Why do we see symmetry everywhere in science and nature?

[docnet]

In your own words, why do humans look for and prefer symmetries in mathematics, physics, philosophy and in general?

 

[jedishrfu]

One answer would be Noethers Theorem that says where there’s a symmetry in the action of a system there’s a conservation law.

https://en.wikipedia.org/wiki/Noether's_theorem

 

[Klystron]

In your own words, why do humans look for and prefer symmetries in mathematics, physics, philosophy and in general?

Human brains developed to improve reproductive success. This requires recognizing prospective mates.

Human bodies exhibit bilateral and related symmetries. Therefore, recognizing and responding to symmetries provides an important primary mechanism for identifying and selecting mating partners.

 

[jack action]

It is helpful to see what you can't see. Literally, your brain has to interpolate surroundings to fill in a blind spot you have in your eyes. Symmetry makes the process a lot easier.

In a more abstract sense, you can take the example of Fourier series. The function that defines it varies from $-\infty$ to $\infty$. We can't "see" the locations near infinity - thus, we can't see the result of the function either - yet symmetry let us imagine with certitude what the function would look like at these positions.

 

[gmax137]

Time was, the opposite of 'symmetry' was deemed obvious. The Earth was a special place (center of all creation), humans had a special place (lords over Earth), and so on. I think that, as we realized that dropping these "special" attributes led to real progress, we adopted the ideas of symmetry: there are no special places.

 

[vela]

Physics students like it because if they're ever asked by their professor why some term is equal to 0 and they don't know why, they can answer (in a dumb guy voice), "Uhh... symmetry?"

 

[bhobba]

It is possible that could be answered by biological psychology, but right now I don't think anybody knows why. The related question is why does nature prefer it? Noether was a bolt from the blue and often leaves students in shock when they find out about it. IMHO it should, in basic terms of course, be part of primary school science, but 'why' Noether really is a deep question. Then we have the gauge theories of the standard model. Even GR can fit into the gauge formalism:
https://arxiv.org/pdf/1905.08113.pdf

Why I think is a deep mystery - we are going to have to wait for further breakthroughs to answer it.

Thanks
Bill

 

[Klystron]

We may be suffering from observer bias. Two eyes; we see two eyes; we see with two eyes. The brain has two hemispheres. The body exhibits bilateral symmetry. We observe symmetry; so, assume Nature must be congruent?

 

[Jarvis323]

Do we really though? Or do we prefer broken symmetry to the extent that we can understand it, and continually challenge ourselves to understand more and more asymmetrical, or irregular patterns?

 

[bhobba]

We may be suffering from observer bias. Two eyes; we see two eyes; we see with two eyes. The brain has two hemispheres. The body exhibits bilateral symmetry. We observe symmetry; so, assume Nature must be congruent?

Perhaps. But I think more research is needed. Others may know if such research has been done.

Thanks
Bill

 

[BillTre]

It is possible that could be answered by biological psychology, but right now I don't think anybody knows why. The related question is why does nature prefer it?

It would not be surprising if animals of a species preferred others in the species that are more symmetrical in appearance.
The default appearance for individuals of a species would be symmetrical.
One kind of deviation from symmetry could be from a flawed genetically encoded developmental process. In this case, it would be adaptive to not be attracted to asymmetrical individuals as mates (in the reproductive sense).
This could well be selected for, as a way to find better quality mates (which is assumed to be behind a lot of sexual selection).

 

[bhobba]

This could well be selected for, as a way to find better quality mates (which is assumed to be behind a lot of sexual selection).

It has been established that as far as sexual attraction goes any deviation from ideal facial symmetry reduces attractiveness because it may indicate someone who is not as healthy. In fact experiments have been done where they asked people to pair photographs of men and women according to how attractive they were. This correlated with those that were in relationships. So maybe there is some scientific data about why we prefer symmetry.

Thanks
Bill

 

[etotheipi]

In your own words, why do humans look for and prefer symmetries in mathematics, physics, philosophy and in general?

