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On February 26 2009 17:57 PH wrote:Show nested quote +On February 26 2009 16:40 Zortch wrote:On February 26 2009 16:35 pavement ist rad wrote:
I think you don't understand pure math.
Applied math is a branch of math that has real world application, and is motivated by physics, engineering, etc.
Pure math, on the other hand, explores mathematical ideas simply for the beauty of understanding it. If you approach those problems you listed (prime numbers, polynomials, etc), as you would approach something like art, you might see it differently. Mathematical proofs have a certain aesthetic, and I think those who study math see the elegance in them. QFT Also, there is definetly mathematical intuition. I'm sure everyone has some on some level. For a simple example, if you multiply two big numbers togeher your intuition tells you that you will get a bigger one. You can see why it should be that way, but oly because you have multiplied a lot of numbers. If you later work with other mathematical objects you can develop intuition about them too. Doesn't that scare you though? I don't know much about math, but I like to think that math, considering what it is, has a logical basis free of psychologicism...to think otherwise is frightening in its implications, imo. T_T
It's not that maths stems purely from people's intuitions. A good intuition will help you explore and understand certain concepts but you still have to prove them using solid theory.
There is a kind of "opinion" in maths. In that it depends on what axioms you're starting with. But almost everyone has agreed to use certain axioms because they work well and correspond with what happens in the observable world.
In that sense it is possible to create an entirely different mathematics that is still logical and works, but no one else is going to agree to follow your definitions. There's nothing to be afraid of.
I don't like when people say mathematics/logic is how our universe works. It's more like the language people use to interpret the universe we live in.
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On February 26 2009 14:38 freelander wrote:Show nested quote +On February 26 2009 14:37 Boblion wrote:
Most of algebra is like astrology :> ??
Cabalistic methods + content completly unrelated to real world Ftw
/rant
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If it didn't make any sense I don't know how the hell are those satellites and space shuttles/stations with people in it up there.
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Calgary26003 Posts
Yes, math makes sense.
No, you don't make sense.
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On February 27 2009 00:14 EsX_Raptor wrote:
If it didn't make any sense I don't know how the hell are those satellites and space shuttles/stations with people in it up there.
Pure mathematicians are too challenged to build satellites and space stations. They evolved in several more adapted species ranging from technicians to engineers and physicians.
o,o
+ Show Spoiler + ok i stop to bash math, i swear :D
But seriously when you talk about real world with a math teacher it is like if you made a blasphemous remark :>
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On February 27 2009 01:04 Boblion wrote:Show nested quote +On February 27 2009 00:14 EsX_Raptor wrote:
If it didn't make any sense I don't know how the hell are those satellites and space shuttles/stations with people in it up there. Pure mathematicians are too challenged to build satellites and space stations. They evolved in several more adapted species ranging from technicians to engineers and physicians. o,o + Show Spoiler + ok i stop to bash math, i swear :D
But seriously when you talk about real world with a math teacher it is like if you made a blasphemous remark :>
I am fairly sure that physicians have nothing to do with space shuttles being fired towards the moon...
Anyway a lot of the maths development throughout history was made by physicists simply because it was needed for new physics discoveries to be made. Like distribution theory and calculus are both based on physics.
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If you can prove math doesn't make sense, good for you, bad for the mathematicians.
If you can't, shut up 
Seriously though, math goes a lot deeper than what most people think. Many mathematical theories have strong physical analogies (check the wiki article on the Riemann hypothesis and the current project to prove it with a physical experiment). I will concede much of modern math is way beyond anything you could ever observe in our reality, and is just plain made up. It's still all based on the same axioms as the rest of maths and as such stands valid and has its own value.
Long story short, "does math make sense" is the wrong question. The right question would be "did you look into it thoroughly enough to make the decision if math makes sense to you".
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On February 26 2009 23:03 Nytefish wrote:Show nested quote +On February 26 2009 17:57 PH wrote:On February 26 2009 16:40 Zortch wrote:On February 26 2009 16:35 pavement ist rad wrote:
I think you don't understand pure math.
Applied math is a branch of math that has real world application, and is motivated by physics, engineering, etc.
Pure math, on the other hand, explores mathematical ideas simply for the beauty of understanding it. If you approach those problems you listed (prime numbers, polynomials, etc), as you would approach something like art, you might see it differently. Mathematical proofs have a certain aesthetic, and I think those who study math see the elegance in them. QFT Also, there is definetly mathematical intuition. I'm sure everyone has some on some level. For a simple example, if you multiply two big numbers togeher your intuition tells you that you will get a bigger one. You can see why it should be that way, but oly because you have multiplied a lot of numbers. If you later work with other mathematical objects you can develop intuition about them too. Doesn't that scare you though? I don't know much about math, but I like to think that math, considering what it is, has a logical basis free of psychologicism...to think otherwise is frightening in its implications, imo. T_T It's not that maths stems purely from people's intuitions. A good intuition will help you explore and understand certain concepts but you still have to prove them using solid theory. There is a kind of "opinion" in maths. In that it depends on what axioms you're starting with. But almost everyone has agreed to use certain axioms because they work well and correspond with what happens in the observable world. In that sense it is possible to create an entirely different mathematics that is still logical and works, but no one else is going to agree to follow your definitions. There's nothing to be afraid of. I don't like when people say mathematics/logic is how our universe works. It's more like the language people use to interpret the universe we live in.
