How To Avoid Math
June 1, 2020 10:33 AM   Subscribe

Laura Kampf gives some Workshop Tips - Measuring, Marking & Math tips about how to avoid using math while making stuff.
posted by zengargoyle (47 comments total) 41 users marked this as a favorite
 
That was pleasant and useful!

The historical rupture that makes geometric constructions not feel like math is really something, though.
posted by clew at 10:49 AM on June 1 [8 favorites]


Oh, I love/hate this framing. I love it because it makes things accessible to folks who have had bad experiences with math. I hate it because she's doing math. She's avoiding calculations. I know so many people who get tripped up with numbers or basic arithmetic but have developed workarounds like these. I wish they knew they were good at math.
posted by feckless at 10:50 AM on June 1 [45 favorites]


Nice video!

It is always interesting to me how "math" is used as a synonym for "arithmetic" (or "constructive geometry"). Are we really avoiding math if we use a physical device that divides a board into n pieces? [Euclid VI, Prop 9]

There were some really great tips in this video, like bisecting the angle with post-its and the use of a storey pole. And seriously the best advice: Avoid measuring whenever possible.
posted by klausman at 10:53 AM on June 1 [4 favorites]


Laura's projects are great BUT every time she does that measuring trick to scribe a "parallel" line with the ruler and a finger, the perfectionist side of me shudders a little. If I did that, by the end of the project I know I'd get 1/8" gaps that I'd be hard-pressed to look past.

I prefer mefi's own asavage's approach, which is similar in that he tends to avoid elaborate predrawn plans, and tends to build stuff in place, but the fact that he always has a super-precise machinist's square on him makes my heart sing.
posted by supercres at 11:07 AM on June 1 [2 favorites]


The most important thing about building shit is to measure as infrequently as possible! If you have a gap and a choice between measuring the gap and transferring the measurement to the piece that fills it, vs bringing the stock over to the gap and holding it up to the gap and marking directly on it what the cut is -- always mark directly. Measuring and transferring results in at least three possibilities for error, while just marking-to-fit puts the error possibility down to the accuracy of your cut (and the thickness of your pencil lines, which is why a marking knife is a wonderful thing to have.
posted by seanmpuckett at 11:58 AM on June 1 [7 favorites]


At the other extreme, Even math used to be done without using math. I had a third-year engineering course in machine dynamics where the professor, an old hand without a graduate degree who just new his stuff really well, put out the option for people to show up to the exam with drafting equipment and provide “graphical solutions” to various vector equations on 11x17 paper. This was in the early 90s and the dawn of the graphing calculator, so almost no one took him up on it, but looking back now it would have been an elegant way to solve the problem, and made marking it so much easier.
posted by cardboard at 12:23 PM on June 1 [1 favorite]


My high school calculus teacher would always accept graphical solutions to any assignment or exam question.
posted by any portmanteau in a storm at 12:26 PM on June 1 [3 favorites]


If it's important, I find it useful to measure things by two totally different methods, and the more different the better. So calculations and a ruler, and also geometric constructions or templates. I'm prone to making big dumb mistakes, and measuring this way helps me catch them. The big dumb mistake I make on a calculation is different than the big dumb mistake I make when using a template, so even if I get them both wrong, I know I made an error.

This means more methods for measurement is useful even if I don't have any math anxiety.
posted by surlyben at 12:29 PM on June 1


bringing the stock over to the gap and holding it up to the gap and marking directly on it what the cut is

That is also measuring!

“graphical solutions”

That is also math!
posted by eviemath at 12:30 PM on June 1 [10 favorites]


 I wish they knew they were good at math

Definitely. There's a lot of mathphobia in the workshop, often because people were streamed too early into "good with numbers" and "good with their hands".
posted by scruss at 12:49 PM on June 1 [5 favorites]


I do find it amazing how quickly graphical methods have fallen out of favour. My dad told me about an exam of his where he had to show the graphical construction for a fairly involved piece of metal-work. By the time I was at a similar sort of level, the most we ever heard about it was "there's a historical graphical way of doing this, but we're not going to show you what it is, you can look it up if you're interested."
posted by regularfry at 12:50 PM on June 1


There's a lot of mathphobia

Also, frankly, a surprisingly large chunk of "math" teachers are just straight-up terrible. Most of mine were recycled gym teachers who pretty much sat and watched us read our ancient, beat-up texts. I mean, these were the kinds of teachers who made mistakes on their own tests, leaving us to argue that no, the correct answer was NOT what he said it was...
posted by aramaic at 12:54 PM on June 1 [10 favorites]


