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particles must inevitably be the result of an elaborate underlying setup. But what we have now seen over and over again in this book is that in fact it is perfectly possible to get phenomena of great complexity even with a remarkably simple underlying setup. And I suspect that particles in physics—with all their various properties and interactions—are just yet another example of this very general phenomenon.

One immediate thing that might seem to suggest that elementary particles must somehow be based on simple discrete structures is the fact that their values of quantities like electric charge always seem to be in simple rational ratios. In traditional particle physics this is explained by saying that many if not all particles are somehow just manifestations of the same underlying abstract object, related by a simple fixed group of symmetry operations. But in terms of networks one can imagine a much more explicit explanation: that there are just a simple discrete set of possible structures for the cores of particles—each perhaps related in some quite mechanical way by the group of symmetry operations.

But in addition to quantities like electric charge, another important intrinsic property of all particles is mass. And unlike for example electric charge the observed masses of elementary particles never seem to be in simple ratios—so that for example the muon is about 206.7683 times the mass of the electron, while the tau lepton is about 16.819 times the mass of the muon. But despite such results, it is still conceivable that there could in the end be simple relations between truly fundamental particle masses—since it turns out that the masses that have actually been observed in effect also include varying amounts of interaction energy.

A defining feature of any particle is that it can somehow move in space while maintaining its identity. In traditional physics, such motion has a straightforward mathematical representation, and it has not usually seemed meaningful to ask what might underlie it. But in the approach that I take here, motion is no longer such an intrinsic concept, and the motion of a particle must be thought of as a process that is made up of a whole sequence of explicit lower-level steps.

So at first, it might seem surprising that one can even set up a particular type of particle to move at different speeds. But from the discussion in the previous section it follows that this is actually an

From Stephen Wolfram: A New Kind of Science [citation]