Ode To Calculus

 The next few posts will be a tribute to mathematics or more strictly the branches of maths that are useful to physicists. For physicists as a whole mathematics is secondary to nature. It is a moot question whether maths is discovered or created. I tend to the view that it is essentially created which no doubt will surprise people after all I am a scientitst and I use mathematics every day and it works so it must be true. Well to some extent, but mathematics can only ever provide a good approximation to an underlying reality. Anyone who has solved a differential equation will know that of all the possible solutions only one will represent the reality that one is trying to model. Certainly it is amazing how given a few basic facts about the world mathematics can extend the relationships and maybe even uncover relatiohnships that we didn't think were there. Maxwell's equations for example. 

But let's not get carried away there are certain constraints on the world. Signals cannot travel faster than the speed of light, there are only 4 space time dimensions, there is only one universe. Any theory such as superstrings or the many worlds interpretation of quantum mechanics which contradict those basic facts is just fantasy and should be called out as such.Also no amount of mathematical reasoning will explain why the Gravitational coupling constant is what it is or the mass of the electron or any fundamental particle. These are givens and any mathematics which claims otherwise is just over reaching itself. There is no need to invoke as some people do God or the anthtopic principle to explain why the world is the way it is, ii just is. Of course once we know some basic facts we can use mathematics to deduce inter-relationships between those facts and that is amazing. One of the reasons it works so well is that nature is approximately linear and calculus exploirs this linearity

Without the invention (discovery) if you prefer of calculus there would be no explanation of the world as it is.  As it was when  Newton and Leibniz invented calculus the laws of motion were explained and the fact that planets moved in ellipses was also deduced thus being one of the greatest intellectual achievements of mankind. The Open university used to include a couple of units in the old course MST209 which has been superseded by MST210 from which this has been dropped. I think that is a pity if anyone reading this blog would like a copy of the missing units please contact me on 

chrisf19572002@yahoo.co.uk 

as it is one of the greatest intellectual achievements of mankind. If you want to understand how physics works then you really must learn some calculus I think it a shame that the currrent Open university course in physics S217 minimizes the use of calculus in it's units. It is often claimed by Arts students that you are ignorant if you haven't read a certain book or watched say a certain Shakespeare play, Well conversely I would argue that if you don't know calculus to at least A level maths and why physicists use it to explain how nature works you are equally just as ignorant. Anyway here is my tribute to one of the greatest inventions of mathematics 

Calculus

You explain how nature works,

It’s a task we should not shirk.

Integration and Differentiation

Gives me such exhiliration¹⁾

 

All the laws of motion,

Are explained without commotion.

When we’ve mastered you,

There is so much we can do.

 

1)    I realise not everyone feels the same way J