Timeline for (Fictive) story of a time where people reasoned only up to isomorphism
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 19 at 22:18 | comment | added | provocateur | Fair enough, I look forward to reading TWF121 in detail. | |
| Nov 18 at 23:28 | comment | added | LSpice | @provocateur, re, I agree that the punchline of the original quote is not the same as the punchline of the quote that I selected, but that's only part of the whole thing! Much of TWF121 is indeed about categorification (and introduces decategorification, I believe, only to make mathematicians who aren't used to thinking that way consciously aware that it is something that is done but need not be), so I still thought that it sounded similar. | |
| Nov 18 at 22:54 | comment | added | provocateur | The whole point of the original quote sounds like the opposite of TWF week 121. The original quote is saying 'today with category theory we go back to these roots', i.e., roots in which we did not think of sets as equinumerous with an abstract set of words like 'one, two, three, ...', but just in isomorphism with each other directly. Decategorification is surely the exact opposite of this. | |
| Nov 13, 2022 at 13:17 | comment | added | Paul Taylor | @DavidTreumann: this was still used in Medieval Europe for recording monetary transactions on tally sticks. When these were declared obsolete in England and burned, the Palace of Westminster caught fire. | |
| Oct 15, 2017 at 22:12 | comment | added | David Treumann | "If things had happened normally, when the shepherds returned the envelope would have been broken open (we do not know why it remained intact) and the number of sheep and goats would have been checked by matching them with the clay balls. There could be no dispute, because two records had been kept: the clay balls for the shepherds, the seal and inscription for the owner." | |
| Oct 15, 2017 at 22:08 | comment | added | David Treumann | and a little later from the same book, now describing an archaeologist's discovery: "...without knowing it, the uneducated servant had repeated a procedure used by equally uneducated shepherds who lived in that region 3500 years earlier. The clay envelope had belonged to an accountant (who, unlike the shepherds, knew how to write). The shepherds had gone to see him before taking their master's flock to pasture. He made as many clay balls as there were animals in the flock and put them into the envelope, which was then closed." | |
| Oct 15, 2017 at 22:00 | comment | added | David Treumann | I think the story is Georges Ifrah's, available in English as From 1 to 0. "Let us imagine a shepherd, unable to count, who has a flock of sheep that he keeps in a cave. There are 55 of them, but he has no understanding of what "the number 55" means. He would like to be sure that all of them come back every evening. One day he has an idea. He sits down at the entrance of his cave and has the sheep go in one by one. Each time one of them passes, he makes a notch in a bone. When all the sheep have passed, he has made exactly 55 notches, without knowing the arithmetic meaning of that number." | |
| Oct 8, 2017 at 8:15 | vote | accept | Maxime Lucas | ||
| Oct 7, 2017 at 8:02 | comment | added | Todd Trimble | @DavidRoberts "Bo Peep" makes her first appearance in Exercise 1.1, page 60, and later the assertion that any injective endofunction on a finite set is a bijection is called "Bo Peep's theorem". I've also heard Paul relate the parable at conference dinners. | |
| Oct 7, 2017 at 5:02 | comment | added | David Roberts♦ | @Todd have you a more precise reference as to where in Paul Taylor's book? It's a beast! | |
| Oct 6, 2017 at 17:27 | comment | added | Todd Trimble | See also the paper Categorification by Baez and Dolan. And don't overlook the same parable being told in Paul Taylor's Practical Foundations of Mathematics. | |
| Oct 6, 2017 at 16:17 | history | answered | LSpice | CC BY-SA 3.0 |