# Why do we prefer symmetries?

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

Klystron
Gold Member
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.

DennisN, jedishrfu and docnet
jack action
Gold Member
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.

Last edited:
docnet
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.

jedishrfu and docnet
vela
Staff Emeritus
Homework Helper
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?"

docnet, bhobba, strangerep and 1 other person
bhobba
Mentor
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

Jarvis323, Klystron and docnet
Klystron
Gold Member
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?

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
bhobba
Mentor
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
Gold Member
2020 Award
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).

Jarvis323, Klystron and bhobba
bhobba
Mentor
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

Klystron and BillTre
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
Mentor
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

hutchphd
Astronuc
Staff Emeritus
In your own words, why do humans look for and prefer symmetries in mathematics, physics, philosophy and in general?
Personally, I look for asymmetries.

bhobba, collinsmark and 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.

bhobba, BillTre, Astronuc and 1 other person
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.

Last edited by a moderator:
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?

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

What?

bhobba and Klystron
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

bhobba and docnet
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.

docnet and Klystron
Klystron
Gold Member
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.

docnet and etotheipi
jack action
Gold Member
I meant, what do you mean there is no meaning?

Life is just a cruel joke, [...]
Isn't that a meaning?

bhobba, etotheipi and BillTre
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.

Klystron