Comments on: JMM notes and snippets http://bit-player.org/2008/jmm-notes-and-snippets An amateur's outlook on computation and mathematics. Wed, 23 Jul 2008 19:14:33 +0000 http://wordpress.org/?v=1.5.2 Comment on JMM notes and snippets by: brian http://bit-player.org/2008/jmm-notes-and-snippets#comment-1591 Tue, 22 Jan 2008 15:30:22 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1591 @Scott Aaronson: When I drew that silly graph, I had in the back of my mind the Laffer Curve. For those who don't remember their Reagonomics, this was Arthur Laffer's justification for reducing taxes on the rich. He noted that total revenue to the government would be zero at a tax rate of either o% or 100%, and so there "must be" a maximum somewhere between those extremes. He drew a curve that looked a lot like the one above. (Though I think maybe his was a parabola rather than a cosine curve.) Martin Gardner (with help from Persi Diaconis) was one of the first to point out that the existence of a unique peak is not to be taken for granted. His Neo-Laffer Curve has a "technosnarl" in the middle. (A redrawn version here: http://en.wikipedia.org/wiki/Image:Neo-Laffer-Curve.svg) Perhaps the real lecture-utility curve suffers from the opposite pathology: It is well-behaved in the middle but not very clearly defined at both ends. @Scott Aaronson: When I drew that silly graph, I had in the back of my mind the Laffer Curve. For those who don’t remember their Reagonomics, this was Arthur Laffer’s justification for reducing taxes on the rich. He noted that total revenue to the government would be zero at a tax rate of either o% or 100%, and so there “must be” a maximum somewhere between those extremes. He drew a curve that looked a lot like the one above. (Though I think maybe his was a parabola rather than a cosine curve.)

Martin Gardner (with help from Persi Diaconis) was one of the first to point out that the existence of a unique peak is not to be taken for granted. His Neo-Laffer Curve has a “technosnarl” in the middle. (A redrawn version here: http://en.wikipedia.org/wiki/Image:Neo-Laffer-Curve.svg)

Perhaps the real lecture-utility curve suffers from the opposite pathology: It is well-behaved in the middle but not very clearly defined at both ends.

]]> Comment on JMM notes and snippets by: Seb http://bit-player.org/2008/jmm-notes-and-snippets#comment-1590 Mon, 21 Jan 2008 21:36:30 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1590 Natural selection. How long would any other universe with different laws have lasted? Or may be there are others around? Would those have developed this blog? Natural selection.
How long would any other universe with different laws have lasted?
Or may be there are others around?
Would those have developed this blog?

]]> Comment on JMM notes and snippets by: Scott Aaronson http://bit-player.org/2008/jmm-notes-and-snippets#comment-1589 Sun, 20 Jan 2008 23:32:41 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1589 In quantum mechanics, it's possible to <i>derive</i> least-action principles by showing that all the paths in a superposition that don't minimize some resource interfere destructively and cancel each other out. I really don't understand this myself, but at least I <i>felt</i> like I understood it the several times it was explained to me; hopefully it's enough of a hint to get you started. My knowledge graph for talks looks different from yours: even if I already know "everything" about a topic, I often learn something from the way the speaker chooses to present the material; while on the left side, my graph is definitely not nonnegative. In quantum mechanics, it’s possible to derive least-action principles by showing that all the paths in a superposition that don’t minimize some resource interfere destructively and cancel each other out. I really don’t understand this myself, but at least I felt like I understood it the several times it was explained to me; hopefully it’s enough of a hint to get you started.

My knowledge graph for talks looks different from yours: even if I already know “everything” about a topic, I often learn something from the way the speaker chooses to present the material; while on the left side, my graph is definitely not nonnegative.

]]> Comment on JMM notes and snippets by: Seb http://bit-player.org/2008/jmm-notes-and-snippets#comment-1588 Sat, 19 Jan 2008 20:43:26 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1588 May be the laws of nature have evolved to the form that we know. May be the laws of nature have evolved to the form that we know.

]]> Comment on JMM notes and snippets by: Seb http://bit-player.org/2008/jmm-notes-and-snippets#comment-1587 Fri, 18 Jan 2008 03:31:06 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1587 I don't see why nature should want. I don’t see why nature should want.

]]> Comment on JMM notes and snippets by: Monte Davis http://bit-player.org/2008/jmm-notes-and-snippets#comment-1586 Wed, 16 Jan 2008 17:55:24 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1586 I hope Bellman kicks off some ideas. I've occasionally tried to explain his "unit cube grows faster than unit sphere" insight with only fair-to-poor success, but you're a much better explainer. One place it crops up with a lot of resonance is in evolutionary thought, when you compare living species to all those that have existed... and then those to all possible phenotypes... and then those to all possible genotypes. It's a useful mind-stretching exercise, changing one's perspective from a Noah's-Ark "plenitude" -- gee, life seems to fill every niche -- to a realization of just how sparse (mathematically speaking) the "tree of life" is. I hope Bellman kicks off some ideas. I’ve occasionally tried to explain his “unit cube grows faster than unit sphere” insight with only fair-to-poor success, but you’re a much better explainer.

One place it crops up with a lot of resonance is in evolutionary thought, when you compare living species to all those that have existed… and then those to all possible phenotypes… and then those to all possible genotypes. It’s a useful mind-stretching exercise, changing one’s perspective from a Noah’s-Ark “plenitude” — gee, life seems to fill every niche — to a realization of just how sparse (mathematically speaking) the “tree of life” is.

