Man Must Measure

It just appeared one day, out of nowhere, on the desk by the bedroom window. I picked it up and looked at it. It was a big book with not many pages in it, and with an arresting title in big black letters on the front, which read: MAN MUST MEASURE.

I must have been 7 or 8 years old, and I was living with my mother in my grandparent’s house when I drank in those words, which seemed to possess the force of a veritable Commandment.

I opened it, and discovered that it was both lavishly illustrated and also filled with numbers and diagrams. It was the strangest and most terrifying book I had ever encountered.

I began to read the book, a little fearful that I wasn’t supposed to be reading it. Much of it seemed incomprehensible, but on the third or fourth page I came across this:

I studied the picture on the right very closely. What on earth were they doing? What were those strange lines in the sand? Little by little, I gradually understood that they were marking out the corner of a pyramid, and the semi-circular lines drawn in the sand were what they used to make the corner exactly square. They drew the lines in the sand, and then they drove stakes into the lines, and finally they brought rectangular stones and fitted them next to the stakes.

I tried it out for myself. My grandfather had an old compass somewhere, which he unearthed for me, and fitted a pencil into. And with these and a ruler I was soon drawing right angles (although for the life of me I couldn’t see what was “right” about them).

Deeper still in the book, I came across another drawing full of semi-circles:

With my grandfather’s compass, I soon replicated this too.

It was an astonishing book, full of astonishing things of a kind that I had never imagined before. It was a book about mathematics and numbers and geometry. It included a demonstration of the Theorem of Pythagoras (which was entirely beyond my comprehension), sextants, clocks, candles, a map of the city of Alexandria, and even a brief history of the world – all in just 70 pages.

I spent hours reading the book, until one day, just as suddenly as it had appeared, it vanished.

But I never forgot it. I never forgot its single Commandment. I wasn’t quite sure why Man had to Measure, but the tremendous power of the book nevertheless impressed that message upon me ineradicably. It’s one reason why, right now, my principal objection to antismoking pseudoscience is that nothing is measured accurately: they’re drawing pictures with stretchy rulers and bendy compasses.

Man Must Measure was one of the formative books of my childhood. It was certainly the strangest and most terrifying book. And three or four years later, at school, when we were taught geometry, I found that I knew half of it already.

And so when I found a secondhand copy online a couple of months ago, priced £19.87, I bought it immediately, surprised that it was so cheap. It remains a brilliant book, even though it’s 60 years old. It does something that most dry, abstract, mathematical textbooks always fail to do: it brings numbers and geometry to life. And it does it by marrying art to mathematics, and showing how to do it.

So I would thoroughly recommend anyone to buy a copy, if only as an investment. I would have happily paid 10 times that amount for it. It hasn’t dated very much either, although the drawing whose caption reads, “Japanese businessmen use the abacus with great skill,” is undoubtedly incorrect. It was probably true in 1955, but I rather suspect that most Japanese businessmen haven’t the first clue how to use an abacus these days.

But if you do buy one, then you must find a boy or girl of about 8 years of age, and arrange for the book to be left on a table in their bedroom for a few weeks. And you might also take the precaution of providing the parents with a compass and a ruler as well. And when you come back to retrieve the book, and you learn that the child has been asking for compasses and rulers, you will know that you have successfully cast the spell of mathematics upon another receptive mind.

About Frank Davis

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30 Responses to Man Must Measure

  1. lysistratatheoriginal says:

    Fantastic, Frank! My granddaughter is just 13, so maybe not yet too old to leave a copy around for her to find when she comes to stay….

    And I don’t know which I find worst: the emotional/moral repugnance I feel at the smoking ban, or the intellectual despair at their manipulated surveys and just WRONG crap measurements to support their false analyses. And not just about smoking.

    I want my granddaughter to grow up to be a proper scientist and an engineer – not necessarily as a career – just as a way of true thinking and living and responding to the world.

    • Frank Davis says:

      Yes, buy one! Buy one!! There are only about 10 of them left in the world.

      And even if your granddaughter doesn’t pick up on it, then maybe your next door neighbour’s little boy will.

      In my small view, this is one of the most brilliant books ever written/drawn.

