Posts tagged with asymmetry

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.

The worst thing about lawyers, in my opinion, is that not everybody can afford one. Our justice system is supposed to make things fair for everyone. In that pursuit it says that everyone is entitled to an advocate. However, advocates are entitled to be paid for their labor and therefore the plaintiffs and defendants of the U.S. must pay.


This economic bar to legal representation does some good. Since it’s costly to litigate, the courts’ burden is less than if lawsuits were free. Small disputes are settled out-of-court; whether this is good or bad, I can’t say.


However, poor people necessarily get less access to justice. Since the law is too complex for an average person to learn (especially if they work for a living), they must hire a lawyer to access justice. Even if they have a perfectly legitimate complaint,

  1. they might not know their complaint is legitimate (since they can’t afford to ask a lawyer);
  2. they are unable to effectively represent themselves and win cases, without the money to afford a lawyer.


By contrast, rich people can ask a lawyer (friend or at-hire) to find out whether this-or-that is illegal. And if they think a case might have a chance, they can go ahead with the suit. Poor people can’t take a case forward unless it’s a sure-fire win.

Progressive Taxation

To my mind, unequal access to the law is one of the best justifications for Progressive Taxation. Which is another topic for another time.

But just to summarize the point:

  • Rich people benefit more from the system.
  • So they should contribute more to paying for it.