Using set theory to answer "does marriage to MJ represent a smaller story-space?"

[MrPalen]

WARNING: If you don't like extended discussion of logical theory, you will not enjoy this post at all.

An argument that often comes up is whether or not Pete being married to MJ creates more limitations on the kinds of things that can be done in the comic than Pete not being married to MJ does. I'm going to use set theory to try and answer this question.

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Before I continue there are a couple things I want to point out at the outset:
- Limitations do not logically imply lower quality. The question is not "are stories worse if Pete and MJ are married than if they aren't"; I'm making no comment about that one way or the other. Even if marriage to MJ is more limiting, that doesn't mean a writer couldn't come up with the best story ever from within that space. Or that Marvel couldn't put out an absolutely terrible comic from within the space of "not married to MJ".
- This is not about One More Day; I'm neither defending OMD nor am I condemning it in this thread. This is not intended to justify nor to discredit anything Marvel or Joe Quesada may have done or said, nor does it have anything to do with their motivations. It is simply an analysis of a question on its own merits.
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I think most people will have probably seen some set theory in high school in a math class, but possibly not, and probably not in-depth. Anyway, it's very simple:

- a set is a conceptual "container", it holds elements.
- for example, the set A = {1, 2, 3, 4, 5} is a set, and its elements are the integers 1 through 5.
- another set could be B = {1, 4}. This is a subset of A, because all of the elements of B are also found in A.
- you can have infinite sets. For example, the set of all positive integers I = {1, 2, 3, 4, ... }
- Sets A and B are both subsets of I.
- Now here's a really interesting point, and one that is key to this discussion: Infinity comes in different sizes!
- To whit: We already have set I, which is the set of all positive integers. Let E be the set of all positive even integers; {2, 4, 6, 8, 10, 12, ... }. Note that E is a subset of I, that is, every element within E is also in I. But, the reverse isn't true! Even though they are both infinite sets, I has all the things that are in E plus a bunch of other things. So while it's a bit weird to say that I (the set of all positive integers) has "more elements" than E (the set of all positive even integers) because they're both infinite sets... it does - all of the even numbers and all of the odd numbers. But since "more" is kind of weird, it's easier to say that it represents a larger space.

Okay, so that's set theory. But set theory is good for more than just numbers. It's also used in logic, with concepts in plain language. Like, you can have set F be the set of all fruit, and set A be the set of all apples, which is a subset of F.

Right. So enough with the numbers and the apples, let's get to Spider-Man.

- Let S be the set of all possible things that can be done in a Spider-Man comic. Let's agree that this is an infinite set. "Possible" means that Marvel would actually publish it (so Peter as a child-molester, or as an adulterer are not considered possible).
- Now, in every possible Spider-Man comic, he is either married to MJ or he isn't. So we can create two subsets of S.
- Let M be the set of all possible things that can be done in a Spider-Man comic if Spider-Man is married to MJ.
- Let N be the set of all possible things that can be done in a Spider-Man comic if Spider-Man is not married to MJ.
- Both M and N are subsets of S, and let's agree that they too are both infinite sets.
- The Union (combining all the elements into one set) of M and N equals S. (e.g. the union of {1, 2, 3} and {2, 3, 4} is {1, 2, 3, 4})
- Now, there are many things that can be done whether or not Pete and MJ are actually married. So M and N will overlap to some degree, that is to say, there will be many elements in M that are also in N. This overlap is called the Intersection of M and N. (the intersection of {1, 2, 3} and {2, 3, 4} is {2, 3}).
- Let's call this intersection R, which is the set of all possible things that can be done in a Spider-Man comic where it doesn't matter if Spider-Man is married to MJ or not.

I think using a diagram would be useful here. For the moment I will be completely agnostic about the relative sizes of M and N and the way they overlap.



