# The essence of physics

Exams are looming, and I’ve had a constant stream of students coming to me this week asking me questions.

One question I’ve had has been asked by two students independently, relating to an example calculation done in a text book. The question goes like this: "I’ve been going through this example, and I get the answer 0.159, but the book says its 160. I don’t get it"

To be honest, I’m a bit saddened that students weren’t able to figure this one out for themselves. Experience tells me that when I am a factor of 1000 out, it’s almost always because of an issue with the units – somewhere a ‘milli-something’ or a "kilo-something" has been overlooked. It is what comes from extracting numbers from a question and putting them into the calculator without thinking about what numbers are being used. And, indeed, if the students had looked at the units the textbook answer was given in, they would have spotted that the book’s 160 mA m-1 is exactly the same as the 0.159 A m-1 the student has. (Here also we have a significant figures issue).

The students’ question says it all.."I get the answer 0.159". But 0.159 what?

Units and dimensions are fundamentally key to physics. There’s probably no other area where they are so critical. One could even say that units is what physics is all about. Describing physical quantities. Units are so important that there is a whole area of branch of physics devoted to establishing them in practical terms – metrology – and international committees dedicated to doing such boring (but essential) things as deciding on what one ampere actually means. Without this, physics will fall apart. This is one reason why lecturers like me bleat on about paying attention to the units.

## 3 Responses to “The essence of physics”

Marcus, I can empathise, I’ve just had a similar conversation with a colleague about some students approach to chemistry. My guess is that some students, the moment they see numbers, they start trying to work out what to do with them without thinking about the context.

Remembering back to when I was studying chemistry, I remember having several lecturers who were obsessive about us writing down the units and I think this was a great thing for them to do. The units can often give you a good idea as to whether you have done the right calculation.

I also have rather disturbing memories as a teaching assistant of having students reaching for their calculator to divide a number by 10, and looking shocked when I told them all they need to do was move the decimal point. An over reliance on calculators is another thing that I think gets in the way of learning about maths, physics and chemistry.

Bring back slide rules. The discipline associated with sorting out all the powers of ten before finding the significant figures on the slide rule was very grounding. in the absence of slide rules, perhaps you could set up sums as a series of single digits times 10 to whatever power, all multiplied together, to help the students learn the importance of getting units and powers of ten right.

We have the same issue in biology : concentration of a solution, area of a microscope’s field of view, transpiration rate over a plant’s surface area… I think you’re right, Mike, many students tend to treat maths rather mechanically, as a sort of ‘coping’ mechanism, & really don’t think deeply about what they’re doing. (Not helped by the fact that a lot of our bio students seem to be ‘maths refugees’!)