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Kindly comments on Does model theory [psychology] predict anything? (book: "How We Reason" (2009)) - Less Wrong
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Imagine poking a needle through the middle of a disk, perpendicular to the disk. Then the needle is horizontal when the disk is vertical, and vertical when the disk is horizontal. So the fraction of vertical needles is going to be the same as the fraction of horizontal disks, and the fraction of horizontal needles is going to be the same as the fraction of vertical disks.
Yes, the way I finally understood this was imagine a horizontal disk whose circumference the equator. It can spin on one axis (through the center of the disk from north pole to south) while remaining horizontal. However a vertical disk oriented along a great circle can spin on two axes while remaining vertical, one from the north pole to the south pole crossing a diameter of the disk and one through the center of and perpendicular to the disk.