Our math teacher gave higher grades to students who could do good graphical solutions. She also taught us about programming during the 1970's, since we had plenty of extra time after she'd taught us the entire official curriculum in half the time. Badass.
posted by mumimor at 1:26 PM on June 1 [5 favorites]


Laura Kampf: “I have this piece of wood and I want to find the middle. How do I do that without measuring at all?”

me: huh, okay, assuming your board is a rectangle, you could draw a diagonal straight line from each corner to its opposite corner, and then draw a line that is perpendicular to one side of the board which goes through the intersection of the two diagonals

Laura Kampf: “Eyeball the middle, mark it from one side, then mark it from the other side which will give two lines pretty close to each other. Then it is very easy to see the middle between those two lines.”

me: whut, how is that going to work, what if you really suck at eyeballing things
posted by 23skidoo at 1:36 PM on June 1 [5 favorites]


Also, frankly, a surprisingly large chunk of "math" teachers are just straight-up terrible.

My wife just finished her teacher's training. She took the math elective and starting this year all teacher candidates had to take a mandatory test before being certified as a teacher. I joked with her that she didn't need to stress about it because all she needed to do was study to an eighth-grade level so she'd be fine, and she was, but there was a lot of anxiety about it for both her and a large part of her classmates. And on one level all you need is to be a grade or two higher than your students and you'll know enough to be able to teach them but at the same time it'll be so incomplete because if the teacher can't see the bigger picture than they can't develop lessons that will teach the current subject while also laying the groundwork for future lessons in a couple of grades.
posted by any portmanteau in a storm at 1:40 PM on June 1 [3 favorites]


assuming your board is a rectangle, you could draw a diagonal straight line from each corner to its opposite corner, and then draw a line that is perpendicular to one side of the board which goes through the intersection of the two diagonals

Or lay a piece of string the length of the board, fold it in half, then mark the board at the bend of the folded string. You can even do it without having to cut the string.
posted by Greg_Ace at 1:55 PM on June 1 [10 favorites]


I love that tip for dividing things into thirds by angling the ruler for easier to use numbers - that's awesome! I love her videos, and there's a lot of overlap here, but here's another one of my favorite youtube woodworkers with his tips for "avoiding math".
posted by ssmith at 2:03 PM on June 1 [1 favorite]


*width of the board...
posted by Greg_Ace at 2:05 PM on June 1


me: whut, how is that going to work, what if you really suck at eyeballing things

Eyeballing is not at all a superpower. It's completely trainable/practicable. Right angles too. When the work doesn't need to be super-precise, it can produce quite acceptable results.
posted by bonehead at 2:17 PM on June 1 [2 favorites]


Or lay a piece of string the length of the board, fold it in half, then mark the board at the bend of the folded string.

String, in my experience as an ex-math teacher, produces inconsistent results when used like this, due to the stretchiness and the hard-to-fold-ability of string- every lesson I tried to do using string as a measuring device ended up with too much varying results among the students. Using the same general principle, I'd do the same thing but with paper: take a piece of paper that is longer than the side of the board you want to determine the middle of, line up one edge of the paper so it aligns with one edge of the side of the board you want to determine the middle of, fold the paper at the other edge of the side of the board you want to determine the middle of, fold the edge of the paper so it aligns with the fold you just made, use the latest fold to mark the board.
posted by 23skidoo at 2:35 PM on June 1 [5 favorites]


Eyeballing is not at all a superpower. It's completely trainable/practicable.

Well sure, but every other hack she showed didn't rely on eyeballing, and would produce rather accurate results, whereas her hack for determining the middle of a board would probably give you something rather close to the middle most of the time, but could also give you something not-close-enough to the middle for your needs
posted by 23skidoo at 2:38 PM on June 1


> me: huh, okay, assuming your board is a rectangle, you could draw a diagonal straight line from each corner to its opposite corner, and then draw a line that is perpendicular to one side of the board which goes through the intersection of the two diagonals

That technique relies on the board being properly square, or at worst a parallelogram. If the cuts are off (or if the board is warped), you're not getting better than a vague approximation anyway.
posted by ardgedee at 2:49 PM on June 1


If your first eyeball is too far off, eyeball the middle of the two eyeballs and then repeat.
posted by RobotHero at 2:54 PM on June 1 [3 favorites]


> what if you really suck at eyeballing things

Draw another mark that represents your best guess as to the halfway point between the two lines.

