[HN Gopher] Rulers of the Ancient World: period correct measurin...
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Rulers of the Ancient World: period correct measuring tools
Author : maxwell
Score : 82 points
Date : 2024-07-11 16:41 UTC (6 hours ago)
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| scubbo wrote:
| This was an impressively-"Garden Path" title, given the noun/verb
| ambiguity of "correct" and the modifier(?)/verb ambiguity of
| "measuring" :)
| singleshot_ wrote:
| You could also read the "period" as punctuation and it still
| almost works. Ambiguously garden-pathable sentence?
| BitwiseFool wrote:
| While I am no apologist for the measurement system we use here in
| the United States, I realized something interesting when trying
| to explain why almost all of our units consist of easily
| divisible sub-units. Imagine you needed to split something up
| into halves, thirds, fourths, sixths, etc.. If you imagine doing
| this with paper, it's fairly easy.
|
| Now imagine Metric, and the need to split something into 10 even
| pieces. We can make this a little easier knowing that we just
| need to split into fifths first, and then halve each of those. Do
| you know how to fold a piece of paper into fifths?
|
| It can be done, and it's remarkable how to do this with a
| straight edge and a pencil. However it is definitely more time
| consuming than being able to fold using easily divisible numbers.
| To that end, once you have a decimal ruler you can just use that,
| but I can see why decimal based measurements were not more common
| in the past.
|
| All that being said, I really wish metrication had been completed
| here in the US before I was born.
| 082349872349872 wrote:
| The nice thing about geometry (as opposed to arithmetic) is
| that it's easy to guess something a little larger[0] than 1/10,
| repeat a series of ten of those units, and then line its end
| points up at an angle to your work and, letting similar
| triangles do their thing, transfer[1] from there...
|
| [0] eg, 1/8 would work, if you insist on subdivisions
|
| [1] assuming space-time is effectively euclidean at the scale
| you're doing this, which even on HN ought to be a safe bet?
| kragen wrote:
| this presupposes a way to construct parallel lines to
| transfer your tenths back to the segment you wanted to
| subdivide; this can certainly be done to three significant
| figures of precision with a compass and straightedge (or
| string and sand table), but it's still extra effort and extra
| opportunities for error compared to simple perpendicular
| bisectors
|
| in some cases, it's not extra effort because you're doing a
| task that requires the construction of those parallel lines
| anyway, of course. laying out tiles on a floor or ripping a
| plank into smaller planks, for example. and if your desired
| parallel lines are perpendicular to the edge of your stela,
| the square that figures so prominently in the freemasons'
| logotype allows you to scribe them easily
|
| (then again, once you're going to the effort of making a
| square, you might as well rule it)
| mitthrowaway2 wrote:
| I don't think objections to US customary units are because of
| base-12 vs base-10. I think it's because it's 12 inches to 1
| foot, 3 feet to 1 yard, 1760 yards to 1 mile, 3 tsp to 1 tbsp,
| 2 tbbsp to 1 fl. oz, 40 fl. oz per quart, 2 quarts per pint, 4
| quarts per gallon, 31.5 gallons per barrel (or 42 if oil), 16
| ounces per pound, 2000 pounds per ton (or 2240 if long ton),
| 1000 mil per inch, and so on.
|
| It's not just a base-12 system, it's pretty random across the
| board.
|
| And even just for "workshop" purposes, things like screw
| diameter (or sheet metal gauge, etc) are only listed in
| fractions-of-an-inch above certain sizes; below that it
| switches to a completely different numbering system, so you end
| up needing a reference chart anyway, which often just displays
| a decimal-inch figure like '#6 screw = 0.138 inch', and now
| you're looking up which fractional-markings that lies between
| on your ruler...
| bee_rider wrote:
| This makes me wonder about an alternate universe where a mile
| has 2310 yards. At least we'd get a bunch of prime factors
| out of it. Although guess being able to repeatedly halve a
| mile is useful for splitting up properties?
| JoeAltmaier wrote:
| Those conversions varied all over the place. But they
| originated in a system of doubling. Used to be two quarts per
| pottle, two pottles per gallon, and so on from there (peck,
| kenning, bushel, strike, coomb)
| davidgay wrote:
| > 40 fl. oz per quart,
|
| That's the imperial quart. The US quart is 32 fl. oz.
|
| And, of course, the US fl. oz is slightly different from the
| imperial one. And neither is 1 (weight) oz of water (but at
| least the weight ozes are the same in US and imperial...).
| saalweachter wrote:
| The imperial fl. oz is 1 weight oz, at least within the
| margin of error of 1824.
|
| It's a shame that everyone broke the "a pint is a pound,
| the whole world 'round" relationship. The US standardized
| its pint too big, the UK switched from a 16 to 20 oz pint.
