In Chris Schwarz Blog, Marking and Measuring

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When I first learned about the so-called Golden Mean or Golden Section I was enthralled by the concept. I actually remember the moment. I was in the National Building Museum in Washington, D.C., in 1996 and just discovering that some of the geometry I learned in junior high actually had a use.

The Golden Section is a ratio (approx 1:1.618) that crops up in nature (such as the shell of a nautilus), Audrey Hepburn’s face and anywhere Elvis is sighted.

It also is supposed to turn up in great furniture and buildings. My efforts at designing furniture using the Golden Section or exploring furniture using the ratio as a guide always proved frustrating. Finding the Golden Section in great works is possible , if you looked in the right places, included parts of mouldings or excluded stiles or otherwise stretched the rules.

Now I’m not saying the Golden Section doesn’t exist, any more than the Trilateral Commission doesn’t exist or that a metal colander isn’t handy for blocking the transmissions from the mother ship.

But it just hasn’t worked for me and the pieces I like to design and the pieces I like to look at. Perhaps I’m not looking in the right place.

So after watching George Walker’s new DVD (“Unlocking the Secrets of Traditional Design”), I was intrigued that he didn’t once bring up the Golden Section, which usually at least rates a footnote in any discussion of design. Instead, he focused on whole-number ratios. And this afternoon, I decided to put his concepts to a quick test.

The cover project for the Autumn 2009 issue of Woodworking Magazine is a schoolbox built using a plan from an 1839 text. The schoolbox is built to the print. There is no modern interpretation of the piece’s form. The piece (which we’ll show here next week) is perfect to my eye.

So I took a pair of dividers to the piece using Walker’s techniques. Its elevation turned out to be a perfect , repeat perfect , 2:3 ratio. Then I decided to explore the piece using the column orders. And the phone rang.

– Christopher Schwarz


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Showing 19 comments
  • Claire

    An interesting discussion.

    It’s splitting hairs a bit, though. There’s not much difference between 1:1.618 (one side is 62% of the other) and 2:3 (one side is 67% of the other). The eye is not going to pick it.

    It’s not too bad for those of us using metrics, but darned if I know how you work out 1.618 times 23 5/8" !!??

  • Bjenk

    Its other name is Phi and it fascinated ancient Greeks because of its often occurrence in geometric constructions. The Renaissance saw hosts of mystics and architects get all crazy over this ratio and gave it almost divine and magical properties.

    It is an irrational mathematical property. If we refer to Roubo, Phi was not part of the rules of the art in the consideration of the proportions of furniture. Proportions were established according to a set of flexible proportions for known forms and Roubo often indicated that one had to follow a good architects’ instructions and basic elements of geometry. Roubo had the king’s architect as a teacher! Most furniture makers in Paris at the end of the 18th century used approximations of known proportions for typical pieces. An armoire had to be between 6 to 8 feet tall, 18 to 24 inches deep and the rest was accomplished through ornementation. The number of drawers, their disposition was accomplished in the same way. Everything from bad taste to work of arts were done here.

    Funnily enough, Roubo laments about fashion trends and bad taste in furniture making and the often poor quality of the work being produced. Most craftsmen had trouble selling quality pieces so they made cheap stuff and followed the trends in taste of their clients. That’s for France though, things may have been different in Colonial America or England or even Germany at the time.

    I’m siding with Larry on this one.

  • Jack Ellinghaus

    David said above: you don’t get a consistent ratio of 1:1.618 until you get into larger numbers. I like to give immediate answers when asked a question and I try to do sub-calculus calculations in my head but my 6-ft folding rule is not calibrated in 1.618ths. A few weeks ago, when my wife asked me to create a corner shelf in the dining room and 32" height seemed to please her, I used the 8:5 (1.6:1) ratio to quickly derive the appropriate width and determined that 20" should be aesthetically pleasing.

    The Golden Proportion is like the Pirate’s Codes; it’s more of a guideline than a hard and fast rule.

  • Kerry Burton

    Its elevation turned out to be a perfect – repeat perfect – 2:3 ratio.

    Hmmmm. Well, the "Golden Ratio" version would have been either 2 : 3.236 or 1.854 : 3. I’d be willing to bet that if you did a side-by-side drawing with either of those ratios (without grid lines) you’d have a hard time picking which was the GR version.

