0248: "Hypotheticals"

[OneLess]

The last part of the cartoon reminded me of the Subtle Knife. What if that were real? Kick-ass...

Spoilers...

But would you really want those shadows running around everywhere?

I'd have mine bite other people. I don't remember if that was possible in the books, but couldn't they at least bite each other? Shadow cockfighting!

Edit: It just struck me that this comic would be really surreal if the beret guy in the 2nd bubble was thinking about what would would be like if he didn't have ice cream

[awkward]

Code: Select all

int i=0;
public int hypothetical(){
i++;
boolean hasKnife = (int)(Math.random()*100)==5;
if (hasKnife)
    return i;
return hypothetical();}

System.out.println(hypothetical()+"hypothetical situations were necessary to break free.");


[hotaru]

Edit: It just struck me that this comic would be really surreal if the beret guy in the 2nd bubble was thinking about what would would be like if he didn't have ice cream

it would be really surreal if that 3rd bubble was the "real" situation on the far left.

[cmacis]

Dammit, there's a reality machine that plays around with mixing levels and I can't/won't look for it right now.

Specifically it reminds me of the bits on GEB where Achilles and the Tortoise are reading stories about themselves and it's written as if they are travelling up and down this stack. In the end they are actually still in danger, but it looks like they're okay.

[LE4dGOLEM]

Dammit, there's a reality machine that plays around with mixing levels and I can't/won't look for it right now.

qntm.org

one of the stories. about the quantum computer: "I don't know Johnny, being God is a big resposibility" IIRC

[macronencer]

Randall, you are a genius.

This made me think of Gödel, Escher, Bach; although I had been aware of the idea of nested thought balloons many years prior to reading that. (Including the idea of being within ones own thought balloon, although that requires some delicate work.) It's a good book.

(Hmm. A comic book version of Gödel, Escher, Bach would be fucking hardcore if it could be pulled off right.)

You may be interested to know that I once made an audio version of Little Harmonic Labyrinth. Doing the infinite sequence of Djinns was the REALLY hard part - especially as this was before modern PCs so I was using a four-track cassette recorder!

No, I'm not going to post it because one day I want to do it again, only better.

[Rocco]

All that work, and they still didn't manage to break the fourth wall.

Best example of fourth wall breaking:
http://stickman.qntm.org/comics.php?n=614

And also, what if the hypothetical guy managed to break out into the real world? Would there be two of him? And what if the guy I'm imagining doing that is standing behind me with the knife?

Another Great Example

[Alan]

What if my hypothetic self did have a device that could break out of hypothetical situations and he handed it to me after he used it?

What would be revealed when I used it?

[screech]

I just suddenly thought of something.

Logically, there are an infinite number of hypothetical situations. In this infinity, there has to be one that has a device allowing the people in the situation to break out - in fact there has to be an infinite number. But there doesn't seem to be anyone breaking through. So there are not an infinite number of hypothetical situations. How can this be true?

And thinking about the above, are we just lots of people in a hypothetical situation?

[cmacis]

Hmm, if one level down is stick people, and our level is 3d people, then another level up is 4d people. Hey, Mr comic writer who is writing me. It's been a bit dull at the moment. Can I have something exciting written in soon?

However, if I am a puppet on a string to a writer, then he was writing that, probably ironically. Though, if you develop a character enough, they practically write themselves.

Now I'm confused and tired.

[Patashu]

I just suddenly thought of something.

Logically, there are an infinite number of hypothetical situations. In this infinity, there has to be one that has a device allowing the people in the situation to break out - in fact there has to be an infinite number. But there doesn't seem to be anyone breaking through. So there are not an infinite number of hypothetical situations. How can this be true?

And thinking about the above, are we just lots of people in a hypothetical situation?

If you think about it, they only hypothetically have a machine that can travel out of hypothetical situations.

[Castaway]

besides, hypothetical situations are just figments of your mind. You don't know if you're in it, so you wouldn't know you'd need to build a machine to escape, nor would you even know where to begin.

[OmenPigeon]

How can it be that no one's brought up the (sadly demised) No 4th Wall to Break? The epitome of metalepsis in webcomics.

[screech]

besides, hypothetical situations are just figments of your mind. You don't know if you're in it, so you wouldn't know you'd need to build a machine to escape, nor would you even know where to begin.