  2. Marvin says:

    Apparantly Frank, it’s not uncommon for us older guys to go back and recapture a significant childhood experience.
    You, with your ‘Man Must Measure’ book and me with a one valve radio, I built when I was 11 years old.

    My father bought me the radio as a kit, but first I had to learn how to solder and also the resistor colour codes etc.
    The radio worked perfectly, first time, but being only 11 years old, I had absolutely no idea HOW it worked, it was just something “magical”.

    I needed to know !!!

    So I decided, if I could get all the parts together, I will build the radio again.
    After a few months searching the Internet, I managed to obtain all the original parts I needed.
    Now, with 50 years experience and armed with modern test equipment, I finally understand what is going on inside the valve.

    It’s a very satisfying experience, as I’m sure you would know.

  3. Lars Folmann says:

    I remember that book from my childhood home, just in a danish translation. I spend many hours studying it.

  4. harleyrider1978 says:


    Roll-your-own cigarette operations to be snuffed out nationwide tonight by Obama

    Posted: Jul. 6, 2012 | 2:01 a.m.
    Updated: Jul. 6, 2012 | 10:42 a.m.
    A tiny amendment buried in the federal transportation bill to be signed today by President Barack Obama will put operators of roll-your-own cigarette operations in Las Vegas and nationwide out of business at midnight.

    Robert Weissen, with his brothers and other partners, own nine Sin City Cigarette Factory locations in Southern Nevada, including six in Las Vegas, and one in Hawaii. He said when the bill is signed their only choice is to turn off their 20 RYO Filling Station machines and lay off more than 40 employees.

    • harleyrider1978 says:

      But a few paragraphs added to the transportation bill changed the definition of a cigarette manufacturer to cover thousands of roll-your-own operations nationwide. The move, backed by major tobacco companies, is aimed at boosting tax revenues

      • churchmouse says:

        Sad news, indeed, harleyrider. End result will be that people start buying a smaller RYO machine and tubes for home use. What do you think?

        • smokervoter says:

          On the RYO amendment.

          Harley, thanks for pointing this out. You really do a great job of keeping us all informed.

          This is the kind of thing which causes my relaxed hand to become a raging mad fist. Max Baucus must be voted out of office for this. Montana is the kind of state with an average smoking prevalence and a small population base in which smokers can and should exercise their power.

          There was a terrific comment from someone in Nevada who quoted Sam Adams thusly “It does not take a majority to prevail….but rather an irate, tireless minority, keen on setting brushfires of freedom in the minds of men.” — Samuel Adams

          A lot of horrid anti-capitalist devils are at work here. Baucus, who carried the water for ObamaCare, the tobacco companies who backed this and the turncoat ex-smoker-in-chief himself.

          These RYO shops were one of the craftiest free market solutions to come along in a long time, a win-win for everyone involved. So far, I’d never encountered one in my home town. I was hoping someone would start one up here.

          I’ve been rolling my own with the filter tubes and a small blue Rizla machine for five years now and I doubt if I’d go back to tailormades even if they dropped the price to competitive levels.

          Ron Paul got 15% of the Republican primary vote in Montana which was 34% higher than his usual 11.2% result and he came in a strong second place. Maybe we can get a combo of smokers and Paulites to run this bastard out of office in 2014.

          He won by 73%-27% in 2008 but they almost ran the SOB out in 1996. They need a strong Republican challenger next time around. I despise this filthy career politician after reading the Wiki page on him. And I despise the tobacco companies that back this amendment.

  5. gimper30 says:

    Man Must Measure….One used (no new) copy on Price: $203 US……Wow!!!!!

  6. c777 says:

    I’m building a patio a the moment one of the hundreds of things I have engineered constructed or built .
    Amazes me how the technique has changed little over millennia ,the nack is to built a pad of sand with inclined sides level off the top then place the next slab or blocks.
    Pyramid building in miniature.
    What have I designed, created, over the years,structures to build brides, electric vehicles, test rigs for high performance engines cable winding machines and many more!
    Now networks and systems.
    Mathematics and measurement are the steeping stones to creating and building.
    Here’s the punch line.
    ASH ,watermelons and the rest of the quacks can only try to pull down and destroy the labours of the good that have taken millennia to create
    Any fool can wreck or destroy the real good people build and create.