Now repeat the same procedure using your new mark. (Ie, mark the distance from one edge to your new mark, then transfer that distance from the other edge.) These two new marks will be quite a bit closer than the first two marks, in fact so close probably that even a person who can't eyeball things will be able to figure out where the middle of the two is.

(If not, just repeat the process again.)

Along the way you've discovered a pretty nice little example of an iterated system that will always converge towards the right answer (as long as you keep choosing a new line that is closer to the center than either one of your marks).
posted by flug at 2:58 PM on June 1 [3 favorites]


Back in the really old times, a stick and a string (or rope) were the main measuring tools for construction. It's even in the Bible. You can do a lot of really good geometry and measuring with those two items, given that they have known lengths. The drafting equivalents are the compass and ruler. Imagine you have to do all your design work using only those two tools (and your pencil obviously). The stretchiness of the string or rope is a problem, but there are solutions for that, both in the form of specialist cord, and in the preparation of the string. A wet or a very dry string is less stretchy.

I can't find it, but I used to have an essay about how the curvature of the stylobate of the Acropolis was in fact the result of using the horizon (which is curved, obviously) as the baseline for measurements. Still, the work done then was really accurate. I'm not sure I'm a fan of eyeballing. What I have learnt from working with excellent crafts-people is that you might as well do it right from the beginning, and that includes taking the right measurements. Often more with a stick and string approach than a laser, but still accurate.
posted by mumimor at 3:10 PM on June 1 [2 favorites]


Half of this stuff I learned when my dad plopped down a portable drafting table, T-square, nice drafting tools, and his Mechanical Drawing book from his university days when I was in seventh grade.

Good dividers have a big adjustment and a tiny adjustment. You eyeball the major division and then divide the error by the steps using the small adjustment until it's perfect enough that the holes are in the right places. You do it over twice or thrice making adjustments to your adjustment divided by the repetition.

... an iterated system that will always converge towards the right answer (as long as you keep choosing ...

Oh, and asavage also does the hold pencil while using other finger to keep distance to draw a line. Definitely not precise but good enough (esp. with a bit of sanding).
posted by zengargoyle at 3:16 PM on June 1 [2 favorites]


You can draw a circle the same way, the trick is to be able to hold the pencil and use your pinky as the pivot and turn the material. Much easier than trying to freehand a circle.
posted by zengargoyle at 3:24 PM on June 1 [1 favorite]


Along the way you've discovered a pretty nice little example of an iterated system that will always converge towards the right answer (as long as you keep choosing a new line that is closer to the center than either one of your marks).

And as long as your initial two marks aren't both on the same side of the middle of the board. When I said "what if you really suck at eyeballing things", I truly meant really suck, not like, C+ mediocre levels of suckage, lol
posted by 23skidoo at 3:48 PM on June 1 [2 favorites]


Oh, watching again she maybe doesn't explain it clearly. I guess I filled in some gaps based on the visuals. She draw the first mark with the ruler and then keeps the ruler in her hand with her thumb on the same spot while she flips to the other side. So the two marks are an estimate, but they're the same estimate from opposite sides.
posted by RobotHero at 4:00 PM on June 1 [2 favorites]


Oh see, that would work much better, if that's what she's doing. I watched the video, and listened to her, and didn't catch all that. #carryon
posted by 23skidoo at 4:02 PM on June 1 [2 favorites]




> So the two marks are an estimate, but they're the same estimate from opposite sides.

Yes, that's the trick.

And if you can manage to get your next estimate closer to the center than to either of those first two marks, you're good to go.

(In fact it will converge if you get it close enough to the center even some of the time. It will just take a lot longer than otherwise. So you can count the number of iterations required and get a very precise measurement of your eyeballing suckage.)
posted by flug at 5:28 PM on June 1 [1 favorite]


What I really wanted to come in and say, though, is that boy does our teaching of basic arithmetic and such-like things, starting in elementary school, suck.

If you have worked with many kids at the elementary school age, even just 2 or 3, you know that math anxiety is a real thing. AND that it is the main barrier between most kids and being able to do a moderate amount of reasonably accurate arithmetic and such.

But the elementary/middle school curriculum couldn't possibly be more carefully designed to maximize math anxiety in people who are prone to it, if they tried. Timed tests on addition and multiplication facts that you MUST pass before moving on to the next level, etc.

A couple of my offspring never really got past the "subtract 2" or "multiply by 4" or some other really, really basic level, and so they were just stuck at that level in "the system" for literally years.

There must be a better way.

