1 = 0

[rwstyles]

I thought that those arms were going to start spinning.

I assume that under normal conditions, taking the correct key would cause the entire tower to rotate, and that the strain would break the braces that just broke, clearing the tower room, so to speak.

[Zwums]

Does this feel a little bit rushed? Maybe I'm just drunk. Oh poo

[Gamer_2k4]

Do I really need to point out that the "proof" of one equaling zero isn't a paradox at all, but just bad math?

[SamWiser]

In this case I think a paradox and bad math are the same thing. Math and logic have a lot in common.

[Liesmith]

The reason it's bad math is that it's logically inconsistent. By altering the universal constants, Psimax is altering the logic, which makes his "bad math" suddenly correct. Once that happens, *poof*.

[Belzera]

So, lets see this 'bad math' is being stopped dead by the power of love and a 'royalled messed up sword'? Man I thought Psions where extremely powerful. XD

[Your.Master]

The thing is, mathematics exists independently of universal constants. It's not physics. So changing universal constants can't make bad math correct. Though in principle with some imagination, it may be able to tear apart the space time continuum without proving 1 = 0.

Soooo I continue to take this 1=0 business as metaphorical / translation-convention.

[mertol]

Who said psimax is messing with maths? Why can't 1 and 0 represent something physical? Maths is just a concept to represent real stuff with.

[Ikul]

No, it really, really isn't.

Because '1' is a mathematically well-defined object: it is the neutral element for the second binary operation in an abelian group with a second binary operation that is associative and is distributive over the abelian group operation. '0' is the absorptive element of the second binary operation, and the neutral of the first. Wherein lies the problem: an element can't be the absorptive and the neutral element of a binary operation at the same time for any group with more than two members.
Proof: Call such an element which is both absorptive and neutral AN. Find a different element in the group in question, say KLJ. And call the binary operation 234. (Notations chose purposefully to demonstrate just how much a matter of personal choice notations are in mathematics.) In that case,
AN 234 KLJ, or 234(AN, KLJ), or 2AN3KLJ4, or however you'd like to write down 'the operation 234 used on the element AN and KLJ of the abelian group' would have to equal AN, because AN is the absorptive element, but it would also have to equal KLJ, because AN is the neutral element. This applies for every element of the Abelian group, thus is proven that every element in the Abelian group would have to equal our element AN.

Now, this is not a paradox - it just means that any abelian group wherein 1 and 0 are equal, will have only one element and that element is one. And zero. Because they're the same. If Psimax' machine were designed to alter reality in such a way that this applied to real numbers, that wouldn't result in the universe ceasing to having existed, it would just mean there would be a universe wherein every number is one, and also zero. It's difficult to imagine but nothing says it's impossible. A universe with quantum mechanics is practically impossible to imagine and yet here we are.


The thing with 'universal constants' and 1=0 is this: universal constants are just numbers you plug into the equations. But 1 = 0 is math, and the rule of thumb is that once you start using numbers you're not actually doing math.
Even the '1' and '0' in the above equations aren't really numbers in that they're not supposed to denote a magnitude or value - they're just shorthand for "neutral element for the second binary..." and so on.
You -could- redefine the /physical constant/ '1' as '23252', which would basically be a rescaling of everything in the universe with no real physical consequences. But the meaning of the '1' in mathematics wouldn't be changed one iota because the '1'in mathematics isn't a constant. Paradoxical though it may seem, it is not, in fact, a value. You could denote the same mathematical concept with the sign '0', you could denote it with the sign [, you could denote it with your own signature for all I care, you won't change the meaning. And if you try denote the mathematical concept currently usually denoted with '0' and the one usually denoted with '1' with the same sign, but that would just be sloppy notation.

[Dusk9]

► Show Spoiler

A wizard psion did it.

[Ikul]

Oh you're fundamentally right. I just wanted to remove some misconceptions readers may have had.

[apotato]

making 1= 0 wouldn't wreck our reality...

but a dice based reality would get royally messed up.

[JustRight]

Does this feel a little bit rushed? Maybe I'm just drunk. Oh poo

I don't recall Thunt ever making a grammatical error before. (missing 'he' in frame 6?)

[ForgetsOldName]

No, it really, really isn't.

