Where does this definition stem from? In addition to the ancient notion of symmetry used by the Greeks and Romans (current until the end of the Renaissance), a different notion of symmetry emerged in the seventeenth century, grounded not on proportions but on an equality relation between elements that are opposed, such as the left and right parts of a figure. Crucially, the parts are interchangeable with respect to the whole — they can be exchanged with one another while preserving the original figure.
Are you saying that if I turn a square 360 degrees it is no longer a square? — tim wood
What about (AB)xC ?
Would that be considered two or three things? — john27
Are you averring that there is such a thing as a square? I myself would say that squareness is a quality, and that quality retained by that thing that possessed it notwithstanding rotation. — tim wood
Or using your criteria of movement as change and change meaning no-longer-the-same, then it would follow that nothing is ever even the same as itself (not least because we know that everything is in constant motion), and thus nothing could ever be sensibly said of anything. (Because the thing spoken of, by the time spoken, would no longer be that thing.) And any abstraction would necessarily apply to no thing - and absurdly, not even to itself. — tim wood
While their may be an iota of wisdom in this, it is at the same time non-sense. — tim wood
Perhaps the bedrock here is that there is no bedrock. Truly all is seeming - qualities - and not being. But we take it for being; it works as being and for being, and that's an end of it! Or where would you go with your ideas? — tim wood
Yeah I don't know where I was going with this. I was drunk at the time I wrote it, sorry. — john27
How would it be possible to apply a force to a thing without in some way changing the thing? — Metaphysician Undercover
Hmm. example please, under your specification.This principle provides for us, the means to understand the reality that a thing may be constantly changing, thereby having contrary properties, yet remain being the same thing. — Metaphysician Undercover
Well, it could have the quality of not-having-been-moved. And by that standard no symmetry is ever preserved. But I am under the impression that symmetry is an important and efficacious scientific concept/principle. If you're correct, all that has to go. Are you correct? And what, exactly, is your "sense of symmetry"?that is not the sense of "symmetry" I am talking about. The question is whether a thing could maintain all of its qualities when being moved. — Metaphysician Undercover
No, I am saying that the square is no longer the same as it was before you turned it. — Metaphysician Undercover
How would it be possible to apply a force to a thing without in some way changing the thing? — Metaphysician Undercover
The strange thing with squares is that they do stay the same after rotation. It's relation with surrounding squares may become different, but the square by itself stays the same. — AgentTangarine
If you play soccer with a ball protected by a coat then the ball beneath the coat will be the same ball before and after the game. Demanding that the ball stays the same under kicks and stops will introduce forces in the ball. Demanding that it stays the same in free flight will render it force free (this is the essence of Noether's theorem,). — AgentTangarine
Since we all and everything are at all times subject to forces, what the heck are you talking about? Special forces of some kind?The force must have an effect, and the effect is to rotate the thing. — Metaphysician Undercover
We've got Agent Smith, and now Agent Tangerine. Where's Agent Bruce? — Metaphysician Undercover
Do all applications of force deform? And is the deformation continuous? if I have a solidly braced steel beam spanning six inches and I hang a feather from it by a thread, will the feather eventually cause the beam to fail, or the thread to cut through the steel? — tim wood
What would reduced computational steps provide other than faster computation?What if there's someone who can do a×b×ca×b×c, three in one go? Kill two birds with one go!? Some of us have leveled up! Time to play catch up! — Agent Smith
What would reduced computational steps provide other than faster computation? — emancipate
I suspect Kim's calculations came directly from the subconscious.
Here's an operation of arity n: — jgill
Better to remain silent and be thought a fool than to speak and to remove all doubt. — Unknown
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