    But perhaps that’s your point?

  • Sam

    Great topic! Thanks for taking this on.

    I think John pulls this all together when he says:

    "The comments regarding designing a piece that just looks right are valid, but only after a person has looked at and studied enough pieces…."

    Keep up the investigation! It helps very much to learn *how* to look at pieces, in order to appreciate what makes them harmonious and beautiful.

  • Steve McDaniel

    You said, "The cover project for the Autumn 2009 issue of Woodworking Magazine is a schoolbox built using a plan from an 1839 text."

    Sounds like an interesting text…

  • Rob Porcaro

    Hi Chris,

    I’m glad you brought up the notion of breaking the rules because they aren’t rules at all.

    Aesthetic "rules", golden or not, are after-the-fact analyses of what WAS done, not how it MUST be done. Artists/designers use experience and intuition to create works that appear the way they want them to be. Later, if examination shows certain tendencies, such as 1.618:1, these may guide future creativity but should never limit or define it.

    I feel this is much of the joy of creativity: you can make it the way you want to, and when it’s "right", when imagination becomes reality, you’ll know it.

    Now THAT is happy woodworking!

    Rob

  • John Walkowiak

    The comments regarding designing a piece that just looks right are valid, but only after a person has looked at and studied enough pieces to know instinctively that it is “right” or “wrong”. This takes into account the shape as well as the wood selection and orientation as well as the type of finish on a piece. This can take years of paging thru books and visiting museums. I am sure we have all seen and built things that just don’t look “right”. Until we have that built in “right” or “wrong” meter, a calculated guide or set of basic rules can be a great help.

  • J Silver

    Charles,
    Unfortunately not I am completely bald, and can’t see to well.
    J Silver

  • Charles Davis

    First time I’ve heard of "mental masturbation"… A bit off topic, but if I do it will hair possibly grow on my head where I’m thinning?
    -Charles

  • David DeLano

    I second the notion of making/designing something that looks and feels right. What we must remember is that the right look and feel, and nature, came first. The Golden Section and Fibonacci sequence were applied later to attempt to formulate what looks right, and to relate it to naturally occurring whole numbers (nature doesn’t usually have irrational numbers). So, when designing, and you don’t know quite what a second dimension should be, check in with the Fibonacci sequence for a "good" possibility.

    As to Fibonacci numbers and predicting the stock market, well, they are also often used in the creation of random numbers….

    D

  • J Silver

    God must of used some incredibly large dividers for his work. Enough with all this mental masturbation. Look at something and let it hit you in a way so
    that you don’t get in your own way. Look at nature and trust what you see and feel because we are still apart of nature. I wonder if I meet the standards for the golden ratio or whatever. By the way I am not a New Age woodworker. Just a hobbiest.
    J. Silver

  • Larry Williams

    Heresy! The golden mean has been so ingrained into contemporary woodworkers, I hope Chris is prepared to be burned at the stake. Even though ideas like the Parthenon’s design being based on the golden ratio have been thoroughly debunked the myth of the usefulness of the golden ratio lives on.

    I think the golden ratio is useful. Its usefulness lies in the fact that its so difficult to use. In an effort to sound knowledgeable, academic or even profound; a designer, author or who ever can take almost any rectangle and claim it to be a golden rectangle. Nobody, not even an editor, will check it. Politicians and used car salesmen would love such a flexible tool.

    For those that insist 17th and 18th Century woodworkers or designers used the golden ratio, there’s always the sector. The sector was a calculating rule commonly used from the 1500’s through the mid 1800’s to solve proportional and other mathematical problems. There’s a good image of one at:

    http://tinyurl.com/krobr5

    and an article on the history of the sector is at:

    http://tinyurl.com/mz2zac

    The unabridged version of Sheraton’s book contains a long chapter dealing with the use of the sector. I’ve never found any reference to a sector that has an increment for the golden mean inscribed on it.

    I’ve been watching George Walker’s video and, unlike the vague mystique of the golden ratio, it presents a good foundation on design. I wish I’d had the information a long time ago.

  • Andrew Watson

    I think that you must have subconsciously garnered a passion for the ratio 3:2 whilst handling all that 35mm film in the darkroom in times gone by, Chris!

