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Salmo Trutta
03-12-2008, 01:22 AM
This may seem like a dumb question. Likely there is a simple answer that I haven’t considered.

The earliest architects and engineers must have needed a straight edge to draw lines for accurate calculations. Nothing, at least that I know of, in nature is a precise physical straight line. I suppose a thin piece of metal could be bent for a straight edge, but this would require that the metal be hammered into a perfectly flat plane. A stretched length of string would be roughly a straight edge, but not a great way to draw a straight line. (As it would bend with the pressure of a writing utensil.)

I would wager that the answer lies in the fact that the surface of liquid forms a flat plane. But how that was transfered to a straight edge is beyond my limited cleverness.

ManiacMan
03-12-2008, 01:41 AM
http://home.comcast.net/~jaswensen/machines/straight_edge/straight_edge.html

Terminus Est
03-12-2008, 01:53 AM
A stretched length of string would be roughly a straight edge, but not a great way to draw a straight line. (As it would bend with the pressure of a writing utensil.)
Take the string and impregnate it with ink, graphite, or even charcoal. Stretch it and pluck it, i.e., lift it perpendicular to the surface then release. Voila!

Salmo Trutta
03-12-2008, 02:00 AM
Those techniques work just fine if I have modern saws, files, sandpaper, and advanced measuring tools. It’s interesting in that I’ve not really considered that people need to make their own reference edges these days.

I’m not sure it is applicable to ancient methods. It also seems like fairly advanced thinking and technique.

Maybe another interesting question would be “when was the first straight edge needed and used for architectural, engineering and/or mathematic purposes?

Salmo Trutta
03-12-2008, 02:04 AM
Take the string and impregnate it with ink, graphite, or even charcoal. Stretch it and pluck it, i.e., lift it perpendicular to the surface then release. Voila!

I suppose that might be straight enough, although there are inconsistancies in the material of the string that would make it less than a perfect straight line.

At some point in time, though, an actual straight edge was made. How?

cmyk
03-12-2008, 02:41 AM
Letting a sheet of some form of fine clay/water mixture to cure might give it a flat enough surface due to gravity. Then maybe some how cut that into a strip to give you a straight edge to pass a pencil across.

From there, you would gradually build and refine more accurate edges, until you could create a nice ruler or square out of wood, or metal.

I'll bet we're missing a very simple solution though, that our modern minds are blind to.

magellan01
03-12-2008, 02:47 AM
I'd say all you have to do is fold something. You give me the most irregular piece of cardboard, tin, etc., all I have to do is fold it over once flat and voila—a straight edge.

TimeWinder
03-12-2008, 03:17 AM
Nothing, at least that I know of, in nature is a precise physical straight line.

Well, if you want perfection, there aren't any even today; just sucessively better refinements. I suspect the real answer to your question is that they found something close enough. Sighting along an edge will tell you if it's straight to a very high degree, and if it isn't, you sand/scrape/whatever. The current theory is that the parthenon stones were flattened by simply putting another stone slab on top of them and moving them in a circle on each other for a long time -- wearing them down to two flat surfaces. The stone fittings of the pyramids were likely created the same way, although it's harder to prove.

And the bit about no straight lines in nature always bugged me; you get into a "No True Scotsman" thing about what a straight line is pretty quick, but there are LOTS of straight lines in nature: the edge of a half-moon, the strands of spider webs, the shape described by anything hanging on a calm day, the path described by any falling object from at least one angle, the surface of water, crystal edges, shear patterns in stone/mud/moved earth, beams of light, the edge of anything folded or bent, scratches of a hard object thrown against another, sight and shadow lines, breakage patterns in stone, and on and on. Even the surface of the ocean is likely straighter than the ruler you used in school, curvature of the earth notwithstanding.

cmyk
03-12-2008, 03:38 AM
I'd say all you have to do is fold something. You give me the most irregular piece of cardboard, tin, etc., all I have to do is fold it over once flat and voila—a straight edge.

Bingo. There's the easiest and fastest way to get something pretty damn straight. Especially with a sheet of tin or copper, maybe even gold?

Mangetout
03-12-2008, 05:32 AM
If you want something as straight as a rule, all you have to do is get it approximately straight, use it to draw a fine line, then flip it over and draw another line immediately touching the first - if it's not straight, the deviations will show you where to remove material from the edge.

