According to Wilczek , symmetry is "Change without change" - the most powerful single principle underlying the laws of both aesthetics and physics. In Wilczek's books, he provides simple examples and a few mind bending ones (such as the symmetry involved in the strong nuclear force - the rules governing quarks). For some reason, he neglects the most common example of symmetry that is always quite literally right in our face. This is the ability of our perceptual system to recognize "objects" in the world - "things" that seem to be the same no matter how they are oriented, how far away they are, or how they are illuminated. Sometimes we only need to hear or smell the "thing" to "see" it in our minds. Anyone who has attempted to "teach" a computer to do anything like this knows how incredible this ability is. And it's totally natural, totally automatic. What's more all "higher" animals (maybe all living th...

Daniel Dennett likes to give Jaynes the benefit of the doubt: “There were a lot of really good ideas lurking among the completely wild junk.” As Dennett hints (with typical subtly), there is a lot of "junk philosophy" around the subjects dear to Jaynes' heart. In this post, I'd like to extract one of Jayne's ideas and wipe a bit of "junk" off it to see where it gets me. At the center of Jayne's theory is the "bicameral mind", which is firmly based on the idea that we have a "right brain" and a "left brain" with notably different capabilities, each capable of acting somewhat on their own. The "right brain" is good at seeing the "big picture" and sends its judgments to the left brain, where they are perceived as speech - sometimes the speech of the Gods. As things get historically more complicated, we evolve our present day "inner chatter", no longer attributed to the Gods (if we are sane), b...

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...

\ Quick and dirty definitions, to be clarified as we go along: R Refers to the "real world" . Accepted wisdom is that we have no direct access to R.  It turns out that we actually do have quite a good access to the R domain - the M/R interface, also known as "Science". For the individual, the I domain is tiny compared to the vastness of both M and R. However, with effort and training, it is possible for the individual to open a tiny peephole into R - at least so far as to put to rest the notion that R does not exist at all - that it's all an illusion. M refers to "meme space" or the entire set of ideas, actual and possible. For example, all of Science exists in M, uncomfortably with all religions, past, present and future. It is everything we know, could know, or think we know, possibly including all those things that may be conceivable by some alien intelligence or even "God." M happily accommodates all the wrong ideas and the opposite of ev...