Is this really induction? Seems more like recursion.

Hovertext: “This would be bad enough, but every 30th or 40th pokéball has TWO of them inside.”

17 Comments

I guess I don’t understand the origins of the “Induction” title and the posting text that disputes that label. Do they come from different sources? Was the title already attached to this when it reached the editors, who then are commenting on it?

I am also very confused. When was this xkcd published? I don’t recognize it as a recent one. And it seems to be missing a lot of context.

It’s 1516: Win by Induction, 24 April 2015 . Explain xkcd has an explanation of how Pikachu chusing Pikachu endlessly is similar to induction, but 1) that’s cheating and 2) having cheated I can’t say I am much the wiser.

I don’t know much about Pokémon, but I believe Pikachu (and maybe all of the others?) is incapable of saying anything other than its own name. Maybe this was intended to prevent just such an eventuality.

Seems the custom here is of not inserting author’s or additional expository material from elsewhere so that this CIDU may elicit our own comments. But narmitaj’s posting makes more analysis somewhat moot.

Speaking of “moot”, here’s last week’s Shoe…
.
Gal says: I’m taking a law class online.
Other person: What’s that like?
Gal: We just had a Zoom call where we all had to be on moot.

It’s a custom but not an enforced or strict rule. If you think it would be useful, you can blamelessly tell us what you found and what you think based on it.

And thanks for the transcription of the Moot Shoe. The cartoon appeared here in the “Saturday Morning Oys – May 22nd, 2021” collection, and didn’t get much discussion.

Danny Boy: Whoops, sorry, forgot to include the context. As narmitaj said, Munroe titled this “Win by Induction”: https://xkcd.com/1516/

Under the Curry-Howard isomorphism, induction and recursion are pretty much the same thing. Not sure how much the wikipedia article on same will help anyone who’s not already aware of this stuff; the basic idea is that proofs are programs and programs are proofs, and an inductive proof turns out to be a recursive program.

By mathematical induction, there is no bound on the number of Pikachu that will emerge. I thought the winning came by exhaustion, as the opponents will finally get tired of this and go away. (Alternately, that there is some number of Pikachu that they cannot beat, and by induction that number can be reached.)

It is also just iteration (minus the part about some Pokeballs having two Pikachu in them), which is equivalent to tail recursion, because Pikachu has a tail.

It does call this reasoning into question that the Pikachu are getting smaller, so it’s possible that the total mass of an infinite sequence of Pikachu might not exceed that of a single very heavy Pokemon.

Dave in Bostom: A hot dog is topologically isomorphic to a hamburger patty, but that doesn’t mean I feel free to call a hot dog a hamburger patty.

Those topological equivalences aren’t technically isomorphisms… but in any case the equivalence of functions and theorems is a lot closer than that. I don’t think it’s a good idea to try to get into technical details here, not least because the site doesn’t really support notation for either math or software. But if anyone wants, I can try…

FWIW, IIRC the Explain XKCD Wiki is run by fans, without the cartoonist’s input.

Dave: I understand the math. I’m saying that isomorphism is a general license to use terms interchangeably.

Why do you say that those topological equivalences aren’t isomorphisms?

Dave: I prefer the Curly Howard isomorphism.

Winter Wallaby says: ” I’m saying that isomorphism is a general license to use terms interchangeably”

Wait, I thought you would be on the “is NOT” side of interchangeability?

I’m assuming that was a typo. As for the topology issue, that’s what I remember from topology but it was decades ago now.

as for the original point… WW, if you understand the math then I should be able to get away with saying “in the proof term for a theorem, application of the induction hypothesis is a recursive invocation of the theorem”, right? It really is the same thing in a very specific way.

If the nth Pikachu is just picking himself, that’s recursion. If the nth Pikachu is picking the n+1th Pikachu, that’s induction.

I guess I don’t understand the origins of the “Induction” title and the posting text that disputes that label. Do they come from different sources? Was the title already attached to this when it reached the editors, who then are commenting on it?

I am also very confused. When was this

xkcdpublished? I don’t recognize it as a recent one. And it seems to be missing a lot of context.It’s 1516: Win by Induction, 24 April 2015 . Explain xkcd has an explanation of how Pikachu chusing Pikachu endlessly is similar to induction, but 1) that’s cheating and 2) having cheated I can’t say I am much the wiser.

I don’t know much about Pokémon, but I believe Pikachu (and maybe all of the others?) is incapable of saying anything other than its own name. Maybe this was intended to prevent just such an eventuality.

Seems the custom here is of not inserting author’s or additional expository material from elsewhere so that this CIDU may elicit our own comments. But narmitaj’s posting makes more analysis somewhat moot.

Speaking of “moot”, here’s last week’s Shoe…

.

Gal says: I’m taking a law class online.

Other person: What’s that like?

Gal: We just had a Zoom call where we all had to be on moot.

It’s a custom but not an enforced or strict rule. If you think it would be useful, you can blamelessly tell us what you found and what you think based on it.

And thanks for the transcription of the Moot Shoe. The cartoon appeared here in the “Saturday Morning Oys – May 22nd, 2021” collection, and didn’t get much discussion.

Danny Boy: Whoops, sorry, forgot to include the context. As narmitaj said, Munroe titled this “Win by Induction”: https://xkcd.com/1516/

Under the Curry-Howard isomorphism, induction and recursion are pretty much the same thing. Not sure how much the wikipedia article on same will help anyone who’s not already aware of this stuff; the basic idea is that proofs are programs and programs are proofs, and an inductive proof turns out to be a recursive program.

By mathematical induction, there is no bound on the number of Pikachu that will emerge. I thought the winning came by exhaustion, as the opponents will finally get tired of this and go away. (Alternately, that there is some number of Pikachu that they cannot beat, and by induction that number can be reached.)

It is also just iteration (minus the part about some Pokeballs having two Pikachu in them), which is equivalent to tail recursion, because Pikachu has a tail.

It does call this reasoning into question that the Pikachu are getting smaller, so it’s possible that the total mass of an infinite sequence of Pikachu might not exceed that of a single very heavy Pokemon.

Dave in Bostom: A hot dog is topologically isomorphic to a hamburger patty, but that doesn’t mean I feel free to call a hot dog a hamburger patty.

Those topological equivalences aren’t technically isomorphisms… but in any case the equivalence of functions and theorems is a lot closer than that. I don’t think it’s a good idea to try to get into technical details here, not least because the site doesn’t really support notation for either math or software. But if anyone wants, I can try…

FWIW, IIRC the Explain XKCD Wiki is run by fans, without the cartoonist’s input.

Dave: I understand the math. I’m saying that isomorphism is a general license to use terms interchangeably.

Why do you say that those topological equivalences aren’t isomorphisms?

Dave: I prefer the Curly Howard isomorphism.

Winter Wallaby says: ” I’m saying that isomorphism is a general license to use terms interchangeably”

Wait, I thought you would be on the “is NOT” side of interchangeability?

I’m assuming that was a typo. As for the topology issue, that’s what I remember from topology but it was decades ago now.

as for the original point… WW, if you understand the math then I should be able to get away with saying “in the proof term for a theorem, application of the induction hypothesis is a recursive invocation of the theorem”, right? It really is the same thing in a very specific way.

If the nth Pikachu is just picking himself, that’s recursion. If the nth Pikachu is picking the n+1th Pikachu, that’s induction.