- There are also the sections of M and N which are not part of their intersection, we'll call these M^ and N^. These are called the Complements of M and N with respect to R (e.g. the complement of {1, 2, 3} with respect to {2, 3} is {1}).
- M^ would be the set of all possible things that can be done in a Spider-Man comic only if Spider-Man is married to MJ. I.e., their marriage is specifically important or relevant in some way. I.e., things that couldn't be done with a marriageless committed long-term relationship.
- N^ would be the set of all possible things that can be done in a Spider-Man comic only if Spider-Man is not married to MJ. e.g., Pete and MJ are in a relationship but the fact that they aren't married is relevant or important in some way, or they aren't together at all.

Okay, so that's the definition of the Spider-Man story-space as it relates to the question of marriage. There is no possible Spider-Man story that is not an element of at least one of M^, M, R, N, or N^ since the union of these is S which has been defined as the set of all possible Spider-Man stories. I don't think any of this should be controversial to anyone.

This next part shouldn't be either, but it sets up the part that will be.

Now in the diagram, M and N are the exact same size. As are M^ and N^. But is that accurate? As we know, even infinite sets come in different sizes. What we want to know is if M (story-space of Pete married to MJ) is smaller than N (story-space of Pete not married to MJ), that is to say, "does marriage to MJ represent a smaller story-space than lack of marriage to MJ". In other words "does marriage to MJ impose more limitations than lack of marriage to MJ" (just as the set of vegetarian meals imposes the limitation that non-vegetarian meals cannot be elements of the set).

Well one thing we know is that there are stories involving Pete and MJ in a committed long-term relationship which work whether or not they are married. This is the area of the story-space is what he have called R. Since R is the intersection of M and N, it gives us no information about the relative sizes of M and N. R takes up the exact same amount of space in both. So, we can eliminate it from our consideration of the question of which of M and N is larger.

We are left to compare the remaining parts of M and N now that R has been removed, namely M^ and N^.



Continued...

[MrPalen]

And now is where the controversy is. How do we figure out whether N^ is larger than M^? Well we are reasoning human beings and we can think about the question reasonably.

A good place to start is to ask yourself "what can I think of that can only happen if Pete is not married to MJ?":

- he could be single, i.e. have no girlfriend or partner
- he could casually date a few different girls
- he could be involved in a love triangle with girl X and guy Y, where he wants girl X but she's torn between him and guy Y
- he could go on a date with Ms. Marvel
- he could be in a committed, long-term relationship with Ms. Marvel
- he could have a bad break-up with Ms. Marvel, complicating his relationship with other heroes
- he could ...
- etc., I could keep this up for some time.

After asking myself that question and beginning to generate a list, it seems clear to me that N^ is an infinite set.

Edit: There is also the set of things where Pete and MJ are together, but their not being married is important. e.g.

- Pete and MJ discussing whether or not they should get married
- Aunt May hassling them about it
- religious zealot characters getting on their cases for 'living in sin'
- running low on ideas here
- someone else proposing to MJ even though she and Pete are together
- legal issues (blagh)
- Felicia Hardy trying to convince Pete that since he isn't technically married, it'd be okay for them to have a romp

We'll call this set R^, things that can be done only if Pete and MJ are in a relationship but not married. It is a subset of N^.

Now I ask myself "what can I think of that can only happen if Pete and MJ are married?", and I come up with:

- the wedding
- a divorce (something Marvel isn't willing to do, so not actually part of the space as it's been defined)
- ...

And then I run out. Now there may be more than those two things, but it immediately strikes me that this is an interesting result. With N^, I could have kept on generating that list for a long time. With M^, I feel completely stuck after just two elements. Let me try again, and really force myself to think.

Well, I guess there are flashback sequences to aspects of the wedding that didn't appear in the comics:
- flashback to the wedding day, showing things we didn't see in the wedding issue
- flashback to Pete having an argument with a lawyer about whether he should get a prenup
- flashback to Pete and MJ discussing whether or not to get a prenup
- flashback to honeymoon stuff we didn't see before

Hmm, what else...
- people giving MJ a hard time about having hyphenated her last name because as a feminist she should have kept her name
- people giving MJ a hard time about having hyphenated her last name because as a wife she should have taken her husband's name
- people giving Peter a hard time for these same issues
- people giving Aunt May a hard time about these issues as they pertain to her nephew and his wife

So, okay, I can keep thinking of things after all, though I'm not sure how many more of those I could do. But there's a marked difference in the types of things I'm coming up with. For one thing they're mostly pretty terrible ideas for stories, though there could be some interesting things done with the wedding flashback idea perhaps. And anyway, as I've said, quality of story is not the same thing as size of story-space.

