1/0

Truly strange webcomic by Tailsteak, with a new strip almost daily.

It features a strange cast of characters such as Junior (an eye with teeth and an attitude), Ghanny (a ghost molecule), Marcus (a living molecule with the fourth wall enabled), MockTailsteak (a Golem created by Marcus), Zadok (another Golem made of straw), Terra (a lesbian earthworm and only female character so far).

What makes this cartoon so funny, is that most characters have their fourth wall disabled, i.e. know that they are comic strip characters, have discussions with their creator, and recently started to debate about the nature of their universe in general. That, and an admitted/proclaimed lack of talent and ingenuity of the creator (for example he creates a character out of another characters rib (the old Eve routine) that ends up looking like a talking rib with eyes and is thus named Ribby the Rib) makes up a great deal of the humor of this strip, which I recommend for you to read. Be forewarned though, this thing is huge, it has lasted for more than 2 years from the the beginning to the end on an almost daily schedule.

The strip has recently ended, but it can still be found online under this address:

http://oneoverzero.keenspace.com/

Presumably, the characters live forth in their new bodies and different new lives.

1/0 is a now completed webcomic which no longer updates. It ran for a thousand strips between the years 2000 and 2003. From the author:

"1/0" is a paradox; in a way that "0/1" is not. Nothing can be divided by zero. If one approaches the formula from the positive side, it would appear that the answer is an infinite positive value. If one approaches the formula from the negative side, the opposite is true. Thus, anything divided by zero is simultaneously positive and negative infinity. "One over Zero" is a paradox in another way too, in a way that transcends mere arithmetic. One is something, and Zero is nothing. The fact that the universe holds something over nothing, that it prefers to exist, rather than not exist, is fundamentally absurd. No being can ever come to deserve its own birth. 1/0 is a cry out against mere logic and efficiency. Stuff exists. All existence, all truth, cannot be ultimately justified: it can only be described, explained, and enjoyed.

1/0 is illogical. 1/0 is irrational. 1/0 is impossible. 1/0 is transcendentally unfair.

1/0 is true. Deal with it.

You can find it at http://oneoverzero.keenspace.com, or at the mirror with better strip navigation http://www.undefined.net/1/0/

While it apparently started out with the idea of being a humor strip, it... well, in my humble opinion, failed miserably at this. As humor goes, I found a chuckle or two at times, but I find there are far better places to get those. Where the humor fails, however, philosophy succeeds. The author/artist of the strip, Mason Williams^*, going by the name "Tailsteak^**" gets to play God, beginning with a "Let there be Light" sequence in the very first strip. The next couple dozen strips start to build a world with certain rules, though it's not described as such at the time. While trying (and perhaps failing) to be funny for eighty odd strips, he builds a setting he can really toy with for the next nine-hundred plus.

Part of the genius of this work is that in his strip, there is no natural 4th wall. All the characters from the start can communicate freely with the author. But later, certain characters get a personal 4th wall installed so that they can no longer have any knowledge of the outside world. The interactions between the "4th walled" and "non-4th walled" characters are fascinating, especially as certain characters attempt to "prove" the existence of Tailsteak... with pitiful success.

While some characters are philosophizing about their own free wills in an analogous way that we ourselves sometimes do, others are trying to discover the laws of physics in this world. Sound effects are demonstrated in a way that only a flatlander could truly appreciate, "horizonite" is mined from... well, the horizon line, and oil is manufactured from grass. And then they have to deal with their own creations, as Tailsteak allows them to make golem children for themselves. But the true driving force comes about when the characters are informed, well in advance, of the self-imposed thousand strip limit. A veritable Armageddon of miniscule proportions.

While it starts out quite slow, I would highly recommend slogging through it in order to get to the really good stuff. It's quite worth it, and reading it all at once is just as interesting as only getting it a day at a time in a tiny trickle. The artwork improves from beginning to end (and is even a plot point, as you might well imagine) and when it finally ends, it makes some very interesting commentary about our own selves.

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Some notable strips:

187 - 4th wall installed

435 - Something of an explanation on the tone and method of the strip

454 - A thank you to my creator, but I'm still mad at you

456-464 - Rules of 1/0 physics

498 - Testing Tailsteak at his word

523 - On false religions

599 - Tailsteak explains his first few strips, apologizes to the characters

619 - Revelations

707 - Rejecting religion in case it tells you not to do something you want to do.

