Is math wrong?

[Red Iron Crown]

Weird that some of you call math a science. It is a logical, theoretical construct; a tool. That tool is incredibly useful in science, but it isn't science. No one does math experiments. Something proven correctly will never be overthrown; it cannot without upsetting the whole apple cart. Science doesn't deal in proof, only weight of evidence and likelihoods.

Given that the tool is logically consistent, it can't really be said to be "wrong". It certainly can be misapplied when used to measure or describe other phenomena, though.

[ZetaX]

Weird that some of you call math a science. It is a logical, theoretical construct; a tool. That tool is incredibly useful in science, but it isn't science. No one does math experiments. Something proven correctly will never be overthrown; it cannot without upsetting the whole apple cart. Science doesn't deal in proof, only weight of evidence and likelihoods.

Given that the tool is logically consistent, it can't really be said to be "wrong". It certainly can be misapplied when used to measure or describe other phenomena, though.

Math is halfway a science (it satisfies the parts about searching and ordering knowledge by rational means), and debatably even a full one (see http://en.wikipedia.org/wiki/Mathematics#Mathematics_as_science).

Anyway, it surely is not just a tool, not any more than e.g. physics. It can be used as one, but there is more.

[K^2]

Modern definition of science implies scientific method, which mathematics lacks completely. But it's not less for it, just the opposite. Science can fail. In fact, it's all it can do. Science can never be right. It can, and often enough is, wrong. It's still very useful, even when completely wrong, but you can't expect some deeper truths from it. That's not what science is for, and consequently, not what it does.

Mathematics is a different story. It cannot be wrong. It is a self-consistent system of rules. It can be useful or useless, and some branches of mathematics are more one than the other. And the intuition math gives us about nature can be completely wrong, but that's our fault for trying to draw hints from something that isn't purposed for it. Mathematics just is. If you think one can find a flaw in it, then you don't understand first thing about it.

[ZetaX]

Modern definition of science implies scientific method, which mathematics lacks completely.

This actually depends in our exact definition of "scientific method".

- If it simply means "testability", then mathematics satisfies it. Every search for proof or counterexample is a test.

- If it includes "falsifiability", then we would need to be careful what we mean by that: a mathematical claim is falsifiable until proven, and even after we found a proof we could still falsify it (by the proof being wrong or by our axioms being inconsistent; so Gödel's incompleteness actually adds some flavour of falsifiability). In the end, we need to distinguish between mathematics as an "endevour to gather knowledge" and mathematics as "all possible implications of logic"; people here used it as both and that's ok, but for this question it is relevant.

- If it also includes "experiments", i.e. tests by doing things in the universe, then we are again borderline. Our brains and thus, assuming materialism, our thoughts are part of the universe, but does that mean mathematics is, too¿ But the search for a proof of a claim by a human in this universe might be considered as an "experiment" after all.

Edited April 4, 2015 by ZetaX

[Xannari Ferrows]

If you think one can find a flaw in it, then you don't understand first thing about it.

Perhaps I can't. Perhaps no one here can... here...

But imagine this: Some intelligent species from several parsecs away, who, lucky enough, could understand and communicate with us. Very technologically advanced, warp capable, and heavily dependent on their own system of mathematics. However, what if their collections disagreed with ours? What if they could find a flaw in our system? Perhaps, something that we can not understand, because of out biological limitations?

Contrary to your point, perhaps they would understand the first, and last thing about it, even that which we cannot perceive. But hey, it's all open to interpretation. That's what mathematics is awesome for: Contrary to popular belief, perhaps it is among the most subjective fields out there, and we're just too blind to realize it.

[Bill Phil]

I'm sure some alien (if they're out there) has actually found a VALUE for i. But it might be a NEW system of mathematics, where adding and subtracting do completely different things from ours...

- - - Updated - - -

Wouldn't Math be something that's observed in the universe? It can't be wrong then. But when we observe it and make a false conjecture, we messed up. Not math. We did.

[Xannari Ferrows]

Wouldn't Math be something that's observed in the universe? It can't be wrong then. But when we observe it and make a false conjecture, we messed up. Not math. We did.

