Dork Scratchings

(sometimes) A few days ago I read this article and realized I'd misunderstood the Continuum Hypothesis.  The Continuum Hypothesis is a statement in the language of set theory that says something like this: There's no set whose cardinality is between that of the real numbers $\mathbb{R}$ and the integers $\mathbb{Z}$. Set Theory Set theory is an axiomatic theory designed to give a rigorous foundation to our intuitive beliefs about sets.  The axioms of set theory take for granted just two things:  That there is a collection - also known as a class - of objects, which are known as sets That there is a binary relation between sets, represented by the symbol $\in$, and where $x \in A$ is read as "x is an element of A". Those two assumptions in themselves do not create any sort of parallel between the objects discussed and the naive concept of the "set".  That's the purpose of the axioms.  There's about 10 of these - known as the Zermelo-Fraenkel axioms ...

Why do we experience time the way we do?  The future seems a very different beast to the past, but as far as we can tell all of nature's fundamental laws are fully reversible.  Take a ball that's just been kicked into the air.  Newton tells us that the ball will lose speed as it rises to it's greatest height at which point it will start to fall and that it will trace out a parabola as it does.  However, if we play the video backwards, the ball will do exactly the same thing,   and this is   because the laws apply equally well when you start with "final" conditions instead of "initial" conditions and rewrite the equations in terms of "backwards time" $\tau = -t$ instead of time $t$. Despite this we do not experience the two directions the same.  In this post I will give an argument for why this is the case - one that borrows from thermodynamics, Hamiltonian classical mechanics, and Landauer's Limit. Phase Space and Entropy The 19th Century I...

Probably to stop them reporting things like this: Smoke from Californian wildfires is turning the sky pink in New York. The president does not want Americans to know.

CAL++(1)                    BSD General Commands Manual                   CAL++(1) NAME      cal++ — displays The Gormanian Calendar SYNOPSIS     cal++ -h     cal++ [-y] [[month] year] DESCRIPTION The cal++ utility displays a simple Gormanian calendar. The options are as follows: -h       help -y      [DEPRECATED] Make Gormanian year match Gregorian year. This is deprecated as it causes Dave Gorman's birthday to inconveniently have different representations in the two calendars. However, the option is included for compatibility with some online calculators. A single parameter specifies the year (1–9999) to be displayed; note the year must be fully specified: “cal++ 89” will not display a calendar for 1989. Two parameters denote the month and year; the month is either a number between 1 and 14 - where 14 rep...