# The origin of a straight line/flat surface **URL:** \ **Category:** Factual Questions\ **Created:** [March 7, 2012, 7:40pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067 "2012-03-07T19:40:44Z")\ **Posts on this page:** 17\ **Page:** 1
**Author:** ![Moris](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/moris/32/2846_2.png) [@Moris](https://boards.straightdope.com/u/Moris)\ **Post date:** [March 7, 2012, 7:40pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/1 "2012-03-07T19:40:44Z")
Forgive me if there’s an obvious answer I can’t figure out. I will probably facepalm myself. We are surrounded with straight lines and flat surfaces: your computer screen, IKEA furniture, bathroom tiles and so on. But how they were made? The factory machines must have been made by other factory machines, and so on. Where is the origin of all that? I can’t think of any straight lines appearing in nature, save for the horizon line, Sun rays and a frozen lake, perhaps. A perfect circle is much more achievable; it’s relatively easy to make a compass or a spinning wheel for clay pottery (although manufacturing of a perfect sphere is beyond me). I’m aware Ancient Greeks were using a straightedge. But when did it all started? How human society - in the Stone Age, perhaps - managed to make something perfectly flat by using stone tools and bones? By “perfectly” flat I mean _reasonably_ flat, not on a microscopic level. And this begs another question: what is the most perfect flat surface/straight line we are able to make nowadays (using laser technology and whatnot)? I mean material object, not the laser beam itself? ---
**Author:** ![aerodave](https://avatars.discourse-cdn.com/v4/letter/a/f08c70/32.png) [@aerodave](https://boards.straightdope.com/u/aerodave)\ **Post date:** [March 7, 2012, 7:50pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/2 "2012-03-07T19:50:47Z")
A straightedge can be made “from scratch”, as long as you’re okay with making 3 of them. By checking different pairs of 3 straightedges against each other (or rubbing them together in a process known as [lapping](http://en.wikipedia.org/wiki/Lapping)), they will all eventually acquire straightness. If you use only 2 edges rubbed against each other, they will mate perfectly, but no necessarily along a straight line. See this page for a description: [http://home.comcast.net/~jaswensen/machines/straight\_edge/straight\_edge.html](http://home.comcast.net/~jaswensen/machines/straight_edge/straight_edge.html) Creating flat plates is similar…it involves using a trio of plates rubbed in two dimensions until they are all flat. ---
**Author:** ![Valgard](https://avatars.discourse-cdn.com/v4/letter/v/7feea3/32.png) [@Valgard](https://boards.straightdope.com/u/Valgard)\ **Post date:** [March 7, 2012, 7:55pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/3 "2012-03-07T19:55:28Z")
So basically how could someone have created a straight line or flat surface early on? Dig a long trench, fill it with water, let it come to rest. There’s a flat, level surface that you can use to mark off the foundation of your (building, pyramid, etc). Or pull a string tight and mark along it. Nice straight line. Cut along the line carefully. Take two reasonably flat surfaces (e.g. two clay bricks) and rub them against each other, they should wear down to a couple of nice flat surfaces. Once you’ve got one flat reference it’s much easier to make more of them. ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [March 7, 2012, 7:57pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/4 "2012-03-07T19:57:11Z")
A taut string is straight. Now nature isn’t abounding with taut strings, but a spider hanging from a strand of silk is one example. This old thread is about “the first straight edge” but includes how to make a flat surface in one of the first replies: > **[The first straight edge](https://boards.straightdope.com/sdmb/showthread.php?t=561315)** > > This question may have already been posed here, but I couldn’t find anything using the search. Google wasn’t much help, either. Anyways, my question is about straight edges. Today we have rulers, levels, and all sorts of instruments to draw and... … **Aerodave** has already explained that while I was searching though… ---
**Author:** ![Pixel\_Dent](https://avatars.discourse-cdn.com/v4/letter/p/bc8723/32.png) [@Pixel\_Dent](https://boards.straightdope.com/u/Pixel_Dent)\ **Post date:** [March 7, 2012, 8:03pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/5 "2012-03-07T20:03:56Z")
The surface of still water is for most intents and purposes flat. Since the middle of the last century window glass has been made flat by floating the molten glass on bath of molten tin. ---
