Printable View
Science is just a method though - that's why we call them the "Natural Sciences" - Mathematics is most certainly a Science though, because it uses the Method.
More to the point, Theoretical Physics is just Mathematics, so if Mathematics isn't a Science then neither is Theoretical Physics. If Theoretical Physics isn't a Science then you're about 30 seconds from our entire conception of knowledge collapsing.
I'm sorry, it doesn't wash.
The difference with science is that your set of proofs are circumsribed by reality. You can't prove something is a valid theory without testing it against something tangible. For all the grief experimental scientists get from theoretical the thing that separates science from philosophy is that proofs need to be tested not just talked about.
Mathematics has the ability to have sets of proofs not constrained to the current universe we inhabit. It is possible to have mathematical models with no 'real' world analogue to test against.
Maths has the ability to deal with things outside that which is physical. Drop a negative apple on my head and I will place maths lower on the totem pole besides science.
This doesn't make Mathematics "not Science".Quote:
Originally Posted by Papewaio
Sure it does, it's just a tool. Refining the tool is something different than science, it's just what's at hand at the time. That mathematicians are incredibly smart doesn't change that they are making tools.Quote:
Originally Posted by Philipvs Vallindervs Calicvla
Mathematics is derived from the "current universe we inhabit", and since it doesn't add something else, it can't magically start dealing with things outside it.Quote:
Originally Posted by Papewaio
Otherwise, I'm going to need some proof to back that up. The proof in the OP, for example, very much deals with "the current universe".
Write out a Googolplex all it's zeros without using scientific notation, cut out a square of area i, pi... there isn't enough atoms in the universe to create a circle that has a circumference exactly equal to pi.
That does not make sense at all, why would atoms in any way be related to piQuote:
Originally Posted by Papewaio
So? A line has infinitely many points on it. Assign each 0 of the googolplex to a point on your line, and you can write out the number of zero's by drawing a line of length lim x->infinity = 10^(10^100)/x = 0. Infinity is a beautiful concept, especially once you realise some kinds of infinity are more infinite than others! Then you realise what you've actually done by the above definition is draw an uncountably infinite number of zeros, which is far more than was ever asked.Quote:
Originally Posted by Papewaio
You are conflating scalars and vectors (pairs). You ask to cut out a square of "left" or "right".Quote:
cut out a square of area i
There is more than enough, provided you start qualifying your dimensions first. Your problem has nothing to do with Math, everything to do with the fact that we are not able to manufacture anything to the degree of precision (infinite) which "exactly" requires. This however does not invalidate pi: in fact pi is very physically manifest in lots of ways.Quote:
pi... there isn't enough atoms in the universe to create a circle that has a circumference exactly equal to pi.
Ask Carl and his apple pi:Quote:
Originally Posted by Fragony
https://www.youtube.com/watch?v=gh4F...eature=related
Now write it out and you will run out of atoms in this universe before finishing it. It is a mathematical concept bigger then this universe.Quote:
Originally Posted by Tellos Athenaios
"You are conflating scalars and vectors (pairs). You ask to cut out a square of "left" or "right"."
Again create a physical object for an imaginary number.
"There is more than enough, provided you start qualifying your dimensions first. Your problem has nothing to do with Math, everything to do with the fact that we are not able to manufacture anything to the degree of precision (infinite) which "exactly" requires. This however does not invalidate pi: in fact pi is very physically manifest in lots of ways."
Pi goes to infinity. Number of atoms in the universe are finite. Therefore it is not possible in this universe to create a physical 1:1 accurate disc that has exactly the ratio of 2pi.r atoms in the circumference to atoms in the radius. In fact the circle really isn't a circle it's a many sided polygon which is the best approximation a finite universe can make. Much better then a triangle made of 3 atoms but just as short from infinity.
Maths isn't restricted to the physical universe as science is. Maths can be purely theoretical, science requires physical experimentation. If we stepped between one universe and another, the atoms could have different sub atomic particles, forces, gravity constant etc The science outcomes would be different as the fundamental forces would be different. Maths on the other hand wouldn't need such a frame shift.