997 - There is no non-creepy way to exit a plane of reality

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* I assume this is his real name. The other alternative is that some other guy wrote and drew it, and then for whatever strange bizarre reason gave the copyright to this Mason person. He never mentions his real name in direct relation to Tailsteak, but I don't suppose that's so particularly odd.

** Tailsteak has apparently registered with E2. I'm told by another noder that at some point he lost his password (and presumably changed his email address) and can no longer log in. Confirmed by JD, who has a picture of the man at UPDATE.

Also confirmed is that his name IS Mason Williams. There goes that other theory and the potential for conspiracy. Foo.

Browse up the internet and you’ll find scores of students wondering what, if anything is the result of dividing 1 over 0. There’s a second, less numerous but still large group of people who think they can “solve” the matter. If any of them posted here on E2 the only possible answer to them would start with the words “Your radical ideas about defining new math…” or something similar.

So let’s tackle the question head on. If lots of things in mathematics are conjured out of thin air (like that pesky thing i whose square is -1) why is it that mathematicians don’t “invent” something that settles the value of 1/0 once and for all?

Useful tip for anyone who deals with mathematics: any time you wish to extend a definition—or explore an old one—see if it “plays” nicely with the old ones. This usually leads to a refinement of your new radical idea.

Let’s see an example. Suppose that I define 1/0 as a number that we will call H. For now we don’t care what it is exactly, but I’ve defined it as so.

Victory! What next?

Well, that number will only be useful after it’s put to work, and to do that we need to see how it behaves. And for that we need a small interlude.

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Interlude: Long ago, people defined the multiplication as an operation, that is, an “action” that acts upon two things. It has a few rules:¹

1. If I take two things out of the set S and multiply them together, the result should also be an element of S
2. The order in which I multiply two things shouldn’t matter.
3. There should be one thing (called the identity) that makes the multiplication useless. In other words, this “identity” when multiplied with “something else” will always result in “something else”
4. If I have a “thing 1” there should be a “thing 2” so that when I multiply them, I get the “identity” as a result.
5. The above pairs of “things that multiplied together give the identity” should be unique.

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That might seem like kids play, right? Some of you might already see that the above rules are how multiplication works, that my “identity” is the number 1 and the “things” are regular old numbers.² Why is this important?

Let’s go back to my number H. How does it behave?

If 1/0 = H it follows that 0 × H = 1 right? So far so good… except this multiplication should work with the above rules. We know that anything multiplied by 0 gives 0; but this H multiplied by 0 gives 1. How?

“Andy, what if H = ∞?” you might ask. That doesn’t work, because the funny squiggle ∞ is not a number. That merits another essay, but let’s leave it there.

If that still doesn’t convince you, let’s see this: how about 2/0? Well, it’s the same as 2 × 1/0 = 2 × H. With a bit of algebra, we see that if 2/0 = 2H it follows that 0 × 2H = 2 right? But we have the same problem: we are multiplying something by 0 and getting a result that is not 0. How? Moreover, given our multiplication rules, we have 0 × 2H = (0 × 2)H=0H.

At this point, some might be tempted to suggest backpedaling and rewriting the multiplication rules. Fine, we can do that, it’s math. We can add clauses and sub-clauses, and special cases… But the more we do that, the more we have to check what else are those rewrites doing.

This is precisely the problem with retconning and traveling to the past: the more you go back to change things, the more things change in the present. In media, this ends up with a lot of weird questions. In math, you end up with useless definitions. A rule that has more exceptions than applications is a lousy rule.

And that’s the final answer. Mathematicians don’t “just invent” a new number that satisfies 1/0 because it tends to screw up lots of things, it doesn’t “play nicely” with existing concepts and as such ends up being a nuisance. Contrast this with complex numbers—the ones with a real and imaginary part—turns out that they do obey many preexisting properties: they can be added and multiplied very much like 2-vectors.

If you want to try it for yourself, write a convincing argument of why 0! = 1. Look for definitions and examples of the factorial process for help.³

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🜞—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️—⚔️

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1. Mathematicians, please understand that this is a simplification for educational purposes. I know I’m skipping over a lot and I’m leaving some properties of multiplication over the reals out for ease of use.

2. Real numbers in this case.

3. For instance, remember that n! = n × (n − 1)!