Because '1' is a mathematically well-defined object: it is the neutral element for the second binary operation in an abelian group with a second binary operation that is associative and is distributive over the abelian group operation. '0' is the absorptive element of the second binary operation, and the neutral of the first. Wherein lies the problem: an element can't be the absorptive and the neutral element of a binary operation at the same time for any group with more than two members.
Proof: Call such an element which is both absorptive and neutral AN. Find a different element in the group in question, say KLJ. And call the binary operation 234. (Notations chose purposefully to demonstrate just how much a matter of personal choice notations are in mathematics.) In that case,
AN 234 KLJ, or 234(AN, KLJ), or 2AN3KLJ4, or however you'd like to write down 'the operation 234 used on the element AN and KLJ of the abelian group' would have to equal AN, because AN is the absorptive element, but it would also have to equal KLJ, because AN is the neutral element. This applies for every element of the Abelian group, thus is proven that every element in the Abelian group would have to equal our element AN.

Now, this is not a paradox - it just means that any abelian group wherein 1 and 0 are equal, will have only one element and that element is one. And zero. Because they're the same. If Psimax' machine were designed to alter reality in such a way that this applied to real numbers, that wouldn't result in the universe ceasing to having existed, it would just mean there would be a universe wherein every number is one, and also zero. It's difficult to imagine but nothing says it's impossible. A universe with quantum mechanics is practically impossible to imagine and yet here we are.


The thing with 'universal constants' and 1=0 is this: universal constants are just numbers you plug into the equations. But 1 = 0 is math, and the rule of thumb is that once you start using numbers you're not actually doing math.
Even the '1' and '0' in the above equations aren't really numbers in that they're not supposed to denote a magnitude or value - they're just shorthand for "neutral element for the second binary..." and so on.
You -could- redefine the /physical constant/ '1' as '23252', which would basically be a rescaling of everything in the universe with no real physical consequences. But the meaning of the '1' in mathematics wouldn't be changed one iota because the '1'in mathematics isn't a constant. Paradoxical though it may seem, it is not, in fact, a value. You could denote the same mathematical concept with the sign '0', you could denote it with the sign [, you could denote it with your own signature for all I care, you won't change the meaning. And if you try denote the mathematical concept currently usually denoted with '0' and the one usually denoted with '1' with the same sign, but that would just be sloppy notation.

This is all true, but I'd phrase it like this.

If 1 = 0 then
1 + 1 = 0 + 1 then
2 = 1 and
2 = 0

Continue like this for a while and you can see that everything = 0.

Here's another way of doing the same thing:

3 = 3
3 * 1 = 3 * 1
3 * 1 = 3 * 0
3 = 0

The universe where one equals zero is just the universe where there is only one thing. Alternatively we can talk about weird universes where 1 = 0 and 2 = 0 but we can't make the leaps to 0 = 2 (it's not symmetric, like saying "truth is beauty, but beauty is not truth") and/or 2 = 1 ("Good is evil and Khan is evil but Khan is not good"). Or there's a universe where addition doesn't behave as expected ("A drop of water added to the ocean adds nothing but a drop of water in the desert is everything") So all these are perfectly possible but they don't really result in a lot of interesting and useful mathematical descriptions of things lying around the house.

[Baeronvonbleat]

You know... conversely, 0 = 1... so once his proof takes effect, everything could just spawn from nothing.

He might not unmake existence, but create every existence.

*edit* Also, a drop of water in the ocean is just as useless as a drop of water in the desert <.< Just saying...

[Kore]

5 x 0 = 2 x 0, so any number is equal? No, it takes energy to reduce evil, and left alone evil will use its energy to corrupt good.

1=0 is hard work, takes "energy" to wipe out monsters, one way or another. "...all the energy it would require". Psi, magic, crossbow bolts and axes... many ways to accomplish.

0=1 only happens occasionally, even in a perfect world an angel may turn to evil. In a basket of good apples, one may start to rot.

1=2 happens easier, a seed of evil grows and spreads, one rotten apple quickly contaminates the one beside it. (Example: The good of goblin slayer killing monsters did not protect him from the evil of associating with them)

If we work together we can clean out the thistles in the garden and rest of garden can grow in peace.

If we instead allow thistles to multiply, soon the garden is overrun with weeds and our only solution will be to plow up entire garden, and few will be saved. The maze of many has become overrun with evil, so Psi max does final solution of plowing entire maze, wiping out all the evil, no good apples left to save.

[MapsGroxily]

5 x 0 = 2 x 0, so any number is equal? No, it takes energy to reduce evil, and left alone evil will use its energy to corrupt good.

