### M Theory Lesson 269

In M theory, viewing the $1$-ordinals as one level trees usually leads us to associahedra polytopes, which can be concretely embedded in a real number space.

These real spaces are useful for analysing physically interesting integrals associated to MZVs, but the question is, what are those real spaces doing there? We don't seem to need them. The association of MZVs to patterns arising from operads is quite functorial, leading one to suspect that MZVs should be defined not from the point of view of standard analysis, but as canonical numerical invariants for categorical structures. Then one wouldn't need to discuss real backgrounds. Then, if we still cared, later one could worry about whether or not these zetas were really the same as the ones that we thought we were talking about when we felt integrals were unavoidable.

These real spaces are useful for analysing physically interesting integrals associated to MZVs, but the question is, what are those real spaces doing there? We don't seem to need them. The association of MZVs to patterns arising from operads is quite functorial, leading one to suspect that MZVs should be defined not from the point of view of standard analysis, but as canonical numerical invariants for categorical structures. Then one wouldn't need to discuss real backgrounds. Then, if we still cared, later one could worry about whether or not these zetas were really the same as the ones that we thought we were talking about when we felt integrals were unavoidable.

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