Tuesday, November 20, 2012

Ancient Essays People Are Reading For Some Reason: Life Is Accumulated Error

[Editor's Note: From 2007]
[Author's Note: There is no editor]

Our Intertunnel friend Patrick down south in the Red Stick State is making a table. He's asked a question, and it was bound to bring on that ol' Sippican logorrhea, mostly off-topic. Here's the question:
Now, since you've offered advice upon the seeking of it, how does one make all the legs on a little table come out the same size? I clamped mine together in sawing and making the dadoes and everything so they'd all be the same height and have the shelves at the same spot and everything, and one leg still came out shorter than the rest (I suspect warpage). Do I just keep sanding the others until they're evened out?
This is interesting as all get-out. We have encountered the confounding and somewhat counterintuitive "Accumulated Error."

There is a long and boring explanation of accumulated error regarding mathematics, science, and especially lately, economics and climate prediction. We need not trouble ourselves with that here, as we begin with our eyes glazed over from hunching over the tablesaw. No need to keep basting them.

What we are referring to is well known to the man who must measure over and over again. If I measure a foot with a ruler, and make a mark, and then measure again from that mark, and then again for a while, certain dreadful things can begin to happen. First, after about 36 tries, I'll be outside, and it's snowing, and I don't want to go there. But more to the point, if I am making an error -- say, the ruler is a little off --and then I continue remaking that error, while using my last erroneous point to start making my next mistake, things can get really bad, really quick. I said "can" get bad, but that's just an expression. They "do" get bad, and you get fired or not paid, and so forth. And the table you made lists to port. What's happening?

Eisenhower might be the most able executive we ever had as chief magistrate. He said: "A plan is nothing; planning is everything." He understood accumulated error. You have to take into account the vagaries of constant changes.

Now, back to our table. It wobbles. Patrick is downcast. We must help.

First, Patrick, you're very cheeky to just make four legs and expect them to turn out alright. A professional wouldn't figure he'd have any sort of success doing that, and make fourteen or so, hoping to get three good ones and one that don't look that bad in firelight. The firelight is generally cast from a lovely blaze in your wintertime fireplace, made from the other ten legs. But you are brave, and do the crossword in pen, and we must help you.

They are all a little different. You tried, but wood is not steel, and you are not a machinist. Your pencil marks waxed and waned in thickness, and the angle of your head when reading the markings on tools and measuring instruments went back and forth like a bent metronome -- hell, the humidity changed and your wood decided it wanted to be closer to the size it was when the birds were chirping in it last week. You are accumulating errors, and you don't know how many ways that material and those tools and your own efforts will betray you yet. Wood only really expands or contracts across its grain, so table legs and so forth don't really get longer and shorter. A dry pine board 11 inches wide might gain or lose 1/8" in width in a week, but a 12 foot long board won't gain 1/8" in length. Tabletops move all around. Legs don't do it much.

Don't fret. Make the table as best you can. Make the pieces as accurately as you can. Align your joints. Center the baulks of wood in the clamps so that the center of the screw is in the center of the board you're clamping, not offset and yanking it one way or the other. Measure assembled rectangles from corner to corner diagonally, and then the opposite diagonal, and when they are the same, the thing is "square." Do your best to not let the errors accumulate; make only one mistake at a time.

It will still wobble. Mine do.

Then take the table, if it's small enough, and place it on the only thing you own that's flat, which is your tablesaw tabletop, and wobble it. Two table legs, diagonal from one another, will not lift off the tablesaw. Leave those alone for now. Wobble the table until the other two legs are both off the saw, and equalize the amount each is off the table. Use something to measure that distance between the bottom of the leg and the sawtable top. Mark that measurement on those two legs I told you to leave alone, those that WILL NOT wobble. I use a scribe, which is like a compass, to make such measurements and markings. Sand or cut to the line. Now the table will not wobble. It's much harder when the table is bigger to find a flat surface to accommodate the four legs. Kitchen counters are generally very flat, especially if they are stone, as many are these days.

If you make a mistake cutting and measuring for the wobble, over and over, eventually you will get to the top the legs, and you'll have a nifty cutting board.

By the way, accumulated error is why climate scientists tell you it's going to be 500 degrees centigrade next summer, or there will be sheets of ice stretching over the Florida panhandle -- depending on who gives them their grant money and whether their ruler has 11-1/2" or 12-1/2" inches to the foot.


Thud said...

Guess who didn't measure the diagonals on the fence panels I am now attempting to fit?....I am definitely a work in progress and luckily God does love a trier.

Bilejones said...

And this is why a story stick is better than a tape on replicated items.

Sam L. said...

You know, you really can't get there from here, and if'n you do, it'll be someplace else.

I could go on, but you get the drift.

soubriquet said...

Oh, now come on, that's why all our english pubs have little pasteboard beermats on the tables, so you can tear and fold them, and use them to shim up the shrt leg and take out the wobble. If everybody scribed their legs on a nice flat machine-bed, like you, why, all the beer-mat makers would be starved within six months.

Anonymous said...

Look, this is simply directing well meaning folks down the wrong kerf.

Everyone knows that to come out ahead you must make multiple mistakes at the same point - saves time, saves effort - and some mistakes are bound to cancel out others.

So, what to do with the wobbly table?

1) real pros only supply three legs - won't wobble


2) you live in a rickety house - move to one where the furniture does not wobble

happy to be of assistance.

TmjUtah said...

I do control and layout for heavy construction. I get to use some truly amazing technology.

The words I start every day with?

"Everything MOVES" and "Did you put a tape on that?"

Helps me stay sane. Mostly.

soubriquet said...

I've re-thought my earlier solution. The preferred one now is... Decide where you want your table. Set it there. Rock it a little. Draw a pencil line around the tips of each of the high pair of legs. Go get a big hamer and pound at the floor inside that pencil line until you have an indent equal to the high-point discreancy. Place your table with the longer legs in the indent. Now you have a no-rocking, non sliding table, fitted to your room. If ever you move, take the hammer with you.

soubriquet said...

I'm sorry, I seem to be missing a couple of consonants there. My doctor warned me to expect that sort of thing.

SippicanCottage said...


I know plain brilliance when I see it.

wolfwalker said...

My first thought on reading this is "So make one leg first, then use that one as a pattern for the other three."

Sensible approach, or betraying the fact I've never done carpentry in my life?

Gringo said...

When I recently built a bookcase, I had to deal with one length made from a board that curved outward, which meant that the shelves I had cut weren't wide enough. I disassembled the bookcase so that the board curved inward, which enabled the shelves to make contact with both lengths.

Perhaps if I had purchased a better quality wood, I would have had straighter boards. Perhaps not.

Which goes to show that "good enough" is hard enough to achieve.

SippicanCottage said...

Hi Wolfwalker- Thanks for reading and commenting.

The making of additional legs from a pattern is better than measuring each one, but it doesn't solve the problem of accumulated error completely. Variations creep in and you have to deal with them.

Hi Gringo- Thanks for reading and commenting.

I buy nothing but the finest wood; most of it makes fine firewood.