Let me fix your sentence to be true:because this would produce a hypotenuse with length "square root of 2" m, which has no exact length.
That's the exact opposite of the problem -- mathematics, quite literally, says absolutely nothing about the physical universe. But the point of your statement is correct: mathematics is not about modelling the physical universe with math. That's the physicist's job!The moral of the story is that mathematics ... should never be taken literlly.
I understand what you said but wasn't it Hilbert who wanted to recreate mathematics making everything finite? Surely he would have known what you were saying. Or maybe by finite he meant something else? His passion for Cantor's infinities is highly bizzare and contradictory to his philiosophy as well?mathwonk said:you have no way to use only finite numbers.
I've always thought such an attitude suffers from tunnel vision -- they focus specifically on the algebraic structure, and ignore that topology does a fine job capturing the notion of a "continuum"."Herein I see the genesis of the conflict between geometrical intuition, ...
You'll have to be more clear on just exactly what you mean by that. Some other things to consider, by the way, are that 1 = 1.00000... has just as many decimal digits as √2 = 1.41421..., and that the decimals are just one way to represent real numbers.one can see that just like the infinit number of decimals in root 2 meters being very likely to be physically impossible
DaveC426913 said:1] It is as impossible to physically construct a line that is exactly 1m in length as it is to physically construct a line that is exactly [tex]\sqrt2[/tex] in length.
I agree and this backs up the fact that theoretical physics which uses different types of ideal mathematical numbers will always be an approximation to reality. Although this approximation may get better as more insightful models are built but by in large, as long as one uses traditional mathematics involving the real number line than one will always be approximating reality.
Theoretical physics says that if you take 2 apples and give an equal number to Bob and Tom, each of them has 1 apple. Physics uses the integers to describe the reality that is the quantity of apples. The physics is perfectly accurate because it is defined to be so. Physics defines a one-to-one relationship between the quantity of apples and the integers. So, by definition, the physics can not be inaccurate.I agree and this backs up the fact that theoretical physics which uses different types of ideal mathematical numbers will always be an approximation to reality. Although this approximation may get better as more insightful models are built but by in large, as long as one uses traditional mathematics involving the real number line than one will always be approximating reality.
I don't think you realize how realize how much you would have to throw away to create a physics theory without mathematics. It doesn't just mean getting rid of calculus, or the real numbers. It also means you can't use the natural numbers. So your theory can't even depend on the ability to count, or do any basic arithmetic.pivoxa15 said:I guess what I am trying to get at is 'what is nature really like, exactly?' Without consideration of any mathematics or even pretending that mathematics was never invented. In other words I want to know, if you like, 'God's thoughts'. This is probably a good analogy because this kind of exactness of describing our Universe is only likely from a higher dimensional point of view.
If only theoretical physics used just integers. But there is a whole lot of more to it including real numbers. For me, that is where the trouble starts. As far as I know, we might say that all theoretical physics is mathematically true but physically true? Most likely, as empirical evidence suggets but exactly? Probably not as many distinguished physicists suggests. People like Hawkings, Einstein, Feymann, Schrodinger.Gokul43201 said:Theoretical physics says that if you take 2 apples and give an equal number to Bob and Tom, each of them has 1 apple. Physics uses the integers to describe the reality that is the quantity of apples. The physics is perfectly accurate because it is defined to be so. Physics defines a one-to-one relationship between the quantity of apples and the integers. So, by definition, the physics can not be inaccurate.
It is highly likely that reality obey logical rules so maybe reality does obey some type of mathematical system that have not been created or even thought about yet. Einstein hinted this point and said 'one can give good reasons why reality cannot be represented as a contiuous field ... Quntum phenomena ... must lead to an attempt to find a purely algebraic theory for the description of reality.'master_coda said:I don't think you realize how realize how much you would have to throw away to create a physics theory without mathematics. It doesn't just mean getting rid of calculus, or the real numbers. It also means you can't use the natural numbers. So your theory can't even depend on the ability to count, or do any basic arithmetic.
Highly likely that reality obeys logical rules? If reality doesn't obey logical rules, then there isn't anything that physics can say about it either, with or without math. The whole point of physics is to come up with logical rules to describe reality.pivoxa15 said:It is highly likely that reality obey logical rules so maybe reality does obey some type of mathematical system that have not been created or even thought about yet. Einstein hinted this point and said 'one can give good reasons why reality cannot be represented as a contiuous field ... Quntum phenomena ... must lead to an attempt to find a purely algebraic theory for the description of reality.'