Axioms are essentially irrefutable facts that have were somehow developed and have been empirically proven over time, no? I study philosophy, not math, so I could be mistaken concerning just about everything I say here...but I thought something that has to do with modern set theory or something or other proved most of the old axioms? I at least know for certain that Fregean logic proved Peano's axioms, but I don't really know anything past that...
In any case, math, before you get into the ridiculously theoretical stuff and at least in part, can be seen as the way in which we can comprehend the inner workings of the universe, no? So long as it continually works, it is true. If that is the case, it may be somewhat fallacious but still safe to make the jump that the universe runs on these kinds of mechanics that are mathematically reducible, no?
However, from there, math being irreducible to pure logic (free of psychologicism) is a scary thought in terms of pondering the metaphyics of the universe, is it not?
I dunno, that's just what I've gathered from my limited foray into this subject area.
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math makes sense relative to human beings.
multiplicity is a function of our brains. it is a tool for perception.
multiplicity does not necessarily exist in reality.
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Basically computer came out of mathsmatics, if you want some practical applications. How the internet works, how the cpu works, and all the underlying hardware depend heavily on math. Computer IS made because people wanted a "function generating machine", also a concept out of math.
and so on...
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Math is the most intimate, artificial things we have. If you think about it... If you live in another universe, as long as you're human, math would make sense to you
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Math needs science to give it meaning. Otherwise, it's just a made up extremely boring universe with made up rules. Science anchors math to reality.
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On February 27 2009 13:03 arcticStorm wrote:
Math needs science to give it meaning. Otherwise, it's just a made up extremely boring universe with made up rules. Science anchors math to reality.
i find it's the reverse, just because that's what i've been told.
math anchors science..? no?
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On February 27 2009 13:09 imperfect wrote:Show nested quote +On February 27 2009 13:03 arcticStorm wrote:
Math needs science to give it meaning. Otherwise, it's just a made up extremely boring universe with made up rules. Science anchors math to reality. i find it's the reverse, just because that's what i've been told. math anchors science..? no?
Experiments anchor all. They are what other things depend on. The fact that they can be described by math just means that nature is objective (or something like that).
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On February 27 2009 14:09 fight_or_flight wrote:Show nested quote +On February 27 2009 13:09 imperfect wrote:On February 27 2009 13:03 arcticStorm wrote:
Math needs science to give it meaning. Otherwise, it's just a made up extremely boring universe with made up rules. Science anchors math to reality. i find it's the reverse, just because that's what i've been told. math anchors science..? no? Experiments anchor all. They are what other things depend on. The fact that they can be described by math just means that nature is objective (or something like that).
the funny thing is that wave-particle duality then goes and gives evidence that it actually isn't what we are testing that is objective, it is our relationship to what we are testing.
not to say the relationship of consciousness and matter isn't part of what constitutes "nature".
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On February 26 2009 15:01 Zortch wrote:
You can always answer "Why?" in math. Just maybe not in the sense some would like.
You can break any mathematical statement down to te axioms (stuff we assume for doing math). Generally set theory, and maybe a bit more stuff depending.
In the OP you said 2+2=4 is just obvious, but really in formal mathematics from the axoims of set theory you can prove the existence of the empty set and we call that 0, and then the set containing the empty set is 1 and the set containing the set containing the empty set is 2 etc. So now you have the natural numbers, and you can define addition in terms of the successor function (just goes to the next one) and it all 'makes sense' based on our reasonable assumptions.
The answer.
Math makes sense insofar as the axioms you start with make sense.
With think that Euclidean axioms, for example, are intuitive/common sense. But math can make sense without them.
We just have to sigh and carry on with our calculations. We know that the symbols carry great power and have tremendous pragmatic import as well as theoretical consistency. Underneath that, we don't know. We just can't peel the world open sometimes you know. Like a mango that isn't ripe.
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On February 27 2009 13:09 imperfect wrote:Show nested quote +On February 27 2009 13:03 arcticStorm wrote:
Math needs science to give it meaning. Otherwise, it's just a made up extremely boring universe with made up rules. Science anchors math to reality. i find it's the reverse, just because that's what i've been told. math anchors science..? no?
Think about the example. 1+1 = 2. Wouldn't it be perfectly possible to invent a mathematical system in which 1 + 1 = 0? By why is that we don't say 1+1 = 0? It's because in the real world when we take one thing and put it with another you get 2. Descriptions of the real world (science) is the context from which we understand mathematical concepts. Multiplication is meaningless until we look at it from, for example the distance = rate* time relation. Science is applied Math, but Math is pointless without science.
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Math is an art and alone the quest for beauty and insight is enough reason to do math.
But since it's so useful math is often misunderstood as a mere tool for science (as displayed in this thread), which is a shame.
Math is our method to understand and describe structurs and behaviour between structurs. If our universe is structured in a way we can understand then some mathematical structure is bound to represent or approximate the real world. Even if you dismiss everything else math is about you have to acknowledge math as the most fundamental research you can do.
As always when people who don't know math try to find an example for why math is pointless your example is badly chosen arcticStorm: The structure where 1+1=0 is a very simple one (a so called finite group) and finite groups are basically everywhere around us, like in a clock where 6+6=12=0. Think about it and you will find representations of 1, + and 0 in the real world where 1+1=0 makes perfect sense.
[EDIT]: And as always with fundamental research: you don't know if the results will be useful.
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EPT
