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So if mathematics is not just about shapes, not about logic, not about physics, and not about numbers, what is it?
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Off Topic What is math?
What is math?
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So if mathematics is not just about shapes, not about logic, not about physics, and not about numbers, what is it?
Lee has written
not about logic
Not really imho, in PC Architecture (Dunno how its really called on english) he have that thing which called "Logic Algebra"
also, math is thing in lua
math.random ftw :3
@Lee:
At first when I saw the title I was thinking, "OMG, not another 9 year old that hasn't gone to school yet -_-'", but now I see that it is rather more intriguing and a thread that works the complexes of my brain.
The question you ask of is a most awkward one, how do you explain something like that..? It's kind of like a pointer in C, it isn't an actual object containing something itself, just a path that 'shows the way' to an object of some sort.
Maybe, i dont really know. Here, in Russia we dont know how its called in english :p
but for us its Logic Algebra anyway :3
http://en.wikipedia.org/wiki/Boolean_algebra_(logic)
That is what I think you are talking about. It is algebra but the missing values can only be either 0 or 1.
Exactly!
But I disagree with geometry. Because when you think of a straight line, technically it is curved because the space is curved.
An “axiom”, in classical terminology, referred to a self-evident assumption common to many branches of science. A good example would be the assertion that
When an equal amount is taken from equals, an equal amount results.
At the foundation of the various sciences lay certain additional hypotheses which were accepted without proof. Such a hypothesis was termed a postulate. While the axioms were common to many sciences, the postulates of each particular science were different. Their validity had to be established by means of real-world experience. Indeed, Aristotle warns that the content of a science cannot be successfully communicated, if the learner is in doubt about the truth of the postulates.
The word "axiom" comes from the Greek word ἀξίωμα (axioma), a verbal noun from the verb ἀξιόειν (axioein), meaning "to deem worthy", but also "to require", which in turn comes from ἄξιος (axios), meaning "being in balance", and hence "having (the same) value (as)", "worthy", "proper". Among the ancient Greek philosophers an axiom was a claim which could be seen to be true without any need for proof.
The logico-deductive method whereby conclusions (new knowledge) follow from premises (old knowledge) through the application of sound arguments (syllogisms, rules of inference), was developed by the ancient Greeks, and has become the core principle of modern mathematics.
Source: Wikipedia.
Conclusion: Maths is a knowledge that is essential to mankind. It is for people who work, more specifically those who build houses because they need math to calculate things often, or if you are playing card games (in example: poker) you'll need to know what the numbers mean in order to know how it works and to be able to play in the first place, also the pilots in the airplanes needs math to be able to calculate things too, such as if a plane is going to be delayed and vice-versa, you can calculate the range, and so much more with math. That's why math is good, but boring aswell, you need a strong and focused brain to be able to handle everything in maths. But all people should at least know some of the basics in math, that's already good in my opinion. It's good to challenge the brain sometimes.
edited 1×, last 31.12.10 01:05:55 pm
Nemesis has written
Not really imho, in PC Architecture (Dunno how its really called on english) he have that thing which called "Logic Algebra"
That's an expression of a subset of mathematics (even a subset of numerics as well) that deals with two arbitrarily defined integers (as a subset of numerics) or simply two values. As logic dictates, because BA is a subset of mathematics does not imply that mathematics is a subset of BA. If you're talking about logic in the form of rationalization, then scroll down.
@KimKat put a great explanation of the nature of mathematics, namely that:
1. Mathematics is atomically composed of unverifiable yet "self-evident" axioms.
2. Within appropriate constraints on the mathematical system, lemmas (proven theorems) can be formed through a compound system of axioms.
3. Mathematical systems are always internally consistent hence they are verifiable.
This however leads to a few meta contradictions. For example, if axioms are the atomic subsets of mathematics, why are they unverifiable? For example, how can you verify that 1+1=2? How do we even understand the concept of 2, or even 1? Logical systems are also not internally consistent. For example, given the following assertions:
1
2
2
P1: P2 is a true statement P2: P1 is a false statement
Attempts to resolve this internally will lead to a contradiction. This leads us to believe that the construction of the propositions is in itself flawed, but if we are able to observe this proposition, it also implies that the construction of the proposition is valid, it's just paradoxical.
On a grander scale, I would even have to argue against TKD's statement that mathematics is a creation of mankind. This would imply that mathematics is bounded to humans and is thus finite as human knowledge itself is finite. Does math exist only if we do, or does it transcend human knowledge? I would argue for the latter as mathematics is continuously developed upon, meaning that we don't actually understand mathematics to its fullest extend.
To this end, I would actually agree with Silent and Sunny Autumn the most, math is pervasive, it's pure, it's elegant, and it is the platform on which rational system can be built with arbitrary constraints. It can be thought of as a philosophy or as an ambitious science. It could be about numbers, about shapes, and about logic, but those do not define what mathematics is.
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But I disagree with geometry. Because when you think of a straight line, technically it is curved because the space is curved.
Lines are described by first order functions of x and y, hence even if the space is curved, a line in a curved plane/n-dimension space is still a line. This however doesn't mean that you're completely wrong. The following is also a linear function
r(t) = (0, t^2) (where r parametrically defines an x-y function with parameter t)
It's a line in the x-y plane, but not so in the y-t plane (if we further define t to be a function of its own right)
Nemesis has written
On a grander scale, I would even have to argue against TKD's statement that mathematics is a creation of mankind. This would imply that mathematics is bounded to humans and is thus finite as human knowledge itself is finite. Does math exist only if we do, or does it transcend human knowledge? I would argue for the latter as mathematics is continuously developed upon, meaning that we don't actually understand mathematics to its fullest extend.
i messed up something but referring ends here lol
nicely thought. this is interesting mix up with philosophy
i messed up something but referring ends here lol
nicely thought. this is interesting mix up with philosophy
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