But in this case, I think it's clear that the story-space for M^ is actually really small. And I think it's so small that it does affect the number of quality stories that can come out of it. Because in order for something to be an element of the set M^, the marriage between Pete and MJ itself has to be important in some way. And I really think there are only a few interesting things to do with that. It may technically be an infinite set anyway, as maybe there are infinite variations on the things I've thought of along with a few other things I haven't thought of. But it would be an infinite set with a very small space. Kind of like the set of all negative integers divisible by a billion, which is much smaller than the set of all integers for example. And once a few of these types of stories had been published, like say some wedding flashback stories which might even be cool, I think after not too long Marvel would not want to do too many more.

So by this reasoning, it seems abundantly clear to me that N^ is a far larger space than M^ (if you disagree, then come up with a list like I have of things which are elements of M^, and/or give us some indication that M^it is at least as large a space as N^).

Which in turn implies that N is a larger space than M.

Which is another way of saying that marriage to MJ imposes more limitations than does the lack of said marriage.

And the final diagram, showing what I think the space actually looks like:

[GRANDPA]

very very interesting

[CyberHubbs]

I tried reading this. I really did.

But it was like staring at the Ark of the Covenant.

[Jim Thompson]

- Let S be the set of all possible things that can be done in a Spider-Man comic. Let's agree that this is an infinite set. "Possible" means that Marvel would actually publish it.

This would be the logical flaw in your premise, as it is impossible to know what Marvel might one day publish.

[Mister Mets]

This would be the logical flaw in your premise, as it is impossible to know what Marvel might one day publish.

We can still make educated guesses as to what's more likely to get published in the future.

And make more definitive hypotheses about the present/ near-future.

If a future EIC ten years from now may believe that divorce is a valid option, it's still worth considering that the current story-space wouldn't include that material.

[Alan2099]

See, way I look at it is like this.

There's stories you can tell with Spider-man.
There are stories you can tell with Mary Jane.
There are stories you can tell with them married.
There are stories you can tell with them as a couple.

Married, you can still tell your Spider-man stories, and you can still tell your MJ stories and your couple stories (give or take a few details here and there.)

Single, you can still tell your Spidey stories, and you can still tell your MJ stories.

However this leaves out the stories you can tell with Girl-X, or Girl-Y,Z, R, F, or whatever, which would be more or less the same amount of stories that could be told with Mary Jane ... per individual new character. AND you can still tell your Mary jane stories and your couple stories.

[Hertz]

Hey Jim, you forgot this part.

And the final diagram, showing what I think the space actually looks like:

Edit: whoops, forgot the smiley face.

[Jim Thompson]

We can still make educated guesses as to what's more likely to get published in the future.

And make more definitive hypotheses about the present/ near-future.

If a future EIC ten years from now may believe that divorce is a valid option, it's still worth considering that the current story-space wouldn't include that material.

Now you've moved into the fields of probability as opposed to straight algebra -- which is the different between the actual physical number of potential stories and the chances of such a story actually being published. I've no problem with people making arguments based on probabilities -- but when they represent a probability as a fact, I take some issue with it.

[Jim Thompson]

Hey Jim, you forgot this part.

No, I noticed it -- I actually think that was a good thing for him to do.

[Hertz]

Any way, back to being somewhat serious.

First off, I'd like your definition for this.

- he could be single, i.e. have no girlfriend or partner

Is this something where nothing of his romantic life is even mentioned or, is it something that's mentioned to one extent or another that he's got nothing going on in that department during one of the issues or, is it something else?

