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.
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. δ| v, b | < δ| b, v | . (same for δ| v, c |)
- 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.