Perhaps. But remember, math is a construct. We observe the universe, but don't account in our perceptive limitations. The universe, far all we know, is far different than what we see. What we see can be explained, but the outside world cannot. It's like trying to explain what a color looks like to a person that's been completely blind all their life. Or in this case, trying to understand the world on a level of that which we cannot comprehend, because of our own phaneron.

But look at me; ranting on. Maybe we're all wrong, maybe all right. Who knows? Math is a construct after all...

[K^2]

ZetaX, you are pulling at straws. I can see your point that one can approach mathematics as a science in certain contexts. One can think of conjectures as hypotheses. But certain conjectures can be proven true. A hypothesis can never receive that status. The fact that you are absolutely guaranteed no way of proving a hypothesis correct is a foundation of science. Any scientific knowledge is fundamentally statistical. That is an absolute goal in science. In mathematics, it just means that we have not found a proof or a proof that a proof does not exist. Or a proof that nothing conclusive can be said about the statement. In either case, what you call a final result in science is unsatisfactory to a mathematitian. And final result for a mathematical theorem is absolutely unachievable in science.

Are there parallels? Sure. But one can find parallels between science and interpretative dance. That doesn't mean anything, other than broad scopes of subjects.

Perhaps I can't. Perhaps no one here can... here...

But imagine this: Some intelligent species from several parsecs away, who, lucky enough, could understand and communicate with us. Very technologically advanced, warp capable, and heavily dependent on their own system of mathematics. However, what if their collections disagreed with ours? What if they could find a flaw in our system? Perhaps, something that we can not understand, because of out biological limitations?

Like I said, if you think it's possible to find a flaw in mathematics, you don't understand mathematics. The aliens might have a completely different mathematics. They can use a different algebra, which is not derived from counting. And it would be valid. But that wouldn't make any of our algebras less valid. Same for the rest of mathematics. You can have different sets of self-consistent axioms. And we might never discover all of them. And if we find other intelligence, it's likely that they have found things we haven't. But none of it would invalidate mathematics we have.

[Xannari Ferrows]

Like I said, if you think it's possible to find a flaw in mathematics, you don't understand mathematics. The aliens might have a completely different mathematics. They can use a different algebra, which is not derived from counting. And it would be valid. But that wouldn't make any of our algebras less valid. Same for the rest of mathematics. You can have different sets of self-consistent axioms. And we might never discover all of them. And if we find other intelligence, it's likely that they have found things we haven't. But none of it would invalidate mathematics we have.

Well... maybe invalidate wasn't the right words. I apologize for the misunderstanding. But even so, a new question comes up;

What is meant by "invalidate"? It's a strange question, I know. To answer it, we'd have to assume that math has an ultimate goal, and that will lead to a lot of arguments, but for the sake of this discussion, let's assume it means to explain the operations of the universe. Just a vague, and "simple" goal.

The real universe, and our universe; two entirely different phenomenon. One is what we see, one is what it is. They are different, and yet the same thing; a feeling of harmony between a melody and countermelody. I'm not saying what we have now is wrong for the universe we see, but perhaps for the universe of what is; the note may be G on our countermelody, but a Db on the main melody. Maybe the aliens that were spoke of play the main melody, and see the real universe. If perhaps, they could convey to us what the...

Good god this is hard to explain... let me put it this way. We see G, but the universe sees Db. That doesn't mean what we see is "wrong", so to speak, but it... is? At the same time? Like a false truth? I feel like I'm trying to explain the fourth dimension here using third dimensional laws.

It's like this is the only understanding of the universe that we know how to have, and live by. A way of living beyond the confines of our minds is that which we cannot comprehend, so we stick to what we do, even if it is not true to the real universe. This does not mean we're wrong, but that the universe is fundamentally different from our understanding on a level on which we never could understand.

I'm gonna explode here. I need an aspirin.

Edited April 6, 2015 by Xannari Ferrows

[Van Disaster]

Wouldn't Math be something that's observed in the universe? It can't be wrong then. But when we observe it and make a false conjecture, we messed up. Not math. We did.