But since there are an infinite number of them, in at least one of them they would know.

[macronencer]

besides, hypothetical situations are just figments of your mind. You don't know if you're in it, so you wouldn't know you'd need to build a machine to escape, nor would you even know where to begin.

But since there are an infinite number of them, in at least one of them they would know.

I probably don't need to point this out, but this whole "infinite in number implies unlimited in variety" nonsense is fallacious in the extreme.

Were it true, one could use it to prove that, since the positive integers are infinite, at least one of them must be the square root of 2.

It is possible to have an infinite subset of an infinite set!

And if anyone says, at this point, "but let's hypothesize that it isn't a fallacious argument," my hypothetical dagger will reach out from the page and hypothetically stab them.

Thank you.


P.S. I blame Douglas Adams, with his "The Universe" guide entry - man, was that thing full of holes.

[joeythehobo]

I probably don't need to point this out, but this whole "infinite in number implies unlimited in variety" nonsense is fallacious in the extreme.

Were it true, one could use it to prove that, since the positive integers are infinite, at least one of them must be the square root of 2.

It is possible to have an infinite subset of an infinite set!

And if anyone says, at this point, "but let's hypothesize that it isn't a fallacious argument," my hypothetical dagger will reach out from the page and hypothetically stab them.

Thank you.

Dang. You stole my thunder before I could even weald it.

:: sadly sets his witty remark back into his pack ::

[macronencer]

Dang. You stole my thunder before I could even weald it.

:: sadly sets his witty remark back into his pack ::

Sorry. I know exactly how that feels

[Rocco]

I just suddenly thought of something.

Logically, there are an infinite number of hypothetical situations. In this infinity, there has to be one that has a device allowing the people in the situation to break out - in fact there has to be an infinite number. But there doesn't seem to be anyone breaking through. So there are not an infinite number of hypothetical situations. How can this be true?

And thinking about the above, are we just lots of people in a hypothetical situation?

I like this logic.

But unlike dealing with nature and science, hypothetical situations arise (or rather don't arise, because this is all made up in the first place) when a conscious mind considers it. It can't be assumed that any mind anywhere along your chain of hypothetical situations will ever decide to create another. And so there isn't necessarily an infinite number of hypothetical situations, just an infinite number of possible hypothetical situations.

I probably don't need to point this out, but this whole "infinite in number implies unlimited in variety" nonsense is fallacious in the extreme.

Were it true, one could use it to prove that, since the positive integers are infinite, at least one of them must be the square root of 2.

It is possible to have an infinite subset of an infinite set!

And if anyone says, at this point, "but let's hypothesize that it isn't a fallacious argument," my hypothetical dagger will reach out from the page and hypothetically stab them.

Thank you.

Infinity is a hypothetical consideration in itself, just like the square root of 2. Human minds aren't capable of really comprehending either. But yeah, just cause there's no such thing as a biggest number, there's not necessarily not such a thing as a nonexistent number. Or something.[/quote]

[macronencer]

Infinity is a hypothetical consideration in itself, just like the square root of 2. Human minds aren't capable of really comprehending either. But yeah, just cause there's no such thing as a biggest number, there's not necessarily not such a thing as a nonexistent number. Or something.

I see where you're coming from. However, I feel that humans DO comprehend infinity. Just because we can't imagine each item in an infinite set individually, doesn't mean we can't use "keep adding another and never stop" as a mental shorthand that encompasses the idea. I think it would be more accurate to say that we can't visualize infinity.

You might say that the shorthand I describe above is only part of the story, and that infinity is more than that. But then, one could also argue that a lot of our other knowledge doesn't count as "comprehension" either - for example, imagine a chair (without looking at a real one), and you bring to mind a highly stylized chair, probably without a fullly detailed grain pattern on every leg, woodworm, dust, fluff on the cushion, a jam smear left by a kid - all of the things that real chairs sometimes have. However, that doesn't make our mental model of a chair useless: far from it - all that detail would just get in the way. In the same way, the ability to actually visualize infinity, if we had it, would not be that useful to us. Far better to abbreviate the concept and put it to use in maths, in a more manageable form.

[joeythehobo]

I see where you're coming from. However, I feel that humans DO comprehend infinity. Just because we can't imagine each item in an infinite set individually, doesn't mean we can't use "keep adding another and never stop" as a mental shorthand that encompasses the idea. I think it would be more accurate to say that we can't visualize infinity.