Telemark
03-12-2008, 07:55 AM
I’m not sure it is applicable to ancient methods. It also seems like fairly advanced thinking and technique.
Those ancients were an extremely bright bunch. Advanced thinking and techniques are not a recent invention.

Giles
03-12-2008, 08:20 AM
It's been a while since I saw bricklayers at work, but one tool that they used to use to get bricks in a straight line was string. I think that would have been available to the Egyptians and the Greeks as they built the pyramids and the Parthenon.

You can also use a piece of string to construct a right angle for the corners of your pyramid, temple, etc.: mark off 12 equal sections on the string, then (with a couple of friends if the string is long enough) make a 3-4-5 triangle. As Pythagoras knew (but did not discover) the largest angle of that triangle is a right angle.

CalMeacham
03-12-2008, 08:30 AM
:
Originally Posted by Terminus Est
Take the string and impregnate it with ink, graphite, or even charcoal. Stretch it and pluck it, i.e., lift it perpendicular to the surface then release. Voila!

I suppose that might be straight enough, although there are inconsistancies in the material of the string that would make it less than a perfect straight line.

It's a damned good line for construction purposes. This is the purpose of a chalk line -- a string on a spool in a housing filled with chalk. You have one guy hold the end while the other guy walks out the line. They hold it taut a couple of inches above the surface and snap it as indicated. You get a very staight line for building or painting. I've done it myself often enough.

As for a straight surface -- liquids allowed to sit still will produce a very good flat surface. If you let something that is liquid congeal or solidify, it will have a very straight surface you can use as a reference.

Mangetout
03-12-2008, 08:32 AM
I would wager that the answer lies in the fact that the surface of liquid forms a flat plane.Actually, it doesn't. It forms a curve approximately of the same radius as the Earth.

OK, that's 'flat' as far as most small-scale practical applications require it...

03-12-2008, 08:58 AM
Those ancients were an extremely bright bunch. Advanced thinking and techniques are not a recent invention.This is a mantra I often recite to myself. The people of thousands of years ago were just as intelligent as we are today. They had less technology, less absolute knowledge, and less history to learn from, but their reasoning ability was just as sharp. If they could find ways to apply the things they learn and discover, they could achieve no end of amazing things. And, indeed, they did.

rowrrbazzle
03-12-2008, 02:27 PM
FYI the earliest known devices to draw theoretically straight lines are the Sarrus linkage and the Peaucellier-Lipkin linkage.

The arms of the Peaucellier-Lipkin linkage don't have to be straight. Only the indicated distances must be equal. This can be accomplished by stacking those arms and drilling through them all at once.

I'm not sure if an analogous construction method can be used with the Sarrus linkage, but it seems simple enough that the ancients could have discovered it.

Napier
03-12-2008, 02:41 PM
In optics, you grind surfaces by rubbing them together with some kind of abrasive. The surfaces become spherical while you do this, with the radius depending on the strokes you use. Spherical surfaces are the only ones that remain in contact throughout all the sliding and rotating.

A special case is the flat surface, which you could always consider spherical with infinite radius. Opticians can make very flat surfaces by grinding together three different objects, two at a time, and changing out which of the three is set aside. Flat surfaces are the only surfaces such that 3 of them will mate this way.

Bosda Di'Chi of Tricor
03-12-2008, 05:00 PM
The edge of a large Quartz crystal might have provided a model.

scr4
03-12-2008, 05:08 PM
If you want something as straight as a rule, all you have to do is get it approximately straight, use it to draw a fine line, then flip it over and draw another line immediately touching the first - if it's not straight, the deviations will show you where to remove material from the edge.
Not necessarily. If you do that with an S-shaped edge (or any edge that is rotationally symmetric about its middle), there will be no deviation between the edge and the line. I think you need three edges, like ManiacMan's link and Napier said.

Mangetout
03-12-2008, 05:17 PM
Not necessarily. If you do that with an S-shaped edge (or any edge that is rotationally symmetric about its middle), there will be no deviation between the edge and the line. I think you need three edges, like ManiacMan's link and Napier said.
I said flip - you're rotating (OK... we're both rotating - but what I mean is draw a line against the would-be-straight edge, then flip the piece over the line you just drew.

Napier
03-12-2008, 05:24 PM
Mangetout's suggestion is right, and is equivalent to folding.

R. P. McMurphy
03-12-2008, 05:45 PM
Well, if you want perfection, there aren't any even today; just sucessively better refinements.

