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 pri**v**ate sector, **c**harity sector, or pu**b**lic sector. It’s easier for **v** managers to cross over into **b** | **c** than for **c** | **b** managers to cross over into **v**.
So pri**v**ate is close to pu**b**lic, but not the other way around. Or rather, **v** is clos*er* 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.

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

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Tags: Abelian, asymmetric, asymmetry, business, business school, commutativity, distance, investment banking, marketing, math, mathematics, maths, metric, non-Abelian, non-commutative, noncommutative, PR, quantum field theory, quantum physics, quasimetric, quasimetrics, symmetric, symmetry

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