  7. beobrigitte says:

    Great post! It does remind me of my last pre-school “holiday” being parked with an aunt and uncle who didn’t have children. (My parents had a brilliant sense of humour!)
    Being pretty bored, I did scout around my uncles little library and found some heavy book with “loads of pictures” in it. My aunt immediately noticed the quietness in the house and it did not take her long to find me and, to my surprise, she did allow me to continue my “reading”. Indeed, there were pictures in this book similar to the above ones and just HAD to try one or two examples, so I went outside, found a stick and began to edge an (imperfect!) circle in the middle of their well-maintained lawn. It did not take my aunt long to find me and just after she finished with her “hair-dryer” impression, my uncle came home from work. He didn’t say much but issued me with chalk and string, and told me to use the road. Unfortunately the (imperfect) circles, half-circles and lines were visible to the neigbourhood for weeks after until it finally rained.

    It would seem that nowadays children do not have the option to be “bored”, nor the ability to look themselves for entertainment. Mummy and Daddy are doing this for them, just in case there is some form of, most often imaginative, danger lurking somewhere. To me it seems that these children are in danger of becoming adults who do not have the ability to ask questions and find answers/solutions for themselves.

  8. nisakiman says:

    “…I rather suspect that most Japanese businessmen haven’t the first clue how to use an abacus these days.”

    Don’t bet on it, Frank. In the back streets of Chinatown in Bangkok it’s not unusual at all to see the (older) Chinese business owner rattling away on an abacus. At lightning speed, I might add. So I wouldn’t be surprised if some of the older generation in Japan are more comfortable with the abacus they know and trust rather than with an electronic calculator.

  9. harleyrider1978 says:

    Bank Aid 1930s Stimulus bank aid 2010 both failures


    Brooklyn Daily Eagle
    Tuesday, Oct. 29, 1929

    The front page banner headline says it all: “BANK AID FAILS IN STOCK DUMPING.” Secondary headline screams: “8,370,000 SHARES SOLD BY NOON AS HYSTERIA REIGNS.” The story begins: “Stocks crashed again today under another wave of panicky selling, a wave that has never before been equalled. Thousands of shares were dumped overboard in blocks and the market was completely demoralized.” This issue also publishes the losses of the largest U.S. companies like American Telephone, General Motors and others.

    The most famous day in stock market history, “Black Tuesday,” took place 75 years ago on October 29th, 1929. It is often thought of as the day that sent the United States into the Great Depression. By the end of the day, some 16.4 million shares had traded, fortunes were lost, and the Roaring Twenties came to an abrupt halt. Stock prices didn’t recover to pre-1929 levels until 1954!

    I rarely am able to locate even a single Stock Market Crash newspaper from 1929, so it came as a surprise when this issue found its way into our inventory. It’s the complete newspaper in very good condition with some minor chipping at the right margin affecting a few letters. I would absolutely have this professionally framed for my office or boardroom. It shouldn’t last long.


  10. Junican says:


    Why don’t you scan it and publish it as a separate page here? It must be way out of copyright.

    • Frank Davis says:

      I was thinking about this possibility last night. I don’t know what copyright rules are. It was published in 1955.

      Main problem is that the book is bigger than my scanner, so pages would have to be knitted together from 2 scans, which would be a big chore with 70 pages.

      • The Man With Many Chins says:

        Frank, I think copyright duration is 70 years after the death of the author, or if its an arrangement with no specific author, 25 years after the last edition.

        Was it published in the UK or the US?

        • Frank Davis says:

          My copy was published in the UK by Rathbone books in 1955. The author’s name was Lancelot Hogben, but there are several artists who illustrated it as well.

  11. churchmouse says:

    From Stanton Glantz’s blog — NY town wants tobacco display ban (emphases mine). NB – he misspells ‘Haverstraw’ in the blog post ;) :

    Submitted by sglantz on Thu, 2012-06-28 15:45

    Haverstraw, NY, (population 12,000) has passed the first-in-the-nation tobacco product display restriction enacted in April. This is an important development because it represents the first such effort by a local government under the authority returned to them by the Family Smoking Prevention and Tobacco Control Act.

