They then veer off into saying things about religion. I suspect this may be due to the title of this blog.
I just want to state that "God Plays Dice" has nothing to do with the Judeo-Christian-Islamic-etc. deity. It is a reference to the following quote of Einstein, in a letter to Max Born:
Quantum mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal but hardly brings us closer to the secrets of the Old One. I am at any rate convince that He does not play dice."(I'm copying this out of Gino Segre's Faust in Copenhagen; it's originally from Einstein's letter to Born, December 4, 1926, which is reprinted in The Born-Einstein Letters.) The "Old One" to whom Einstein is referring here was, as far as we know, not what is usually meant by "God"; I suspect that this is why the translator (Irene Born) chose this translation, although I don't know what Einstein said in the original German. To be totally honest, I don't know if the original was even in German.
The purpose of the title is that I feel that probability is an important tool for understanding the world, which Einstein may have been a bit skeptical about, at least in the case of quantum mechanics. And there's something of a tradition in the titling of math blogs of taking sayings of well-known mathematicians and "replying" to them. (By "tradition" I mean The Unapologetic Mathematician also does it, in response to Hardy's A Mathematician's Apology.)
Also, for some reason I had thought it was Bohr, not Born, that he wrote this to. I suspect this is because I've heard more things about Bohr than Born, and they sound similar.
I suspect the people at the forum in question won't read this, though. But making this post makes me feel like I've replied to them.
edited, 5:56 pm: I was wondering if there were any blogs whose titles riff on the quote that "A mathematician is a device for turning coffee into theorems" (usually attributed to Erdos, but supposedly actually due to Renyi). I found Tales from an English Coffee Drinker. The quote from Goethe, "Mathematicians are like Frenchmen: whatever you say to them they translate into their own language and forthwith it is something entirely different", also would be good as a source for a blog title.
19 comments:
I take it that the title of a math blog that almost but didn't quite come into being, Coffee and Mathematics (which Charles Siegel at Rigorous Trivialities brought to our attention), was intended to be just such a riff on Erdos's quip.
"It is a reference to the following quote of Einstein, in a letter to Max Born"
I was mildly surprised to read the above statement in your post, for I had always assumed that the idea for your blog title was derived from Stephen Hawking's famous quote:
" God not only plays dice but... He also sometimes throws the dice where they cannot be seen. "
My belief in that assumption was also strengthened by the fact that Hawking's mother's name was Isobel!
I guess I was wrong.
I don't know for sure, but I can only assume that Hawking's quote follows from Einstein's.
Oh, that's definitely true! Hawking's statement was certainly made in response to that famous quote of Einstein. All this of course goes on to show that you are in the same league as Hawking! :)
Ok annoyingly long question earlier. Simple version: Algebraic manipulation, necessary skill or vestige of on a by gone era before cheap computational power?
Sorry, for all my absurd thoughts, but since I'm new to all this and my friends didn't such things, I have no real concept of what it means to be math student... what skills i should focus on acquiring and what can be safely "ignored".
Kurt:
If I may answer your question in brief (to the best of my ability), I will just say that traditional skills associated with algebraic manipulation these days are certainly getting obsolete, so to speak, especially with the proliferation of powerful math software. However, the neglect in development of some of those basic algebraic skills may lead to a situation wherein a student's mathematical ability may be somewhat "diminished". To take a more simple example, it may seem almost useless to learn to add/subtract numbers, given that calculators can deal with such mundane computation almost instantly, but not knowing how to add/subtract numbers can definitely deprive a student the opportunity to learn some of the fundamental mathematical ideas behind such computation.
Coming back to your question, a lot of times, the ability to "finish" a mathematical proof requires one to have a thorough knowledge of some of the basic techniques in "algebraic manipulation". What is more, some of those basic algebraic "skills" can be improved upon or generalized to yield even more useful techniques. This is something we do in mathematics all the time.
I am sure there is a lot that others on this blog can add to what I have already said.
i don't know about what 'the old one thinks' but i know in the true religion the Mets lead the Phillies by a 1/2 game.
While we're on the subject, my favorite quote on mathematics and religion is by Bertrand Russell:
"If a religion is defined to be a system of ideas that contains unprovable statements, then Gödel taught us that mathematics is not only a religion, it is the only religion that can prove itself to be one."
I've always been rather fond of the story about G. H. Hardy and Ramanujan and the number 1729, and so I considered naming my blog "Uninteresting Numbers".
I believe Einstein's letter was in german: http://de.wikipedia.org/wiki/Gott_w%C3%BCrfelt_nicht
It's not a blog, but Brainfreeze Puzzles has the tagline "we turn coffee into puzzles".
By the by, if you think deeply about the relationships that are implied by a lot of algebraic manipulation [at least of the multivariable kind], you can glean a lot of geometric insight. That we spend our formative years grinding away at small problems of algebra is so that we can not worry about our execution when we tackle bigger problems. Some people, though, never stop grinding the small problems, and they grind the glass of the lens to a fine, wispy dust.
"By the by, if you think deeply about the relationships that are implied by a lot of algebraic manipulation [at least of the multivariable kind], you can glean a lot of geometric insight. That we spend our formative years grinding away at small problems of algebra is so that we can not worry about our execution when we tackle bigger problems. Some people, though, never stop grinding the small problems, and they grind the glass of the lens to a fine, wispy dust."
Doesn't that imply that a computer could be used to check for violations of algebraic rules freeing one of such pedestrian concerns. Really is this any different than spell check? Or, Grammar check? A little red line appears under the violation. If you wish to ignore it for your purposes so be it.
"... God does play dice with the universe. All the evidence points to him being an inveterate gambler, who throws the dice on every possible occasion. "
(-- Stephen Hawking)
______
http://www.hawking.org.uk/lectures/dice.html
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"Einstein was very unhappy about this apparent randomness in nature. His views were summed up in his famous phrase, 'God does not play dice'. He seemed to have felt that the uncertainty was only provisional: but that there was an underlying reality, in which particles would have well defined positions and speeds, and would evolve according to deterministic laws, in the spirit of Laplace. This reality might be known to God, but the quantum nature of light would prevent us seeing it, except through a glass darkly.
Einstein's view was what would now be called, a hidden variable theory. Hidden variable theories might seem to be the most obvious way to incorporate the Uncertainty Principle into physics. They form the basis of the mental picture of the universe, held by many scientists, and almost all philosophers of science.
But these hidden variable theories are wrong. "
(-- Stephen Hawking)
The exchange obviously took place in German - how else would two native German speakers, at that time both professors in German universities, communicate after all... (most exchanges about quantum mechanics were conducted in German at that time, for sure)
Actually, perhaps Einstein intended a pun: a piece in the game of backgammon is called "Stein" in German; using the indefinite article, "ein Stein".
But Einstein refused to believe he's being moved according to a dice roll :)
I'm glad you've given the background to the title in this post, because I've often wondered about its genesis and meaning. Though any regular reader can see that you're not ever writing about religion.
I think it would be cool to put that info somewhere in your "about" section, where I had originally looked to find an explanation.
Hi, just came across this posting when playing with the backlinks feature on blogger. "Tales from an English Coffee Drinker" is my blog. The source for the blog title was actually the novel "Confessions of an English Opium Eater" by Thomas De Quincey. I went with tales instead of confessions as I didn't really feel like I was confessing anything!
Hello,
I've just started my own blog and i'm really happy to find articles like this
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