2021

Here is an example of how numbers can give us hard puzzles: The obvious point, for the naturals is that 3n + 1 converts an odd to an even and division by two pulls out an odd factor or else gets into the chain of powers of two, which has precisely one odd member, 1. Where, of course, conveniently, 3 * 1 + 1 is 4. Thus the halting loop. (The negatives bring in other loops on their side of zero.) So, the [pseudo-?]algorithm — does it always halt? — is searching for the ladder of powers of 2. Find it and you halt, fail and you explode into a halting fail. Or, is there another loop in the positive Read More ›

Vivid recently reminded us of the painful, bloody lesson of history taught by Hitler’s seizure of power in 1933. I responded, noting: [I]sn’t it interesting that the Reichstag Fire crisis isn’t a standard part of our general education package. It almost makes one wonder why it is that the story of how the most universally acknowledged unmitigatedly evil dictator seized absolute power through agit prop and lawfare is somehow pushed to the margins of our common fund of knowledge. Not quite a conspiracy of silencing but at least a common evasion of plain duty by those who inform and educate us. Ironically, on a topic where learning this is vital to defending our civilisation, the common thought association fed by Read More ›