Would a laser beam be sufficiently close to a "perfectly straight line" or will Einstein's theories serve to prove that the laser is not "straight" due to the effects of gravity? If that's the case, I give up on seeking perfection.

mwbrooks
03-12-2008, 06:47 PM
This may seem like a dumb question. Likely there is a simple answer that I haven’t considered.

The earliest architects and engineers must have needed a straight edge to draw lines for accurate calculations. Nothing, at least that I know of, in nature is a precise physical straight line.

It seems likely that the impetus to create a straight edge would have started with the invention of the spear (http://en.wikipedia.org/wiki/Spear). The first and most obvious test of a straight edge is to sight along it and make corrections by scraping. With patience, you can actually achieve a very straight edge that way, especially if you start with a good piece of straight-grained wood.

The idea of comparing at least three examples to refine straightness probably came up while spears and arrows were still the high tech application. By the time folks started working stone they probably had a pretty good idea of how to create as straight an edge as they needed for short work.

As for longer lines, folks would have thought of stretching a string pretty quickly when the need arose. I gather that's been standard practice for dividing up the Egyptian flood plains for agriculture for a very long time. For even longer work, the establishment of sight lines is pretty evident in old works like Stonehenge. No lasers required!

As for using liquid leveling to create a flat, I'm sure that came into the arsenal of measurement too. I was taught in school that the ancient Greeks sometimes used wax tablets as "erasable" writing surfaces, so they would have known of its self-leveling tendencies. (BTW: at that scale, I think surface tension around the edges would affect flatness more than the Earth's curvature.)

Carson O'Genic
03-12-2008, 07:39 PM
What is your definition of "straight"?
Taut string or wire suffers catenary curvature.
ManiacMan's post is the straight dope on making one;three lines are brought to truth with each other.
Cast iron edges are used by millwrights/fitters/machinists, the best true to .0001/12" obtained by hand scraping.Practical lengths are about 8',which will take two grown men to handle.

HMS Irruncible
03-12-2008, 08:28 PM
At some point in time, though, an actual straight edge was made. How?
The only teenager in school who couldn't get a fake ID decided he'd protest by drawing black X's on his hands with magic markers and run around saying "I don't need alcohol to have a good time" until he turned 21.

Mesquite-oh
03-12-2008, 11:58 PM
The only teenager in school who couldn't get a fake ID decided he'd protest by drawing black X's on his hands with magic markers and run around saying "I don't need alcohol to have a good time" until he turned 21.Ahh the 80's. I thought the first joke was going to have to do with becoming hetero. Back to the OP, the methods we used as kids was to roll the item, then bend (like a pool cue) or get into my Dad's tool box and use his plumb bob (weight on a string) or that purple snapping string thing that puts a line on the ground.

Derleth
03-13-2008, 05:59 AM
The only teenager in school who couldn't get a fake ID decided he'd protest by drawing black X's on his hands with magic markers and run around saying "I don't need alcohol to have a good time" until he turned 21.I though it was the first kid who decided to stop hanging out with the living dead.

(OK, you beat me to it. xXDamnYouXx!)

Nava
03-13-2008, 07:27 AM
As for a straight surface -- liquids allowed to sit still will produce a very good flat surface. If you let something that is liquid congeal or solidify, it will have a very straight surface you can use as a reference.

At times when I didn't have a pre-built level, I've just filled a square glass with water. Works just fine for picture-hanging purposes.

And of course getting a vertical straight line is still done with string and a tiny piece of lead.

Quartz
03-13-2008, 07:34 AM
I'd say all you have to do is fold something. You give me the most irregular piece of cardboard, tin, etc., all I have to do is fold it over once flat and voila—a straight edge.

This only works if the surfaces are flat - if you fold a piece of bubblewrap or corrugated cardboard then the resultant edge is going to be ridged.

chowder
03-13-2008, 07:42 AM
This is a mantra I often recite to myself. The people of thousands of years ago were just as intelligent as we are today. They had less technology, less absolute knowledge, and less history to learn from, but their reasoning ability was just as sharp. If they could find ways to apply the things they learn and discover, they could achieve no end of amazing things. And, indeed, they did.

Bit of a contradiction there old chap.

They had less technology than us therefore their intelligence must have been less otherwise their technology would have been the equal of ours.

Or summink

Derleth
03-13-2008, 07:45 AM
Bit of a contradiction there old chap.

They had less technology than us therefore their intelligence must have been less otherwise their technology would have been the equal of ours.

Or summinkNo. Intelligence is the ability to problem-solve, not the amount of time you've had to build toys.

