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Mathematics
ThailandTom
Veteran
Mathematics seems to be a universal language, wherever you go in the world numbes do not change. You can take 2 objects and put them next to another 2 objects and have 4 objects. This is evident. I was thinking however that when you get in to the really intricate equations used in physics today, can this math be trusted? I am ignorant to it obviously as I do not have the ability to understand it, but is math something we have invented, thus could have some flaws, or is it something that we found that exists in its own way so to speak.
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http://www.homeschoolmath.net/teaching/fibonacci_golden_section.php
2. Yep. For a whole 12 year education (elementary+middle+high school) , 2+2 = 4. Once you get in the 'darker' corners of elementary maths, you'll see algorithms that will prove, somehow that 1 = 0 ( I don't know, but I saw in my 12 grade maths manual one problem that asked me to demonstrate that 1=0 using Boolean Rings).
3. Math and physics have a reaaaally close relationship. Math is the support pillar of physics.
4. Math is an 'exact science' , meaning that , let's say 2x=4 => x=2. Why doesn't this 'x' equal 1,5 ?? ( get it ??)
My question or intention of making this thread was that is math manmade or is it something we have discovered that is a law if you will, and I think you have answered that so thanks
The thing that is manmade is the number system we use (decimal system, counting in groups of 10), but the mathematical formulas themselves will hold everywhere in the universe. They need no experimental proof because they are their own proof.
Maths was discovered by man, when he observed that 'quantity matters' ( in a large sense), and that his many aspects of life (we are talking about neolithic age here) were dictated by how much resources he had. By managing the quantity of resources , man discovered the basic maths operations ( +, - , * , : ). After years of managing resources and such, he discovered other aspects, like geometry, by which, he could prove ( even in Pythagora's and Euclid's time) that maths is an 'exact science' ( take the example of Pythagora's golden numbers ).
Can this math be trusted to describe reality?
If you want to describe something you need a language. I could say if i throw something in the air it comes down. Better would be it comes down and the height difference between two following points in time is increasing.The best way to describe it is: h(t) = h0 - 1/2*g*t*t. In my language explanation i already used the words difference, two and increasing which are all mathematical concepts.
Physics looks at things and then tries do describe the behaviour. Physics uses mathematics as language because it is very precise. There is no room for interpretation.
Once we have a mathematical model for the observed behaviour we can start to push it a little further. What does the equation give us if we put values in it we have not observed? The predicted results maybe or maybe not observerd in further experiments.
If the predictions are observed its a good model if not its not
There is no place for trust in this. Either the model describes the behaviour correct or not.
If its a good model or not, the description of something is not to be confused with the something. Physics is not reality, it just describes it. Models are templates which are put over reality.
One famous example of a mathematical theory with, yet, no observed predictions is string theory. A very complex mathematical model where the behaviour of the known particles is created by strings. Right now we dont know if there is anything to these strings or not many people believe there is. We have to wait until experiments show it.