The Work of Art

MEASURE & BEAUTY

Contrary to what a critic might say, you need no degree in art, either to measure or to make beauty.

The process of measure, like art, cannot just be, but must always do. What does it do? Measure relates us to each other and to life. Historically, we defined inches, like feet, by the size of our body parts, and in many languages the word for inch is the same as or derived from the word for “thumb” (Spanish “pulga,” etc.) In addition, four fingers, each with three joints, make a convenient counter for a twelve inch foot. So feet and fingers fundamentally relate us to the things we measure, both physically and conceptually, by holding them against our own bodies. Some metrologists (students of measure), suggest that one foot = approximately 1/360,000 of one degree of the circumference of the earth: thus 1/360,000 x 360 = earth’s approximate circumference. Wouldn’t that make a lovely proportion by which to know our place and our planet?! And doesn’t it make sense of geometry, a word that means, literally, “measure of the earth”?

The idea of measure as relation even lies behind the modern, standardized unit of the metric system, which originally defined the meter as the ten-millionth part of one-quarter of the circumference of the earth. Later, we tried to “fix” it by marking out one exact meter of nearly pure platinum – but even platinum shrinks or grows minutely with changing temperature. Now, we define a meter as the distance traveled by light in an absolute vacuum in 1⁄299,792,458 of a second. But even time can’t escape the vagaries of relationship, whether you measure it the old way – from daylight to daylight, which always changes, of course, season to season – or whether you measure it the newest way, according to how fast radioactive cesium decays – which rate varies according to gravity, so that even atomic clocks run fast or slow depending on where they are in relation to the center of the earth! (Given our common experience of “how time flies” or “stands still” why should we expect time to give us a more stable unit of measure?)

The word “measure” comes from Latin, mensis, meaning “month.” In English, “menses” is the monthly female cycle of fertility by which every one of us is born. Mensis and month are derived from a root for “moon.” So measure and number don’t come to the same thing. Let me put that another way: to give something a number – or even a ratio – is not always enough to take its measure. By the same token, to measure something requires more than simply giving it a number.

For example, consider the relations between our experience of time and the activity of measuring. Obviously, we first measured our days by the cycle of sunrise and sunset. Weeks and months appeared to us when we noticed the moon shrinking and growing in weekly phases which we identified as the dark “new moon,” the waxing crescent, full moon, the waning crescent, and back again. We named these periods “turnings” (the original meaning of “week”) and “moons.” The words refer to a shared experience of an ever-repeating annual cycle of 7-day weeks, 4-week months, and 12-month years.[1] This common experience of daily (related to the word “dawn”) and monthly changes in the sky is both a mental and physical basis for better understanding measure.

In this profoundly fundamental way, measure allows us not just to quantify, but to qualify our experiences: inches & feet; ounces & pounds; quarts & gallons; speed, volume, color, texture (smooth or rough being a measure of surface variation), contrast, proportion, balance, justice – all provide real experiential measures of our life on earth. We may take for granted our received knowledge of math, science, and how the world works, but if we follow its roots we’ll end up in those measures we can actually see and feel. Every measure helps us distinguish bad from good – and goodness is the essential measure of beauty (via the Latin word for goodness, “bonum”).

The goodness we can experience comes to us through our senses, through our body. To illustrate the relationship between experience and concept, let’s take, for example, Leonardo DaVinci’s famous drawing of the “Vitruvian Man,” by which he meant to illustrate a “true” measure of both man and a more universal concept of beauty that man shares with the rest of creation. The first thing you may notice about the drawing of the man is that it’s framed by both a circle and a square. What you might not notice is that the circle – an archetypal and universal symbol of the unity of all things – not only surrounds the man, but centers at his navel (where life physically attached him to his mother – about 5 weeks after the union of sperm and egg). As a universal symbol of perfection and wholeness, the circle describes not only center and limits, but also completeness.

The square is another universal symbol, but it represents the created, material world – and also, in this picture, marks an equality of measure between the height, and the width of the outstretched arms of the man.[2]

The marks along the baseline of the drawing, under the man’s feet, indicate fundamental proportions. The navel, for example, in addition to centering the circle, also divides the man’s height into classical proportions expressed by the ancient sages as “the Golden Mean.” It occurs when the ratio of the parts equals the ratio of large part to whole. (Numerically, it occurs at approximately 0.618… – but more about numbers later.) Conceptually, it expresses a universal relationship between growth and form, between spirit (which motivates growth) and matter (the product of growth). Leonardo’s Vitruvian man, as well as the bodies of most adult humans, display approximately “golden” relations between the lengths of fingers and hand, hand and forearm, forearm and far shoulder, fingertip to shoulder and full armspan.