]]> Comment on JMM notes and snippets by: George Bell http://bit-player.org/2008/jmm-notes-and-snippets#comment-1585 Mon, 14 Jan 2008 22:43:59 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1585 Oops, my phone number is not prime. I typed "Factor[#]" in Mathematica, but you should use "FactorInteger[#]". But my street address is a factorial. Oops, my phone number is not prime. I typed “Factor[#]” in Mathematica, but you should use “FactorInteger[#]”. But my street address is a factorial.

]]> Comment on JMM notes and snippets by: George Bell http://bit-player.org/2008/jmm-notes-and-snippets#comment-1584 Mon, 14 Jan 2008 22:38:25 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1584 My phone number is prime, and my street address is 7!=5040. What are the odds of that? My phone number is prime, and my street address is 7!=5040. What are the odds of that?

]]> Comment on JMM notes and snippets by: brian http://bit-player.org/2008/jmm-notes-and-snippets#comment-1582 Mon, 14 Jan 2008 16:43:33 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1582 @Monte Davis: Thanks for the suggestion. I don't know whether I have anything further to add. As a starting point, I should go back and reread Richard Bellman's famous essay on "the curse of dimensionality." I've just made a note to do so. @Monte Davis: Thanks for the suggestion. I don’t know whether I have anything further to add. As a starting point, I should go back and reread Richard Bellman’s famous essay on “the curse of dimensionality.” I’ve just made a note to do so.

]]> Comment on JMM notes and snippets by: brian http://bit-player.org/2008/jmm-notes-and-snippets#comment-1581 Mon, 14 Jan 2008 16:25:49 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1581 @Jim Ward: I have a grandtoddler who is transfixed by Thomas the Tank Engine &#38; friends. I would love to see a learned discourse on the sociology and psychology of this curious world (perhaps on the model of "The Physics of the Buffyverse"). But I'm not the one to write it. Don't tell my grandkids, but I find Thomas insipid. @Jim Ward: I have a grandtoddler who is transfixed by Thomas the Tank Engine & friends. I would love to see a learned discourse on the sociology and psychology of this curious world (perhaps on the model of “The Physics of the Buffyverse”). But I’m not the one to write it. Don’t tell my grandkids, but I find Thomas insipid.

]]> Comment on JMM notes and snippets by: brian http://bit-player.org/2008/jmm-notes-and-snippets#comment-1580 Mon, 14 Jan 2008 16:09:31 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1580 On phone numbers: If Conrey had said to an audience of mathematicians, "Raise your hand if your phone number is <em>not</em> prime," I hope that at least half the hands would have gone up! On phone numbers: If Conrey had said to an audience of mathematicians, “Raise your hand if your phone number is not prime,” I hope that at least half the hands would have gone up!

]]> Comment on JMM notes and snippets by: Monte Davis http://bit-player.org/2008/jmm-notes-and-snippets#comment-1579 Mon, 14 Jan 2008 15:22:59 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1579 <i>The ordinary Euclidean distance function ... in a million-dimensional space... doesn’t tell us much... there’s so much elbow room in a high-dimensional space that “closeness” doesn’t mean much.</i> This is important, and may be less widely understood than you think. I can readily grasp that the 747 which "on the map" appears to be about to hit me is in fact safely six miles up; in principle we should be able to extrapolate that to higher dimensionality, but in practice laymen rarely have occasion to do so. As I recall from undergraduate physical chemistry, even math-minded students had to work hard to get any feel for &#62;3D phase spaces, ergodicity and all that. So... I'd love to see an entire post (or column) devoted to this, pretty please. The ordinary Euclidean distance function … in a million-dimensional space… doesn’t tell us much… there’s so much elbow room in a high-dimensional space that “closeness” doesn’t mean much.

This is important, and may be less widely understood than you think. I can readily grasp that the 747 which “on the map” appears to be about to hit me is in fact safely six miles up; in principle we should be able to extrapolate that to higher dimensionality, but in practice laymen rarely have occasion to do so. As I recall from undergraduate physical chemistry, even math-minded students had to work hard to get any feel for >3D phase spaces, ergodicity and all that.

So… I’d love to see an entire post (or column) devoted to this, pretty please.

]]> Comment on JMM notes and snippets by: Jim Ward http://bit-player.org/2008/jmm-notes-and-snippets#comment-1578 Mon, 14 Jan 2008 12:07:52 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1578 How about dualistic underpinnings - perhaps there's a god of optimization (female) at war with the god of entropy (male)? I got interested in male/female dichotomies while watching Thomas the Tank Engine with my toddler. How do we know steam engines have only two sexes? There could be as many as five. My phone number is divisible by 16. How about dualistic underpinnings - perhaps there’s a god of optimization (female) at war with the god of entropy (male)? I got interested in male/female dichotomies while watching Thomas the Tank Engine with my toddler. How do we know steam engines have only two sexes? There could be as many as five. My phone number is divisible by 16.

]]> Comment on JMM notes and snippets by: Daniel http://bit-player.org/2008/jmm-notes-and-snippets#comment-1577 Fri, 11 Jan 2008 06:44:04 +0000 http://bit-player.org/2008/jmm-notes-and-snippets#comment-1577 My phone number is not prime. My phone number is not prime.

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