You might say that the shorthand I describe above is only part of the story, and that infinity is more than that. But then, one could also argue that a lot of our other knowledge doesn't count as "comprehension" either - for example, imagine a chair (without looking at a real one), and you bring to mind a highly stylized chair, probably without a fully detailed grain pattern on every leg, woodworm, dust, fluff on the cushion, a jam smear left by a kid - all of the things that real chairs sometimes have. However, that doesn't make our mental model of a chair useless: far from it - all that detail would just get in the way. In the same way, the ability to actually visualize infinity, if we had it, would not be that useful to us. Far better to abbreviate the concept and put it to use in maths, in a more manageable form.

Reminds me of Plato's theory on a metaphysical "Idea" world. Where all the perfect copies of our objects and things lie. Then, only copies are put here; slightly different, but always varying copies. Like you said, we don't imagine all the details. But, then again, it's not the details that we need, just the idea which allows us to comprehend all chairs. If we really did embed the idea of that stain as you mentioned, then any chair without those attributes would seem foreign or possibly incomprehensible.

[Castaway]

Wait, are you talking about Plato's theory of an alternate "world" where everyone is how they see themselves? Because that would be very finite.

[macronencer]

I don't like Plato's "ideals", because he thought that they literally existed (in the "noumenal" world). I think that's crazy! If he'd just said that he was using them as abstract metaphors to help us think, then I could respect him.

I think we're drifting off topic a little!

[Kin]

Suppose you were unaware of the end of the bubble. Suppose as you lunged outwards you traded world, as the other hypothetical lunged into yours. And in reality, the world you live in is changing consistently but is unnoticeable in its doing. You would feel a little stupid, but go on, when you really didn't feel you went anywhere... [/oneofmyfears]

[mootinator]

If we really did embed the idea of that stain as you mentioned, then any chair without those attributes would seem foreign or possibly incomprehensible.

Which is why the concept of a robot eye is so difficult to implement. Humans have the natural ability to make these abstractions. We know something is a chair intuitively, so we sit on it. But how do we tell a machine what a chair is, or even fully understand 3d space enough to identify a chair from any angle, given a constant stream of details (millions of pixels).

[GGLucas]

On the infinite thing, I think you'll need to distinguish between an infinite string of things that are following a pattern, and an infinite amount of things following a chance.

The positive integers follow a pattern, so that might explain why the square root of 2 isn't in there, but look at is in this way:

If the chance of something happening is 1/2, then in 3 scenarios, the chance of it not happening will be (1/2)*(1/2)*(1/2) = 1/8, in an infinite amount of scenarios, the chance would be (1/2)^infinite, which we can accept as being 0 (just like (1/2)+(1/4)+(1/8 )+(1/16)...ad infinitum...is accepted as 1)

Of course, if the chance is 0 in the first place, then it won't be possible in any of the situations, but we can only say something is impossible by looking at the set assumptions that we have, and those can change too.

Hence, if something is a chance (and, mostly, everything is), we can say that in an infinite amount of scenarios, every possible situation will happen.

[macronencer]

On the infinite thing, I think you'll need to distinguish between an infinite string of things that are following a pattern, and an infinite amount of things following a chance.

The positive integers follow a pattern, so that might explain why the square root of 2 isn't in there, but look at is in this way:

If the chance of something happening is 1/2, then in 3 scenarios, the chance of it not happening will be (1/2)*(1/2)*(1/2) = 1/8, in an infinite amount of scenarios, the chance would be (1/2)^infinite, which we can accept as being 0 (just like (1/2)+(1/4)+(1/8 )+(1/16)...ad infinitum...is accepted as 1)

Of course, if the chance is 0 in the first place, then it won't be possible in any of the situations, but we can only say something is impossible by looking at the set assumptions that we have, and those can change too.

Hence, if something is a chance (and, mostly, everything is), we can say that in an infinite amount of scenarios, every possible situation will happen.

I have a feeling that ultimately this is going to come down to your gut reaction. Mine is that in an inifinite number of universes, it is NOT the case that everything imaginable happens. Perhaps I'll have difficulty proving it, but I nevertheless think it's true.

