square Trifoil – reflection – symmetry-breaking and such

You can’t exclude the middle.   There’s not just “This and its Opposite” – there’s always something inbetween…
The Trifoil knot (shown here differently than its usually “3 ring” style, which looks all mystical and stuff) has something called chirality.  Fancy word.  It means “handedness”.

Put your left hand and right hand together.  Try to get them to be the same.  Sure, you can get them to face each other, but.. stick one on top of the other.  No matter how hard you try, you can’t match them up so that you have two left hands or two right hands.

And that, my friends, goes down deep into the core of … well … everything.  Lots of things can match up and become the same thing in exactly the same way.

But … not if something has chirality.   That’s what “symmetry breaking” is all about.  Your left and your right are different and… that’s that.  They’re different.

Things spin right and things spin left. and you can twist and turn and flip it around – no matter how hard you try, you can’t turn one into the other without a mirror.

I like this image because it also doubles as an excellent pattern for cleaning a window or a room with.  I discovered it the hard way when I was going through “What’s the most efficient way to do everything?” phase last year, only to find out tonight, that it’s something far cooler than just a great way to clean a whole window in a single, smooth swipe.

Notice: It’s over-under-over.  Or under-over-under.

If this is over your head, don’t feel bad.  It’s over the heads of some of the toughest thinkers out there… people way smarter than I could ever be…. and yet… it’s not so hard really, as long as you’re willing to have a left-hand and a right-hand that are forever mirrors yet never entirely the same.330px-Trefoil-non-3-symm.svg

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