100 Years of Feynman

Today marks the centenary of the birth of Noble Prize-winning physicist, science communicator and bongo player Richard Feyman. It’s great to see so many articles about him today, so I was wondering how to do my own quick tribute before I head to London for the Royal Astronomical Society Annual General Meeting this afternoon.

With university exams coming up it seemed a good idea to celebrate Richard Feynman’s legacy by combining todays 100th anniversary with some tips (inspired by Feynman) about how to tackle physics problems, not only in terms of how to solve them but also how to present the answer in an appropriate way.

Richard-Feynman-cornellI began with Richard Feynman’s formula (the geezer in the above picture) for solving physics problems:

  1. Write down the problem.
  2. Think very hard.
  3. Write down the answer.

That may seem either arrogant or facetious, or just a bit of a joke, but that’s really just the middle bit. Feynman’s advice on points 1 and 3 is absolutely spot on and worth repeating many times to an audience of physics students.

I’m a throwback to an older style of school education when the approach to solving unseen mathematical or scientific problems was emphasized much more than it is now. Nowadays much more detailed instructions are given in School examinations than in my day, often to the extent that students  are only required to fill in blanks in a solution that has already been mapped out.

I find that many, particularly first-year, students struggle when confronted with a problem with nothing but a blank sheet of paper to write the solution on. The biggest problem we face in physics education, in my view, is not the lack of mathematical skill or background scientific knowledge needed to perform calculations, but a lack of experience of how to set the problem up in the first place and a consequent uncertainty about, or even fear of, how to start. I call this “blank paper syndrome”.

In this context, Feynman’s advice is the key to the first step of solving a problem. When I give tips to students I usually make the first step a bit more general, however. It’s important to read the question too. The key point is to write down the information given in the question and then try to think how it might be connected to the answer. To start with, define appropriate symbols and draw relevant diagrams. Also write down what you’re expected to prove or calculate and what physics might relate that to the information given.

The middle step is more difficult and often relies on flair or the ability to engage in lateral thinking, which some people do more easily than others, but that does not mean it can’t be nurtured.  The key part is to look at what you wrote down in the first step, and then apply your little grey cells to teasing out – with the aid of your physics knowledge – things that can lead you to the answer, perhaps via some intermediate quantities not given directly in the question. This is the part where some students get stuck and what one often finds is an impenetrable jumble of mathematical symbols  swirling around randomly on the page. The process of problem solving is not always linear. Sometimes it helps to work back a little from the answer you are expected to prove before you can return to the beginning and find a way forward.

Everyone gets stuck sometimes, but you can do yourself a big favour by at least putting some words in amongst the algebra to explain what it is you were attempting to do. That way, even if you get it wrong, you can be given some credit for having an idea of what direction you were thinking of travelling.

The last of Feynman’s steps  is also important. I lost count of the coursework attempts I marked this week in which the student got almost to the end, but didn’t finish with a clear statement of the answer to the question posed and just left a formula dangling.  Perhaps it’s because the students might have forgotten what they started out trying to do, but it seems very curious to me to get so far into a solution without making absolutely sure you score the points.  IHaving done all the hard work, you should learn to savour the finale in which you write “Therefore the answer is…” or “This proves the required result”. Scripts that don’t do this are like detective stories missing the last few pages in which the name of the murderer is finally revealed.

So, putting all these together, here are the three tips I gave to my undergraduate students this morning.

  1. Read the question! Some students give solutions to problems other than that which is posed. Make sure you read the question carefully. A good habit to get into is first to translate everything given in the question into mathematical form and define any variables you need right at the outset. Also drawing a diagram helps a lot in visualizing the situation, especially helping to elucidate any relevant symmetries.
  2. Remember to explain your reasoning when doing a mathematical solution. Sometimes it is very difficult to understand what students are trying to do from the maths alone, which makes it difficult to give partial credit if they are trying to the right thing but just make, e.g., a sign error.
  3.  Finish your solution appropriately by stating the answer clearly (and, where relevant, in correct units). Do not let your solution fizzle out – make sure the marker knows you have reached the end and that you have done what was requested. In other words, finish with a flourish!

There are other tips I might add – such as checking answers by doing the numerical parts at least twice on your calculator and thinking about whether the order-of-magnitude of the answer is physically reasonable – but these are minor compared to the overall strategy.