Secondly, this is fairly well put together. That being said, it still comes across as trying to present opinion as fact. The main problem I have here is that, you seem to be basing all this (N^ > M^) on what you can conceive of and nothing more than that.

For example: M.J. and Pete have a kid (only going to happen if they're married based on your definition of "possible")
M.J. gets a role in a movie where she has to do a love scene (tasteful or otherwise, also, different connotations if they're married)
Pete has to do something that could potentially sterilize him (again, different connotations/story if they're married)

Now for a bit of levity.

- he could go on a date with Ms. Marvel
- he could be in a committed, long-term relationship with Ms. Marvel
- he could have a bad break-up with Ms. Marvel, complicating his relationship with other heroes

Since she's "dead", these get blown right out of the water.

[RDMacQ]

I tried reading this. I really did.

But it was like staring at the Ark of the Covenant.

Y'know, I've always thought that looking at Rob Liefeld art for too long would have the same effect.

On a related note, is anyone really surprised that Rob Liefeld is involved with the Armageddon?

[RDMacQ]

I think this is all a little silly because there is really no way to determine "story space" since it is an intangible substance. The creative process can't be boiled down to a simple algebraic equation.

[MrPalen]

he could be single, i.e. have no girlfriend or partner

Is this something where nothing of his romantic life is even mentioned or, is it something that's mentioned to one extent or another that he's got nothing going on in that department during one of the issues or, is it something else?

It just means what I said. He doesn't have a girlfriend/wife/partner, and it this is shown or referenced in the story in some way. For example, he meets a girl and wonders whether or not he should ask her out. Or we see that he's lonely and he has a conversation with a shrink or a friend about how he doesn't know if he'll ever find the right girl. Etc.

Secondly, this is fairly well put together.

Thanks.

That being said, it still comes across as trying to present opinion as fact. The main problem I have here is that, you seem to be basing all this (N^ > M^) on what you can conceive of and nothing more than that.

The definitions of the sets of Spider-Man stories (S, M, N, R, M^ and N^) I am presenting as "fact", in the same way I would present "There is a set of all possible meals, and chicken dishes are a subset of it" as fact.

In the part about trying to figure out whether N^ is larger than M^, I present reasoned argument, and I invite reasoned counter-argument.

For example: M.J. and Pete have a kid (only going to happen if they're married based on your definition of "possible")
M.J. gets a role in a movie where she has to do a love scene (tasteful or otherwise, also, different connotations if they're married)
Pete has to do something that could potentially sterilize him (again, different connotations/story if they're married)

Except that it's clear that Marvel does not want to allow Peter to have children whether he's married or not, for reasons having to do with aging the character. So we don't even need to get into whether or not they'd allow it if he were unmarried.

Now for a bit of levity.

Since she's "dead", these get blown right out of the water.

Whaaaaaat! Actually, say no more. I haven't been keeping up with her solo series lately but I plan to at some point.

[stillanerd]

And now is where the controversy is. How do we figure out whether N^ is larger than M^? Well we are reasoning human beings and we can think about the question reasonably.

A good place to start is to ask yourself "what can I think of that can only happen if Pete is not in a committed long-term relationship with MJ?". When I ask myself this question, I come up with things like:

- he could be single, i.e. have no girlfriend or partner
- he could casually date a few different girls
- he could be involved in a love triangle with girl X and guy Y, where he wants girl X but she's torn between him and guy Y
- he could go on a date with Ms. Marvel
- he could be in a committed, long-term relationship with Ms. Marvel
- he could have a bad break-up with Ms. Marvel, complicating his relationship with other heroes
- he could ...
- etc., I could keep this up for some time.

After asking myself that question and beginning to generate a list, it seems clear to me that N^ is an infinite set.

Now I ask myself "what can I think of that can only happen if Pete and MJ are married?", and I come up with:

- the wedding
- a divorce (something Marvel isn't willing to do, so not actually part of the space as it's been defined)
- ...

And then I run out. Now there may be more than those two things, but it immediately strikes me that this is an interesting result. With N^, I could have kept on generating that list for a long time. With M^, I feel completely stuck after just two elements. Let me try again, and really force myself to think.

