Item: They’re renovating the house across the street from us; a big job with the basement enlarged and the whole structure raised a few feet. The trouble is, from our front porch it looks like it’s ever-so-slightly tilted. Item: I was doing some photo-editing and having a little trouble getting one shot satisfactorily leveled. Those who’ve worked with Photoshop or equivalent know that a tilt of much less than 1º is obvious to an attentive eye.
[The comments on this piece are remarkable; you might a perusal rewarding.]

I wonder what evolutionary pressure drove the human mind’s exquisite sensitivity to the condition where a line deviates slightly from the “horizontal” or “vertical”, that is to say whose angle is almost but not quite 0 or π/2 radians from the vector representing the local gravitational field, best thought of as an arrow pointing at the centre of the earth.

This raises another question that’s long troubled me (unlike the first one, I suppose it has an easy answer): Where do straight lines come from?

More concretely: How do they make rulers? And every other artifact such as those that fill my living room whose edges are straight enough to satisfy the demanding human eye? I know how to stretch a string, but asked to construct, starting with raw materials, any object whose edge needed to be straight, I wouldn’t know where to start.


Comment feed for ongoing:Comments feed

From: Ted Han (Dec 12 2008, at 00:49)

Who says it's evolutionary?

Why couldn't it have been learned behavior? The Müller-Lyer Arrow Illusion ( ) is a good example. This is a case where familiarity w/ lines and angles are clearly culturally based, and if you don't come from a culture familiar w/ the necessary conditions, you clearly perceive lines & angles differently.

RE creating straight edges: Googling turned up this interesting article:


From: Dustin (Dec 12 2008, at 01:08)

Anthro-wise I suppose straight lines originate in the observation of gravity's effects. i.e. your fruit not rolling away from you when on the flat surface.


From: Derek K. Miller (Dec 12 2008, at 01:12)

Don't carpenters and such often chalk (or ash) a string, stretch it taut, then snap it against a surface to mark a straight line for cutting? Or use a plumb bob for verticals?

I guess these days you could use a laser level, but that's probably cheating.


From: Mike (Dec 12 2008, at 01:24)

Not sure I see the problem, unless you're being very draconian in your definition of "raw materials". You don't need specialist tools to grind something down, and a straight line to compare against isn't hard to find.

Still, sheltered water is a flat surface. A long, thin, weighted fiber is a straight line. Both are somewhat inconvenient to work with, but you only need to do so once.


From: richard kennedy (Dec 12 2008, at 02:04)

Hi Tim,

In engineering they used to make flat reference plates by hand that were

so flat you had to slide them apart because they stuck together.

I've never seen it done but I was told that the technique was to make 2 plates, cover one in dye then

place one on top of the other. Moving the top plate will make marks in the

dye that show were the high spots are. Then you use a scraper to flatten the hills, and keep repeating until the plates are flat.

After all that a ruler is easy.


From: Doug (Dec 12 2008, at 02:31)

Any good machinist can tell you how to create a straight edge or a right angle. This web page explains the making of a strait edge:

(I have no connection to the owner/author of the web page it was selected at random from a set of available pages.)


From: Graham (Dec 12 2008, at 02:58)

The average ruler is injection moulded, which means someone's cut a ruler-shaped hole in a piece of metal to make the mould, for which all you need a lathe with straight runners.

The runners are either made on another lathe, or through extrusion. Extrusion can create a visually straight edge without requiring an equally straight master.


From: robert (Dec 12 2008, at 05:31)

>> I know how to stretch a string, but asked to construct, starting with raw materials, any object whose edge needed to be straight, I wouldn’t know where to start.

1 - take the "ruler" blank. secure it.

2 - take an object (say, twig), use it to make four points on the blank such that the diagonals are equal length. This establishes a true rectangle. A piece of string will do for that.

3 - snap a chalk line with that piece of string between the two points you want to be the ruler edge.

4 - cut


From: Eric Sharakan (Dec 12 2008, at 05:33)

Hah! As a kid, I often wondered the same thing about how they made rulers so straight! One thought I had for creating a straight line assumes one has a sheet (however irregularly-shaped) of paper. Folding it & creating a nice neat crease results in a straight line.


