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Knuth answers this question in chapter 0.

by tightbookkeeper 2y ago

cloogshicer 2y ago
In which book? Sounds interesting.
- tightbookkeeper 2y ago
  Art of computer programming volume 1. It’s an exercise with a solution at the end.
  - cloogshicer 2y ago
    Thank you, will look into it!
drpossum 2y ago
You've misunderstood the difference of "sameness" those two works are trying to address. Knuth is not using an equivalent idea of "sameness" as discussed above. Two people each going by Philosophy of Computer Science and the Art of Computer Programming exercise notion would not always agree if two programs are "the same". It's also a bridge too far to make a blanket statement of Knuth "already answered this" (it's also not accurate to attribute that idea to Knuth; e.g. Church did work exactly on this decades before). Meaningful discourse and mathematical analysis requires nuance and degrees of equivalence and mixing them up makes it needlessly confusing and difficult. Sameness as "same input same output" is NOT the same as the "isomorphic equivalence" which is more difficult, strict, and abstract. In this sense they are the same if they follow the same "steps" (also isomorphic between programs), i.e. they are different representations of the same algorithm.
- tightbookkeeper 2y ago
  > same input same output He doesn’t say this. > NOT the same as the "isomorphic equivalence" which is more difficult, strict, and abstract. This is what the exercise is about. So I would recommend reading before making assumptions. Of course there are more than one definition of equivalence and isomorphism, but the one explored there is just as interesting as the comment I’m replying to. drpossum you stop with these gotcha posts? This is our 3rd encounter.
  - drpossum 2y ago
    I hadn't noticed, but it's a free board.
    - tightbookkeeper 2y ago
      I only noticed because I was perplexed by the comment. If I’m hitting this issue at random, others are hitting it too.
jkaptur 2y ago
Interesting! That exercise is what I expected the Angius and Primiero paper to be.

Knuth answers this question in chapter 0.

cloogshicer 2y ago

In which book? Sounds interesting.

tightbookkeeper 2y ago
Art of computer programming volume 1. It’s an exercise with a solution at the end.
- cloogshicer 2y ago
  Thank you, will look into it!

drpossum 2y ago

You've misunderstood the difference of "sameness" those two works are trying to address. Knuth is not using an equivalent idea of "sameness" as discussed above. Two people each going by Philosophy of Computer Science and the Art of Computer Programming exercise notion would not always agree if two programs are "the same". It's also a bridge too far to make a blanket statement of Knuth "already answered this" (it's also not accurate to attribute that idea to Knuth; e.g. Church did work exactly on this decades before). Meaningful discourse and mathematical analysis requires nuance and degrees of equivalence and mixing them up makes it needlessly confusing and difficult. Sameness as "same input same output" is NOT the same as the "isomorphic equivalence" which is more difficult, strict, and abstract. In this sense they are the same if they follow the same "steps" (also isomorphic between programs), i.e. they are different representations of the same algorithm.

tightbookkeeper 2y ago
> same input same output He doesn’t say this. > NOT the same as the "isomorphic equivalence" which is more difficult, strict, and abstract. This is what the exercise is about. So I would recommend reading before making assumptions. Of course there are more than one definition of equivalence and isomorphism, but the one explored there is just as interesting as the comment I’m replying to. drpossum you stop with these gotcha posts? This is our 3rd encounter.
- drpossum 2y ago
  I hadn't noticed, but it's a free board.
  - tightbookkeeper 2y ago
    I only noticed because I was perplexed by the comment. If I’m hitting this issue at random, others are hitting it too.

jkaptur 2y ago

Interesting! That exercise is what I expected the Angius and Primiero paper to be.