Symmetry: is it a true principle?

Metaphysician Undercover

I answer this with a simple "no". The concept takes differences which are not relevant to the purpose at hand, and designates them as not differences at all. Of course, to designate a difference as not a difference is contradiction.

Here's a descriptive statement from Stanford Encyclopedia of Philosophy:

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.

You'll see from this description, that "symmetry" can only be a true principle is the figure which is said to be symmetrical is removed from its context, its location. The right side and the left side of a figure are differentiated by the location of the figure within a larger environment. Interchangeability of the right and left, which constitutes "invariance", is only possible if the figure is considered to exist free from any context, without a location. Of course nothing really exists without a location, so "symmetry" in this sense is is just a false principle. It cannot be applied to anything real.

This falsity has a wide range of ramifications in the current application of symmetry principles. By removing the thing which is said to be symmetrical, from any possible location, in order to say that it is a symmetry, we necessarily free that symmetry from any effects of its environment. It is fundamentally absolutely free. In other words, we remove any true constraints imposed by the natural environment on the thing supposed to be a "symmetry", in order to allow that it is a symmetry. Then one might create artificial constraints which are supposed to model the symmetry's reality. But in designating the thing a "symmetry", in the first place, the possibility of reality has already been removed. And so, such a model is completely conjectural because the "symmetry" is a fiction which is impossible to have a real existence in the first place.

For reference: https://plato.stanford.edu/entries/symmetry-breaking/

Agent Smith

What keeps me up at night is a simple fact: our minds and our tools (e.g. logic & math) seem capable of at most binary operations. As an example consider what in my book is a ternary operation viz. $a \times b \times c$ (volume of a cuboid).

How do we actually perform this operation?

If everyone is like me, this way :point: $(a \times b) \times c$ . That is to say we can handle, max, two things at one go.

What does this have to do with symmetry? The binary aspect of the low hanging fruit in re symmetry (reflections) is apparent. All we now need is some way to describe what in common parlance is termed opposite (negative, numerically/negation, logically). We end up with a yin-yang symmetry of opposites that cancel each other out $(+a + -a = 0)$ .

What if there's someone who can do $a \times b \times c$ , three in one go? Kill two birds with one go!? Some of us have leveled up! Time to play catch up!

Josh Alfred

Its a principle that is applicable or manifested in most every level of the universe/existence. From the symmetry of electrons and protons (ratios) to the symmetry of binary star systems, it is a universal contingent. Anatomically, the brain and the body working as one, are a symmetrical structure with binary function.

john27

↪Agent Smith

What about (AB)xC ?

Would that be considered two or three things?

tim wood

↪Metaphysician Undercover

Are you saying that if I turn a square 360 degrees it is no longer a square?

T Clark

↪Metaphysician Undercover

In general, symmetry seems like a useful concept in many contexts. It can represent important underlying principles of organization.

As for symmetry in relation to symmetry breaking, I admit that's an idea I've struggled with. My unsatisfactory solution is to think about such situations as phase changes, which is a concept I find easier to understand. I'll keep trying to figure this out.

Metaphysician Undercover

Are you saying that if I turn a square 360 degrees it is no longer a square? — tim wood

No, I am saying that the square is no longer the same as it was before you turned it. The fact that you turned it means that you changed it and it is no longer the same. So if you represent a square as being able to be turned without being made different than it was before you turned it, you make a false representation.

tim wood

↪Metaphysician Undercover

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.

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.

While their may be an iota of wisdom in this, it is at the same time non-sense.

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?

Agent Smith

What about (AB)xC ?

Would that be considered two or three things? — john27

I see no difference between (AB)×C and A×B×C and (A×B)×C. :chin:

Metaphysician Undercover

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

The point is not whether a thing would maintain one, or even some, of its qualities, when being moved, 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. In pop metaphysics, "symmetry" is taken to refer to a thing, which has transformational invariance. There is assumed to be real symmetries existing in the world, things which are defined by this feature, (which is not a real feature, but an abstract tool). Consider that moving something requires the application of a force. How would it be possible to apply a force to a thing without in some way changing the thing?

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

This is not relevant. The law of identity allows that a thing changes, as time passes, yet the thing maintains its identity as the same thing. A thing's "identity" is not based in properties or attributes, its based in the thing's temporal continuity of existence. 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.

While their may be an iota of wisdom in this, it is at the same time non-sense. — tim wood

I don't see the basis for your accusation of "nonsense". Is that your general approach to things you do not understand? Instead of trying to understand you just designate it as nonsense.

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

This is self-defeating, as self-contradicting. You are saying we assume being (take it for being), when it's really not being. Yet you say "truly all is seeming". Well, it seems to be being, so your claim of "not being" is completely unsupported.

john27

↪Agent Smith

Yeah I don't know where I was going with this. I was drunk at the time I wrote it, sorry.

Agent Smith

Yeah I don't know where I was going with this. I was drunk at the time I wrote it, sorry. — john27

Drunk? $C_2H_5OH$ is supposed to make you think better!

john27

↪Agent Smith

Oh really? I guess I'll just have to try again then.

Agent Smith

↪john27

Have a gander here.

Alcohol impairs judgment! It also makes you philosophical! :chin: Are all philosophers drunk (on ideas)?

Is $C_2H_5OH$ = Ideas?

What's your poison?

Socrates, shaken not stirred!