It is because people try to look for non-existent meaning in what is a purposeless and messy existence!

 

[bhobba]

It is because people try to look for non-existent meaning in what is a purposeless and messy existence!

Yes - but the interesting thing is they sometimes find them.

Thanks
Bill

 

[Astronuc]

In your own words, why do humans look for and prefer symmetries in mathematics, physics, philosophy and in general?

Personally, I look for asymmetries.

 

[Jarvis323]

It is because people try to look for non-existent meaning in what is a purposeless and messy existence!

The challenge isn't finding meaning and purpose. We're pretty much swimming in an ocean of that stuff. The challenge is making sense of it, interpreting it, and not being overwhelmed by it.

 

[etotheipi]

The challenge isn't finding meaning and purpose. We're pretty much swimming in an ocean of that stuff. The challenge is interpreting it and not being overwhelmed by it.

Nah, I was saying the exact opposite! There is no underlying meaning; we have at best an operational understanding of the universe, and questioning why things are the way they are is a woolly philosophical question.

Nature doesn't care how you interpret it, and neither should we. That symmetries are maybe "visually appealing" is nothing more than a gimmick; it's just because people like pretty-looking things.

 

[Jarvis323]

Nah, I was saying the exact opposite! There is no underlying meaning; we have at best an operational understanding of the universe, and questioning why things are the way they are is a wooly philosophical question.

Nature doesn't care how you interpret it, and neither should we. That symmetries are maybe "visually appealing" is nothing more than a gimmick; it's just because people like pretty-looking things.

If there is no meaning in anything, then what is your basis for concluding that there is no meaning in anything?

 

[etotheipi]

If there is no meaning in anything, then what is your basis for concluding that there is no meaning in anything?

What?

 

[Jarvis323]

What?

I meant, what do you mean there is no meaning?

 

[etotheipi]

I meant, what do you mean there is no meaning?

Life is just a cruel joke, nothing is important and we'd be better off if nothing ever existed

 

[Jarvis323]

Life is just a cruel joke, nothing is important and we'd be better off if nothing ever existed

The world can be cruel, and I'll admit that my life has been like a nightmare at times. But there is a whole lot to be enamored with in the world. We don't necessarily need a well defined grand purpose. Enjoy the weather, watch the birds and insects, breath in the air, interact with your environment, exercise the mind, and try to stay healthy. If it's your environment that is getting you down, then try to change it, or try to find somewhere better. Or try to see things from different perspectives, and try to recognize and appreciate the things you take for granted.

 

[Klystron]

Personally, I look for asymmetries.

{snip}
Nature doesn't care how you interpret it, and neither should we. That symmetries are maybe "visually appealing" is nothing more than a gimmick; it's just because people like pretty-looking things.

Ah, but artists often emphasize asymmetry in their compositions. The vase is depicted at an angle. The painter places the principle point of interest off-center according to arcane formulae. The center cannot hold. An Amazon covers one breast. Batman gets boring but the Joker entertains with the unexpected, like Dickens's more eccentric characters. Glaze runs willy-nilly down fine porcelain.

If this contradicts my post in the "Inadvertent Plagiarism" thread, that people prefer the familiar; this seeming contradiction supports the argument that the eye is drawn to the exception, the unusual, to (slight) imperfections.

 

[jack action]

I meant, what do you mean there is no meaning?

Life is just a cruel joke, [...]

Isn't that a meaning?

 

[Jarvis323]

Ah, but artists often emphasize asymmetry in their compositions. The vase is depicted at an angle. The painter places the principle point of interest off-center according to arcane formulae. The center cannot hold. An Amazon covers one breast. Batman gets boring but the Joker entertains with the unexpected, like Dickens's more eccentric characters. Glaze runs willy-nilly down fine porcelain.

If this contradicts my post in the "Inadvertent Plagiarism" thread, that people prefer the familiar; this seeming contradiction supports the argument that the eye is drawn to the exception, the unusual, to (slight) imperfections.

