The square root of +2 differs from the square root of -2. The reality of imaginary numbers demonstrates that one is not a mirror image of the other. — Metaphysician Undercover
Can't the metric of space have a symmetry? — Raymond
What's a mirror image (to you)? — Agent Smith
We discussed this earlier in the thread. A mirror image is not a symmetry because the mirror shows the features of the left side of my body as being on the right side of my body. So when the mirror does what it does, to turn the image of my body from frontward facing to backward facing (from my perspective), it does something which makes the backward facing image of me, not perfectly symmetrical with the frontward facing image of me. — Metaphysician Undercover
The lateral inversion in (vanity) mirrors — Agent Smith
he lateral inversion in (vanity) mirrors accounts for the change in valence/sign: good reflected becomes bad, positive becomes negative, left becomes right, top becomes bottom ( :chin: ). — Agent Smith
But the mirror image is not such a turn, it is a reflection. — Metaphysician Undercover
nterestingly, the "intention" or idea seems to be to destroy the symmetry. — Agent Smith
t depends on how you mirror the 2. You can mirror it with a mirror perpendicular to the 2. Then the mirror image of 2 and the 2 are symmetric wrt each other. — Raymond
But what if it has length only? Front and back are symmetric then, like the 2 facing 1 or 3. — Raymond
How do you involve complex numbers here? I'm not sure I understand. — Raymond
Where does the mirror fit then? — Metaphysician Undercover
What about the two hydrogen atoms in water. Aren't they symmetric somehow? — Raymond
Isn't symmetry about two different things being the same? Left and right are symmetric. If you let things move to the left it's the same as making them move to the right. — Raymond
There's a chapter on Newton's 3rd law: — Agent Smith
The 1st law of thermodynamics: energy can neither be created nor destroyed (the law of conservation of energy). This doesn't feel like symmetry as there's no polarity reversal even though there's conservation of magnitude. — Agent Smith
Anyway, symmetry, mirror symmetry to be precise, is about, mathematically speaking, magnitude and sign. The magnitude is conserved (there's a similarity between left and right), but then there's a difference too, the sign flips (left becomes right and vice versa aka lateral inversion). — Agent Smith
Symmetry, in its modern conception of mathematics, involves exact equivalence, invariance. Any such reversal is not a part of the symmetry, but evidence of asymmetry. A difference is not a part of the symmetry. — Metaphysician Undercover
We went through this already, a mirror image is not a symmetry under this definition. — Metaphysician Undercover
Emmy Noether's work on mathematical symmetry (doesn't look like she's talking about mirror symmetry) became the basis for (derivation of) the conservation laws in science. — Agent Smith
I wonder what definition of symmetry Noether was working with. Looks like basic algebraic equality of the left hand side (LHS) to the right hand side (RHS) of an equation. No sign to flip/not. A balance/scale type of symmetry with equal "weights" on both sides; yet even here too the "weights" act in opposite directions (rotationally, one is clockwise and the other is anticlockwise). — Agent Smith
When two things which are different, are said to be equal, the difference between them has already been excused in that judgement of equal. So we now have a second level of excusing differences for the sake of symmetry, the excuse which exists right at the level of producing the equation. — Metaphysician Undercover
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