There are multiple kinds of symmetry. In general they are characterized by a simple unit that is repeated and transformed in some way.
Mirror symmetry - this is what people typically think of when they talk of symmetry. In this case the base unit is mirrored along an axis producing a copy with its geometry swapped across the axis.
Rotation symmetry - here the unit is repeated by rotating it around an axis. Many plants and some animals like starfish exhibit rotational symmetry.
Translation symmetry - the unit is shifted along an axis one or more times. A chain shows translation symmetry.
Scaled symmetry - in this case the unit is scaled while repeated. A matryoshka doll would be an example.
Symmetries can be combined in various combinations like rotation+scaled (Nautilus)
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. the genes of a centipede do something like specify "here is a body unit with legs" build more until a different gene says "stop". Even then, the gene specifing the body unit is more likely to specify "here is half a segment" and "stick a segment here and repeat that 4 times making each one smaller" to add the leg.
This repetition of units takes less information and results in lots of symmetry as the units are transformed across different axes of symmetry.
Fractals are another example of the repeating action producing repeating units with symmetry.
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)))) ).
> 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.
>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.
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.
Noether's theorem gives you conservation laws from continuous global symmetries, like those you've noted. Under certain conditions this can be extended to discretized global symmetries (as in, for instance, a crystal lattice) but there's no analogue for the true discrete symmetries exhibited by most body plans.
In sexual selection, a type of evolutionary selection driven by mate choice rather than raw survival fitness, yes, that piece of Darwin's writing which was suppressed by Victorian ideology for about 100 years until being rediscovered in the 1960s, symmetry is an easy show of control over the physical enviroment.
By making more than one of identical somethings, you're showing that it was not through chance or accident that you developed this piece, but through deliberate growth and control, and you can prove it, because you've made two or more of them, and the viewer can easily check them against each other.
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.
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?
My point is that these minor differences actually make a really noticeable (and often kinda disturbing) difference which you can see by mirroring half of a human face on a photo, so I'm not sure if there's a real evolutionary pressure towards making it look as symmetrical as possible.
I'm surprised that this is characterized as such a novel idea in the article because I'm almost certain I've had this discussion ages ago on HN here. I think it was someone asking "why the hell are there spirals everywhere" and multiple people pretty quickly pointed out that self-repeating, symmetric, and fractal patterns are simply a very easy, 'low-information' ways to build larger structures.
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/...
> 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/...
Just for fun, note that those numerators and denominators reflect the coefficients (1 and 1) in the Fibonacci recurrence equation F_n = 1*F_{n-1} + 1*F_{n-2}.[1]
Any sequence obeying this equation will converge to the same ratio between adjacent terms. But the Fibonacci series is "perfect" in that it bottoms out at 1 and 1, never interrupting the pattern even after an infinite number of terms have gone by.
In contrast, if you defined a similar series starting at 3 and 4, that series would converge to the continued fraction 1/(1+1/(1+1/1+(1/ ... 1+(3/4) ))), which is exactly equal as long as you can't get across the infinite number of 1s in the expansion of "...".
[1] As an example of how this works, if you have the recurrence relation f(k) = 3f(k-1) + 2f(k-2), then the limit of f(n)/f(n-1) as n goes to infinity is the continued fraction 3 + 2/(3 + 2/(3 + 2/(3 + ...
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.
Think about your blood vessels. They run, and branch, and then branch again, in an intricate pattern. Your DNA has to encode for this, but our DNA holds a finite amount of information.
So does it seem more likely that your DNA holds bit of information for every branch of every blood vessel? Or instead, does it just encode the information of “blood vessel branches half way into a new blood vessel, recursively”.
The fractal can be encoded with fewer bits, as the instructions to make the original vessel can be repeated at the split point.
It’s kind of like… you don’t store information of all humans in your lineage. Rather, you store information for one human, as well as information for how to make copies.