Maths on it's own isn't much use - has to be utilised in say, astrophysics, or engineering, and at that point it's as correct as our ability to observe and apply; if an area of maths is based on incorrect observation then yes it can be wrong.

Having said that one of the first things my engineering degree taught me was that engineering was all about finding the best approximation

[ZetaX]

if an area of maths is based on incorrect observation then yes it can be wrong.

No area of math is based on observations of that kind; logical ones at best, if any at all (that's part of the debate). The only thing that is wrong in your example is the conclusion, but the implications itself are perfectly fine.

[Van Disaster]

I would argue that all of it is based initially on observation and proven in execution - and something can be internally consistent but still be wrong - but then I'm only an applied mathematician

[ZetaX]

I would argue that all of it is based initially on observation and proven in execution - and something can be internally consistent but still be wrong - but then I'm only an applied mathematician

As said: the conclusion can be wrong while the argument itself is correct (mostly by "ex falso quod libet": anything follows from a wrong assumption). The problem comes from reality in this case, more accurately our incorrect (non-mathematical) observations in the beginning. If we would live in a universe where this initial assumption was correct, then so would be the conclusion (assuming we did not make a logical mistake, but this is not what was meant, I think).

In other words, the mathematics is (by definition¿ I just don't see how else to define "mathematics" here) solely the internal part you mentioned, so if that is consistent, the mathematics is correct; doesn't make it any more useful for practical purposes, though.

[YNM]

Math can only be wrong... by math.

So no, it can't be wrong. If your proof to prove a thing is wrong, is wrong on itself, how could you see that it's wrong ? You even have to believe that parts the wrong thing is right ! We don't have anything wrong - we only have improper things. Not proper means unsuitable for use... and hence should not be used. Mathematics is not dependent on observations - it's only dependent on logic. And as I said, only the proper maths will have a use in the real world (like physics or biology or chemistry or any other part of science) as the improper one would lead to wrong figures.

[Fel]

I think I'll mix my ignorance / misunderstanding with my logic to write out a silly opinion then go back and read what other people wrote ;p

One of the strange issues with math is that, as an idea, it becomes hard for us to actually claim to have created it, we "discovered it" yes... but did not create it. At the simplest form, we should accept that if Jill has 2 apples and gives Bill one apple... Jill will have only 1 apple left is a fundamental truth that has always held true. Why, assuming that dinosaurs could count, we could easily claim that "I had 6 eggs... a raptor stole one... now I have 5" could very well have gone through the mind of one.

Another issue is that math does undergo adaptation. You'd have to read up on this (as calculators will lie to you) but 1 > i is an undefined operation. For years, ">" was used to compare real rational numbers. Writing proofs for > did not take into consideration the idiosyncrasies imaginary numbers brought and hence conditions on > being restricted to "comparison within the same number line" (i.e. you can compare 1 + i > 2 +i or 1 + i > 1 - i, but not 1 > i) had to be put into place.

The problem is... math being wrong is impossible. No matter what the universe is like, if you have 2, and you remove one, you will always end up with only one. "Counting" isn't a human construct; it simply is. There are languages that don't have a numerical system; but that only points to the civilization not having a need for quantities; not that humans simply "adopted" what is known as counting from other humans.

What I am driving at is that math cannot be wrong... but it can be incomplete. Math isn't like the horrific standards committees, pontificating about how important they are, and demanding people adhere to "standards" agreed upon by a select few. Math is self deriving. Math expands ONLY if you can get from point a to point b using existing axioms. To say that it is WRONG is to claim fundamental truths are uniquely human constructs; which is exactly what math aims not to be.

[Fel]

I'm one to say that Math itself is conceptual. Just as we filter the real world through our minds, we try to understand what is filtered by creating a system of comprehension in order to explain it, whatever it is. Some things we can explain with emotion, or words, but for the mechanics of our world, we use math.

Perhaps the real world works far different from how we think, but our knowledge has allowed us to understand our world and universe on the only level we know how to.

Meh... cognitive philosophy. This isn't about math, this is about what the mind is; if there even is a mind. Do we have duality (body and soul) or are we simply our body? Can one exist without the other? Are we a collective mind with multiple bodies, and individuality is solely due to differences between the localized members of the mind and the interface between the supermind.