To give a possible example that might help explain what I mean: If evolution were to continue ad infinitum on this planet (assume for a moment that the Earth and Sun last for ever and don't change significantly). Would any animals evolve wheels? How about the ability to zap each other with bio lasers? I can dream up quite a few of these - attributes that sound whacky, but are just about believable: and yet, it's quite possible that the way evolution works means that some of them will simply never happen, no matter how long it takes.

Isn't it possible that the laws of physics are like that, too? That there are certain things that we might feel are feasible, but, due to some impenetrably complex phenomenon in physics, of which we are unaware, simply cannot happen, even in an infinite number of universes?

And the same thing applies to hypotheticals...


Or, here's another example. How many times does the letter "G" appear in the decimal expansion of pi? None at all, of course. But if you didn't know what you were looking at, and thought that both letters and numbers could appear, you might say "as this is an infinite, non-repeating sequence, there must be a G sooner or later". Wrong! You missed the fact that G simply cannot be expressed on that substrate...

I'd better stop now. It's late, and I've just played a gig with my band so I'm a bit manic. Can you tell?

[cmacis]

This has quickly reduced to the problem of the infinite number of monkeys on typewriters. Unless it is impossible, they will write absolutely everything that is true, everything that is false, every piece of literature. However, it will be hidden in a lot of noise.

Consider a roulette wheel. Instead of 0 to 49, let it be labelled " ", " a",...."zzzzzzzzzzzzzzz" up to a few megabytes of characters. So every character string of several megs of length is on the roulette wheel. I'll be betting on the string "The quick brown fox....". What are my odds of winning? Assuming that I bet until I win then, for some n in the naturals, my odds of winning at the first time are p, and losing q=1-p. For the second time pq, then pqq etc. The limit as n goes to infinity of p*(1-p)^n, where p,q are reals between 0 and 1 is clearly 1.

That's one reason I want to live in an infinite universe. It really screws up probability theory.

Lemma: any event that has happened/is happening has a non-zero probability.
Proof: zero probability events are impossible. No impossible event can happen, as that is a contradiction.

If the universe is infinite in space, then anything that has happened is happening somewhere in the universe, if probability theory holds. Furthermore, any event that could have happened (Hitler winning WWI single-handedly, the xkcd fora being purple, etc) is happening somewhere.

If the universe is infinite in time, then all this will happen again, with every possible variation played out.

[yy2bggggs]

Lemma: any event that has happened/is happening has a non-zero probability.
Proof: zero probability events are impossible. No impossible event can happen, as that is a contradiction.

Bah! Take that roulette wheel again. Now, label the points from [0,1) using the reals (I know, this requires very tiny molecules, which are expensive). When it stops it lands on a point. The probability that it will land from [0, 0.5) is 0.5. The probability it will land from [0, x), 0<=x<1, is x. In general, the probability that it lands in a particular range is equal to the total length of that range.

The length of a point is 0, so the probability that it will land on a particular point is 0. But it's still possible. It's impossible, however, for it to land on 1, or 2.

So, it gets worse than that. You have events with 0 probability that are possible, and events with 0 probability that are impossible.

[OneLess]

What if my hypothetic self did have a device that could break out of hypothetical situations and he handed it to me after he used it?

What would be revealed when I used it?

That God is actually just a really old angel and hell is a dimension where dead people from all the other dimensions are sent

[Lothar]

Bah! Take that roulette wheel again. Now, label the points from [0,1) using the reals...

I think this quote:

That's one reason I want to live in an infinite universe. It really screws up probability theory.

implies his zero probability lemma assumes a finite number of possible states. In that case, any event is possible only if it has non-zero probability.

---

Anyway, I put forward that any hypothetical situation could happen hypothetically.

[macronencer]

If the universe is infinite in space, then anything that has happened is happening somewhere in the universe, if probability theory holds. Furthermore, any event that could have happened (Hitler winning WWI single-handedly, the xkcd fora being purple, etc) is happening somewhere.

If the universe is infinite in time, then all this will happen again, with every possible variation played out.

NO! You can't use probability like that. You are elevating it to the status of a physical law, when in fact it is more of an abstract tool for making predictions. Please re-read my post above. I'm saying that just because something SEEMS to have a non-zero probability doesn't make it possible. My statement was really about the impossibility of determining which events are possible

To use your example: what if the typewriters the monkeys are using have a design fault that means that you can never type a 't' after an 'i'? Many English words would effectively be prohibited, and almost no recognizable books would appear in their entirety - yet, the letters would still look random at first glance, and we might be totally ignorant of the design flaw, so we'd be sitting around literally for ever, waiting for A Midsummer Night's Dream.

