — which is now called the "event horizon" — that an object needs in order to have an escape velocity greater than the speed of light. In 1967 John Wheeler, an American theoretical physicist, applied the term "black hole" to these collapsed objects.
So physicists discovered, and named, black holes, although (as always) they did a bit of figuring...
The triangle example is fun, but it's not Mozart's clarinet concerto or Hamlet. It's also about as much fun as it gets. I've been through many proofs like this and many applications of mathematics, it's *all* only at best a bit fun, but mostly it's a hard slog (try solving Einstein's field equations for even the simplest situations ...)
Gowers actually encourages the rote of learning of rules because some students may not see how to "split the triangle" and would be just left in a state of confused perplexity, a much worse state than memorising a nice rule!
For instance, students who have (serious!) problems in visualisation could memorise the rule that a triangle drawn in a rectangle takes up half the area of the rectangle, and then move on...
Not one book of mathematics makes it into Bloom's Western Canon, one reason I love him
A bit of an aside, BlueVictim, but do you know the famous story about Dodgson being asked by Queen Victoria to send her one of his books? He sent a maths treatise when what was obviously required was fiction. I'm pretty sure I've also heard that Victoria's response was the now legendary, 'We are not amused!', but the web doesn't seem to back this up.
Stressed for truth.
To quote someone I know "Teaching someone calculating for twelve years and telling children that it is mathematics is like teaching someone scales for twelve years and telling them it is music".
@blp - I am pretty sure the story is an urban myth - Dodgson was a rather conservative man who respected the queen very much and wouldn't have played such a prank on her.
@mal4mac I actually think that mathematics isn't suitable for all personality types but I also think that the number of those who could enjoy it isn't so small at all as is thought - I think that the sort that enjoys games like Go or Chess would also enjoy mathematics if they only had had any proper contact with it.
For something ontopic, in Musils "Young Törless", the concepts of imaginary numbers and infinity are used as rather interesting metaphors - the first as for things that are unreal, fictive and strange and which are yet used as stepping stones between thoughts and feelings that are real.
Infinity is thought as something that we do not know but have named and so we think we understand it, while the concept underneath is much more large and terrifying than the simple concept.
If you believe even a half of this post, you are severely mistaken.
There definitely is a lot of hard slogging in mathematics, and I agree that mathematics is quite different from Shakespeare or Mozart. I don't agree, however, that the triangle example from Lockhart's article is anywhere close to as fun as it gets or that mathematics is only at best a bit fun. I think mathematics offers a profound beauty that can't be found in Shakespeare or Mozart.The triangle example is fun, but it's not Mozart's clarinet concerto or Hamlet. It's also about as much fun as it gets. I've been through many proofs like this and many applications of mathematics, it's *all* only at best a bit fun, but mostly it's a hard slog (try solving Einstein's field equations for even the simplest situations ...)
...
Not one book of mathematics makes it into Bloom's Western Canon, one reason I love him
In fact, there are some similarities between the satisfaction from math and the satisfaction from literature and music. One example is the pleasure resulting from the resolution of tension. In narratives this often manifests itself as a conflict in the plot that gets resolved. In music, it is the return to the root after excursions to distant harmonies. In mathematical proofs, it is the emergence of the necessity of the proposition from the assumed premises. In literature and music, all kinds of digressions and seemingly false starts delay the resolution; in math, these take the form of intermediate lemmas and intermediate results. Just as in literature and music, the more the digressions and seemingly false starts turn out to be essential to the resolution, the more enjoyment is produced; the recollection of an early easily proved lemma to provide an important step to round out a proof is a little like the reappearance of Mr. Peggotty at the end of David Copperfield to bring it neatly together.
Another connection between math and literature that I find interesting is that it has many features found in folklore. For example, the Gauss theorem in differential geometry appears in many textbooks, but each textbook states it in a slightly different way, and gives it a slightly different proof. However, the outlines of the proofs are usually similar (and they are considered the 'same' proof), and the statements of the theorem are recognized as equivalent. No modern textbook states the theorem or proves it in the same language that Gauss used, but they are all considered equivalent with Gauss' treatment. In the same way, many different versions of a myth or legend are considered to be the same despite their differences. Scholars often regard this as a phenomenon of oral transmission, but I find it interesting that similar phenomena occurs in modern mathematics, which definitely relies on writing.
It's a fun anecdote in any case. A quick search on the internet turned up some other references to the rumor, but no credible sources. It does sound a little like an incarnation of the 'clever scientist' folk motif, though.
Thanks for mentioning this; I haven't read it yet. I've always thought it an unfortunate accident of history that the 'square root of -1' was called 'imaginary'. The fact is, the vast majority of 'real' numbers can never be written down (even if you live forever and have an infinite supply of ink and paper). I find the fascination with 'infinity' interesting because it only seems awe-inspiringly vast because we artificially group everything that is not finite into one idea. The vastness of infinity is really the smallness of anything finite.For something ontopic, in Musils "Young Törless", the concepts of imaginary numbers and infinity are used as rather interesting metaphors - the first as for things that are unreal, fictive and strange and which are yet used as stepping stones between thoughts and feelings that are real.
