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Counterpoint: he notes our techniques are based on writing, but it goes deeper: our symbolic writing (including mathematical notation) is based on speech, for w

by 6ren 13y ago

Counterpoint: he notes our techniques are based on writing, but it goes deeper: our symbolic writing (including mathematical notation) is based on speech, for which we have dedicated linguistic structures in our brains, much as we have a visual center. It is deep-seated, and many have argued fundamentally entwined with sapience. Thus, even if it's not theoretically the best way, it might be the best way for us. But I'm going to argue it is the theoretically best way: Linguistic descriptions have a key advantage over pictorial in that they represent or reference rather than show. This enables them to be compact, and omit unnecessary detail. (Of course, showing rather than telling is a strength of visual representation). Yes, you can have a hierarchy of visual systems, and zoom-in or hide. But a fundamental problem here I think is in choosing the hierarchy - that is, the way the system is modularized. Different modularizations of the same system are often appropriate for different uses of that system, or for considering different aspects of it. For even a slightly complex system, there are a huge number of different modularizations possible, and not all of them are useful. Often, you'll start with a poor one, and eventually have insights moving you towards the ideal one. (Of course, sometimes the "right" modularization is obvious, especially for well-known families of problems). All this is very difficult. My point is that it is easier to switch modularities linguistically than pictorially, by changing your concepts. Without the right modularity, it's difficult to pictorially show just the aspects of interest instead of the whole picture. In contrast, one can linguistically omit detail by referencing it (implicitly, as a separate module). Maybe it's possible to do this visually, though I suspect it thereby would have become linguistic! [Though the above is a counterpoint, I'm very impressed with the talk. He's working both ends of abstraction, with concrete working software demonstrating cool useful practical techniques that, while not universal, would be helpful in many domains; and also framing it within, and using it to illustrate, the deep universal and philosophical idea of unthinkable thoughts. BTW e.g. uncomputable numbers.]

natural219 13y ago
My gut reaction is to say that all three of these ways of thinking (interactive, visual, and symbolic) are all useful and should be used where their advantages can be best applied. As a shallow example, I think that the basic visual/interactive representations can be fantastic teaching tools, and once you get an intuitive feel for how the system behaves, you can then switch to symbolic representation and move on to the more higher-order systems which those building blocks are composed of. I thought it was interesting that when he compressed the paragraph describing an equation to is algebraic representation (x2 + 2x = 10), we immediately grokked the algebraic version better, because we have loads of experience reading and manipulating the algebraic expression. If I think back to my own learning career, however, I learned the basic tenets of algebra using -- you guessed it -- interactive and visual representation through Hands-On Equations [1] [1] http://www.borenson.com/ http://www.borenson.com/ (now that I think about it, Hands-On Equations serves as a very nice "tldr" for this speech and the related concepts)
gbog 13y ago
I don't know, maybe the good old separation between soft and hard science can help here. On the speech side, in soft science, I think the most powerful transmission of knowledge if by pure speech, oral speech, like in podcasts. A good lecturer will branch his brain on yours and will have a very high and precise throughput, only by spoken words. That's for history, politics, philosophy, soft sciences. The best example I know of this effect is the courses of Jankelevitch (in French), it's really like a good ride on the back of an experimented motorbike driver knowing the region like the back of his hand. On the other side, the pinnacle of hard sciences, geometry, logic, topology, are very visual and symbolic by essence. A proof is only an explanation of a truth that is already there, that some can "see in their mind". I wouldn't imagine being able to follow a math class without a black board, that would be like a piano lesson without a piano.
tmerr 13y ago
Albert Einstein in a letter to Jacques Hadamard: The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined. .... This combinatory play seems to be the essential feature in productive thought before there is any connection with logical construction in words or other kinds of signs which can be communicated to others Good thought doesn't have to be linguistic. I speculate that the reason most of us only think in words because it's the way we're taught. We can hear the word "dog" because at a young age we were told about the association from each letter => sound. "What does A sound like? aaaaah". But what if instead our parents and teachers taught us that A was a picture? A could be a red square, and B a purple box. "DOG" might be a pink triangle next to a red and a green circle. Great, then you start to remember those three shapes as one image, just as you remember the sounds "duh" "aww" "guh" as one. And you would learn to assemble them together in all the same ways. I bet you would get very good at it. I think that every verbal system could be represented in a visual system by just replacing each sound with a shape. I actually know of people who do this, who do this fully, just not with boxes and circles. The deaf. They can learn how to read despite having no hearing. They will report that instead of using sounds they think in a combination of hand signs and images. This is the only group of people I know that replaces all sounds with images, but there are a lot of examples of in-betweens too. Vladimir Nabokov, the author of Lolita: The long "a" of the English alphabet has for me the tint of weathered wood, but a French "a" evokes polished ebony. This black group also includes hard "g" (vulcanized rubber) and "r" (a sooty rag being ripped). Oatmeal "n", noodle-limp "l", and the ivory-backed hand mirror of an "o" take care of the whites. I am puzzled by my French "on" which I see as the brimming tension-surface of alcohol in a small glass. Richard Feynman: When I see equations, I see the letters in colors – I don't know why. As I'm talking, I see vague pictures of Bessel functions from Jahnke and Emde's book, with light-tan j's, slightly violet-bluish n's, and dark brown x's flying around. And I wonder what the hell it must look like to the students. tl;dr you can do everything visually. Or you can mash up visuals and words. The problem of "choosing between hierarchies" isn't actually a problem, because just as you can make a sound to decide, you can make a visual symbol. If this were false then you would have to explain how sign language works.