From: Kevin Reid (Dec 12 2008, at 06:09)

I have no idea what the actually practical, or historical, ways to bootstrap straight lines are, but a couple of ideas:

• It is possible to create mechanical linkages which generate straight lines; for a linkage all you need is bars with pivot points the same distance apart, which _might_ be easier to construct than straight lines.

• You can take your string and use it to make a straight line mark on a flat surface. You can get flat solid surfaces from liquids (e.g. float glass).


From: James Aylett (Dec 12 2008, at 06:15)

You can construct (in the technical sense of drawing) collinear points using a protractor. (You can make one out of two twigs and some twine, providing you lash them together well enough that they won't move with respect to each other.)

Given two colinear points, you can construct more points on that line (you can certainly do it by using them to construct orthogonal lines and then using them to construct more points on the original line; there may be an easier way).

I *guess* you could use that to create a long series of colinear points, and then gradually whittle the edge down to match the (effectively) dotted line. I've never tried it, but that would be my first attempt.

(Looking at the plasterwork in the corner of my home office, these lines are only broadly straight; they wiggle but maintain the correct direction. However unless I look closely, I don't notice this, which suggests it's good enough to avoid whatever mental machinery is spotting off-by-delta at corners. One of these corners I'm pretty sure isn't actually a set of right angles, although I can't be bothered to climb up there to measure them with.)

I can't remember when geometric construction was discovered, though. Or when we started building things with straight edges, for that matter.


From: Jake (Dec 12 2008, at 06:17)

gravity. chalk line.


From: Dave Pawson (Dec 12 2008, at 07:09)

Where do straight lines come from

How about light. Or at least, light at the lengths we see 'rays' at.


From: PJ (Dec 12 2008, at 07:10)

They make flat planes of glass (or used to) by melting the raw silica on top of a puddle of molten lead, then letting the pair cool; they don't bond, so you can lift the glass off later and it's as flat as gravity can make a liquid, which for reasonable sizes might as well be exactly flat.


From: Ryan Mulligan (Dec 12 2008, at 07:12)

You answered your question. You use gravity to make straight lines. The tool used is called a plumb line.

After you use gravity to make straight line you can use that line to make other straight ones.


From: James Aylett (Dec 12 2008, at 07:31)

Realised too late that I made that way too complex by introducing right angles. If you don't need orthogonal things, you can make do with a piece of string. Stretch it taught, secure at both ends.

Thinking about it, I've seen builders lay out walls like that.

Construction works when you need right angles, though: it can give you colinear points at right angles to an existing straight line. (Use this to make a crude set square for corners, for instance.)


From: scott (Dec 12 2008, at 07:51)

Make a straight edge?

Fold a piece of paper. In order to make it *not* straight you have to deform the paper in some way. I've often made a ruler out of a random piece of scrap when no other was available.

Make a perfect right angle?

Fold a piece of paper twice.


From: Michael Buckbee (Dec 12 2008, at 08:05)

I think it is all about the plumb bob -

Checkout the decidedly non ancient but interesting hack that they used to get a horizontal level from a plumb bob (the pic in the upper right)

- Mike


From: Forest (Dec 12 2008, at 09:40)

Fun questions. Reminds me a question a drawing professor would ask first year students. "Are there lines in nature?"

The prof never gave a definitive answer but the question did spark some great conversations at the local coffee house.


From: Karl Anderson (Dec 12 2008, at 10:59)

It's also interesting to wonder how the first lathe lead screw was made, because the quality of the made screw depends on the one used to make it.


From: jack (Dec 12 2008, at 11:10)

It's always funny to see people try to backfill "natural" explanations for cultural phenomena. People, your concepts of "straight" and "horizontal" and so on are culturally determined. This is a question for a science historian, not an evolutionary biologist.

The idea has been around for a long time, obviously -- one supposes Pythagoras had a pretty good idea of it, and the Egyptians had it and lost it along with their empire -- but was not a part of the broader culture until the development of modern architectural techniques.

The first formal definition of straightness can be considered a side effect of the development of the IS system; the Paris Academy of Sciences didn't include it in their original report to the French National Assembly, but it was developed later in the 1790s as part of the effort that went into the creation of the Meter of the Archives. I'm pretty sure the original work was done by Méchain either during or just after the Dunkirk-Barcelona meridian measurements, but I can't find my reference on that right now.

