Hacker News Reader

Hacker News

Comment by da39a3ee | Hacker News Reader

Parent Full thread

da39a3ee

If you think something is absurdly obvious you usually need to re-read what you've read.

View on HN

No. It's not that rare for absurdly obvious things to get published to great fanfare.

I'm still bitter about "De Morgan's Laws". There are two of them:

1. If two things are not both true, then one or more of them is false.

2. If neither of two things is true, then both of them are false.

Of course this is obvious to everyone. Writing it down did not merit having it named after yourself. I guarantee many other people had also written it down earlier.

Obligatory xkcd: https://xkcd.com/2042/

The art museum visitor would be unambiguously correct in the case of De Morgan's laws. Rolle's Theorem depends on some fairly tricky setup work.

But for an even more obvious theorem that was actually difficult to prove (Rolle's theorem isn't), see https://en.wikipedia.org/wiki/Jordan_curve_theorem

("Any path which begins in the interior of a closed curve, and ends in the exterior of the same curve, must cross the curve at some point.")

From that link:

"The first formal proof of the Jordan curve theorem was created by Hales in the HOL Light system, in January 2005, and contained about 60,000 lines. Another rigorous 6,500-line formal proof was produced in 2005 by an international team of mathematicians using the Mizar system. Both the Mizar and the HOL Light proof rely on libraries of previously proved theorems, so these two sizes are not comparable."

A great and hilarious example of that is this heavily cited paper titled "A mathematical model for the determination of total area under glucose tolerance and other metabolic curves."[0]

The title of this paper is not misleading at all. They basically just reinvented Riemann sum in 1994.

0. https://pubmed.ncbi.nlm.nih.gov/8137688/

Whle these are "consequences" of DeMorgan's laws, they are written in the logical predicate format

And you can bet a lot of node developers will get tripped up by those if they need to simplfy or rewrite an if statement

It's "obvious" but not so much (especially for the time), and shows the importance of publishing (formalizing and adding your name) to things that might be obvious but maybe not

Interestingly, both rules are rejected in so-called "intuitionist" math. They introduce a third state any proposition can be in, as long as it hasn't been proven true or false (using other axioms). The math that derives from that is pretty nutty, like most things spawned after Godel numbering was discovered.

Don't forget the celebrated Bayes theorem that falls directly out of the definition of conditional probability P(A|B) = P(A & B) / P(B).

If you had to squint at it and turn that into P(B|A) = P(A & B) / P(A), you'd realize that you can simply multiply the top and bottom by P(A), then pull out the remaining P(A)/P(B).

       P(A & B) / P(B)
     = P(A & B) * P(A) / (P(A) * P(B))
     = P(A & B) / P(A) * P(A) / P(B)
     = P(B | A) * P(A) / P(B).

Knowing that true things are obviously true is easy. The difference between naive and professional mathematician is the ability to be precise enough to avoid knowing that false things are "obviously true".

To wit, what you stated is not De Morgan's law.

> De Morgan is given credit for stating the laws in the terms of modern formal logic, and incorporating them into the language of logic

True, and there are lots of these (Bayes's theorem, Bresenham's line drawing algorithm, Dijkstra's shortest path algorithm all spring to mind). But I kind of assume that it's because it's useful to have a name for De Morgan's Laws and these others (so it stuck as a good meme in the original meaning of "meme"), rather than because we're all so impressed with this amazing result.

Reply on news.ycombinator.com