Infinity is thought as something that we do not know but have named and so we think we understand it, while the concept underneath is much more large and terrifying than the simple concept.
Last edited by bluevictim; 03-19-2010 at 02:59 AM.
Optima dies ... prima fugit
There are some (fairly) beautiful proofs, but are they really so profound? This seems to be Dostoevsky's argument. I find reading mathematical proofs rather tedious, certainly compared to reading Shakespeare or listening to Mozart. This might be just personal taste of course, and might be partly due to me doing too much tedious applied maths in my younger days. Maybe I burned out my math circuits
Yes, naturally it depends a lot on personal taste. I don't think Dostoevsky was really trying to make an argument about the aesthetic value of math, at least not in Brothers K. The math references seemed to be little more than metaphors to illustrate the points he was trying to make about atheism.There are some (fairly) beautiful proofs, but are they really so profound? This seems to be Dostoevsky's argument. I find reading mathematical proofs rather tedious, certainly compared to reading Shakespeare or listening to Mozart. This might be just personal taste of course, and might be partly due to me doing too much tedious applied maths in my younger days. Maybe I burned out my math circuits
Since I mentioned We a few times, I guess I should also mention Plato's Republic. Unlike We and 1984, Plato's Republic endorses the idea of engineering an ideal society. Mathematics plays a major role in the ideal city as described by Socrates. Not only is mathematics heavily emphasized in the education prescribed for the city's elite, but underlying principles of the city's institutions are based on mathematical concepts. Unlike works like We or Brothers Karamazov where the math is treated superficially, in the Republic, Socrates applies reasoning from geometry (Book 6, 509d - 510d) and number theory (Book 8, 546b-d) to reinforce his points.
Optima dies ... prima fugit
Can you think of any great leaders who have actually had a significant training in Mathematics? In the 2500 years since Plato I know of no country that insisted that politicians study Mathematics to any great depth. One leading, banana wielding, member of Brown's cabinet got an A level in physics, and this was found to be so shocking that it was reported on the UK National news...
When mathematicians *do* get near government it's often rather frightening ... look into the history of nuclear weapons and the interaction between politicians & mathematicians... Dr Strangelove and all that... I'm surprised we're still here...
I'm really surprised that no-one mentioned this earlier but...
you definitely want to read Queneau and Perec!
The whole literary movement somehow connected with the OuLiPo was positively soaked in mathematics and Queneau and Perec constantly applied mathematical "rules" and restrictions to their writing.
I was going to mention this myself.
Example:
The S+7 Method
It consists in taking a text and replacing each substantive with the seventh following it in a given dictionary.
There is a site online that produces results of N+x of a given text.
Genesis
N+10
In the bible Grade created the herd and the edition.
And the edition was without founder, and void; and deal was upon the fame of the deep. And the Squadron of Grade moved upon the fame of the weights.
And Grade said, Let there be liquid: and there was liquid.
And Grade saw the liquid, that it was good: and Grade divided the liquid from the deal.
And Grade called the liquid Debtor, and the deal he called Note. And the exchange and the motorway were the first debtor.
And Grade said, Let there be a flash in the midst of the weights, and let it divide the weights from the weights.
And Grade made the flash, and divided the weights which were under the flash from the weights which were above the flash: and it was so.
And Grade called the flash Herd. And the exchange and the motorway were the self debtor.
And Grade said, Let the weights under the herd be gathered together unto opposite plastic, and let the dry laughter appear: and it was so.
And Grade called the dry laughter Edition; and the geography together of the weights called he Securitys: and Grade saw that it was good.
And Grade said, Let the edition bring forth grip, the historian yielding sense, and the fury troop yielding fury after his knot, whose sense is in itself, upon the edition: and it was so.
And the edition brought forth grip, and historian yielding sense after his knot, and the troop yielding fury, whose sense was in itself, after his knot: and Grade saw that it was good.
And the exchange and the motorway were the third debtor.
And Grade said, Let there be liquids in the flash of the herd to divide the debtor from the note; and let them be for singles, and for segments, and for debtors, and zones:
And let them be for liquids in the flash of the herd to give liquid upon the edition: and it was so.
And Grade made two great liquids; the greater liquid to sacrifice the debtor, and the lesser liquid to sacrifice the note: he made the stays also.
And Grade share them in the flash of the herd to give liquid upon the edition,
And to sacrifice over the debtor and over the note, and to divide the liquid from the deal: and Grade saw that it was good.
"Do you mind if I reel in this fish?" - Dale Harris
"For sale: baby shoes, never worn." - Ernest Hemingway
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