by 6ren 13y ago

natural219 13y ago

My gut reaction is to say that all three of these ways of thinking (interactive, visual, and symbolic) are all useful and should be used where their advantages can be best applied. As a shallow example, I think that the basic visual/interactive representations can be fantastic teaching tools, and once you get an intuitive feel for how the system behaves, you can then switch to symbolic representation and move on to the more higher-order systems which those building blocks are composed of. I thought it was interesting that when he compressed the paragraph describing an equation to is algebraic representation (x2 + 2x = 10), we immediately grokked the algebraic version better, because we have loads of experience reading and manipulating the algebraic expression. If I think back to my own learning career, however, I learned the basic tenets of algebra using -- you guessed it -- interactive and visual representation through Hands-On Equations [1] [1] http://www.borenson.com/ http://www.borenson.com/ (now that I think about it, Hands-On Equations serves as a very nice "tldr" for this speech and the related concepts)

gbog 13y ago

I don't know, maybe the good old separation between soft and hard science can help here. On the speech side, in soft science, I think the most powerful transmission of knowledge if by pure speech, oral speech, like in podcasts. A good lecturer will branch his brain on yours and will have a very high and precise throughput, only by spoken words. That's for history, politics, philosophy, soft sciences. The best example I know of this effect is the courses of Jankelevitch (in French), it's really like a good ride on the back of an experimented motorbike driver knowing the region like the back of his hand. On the other side, the pinnacle of hard sciences, geometry, logic, topology, are very visual and symbolic by essence. A proof is only an explanation of a truth that is already there, that some can "see in their mind". I wouldn't imagine being able to follow a math class without a black board, that would be like a piano lesson without a piano.

tmerr 13y ago

Albert Einstein in a letter to Jacques Hadamard: The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined. .... This combinatory play seems to be the essential feature in productive thought before there is any connection with logical construction in words or other kinds of signs which can be communicated to others Good thought doesn't have to be linguistic. I speculate that the reason most of us only think in words because it's the way we're taught. We can hear the word "dog" because at a young age we were told about the association from each letter => sound. "What does A sound like? aaaaah". But what if instead our parents and teachers taught us that A was a picture? A could be a red square, and B a purple box. "DOG" might be a pink triangle next to a red and a green circle. Great, then you start to remember those three shapes as one image, just as you remember the sounds "duh" "aww" "guh" as one. And you would learn to assemble them together in all the same ways. I bet you would get very good at it. I think that every verbal system could be represented in a visual system by just replacing each sound with a shape. I actually know of people who do this, who do this fully, just not with boxes and circles. The deaf. They can learn how to read despite having no hearing. They will report that instead of using sounds they think in a combination of hand signs and images. This is the only group of people I know that replaces all sounds with images, but there are a lot of examples of in-betweens too. Vladimir Nabokov, the author of Lolita: The long "a" of the English alphabet has for me the tint of weathered wood, but a French "a" evokes polished ebony. This black group also includes hard "g" (vulcanized rubber) and "r" (a sooty rag being ripped). Oatmeal "n", noodle-limp "l", and the ivory-backed hand mirror of an "o" take care of the whites. I am puzzled by my French "on" which I see as the brimming tension-surface of alcohol in a small glass. Richard Feynman: When I see equations, I see the letters in colors – I don't know why. As I'm talking, I see vague pictures of Bessel functions from Jahnke and Emde's book, with light-tan j's, slightly violet-bluish n's, and dark brown x's flying around. And I wonder what the hell it must look like to the students. tl;dr you can do everything visually. Or you can mash up visuals and words. The problem of "choosing between hierarchies" isn't actually a problem, because just as you can make a sound to decide, you can make a visual symbol. If this were false then you would have to explain how sign language works.