 

[jedishrfu]

It means art is interesting because at its heart is an asymmetry that intrigues the viewer. Chinese painting often expresses that idea.

First, the picture isn't vertically or horizontally symmetric but there are symmetries in the leaf groupings although not exactly.

We search the painting these symmetries and this is how we appreciate its message.

 

[etotheipi]

I don't know what you guys are smoking but you better let me know where I can get hold of some because I have no idea what anyone's talking about any more

 

[jedishrfu]

Don't smoke no dope.

We're talking about the importance of symmetries and in art, it becomes something to use but not overuse. Artists will try to balance their painting in an asymmetrical way.

 

[Klystron]

Sorry, I have no idea what any of that means

Even the Batman reference? I was agreeing with your secondary point about beauty with a barrage of asymmetric examples from Art.

The 18^th Century bella donna (beautiful lady) wore a single mole on her powdered cheek to draw the eye of potential suitors. The mathematics grad student surveys raw data and first removes outliers. Measurement histograms require error bars. Gaussian distributions of actual data are often skewed?

 

[etotheipi]

I don't understand what you mean by

The painter places the principle point of interest off-center according to arcane formulae. The center cannot hold.

What does it mean for a "center" to "hold"?

 

[Klystron]

I don't understand what you mean...What does it mean for a "center" to "hold"?

I was employing a poetic reference from Yeats:

Turning and turning in the widening gyre
The falcon cannot hear the falconer;
Things fall apart; the centre cannot hold;
Mere anarchy is loosed upon the world,
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity

Letting you know that many other creative people share your angst.

 

[etotheipi]

But I found many paintings where the focus is in the centre, so I don't know what you mean saying the painter cannot put the focus in the centre?

 

[BillTre]

Symmetries also often nice looking can become boring if they are always present.

Art often involves deviations from something (like symmetry) which are then used to attract attention.
Controlling the way attention is focused is behind a lot of visual art and page layout design. There are many visual tools for doing this.
The better this is done, the better the art (I conjecture).

Another view:
What can be seen as superficially symmetric, can be revealed to be asymmetric at deeper levels.
An example is the human body, largely symmetrical when viewed externally, but with many asymmetries hidden internally.
A deeper understanding is achieved through the appreciation of the underlying asymmetries.

In explanations:
Symmetry is nice, in that the explanations would seem to be simpler.
A simpler explanation is appealing for Occam razor-like reasons.
Asymmetries arise when forced to deal with exceptions.

 

[Klystron]

But I found many paintings where the focus is in the centre, so I don't know what you mean saying the painter cannot put the focus in the centre?

View attachment 280605View attachment 280606View attachment 280607

Not all paintings, surely. Your first two selections suffice to emphasize mild asymmetries in art.

Look at La Giocanda's mouth, that famous quirky smile. See the angle of her body. What is she grasping in one hand? Is she balancing her body on the nearly invisible arm of the chair? Leonardo contradicts the mundane Earth tones of Mona Lisa's sedate gown with a devastated asymmetrical background.

Vincent's portrait of brother Theo as himself wearing poor disheveled clothing, the misshapen hat, the iconic single ear, scream out of the canvas "Ayudame, por favor! Help me, while you can."

Stare into the asymmetric eyes and view the halo of insanity surrounding Van Gogh.

By now you can recognize the incongruity of the third painting. A green apple substitutes for Everyman's face. The very fact that the figure is rigidly centered emphasizes the satire; decries the sameness of the brick wall separating Modern Man from the stormy seas. Great choices!

 

[etotheipi]

Woah, that's so cool! I hear you man, I like how you gave them all a little story, helps me to see where you're coming from

What's up with the one you just posted? Is the brown thing supposed to be a wall separating order from chaos? What are those guys on the road doing?!? It's funny, it looks sort peaceful but also violent and stormy at the same time. I guess it's the whirly brush strokes and stuff.

i could totally get into this art thing, haha