The distance from your house to the grocery must be the same as the distance back, but 20th-century mathematicians speculated about circumstances where this might not be the case.

Very small-scale physics is non-commutative in some ways and so is distance in finance.

But non-commutative logic isn’t really that exotic or abstract.

  • Imagine you’re hiring. You could hire someone from the private sector, charity sector, or public sector. It’s easier for v managers to cross over into b | c than for c | b managers to cross over into v.

    So private is close to public, but not the other way around. Or rather, v is closer to b than b is to v.  δv, | < δb| . (same for δ| vc |) 


  • Perhaps something similar is true of management consulting, or i-banking? Such is the belief, at least, of recent Ivy grads who don’t know what to do but want to “keep their options open”.

    This might be more of a statement about average distance to other industries ∑ᵢ δ| consulting, xᵢ | being low, rather than a comparison between δ| consulting, x |   and   δ| x, consulting | . Can you cross over from energy consulting to actual energy companies just as easily as the reverse?

     
  • Imagine you’re want a marketing consultant. Maybe some “verticals” are more respected than others? So that a firm from vertical 1 could cross over into vertical 2 but not vice versa.
  • Is it easier for sprinters to cross over into distance running, or vice versa? I think distance runners have a more difficult time getting fast. If it’s easier for one type to cross over, then δ| sprinter, longdist |    δ| longdist, sprinter |.
  • It’s easier to roll things downhill than uphill. So the energy distance δ | top, bottom |  <  δ | bottom, top |.
  • It’s usually cheaper to ship one direction than the other. Protip: if you’re shipping PACA (donated clothes) from the USA to Central America, crate your donation on a Chiquita vessel returning to point of export.

Noncommutative distance, homies. (quasimetric) And I didn’t invoke quantum field theory or Alain Connes. Just business as usual.

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