Certain people are just never going to produce the answer to a question like "What is 21 minus 2?" quickly.
Ever.

Repeat the problem/question/flashcard a thousand times. 10 thousand. A million.

Recall never improves.

It's always there--slow. But it never speeds up.

In fact, recall slows down due to said child realizing somewhere along the way that math flashcards are torture.

But: Slow recall is fine. Or maybe no recall at all of that happens to a particular blind spot of your brain. There is no crying need to be able to recall 21 minus 2 at any particular speed in real life.

But in the system that kid--who just can't recall 21 minus 2 or can't do it fast enough for whatever state standards some group of nincompoops in a boardroom have dreamt up--is stuck there at the 2nd grade level and can never move forward.

P.S. That same kid can rather easily understand all sorts of concepts from algebra, algebraic geometry, calculus, topology, abstract algebra etc etc etc. (Again, based on actual experience.)

But 21 minus 2 never speeds up at all.

(Or if it does, it's due to further innate brain development 5, 10, 15, 20 years later--nothing at all to 10 quibillion useless and confidence-defeating repetitions.)

Meanwhile kid who can perfectly well understand algebra, algebraic geometry, calculus, topology, abstract algebra, etc content believes themselves to be "dumb at math" due to the idiot way arithmetic is ramrodded down kids' throats in first and second grades.

/End rant
posted by flug at 5:38 PM on June 1 [8 favorites]


The NYT has an excellent article from 2014 about why math comprehension in the US is so poor.

The tl;dr is that Americans have developed excellent new ways of teaching math several times over the years that show real, concrete improvements in student math ability, methods that were enthusiastically adopted by countries like Japan in the 80s with remarkable results, but that American educational and teaching institutions do a piss-poor job of training teachers in these methods. The result in America is a cycle of faulty implementation of new methods, confused and angry students and parents when inadequately trained teachers fail to properly implement the new methods, and then a retreat to the old methods. The old methods rely on rote memorization of procedures and formulas divorced from underlying mathematical principles that focus on what one academic in the article calls merely "answer-getting", which tends to produce very poor mathematical ability because students never gain a coherent understanding of math. And worse, as each cycle crashes and burns in the US, it serves to reinforce the idea in the populace that all math reform is ridiculous and futile, making improving math education that much harder each time.
posted by star gentle uterus at 8:05 PM on June 1 [4 favorites]


I was never any kind of bad ass framing carpenter but at one point I could just hold up a piece of blocking look where it was going and cut it to size. The eyeball is definitely trainable.
posted by Pembquist at 9:10 PM on June 1 [1 favorite]


Prescription glasses wearer with a prism in both lenses. Eyeballing will never work for me, bring on the squares, jigs, tapes, rulers, dividers, and scribing gauges please. Also people that are even halfway decent at shooting pool (the game, this is not code talk for something crafty) are like wizards to me for the same reason.
posted by RolandOfEld at 11:03 PM on June 1 [2 favorites]


I always like to discover new *estimating* tricks. Often a good estimate is more than adequate.

Square roots are a pain without a calculator. Let's learn two tricks. First, you have to know the common squares up to 81. 6*6 = 36, 7*7 = 49, 8*8 = 64, etc. (The more the better!)

Lets try the area of a square. How long is each side of 38 square cm? The root of 38 is just a little more than the root of 36. 6 point-something miles on a side. Call it 6.1. Error: 1%.

Second trick: for multiples of 10, remember that the square root of 10 is, eh, about 3.16. Just a *shade* bigger than Pi, right?

Now: what's the side of 500 square feet? 500 is 50 * 10. Multiply the roots! Sqrt(50) is about 7. Sqrt(10) is 3.16. So: about 7*3 = 21. Plus a little more, call it 22 feet on a side. Error: 2%.

No batteries, no pencil!
posted by Twang at 1:38 AM on June 2 [1 favorite]


Laura Kampf: “I have this piece of wood and I want to find the middle. How do I do that without measuring at all?”

me: huh, okay, assuming your board is a rectangle, you could draw a diagonal straight line from each corner to its opposite corner, and then draw a line that is perpendicular to one side of the board which goes through the intersection of the two diagonals

Laura Kampf: “Eyeball the middle, mark it from one side, then mark it from the other side which will give two lines pretty close to each other. Then it is very easy to see the middle between those two lines.”

me: whut, how is that going to work, what if you really suck at eyeballing things
My initial attempts at eyeballing the middle would be further than the opposite edge, and subsequent attempts at finding the centre of the new lines would lead to a rapidly diverging series.
posted by Ned G at 2:38 AM on June 2


