Comments on: Use the Native Architecture http://www.overcomingbias.com/2008/08/use-the-native.html Overcoming Bias is economist Robin Hanson’s blog, on honesty, signaling, disagreement, forecasting, and the far future. Sat, 11 Feb 2012 23:03:19 +0000 hourly 1 http://wordpress.org/?v=3.1.3 By: Dreamer http://www.overcomingbias.com/2008/08/use-the-native.html#comment-397596 Dreamer Tue, 26 Aug 2008 09:38:43 +0000 http://prod.ob.trike.com.au/2008/08/use-the-native-architecture.html#comment-397596 Yes, absolutely. This is something I think about a lot, and as a mathematician, my capicity to visualise mathematical ideas is exactly where I pin the physical location of my maths talent (metaphorically speaking, of course). Particular agreement with Jadagul on how to read a textbook. I'm going to throw it into the air that maybe a computer-science way of understanding this is that difficult mathematical ideas are somehow "large" in a memory sense, and talented mathematicians are mentally equipped with very large "mathematics buffers". In my experience of teaching mathematics to those who are struggling with high-school level stuff, the problem seems intuitively that they can't fit an entire mathematical idea into their head at once. Yes, absolutely. This is something I think about a lot, and as a mathematician, my capicity to visualise mathematical ideas is exactly where I pin the physical location of my maths talent (metaphorically speaking, of course). Particular agreement with Jadagul on how to read a textbook.

I’m going to throw it into the air that maybe a computer-science way of understanding this is that difficult mathematical ideas are somehow “large” in a memory sense, and talented mathematicians are mentally equipped with very large “mathematics buffers”. In my experience of teaching mathematics to those who are struggling with high-school level stuff, the problem seems intuitively that they can’t fit an entire mathematical idea into their head at once.

]]> By: mjgeddes http://www.overcomingbias.com/2008/08/use-the-native.html#comment-397595 mjgeddes Tue, 26 Aug 2008 08:52:24 +0000 http://prod.ob.trike.com.au/2008/08/use-the-native-architecture.html#comment-397595 The underlying power of metaphors comes from analogies, which, I claim, is <b>all</b> of intelligence, the <b>whole</b> basis for intelligence - that is to say, all other forms of reasoning (such as deductive/predicate, bayesian/probabilistic etc) are merely special cases of analogies: I claim that analogy formation is beyond the scope of Bayes. That's a big claim (and remember readers, you heard it explictly publically stated here by me first). Although you and Eliezer no doubt think that Bayesian reasoning is more general than anlogy formation, there is little basis for your beliefs- in fact - he and you have both got it the wrong way around. (Its Bayes that's the special case of analogy formation, not vice versa). Further, analogy formation is closely related to ontology merging, the ablity to communicate (or 'map') a valid concept from one knowledge domain to another novel knowledge domain. I repeat my big claim: this is <b>all</b> of intelligence; ontology/knowledge representation is <b>all</b> of the AI problem. Refer to the detailed discussion by Steven Pinker in his new book <a href="http://www.amazon.com/Stuff-Thought-Language-Window-Nature/dp/0670063274/ref=pd_bbs_2?ie=UTF8&s=books&qid=1219740313&sr=8-2" rel="nofollow">'The Stuff of Thought'</a> on the power of metaphor/analogy. Incidentally, here's a pro tip for you AI wannabes: ontology is the concrete version of pure math (ie ontologies are 'mathematical artifacts', or to use an analogy/metaphor, ontologies are to pure math as physical objects are to physical laws). I realized this myself months ago, but I was very pleased to get confirmation: first from Pinker, then, from references to other philosophers, who had independently realized this: <a href="http://en.wikipedia.org/wiki/Mathematical_beauty" rel="nofollow">Mathematical Beauty!</a> "Twentieth-century French philosopher Alain Badiou claims that <b>ontology is mathematics.</b> Badiou also believes in deep connections between math, poetry and philosophy." The underlying power of metaphors comes from analogies, which, I claim, is all of intelligence, the whole basis for intelligence – that is to say, all other forms of reasoning (such as deductive/predicate, bayesian/probabilistic etc) are merely special cases of analogies: I claim that analogy formation is beyond the scope of Bayes.

That’s a big claim (and remember readers, you heard it explictly publically stated here by me first). Although you and Eliezer no doubt think that Bayesian reasoning is more general than anlogy formation, there is little basis for your beliefs- in fact – he and you have both got it the wrong way around. (Its Bayes that’s the special case of analogy formation, not vice versa).

Further, analogy formation is closely related to ontology merging, the ablity to communicate (or ‘map’) a valid concept from one knowledge domain to another novel knowledge domain. I repeat my big claim: this is all of intelligence; ontology/knowledge representation is all of the AI problem.

Refer to the detailed discussion by Steven Pinker in his new book ‘The Stuff of Thought’ on the power of metaphor/analogy.

Incidentally, here’s a pro tip for you AI wannabes: ontology is the concrete version of pure math (ie ontologies are ‘mathematical artifacts’, or to use an analogy/metaphor, ontologies are to pure math as physical objects are to physical laws). I realized this myself months ago, but I was very pleased to get confirmation: first from Pinker, then, from references to other philosophers, who had independently realized this:

Mathematical Beauty!

“Twentieth-century French philosopher Alain Badiou claims that ontology is mathematics. Badiou also believes in deep connections between math, poetry and philosophy.”

