December 28, 2009

Popular Maths

Christmas is over, and a lot of us are presumably already enjoying our new presents. For me, no Christmas is complete without getting at least a couple of books, a present I always welcome. Lest I should sound like a total dweeb, I'd like to point out that I also wished for, and received, more standard presents. Still, a geek is a geek, and if you have followed my blog thus far -- or if you've had a peek at the 'About Me' section -- you may not be surprised to hear that I'm often given books discussing mathematical topics.

This year, however, I explicitly stated that I did not wish for any such books.

The reasons are twofold: First, it is a lot easier for me to decide which books are interesting and at the right level, and which books are too dull or too trivial. Additionally that means I can buy them second-hand, which saves money as well as paper. It is the second reason, though, that I want to focus on in this post. It may sound odd, but the majority of popular maths books that could potentially be a Christmas present, do not in fact target mathematicians like myself. Rather, they are meant to be enjoyed as gentle introductions to certain maths-related topics, to people whose main area of expertise is not maths. An appetizer, if you will. So whenever Iget one of these books, I always feel a little sad that whoever bought the book for me, did not buy it for him- or herself. 

Popular science books (books on popular science), such as Richard Dawkins' 'The Selfish Gene' and Bill Bryson's 'A Short History of Nearly Everything, are cropping up everywhere. Likewise, there are also plenty of popular maths books out there, some of which have received considerable attention and praise from the general public. Ian Stewart is worth mentioning in this context due to the popularity and success of his popular maths books, ranging from the serious, but still accessible, works ('Does God Play Dice', 'Letters to a Young Mathematician') to the more playful ones ('Professor Stewart's Cabinet of Mathematical Curiosities', 'Math Hysteria'). Then there are books which explore presents one concept in detail, but in layman terms (like 'Imagining numbers', 'Fermat's Last Theorem'), books which explore a wide range of topics on a superficial level (like "Why Do Buses Come In Threes?' or 'How to Cut A Cake'), books which give a brief introduction to maths in general ('Introduction to Mathematics'), and so on.  Not to mention the somewhat childish yet extremely enjoyable 'Murderous Maths' series. I have read many of these, and always find them agreeable to read, but when I'm confronted for the 55th time with a detailed presentation of the golden ratio, I can't help thinking: I shouldn't be the one reading this.

Stephen Hawking writes in 'A Brief History of Time':

Someone told me that each equation I included in the book would halve the sales

Most popular maths books are therefore written in an informal style and contains as few equations as possible, so as not to scare the reader. In fact, this is the main feature that distinguishes a popular maths book from a standard maths book. The author usually takes care not to lose the reader in his reasoning, and it is these clear explanations that sometimes make me realise: someone else should read this. I think this is where the problem lies. People think that any kind of maths is beyond them, and that they will never be able to understand or appreciate it. They think that what lies between the covers of those books is an inaccessible world, when in fact the content of such books is not the 'real' maths that university students are being taught, but a modified version of it, specifically designed to be understood by the non-specialist. My Algebra lecture notes are an example of a text that requires a certain degree of mathematical ability to read; 'How To Cut A Cake' isn't.

Please, come visit Mount Maths. It's a little lonely up here. But the view is incredible.


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  1. Sue

    Though my daughter is a mathematician, she never romantises or mystifies maths. I’m not completely sure whether this is because she doesn’t find it romantic or mystical or whether she prefers to look at it as an old friend who has no “side” to him. I think she thinks that everyone is a mathematician, she’s certainly convinced that there is one lurking inside me – maybe she just doesn’t want to be lonely on top of the mountain. For Christmas she gave me a book of mathematical poetry and I gave her a mathematical bracelet – I saw it and thought of her. If you like I’ll share some of the poems on here.

