Attempting the Impossible: Describing Comics with Math

So I've been working on this idea lately — that sequential art, in general, follows several conventions that one finds throughout all instances of sequential art. That, over the years, something of a language has evolved, and that it has its own unique semantics and "grammar". This idea of mine evolved with time into a conception that one could describe the inner workings of sequential art entirely through formal language.

Thus, I present to you, for your edification and enjoyment: Artis Sequentis Principia Mathematica. An attempt to deduce all known truths about comics from first principles using a set of axioms.

Be aware that it's by no means a finished work — it's still in progress, hence the blog format, and it'll be revised as I work on the concepts over time.

Now, I'm no mathematician, my training is in climatology, but I have a lot of interest in math. The genesis of this work comes from a formal logic class I'm taking, which introduced me to Wittgenstein's truth tables. I was hooked, and looked beyond the class material, further into mathematical logic. So, for the purpose of this work, I'm teaching myself mathematical logic with a few books I checked out from the library. It's going to be interesting.

However, I would greatly appreciate any input or feedback from any math majors or mathematicians, or basically anyone who has opinions about the structure or nature of comics.

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Wow, it's like that thing you did before, but somehow more frightening.

So far I've read the introduction (I'm still going). I have two questions. Did you modify that from the Principia Mathematica itself? And two: Are you sure you mean empiricism? Deductive logic isn't based on empirical data.

edited 29th Nov '10 10:15:51 PM by Tzetze

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At your service, [AOD]. Reading through what you have so far right now.

edited 29th Nov '10 10:17:23 PM by Ponicalica

the future we had hoped for

Okay, reading some more. (I should mention that I have very little formal training but a strong interest)

1.1.5 seems unnecessary; if you say that a set (well it's ordered, so a tuple, I think?) is finite, there's no point in prohibiting elements past the last. You can't hypothesize an element of subscript n > m if e_m is the last element of a tuple, in the same way you can't postulate a fourth coordinate in a system you've explicitly said has three dimensions.

1.1.6 relies on two undefined terms, «element» and «sequentially». Hopefully those come later...

edited 29th Nov '10 10:24:33 PM by Tzetze

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I'm taking Discrete Math, and I can say it's downright scary how much this makes sense.

edited 29th Nov '10 10:26:01 PM by ColorPrinter

Yeah, it's a little disorganized, haha...

Tze Tze: I see your point. I've already explicitly said that the system ends at m elements, so there's no point in saying an "after". What I really meant, though, was to imagine that an algorithm going through the sequence, upon reaching the end, would return "false" if it was asked to look further.

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If the system ends at m elements, it's usually not even allowed to reference the m+1th element. Occasionally you will want to have a formula that references something like that—if you're adding things up, for example, and then you would explicitly define such a reference as zero in the formula itself, or mention in a note after the formula to exclude certain terms.

This is just the intersection P_n ∩ P_n+1, no?

I think I might write a detailed analysis/critique of what you have so far tomorrow, though tonight I'm too sleepy. Also, I hate not having TeX on the fora when I'm trying to do mathy stuff.

edited 29th Nov '10 10:35:34 PM by Ponicalica

the future we had hoped for

That's so. In fact I think that section — 1.3 was it?— is going to be obsolete with the new section I've started working on— 1.5. I'll develop it further.

A detailed critique by someone who's not literally learning this stuff with mathematical logic textbook in one hand, the library's copy of Principia Mathematica in the other, and frantically typing out words using his penis, would be really appreciated. Thanks a lot Ponicalica.

But hey, I've always thought the best way to learn a thing is to dive right in and do it.

edited 29th Nov '10 10:43:45 PM by [AOD]

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Yeah, on that note, does Blogger accept HTML entities? If so you could use → or &subseq; instead of the technically inaccurate > for material implication.

I'm not sure that I understand 1.1.6, given the next page. Is it that e_t→e_t+1 for t < m?

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Yeah!

I should probably write it like that, huh?