Well, I guess there are flashback sequences to aspects of the wedding that didn't appear in the comics:
- flashback to the wedding day, showing things we didn't see in the wedding issue
- flashback to Pete having an argument with a lawyer about whether he should get a prenup
- flashback to Pete and MJ discussing whether or not to get a prenup
- flashback to honeymoon stuff we didn't see before

Hmm, what else...
- people giving MJ a hard time about having hyphenated her last name because as a feminist she should have kept her name
- people giving MJ a hard time about having hyphenated her last name because as a wife she should have taken her husband's name
- people giving Peter a hard time for these same issues
- people giving Aunt May a hard time about these issues as they pertain to her nephew and his wife
- something to do with extreme religious fundamentalism and Pete and MJ "living in sin" (though I don't know how likely Marvel would be to publish something like that)

So, okay, I can keep thinking of things after all, though I'm not sure how many more of those I could do. But there's a marked difference in the types of things I'm coming up with. For one thing they're mostly pretty terrible ideas for stories, though there could be some interesting things done with the wedding flashback idea perhaps. And anyway, as I've said, quality of story is not the same thing as size of story-space.

But in this case, I think it's clear that the story-space for M^ is actually really small. And I think it's so small that it does affect the number of quality stories that can come out of it. Because in order for something to be an element of the set M^, the marriage between Pete and MJ itself has to be important in some way. And I really think there are only a few interesting things to do with that. It may technically be an infinite set anyway, as maybe there are infinite variations on the things I've thought of along with a few other things I haven't thought of. But it would be an infinite set with a very small space. Kind of like the set of all negative integers divisible by a billion, which is much smaller than the set of all integers for example. And once a few of these types of stories had been published, like say some wedding flashback stories which might even be cool, I think after not too long Marvel would not want to do too many more.

So by this reasoning, it seems abundantly clear to me that N^ is a far larger space than M^ (if you disagree, then come up with a list like I have of things which are elements of M^, and/or give us some indication that M^it is at least as large a space as N^).

Which in turn implies that N is a larger space than M.

Which is another way of saying that marriage to MJ imposes more limitations than does the lack of said marriage.

And the final diagram, showing what I think the space actually looks like:

All right, I know you and I got into an argument on this matter before when you postulated your theory on another thread and there were some misunderstandings what you were saying on my part. This time, I think you've put together a better presentation for your argument that is clear enough to understand.

However, your argument is still very, very flawed.

As you imply, there are certain things Spider-Man as a character shouldn't do, or at least not without a good enough reason provided in the story. Therefore there are certain kinds of stories that can't be told with Spider-Man because it would be contrary to who he is as a character. This I agree with. However, once you start breaking down into what stories you can tell with a married Spider-Man vs. what stories you can tell with a single Spider-Man within that context, that's where it collapses.

This is because, rather than rooted in mathematical certainty as your argument suggests, it's really based on the assumption that there are only a limited number of married Spider-Man stories--not because certain married stories would require Spider-Man to act out of character, but because you can't imagine any more beyond the confines of "wedding" and "divorce." And just because you can't imagine more than those two stories that "require Spider-Man to be married" doesn't mean somebody else can. As a result, rather than it being backed up by mathematical fact, it's really backed up by conjecture and opinion, which as a result, doesn't actually prove your argument as fact.

Now does this mean you could be right and that there are fewer stories you can tell with Spider-Man being married than you can if he's single? Perhaps. But I could just as easily say there could be fewer stories one can tell with Spider-Man as an adult than one can if he's still a teenager. Or I could say there could be fewer stories with Spider-Man fighting crime in New York City than there are if he's fighting crime while traveling the backroads of America, or backpacking in Europe, or traveling through time and space or whatever. And that's the point. I don't really know. I'm limited by my imagination and whatever skills as a writer I have to come up with those stories. And that's the point. Just because you can't imagine more stories with a married Spider-Man that are dependent upon him being married doesn't mean there are fewer of those stories.