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Gunnar_Zarncke comments on Open thread, Jan. 18 - Jan. 24, 2016 - Less Wrong
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Is here any interest in posts about parenting with a lesswrong touch? Example:
Mental Images Part of Philosophy with Children
This evening my oldest asked me to test his imagination. Apparently he had played around with it and wanted some outside input to learn more about what he could do. We had talked about https://en.wikipedia.org/wiki/Mental_image before and I knew that he could picture moving scenes composed of known images. So I suggested
The latter took quite some time, partly because he had to assign colors and such so that he could fully picture this and then the image in the mirror. I checked by asking where the handlebar is and the bell. I had significant difficulties to imagine this and correctly place the bell. I noticed that it is easier to just see the bell once the image in the mirror has gained enough detail (the walls before and behind me, the corner, the bike leaning on the corner, the handlebar).
I also asked for a square circle which got the immediate reply that it is logically impossible.
If you have difficulties doing these (are judge them trivial): This is one area where human experience varies a lot. So this is not intended to provide a reference point in ability but an approach to teach human difference, reflection and yes also practice imagination - a useful tool if you have it. If not you might be interested in what universal human experiences are you missing without realizing it.
I'm currently writing these daily and posting them on the LW slack and the less-wrong-parents group.
I am now imagining a square circle. That's interesting.
Can you describe it?
It's circular, and square.
That's literally all there is. I can't imagine it visually, the way I usually would. Wonder why. :P
― Lewis Carroll
See also this article discussing the usefulness of believing impossible things.
I can imagine it. You just have to embed it in a non-Euclidean geometry. A great circle can be constructed from 4 straight lines, and thus is a square, and it still has every point at a fixed distance from a common center (okay, 2 common centers), and thus is a circle.
The four straight lines in your construction don't meet at right angles.
Sparks of Genius has a lot of challenges for the imagination. What geometrical figure has a circular cross section and a square cross section? Circular, square, and triangular cross sections?
That book looks interesting. Added it to my wish list. Here is a summary: http://vnthomas1.blogspot.de/2009/06/sparks-of-genius-13-thinking-tools-of.html
We talked about 3D objects being square from one side and circle from the other - for example a cylinder. But he rejected this approach (though he was able to visualize the form). He considered taking circle and square apart and putting it back together into something like a rounded square but rejected that too as neither square nor circle.
My guess is that your son doesn't have a solid grasp of the idea of a cross section. Actually, I don't quite feel good about a cylinder having a square cross section. It's as though it's wrong to neglect the idea that a cylinder is round.
Consider a square in front of you with its edges horizontal and vertical. (Say, drawn on your monitor.) Then consider the line running from the top of the square to the bottom of the square that passes through the center of the square. What happens when you rotate the square around that line?
That was also my first impression. But we talked about it a bit longer. I think it clicked when he mentioned how he looked (in imagination) at the form such that the top becomes a straight line (like looking a paper from the side) and the same with the bottom.
I think your link didn't happen correctly.
Thanks for letting me know.