| legitster wrote:
| Yeah, it's crazy to see my dad at work in his shop - the amount
| of intuition he has of fractional measurements is insane, but
| he can do the math so quickly.
|
| In that specific context, if you were to do the math with
| decimal measurements it would take longer and leave you with
| some funky units. It's hard to describe how you work with the
| fractions - but the lumber and the saw blades and the screws
| and even the finishes all come in these standardized fractional
| increments that are easy to work with.
|
| And the skill required of a project is directly related to the
| precision of the measurement you go down to - 1/8, 1/16, 1/32,
| etc. It all just kinda works.
| itishappy wrote:
| > If you imagine doing this with paper, it's fairly easy.
|
| Halves and forths are easy. Thirds, fifths, and sixths are not.
|
| There are constructions for the odd fractions, but they're not
| particularly intuitive.
|
| https://abrashiorigami.com/dividing-paper-into-thirds-fifths...
| wongarsu wrote:
| > Now imagine Metric, and the need to split something into 10
| even pieces
|
| That's only true if you assume that in metric everything starts
| out as 1, 10 or 100 units. But that's not really what happens.
|
| For example kitchen appliances and furniture basically works on
| multiples of 60cm: an oven or dishwasher fits in a 60cm slot,
| and accordingly your cabinets will be one appliance wide
| (60cm), two appliances wide (120cm) or half an appliance wide
| (30cm). And you will find that halfes, thirds, fourths or
| sixths of 60cm are easy to calculate. Lots of other furniture
| works on multiples of 80cm. Those don't have nice thirds, but
| halves, fourths, eights, sixteenths, doubles, triples,
| quadruples all work great.
|
| And this happens not only in furniture but in everything.
| Having things 1.2, 1.5 or 1.6 of whatever unit you are
| measuring is common and allows you to have nice fractions. We
| just never write them as fractions. And honestly 45 + 7.5 is so
| much easier to do that 3/8th + 1/16th (of 120)
| ahazred8ta wrote:
| TLDR - an ancient measuring rod project (modern reproductions)
| fusslo wrote:
| thats a really cool project. I would've loved making them while
| taking my history electives in college. There's something really
| nice about making something that gets tied to what you're
| learning.
|
| Since they talk about Roubo, can I ask if any other amateur
| woodworkers just don't use a ruler?
|
| I used to 3d model everything and make simple dimension drawings
| for parts. Since I started mostly using hand tools I just stopped
| measuring. Each part is a proportion of the other parts. I find
| it a whole lot easier, more forgiving, and easier to correct. I
| do use dividers, however.
|
| Just curious if I'm the only one. Of course my disclaimer that
| the most complicated thing I made without a ruler is a dutch-
| style workbench out of oak. The most complicated thing I made
| from my old way of cad was probably a set of fairly complicated
| shelves
| lostlogin wrote:
| > There's something really nice about making something that
| gets tied to what you're learning.
|
| Steiner schools are right into this way of learning. I'm a
| survivor of that system and now my child goes there. Its
| interesting seeing it play out from a parents perspective and
| it's given me more appreciation for my parents efforts.
| mauvehaus wrote:
| Furniture maker (professionally):
|
| I typically do Sketchup for design drawings because it's easier
| for clients to see things in 3D. Do I love it? No, but I'm
| reasonably quick using it, so I do. It's also a hell of a lot
| easier to make big changes than working on paper.
|
| Shop drawings I do by hand. How much measuring I do depends
| greatly on how what I'm trying to achieve:
|
| If the piece is based heavily on proportions and symmetry[0],
| I'll use dividers a lot more than a ruler.
|
| If I need to hit certain measurements for practical reasons,
| it's a bit of both.
|
| If I'm strictly reproducing a design model, I'll have the ruler
| out pretty exclusively. Sketchup does do division/even spacing
| with array copy, so I can usually work out what I want pretty
| closely.
|
| If I'm reproducing a piece from a photo[1], it's a lot of both,
| some educated rounding to a reasonable fraction, and I've gone
| entirely crosseyed by the end of the day.
|
| Occasionally, I'll do something almost entirely without firm
| measurements. My tool tote is based on my hand span (because
| that's about the width you can comfortably carry along your
| side), and there were no drawings to speak of. Everything was
| dimensioned at the bench. Stick chairs and stools tend to be
| pretty similar; if I'm building them out of scrap, I design
| around the available wood. I'm not sure I'd build any for money
| yet though. I have a few more learning experiences in me before
| I do that.
|
| [0] https://www.longwalkwoodworking.com/cabinet-on-stand
|
| [1] https://www.longwalkwoodworking.com/federalclock
| jacobolus wrote:
| You might enjoy https://www.byhandandeye.com/books/ which is
| all about this style of design.