    As we have learned so well from the progress made on smokefree environments, small communities led the way. Their successes and the precedents they created beginning in the early 1980s laid the groundwork for all the progress since then. As a result, it is very important for Kaverstraw to succeed.

    Unfortunately, Big Tobacco understands the importance of precedent even better than the public health community and has ganged up on this very small village with a lawsuit filed by 7 tobacco companies and the New York State Convenience Store Association. (Here is their press release announcing the suit.) …

    … if the communities have the wherewithal to defend themselves, they usually win. The other good news is that — unlike smoking and health litigation — is that these cases are not all that expensive to defend. The issues are purely legal, so there is not extensive (and expensive) discovery. When we asked city attorneys what it cost to defend challenges of clean indoor air laws, they said it was about like a heavily contested zoning decision. …

    A news story on the law suit quotes Maureen Kenney, director of POW’R Against Tobacco, as saying that, “The Center for Public Health and Tobacco Policy out of
    New England Law in Boston will be reviewing the complaint and providing the village with educational information.”

    I am glad to see that public health advocates outside Haverstraw are coming to its aid and urge state and national organizations to join in supporting Haverstraw as well.

    This is a critical time for state and national organizations to provide appropriate support the town’s legal defense (including if needed amicus briefs and even direct legal assistance) and shine a light on the insidious behavior of the tobacco industry as they once again, throw their weight around and pick on the ‘little guys’ as they work to protect the health of their youth.

    If you are interested in helping, contact Maureen Kenney, who is coordinating support for Haverstraw:

    Maureen Kenney| Director | POW’R
    Against Tobacco
    American Lung Association of the Northeast
    White Plains, NY | Hauppauge, NY | Waltham, MA
    237 Mamaroneck Ave, Suite 205, White Plains, NY 10605
    914.347.2094 X15 | |

  12. Scot says:

    I take it you didn’t do Technical Drawing at school Frank?

    The old school drawing board, set squares and compasses?

    I did it twice, passed my “O” Grade, then failed the Higher, but they gave me a complimentary 2nd “O” Grade…

    I still use it as an extra qualification in job apps etc, so it did have its uses!

  13. smokervoter says:

    This book looks terrific, I love old-school knowledge. Is there a section on finding level by use of a ‘water level’? By that I don’t mean a four foot water level or spirit level. I mean a container of water with a long section of clear plastic tubing hooked up to it. They’re deadly accurate. I’ve been using them for building things since 1978.

    Using mine, I double-check the accuracy of foundation forms done with transit-levels before the concrete pour and have detected treacherous errors. Nowadays all the lamebrain young builders swear by their $1000 a pop lasers. Water seeks its own level.

    Mine cost about $15.

  14. Pingback: What Is Science? | Frank Davis

  15. P Manning says:

    Probably the single most formative life changing book I have ever read. I read it at 6 or 7yrs old. I read it every day at school for as long as I could, or more, for months. I was besotted with it. I couldn`t wait to open it.
    Today I am an optician who likes art, deserts and bricklaying.

  16. Pingback: Stock Market Crash Of 1929

  17. Reblogged this on My '3D Metric' Universe… and commented:
    Woman must measure, too! Especially on-screen!!!…

  18. thonyc says:

    I realise that this blog post is six years old but I have only just discovered it. I was considerably younger when I first came across Man Must Measure in our children’s book cupboard (I come from a heavy weight book reading family). I assume it had been bought for my elder brother, who was six years older than me. I was totally fascinated by this book and soaked it up like a sponge. I sometimes wonder if it played a role in my becoming a historian of mathematics!

    • Frank Davis says:

      I didn’t know there were historians of mathematics. But if the book had the same effect on you as it did on me, I can well imagine that you would have seen that there was a very long history of mathematics.

  19. Graeme Bond says:

    I just discovered this blog when I went looking to see if I could buy a copy of Man Must Measure.
    I can, but it is way too expensive.

    Who owns the copyright? This is a book that should be re-published if ever there was one.

    My own experience was like others here when I discovered it in the school library and was fascinated. Mathematics never came easy to me, but inspired by the lesson of that book, I stuck at it, worked hard and ended up passing through to university where it was a sub-major in my course.

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