4 ms·

from https://news.ycombinator.com/item?id=41077201 https://news.ycombinator.com/item?id=41077201 : Two apples are the same as two apples. Two apples are not t

from https://news.ycombinator.com/item?id=41077201 https://news.ycombinator.com/item?id=41077201 : Two apples are the same as two apples. Two apples are not the same as two oranges. Two ripe apples are not the same as two rotten apples, even though they are both two apples and two apples. Two fruits are the same as two fruits, even though they could be two apples and two oranges.

geye1234 2y ago
In each case they are alike in certain respect(s) and different in certain respect(s). For example, in the first example, the apples are instantiations or examples of the same thing. So they are alike in that regard. But they differ in other regards, most obviously in the bundle of matter that makes them up. In the third example, pretty much the same thing, with some additional detail. In the second and fourth examples, they are not examples of the same thing. But 'fruit' doesn't imply any species of fruit -- it's generic in that regard -- so apples and oranges share that genus while being different species. Being an apple and being an orange both imply being a fruit; but being a fruit doesn't imply either of the others.
gradschoolfail 2y ago
If mathgenius is to be believed, decategorization is about paying attention to the map from apples to oranges.. riffing on that, designori will try to unify the shiny and the essential.. and though John “Designor” Henrys are memorialized, nobody sane would want to be John Henry … question: how would “the central bank” help? L: https://mathoverflow.net/questions/456414/what-is-decategorification https://mathoverflow.net/questions/456414/what-is-decategori...
- 082349872349872 2y ago
  In the Acemoglu and Restrepo model, a low interest rate results in automating all current tasks, while a higher one results in new labour-intensive tasks being added to the model economy as fast as old ones are being automated away. (incidentally, they also had some regime in which automation was predicted to increase wages, but I didn't read that closely) riffing* off https://math.ucr.edu/home/baez/week121.html https://math.ucr.edu/home/baez/week121.html I think decategorisation is about forgetting the differences between the maps into and out of two apples and two oranges (and even two fruits), leaving us with just a (relabelable) set of cardinality 2? (via JvN's construction: {∅,{∅}}) EDIT: taking connected components of the projection down to the "largest groupoid" sounds very similar to https://en.wikipedia.org/wiki/Weak_component https://en.wikipedia.org/wiki/Weak_component : the finest partition (here, of objects from the original category) that is totally ordered by reachability (direction of arrows from the original category).
  - gradschoolfail 2y ago
    Ah i didnt see that JCB and got it flipped again (and misspelled as a bonus) — had better do this after a long walk (or sleep) Ps that was a helpful blogpost, as well as a very concrete wiki eg! Thanks for distilling A&R: f(o)rex “thinking” and “writing” can be quite labor-intensive, but we’d like to have finer distinctions between the types — what kinds “should” be added vs replaced.. so we should also pay attention to exchange rates?? (as a first guess, optimizing shiny vs essential — “form follows function” for reverence [why dont hackernewsies revere brutalism?] — for bosons, fermions & everything in between)
    - 082349872349872 2y ago
      I like the full ANW quote: > “It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.” but it does make sense it's normally truncated in citation: at the beginning of the XX he might have been able to expect the casual reader to appreciate a simile involving cavalry charges, and probably even Euclid, a couple of thousand years earlier, would've appreciated it, but we need a new simile for new millennia. Operations of thought are like power-ups in a game — they are strictly limited in number, they are time-boxed, and must only be made at decisive moments? https://archive.org/details/introductiontoma00whitiala/page/61/mode/2up https://archive.org/details/introductiontoma00whitiala/page/...
      - gradschoolfail 2y ago
        I had a vision of the future days, One without golden bouoys or silk-clad popes; Where all the might of consumers harnessed, For health of earth and all the god’s creatures. Without irony the downtrickle shall, be Fully potable. The Apotheosis of Californication Is Neither Roman Nor British
      - 2y ago

geye1234 2y ago

In each case they are alike in certain respect(s) and different in certain respect(s). For example, in the first example, the apples are instantiations or examples of the same thing. So they are alike in that regard. But they differ in other regards, most obviously in the bundle of matter that makes them up. In the third example, pretty much the same thing, with some additional detail. In the second and fourth examples, they are not examples of the same thing. But 'fruit' doesn't imply any species of fruit -- it's generic in that regard -- so apples and oranges share that genus while being different species. Being an apple and being an orange both imply being a fruit; but being a fruit doesn't imply either of the others.

gradschoolfail 2y ago

If mathgenius is to be believed, decategorization is about paying attention to the map from apples to oranges.. riffing on that, designori will try to unify the shiny and the essential.. and though John “Designor” Henrys are memorialized, nobody sane would want to be John Henry … question: how would “the central bank” help? L: https://mathoverflow.net/questions/456414/what-is-decategorification https://mathoverflow.net/questions/456414/what-is-decategori...

082349872349872 2y ago
In the Acemoglu and Restrepo model, a low interest rate results in automating all current tasks, while a higher one results in new labour-intensive tasks being added to the model economy as fast as old ones are being automated away. (incidentally, they also had some regime in which automation was predicted to increase wages, but I didn't read that closely) riffing* off https://math.ucr.edu/home/baez/week121.html https://math.ucr.edu/home/baez/week121.html I think decategorisation is about forgetting the differences between the maps into and out of two apples and two oranges (and even two fruits), leaving us with just a (relabelable) set of cardinality 2? (via JvN's construction: {∅,{∅}}) EDIT: taking connected components of the projection down to the "largest groupoid" sounds very similar to https://en.wikipedia.org/wiki/Weak_component https://en.wikipedia.org/wiki/Weak_component : the finest partition (here, of objects from the original category) that is totally ordered by reachability (direction of arrows from the original category).
- gradschoolfail 2y ago
  Ah i didnt see that JCB and got it flipped again (and misspelled as a bonus) — had better do this after a long walk (or sleep) Ps that was a helpful blogpost, as well as a very concrete wiki eg! Thanks for distilling A&R: f(o)rex “thinking” and “writing” can be quite labor-intensive, but we’d like to have finer distinctions between the types — what kinds “should” be added vs replaced.. so we should also pay attention to exchange rates?? (as a first guess, optimizing shiny vs essential — “form follows function” for reverence [why dont hackernewsies revere brutalism?] — for bosons, fermions & everything in between)
  - 082349872349872 2y ago
    I like the full ANW quote: > “It is a profoundly erroneous truism, repeated by all copy-books and by eminent people when they are making speeches, that we should cultivate the habit of thinking of what we are doing. The precise opposite is the case. Civilization advances by extending the number of important operations which we can perform without thinking about them. Operations of thought are like cavalry charges in a battle — they are strictly limited in number, they require fresh horses, and must only be made at decisive moments.” but it does make sense it's normally truncated in citation: at the beginning of the XX he might have been able to expect the casual reader to appreciate a simile involving cavalry charges, and probably even Euclid, a couple of thousand years earlier, would've appreciated it, but we need a new simile for new millennia. Operations of thought are like power-ups in a game — they are strictly limited in number, they are time-boxed, and must only be made at decisive moments? https://archive.org/details/introductiontoma00whitiala/page/61/mode/2up https://archive.org/details/introductiontoma00whitiala/page/...
    - gradschoolfail 2y ago
      I had a vision of the future days, One without golden bouoys or silk-clad popes; Where all the might of consumers harnessed, For health of earth and all the god’s creatures. Without irony the downtrickle shall, be Fully potable. The Apotheosis of Californication Is Neither Roman Nor British
    - 2y ago