And, yeah I do think Blogger accepts that. I was only using > as a convenient shorthand until I could figure out how to do the horseshoe-shaped symbol for material implication.

Though is that used anymore in logic? Have they moved over to arrows since the horseshoe symbol kinda resembles "Superset"?

edited 29th Nov '10 10:46:59 PM by [AOD]

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Actually you probably should ignore 1.3 — I was mulling it over one day and I think the way I've defined "Panel" makes it incredibly vulnerable to Russell's Paradox. This will be dealt with when I finish the functional definition in 1.5.

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Hmm... I'm not following the Uniqueness Theorem. Where is the support for the statement that an element in panel N is not in panel N-1 or N+1?

Do you highlight everything looking for secret messages?

It's actually exactly the same symbol. Thing is that mathematicians use an arrow while logicians use ⊃, is how I think it goes.

Which is &sup;, not &subseq;. Doy

edited 29th Nov '10 11:02:07 PM by Tzetze

[1] This facsimile operated in part by synAC.

128:

With 1.3 I tried to prove it through the definition of "Panel" as "that set of all elements that do not belong to any previous or following panel". So to prove that, I said "Let's imagine a panel that was the union of two panels". So all elements in that one would have the property of not belonging to either, nor the union, so they'd belong nowhere, and therefore elements would have to belong to one or the other.

I don't really like defining "Panel" that arbitrarily though. I've come up with a new definition as "that which maps a segment of elements from the ordered list e1, e2, ..., et to one out of a set of boundaries G, selecting how many elements per G with an index k".

So basically, it'd take some number of elements, specified by the list k, and put them into separate G's. If, for the such and suchth G, k={...,...,...,6,...}, it'd take a sequence 6 elements long and put it in G. It's gonna be freaking complicated to write this down, so in 1.5 I'm gonna define the function explicitly (this is why it's taking so long to actually write this) and then refer to a "Panel Operator" from then on, defined by Pn{E,G,k}.

If anyone can help me simplify all this notation and getting all my indices straight, I'd really appreciate it, because this is what's really killing me at the moment.

I don't know how to prove that elements mapped this way would be absolutely part of the G they're supposed to be in.

Tzetze:

No, but I crib liberally from Russell's theory of types for inspiration for "Panel" vs "element". So a Panel is quite a distinct thing from an element, so you can't have something like "panel of panels that do not belong to themselves". And yeah, hrm, I guess I kind of meant that comics have these rules, which we notice (empirically) and are trying to deduce (logically) useful theorems about comics in general.

And, yeah, I think I'll be using the arrow since I also use the horseshoe for "subset".

edited 29th Nov '10 11:11:38 PM by [AOD]

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Hm. Your definition in 1.1.4 defines a panel as a subset of elements. Which implies nothing about order.

Random empirical case: Bottom two panels here.◊

Do you highlight everything looking for secret messages?

Oh, I see!

Well then how would I show that something must belong to one and only one panel?

Also, with your case, I know it's unintuitive, but the fact that there's a gutter there would mean that it divides the thing into two separate panels. Hence the dude's hand is actually part of the last panel, while his arm is part of the penultimate panel. They're, in a sense, parts of separate universes!

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I think this new definition will work.

Also: Yup! =) Except ... bigger. I realized that the thing I did before was building on a foundation that didn't exist... yet. I'd have to define everything about it, brick by brick, so I had to go back and define precisely what panels, elements, and things were, and how they were related to each other. That's what I'm doing now. The goal is, hopefully, to finish laying the bedrock so I can get to that thing before, in part II.

Also: Thanks to Tzetze for recognizing that the set of elements is a tuple. I've been labeling it wrong this whole time!! Man.

edited 30th Nov '10 7:35:57 AM by [AOD]

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An artist friend of mine recently commented that in my system, an empty panel would have no meaning. However, artistically speaking, there is value in negative space.

Basically, that my system doesn't really account for "Zero".

Are there any suggestions or ideas?

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Location in a frame of an element is important, in general.

Do you highlight everything looking for secret messages?