Laura's method works even if you do overestimate. It will always converge.
posted by bonehead at 5:57 AM on June 2


I mean, I don't want to pull out the equations on a thread specifically about avoiding them, but the series only converges if you draw a line on the piece your working on. If your first estimate is so bad that you make a mark on the table, the series diverges
posted by Ned G at 6:23 AM on June 2


I'll admit you'd have to be really bad at eyeballing for that to happen, but that's the joke I was aiming at (and missing, leading to this diverging series of comments)
posted by Ned G at 6:26 AM on June 2


ha, I refuse to believe that anyone is so bad at eyeballing that they do not understand that the midpoint of a line segment must be somewhere on that line segment
posted by 23skidoo at 7:36 AM on June 2


Divergence diversion
posted by Greg_Ace at 8:32 AM on June 2


As an engineer learning woodworking, I've had to unlearn a lot of "calculation based math" and get better at this kind of stuff. At first I'd do something like plan a 20 degree dovetail, calculate the lengths and transfer that to the board multiple times. Now I lay out a 1 in 7 line on some scrap, set up an angle finder, and happily don't have to care about measuring past the first line.

It's a very different way of thinking, and a useful one at that. More outcome focused: it doesn't matter what the angle or length might end up as, as long as it functions as it needs to. Versus using a schematic with precise lengths and angles everywhere: the desired outcome can be obscured by the detail.

Of course, there's a lot of knowledge about the process of working with wood that's needed, before the understanding of when you can and can't ignore a particular dimension is really useful. I've got a few pieces that ended up far smaller than originally planned because of premature cuts...
posted by Jobst at 10:27 AM on June 2 [2 favorites]


It's one reason why I think "analog" woodworking especially will remain popular, as opposed to switching to CAM. When you're programming a machine, it's very engineering mathy, you do need to work out those angles, cut depths, feed rates. Then you put it on a vacuum table, push a button and watch the machine work.

Kampf is very much the opposite. She frequently works with barely a sketch to start and dimensions her parts as she goes to match with what's in her head. Her measurements are intuitive and to simply fit as she thinks necessary. This doesn't produce a less precise or sloppy work, it's simply more ad hoc, rather than planned. Her process is also about feeling the texture of the wood and materials as she works, which also contributes to her decision-making.

The first is really good for for jobbing or selling multiple pieces, but the later works just fine for the singular one-off work, which is how she makes her living. Jimmy Diresta has a very similar process; you almost never see him use a tape in his builds either. It's not even that one is industrial the other for private enjoyment, both kinds of work can be used to make a living and increasingly hobbyists have access to computerized tooling too. The decision to put the work into an abstract design and have a machine build (see for example Frank Howarth's builds) vs designing as you go with hand tools is fascinating to watch.
posted by bonehead at 11:58 AM on June 2 [2 favorites]


I love that tip for dividing things into thirds by angling the ruler for easier to use numbers

My wife just showed me that today! I recognized having seen it before but it was not in my use-vocabulary. Now I have to find some things to divide.

The math of shop work is interesting, and feels like it should be interestingly formalizeable. You often don't care about two things matching a number, you care about them matching each other. So you don't measure on each, you measure on one and cut the other to match.

There was a section of Fine Woodworking (in the 1980s this probably was) that had brief shop tips, which often got into shop math like finding the center of a circle, and readers would send in five different methods.
posted by away for regrooving at 11:12 PM on June 2


I'm good at math but don't measure things out in too much detail and instead prefer to mark what I've got and work with that because there's always something that'll spring up to complicate my plans once I start making it - "No plan survives first contact with the enemy" and all.

The most important thing about building shit is to measure as infrequently as possible! If you have a gap and a choice between measuring the gap and transferring the measurement to the piece that fills it, vs bringing the stock over to the gap and holding it up to the gap and marking directly on it what the cut is -- always mark directly.

This morning I installed a new latch on our gate. I looked at the installation diagrams and how my gate was set up and realized that the two were way too different for me to follow the diagrams and ended up working "backwards" and placing everything on the gate as I was going to make sure that it would all work. At one point I had to add some additional wood onto my gate and instead of measuring the angle I'd need to cut my wood I just brought my wood to the gate and marked the two points the diagonal would have to go through and then adjusted my mitre saw to cut between those two points. I have an angle finder but there was no need to use it as marking the wood would give me the same result.
posted by any portmanteau in a storm at 12:17 PM on June 3


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