Life’s preference for symmetry is like ‘a new law of nature’

> Translation symmetry - the unit is shifted along an axis one or more times. A chain shows translation symmetry.

Worth noting that in the biological context this has its own dedicated term, "segmentation".

> One theory of why you see so much symmetry in biology is that it takes less information to build something using symmetry than specifying the whole directly

People have also observed that the environment is fundamentally indifferent to which direction you're facing (especially if you're capable of turning yourself). This goes a long way toward explaining why mirror and rotational symmetry might be a good idea even if they were more difficult to specify.

Are there anycases of plausible temporal symmetry, especially emergent that don't have obvious triggers.

symmetries give us the laws of conservation (time symmetry, conservation of energy; rotation symmetry, conservation of angular momentum etc)

Another way to say that is symmetry and compressibility are essentially synonymous. Any redundancy in a system can be compressed, leading to a reduction in size. Thus, the ability to compress a system is essentially finding what symmetries you can exploit in the system to reduce the representation.

In my opinion, the reason why we see so much symmetry in nature is because living things are always trying to balance an economy of "source code" size (DNA) with expressibility and/or versatility.

I think compression is kind of the overarching generalization but another type of symmetry commonly run into is composeability ( f(g(h(...(x)))) ).

Small note: Having looked at geometric algebra, both rotations and translations are based on combining 2 mirror operations. If the mirrors are parallel it's a translation, otherwise it's a rotation.

>One theory of why you see so much symmetry in biology is that it takes less information to build something using symmetry than specifying the whole directly.

This makes a lot of sense.

It works the same way in computer programming. Instead of rewriting generic code for every new program, components can be split off into separate files and called when needed in a standardized way. This speeds up development and leaves less room for error.

It's not very far fetched to think other life forms are using the same strategy unconsciously to fuel their own evolution.

Early lifeforms in the Ediacaran period favored glide symmetry aka translational.

A deeper way to think about this is that any phenomenon that pumps out entropy from the system by injecting work + heat tends to stand up like a sore thumb in the rather dull sponteneaty of nature. I don't mean entropy in the naive sense (order vs disorder), but as dispersal of energy (third law). Not sure what the cause of such locality is - perhaps we can call that intelligence?

Symmetry appears in creatures that spawn out sperm into the sea and let it land where it may, and many other very simple life forms with non-sexual reproduction, or reproduction where attraction isn't a factor, as in most plants. I'm sure symmetry may also add attractiveness as a kind of fitness display, but it's a much more fundamental thing since it's also present in life forms like plants which do evolve through sexual selection but without animalian fitness displays, and in non-sexually reproducing life forms.

Have you ever seen how symmetrical human faces look like? Do you consider them more attractive than regular, asymmetrical ones?

A preprint of the information that was derived to make the above article has been available for a year.

https://www.biorxiv.org/content/10.1101/2021.07.28.454038v2

a mind-rewiring video by numberphile concerning the golden ratio [0] made sense of all the spiral overlay art:

yes, plants use it because it is an optimal solution for minimizing overlap when sprouting leaves during growth, maximizing spatial coverage

but also, as a number that is least able to be approximated by rational, erm, ratios - it is a pattern that most closely approximates random patterns. So more than any other spiral, a fibonacci spiral has the highest likelihood of overlapping random points in 2D space... (and fibonacci series converges on the golden ratio because they are equivelent expressions of the continued fraction 1+(1/(1+(1/(1+(1/(1+(1/...

[0] https://youtu.be/sj8Sg8qnjOg

>'low-information' ways to build larger structures.

And I assume that these low-information ways are more likely to emerge by random chance, because you have to get fewer bits right?

The problem with spirals, though, is that they are not symmetric. They are either left-turning or right-turning, not both.

Yeah, it's not a novel idea. Gregory Chaitin has been talking about this for a long time. And a whole bunch of other people. I can't find all that many of them listed in the citations of this work, though. And the Twitter thread on it makes it seem as if their idea of looking at evolution through the lens of AIT was original. Which is not the case at all.

yeah. 'go forward and up, turn right'

don't need to know where you are

I got paywalled, but the title is bogus if you consider biology at the molecular level, where everything is chiral and shape matters.

I really appreciate this [1] post though.

[1] https://news.ycombinator.com/item?id=30892299

They're also info-compressed. You can re-use the same DNA for both sides. This means you have less meaningful information to maintain against random mutation pressure over time.

Symmetry is also challenging to maintain and very visible; any malformation is obvious. This is useful in showing health and genetic fitness to mates.

Many tasks are also inherently symmetrical, like locomotion. Evolving the two legs totally separately would be very error-prone and you'd never quite get it right. Having them both just be copies of the same structure is much cleaner and always efficiently completes the task.

Same for things like binocular vision, having ears that hear equally and so can easily echolocate, etc.

"symmetrical structures are stronger" - citation needed.

Stronger under what condition? For the same amount of material? For the same amount of information needed to describe how to build the structure?

Do we see evidence of structures which don't require strength being more likely to evolve to be asymmetric?

Or do you just mean 'stronger' in a survival-of-the-fittest sense - symmetrical structures are fitter?

It's not at all obvious to me that this should be the case. Indeed, some very strong natural structures like shells are not symmetric at all.

"Entropically more favorable to construct" was my first thought. If you have the option of a structure to do X with 8 copies of one molecule in a radially symmetric arrangement, and a structure to do X with 5 different molecules that have only a single possible arrangement, having a random assortment of those molecules in solution (or cytoplasm), you're a lot more likely to get working copies of the symmetric structure, and non-working copies of the particular structure. Think viral nucleocapsid self-assembly in cells.

The decreased coding required is a nice bonus, which probably contributes.

Nature uses symmetrie when it is useful, but if it isn't it doesn't. Many such examples, L-sucrose vs R-sucrose, male-female differences. The same in physics and mathematics, Higgs mechanism is dependent on symmetry breaking of the weak force, and in mathematics the very nature of symmetry (group theory) has all sort of random exceptions of the pariah group of the sporadic simple groups.

Great channel, thanks for the heads up!