• What’s the go of that? What’s the particular go of that? (James Clerk Maxwell (1831-1879) Scottish physicist. Comments made as a child expressing his curiosity about mechanical things and physical phenomena)
• Why are things as they are and not otherwise? (Kepler (1571-1630))
• To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science. (Einstein)

# From Questioning to Understanding

BodyandSoul encourages you to be critical, to ask questions, and only accept what you can understand on rational grounds. You will find that the nature of mathematics invites to such a critical approach, because in mathematics you draw conclusions from certain assumptions using logic and symbolic or numerical computation. If the assumptions are clearly stated, and each logical and computational step is open to inspection, then it is possible to objectively check if mathematical conclusion or result is correct or not, up to the correctness of the assumptions.

In other words, you will be able to work very much like a scientist, like a critical scientist who constantlyask ther questions Why? and Why Not? You will yourself discover some of the power of this approach (andalso some of its limitations).

As a child you asked many questions, but then later in school you learned not to ask too much. In a way youshould now try to recover from this effect of your schooling and return to the questioning of your childhood.

It is not always so easy but it can be very rewarding. The Internet and the computer are at your disposal, anddo not get tired by too many questions (like maybe your teachers, friends and family) or much work,and thus can give you good answers if you can only discriminate. To learn to do so is part of the criticaltraining you can get through BodyandSoul.

You will discover that to say that you understand something of a some physical process, typically meansthat there is an underlying mathematical model with certain properties. For example, if you say thatyou understand the motion of pendulum swinging back and forth, as a repeated exchange between potential and kinetic energies, it means that you know the equations of motion of the pendulum and you can prove e.g. thatthe sum of potential and kinetic energies remains constant.

Or if you say that you understand how an ice skater can increase the spin faster by pulling the armstight into the body, it means that you know the equations of motion and the connection between spinand moment of inertia.

# Some Questions

As a mathematical scientist you should be ready ask for example, WHY is it so that

• $1+1 = 2$
• $(-1)\times (-1) = 1$
• $2+3 = 3+ 2$
• $\exp(a)\exp(b) = \exp(a+b)$
• $\log(ab) =\log (a)+\log(b)$
• $\exp(\log(a)) =a$
• $\sin(t)^2+\cos(t)^2 = 1$
• length of the perimeter of a circle of unit radius $=2\pi$
• area of a circular disc of unit radius $= \pi$
• volume of a sphere of unit radius $=\frac{4}{3}\pi$?

Maybe you already know good answers, but if you don’t know, don’t worry; you will naturally discover the answers as you go along, and answers to many more questions… Spinning quickly by decreasing the moment of inertia while keeping total angular momemntum constant. Clerk Maxwell as a child with his kind mother answering his questions: What's the go of that? What's the particular go of that?