3 ms·

How does this relate to linear(/affine) as in e.g. y = mx (+ b) ?

by gugagore 9y ago

drdeca 9y ago
It's related to linear logic and affine logic, and both are kinda related to linear algebra I think. With linear algebra, a function f is linear if, for any a,b, f(a+b)=f(a)+f(b) Suppose there is a vending machine that sells soda for $1 each (doesn't have a menu, just dispenses the soda, for simplicity). If you put in $1, you get a soda. If you put in $1+$1, you get a soda + a soda. The amount of soda you get is linear in the amount of money you put in. This might not be a correct explanation of why it is called linear. Also I don't really understand how the affine fits in this analogy, other than that "affine" is a somewhat weaker assumption than linear. I hope someone can give a better answer than I did, because I thought I knew the answer, but when I tried to explain it, I found that I did not really know the answer.
JadeNB 9y ago
I wondered the same! It seems to have to do with Girard's idea that linear logic involves 'additive' and 'multiplicative' 'universes' (all words in quotes because I've only skimmed to try to get an idea—even the editors of TCS apparently found the paper unreferee-able). See logical p. 3 (physical p. 4) of http://iml.univ-mrs.fr/~girard/linear.pdf http://iml.univ-mrs.fr/~girard/linear.pdf . (How exponentials fit into the picture I don't know.) Then drdeca (https://news.ycombinator.com/item?id=14684219 https://news.ycombinator.com/item?id=14684219) 's explanation of why affine logic is so called seems plausible, but I haven't looked into it.
JadeNB 9y ago
It was suggested on LtU that Girard explicitly addressed this connection, although it may still be somewhat rarefied; see the "Added in print" note at the bottom of logical p. 131 of http://www.sciencedirect.com/science/article/pii/0168007288900255 http://www.sciencedirect.com/science/article/pii/01680072889... .

3 ms·

How does this relate to linear(/affine) as in e.g. y = mx (+ b) ?

by gugagore 9y ago

How does this relate to linear(/affine) as in e.g. y = mx (+ b) ?

drdeca 9y ago
It's related to linear logic and affine logic, and both are kinda related to linear algebra I think. With linear algebra, a function f is linear if, for any a,b, f(a+b)=f(a)+f(b) Suppose there is a vending machine that sells soda for $1 each (doesn't have a menu, just dispenses the soda, for simplicity). If you put in $1, you get a soda. If you put in $1+$1, you get a soda + a soda. The amount of soda you get is linear in the amount of money you put in. This might not be a correct explanation of why it is called linear. Also I don't really understand how the affine fits in this analogy, other than that "affine" is a somewhat weaker assumption than linear. I hope someone can give a better answer than I did, because I thought I knew the answer, but when I tried to explain it, I found that I did not really know the answer.
JadeNB 9y ago
I wondered the same! It seems to have to do with Girard's idea that linear logic involves 'additive' and 'multiplicative' 'universes' (all words in quotes because I've only skimmed to try to get an idea—even the editors of TCS apparently found the paper unreferee-able). See logical p. 3 (physical p. 4) of http://iml.univ-mrs.fr/~girard/linear.pdf http://iml.univ-mrs.fr/~girard/linear.pdf . (How exponentials fit into the picture I don't know.) Then drdeca (https://news.ycombinator.com/item?id=14684219 https://news.ycombinator.com/item?id=14684219) 's explanation of why affine logic is so called seems plausible, but I haven't looked into it.
JadeNB 9y ago
It was suggested on LtU that Girard explicitly addressed this connection, although it may still be somewhat rarefied; see the "Added in print" note at the bottom of logical p. 131 of http://www.sciencedirect.com/science/article/pii/0168007288900255 http://www.sciencedirect.com/science/article/pii/01680072889... .