Earlier I re-posted a blog entry by George Walker in which he expounded on the once highly important tool known as dividers. This is a tool that was once so highly valued not a single artisan or scholar would be without it. Artists, carpenters, masons, joiners, mathematicians and philosophers all felt that they could not perform their chosen profession without a pair of dividers. So what changed? Why did this once exalted tool fall out of grace? I’m not an expert by any means, but here is my opinion, for what its worth.
As the systems of measure became more standardized the need for dividers started to diminish. High level systems of mathematics were developed and the divider was replaced with abstract numbers. That’s not necessarily a bad thing. Differential calculus comes in handy. The difficulty is that we all but abandoned the practical methods of solving problems. Before high level, theoretical mathematics, dividers and geometry were utilized to solve all manner of problems. So every learned individual, on some level, was taught to utilize dividers in a hands-on practical way.
Over time, theoretical mathematics slowly replaced the practical. Post WWII ushered in the final transformation from practical to theoretical mathematics in the school system. The Cold War and the space race had every school preparing students to become engineers or at least for advanced college degrees. That then degraded into “new math” and abstract mathematics being introduced to younger and younger students. On average a child needs to reach a certain age of development before their brains are capable of abstract thought. The type of thought need for algebra. This has led to students simply learning steps to get a solution and not learning why. Which in turn leaves them with no way to apply the steps in a practical application.
Ok, Ok, I hear you. Greg! What does this rant have to do with dividers? Well, with dividers and a straight edge, we common folk can solve complex mathematical problems and only have to know very little if anything about the actual mathematics. This is real world practical application that we can apply to areas of our lives!
I use the proportional method for designing and laying out of my projects. Without dividers this method would be all but impossible. They dictate everything. I’m also addicted to the tools themselve. “Hello, my name is Greg and I collect dividers.” I like the wing type most of all. The better ones have a fine adjustment nut that lets you sneak up on a setting and they have a stout thumb screw lock. Some are marketed as ‘carpenters dividers’ and have at least one steel point that can be removed and a pencil substituted into it’s place. This style comes in handy and can do double duty as dividers and as a compass. It’s good to have a few sets of dividers of varying sizes. I have a small 3″ leg set and go all the way up to a 12″ leg set. But a couple pair will be all you will need. You can always add to your collection later. Unless you have money to burn, stay away from new. Second hand is the way to go. Flea markets, antique stores and Ebay are the places to look. It’s hard to get burnt when buying dividers. Simply make sure no parts are missing, the legs are straight and of the same length and will be in good shape.
Dividers are absolute. You are physically manipulating them. What you see, is what you get. Here is an overly simple example but follow me to my point.
Let us suppose that you wish to divide a distance by (5). So you take a measurement with a tape measure and do the math and get an answer. Maybe you measured correctly, maybe your math was sound. Now you take that (1/5) measurement that you calculated and start laying it out across you original length. Suppose that you are really bold and skip the layout and just cut the (5) parts to fit based on your calculations. There is lots of room for error in that methodology.
Now let us work out the problem using dividers. You set the dividers to you best guess as to what (1/5) should be. Starting at one end of the original length you step off (5) paces. You guessed wrong. You adjust your dividers by approximately (1/5) the error and step off the (5) paces again. Your really close this time. One more small adjustment and you step off the (5) paces again. This time your exact. Your dividers are now set to exactly (1/5) of the original distance. You can trust it, you’ve seen it with your own eyes. You have physically manipulated the dividers within the space.
No math calculation, no room for error. I don’t know about you, but I’ll take absolute every time. By eliminating the mathematical calculations and physically manipulating the dividers in your layouts, errors can be greatly reduced. The process of using dividers results, by default, in your checking for accuracy. No system is error proof however. Care must be taken. My point is that dividers will provide you with a system of layout that reduces the chance of a careless mistake as well as changing the way you think about the physical space of your work. So buck the system and join me in my crusade for practical mathematics and proportional design. Step off in the right direction and acquire two or twenty sets of dividers. (Did I mention I have a problem?)