**Author:** ![Michael63129](https://avatars.discourse-cdn.com/v4/letter/m/3da27b/32.png) [@Michael63129](https://boards.straightdope.com/u/Michael63129)\ **Post date:** [March 7, 2012, 8:05pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/6 "2012-03-07T20:05:51Z")
It’s pretty easy to make flat glass by spreading molten glass over a liquid: > [@](#): > > [Float glass](http://en.wikipedia.org/wiki/Float_glass) is a sheet of glass made by floating molten glass on a bed of molten metal, typically tin, although lead and various low melting point alloys were used in the past. This method gives the sheet uniform thickness and very flat surfaces. Modern windows are made from float glass. Most float glass is soda-lime glass, but relatively minor quantities of specialty borosilicate[1] and flat panel display glass are also produced using the float glass process. Also, a string with a weight on it will make a perfectly straight vertical line. As for the flattest surface ever made, a quick Google search brings up [this article](http://www.news.cornell.edu/chronicle/98/3.19.98/flat_surfaces.html)from 1998 that says that it would be achieved in the next 5 years (don’t know if it happened; however, they recently made the [most perfect sphere](http://www.theage.com.au/news/national/making-an-exact-difference/2007/06/14/1181414466901.html), so that should be possible): > [@](#): > > Melissa Hines is a researcher in search of perfection. Her goal is a mirror surface on which not even a single atom is protruding above the surface. ---
**Author:** ![Dallas\_Jones](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dallas_jones/32/3277_2.png) [@Dallas\_Jones](https://boards.straightdope.com/u/Dallas_Jones)\ **Post date:** [March 7, 2012, 8:11pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/7 "2012-03-07T20:11:56Z")
Carpenters today still set out a straight line using a string and powdered chalk. A snap line uses a string coated with powdered, usually colored chalk. The string is stretched taut, then you pull up on the line ‘snapping’ a mark in whatever you intend to cut or attach something to. It’s old technology and it still works great. [How to Use a Chalk Snap Line](http://homerenovations.about.com/od/toolsbuildingmaterials/ss/chalksnapline.htm) ---
**Author:** ![Senegoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/senegoid/32/6606_2.png) [@Senegoid](https://boards.straightdope.com/u/Senegoid)\ **Post date:** [March 7, 2012, 8:22pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/8 "2012-03-07T20:22:07Z")
> [@Moris](#): > > We are surrounded with straight lines and flat surfaces: your computer screen, IKEA furniture, bathroom tiles and so on. But how they were made? **The factory machines must have been made by other factory machines, and so on**. Where is the origin of all that? This. It’s factory machines _all the way down!_ 😛 Related phenomena are known. Example #1: In the mid-70’s, when Pascal was the predominant Computer Science Religion, it was an article of faith that Pascal compilers were written in Pascal. According to my then-roommate who was a student in that field, it was a blasphemy, and indeed it was even beyond imagination, to suggest or question that anyone would write a Pascal compiler in any language other than Pascal. So how was the _first_ Pascal compiler written? Well, in Pascal, apparently. (Refugees from that era may remember that one of the earliest implementations was for the Control Data 6000/7000 series machines, and that it was so horrendously awful that a whole generation of Computer Science students’ minds were poisoned into believing that Pascal was surely a Gift From The Gods, in order to rationalize in their minds why they would ever use such an abomination.) Example #2: I recently picked up a stack of old (but possibly still useful) computer programming books at a thrift store for 10 cents each, including SQL Visual Quickstart Guide by Chris Fehily (Peachpit Press, 2005). In the introduction, on page xviii he lists topics not covered in the book: [QUOTE=Fehily] Advanced programming or administration. I don’t cover installation, privileges, triggers, recursion,\* stored procedures, replication, backup and recovery, optimization, cursors, collations, character sets, or translations. [/quote] (What’s that leave to cover anyway? This book is 450 pages long.) The footnote clarifies why he doesn’t cover recursion: [QUOTE=Bottom of same page] [sub]\* To understand recursion, you must first understand recursion.[/sub] [/quote] It’s straight edges, factory machines, and recursion _all the way down_. ---
**Author:** ![Dallas\_Jones](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dallas_jones/32/3277_2.png) [@Dallas\_Jones](https://boards.straightdope.com/u/Dallas_Jones)\ **Post date:** [March 7, 2012, 8:22pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/9 "2012-03-07T20:22:46Z")
As a side note to **Michael632129** ’s post about float glass, an engineer I used to work with left the company briefly to work for a glass manufacturer. He said that due to the energy costs of heating up the float metal, that if something broke down on the packaging/finished product end of the production line, they had an arm that would just come out and start breaking the glass off the end of the line. It was easier to recycle the broken glass because all of the raw materials and most of the energy, had been used to make it the first time, than to shut down the whole process and start it up again. ---
