Could Math Ever Be Proven Wrong?

[trunks200]

Uh. No. In a modulo-2 system 1+1 is not equal to 10 or 2. It’s equal to 1.

Actually (1+1)mod 2 = 0, but what i wrote was somewhat of an digression the get to the point of math transitivity. And ulitmatelly it is a whole different story than 1+1 which can only have one value, which may be represented differently in various system but in abstract it stands for the same result.

Aha, your original example said nothing about weight!

Yes because my orginal example was suitable for the equation.
What you brought as an contraddiction was a whole different equation, which because of the peculiar character of objects of addition was no longer suitable to be represented by this particular equations ( but hey we can always count atoms of combined pile of dust ).

But there are plenty of other situations where different maths are better suited to the problem at hand.

I’m not denying that. All i am saying is that particular operation, which is 2+2 will allways equal 4 in decimal system. 2+2 sets not only an operation itself but also the background enviroment. 2+2 in form presented means that having axis described by decimal system where Vx,y,V_ncN y-x=n(delta) and each next is greater than its predecessor, shifting 2 to the successor of the succesor of 2 will always end up on position 4. This is all but different than any modulo or custom group operation.

Basically, we can construct axiomatic systems and prove things within them. Sometimes these axiomatic systems make accurate predictions about the behavior of the real world. The sorts of predictions we want to make determine which axiomatic system (if any) it’s best to use.

This is too far away from disscussing whether or not 2+2 may equals something other than 4.

Actually, in modulo 1, 1+1=1. But in this system, it’s also true that 1+1=0, and 0+0=1, and a bunch of other things. This is because, in a modulo-1 system, 0=1. There’s only one integer, and it can equally well be called by the name of any integer. It’s a very boring system.

No Z1 has an empty domain and codomain. You have no elements in Z1 to work with so 1+1 operation in Z1 is not even possible as Z1 has no clue about what the hell ‘1’ even is.

Right. 1+1 = 2, with logical certainty. But that doesn’t mean that it’s necessarily a good model for anything in the real world. It works pretty well for whole apples: put one apple with one apple and you have two. But if you mix a gallon of water and a gallon of ethanol, you don’t end up with two gallons of mixture. That doesn’t mean that 1+ 1= 2 is wrong; it just means that numeric addition isn’t a good model for mixing volumes of alcohol and water.

As it was said before 1+1 also sets the background enviroment which is adding elements of the same abstract pattern. Here you would have 1(x)+1(y) where x and y would be a density.

Everything in this world is being prooven by some sort of logical conclussion. Thats why math as an human-made representation of pure logic cannot be prooven wrong just like truth cannot be proven to be false.

Regards

Ziom

[Skammer]

@DrMatrix

Godel’s second theorem says: If there exists a proof of consistency of a system, then the system is not consistent. Therefore to prove a system consistent, we need to show that there does not exist a proof of consistency. The problem with this is that an inconsistent system can prove anything.

Derleth recommended Gödel, Escher, Bach: an Eternal Golden Braid by Douglas Hofstadter. I love that book. Hofstadter gives an excellent explanation of Gödel’s theorems (among a lot of other topics). I recommend the book highly.

For the record, this is where I decided I was too stupid for this thread and went to look for new Game of Thrones posts.

[trunks200]

@leahcim

This is the first and only time when I have seen “probability that math is wrong” compared to a more conventional probability in a result.

But is LFT prooven or not? Beacuse if it is not then technicaly disrpooving it does not make math being able to be disprooven.

But the axia used in math is not of this physical world, but a ideal mathmatical universe. It works good enough for earth, but that is already intentionally introducing errors from real to idea model. So the math is not wrong, even near a black hole, You are just using one model which does not relate to the physical reality at that location.

Math is flexible enough to be suitable for any world within our Universe, the only problem is the ammount of variable data to be taken under account. If math would only work in selected ideal enviroment then it arbitrary value would be close to none.

Regards

Ziom

[RadicalPi]

@kanicbird

But the axia used in math is not of this physical world, but a ideal mathmatical universe.

I wanted to point out that the plural of “axiom” is not “axia,” but rather “axiomata” or “axioms.”

[SUP]I know this doesn’t contribute to the discussion, but it was bothering me.[/SUP]

[Leo_Bloom]

@johnpost

zombie or no

… there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don’t know we don’t know. …

This eminently sensible and memorable observation, it should be noted, was made by Donald Rumsfeld, the Secretary of Defense under George S. Bush, who was mocked for it by people who assumed, without thinking about it, that the words were double talk to avoid answering.

It ultimately may well have been (I don’t know the original context), but it is still a valuable way to think about things sometimes.

[Jragon]

However, there are some open problems that could be proven in such a way that fuck everything up. For instance, have fun with cryptography if it’s proven P=NP.

[billfish678]

@Jragon

However, there are some open problems that could be proven in such a way that fuck everything up. For instance, have fun with cryptography if it’s proven P=NP.

I recently saw a movie called P=NP. Kinda a low budge movie with 4 mathematicians who have done just that. The whole movie is them basically realizing the deep shit this is gonna cause. Its the mathematical equivalent of inventing the atomic bomb.

I enjoyed it.