Since my younger years I have been fascinated with gravity. What is it … why … It feels mysterious. When I first watched Star Wars, the impact of seeing a planet with the low frequency sound rumbling in the cinema oozed power. It was like you could feel the massive planet through the screen. You could sense gravity!
As a structural engineer, it is unlikely that a working day goes by without using Newton’s second law, 
. As always, 
is force, 
mass and 
acceleration. Firstly, in structural engineering in the UK, we are mostly involved with ensuring no motion occurs. We assign the acceleration due to gravity 
to without little thought. Of course, Newton also had a law of gravitation. We are simply told:
(1) 
We then assume that as we live on a planet with mass 
and an object has mass at a distance 
from the centre of mass of the planet. Then we can equate Newton’s second law with the law of gravitation to get:
(2) 
We can then work out loads to apply in our calculations. All is good. But what has happened? Firstly, these are numbers. How are these related to forces? Of course, our concept of a force is a vector and what we have considered above is the square root of the scalar product of the vector quantities with themselves. This means we need to understand what a vector is. For this we need linear algebra and the concept of a vector space. For a vector space we need the concept of a Group and a Field. To understand Groups and Fields we need to have a grasp of Set Theory. Do all vector spaces have a scalar product defined? Then, we need to understand how manifolds allow the mapping of real world objects to mathematical space. This is before we even start on what we have assumed above …. that Interial mass is the same as gravitation mass. Then there is the matter of how can this force act instantly across space. We have not even dared to ask what a number is yet.
Whilst I practice as an Engineer, these questions have continued to burn inside of me. I am never satisfied with ‘it just does’. These writings are the result of my life long quest to learn the background to what, in my younger years, I took for granted in the drive to design steel beams and concrete frames. This is the best explanation I have for this blog in which, I hope over time, to set down some of this learning.
The starting place is Set Theory.