Deadly interesting stuff.... but I don't particularly feel like arguing it right now.

Needless to say, you seem to be referencing Descartes (Meditations) / Plato (Allegory of the cave) in terms of how the body blinds the mind. This tends to result in disembodiment where we have minds without bodies, or minds exchanging bodies. But the otherside points out that a mind without a body is as worthless as a body without a mind, that there is an interdependence of the two... this, perhaps, is more suited to your argument as it would hold that HOW a person thinks is restricted by their body; whereas Descartes believes that the body and mind are separate and one can simply choose to ignore the effects of the body.

Meh, like many things in cognitive philosophy, you're in an unprovable position. We could create a mind and show that it "learns" in a particular manner; but then we can state we were influenced by our understanding of our own minds (connectionism) and hence did not create an impartial test. Even if we meet an alien race whose understanding of math is the same as ours doesn't refute that there can be an alien race whose understanding of math is vastly different from ours.

You're just going to end up with this argument in the end anyways "Math cannot be proven not to be wrong therefore it is possible math is wrong". It is a mathematically valid argument () because any proof to disprove math relies on our understanding of math to disprove it. OF COURSE, if math is WRONG that means the above postulate can ALSO be wrong!

"Math cannot be proven not to be wrong, therefore it is possible math is wrong... but because it is possible math is wrong, it may be impossible for math to be wrong".

Note: This assumes that everything we know about logic is wrong, the last part MAY BE A CORRECT ARGUMENT if, and only if, math incorrectly has labeled it as not being a correct argument. So there... I just broke the universe!

That's the issue. Trying to explain mathematics in the sense of operation within the unfiltered world would be like trying to create a new word that makes absolutely no sense, or perhaps trying to pronounce a word through a noise we cannot make. I can't say the math we know is wrong, but it is beyond me, and everyone's understanding since we are forced to adhere to what our brain tells us.

Really, you're so talking about cognitive philosophy it is impossible to address any of your subsequent posts without using it. This directly parallels the effects of disembodiment; having near nothing to really do with "math" and everything to do with the mind.

Edited April 6, 2015 by Fel

[Xannari Ferrows]

Meh... cognitive philosophy. This isn't about math, this is about what the mind is; if there even is a mind. Do we have duality (body and soul) or are we simply our body? Can one exist without the other? Are we a collective mind with multiple bodies, and individuality is solely due to differences between the localized members of the mind and the interface between the supermind.

Deadly interesting stuff.... but I don't particularly feel like arguing it right now.

Needless to say, you seem to be referencing Descartes (Meditations) / Plato (Allegory of the cave) in terms of how the body blinds the mind. This tends to result in disembodiment where we have minds without bodies, or minds exchanging bodies. But the otherside points out that a mind without a body is as worthless as a body without a mind, that there is an interdependence of the two... this, perhaps, is more suited to your argument as it would hold that HOW a person thinks is restricted by their body; whereas Descartes believes that the body and mind are separate and one can simply choose to ignore the effects of the body.

Meh, like many things in cognitive philosophy, you're in an unprovable position. We could create a mind and show that it "learns" in a particular manner; but then we can state we were influenced by our understanding of our own minds (connectionism) and hence did not create an impartial test. Even if we meet an alien race whose understanding of math is the same as ours doesn't refute that there can be an alien race whose understanding of math is vastly different from ours.

You're just going to end up with this argument in the end anyways "Math cannot be proven not to be wrong therefore it is possible math is wrong". It is a mathematically valid argument () because any proof to disprove math relies on our understanding of math to disprove it. OF COURSE, if math is WRONG that means the above postulate can ALSO be wrong!

"Math cannot be proven not to be wrong, therefore it is possible math is wrong... but because it is possible math is wrong, it may be impossible for math to be wrong".

Note: This assumes that everything we know about logic is wrong, the last part MAY BE A CORRECT ARGUMENT if, and only if, math incorrectly has labeled it as not being a correct argument. So there... I just broke the universe!

Really, you're so talking about cognitive philosophy it is impossible to address any of your subsequent posts without using it. This directly parallels the effects of disembodiment; having near nothing to really do with "math" and everything to do with the mind.

