## Symmetry: is it a true principle?

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• 1.2k
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.

What's a mirror image (to you)?
• 649
-2 and 2 are not symmetric. They are antisymmetric.
• 9.4k
Can't the metric of space have a symmetry?

What I believe is that such a symmetry is imaginary, and not a true representation of space. We make up the symmetry principles, and apply them because they are very useful. But then we have to deal with what is left over, the aspects of reality which don't fit into the artificial symmetry. So if we represent space as a thing, we should consider the same principle. If we represent it as symmetrical, we ought to accept that there are aspects of it which vary from that symmetry, that we still need to describe. This is the difficult part of description, accounting for the aspects of the described thing, which do not quite fit into the parameters of the descriptive terms. So in cosmology they propose names like dark energy and dark matter to describe the features which do not fit in to their descriptive models.

What's a mirror image (to you)?

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.
• 1.2k
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.

The 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: ).

Did you know, since our eyes aren't mirrors but lenses, the world is upside down in our retinas? The brain rights the image, including the lateral inversion.

We could say that, re Daoism, the more x you are, the more -x you are: the more logical you are, the more insane you are (there's a thin line betwixt madness and genius). Cylindrical universe (ancient video games).
• 649
The lateral inversion in (vanity) mirrors

Again you made me laugh Agent! How much do I owe you?

Did you know people, after wearing upside-down glasses for a while, see everything normal again?
• 9.4k
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: ).

No. the rotation (or change in valence) is the 180 degree turn, to be facing the other way. That the left becomes the right when the turn around occurs indicates that the representation is limperfect.

Think of it this way. The 2 has two parts because that's what "2" symbolizes. If the 2 were to turn from facing the 3, to become facing the 1, it's right part would remain its right part, and its left part remain its left part. But the mirror image is not such a turn, it is a reflection. And so the left and right do not get properly represented in the reflection because it's not a true turn, but a representation which is deficient.

When -2 is compared with +2, for symmetrical value, the deficiency is even greater, more complex, than the deficiency of the mirror image. This is evidenced by imaginary numbers. A whole system of imaginary numbers must be employed to create the illusion of symmetry. In the case of the mirror, the deficiency can be traced to the activity occurring at the medium, the mirror. In the case of the numbers, a faulty conception of zero is indicated.
• 1.2k
:smile:

Yes, you're right! Symmetry is an illusion. Your thesis and my antithesis (to your thesis) is not all like a reflection in a mirror: (laterally) inverted i.e. opposite in valence and equal in force. Interestingly, the "intention" or idea seems to be to destroy the symmetry.
• 649
But the mirror image is not such a turn, it is a reflection.

It 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.
• 9.4k
nterestingly, the "intention" or idea seems to be to destroy the symmetry.

It's not to "destroy the symmetry", but simply to see it for what it has become, a tool which has limited capacity, rather than a reflection of reality. Traditionally we'd see the appearance of symmetry in nature as something beautiful. But we'd always know that any deeper analysis of the beauty would reveal discrepancies, and the appearance of perfect symmetry is just an illusion. But this in an odd way, only adds to the beauty of the natural world, and all those little discrepancies would contribute to wonder, which is the philosophical attitude.

Now the tool, symmetry in principle, has become so powerful in its mathematical applications, that we dismiss all those discrepancies as insignificant, assume that the thing which appears to be symmetrical really is symmetrical, and this kills the philosophical attitude.

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.

A mirror only creates a reflection of something, if the thing has width, so this wouldn't work.
• 649

But what if it has length only? Front and back are symmetric then, like the 2 facing 1 or 3.

How do you involve complex numbers here? I'm not sure I understand.
• 1.2k
I'm sorry we couldn't come to an agreement on the matter.
• 9.4k
But what if it has length only? Front and back are symmetric then, like the 2 facing 1 or 3.

Where does the mirror fit then?

How do you involve complex numbers here? I'm not sure I understand.

It was the agent's suggestion, that -2 is the mirror image of +2, which got complex numbers involved
• 649
Where does the mirror fit then?

Perpendicular to the screen, left or right to the 2.
• 9.4k

Then the perpendicular direction is "the front", in relation to the mirror, because the mirror switches the direction front to back. You might call it right and left, but the result is the same, the right becomes the left when the mirror switches the image. And the side toward the 1 is different from the side toward the 3.
• 649

What about the two hydrogen atoms in water. Aren't they symmetric somehow?
• 649

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.
• 9.4k
What about the two hydrogen atoms in water. Aren't they symmetric somehow?

I think the bonding of those atoms is actually quite complicated.

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.

Two different things being the same is contradiction. Left and right, as principles are symmetrical, but the issue is not symmetry in theory. In practice, making something move to the left is not the same as moving it to the right.
• 649

Then there is only one actual symmetric thing. The singularity at the big bang. Spatiotemporally a pure symmetry. There was time but without direction. In the universe there are no exact symmetries, irreversible processes only and no truly periodic clock. At the big bang the opposite. The symmetry materially, so truly, broke when the virtual got real.
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