Scientific knowledge comprises knowledge taken at discrete slices of the Renormalization Group over observable phenomena . These are slices because observation always has to occur…
actually, maybe i’m wrong.
anyway, the general idea i wanted to express was imaginging scientific disciplines as carving out slices/spans over the RG group, kind of picturing the RG group as a cylinder where the vertical dimension of the cylinder is the “resolution” of the observation/phenomena. This was sparked by the wikipedia article about Cascadia, which also discusses the “bioregionalism” movement. this got me thinking about how within ecology, the notion of “region” is defined at a variety of scales. The hypothesis was that the space of these scales is continuous and therefore we should be able to define a coarse grained abstraction whose resolution is bounded above and below by any two arbitrary, previously defined abstractions. which is to say, if ecology currently has sub-specialties for people who study aggregates of ecological behaviors at resolutions x, y, … n, we can always invent a new specialty that studies phenomena at a new scale between x and y previously characterized scales.
biology → ecology → bioregional ecology → … → chemistry → chemical kinetics → … physics → statistical mechanics → … → field theory → quantum field theory
let’s assume QFT is the “bottom”.
- my thinking was: “I’m pretty confident we can take a slice through any arbitrary part of that stack”
but the more I think about it, I’m not sure that’s how it works.
so the first issue is that those disciplines aren’t slices: they’re spans. If they were just slices the idea would work, but they’re not, so it’s possible that they can overlap and that the set of all sciences could then be covered. congrats: you proved yourself wrong!
but I think that’s actually wrong too and here’s why.
it’s not a cylinder. it’s high dimensional.
in addition to partially defining itself over a scale of resolution, a “discipline” defines itself as a region in the semantic space. its attention is constrained to some subset of phenomena…
or rather, given some discipline…
following the direction of this though, I think there’s a potential proof that a universal law has to exist. some single fundamental law from which all other dynamics at all scales of resolution are consequent.
or
there are infinite possible observable laws at any scale of resolution.
jesus, is this what theoretical physics is? this is just philosophy.
i’ve stopped caring. i’m moving on from this idea.