Anyway, I put forward that any hypothetical situation could happen hypothetically.

I think I can agree with that!

[warriorness]

This comic inspired me to go seek out a webcomic I used to read seven years ago (one that had no fourth wall from the beginning). Only a few strips in, a character does exactly the opposite as what happens in this xkcd, and is never seen again.

The last part of the cartoon reminded me of the Subtle Knife. What if that were real? Kick-ass...

Spoilers...

But would you really want those shadows running around everywhere?

Well that's just in that one world!
Screw them

Also, that ending is sad :/

All the specters were only in Citagazze because they invented the subtle knife and they used it the most. You'd get just as many specters in your world if you used as subtle a knife as often.

God, I love that series. Must've read it six times at least; can't wait until the movie (from the trailers I think it'll do the series justice).

[cmacis]

Wow, the eye is pacman

[bbctol]

Yes! I love 1/0! That is my favorite comic strip of all time! (And yes, it is better than xkcd. Sorry!)

[warriorness]

Yes! I love 1/0! That is my favorite comic strip of all time! (And yes, it is better than xkcd. Sorry!)

I used to post on a forum with Tailsteak (the author) (according to Wikipedia, he's married now o_O). For some reason I quit reading it after he'd announced he was ending it soon but before he ended it. Now I have to read through the whole archives again because I've forgotten it all.

[Rocco]

If the universe is infinite in space, then anything that has happened is happening somewhere in the universe, if probability theory holds. Furthermore, any event that could have happened (Hitler winning WWI single-handedly, the xkcd fora being purple, etc) is happening somewhere.

If the universe is infinite in time, then all this will happen again, with every possible variation played out.

NO! You can't use probability like that. You are elevating it to the status of a physical law, when in fact it is more of an abstract tool for making predictions. Please re-read my post above. I'm saying that just because something SEEMS to have a non-zero probability doesn't make it possible. My statement was really about the impossibility of determining which events are possible

To use your example: what if the typewriters the monkeys are using have a design fault that means that you can never type a 't' after an 'i'? Many English words would effectively be prohibited, and almost no recognizable books would appear in their entirety - yet, the letters would still look random at first glance, and we might be totally ignorant of the design flaw, so we'd be sitting around literally for ever, waiting for A Midsummer Night's Dream.

Anyway, I put forward that any hypothetical situation could happen hypothetically.

I think I can agree with that!

Also, Einstein himself said: "It used to be thought that if all things disappeared from the world, space and time would be left. According to relativity theory, however, space and time would disappear along with the things."

[Keand64]

This comic reminds me of a conversation I had with a friend one day:

Aaron: You know pokemon stands for poket monsters, so pokecenter is a poket center, pokemart is a poket mart, etc.?

Me: hmm...Hyopomon: Hypothetical Monsters. Its just like pokem, except hypothetical: What if I sent out charizard?

Aaron: Hypothetically, what would happen if I chose pikachu, and used thunderbolt?

And so on and so forth.

[Ggrogg]

There's an incredibally interesting book called "Meanwhile: Pick any path" which is a graphic novel that starts out with the main character, Jimmy, deciding whether to order chocolate ice cream or vanilla ice cream from an ice cream store. The story is a very interesting Choose Your Own Adventure style story and depending on which ice cream you pick one of two things happens. If you pick chocolate Jimmy goes home, his dad asks how his day went, Jimmy says he had some delicious chocolate ice cream, and that's the end of the story. But... if you pick the other ice cream Jimmy gets an upset stomach and stops at house of a (mad?) scientist to use his restroom and the scientist lets Jimmy try out one of his three new inventions: a time travel machine, a machine that allows you to switch memories with someone else, or his Killitron 2000 untested doomsday device. The story goes from there and technically has 3,856 different choices you can make. The story seems simple but starts to delve into quantum mechanics, physics, and all sorts of related things. It is entitled Meanwhile because at one of the possible points in the story a character explains to Jimmy about the concept of parallel universes and that while Jimmy is here talking to him, Meanwhile, he is somewhere else doing something else.

What does this have to do with this comic? Well, it made me think of the book with it's beginnings about ice cream and then hypothetical situations. That's all