Don't Mistake the Light for a Star

“Einstein’s Physics was exceptional but his Mathematics was pathetic” is a statement my friend made. At first it seemed baffling as to how a Physicist could possibly be poor in Mathematics. Later the same fellow told me that he himself could not come to agree with this view. As Physics involves high level Mathematics it is staggering to imagine how someone can come up with breakthroughs without adequate facility with Mathematical thinking. Put mathematical thinking in quotes and you get the answer. ‘Mathematical thinking’ is different from the subject ‘Mathematics’ as we know it.  What is the difference? 

Mathematical thinking is a way of finding out insights. It is an approach towards unravelling, conceiving or demystifying a riddle, a form or a problem. It is not exactly common sense logic. It has its rigour and its flavour. Mathematics as a subject makes use of Mathematical thinking. There are operations involved in Mathematics such as Arithmetic operations. It is quite possible for a Physicist to have conceptual insights in Physics and still struggle in Mathematics. These conceptual insights are based on aspects of the physical world. His Mathematical thinking may help him arrive at some conjectures about the physical world. When it comes to Mathematical calculations, such a person can experience difficulty as it is a matter of understanding conventions. Concepts and conventions are not the same. 

Physics attempts to explain the physical real world based on spatial elements that are unique to the subject. The spatial elements are restricted to the real world as we see it. The scope of our understanding depends on our perception and Mathematical work.  

Mathematics is abstract. Its abstraction is insulated from the real world and the implications are articulated with reference to the real world. There is free play possible because it takes you beyond the real to the conceptual and imaginary.

In physics, the physical world context takes the student in a direction which gets descriptive and theoretical. The abstraction is an articulation of insight in natural language. 

For example; ‘light’ is a natural phenomenon. It may be represented by a notation or a symbol in Mathematics. This representation is a trait of Mathematical thinking. Mathematical thinking is a form of approach different from intuitive logic. The arguments follow a ‘formal’ structure unlike those in our conversations. 

In Physics, ‘light’ is both a phenomenon and a trait. In Mathematics it could be a noumenon. A noumenon is an idea, subject or insight known without sensory perception. This means that our sensory perception can be limited and deceptive. A physicist recognizes this and uses a Mathematical approach to overcome the limitations of spatial dimensions. Granted that a light year is the distance traveled by light in one year, the star that you see may actually be dead. The light from the star may have taken several years to reach the earth. The star may have died by the time the light reaches the earth. What you see is the light of a dead star. Looks like dead stars leave impacts for us to see. Don’t mistake the light for a star.