Subsequent standard bases for straightness became more esoteric, of course; they concluded pretty quickly that the Meter of the Archives shouldn't be used for this purpose, so they came up with a different base. It was defined in terms of a certain number of kilograms of tension in a platinum wire. The current standard has something to do with rolling a cesium clock down an inclined plane, I think; it's way over my head and I'm not a physicist.

But the concept is the same, and is pretty simple: the standard is determined and maintained by a standards body, and all our rulers and so on are copies with greater or lesser fidelity. In the states, our comparators are maintained by NIST.


From: JB (Dec 12 2008, at 12:04)

Dudes, to all the "it's culturally determined" people, what precious little I remember from introductory neuroscience leads me to believe that one of the few things scientists were relatively confident of w/r/t to the functioning of the visual system was that recognition of horizontal and vertical lines is _not_ culturally determined. Quite the opposite in fact: there's hardware support for it.

I don't remember this too well, but apparently its baked in at a fairly low level: maybe in the retina or optic nerve, but _certainly_ within the first few layers of the occipital lobe. There's a layer somewhere full of neurons that if you jab an electrode into, you see a flood of action potentials when the attached eye is seeing a perfectly vertical line, and then a steep fall-off as you rotate off the vertical. Similar neurons exist for horizontals (as well as other low-level features like light/dark transition, motion in various parts of the visual field, edge detection, etc.)

Again, I'm going from old collegey memories here but if I'm not mistaken these same neurons exist in animals. I think the cat was used as an example? Like you can pop open the back of a cats head, stick some electrodes the proper depth into the visual cortex of the cat, and you'll find these vertical/horizontal detecting neurons.

I have no idea what they are for, evolutionarily, but I'm happy to speculate: Maybe they are there to augment the vestibular system for orientation? Kind of like how pilots rely on an artificial horizon gauge. Many places at least the horizon is quite flat so good access to your orientation relative to it through the visual system may help reduce error from the vestibular system? Ok, this last paragraph is all BS.


From: Derek K. Miller (Dec 12 2008, at 22:45)

In a followup post to this one on my blog:

I ask if it's possible to establish a scale of how far "away from scratch" many modern objects are.

For example, you can apparently make your own straight edge from scratch ("scratch level 1") using the techniques above, and any kid can make a level-1 sharp stick by breaking it off a tree and rubbing it against a hard surface like a rough stone.

But something like a stove or a car or a computer (or even a doorknob) is manufactured using steel and electricity and precision-made components from factories, which themselves need factory-built tools to build, and so on. Their "scratch level" might be in the dozens.


From: John Turnbull (Dec 13 2008, at 00:23)

While I enjoy Jack's history of the cultural formalism of "straight" -- and I happen to be in Paris where the conflict between straight and wandering is built into the city as a result -- I have to side with the biologicals on this one. Even a tiny, primordial swimmer needs horizontal (the overhead surface of the swamp) and vertical (the path of a rising bubble) to find lunch. While dining, it might have enjoyed the sight of straight (a ray of sunshine through the murk).


From: Stephen Brooks (Dec 23 2008, at 07:31)

JB, your last paragraph isn't BS. There used to be a tourist trap in southern New Brunswick, Canada called "Mystery Crater." What had happened was that the limestone beneath a swath of forest had eroded out from under, and that whole section of forest floor had collapsed just a bit, so that all the trees were 5 or 6 degrees from vertical.

Because ALL the trees were like that, and we expect trees to pont straight away form the center of the earth, it was VERY difficult to keep your balance.


From: Gordon Anderson (Dec 31 2008, at 12:06)

sorry for the Vancouver specific comment, but for all you readers who are familiar to it, next time you drive over the Burrard Street Bridge or down Beach avenue, take a look at the round apartment tower just north of the bridge. I appears to lean a bit, but of course it doesn't, the illusion is caused by the slope of the bridge or the street, and the amibiguous edge of the building. You think you are on the straight and level, therefore the building must not be plumb.

Happens all over, check your own house for plumb, Tim.


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