My Faults My Own

…willing to sacrifice something we don't have

for something we won't have, so somebody will someday.

IN WHICH Ross Rheingans-Yoo, a sometimes-poet and erstwhile student of Computer Science and Math, oc­cas­ion­al­ly writes on things of int­erest.

Reading Feed (last update: November 24)

A collection of things that I was glad I read. Views expressed by linked authors are chosen because I think they're interesting, not because I think they're correct, unless indicated otherwise.


(23)

Blog: Marginal Revolution | The Republican Club — why is this painting interesting? — Tyler plays art critic; see also The Democratic Club, by the same artist.

Blog: Marginal Revolution | A Time to Fast — on calorie reduction strategies.


(22)

Blog: Marginal Revolution | The best results on assortative mating and inequality I have seen — "Individuals face a large degree of uncertainty about their permanent wages early in their careers. If they marry early, as most individuals in the late 1960s did, this uncertainty leads to weak marital sorting along permanent wage. But when marriage is delayed, as in the late 1980s, the sorting

READ MORE

A Meditation on π

note: This is not a volley in the \(\pi-\tau\) debate, of which Vi Hart is undisputed monarch -- and right, as well -- as far as I'm concerned.


(1)

A few number-theoretic \(\pi\) facts:

  • \(\pi\) is provably transcendental, thus also irrational.
  • \(\pi\) is suspected, but not known, to be normal, a generalization of transcendence.
  • \(\pi\), provably, has Liouville-Roth constant (or irrationality coefficient) no greater than \(7.6063\), and is suspected to have constant no greater than \(2.5\). (As a consequence of its irrationality, its L-R constant is \(\geq2\).)

Note, though, that each of these things is also true of literally 100% of numbers. And before you scoff at my use of the figurative 'literally', no no -- measure-theoretically, the non-(normal, transcendental, irrational, irrationality-coefficient-less-than-8) numbers make up exactly, mathematically 0% of the number line.

For the record: irrational algebraics like \(\sqrt2\) are also nonterminating and nonrepeating, and it's not clear what features of the stringwise-local decimal expansion (which seems to be the only thing \(\pi\) enthusiasts focus on,

READ MORE
1 / 1