**Author:** ![Moris](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/moris/32/2846_2.png) [@Moris](https://boards.straightdope.com/u/Moris)\ **Post date:** [March 7, 2012, 9:46pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/10 "2012-03-07T21:46:03Z")
> [@aerodave](#): > > A straightedge can be made “from scratch”, as long as you’re okay with making 3 of them. By checking different pairs of 3 straightedges against each other (or rubbing them together in a process known as [lapping](http://en.wikipedia.org/wiki/Lapping)), they will all eventually acquire straightness. If you use only 2 edges rubbed against each other, they will mate perfectly, but no necessarily along a straight line. See this page for a description: [http://home.comcast.net/~jaswensen/machines/straight\_edge/straight\_edge.html](http://home.comcast.net/~jaswensen/machines/straight_edge/straight_edge.html) > > Creating flat plates is similar…it involves using a trio of plates rubbed in two dimensions until they are all flat. Thanks for that link, Dave. Very interesting read. There’s a book title that immediately caught my attention…“Foundations of Mechanical Accuracy”. (if I’ll be able to find it somewhere with a wallet-friendly price). I’m little skeptical about rubbing two stones together; my muscle movement is not uniform - a surface would be smooth, but probably slightly bulging. However, other techniques mentioned here are really ingenious…and when I see some things still working perfectly for carpenters and tailors after all these years of human progress, somehow it makes me feel glad.🙂 ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [March 7, 2012, 10:25pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/11 "2012-03-07T22:25:23Z")
> [@Senegoid](#): > > > [@](#): > > > > Originally Posted by Bottom of same page > > > > - To understand recursion, you must first understand recursion. Have you googled _recursion_? Go on - try it… ---
**Author:** ![Half\_Man\_Half\_Wit](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/half_man_half_wit/32/21766_2.png) [@Half\_Man\_Half\_Wit](https://boards.straightdope.com/u/Half_Man_Half_Wit)\ **Post date:** [March 7, 2012, 10:37pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/12 "2012-03-07T22:37:52Z")
Folding something, like a big leaf etc., should also yield a straight edge. ---
**Author:** ![sweeteviljesus](https://avatars.discourse-cdn.com/v4/letter/s/898d66/32.png) [@sweeteviljesus](https://boards.straightdope.com/u/sweeteviljesus)\ **Post date:** [March 7, 2012, 11:05pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/13 "2012-03-07T23:05:31Z")
> [@Moris](#): > > I’m little skeptical about rubbing two stones together; my muscle movement is not uniform - a surface would be smooth, but probably slightly bulging. However, other techniques mentioned here are really ingenious…and when I see some things still working perfectly for carpenters and tailors after all these years of human progress, somehow it makes me feel glad.🙂 The trick to producing a flat plate is to rub it in a figure 8 motion. ---
**Author:** ![Napier](https://avatars.discourse-cdn.com/v4/letter/n/ce73a5/32.png) [@Napier](https://boards.straightdope.com/u/Napier)\ **Post date:** [March 7, 2012, 11:21pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/14 "2012-03-07T23:21:22Z")
The trick to producing a flat plate is making them in threes per aerodave’s post. Rubbing two surfaces together until they fit perfectly only guarantees spherical surfaces, with the radius depending on how you moved them. Only when you iterate between three do you drive the radius to infinity and so generate flat surfaces. ---
**Author:** ![Mangetout](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mangetout/32/19_2.png) [@Mangetout](https://boards.straightdope.com/u/Mangetout)\ **Post date:** [March 7, 2012, 11:43pm UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/15 "2012-03-07T23:43:08Z")
There are a number of linkage mechanisms that will produce straight lines - details here: > **[Straight-line mechanism](https://en.wikipedia.org/wiki/Straight_line_mechanism)** > > A straight-line mechanism is a mechanism that converts any type of rotary or angular motion to perfect or near-perfect straight-line motion, or vice versa. Straight-line motion is linear motion of definite length or "stroke", every forward stroke being followed by a return stroke, giving reciprocating motion. > The first such mechanism, patented in 1784 by James Watt, produced approximate straight-line motion, referred to by Watt as parallel motion. > Straight-line mechanisms are used in a variety ... (NB: although these are often shown as constructed from straight members, there is no real requirement for the parts to be straight - only rigid) ---
**Author:** ![rowrrbazzle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/rowrrbazzle/32/414_2.png) [@rowrrbazzle](https://boards.straightdope.com/u/rowrrbazzle)\ **Post date:** [March 8, 2012, 4:40am UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/16 "2012-03-08T04:40:42Z")
My post from an earlier thread: > [@How was the first straight edge made?](https://boards.straightdope.com/t/how-was-the-first-straight-edge-made/441082/16): > > FYI the earliest known devices to draw theoretically straight lines are the Sarrus linkage and the Peaucellier-Lipkin linkage. > > [Sarrus linkage - Wikipedia](http://en.wikipedia.org/wiki/Sarrus_linkage) > > [Peaucellier–Lipkin linkage - Wikipedia](http://en.wikipedia.org/wiki/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. ---
**Author:** ![Novelty\_Bobble](https://avatars.discourse-cdn.com/v4/letter/n/a3d4f5/32.png) [@Novelty\_Bobble](https://boards.straightdope.com/u/Novelty_Bobble)\ **Post date:** [March 8, 2012, 8:39am UTC](https://boards.straightdope.com/t/the-origin-of-a-straight-line-flat-surface/615067/17 "2012-03-08T08:39:35Z")
With no snarkiness intended to the OP, can I just say that this thread had produced some of the most interesting content from the most unpromising of starting questions. Carry on…