Analogies

Semester has been going just over two weeks here at the University of Waikato, and I’m getting back into the swing of teaching after the summer break. One thing that struck me today, while thinking about my lectures, was how much I use analogies while teaching physics.

That’s maybe not all that surprising, since physics is full of analogies. A much used one is the similarity been water flow in a pipe and electricity. In this case the flow rate of water (litres per minute) is analogous to the electrical current (amps) – electrical current being a flow of electrical charge. And the pressure of the water (pascals, or Newtons per metre squared, or psi in old units) is analogous to the voltage.

In an electrical wire, it’s possible to have high voltage but low current (analogous to putting a very small nozzle on your hosepipe but turning on the tap maximum)  or a very low voltage but a high current (analogous to having a huge pipe driven by little pressure – kind of like a river).

There are many other examples. Back in October, a school student asked my why so many physics equations looked the same – they had the same kind of structure – despite being about different phenomena. It’s a hard question to answer. At a deep level, I would have to say it is because of an underlying order and simplicity about how the universe works.  The maths behind physical phenomena, is, at a deep level, very simple, and the same maths occurs again and again.

Theoretical physicist Paul Dirac said ‘God used beautiful mathematics in creating the universe’. Now you might argue about how the mathematics came about, but it’s hard for anyone to deny that the mathematical structure of the universe is beautiful.  (Why we find it beautiful is another question – maybe if we lived in a universe of chaos  we would find chaos beautiful). So many ‘laws’ of physics can be expressed in very simple terms (F=ma, E = m c squared, conservation of energy etc etc), and I am left wondering why God made them as they are. 

In the absence of an answer, I’ll continue to use the raft of convenient analogies in my lectures.

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