BOXES One fanciful vision of the (flat) Earth was that it was supported on the back of a turtle, which was, in turn, standing on another turtle and so on:  Turtles all the way down . Similarly, I find it useful to think of "boxes within boxes all the way down." Box 1 is the world we experience "in our head," which includes all experience and everything we know. In particular, it includes what we have been taught and what we have been taught to assume, which is, to a certain extent, " programmed ". Box 1 is the " matrix " of individually shared reality. But, unlike the Matrix of Science Fiction fame, our matrix depends deeply on the "real world" outside and our senses within, as eloquently explained by Antonio Damasio . Our evolutionary survival strategy involves survival as a member of a group, or " super person ". Not only do we not "think for ourselves," we can't . We experience ourselves as o...

I have a coffee cup in front of me (I usually do). If I rotate it or move or see it in different light it my brain automatically makes me experience it as the same cup. If you have ever tried to make a computer figure this out, you will see how astonishing this is. What's more, the cup will be seen as the same cup tomorrow and the same as the cup that I washed a week ago (or is it two weeks? The point is, that doesn't matter). This is symmetry under a transformation in time and space . It takes place so automatically that most of us will go through our entire lives without thinking of it at all. There is another, related, trick that the brain does. It makes me "see" the cup as a form . A form is a bunch of "stuff" that is more or less arbitrarily treated as the "same thing". My dog is quite capable of seeing a flying tennis ball as a "thing" that can be snatched out of the air, but she seems to be uninterested in the "things" sh...

Here is a quick, painless introduction to the kind of symmetry that you probably learned in school. In that lesson, we learn that there are different kinds of symmetry: Rotational Translational Mirror and so on. What this video (and your teacher) did not explain was what symmetry is in general.  If you learned about symmetry in University Math, your idea was  expanded a bit  to come closer to what symmetry is  in general . The first step is to think of symmetry as a set of transformations (rotate, move, flip) rather than a property of whatever it is that is being transformed. And that's just the start. For example, in physics, you learned the Lorentz Transformation  is a symmetry group in the "real world" that leaves the laws of physics unchanged. Newton's laws are not symmetric in this sense but with a bit of tweaking (Special Relativity) they can be fixed. In  physics , the Lorentz transformation (or transformations) are  coordinate tr...