]]> By: anon http://www.overcomingbias.com/2008/08/use-the-native.html#comment-397594 anon Tue, 26 Aug 2008 07:58:00 +0000 http://prod.ob.trike.com.au/2008/08/use-the-native-architecture.html#comment-397594 Jadagul, do you have ant references detailing the principles of good mathematical visualization, or providing case studies/examples? It seems that mathematicians have had no interest in documenting this since the closest that comes to mind is cognitive science research, including Lakoff and Nunez's controversial work, <i>Where Mathematics Comes From</i>. Jadagul, do you have ant references detailing the principles of good mathematical visualization, or providing case studies/examples? It seems that mathematicians have had no interest in documenting this since the closest that comes to mind is cognitive science research, including Lakoff and Nunez’s controversial work, Where Mathematics Comes From.

]]> By: Jadagul http://www.overcomingbias.com/2008/08/use-the-native.html#comment-397593 Jadagul Tue, 26 Aug 2008 06:01:52 +0000 http://prod.ob.trike.com.au/2008/08/use-the-native-architecture.html#comment-397593 Douglas, different people visualize in different ways. The textbook tries to give you enough details that you can reconstruct the argument, while giving you few enough that you have to actually reconstruct it, which forces you to frame it in a way that makes sense to you. (I avoid the word 'visualize' because there never seems to be much that's actually visual about the way I understand math proofs; this is sort of the point). Douglas, different people visualize in different ways. The textbook tries to give you enough details that you can reconstruct the argument, while giving you few enough that you have to actually reconstruct it, which forces you to frame it in a way that makes sense to you. (I avoid the word ‘visualize’ because there never seems to be much that’s actually visual about the way I understand math proofs; this is sort of the point).

]]> By: Douglas Knight http://www.overcomingbias.com/2008/08/use-the-native.html#comment-397592 Douglas Knight Tue, 26 Aug 2008 05:51:12 +0000 http://prod.ob.trike.com.au/2008/08/use-the-native-architecture.html#comment-397592 I don't see how Jadagul is disagreeing with steven. Math books give too much detail in proofs; rather, they give the wrong details. They should tell you how to reconstruct the proof, not give you touchstones. Visualization is a part of that. I don’t see how Jadagul is disagreeing with steven. Math books give too much detail in proofs; rather, they give the wrong details. They should tell you how to reconstruct the proof, not give you touchstones. Visualization is a part of that.

]]> By: Larry D'Anna http://www.overcomingbias.com/2008/08/use-the-native.html#comment-397591 Larry D'Anna Tue, 26 Aug 2008 05:26:26 +0000 http://prod.ob.trike.com.au/2008/08/use-the-native-architecture.html#comment-397591 Jadagul: I agree. You aren't really reading a math text if you don't have a pencil in your hand and plenty of scratch paper. Jadagul: I agree. You aren’t really reading a math text if you don’t have a pencil in your hand and plenty of scratch paper.

]]> By: Jadagul http://www.overcomingbias.com/2008/08/use-the-native.html#comment-397590 Jadagul Mon, 25 Aug 2008 21:55:11 +0000 http://prod.ob.trike.com.au/2008/08/use-the-native-architecture.html#comment-397590 Steven, math texts aren't supposed to be a good way of visualizing the argument. They're supposed to be a skeleton; every prof I've talked to agrees that you're basically supposed to be rewriting any argument you care about as you read it. I know that if I find an argument confusing I can generally figure it out by starting at the top and writing it out as I would notes for a proof I'm working on myself. The math text isn't supposed to be the understandable version; it's supposed to be the cliff notes so you can make your own understandable version. Steven, math texts aren’t supposed to be a good way of visualizing the argument. They’re supposed to be a skeleton; every prof I’ve talked to agrees that you’re basically supposed to be rewriting any argument you care about as you read it. I know that if I find an argument confusing I can generally figure it out by starting at the top and writing it out as I would notes for a proof I’m working on myself.

The math text isn’t supposed to be the understandable version; it’s supposed to be the cliff notes so you can make your own understandable version.

]]> By: Floccina http://www.overcomingbias.com/2008/08/use-the-native.html#comment-397589 Floccina Mon, 25 Aug 2008 21:35:47 +0000 http://prod.ob.trike.com.au/2008/08/use-the-native-architecture.html#comment-397589 Math-U-See seems interesting. http://www.mathusee.com/ Math-U-See seems interesting.
http://www.mathusee.com/

]]> By: anon http://www.overcomingbias.com/2008/08/use-the-native.html#comment-397588 anon Mon, 25 Aug 2008 20:33:02 +0000 http://prod.ob.trike.com.au/2008/08/use-the-native-architecture.html#comment-397588 <i>It sure complicated the math by dispersing it all over the place.</i> On the contrary, two-dimensional "boxed" representations of complicated expressions may be more intuitive than conventional math layout. Here is <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.39.9450" rel="nofollow">one paper on Citeseer</a> which uses such a notation to analyze the computer proof of the Robbins-Boolean problem. It sure complicated the math by dispersing it all over the place.

On the contrary, two-dimensional “boxed” representations of complicated expressions may be more intuitive than conventional math layout. Here is one paper on Citeseer which uses such a notation to analyze the computer proof of the Robbins-Boolean problem.

]]> By: Michael Drake http://www.overcomingbias.com/2008/08/use-the-native.html#comment-397587 Michael Drake Mon, 25 Aug 2008 19:11:39 +0000 http://prod.ob.trike.com.au/2008/08/use-the-native-architecture.html#comment-397587 "when my psychology teacher put up a string of twenty digits on the board and asked us to memorize them, I was able to do it. " Did you use rhythms or add "lyrics" to the tunes? “when my psychology teacher put up a string of twenty digits on the board and asked us to memorize them, I was able to do it. ”

Did you use rhythms or add “lyrics” to the tunes?

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