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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 i
by Tagbert 5y ago
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.
- thaumasiotes 5y ago> 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.
- deleted 5y ago[deleted]
- mistermann 5y agoAre there anycases of plausible temporal symmetry, especially emergent that don't have obvious triggers.
- ffhhj 5y agoLike reproduction?
- mistermann 5y agoI'm kinda thinking of emergent patterns that can be observed in aggregate trends, that do not have obvious ~logical causality behind them. It's kind of a hard question to ask.
- lazyant 5y agosymmetries give us the laws of conservation (time symmetry, conservation of energy; rotation symmetry, conservation of angular momentum etc)
- hither_shores 5y agoNoether'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.
- abetusk 5y agoAnother 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)))) ).
- captn3m0 5y agoThis reminds me of the Hutter Prize, which equates compression with AI. https://en.m.wikipedia.org/wiki/Hutter_Prize https://en.m.wikipedia.org/wiki/Hutter_Prize
- ToJans 5y agoSmall 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.
- Epiphany21 5y ago>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.
- therealbilly 5y agoEarly lifeforms in the Ediacaran period favored glide symmetry aka translational.