And another thing is not to be discouraged if you find physics problems difficult. Never give up without a fight. It’s only by trying difficult things that you can improve your ability by learning from your mistakes. It’s not the job of a physics lecturer to make physics seem easy but to encourage you to believe that you can do things that are difficult!

 

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16 Responses to “100 Years of Feynman”

  1. Dipak Munshi Says:

    As an undergraduate, we had two set of books Feynman’s lecture of
    Physics and Landau & Lifshiz A course of theoretical physics.

    However, not much is known about Landau except his death and
    the car crash. I read so much about Feynman which gives a very accurate idea of his personality. Not as much is known though about
    Landau as he worked from behind the iron curtain.

    Life of these two great scientists provide an interesting
    idea about the interplay between science and society.

    There are many quotes (and equations) by Feynman,
    but the one I want my daughter to remember for
    the rest of her life is the one below:

    “You have no responsibility to live up to what other people think you ought to accomplish. I have no responsibility to be like they expect me to be. It’s their mistake, not my failing.” R.P.Feynman

    • Anton Garrett Says:

      Much is known about Lev Davidovich Landau. 30 years ago I wrote a biographical sketch of him for the Australian version of Physics World (UK) / Physics Today (USA), and I had plenty of material to draw upon. At least two major biographies of him have been published since. I can give you the references if you wish.

      • Dipak Munshi Says:

        If you publish the articles and put the references here it may be
        useful to others too. I am sure Landau’s work is well known to the scientists but I don’t think he is as well known as Feynman. Many think Silk damping should Landau-Silk damping and Raychoudhury equation should have been Landau-Raychoudhury equation. Maybe you will do a blog on Landau sometime too – not just about his science but about his social/religious/political views.

      • Anton Garrett Says:

        If Peter gives me a guest column then I’ll gladly do a post about Landau by updating and shortening the article I wrote while a postdoc at Sydney, including the facets of his life you request, and including the references.

      • telescoper Says:

        Yes, please send and I’ll post it.

  2. In a book by Cliff Stoll, he quotes “10 rules of chess” he had seen somewhere. Nr, 2 was “Always make the best move.” Does one really need the others?

  3. The shocking thing about this is that I remember when Feynman died, and I remember thinking he died much too young. How can he have been born 100 years ago? But I looked it up and it is indeed over 30 years since his death.

    • Asimov once wrote an essay where he compared various timescales to a year. (This is in general very interesting. Imagine that the history of the Earth is one year. When did dinosaurs appear? How long did they last? Ditto for humans.) One timespan was the history of the United States. When writing, he exclaimed that he remembered D-Day as if it were yesterday and was astounded that the equivalent of a month (i.e. a a twelfth of the age of the USA) had passed between D-Day and writing the essay.

      • Last year was the hundredth anniversary of the birth of Papa John Creach, arguably the earliest-born rock musician. (“Papa” comes from being older than his rock-music colleagues, but in the mid-1970s Creach was not yet 60, which these days isn’t that old for a rock musician. Ringo Starr will be 80 in a couple of years.)

        It depends on the definition, of course, but the highest age at which a rock musician has performed is a prize probably claimed by John Mayall, born in 1933 and still recording and playing live.

        Tempus fugit. Ars longa, vita brevis. Memento mori.

      • Anton Garrett Says:

        I saw John Mayall live last year!

  4. Shantanu Says:

    His greatest contribution to Astronomy is his solving the mystery of the challenger accident. Note sure HST would have been launched (when it was) had the cause of the challenger accident not been found. Its such a tragedy that Dick Feynman did not love long enough to witness the discovery of the accelerating universe

    • Anton Garrett Says:

      It was no mystery. The engineers at Morton Thiokol, under pressure from NASA to launch, told them that the O-rings would be OK at the much lower temperature experienced that day. One of these men told his wife the night before that Challenger would blow up, and when it did those engineers knew instantly what had gone wrong. See the Wikipedia article on the incident:

      https://en.wikipedia.org/wiki/Space_Shuttle_Challenger_disaster

  5. […] couple of months ago a comment appeared (on a post about Richard Feynman) that said `not so much is known about Landau’. That was […]

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