Metaphysician Undercover

↪Agent Smith

Whatever you say Bruce.
https://www.youtube.com/watch?v=l9SqQNgDrgg

Agent Smith

:heart:

tim wood

How would it be possible to apply a force to a thing without in some way changing the thing? — Metaphysician Undercover

You can apply force all day long and not change a thing. Example: hang a weight from a steel beam; nothing happens. Nothing changes. Perhaps you're thinking here about work. Even then, though, there are things you can do work on that after the work is done, you cannot tell that the work is done. Another example, rotation on an axis or a pivot.

And you speak of identity being preserved. Agreed. But that because at least some qualities preserved - but how can that be if motion changes all qualities?

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

Hmm. example please, under your specification.

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

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"?

AgentTangarine

No, I am saying that the square is no longer the same as it was before you turned it. — 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

How would it be possible to apply a force to a thing without in some way changing the thing? — Metaphysician Undercover

The concept of force is closely related to symmetry. It can even define force.

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,).

Metaphysician Undercover

↪Agent Smith

We've got Agent Smith, and now Agent Tangerine. Where's Agent Bruce?

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

That's the problem though, how can a thing be rotated like that (a force being required to rotate the thing) without changing the thing? The force must have an effect, and the effect is to rotate the thing. But nothing else changes so there must be a change to the thing rotated to account for the expenditure of force required to rotate it.

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

Clearly the ball is changed, even after employing the "coat" as a sort of forcefield to protect the ball. The forcefield is not absolute, perfect, ideal, or else the ball inside would have eternal existence exactly as it is, inside that forcefield, never being capable of being changed in there.

AgentTangarine

↪Metaphysician Undercover

Agent Tangerine, the infamous cousin of Agent Orange...

You touch upon a deep issue here, as a matter of fact! It is claimed that symmetries lay at the basis of forces.The $SU(2)_l \times SU(1)_y$ symmetry for the so-called unified force (splitting in the EM force and weak force after a break of symmetry, namely that of the Higgs potential) the $SU(3)$ symmetry for the color force, and a coordinate symmetry for general relativity. You can perform symmetry operations without truly change a system. This is simply done mentally, and by demanding symmetry, forces arise, while in fact it's the other way round. It are forces which give rise to symmetry principles. You can literally force symmetry transformations upon nature, like you do with the squares, and retrospectivelyclaim that forces are the result, but that's indeed putting the horse behind the wagon. You can rotate all points of a square locally and say that because of this forces will appear in the square to let it keep its shape (making it symmetrical wrt to local rotations or gauges), but as you say, you have to pull and push it first for these forces to appear.

Symmetries are useful, but they are not the foundations of nature. They are projected on nature, and claimed to be axiomatic causes. I think it's the other way round. Symmetries and connections are axiomatized causes of forces, but it are the forces that cause symmetries and connections.

tim wood

The force must have an effect, and the effect is to rotate the thing. — Metaphysician Undercover

Since we all and everything are at all times subject to forces, what the heck are you talking about? Special forces of some kind?

Agent Smith

We've got Agent Smith, and now Agent Tangerine. Where's Agent Bruce? — Metaphysician Undercover

That's actually Agent TangArine. I don't know where Agent Bruce is. He's probably gettin' his ass kicked by Mr. Anderson! :grin: I better lay low for a while, huh?

T Clark

You can apply force all day long and not change a thing. Example: hang a weight from a steel beam; nothing happens. — tim wood

The beam bends. Not much, but enough to provide an equal and opposite reaction to the force you have applied.

tim wood

↪T Clark

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?

@Metaphysician Undercover is arguing here that force breaks the possibility of symmetry because no thing subject to force remains the same. Since there is always force, then according to MU, there can never be any symmetry. Do you have a response to that?

T Clark

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

The model for application of a force to something solid is a spring. Apply the force and the spring deflects elastically as long as you don't overload it. For elastic materials, applied force (stress) is proportional to deflection (strain). The greater the deflection, the greater the force (reaction). A spring will deflect under the force of a load as required to resist the load.

So, yes. If you hang a feather from a solidly braced steel beam, the beam will deflect enough to provide a reactive force to the feather just as if it were a spring. Steel behaves elastically within the stress range provided by a feather. If you use something much heavier, it may stress the steel beyond it's elastic range. If that happens, the steel will continue to deflect and will eventually fail.

Heracloitus

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?

Agent Smith

What would reduced computational steps provide other than faster computation? — emancipate

Good observation. Speed can, after a certain point, look like magic. Do you know of so-called idiot savants (hopefully this isn't a pejorative term)? One I read about was the late Kim Peek. I don't know if the film Rain man (Dustin Hoffman & Tom Cruise) was based on him or not. Anyway, he was reputed to have the ability to calculate and tell you the day of any given date (DD/MM/YY) backwards and forwards in record time. There's an algorithm (step by step procedure) for such caculations but Kim Peek's feats of speed and 100% accuracy gives me the impression that he was performing these calculations simultaneously and not in stages (the way a normal person would). It seems as though instead of binary thinking $[(a \times b) \times c]$ , Kim was actually capable of ternary and higher thinking $[a \times b \times c]$ .

jgill

↪Metaphysician Undercover

Even as a mathematician, beyond equivalence relations the word "symmetry" has always left me a bit uneasy, so I have avoided it. And in modern physics I not infrequently look it up.

↪Agent Smith

I suspect Kim's calculations came directly from the subconscious.

Here's an operation of arity n: $\bigcap\limits_{k=1}^{n}{{{A}_{k}}}$

Agent Smith

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

Should've kept my mouth shut! :grin:

180 Proof

As for symmetry in relation to symmetry breaking, I admit that's an idea I've struggled with. My unsatisfactory solution is to think about such situations as phase changes, which is a concept I find easier to understand — T Clark

Same here. :up:

Symmetry: is it a true principle?

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