Mangetout
03-13-2008, 07:47 AM
They didn't have our mastery of materials and techniques specific to those materials, but those things aren't based on our individual intelligence anyway - you're a smart guy, chowder, but you didn't work out how to smelt the metal you use, or make the semiconductors in your phone, etc.

Our technology is largely a result of the accumulated application of intelligence - but exactly the same kind of intelligence our ancestors had.

Napier
03-13-2008, 08:45 AM
>Would a laser beam be sufficiently close to a "perfectly straight line" or will Einstein's theories serve to prove that the laser is not "straight" due to the effects of gravity?

Einstein's theories are about straight lines, more than being about whether light follows them. For example, there are distant astronomical objects such that multiple straight lines go from here to there and get pretty far apart at times. But the lines are straight.

>Taut string or wire suffers catenary curvature.

Nava's hanging one doesn't.

Carson O'Genic
03-13-2008, 10:10 AM
[QUOTE=Napier
>Taut string or wire suffers catenary curvature.

Nava's hanging one doesn't.[/QUOTE]

Touche.But we were talking edges,straight, not plumbs,bob.

WarmNPrickly
03-13-2008, 10:59 AM
Somebody up there mentioned a quartz edge, which along the same lines as muscovite (http://en.wikipedia.org/wiki/Muscovite). Even today muscovite is used in atomic force microscopy to produce atomically flat surfaces.

chowder
03-13-2008, 12:28 PM
Derleth/Mangetout:

I stand corrected

Can Handle the Truth
03-13-2008, 12:36 PM
What about ice? How flat would an ice surface be if the water was allowed to freeze undisturbed?

spinky
03-13-2008, 01:56 PM
Touche.But we were talking edges,straight, not plumbs,bob.A taut line with a slight catenary curve is still straight in the vertical plane, so would make a good straightedge for a lot of situations.

Still, with all the reasonable suggestions, it seems like this one was nailed in the first response.

brujaja
03-13-2008, 02:03 PM
The first straight edge was in 1980, according to this site (http://en.wikipedia.org/wiki/Minor_Threat)

mwbrooks
03-13-2008, 04:34 PM
What is your definition of "straight"?
Taut string or wire suffers catenary curvature.

Only in Z. Works fine for laying straight lines on an X-Y plane, such as a mud flat.

What about ice? How flat would an ice surface be if the water was allowed to freeze undisturbed?
Depending on its size and whatnot, it might tend to heave up in the middle. I've seen ice cubes frozen with a one- or two-inch spike growing out of the top surface. (I forget the mechanism, it was explained in Scientific American a few years back, I think).

The first straight edge was in 1980, according to this site
Thanks for the link. I was suffering from major whoosh.

mwbrooks
03-13-2008, 04:42 PM
What about ice? How flat would an ice surface be if the water was allowed to freeze undisturbed?

Actually, I'm forgetting one instance in which allowing a liquid to freeze produces a reliably flat surface. I recall reading a very long time ago that the key advance that made movable type really practical was development of an alloy that did not shrink or expand when it cooled from liquid to solid, allowing a "true" type face to be cast easily. Sorry, no cite at hand.

Bosda Di'Chi of Tricor
03-13-2008, 05:59 PM
Bit of a contradiction there old chap.

They had less technology than us therefore their intelligence must have been less otherwise their technology would have been the equal of ours.

Or summink

I hope that was a whoosh. :dubious:

Mangetout
03-13-2008, 06:06 PM
Depending on its size and whatnot, it might tend to heave up in the middle. I've seen ice cubes frozen with a one- or two-inch spike growing out of the top surface. (I forget the mechanism, it was explained in Scientific American a few years back, I think).The surface freezes around the edge - the unfrozen middle heaves through expansion - as the freezing extends inward, the heaving becomes more pronounced, until the zone that is freezing is actually forming the walls of a rising tube.

There used to be controversy over this, but I believe the above has now been confirmed by observation.

Lumpy
03-13-2008, 08:16 PM
I've read that the ancient Egyptians leveled the sites of the great pyramids by building a dike around the site, flooding it with water, drilling reference holes to identical depths from the water's surface, and then flattening out the site to the bottoms of the holes. Opposite corners of the pyramids are level to within an inch or so.

Tuckerfan
03-14-2008, 05:57 AM
Straight edges are actually pretty easy to make, all it takes is a good hand and plenty of patience. A skilled draftsman or artist can make a reasonably straight line with no tools at all, other than a writing instrument.

