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im sure this question has been asked before, but why is nature so symmetrical, and spherical? even down to the cells, atoms, dna and so forth...
flowers, faces, eyes, hands, the list is endless! why is this? is there an answer? has anyone actually scientifically studied it?
flowers, faces, eyes, hands, the list is endless! why is this? is there an answer? has anyone actually scientifically studied it?
Answers
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Uniformity.
For asymetry one location must be special over another.
Consider a raindrop, the constitution of it is uniform, same water material everywhere the forces on it act the same at all part of it and so it is spherical.
Where you have uniformity you have symmetry.
But symmetry isn't as all pervasive as you suggest. Almost the direct opposite is a fractal. A fractal becomes more complex the closer you look at it like a coastline, the bark patterns of a tree etc.
Stuff like this:
http://www.ba.infn.it/~zito/project/nfractals. html
For asymetry one location must be special over another.
Consider a raindrop, the constitution of it is uniform, same water material everywhere the forces on it act the same at all part of it and so it is spherical.
Where you have uniformity you have symmetry.
But symmetry isn't as all pervasive as you suggest. Almost the direct opposite is a fractal. A fractal becomes more complex the closer you look at it like a coastline, the bark patterns of a tree etc.
Stuff like this:
http://www.ba.infn.it/~zito/project/nfractals. html
The answer is efficiency in evolution with a little bit of surface tension thrown in.
Imagine you are designing a robot, you think about what it has to, then you try to work out the most efficient way to do it.
Very often one big part is not suitable so you duplicate a small one, an efficient process in itself, you put all these smaller parts as close together as you can remembering they all have to be connected up to receive and deliver. If you put each connecting part as close together as you can you end up with a circle (like flowers do)
If you develop a part that works then find you need two, the second part will work better if you put it on the other side, making a handed duplicate is almost as easy as
making the first one, many of nature�s cells are handed.
If you look at nature�s way of doing things you have a job to work out a better way.
And the surface tension, lets stick together then when we are needed we will all be there.
For example a water droplet in space is spherical. It�s probably something to do with electrical charges generated when the molecules congregate.
Imagine you are designing a robot, you think about what it has to, then you try to work out the most efficient way to do it.
Very often one big part is not suitable so you duplicate a small one, an efficient process in itself, you put all these smaller parts as close together as you can remembering they all have to be connected up to receive and deliver. If you put each connecting part as close together as you can you end up with a circle (like flowers do)
If you develop a part that works then find you need two, the second part will work better if you put it on the other side, making a handed duplicate is almost as easy as
making the first one, many of nature�s cells are handed.
If you look at nature�s way of doing things you have a job to work out a better way.
And the surface tension, lets stick together then when we are needed we will all be there.
For example a water droplet in space is spherical. It�s probably something to do with electrical charges generated when the molecules congregate.
Symmetry is the way identically shaped/sized particles fit together with attraction. For fluid matter on a large scale gravity will pull the parts into the least possible volume producing a sphere.
Symmetry is an attractive way of viewing things so the there is the temptation to perceive symmetry even where it is only approximated.
symmetry
Symmetry is an attractive way of viewing things so the there is the temptation to perceive symmetry even where it is only approximated.
symmetry
Issues of replica-symmetry breaking for the amorphous solid state of vulcanized macromolecules
Abstract. The statistical mechanics of vulcanized (i.e. permanently randomly crosslinked) macromolecular matter can be formulated, using the replica technique, as the n to 0 limit of a theory containing n+1 coupled replicas. Within the framework of a replica-symmetric variational mean-field approach, this theory describes an equilibrium phase transition, upon sufficient vulcanization, from a liquid to an amorphous solid state. We consider a natural extension of this framework, which admits the possibility of the spontaneous breaking of replica symmetry, and find that-at least at the mean-field level-replica symmetry appears to remain intact. We discuss the physical origin of this absence of replica-symmetry breaking, as well as a possible strategy for a theoretical refinement that may yield replica-symmetry breaking.
Love it :)
Abstract. The statistical mechanics of vulcanized (i.e. permanently randomly crosslinked) macromolecular matter can be formulated, using the replica technique, as the n to 0 limit of a theory containing n+1 coupled replicas. Within the framework of a replica-symmetric variational mean-field approach, this theory describes an equilibrium phase transition, upon sufficient vulcanization, from a liquid to an amorphous solid state. We consider a natural extension of this framework, which admits the possibility of the spontaneous breaking of replica symmetry, and find that-at least at the mean-field level-replica symmetry appears to remain intact. We discuss the physical origin of this absence of replica-symmetry breaking, as well as a possible strategy for a theoretical refinement that may yield replica-symmetry breaking.
Love it :)
I think Danny's really talking about geometrical symmetry.
But in Physics symmetry has a special and very powerful place.
Symmetry means that things stay the same when you vary something else.
For example translational symmetry means that if you move a system from one place to another nothing changes and everything works as normal.
Critically this can be shown to require the conservation of momentum.
Each symmetry has a corresponding conservation law.
Time symmetry implies conservation of Energy etc.
This is called Noethers Theorum and tells us something very special about the way the Universe works.
http://en.wikipedia.org/wiki/Noether%27s_Theor em
But in Physics symmetry has a special and very powerful place.
Symmetry means that things stay the same when you vary something else.
For example translational symmetry means that if you move a system from one place to another nothing changes and everything works as normal.
Critically this can be shown to require the conservation of momentum.
Each symmetry has a corresponding conservation law.
Time symmetry implies conservation of Energy etc.
This is called Noethers Theorum and tells us something very special about the way the Universe works.
http://en.wikipedia.org/wiki/Noether%27s_Theor em
Least energy, in many cases.
Why are rain-drops hemispherical when they're on a flat surface?
It's easier for the molecules to be in a lower energy state when formed as a hemisphere (would normally be a sphere if it wasn't for the flat surface), and so they form a hemisphere to reduce their energy.
Why this is is all down to surface tension, and other effects like that (I believe it's explained somewhat above).
Why are rain-drops hemispherical when they're on a flat surface?
It's easier for the molecules to be in a lower energy state when formed as a hemisphere (would normally be a sphere if it wasn't for the flat surface), and so they form a hemisphere to reduce their energy.
Why this is is all down to surface tension, and other effects like that (I believe it's explained somewhat above).
There are some very powerful ways in which nature is NOT symmetrical. Matter/ anti-matter for instance. We live in a universe (or at least a corner of a universe), that is pretty much all matter. If the universe was locally symmetrical for matter/ anti-matter then we'd never have come into existence.
If 4 separate atoms link to the same carbon atom then they form the corners of a tetrahedron. If these atoms are of 4 different elements then there are two ways of forming these bonds giving you two "different" compunds. In inorganic chemistry this sort of difference can be ignored; chemical reactions carry on as normal. Inside living systems, however, you generally find that one of the pair of substances is acceptable and the other is not because the enzymes moderating the organic reactions are themselves "handed" and can operate on only one type of structure.
If 4 separate atoms link to the same carbon atom then they form the corners of a tetrahedron. If these atoms are of 4 different elements then there are two ways of forming these bonds giving you two "different" compunds. In inorganic chemistry this sort of difference can be ignored; chemical reactions carry on as normal. Inside living systems, however, you generally find that one of the pair of substances is acceptable and the other is not because the enzymes moderating the organic reactions are themselves "handed" and can operate on only one type of structure.
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