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Comment by dukeofdoom | Hacker News Reader

One thing I would like to understand is why in our universe we can have two things that combine to nothing. But we can't have 3 things that combine to nothing. Can someone smarter give an explanation.

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In Quantum Chromodynamics we have 3 things that combine to nothng though.

What are you thinking about here? If it is "matter/antimatter" "particles/antiparticles" then this is not true. There are still conserved quantities in annihilation of particles and antiparticles which makes other particles and/or energy come out of these annihilations.

Which are the two things that combine to nothing?

Particles and antiparticles.

But I think he's trying to make a slightly more general point: why are "parities" (2-fold symmetries) so common in nature and mathematics? Why not more 3-fold symmetries?

As the other reply said, in QCD you have "3 things that combine to nothing." If I had to guess why they are not so common I would say that the more variables you add in a theory the more complicated you make it. So by Occam's razor we try to go for the simpler models/structures.

One line of thought here is that maybe there do exist larger, more complex symmetry groups that can broken to create more complex "charge" particles (e.g. electric charge < color < something else < ...), but that the masses of particles involved are so large, their lifetimes so short, etc, such that we'd never actually observe them (or at least, we can't yet observe them) and that the more complex the group, the less relevant the physics actually becomes.

(Obviously I can't say whether that is true or not, but it might be a possible explanation of current observations).

Occam's razor is a heuristic not a law so this isn't really a satisfactory explanation

Maybe sound is an illustrative example. The air pressure is a positive scalar quantity. We are interested in the deviations from the mean. Deviations can be both positive and negative. A positive and a negative deviation cancel (in absolute terms: a larger than normal pressure and lesser than normal pressure will average to something more typical)

This is a good explanation for e.g. electric charge (which is scalar, just like presure), but color in QCD really is a bit more multidimensional in behavior where you can get things like red + green = -blue and so-on.

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