In the case of a spear, the shaft most likely would have been made from a sapling tree which was reasonably straight to begin with, then the irregularities would have been removed by sand rubbed by hand (most likely protecting the hand with leather) while the shaft is turned by hand. One technique not mentioned, that most likely would have been used at some point, is the use of paint. You put paint on a surface, let the paint dry, and then lightly rub the surface with an abrasive, and high spots will show up as paint free areas, apply more paint, rub again, check for high spots and continue until it's level.

Hand polishing (or lapping) can be surprizingly accurate. In shop class, I made a rather complicated (and large) vise, and after heat treating, I needed to get the surface of the fixed jaw as flat as possible. I tried everything to get it flat, from using the school's wire-EDM machine, to the surface grinders, and every time wound up with less than desirable results. Finally, I took a lapping stone and began polishing it by hand. Many, many, many, many hours later, it was flat to within .0001 of an inch across it's entire surface. To give you an idea of how this compares with what I have to deal with in industry, most things have to be flat to within .001 - .005 of an inch.

Napier
03-14-2008, 08:15 AM
>I recall reading a very long time ago that the key advance that made movable type really practical was development of an alloy that did not shrink or expand when it cooled from liquid to solid...

There are various casting alloys that differ slightly in how their volume changes during freezing. Some of these work at very low temperatures, even high room temperatures. Many of them have indium and tin and bismuth and similar metals, and they are sometimes eutectic (alloyed in a ratio that minimizes the melt temperature). You choose these partly on the basis of exactly how much growth or shrinkage your application wants.

I think freezing water is unusual because it would like to freeze from the top down, and depending on how the edges are treated you can get a flat frozen piece because of this.

Mangetout
03-14-2008, 08:42 AM
In the case of a spear, the shaft most likely would have been made from a sapling tree which was reasonably straight to begin with, then the irregularities would have been removed by sand rubbed by hand (most likely protecting the hand with leather) while the shaft is turned by handSpears and especially arrows were also straightened by heating and bending - sighting along them and rotating to spot the 'wiggle' - then bending carefully in the right spot either by hand, or across a notched stone, or using a tool that looks like a ring on the end of a stick.

muldoonthief
03-14-2008, 08:42 AM
I would wager that the answer lies in the fact that the surface of liquid forms a flat plane. But how that was transfered to a straight edge is beyond my limited cleverness.

Just so you know, this is how they started making cheap window glass back in the 50's, called Float glass (http://en.wikipedia.org/wiki/Float_glass) - pouring molten glass on molten tin. Before that, window glass involved rollers and polishing, but float glass got you very flat surfaces for free.

Tuckerfan
03-14-2008, 08:51 AM
Spears and especially arrows were also straightened by heating and bending - sighting along them and rotating to spot the 'wiggle' - then bending carefully in the right spot either by hand, or across a notched stone, or using a tool that looks like a ring on the end of a stick.
True, but that won't get out the lumps caused by knots.

Mangetout
03-14-2008, 09:00 AM
True, but that won't get out the lumps caused by knots.
That's right - for something as big as a spear, they'd be sanded or shaved off - for arrows, it's a bit easier to find straight lengths of sapling that are not significantly knotty.

Either way, a combination of techniques would probably be used to achieve a good straight shaft.

mwbrooks
03-14-2008, 09:57 AM
Just so you know, this is how they started making cheap window glass back in the 50's, called Float glass (http://en.wikipedia.org/wiki/Float_glass) - pouring molten glass on molten tin. Before that, window glass involved rollers and polishing, but float glass got you very flat surfaces for free.

And, just for the sake of dotting the "t"s and whatnot, two other methods of producing plate glass were: blow a large cylinder then cut and unroll it, or blow a sphere, open the end, and spin it out into a disk. The latter type was called "crown glass" because of the characteristic "crown" deformity in the center. Or so I've heard.

Chronos
03-14-2008, 02:40 PM
It should be noted that, even in flat, Newtonian space, a laser beam still isn't necessarily a straight line. The path of any individual photon is, but the beam is made up of many photons. If I stick a laser pointer on a turntable, the beam will have a spiral shape.

Gary "Wombat" Robson
03-14-2008, 04:40 PM
The first straight edge was in 1980, according to this site (http://en.wikipedia.org/wiki/Minor_Threat)Thank you for posting that link. I had no idea what Mesquite-oh and Derleth were talking about until I read that.