    Andrew

  • MikeH

    For quite a time, at least until the quants took over, after having surpassed Elliot Waves and driving momentum swing plays into ill repute, Fibbonnaci ratios were the lastest and greatest thing to predict the behaviour of the stock market, even when the market did what it wanted to do outside the scope of Fib ratios, in reaction to which, the Fibbers derived (devised?) some seondary ratio which was the fall back position to which the markets secondary reaction was supposed to retrace before it rebounded, or tumbled yet again, whatever, depending on the predominant direction of the secular trend provided of course that the tide off the coast of Peru was shifting in the required direction.

    Others look at things more simplistically, and realistically, if I dare opine. The famous J.P.Morgan of both history and legend, when asked what the market was going to do, always replied, with dead certain accuracy, each and every time, unerringly, "The market is going to fluctuate."

    Sorry folks, I guess I got a little carried away there, but the point of it all, is to second the notion proffered by Chris in initiating this thread, that if it looks right, and the looking feels good, that’s all that’s really necessary, regardless the arithmetic. 2:3 is as good a starting point as any for initiating a design. Going beyond to consider the third dimension (I build a lot more boxes than I do furniture, so thinking in 3-D from the outset is my usual approach), other commonly utilized ratios come to mind, some of which are: the Double Cube (1:1:2); the Root of Two Box (1:1:1.4); the 1:2:3 box (just one 3-D form of the good old 2:3 standby); and of course our erstwhile Golden Rectangle, which I propose with tongue firmly planted in cheek, be redubbed, at least in its cubic form, the Golden Golden Rectangle (1:.62:1.62).

    I also think that David makes a very cogent point in proposing the use of a Fibonnaci series to design one’s project beyond the scope afforded by its first few elements, and further suggests, that going beyond its early stages, gets us back to the Golden Ratio ratio again, despite the presumed requirement that the rational dimensions of projects approaching it, need to be quite large indeed, which I might only speculate, not being a mathematician of course, would endlessly subject our projects to the unyielding strictures of the Law of Large Numbers. 😀

    So after all is said and done, what do the Gold Rec, Fib rats, and so on, aside from their underpinning of certain elements of furniture design, architecture, and certain naturally occuring phenomena, inter alia, have to do with predicting the future path of the stock market? I think that Louis Rukeyser, IMHO one of the finer financial pundits of recent times, albeit one perhaps prone to the terse, given his liberal use of abbreviations, said it best when offering his own spin on JPM’s dictum. He said, and it’s been a while now, so I hope I’m citing accurately, "The market will generally continue to fluc. At times, it will fluc down, and at other times, it will just plain fluc up."

  • Floss

    Chris,

    Everybody knows that a metal colander is useless without foil wrapped antennae.

    Otherwise you just look like a silly fool with kitchen tools on your head.

    F.

  • Charles Davis

    Every woodworking book I read seems to have a golden rule/ratio section or "guilt section" as I call it. It’s nice to hear your take on it. I guess it would be nice if things I make happened to satisfy such rules but for me those rules are like stop signs… a mere suggestion.

    Imagine if everyone built according to the golden ratio… how ugly would that uniformity be after a while?
    -Charles

  • David DeLano

    I’ve been more of a reader than commenter, but, my "real" occupation is that of software developer, and my real calling is as mathematician, so….

    When applying the 1:1.618 ratio to most things, including woodworking, it’s better to use Fibonacci numbers instead. The sequence is found by adding the two previous numbers of the sequence to get the next number, so 1, 1, 2, 3, 5, 8, etc. Now take the ratio of any two adjacent numbers, 2:3, 3:5, 5:8. You’ll find these ratios much more useful to use. I’ve also used multiples of these sequences. As the scope of this ratio progresses, the ratio approaches 1.1618 (so you just need to make larger projects ;-).

    David

  • Jonas Jensen

    I have designed and made cutting boards using the golden section as described by Adam Cherubini in the first article about arts and mysteries. That has worked fine for me, but I agree, that sometimes you just have to make things so it will look right to you, and then it doesn’t matter if the ratio is 2:3 or another whole number, as long as it is pleasing to the eye.

    Jonas

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