The article mentions the human heart is asymmetrical, which was an exception I thought of immediately. And actually there are many more internal organs that are too (maybe more than are not?), such as:
- lungs (the right has 3 lobes, the left only 2)
- stomach
- pancreas
- instestines
- gall bladder
- liver
I once heard of someone that went to the ER for appendicitis and when they imaged him, some of his internal organs were left-right reversed!
"Why does symmetry reign supreme? Biologists aren’t sure — there’s no reason based in natural selection for symmetry’s prevalence in such varied forms of life and their building blocks."
Of course there is a natural selection reason - symmetrical structures are stronger.
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.
"Some owls have ears located directly across from each other, in symmetrical placement. Others have asymmetrical placement, where an ear on one side of the head is located above the one on the other side of the head, which increases their ability to locate sound on a vertical axis. These owls use their uneven ears to judge exactly where sound is coming from."
Interesting to see the confirmation - Horizontal alignment (symmetry) is best for most animals because they really need to echolocate on the horizontal plane. For the few that don't, some have adapted!
"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.
Fiddler and hermit crabs, plus many lobsters, have distinctly asymmetric claws, with one specialized for crushing and another for manipulation or cutting.
You pointed at crabs and lobsters as proof of the frequency of asymmetry by citing two of the hundreds of species having two of their eight appendages being asymmetrical. I would suggest this might be confirmation bias in action.
The universe appears to be fractal-like in nature, so I would speculate these biological symmetries are a reflection of the symmetries we find in the laws of physics, too.
ScienceClic is an extremely underrated YouTube channel producing incredible visualisations for scientific theories. They manage to cover some very advanced concepts, in an easily accessible way.
Their video on "The Symmetries of the Universe" was eye-opening, and somewhat mindblowing in the context of the bigger picture:
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.
Personally I consider any "random" abberations to be symptoms of the hairy dog theorom: you cant comb all the hair to lie flat, somewhere on the spherical dog, you're going to get a cowlick, it is unavoidable
in the meantime, chirality is simply mirror symmetry : curious part to me, is how mirror symmetry works out as one half being the "inside out" version of the other, turn a left handed glove inside out and it will fit the right hand. Maybe points to 4th dimensional stuffs, I never could grok how to turn a sphere inside out without pinching
Here are two classic youtube videos on the topic of sphere eversion; they mostly overlap, but I am posting both for double the hilarity in the comment sections :)
This is tautological; it's a slight rewording of "Nature favors symmetry when nature favors symmetry." This can be seen to be true without knowing anything about nature or symmetry, so it's a singularly unilluminating proposition about either. From my point of view, the interesting question is this: when are those times, and what are the particular properties of nature, or of symmetry, that causes nature to favor symmetry at those times but not others?
The article kinda says the opposite: that even when symmetry gives the organism no particular advantage, it still tends to get used because it's easier to code in the DNA.
That doesn't mean there will be no counterexamples ever. Sometimes asymmetry gives an advantage so it's worth the extra coding.
I always just assumed that it can be expressed with very little information so it's simpler. Simpler things are more likely to happen via random processes.
Mirror symmetry - this is what people typically think of when they talk of symmetry. In this case the base unit is mirrored along an axis producing a copy with its geometry swapped across the axis.
Rotation symmetry - here the unit is repeated by rotating it around an axis. Many plants and some animals like starfish exhibit rotational symmetry.
Translation symmetry - the unit is shifted along an axis one or more times. A chain shows translation symmetry.
Scaled symmetry - in this case the unit is scaled while repeated. A matryoshka doll would be an example.
Symmetries can be combined in various combinations like rotation+scaled (Nautilus)
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. the genes of a centipede do something like specify "here is a body unit with legs" build more until a different gene says "stop". Even then, the gene specifing the body unit is more likely to specify "here is half a segment" and "stick a segment here and repeat that 4 times making each one smaller" to add the leg.
This repetition of units takes less information and results in lots of symmetry as the units are transformed across different axes of symmetry.
Fractals are another example of the repeating action producing repeating units with symmetry.