To actually know the Golden Mean however, it’s best to participate in the process by which it comes to life and then grows. You can do this easily enough by simply copying the series of little boxes in the figure; work freehand, or if you’re more mathematically inclined, use a ruler on graph paper – it doesn’t matter. But do it several times. Share it with someone else. If you’re a numbers person, do the math (more about that soon – worth trying even if you’re not a numbers person). Even better than drawing, if you have the time and carpentry skills, is to make a compass with a special third, “golden” leg that marks the Golden Mean. Then you can actually demonstrate it on a human body, which changes everything. As you measure the points where the Golden mean applies to their body, your subject will typically submit with an air of mildly embarrassed condescension: “OK, so your stick points to my navel, that’s just great. Now what?” But by the time you get to her hand and fingers, having displayed the same proportion in the full body, torso, limbs, and lower arm, the response is often reduced to an open mouth and a slack jaw: “WOW!” While these “Golden” proportions are not precisely and universally equal, life makes every body to similar proportions, according to a common measure of beauty that it shares with the rest of life: WOW!)

HOW TO MAKE GOLDEN CALIPERS

Buy 1-1/2” x 1/2” milled molding from the lumber yard. You will need 4 straight, uniform sticks, free from any warping, 2 at 56 inches, 1 at 35-1/2, and 1 at 22-1/2 inches. Taper each of the three longest sticks, symmetrically, so that one end is 1/2 inch wide. Sharpen the final inch of length to a point. Round the other end into a half circle. Taper the shortest stick to 1 inch wide, and round both ends. For the next step, you will need soft rivets or nuts and bolts about 1-1/4” long, and washers. Lay the 56” sticks on top of each other. With a drill bit sized for your rivets or bolts, drill one hole through the center of the wider end, exactly 55 inches from the point. Drill another hole exactly 34” from the point. Through the wide end of the 35” piece, drill a similar pair of holes, one exactly 34” from the point, and the other exactly 13 inches from the point. On the shortest stick, drill both ends so the holes are exactly 21” apart, and 3/4” from the end. Using your bolts or rivets, attach the two wide ends of the longest sticks. Set them on the ground and spread them into a “V”. Attach the wide end of the 35” stick to the middle hole of the bottom 56” stick; turn the assembly over. Attach the wider end of the 22” stick to the remaining hole on the other leg of the “V,” and the narrow end of the 22” stick to the remaining, lower hole of the 35” stick. You now have a set of calipers that will indicate (approximately) the Golden Mean in any span from 110” to 4”.

[1] There are actually more than twelve and less than 13 lunar cycles in the amount of time it takes the earth to make a full circuit around the sun, which makes for some very interesting and useful stories. For edifying and important additions to this discussion of measure, I recommend Sun Moon and Stars, by Robin Heath, in the Wooden Books series. 

[2] Ancient philosophers understood the circle as a perfect expression of unity. Indeed, “uni-verse” means, simply, “one complete turn,” as in the daily turning of the earth around the sun, the turning of the seasons around the year, or the turning seasons of a human life. The circle indicated a holy one-ness that contained everything (that we use a circle today to symbolize zero is a curious mathematical convention; zero actually serves two purposes: one is to mark the columns we use to indicate numbers of ones, tens, hundreds, etc. The other purpose is to indicate the concept of nothingness, which we managed to do without for millennia, since it was so hard to imagine “nothingness” in a world so full of life. Indeed, zero came into use in the west at about the twelfth century, along with Arabic numbers and computational methods.) The square, by contrast, expressed solidity, reality, and the earth. The ancients also associated the square with the number four, for the cardinal directions, east, west, north, and south; the four seasons; as well as for the intersection of up and down, and left and right; heaven and hell, life and death (these latter are also expressed in the cross, which is contained by and defines the equality of a squares’ vertical and horizontal measures). For more along these lines, and for a delightful and practical geometric romp through the numbers, see A Beginner’s Guide to Constructing the Universe: The Mathematical Archetypes of Nature, Art, and Science – A Voyage from 1 to 10, by Michael S. Schneider.