Sunday, 3 May 2009
10:50 PM
I’m going to propose to you that each of the items in the following picture is an eight-dimensional object:
Eight? Yes. Or more. Or fewer. It all depends.
Of course, I’m screwing with you. (haha, get it?) I'm using a mathematical definition of dimensions: In Cartesian terms, an object's dimension is "correlated with the number of coordinates that is required to map it."[1] It seems probable that when Descartes was inventing analytic geometry, he did not realize that he could have been analyzing a problem I've been having with coffee cans. Which I'll get to in a moment.
So, eight dimensions? Here are eight attributes/characteristics/coordinates/dimensions to identify this object uniquely:
| Fastener type | screw | | Category | machine screw | | Drive type | Philips | | Length | 3/4" | | Diameter/Gauge | #8 | | Thread count[2]/pitch | 32 | | Material | Zinc-plated steel | | Head style | pan |
Go on down to the hardware store and take a stroll through the eponymously labeled Hardware department. Screws, nuts, bolts, washers, pins, nails, anchors ... this department consists of a very large number of small boxes. The boxes are grouped by the categories listed above, and probably several more, like measuring system (US or metric)[3]. If you're in a playful mood, approach an employee who’s skulking about and ask them if they can help you find "a screw." Count the number of questions they have to ask you before you settle on one particular fastener. That's the measure (well, one measure) of how many dimensions the fastener has.[4]
Let's go back to the screw at the beginning. If I ask my lovely bride what this thing is, she can tell me precisely: "Yeah, it’s a screw." Which is to say, it's not a pony. Those eight dimensions? Who cares. Sarah has no more need to distinguish screws by thread count and head style than I have to categorize, dunno, crochet needles by diameter and length (and 12 more dimensions, no doubt), or women's sandals by size and style and color (ditto), or letters by font and size (wait, no, that one I need).
I've been thinking a lot about the dimensions of fasteners because when the frogs are croaking and the woodpecker is whanging on our chimney flue, it's time for my annual garage cleaning and organization festival. Among this year's organizing tasks was what to do about all the damn fasteners that I've accumulated over the decades as leftovers from dozens of home-improvement projects.
 When I first met Sarah, she had a simple approach to this task. Nails, screws, hooks, whatever -- it all went into a coffee can. When she needed a nail to hang a picture, she could root around in the can and pick out a likely looking piece of hardware. Which is to say, Sarah utilized a one-dimensional system -- the number of variables by which she organized fasteners was 1, namely, the can.
My collection used a system that was basically a version of this. I had nails and screws and hooks and miscellaneous stuff "organized" in every conceivable container from Tupperware to cottage-cheese tubs. Among all these I had one can labeled "Screws," another "Washers," another "Nuts." Any time I needed a fastener, I would dump some containers and rake through them to find, say, a 1/4" screw and matching nut and washer.
In my dreams, my garage would be organized like a hardware store, with little bins for every conceivable value of every dimension of every fastener I have. If I wanted a 2-inch #14 machine screw with coarse threads and made out of brass, why, I'd just pull out the right bin and I'd be all set.
But does that even make sense? How many dimensions do I actually need, anyway? If I had the eight- or ten-dimensional system that a hardware store uses, three-fourths or more of the bins would be empty. When I go scrounge around for a screw, what exactly are the characteristics that will help me home in on the fastener I need? Or stated in another, more practical way: how many coffee cans was I going to need to organize everything well enough that I could find stuff when I want it?
This is where dimensionality becomes subjective. If you were organizing your fasteners, you might decide that after you've sorted everything into nails and screws, the next most important characteristic is length. You would have bins (or in my case, cans) that might be labeled "Screws- 1 inch," "Screws-2 inch," "Nails-1 inch," "Nails 3-inch," and so on. Me, I might decide after sorting screws and nails that I want to sort screws into type (wood screw, machine screw), then size (1 inch), then coating (zinc, brass).
 Point is, the dimensionality -- the sum of the characteristics that puts the screws and nails into individual cans -- becomes a matter of utility, of experience, and perhaps of personality. My collection of machine screws might be three-dimensional; yours, two- or five-dimensional.
And we don't even have to fix on a single dimensionality. I might sort most of the screws using three dimensions, then have a can for "Screws larger than 4 inches." Or I might throw all carriage bolts into one can. And I might have a can labeled "Tuftex Deck Drain Fasteners" (I do), whose dimensionality (1) has no relationship to anything else in other cans.
Categorizing and organizing is an exercise that can sort of run away from a person who has tendencies toward obsessiveness. It can become a thing onto itself, where the goal drifts from having a way to quickly find a bolt when you need one to the goal of devising a perfect system, each dimension identified and labeled, a can available for every possible value of every possible dimension. I know this, because as I organize all my screws and nuts and nails, I can feel that tug toward the ever-finer categorization of everything in the shop.
In the end, tho, practicality has to rule. I don't have enough cans; I don't have enough space for those cans, even if I had them; and I certainly don't have time to get out tweezers and calipers to examine every last fastener and make sure it goes into its proper home.
So I now have a shelf of cans for pretty much everything. Some of the fasteners are finely differentiated, some a little less so, and I still have a couple of cans that could have a label on them that says "Screws (1 dimension)" Instead, tho, those cans are labeled "Miscellaneous." And that will have to do for now.
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