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by ctoth
1090 days ago
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In terms of reading the notation out loud, if there is verbal ambiguity, remove it? For instance, for your example:
"X plus B quantity squared"
or "x + b squared" You can also do things like change the pitch of speech as symbols are nested, play specific tones to represent symbols, pan things across the stereo field to represent groupings, and otherwise make the symbolic equation into a multimodal experience. But of course, you can't do any of this if the semantic representation of the equation is lost and it is rendered as strictly graphics or whatever. I'm a bit confused to your original point about visualization because how ever in the world could I program if I couldn't abstractly manipulate symbols? I suppose not visually, but there's something non-word-oriented happening in my head. |
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I guess I find that programming is somewhat more word-oriented than pure math. For instance, how do you think about complex exponentiation, or a rotation matrix? Do you bring to mind the sensation of spinning around? For myself, I bring to mind the image of the entire complex plane rotating and stretching along a spiral, but I'm led to believe that those who are blind from birth aren't really capable of doing that.
Harder examples might include fourier series, convolution, gradient descent, etc.
I think you could almost consider the visualization of these things like a crutch. I wonder if not being able to visualize them might remove preconceived notions about how they behave, and give you different insights.