This post directly puts into words my love and affection for topics like this. The brain is such an amazing thing. To be honest, that is why the post was created. I never really wanted to discuss mathematics, but to explore the brain on a fundamentally higher level of understanding; to determine what is can do when it is asked about the unknown/unconsidered. It's absolutely stellar to me.

Here's something else to think about: You've been reading this post from start to finish, yes? So, without re-reading everything, how much time has passed since you began? I bet most of you will set somewhere around a 5 to 10 second range. That's fine, but do you truly know? Be honest...

If you don't, that's perfectly alright, but here's my question: If you don't know, why did you set a limit for yourself? It's an interesting thought to follow.

Were you that confident? Or were you blind?

But back to the original topic. I really only make these threads to explore the vast expanse of different human minds. No option is wrong. ...I'm not going to jail or anything for admitting this, right?

[Flixxbeatz]

...but what if math is not kill? LOOMINARTY CUNFRMD

on a seriously note, well who knows at the moment. I will continue believing that 4 + 5 = 9, unless scientists and mathematicians will have a groundbreaking discovery proving that our known math is wrong, and that 4 + 5 = 6.

Pic related:

Edited April 6, 2015 by Flixxbeatz

[RainDreamer]

There are a lot of proof for 0.9999.... = 1 around too.

[rpayne88]

Can I say its a confusing PITA to learn?

[Red Iron Crown]

Pic related:

That's what happens when you divide by zero, both sides were divided by (a- which is zero because a=b.

There are a lot of proof for 0.9999.... = 1 around too.

There's a lot of proof for that because it is true.

[Brotoro]

Red Iron Crown is correct on both counts.

[Robotengineer]

Have the incompleteness theorems been mentioned yet?

[ZetaX]

Have the incompleteness theorems been mentioned yet?

I used it to describe how mathematics might be falsifiable and therefore could actually be a science (see K^2's second to last post and my response).

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ZetaX, you are pulling at straws.

No I am not. I was just explaining why it is not as crystal-clear as you said. It totally depends on your definition of "science" (I listed three properties) and "mathematics" (the implications itself or our knowledge) and I tried to explain that. You have a very specific definition of those in mind, but did not state them (and you don't need anymore: I got them form your post). So I elaborated on the possibilities and what they imply. Those terms are obviously not that universally and absolutely defined as one might wish them to, and part of that is exactly what this discussion is about.

And in case that was not clear before: I am not even claiming that mathematics is a science (nor that it is not). Essentially, this question is uninteresting to both; I see it more as a lingustical and philosophical question.

The following are more of an elaboration of the above than new arguments; to make it more probably I am understood correctly:

But certain conjectures can be proven true.

This requires an elaboration of "proven". Our knowledge of something cannot be that absolute, surely the probabilities are often ridiculous, even compared to the next example, but they still won't be 0 or 1 because we are fallible. In this sense: mathematics as a field of research is the one that is most correct.

A hypothesis can never receive that status. [...]

How about "the sun is not powered by a giant pink frog"¿ The level of that being true is probably comparable to that of many mathematical theorems (we know with an absurdely high probability, but there could still be an error in every argument we know).

You probably want to restrict yourself to positive statements for hypothesises. Yeah, might be a bit nitpicky, but I hope this shows why for this kind of things we should try to be as exact as possible: we cannot assure that everyone else has our definitions and there is none that is that universally accepted.

Any scientific knowledge is fundamentally statistical.

As is our knowledge about mathematical statements. This does not say anything about the statement itself.

Are there parallels? Sure. But one can find parallels between science and interpretative dance. That doesn't mean anything, other than broad scopes of subjects.

That's essentially the fallacy of black and white. The parallels between mathematics and science are very close, while those between any of the latter and interpretative dancing are not. Or as one of my stupid analogues: there is also a parallel between Newton's laws and relativity.

[pirhosein]

zero  is not anything. zero is everything or zero Equal with infinity 

So let's conclude that mathematics starts this way: 02...

0<>2

0=2

 

Edited July 9, 2019 by pirhosein
We must going to zero(0). No going to infinity