1=0 is hard work, takes "energy" to wipe out monsters, one way or another. "...all the energy it would require". Psi, magic, crossbow bolts and axes... many ways to accomplish.

0=1 only happens occasionally, even in a perfect world an angel may turn to evil. In a basket of good apples, one may start to rot.

1=2 happens easier, a seed of evil grows and spreads, one rotten apple quickly contaminates the one beside it. (Example: The good of goblin slayer killing monsters did not protect him from the evil of associating with them)

If we work together we can clean out the thistles in the garden and rest of garden can grow in peace.

If we instead allow thistles to multiply, soon the garden is overrun with weeds and our only solution will be to plow up entire garden, and few will be saved. The maze of many has become overrun with evil, so Psi max does final solution of plowing entire maze, wiping out all the evil, no good apples left to save.

While this is a good theory it doesn't add into the bigger picture: he's only removing, in general, 3 people from the realities within the maze: Forgarth, Minmax and Kin. This would barely make any mark on the good/evil garden of all the realities; this would be more comparable to saving a tiny grass seedling while the rest of the garden grows tainted.

I don't think it's a good standby for him anyway, since he's done plenty evil already despite thinking of himself as 'Neutral'.

[Kore]

While this is a good theory it doesn't add into the bigger picture: he's only removing, in general, 3 people from the realities within the maze: Forgarth, Minmax and Kin. This would barely make any mark on the good/evil garden of all the realities; this would be more comparable to saving a tiny grass seedling while the rest of the garden grows tainted.

I don't think it's a good standby for him anyway, since he's done plenty evil already despite thinking of himself as 'Neutral'.

He is trying to remove hundreds in total of some of most corrupting seeds in any universe. "since he's done plenty evil already" He is wise enough to also remove himself.

[apotato]

you could technically argue the Maze of many doesn't exist anyway. it clearly exists outside of time so reality 156 simultaneously entered and left the maze if the win scenario is not a red herring. if it DOESN'T exist outside of time then 1.9 million attempts would have caused FMK to be so far behind the story they are now irrelevant to it's outcome.

so either you enter and simultaneously leave with knowledge of only your successful attempt, or you enter and effectively become irrelevant to the storyline since FMK (if we assume each failed run was 1 day) has been gone over 5000 years.

the other situation is that the win scenario is a fake and the real exit from the maze is the jade teapot. at which case if psi-max is unaware of this he's committing an unnecessary mass genocide.

[Krulle]

Well, the equation 1=0 purposefully disregards something in mathematics.
The order of the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is not mathematically defined.
They are given by language (signomancy).
Then comes the only postulate in mathematics which is real math, but cannot be proven (as it is basically defining the order of the numbers, givenby signomancy):

1+1=2

Everything else in mathematics follows out of that.
All other postulates in mathematics have been proven, or, given time, will be proven.

[Your.Master]

Well, the equation 1=0 purposefully disregards something in mathematics.
The order of the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 is not mathematically defined.
They are given by language (signomancy).
Then comes the only postulate in mathematics which is real math, but cannot be proven (as it is basically defining the order of the numbers, givenby signomancy):

1+1=2

Everything else in mathematics follows out of that.
All other postulates in mathematics have been proven, or, given time, will be proven.

None of that sounds true, I'm afraid. Unless you have a deviant definition of "postulate in mathematics which is real math". Such an axiom does not define the order of real numbers, for instance. You can't go from 1+1=2 to 3<Pi<4 without sidestepping through some other ideas (eg. Euclidean geometry and his axioms).

There's a LOT that cannot be extrapolated from 1+1=2. There is actually a thing where mathematicians go off and try to figure out what is the minimal set of irreducible axioms required to prove certain statements: http://en.wikipedia.org/wiki/Reverse_mathematics.

For another, Godel's incompleteness theorem guarantees that not all other postulates which are in fact true will ever be proven true. See http://en.wikipedia.org/wiki/G%C3%B6del ... s_theorems. I don't think the axiom "1+1=2" is sufficient to invoke Godel's incompleteness theorem, but it's also not sufficient to generate interesting mathematical consequences.

Saying that the order of "the ten digits" is not mathematically defined is misleading. Sure, these sigils and even the thing called "digits" are just notation, and not really the math behind them. The underlying concepts they represent, however, are mathematically defined, and the shortcuts you can make when manipulation operations in certain notations are mathematically proven (eg. the fact that with 23 + 34, you can add the digits individually and come to a result that is correct, with the only "fudge factor" being the notion of "carrying the one" aka accounting for range overflow).