    29 Dec 2009, 00:42

  2. Sue

    There is one that I particularly like and I’ve found myself reading it over and over again as it’s so magical. Here it is:- Against the Text Philosophia Biou Kubernetes (Philosophy the Guide of Life)

    Prothalamion of Quantum Mechanics and Astrophysics

    Part 1: The Stutter of Quanta

    It is impossible. The Uncertainty Principle
    is Planck’s Constant, 6.624 (or 5) times 10 -27
    divided by two pis or more, more.
    It is ridiculous, I am approximate,
    we are either always flying apart and getting larger or getting too close together in too small a way.
    The intrusion of my gross instrument
    distorts my knowledge of exactly
    where you’re at, you are so moving,
    of exactly how you’re moving where you’re at.
    Oh I can know your position but not
    your velocity, your velocity but not your position,
    and your position changes every time you make a motion.
    You have to make a motion to take a position in this matter
    and your position changes every time
    you make a motion and your motions change,
    and you are always taking up positions on my instrument
    and making motions. I think
    that you turn on and off.
    You turn me off and on.
    You part your wave
    and wave your thing
    at me.
    You part your thing
    at me
    and wave your part.

    You part your part
    and wave your wave
    at me.
    You wave and part
    and part and wave
    your thing and part,
    waving,
    at me.

    I withdraw inconsummate
    if you are approximate,
    I am empty, I
    am in val-
    id, I represent no
    knowable abstraction if
    I love you only because
    you have no definite figure.
    My love is incomplete in theory.
    My love is uncertain in principle.
    Whether you matter or
    do not matter, whether
    you are real or false,
    I either love or am the law.
    Therefore I will be as constant
    as Max Planck’s Constant is constant,
    though didvided in this farce
    by two pis or more, more.

    29 Dec 2009, 11:37

  3. Sue

    Part 2: Dierge/Scherzo but know that you’re
    not sensible and that
    you have a cloudy past,
    no definite figure,
    and are infinitely multiple,
    divisibly eternally,
    but you are everything to me
    so I want all of you
    to be (Please be)
    (considered as) my only one,
    I want all of you
    to be my only one.

    In dreams I think
    you are behaving like
    my model universe

    What can I say as we go away
    from one another, you and I,
    except that I am not thoughtful,
    that I am insensitive and imperceptive.
    I don’t even know if I could hope
    that you and I could get together again,
    or else slow down and find stability,
    or simply go awat forever, fast,
    and leave me saying empty verse
    out to an emptying universe:

    Oh I don’t know where you’re going,
    I don’t know where you’re at.
    I don’t know where you come from
    or if you’re coming back,
    so tell me how I love you.

    29 Dec 2009, 11:45

  4. Sue

    Part 3: Antennae of Astrophysics and The End of Optics

    I hear you after I see your light
    and see you after I feel your stroke.
    How you come on and then go off
    without a sound, and then the sound
    sounds. What struck me first,
    and in the afterlight, and then,
    when the noise came later, was
    that touch, sounds and lights
    must move at various speeds,
    but speeds, and light is slow, slow:
    we never see each other now,
    but see each other either long
    or just a little while ago,

    so we live in one another’s pasts,
    you and I, and go into our own
    futures all alone. We are always
    moving apart and getting larger
    and looking smaller, you in your
    beautiful red shift, and me,
    bug-eyed, observatory, shelled,
    waving my antennae out at you
    and flying away. I have my doubts
    that I’m your metamorphic worm,
    yolked in your egg of unknowability
    and flying timewise to be born or burned.

    29 Dec 2009, 11:54

  5. Thank you Sue, that’ll do. Could you tell me what book this is from?

    29 Dec 2009, 12:11

  6. Sue

    You sound like my son, he’s always saying “That’ll do now, Sue”. It’s called “darkmatter” POEMS OF SPACE.

    29 Dec 2009, 16:15

  7. Nick O'Doherty

    You might like Men of Mathematics by E T Bell. Written a while back by a mathematician. It is primarily about the mathematicians, their maths is thrown almost in passing, but it is written for mathematicians.

    18 Jan 2010, 16:26

  8. Sue

    Ironically, I’ve learnt a great deal from times when I’ve made late connections or misconstrued the meaning of things. My partner once spent a whole summer in Margate (his auntie had a guest house there) asking for “Zup” instead of “7 Up”. He openly admits this now.

    24 Jan 2010, 14:31

  9. @ Nick: Ooh, that sounds interesting! Thanks for that!

    01 Feb 2010, 23:15


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