Great Thoughts on Symmetry (not mine)

Greetings True Believers!

Work is well underway on “The Universe in the Rearview Mirror,” and I thought it would be fun to do a core dump of some of the more interesting symmetry quotes that I’ve come across. At very least, they’ll give you an idea of why symmetry is such a big deal. Feel free to use these to spice up your Christmas party conversations.

Herman Weyl, on what symmetry is (from “Symmetry”):

A thing is symmetrical if there is something you can do to it so that after you have finished doing it, it looks the same as before.

Why is this important? As Weyl added:

My work always tried to unite the truth with the beautiful, but when I had to choose one or the other, I usually chose the beautiful.

Nobel Laureate Phil Anderson on the significance of symmetry in Physical Laws:

It is only slightly overstating the case to say that physics is the study of symmetry.

I found this quoted in “First Philosophy: A Theory of Everything” by Spencer Scolar. This isn’t the original source, of course, but he also gives a lot of other good symmetry quotes.

I particularly liked this one from John Wheeler:

There is no law of physics that does not lend itself to most economical derivation from a symmetry principle. However, a symmetry principle hides from view any sight of the deeper structure that underpins that law and therefore also prevents any immediate sight of how in each case that mutability comes about.

And one from his student, the great Richard Feynman:

So our problem is to explain where symmetry comes from. Why is nature so nearly symmetrical? No one has any idea why.

Feynman also has a great thought experiment concerning symmetry in his lectures:

Suppose we build a piece of equipment, let us say a clock, with lots of wheels and hands and numbers; it ticks, it works, and it has things wound up inside. We look at the clock in the mirror. How it looks in the mirror is not the question. But let us actually build another clock which is exactly the same as the first clock looks in the mirror – every time there is a crew with a right hand thread in one, we use a screw with a left-hand thread in the corresponding place on the other… If the two clocks are started in the same conditions, the springs wound to corresponding tightnesses, will the two clocks tick and go round, forever after, as exact mirror images?

PROTIP: If you have a budding (and extremely sophisticated) young scientist in your life and can’t figure out what to get them for the holidays, get them the Feynman Lectures. Do it now!

These common sense thought experiments in symmetry go back a long way, at least to Galileo:

I am certain you both know that an oak two hundred cubits high would not be able to sustain its own branches if they were distributed as in a tree of ordinary size; and that nature cannot produce a horse as large as twenty ordinary horses or a giant ten times taller than an ordinary man unless by miracle or by greatly altering the proportions of his limbs and especially his bones, which would have to be considerably enlarged over the ordinary.

He also described the motivation for what became known as “Galilean Relativity“:

Shut yourself up with some friend in the largest room below decks of some large ship and there procure gnats, flies, and other such small winged creatures. Also get a great tub full of water and within it put certain fishes; let also a certain bottle be hung up, which drop by drop lets forth its water into another narrow-necked bottle placed underneath. Then, the ship lying still, observe how those small winged animals fly with like velocity towards all parts of the room; how the fish swim indifferently towards all sides; and how the distilling drops all fall into the bottle placed underneath. And casting anything toward your friend, you need not throw it with more force one way than another, provided the distances be equal; and leaping with your legs together, you will reach as far one way as another. Having observed all these particulars, though no man doubts that, so long as the vessel stands still, they ought to take place in this manner, make the ship move with what velocity you please, so long as the motion is uniform and not fluctuating this way and that. You will not be able to discern the least alteration in all the forenamed effects, nor can you gather by any of them whether the ship moves or stands still. …in throwing something to your friend you do not need to throw harder if he is towards the front of the ship from you… the drops from the upper bottle still fall into the lower bottle even though the ship may have moved many feet while the drop is in the air …

Einstein (whose work on both Special and General Relativity were very consciously founded on symmetry) had this to say about the C (Charge) symmetry in the universe:

I used to wonder how it comes about that the electron is negative. Negative-positive—these are perfectly symmetric in physics. There is no reason whatever to prefer one to the other. Then why is the electron negative? I thought about this for a long time and at last all I could think was “It won the fight!”

There’s also his classic:

Everything should be made as simple as possible, but not simpler.

And, to finish, a rather romantic quote from Marcus Du Sautoy’s “Symmetry: A Mathematical Journey”:

…only the the fittest and healthiest individual plants have enough energy to spare to create a shape with balance. The superiority of the symmetrical flower is reflected in a greater production of nectar, and that nectar has a higher sugar content. Symmetry tastes sweet.

Like any blog post, this is a fishing expedition, and a lazy way to try to crowdsource research. Send me links to some of your own favorite symmetry quotes, and I’ll be eternally grateful.


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2 Responses to Great Thoughts on Symmetry (not mine)

  1. Guanmin Feng says:

    Many interesting symmetry quotes, but this is my favorite:

    “As far as I see, all a priori statements in physics have their origin in symmetry.”

    H. Weyl, Symmetry (1952).

  2. Excelent colection.

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