Anyway, like ForgetsOldName said very formally and Ikul said more simply, 1=0 isn't actually inconsistent, it just means there is only one number in that "ring" (we can call that number zero if we want). This is the "trivial ring".

Also, note that 1+1=2 isn't inconsistent with 1=0. 1+1=2, and 1=0, therefore 0=2, and that's fine, because everything is 0. Or everything is two. Et cetera.

[hol]

Now it is such a bizarrely improbable coincidence that anything so mindbogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as a final and clinching proof of the non-existence of God.

The argument goes something like this: "I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing."

"But," says Man, "the Babel fish is a dead giveaway isn't it? It could not have evolved by chance. It proves that you exist, and so therefore, by your own arguments, you don't. QED."

"Oh dear," says God, "I hadn't thought of that," and promptly disappears in a puff of logic.

He then goes on to prove that black is white and gets killed on the next zebra crossing!

[nate9799]

First, I love Hitchhikers Guide, so kudos to hol. But in response to Your.Master who said:

Anyway, like ForgetsOldName said very formally and Ikul said more simply, 1=0 isn't actually inconsistent, it just means there is only one number in that "ring" (we can call that number zero if we want). This is the "trivial ring".

Also, note that 1+1=2 isn't inconsistent with 1=0. 1+1=2, and 1=0, therefore 0=2, and that's fine, because everything is 0. Or everything is two. Et cetera.

I accept that this is valid, but let's assume that 1=0 is inherently inconsistent. In other words, lets assume that he has also proved that he has proved that 1 does not equal 0. Therefore we have a contradiction. Anywho, this leads to the principle of explosion (which can be read about here: http://en.wikipedia.org/wiki/Principle_of_explosion). Essentially, any and all statements can be derived from this. why? because a logical deduction (think if then statement) is only wrong if the first statement is true and the second false.
For example, the statement "if Minmax 156 (the usual reality) has less than average intelligence, then Forgarth 156 is a dwarf" would be true, the statement "if Minmax 156 has less than average intelligence, then Forgarth 156 isn't a dwarf" is false.

Because I'm lazy, I'm going to use symbols for now on. T is a true statement, F a false one, and P and Q stand for any statement you or I want it to. P=>Q means if the statement P is true, then the statement Q is true.

So what the two examples above are equivalent to
T=>T
and
T=>F

But if the first statement is false, then no one needs to care about the second statement, as it is not taken into effect. Both F=>T and F=>F are true, which means that for any statement P, F=>P is true. This is going to be very important.

The other thing we will need is a logical rule called Modus Ponens. Basically, if you know the statement P is true, and the statement P=>Q is true, then the statement Q is true.

Now back to the comic. We assumed that Psion Minmax had proven that "1 does not equal 0" (equivalently "1=0 is false" or "NOT(1=0)") is true. If he proves "1=0" is true, then he will have proven the statement "1=0 AND NOT(1=0))" is true. But "P AND NOT(P)" is an inherently false statement. Therefore the statement "1=0 AND NOT(1=0))" is... wait for it... both true and false. but we aren't done. Because "1=0 AND NOT(1=0))" is false, we can substitute it into the statement F=>P to get:
(1=0 AND NOT(1=0)))=>P
because of Modus Ponens, we can conclude that the statement P is true.

BUT WAIT... THERE'S MORE!!!
NOT(P) is also a statement, so we can instead have:
(1=0 AND NOT(1=0)))=>NOT(P)
which gives us that NOT(P) is true, or more concisely, P is false.
because P can stand for any statement, every statement is true and every statement is false.

In conclusion, if Psionic MinMax proves 1=0, then I own Thunt's immortal soul and I will chain him to a desk and force him to churn out Goblins comics for the rest of eternity.

[wonderdrow]

When 1 + 2 = 3 then 2 = 3 - 1

When 1 + Ôê× = Ôê× and 0 + Ôê× = Ôê× then 1 = Ôê× - Ôê× and also 0 = Ôê× - Ôê×

One is nothing in the eye of infinity.

[ActsStupidly]

When 1 + 2 = 3 then 2 = 3 - 1

When 1 + Ôê× = Ôê× and 0 + Ôê× = Ôê× then 1 = Ôê× - Ôê× and also 0 = Ôê× - Ôê×

One is nothing in the eye of infinity.

Thank you for this, I have been trying to remember that little trick ever sense Thunt started this arc. So for like... years....