Physics is more than applied mathematics

A problem set for potential applicants in the foyer of the Cavendish Laboratory. Despite appearances - this is not physics!

A problem set for potential applicants in the foyer of the Physics department of a premier UK university. It looks like physics, but it is in fact maths. The reason is that in the context of this problem, the string cannot pull a particle along at all unless it stretches slightly. Click the image for a larger diagram.

While accompanying my son on an Open Day in the Physics Department of a premier UK university, I was surprised and appalled to be told that Physics ‘was applied mathematics‘.

I would just like to state here for the record that Physics is not applied mathematics.

So what’s the difference exactly?

I think there are two linked, but subtly distinct, differences.

1. Physics is a science and mathematics is not.

This means that physics has an experimental aspect. In physics, it is possible to disprove a hypothesis by experiment: this cannot be done in maths.

2. Physics is about this world and mathematics is not (necessarily).

The canvas for mathematical ideas is much wider than the canvas of physics.

A small subset of mathematics seems to correspond with observable physical phenomena to a shocking extent. This we call applied mathematics. However, mathematics describes many things which don’t correspond to phenomena in this world.

Physics makes use of some mathematical ideas

The productive interplay between experiments and mathematics cannot be better illustrated than in a recent joint biography of Michael Faraday and James Clerk Maxwell.

Michael Faraday didn’t write a single equation in his whole life. Beyond arithmetic he was essentially mathematically illiterate. But he could reason with ideas and images and – most importantly – by experiments.

James Clerk Maxwell’s approach in contrast, used mathematics and experiments in a more balanced manner, but with mathematics as his especial strength.

What united them – and still unites them – is that they were both fascinated by the actuality of the physical world: in short, they both loved Physics. Their ideas – both experimental and mathematical – changed human history.

The complexity of even simple physics

My visit reminded me of the complexity of mathematical descriptions of phenomena which at first sight appear simple. And this put me in mind of a previous article I wrote on what happens when you let go of a stretched slinky spring.

I don’t mind if you don’t read the article, but do enjoy the video.

P.S. If you are interested in the stupid problem at the head of the article, you can read my detailed analysis here (pdf document).

5 Responses to “Physics is more than applied mathematics”

  1. telescoper Says:

    Reblogged this on In the Dark and commented:
    I thought rather hard before reblogging this, as I do not wish to cause any conflict between the different parts of my School – the Department of Mathematics and the Department of Physics and Astronomy!

    I don’t think I really agree that Physics is “more” than Applied Mathematics, or at least I would put it rather differently. Physics and Mathematics intersect, but there are parts of mathematics that are not physical and parts of physics that are not mathematical.

    Discuss.

    • protonsforbreakfast Says:

      Sorry for the delay in replying: somehow this slipped through my e-mail

      I think your second paragraph is right. But I think it is perfectly possible to be an excellent non-mathematical physicist. I think that physical reasoning of a non-mathematical kind is possible and some people are very good at it. However, unless such people speak up, the profession will be swamped by people who think that mathematical aspects of physics are all that matter.

      I think this is what is happening. I don’t try to knock the power or significance of maths in physics – but it needs to be balanced by physical insight and experimental ingenuity.

      M

      • telescoper Says:

        Indeed. Michael Faraday was a great physicist, but knew hardly any mathematics at all…

  2. Paul Stevenson Says:

    Which University is this “premier UK university,” the analysis of whose problem you have linked to in your file named cambridge-physics-question.pdf?

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