| myself248 wrote:
| You're not the only one. https://www.leevalley.com/en-
| us/shop/tools/hand-tools/markin...
| legitster wrote:
| These are beautiful - but the project kind of misrepresents how
| ancient measurements worked.
|
| Outside of building sites in Medieval Europe it would be common
| for the head architect to have the outline of his hand on a sign.
| The idea being that even "crude" measurements like hand-widths
| and thumb lengths would be universally agreed upon for the
| project.
|
| You can see some of this at work watching documentaries of the
| Guedelon Castle project - you see just how little precise
| measurements were actually needed. A lot of tasks we are used to
| accomplishing through high precision measurement, they instead
| use clever tricks of geometry. And jigs - lots of jigs.
|
| In this way, ancient craftsmen were genius - often understanding
| some pretty profound principles of geometry through experience
| and intuition alone. Measurements, such as they existed, were
| always a very "local" affair.
|
| It wasn't until empires and mass manufacturing that the need for
| "standardized" measurements. The intelligence of the individual
| craftsman became less important - the ability to follow
| instructions became more. In a way modern measurements are a form
| of artificial intelligence - an automation tool.
| JoeAltmaier wrote:
| In fact in the US it wasn't until Herbert Hoover, in his
| capacity as Secretary of Commerce in the 1920's, standardized
| everything from pipe gauges and thread counts to bedpans and
| light sockets. He published a government schedule which soon
| got adopted nationwide. It enabled a farmer in Wyoming to order
| parts from a manufacturer in Massachusetts and they would fit
| when they arrived.
| legitster wrote:
| Although, it should be noted that the standardization of
| measurements _themselves_ was mostly done by the founding of
| the country. Authority of the government to "fix the
| Standard of Weights and Measures" is in the constitution.
|
| From its founding, the US had one of the largest contiguously
| agreed upon measurement system in the world, sidestepping the
| problems of European measurement systems which changed border
| to border - even predating the official adoption of the
| Metric system in France. And it's largely why it's stuck
| around until today.
| darby_nine wrote:
| It's also worth noting the government is technically
| transitioning to metric now. There's just no political will
| to enforce this. Shithole country.
| jzxy wrote:
| >It wasn't until empires and mass manufacturing that the need
| for "standardized" measurements.
|
| You have the cause and effect backwards. Mass manufacturing
| didn't create a need for standardized measurements.
| Standardized measurements allowed the existence of mass
| manufacturing. Mass manufacturing wasn't even close to a
| possibility before that. Measurements weren't created for a
| need that didn't even exist yet. You can read on the history of
| the various systems of measurements and their motivations that
| they weren't exactly concerned with ideas of "mass production".
|
| >In 1669, Jean Picard, a French astronomer, was the first
| person to measure the Earth accurately. In a survey spanning
| one degree of latitude, he erred by only 0.44%
|
| 1669! that's long before any attempt at building mechanization
| of labor.
|
| It's like how a lot of math was seemingly useless and existed
| just for its own sake until people found real applications for
| certain algorithms.
|
| The obsession of a handful of people towards precision
| measurement is what allowed the industrial civilization to
| truly emerge.
| legitster wrote:
| Chicken and egg maybe? It depends on where you define the
| start of industrialization. If you did not have cheap,
| available steel no one would have wasted it on pressure
| vessels and saws and instruments of precision. The
| innovations of Darby and Bessemer were done largely by hand-
| measured built machines.
|
| Jean Picard's tools of measurement themselves would have been
| custom built by hand for him, and his results were measured
| in a very regional French measurement of feet.
| Standardization != precision.
| kragen wrote:
| https://en.wikipedia.org/wiki/History_of_geodesy says
|
| aristotle: off by a factor of almost 2
|
| eratosthenes: off by -2.4-+0.8%, or maybe up to 15%, because
| we aren't sure how big his stadia were
|
| ptolemy: at first accepting eratosthenes' figure, he later
| switched to a figure that was about 30% low
|
| aryabhata: probably off by about 0.8%, though again it's
| unclear how big his yojana were
|
| caliph al-ma'amun: probably off by about 0.45%, and in this
| case the source of error is not the unit of measurement but
| the different accounts of how many of them they measured in a
| degree
|
| the fact that 1500 years ago aryabhata bothered to give the
| earth's diameter as 1581 1/24 yojanas strongly suggests that
| he believed the size of a yojana to be defined to within less
| than 26 parts per million; remember that he had to do all his
| calculations mentally or by hand, so extra significant
| figures were extra significant labor
|
| however, all of these measurements postdate the monuments of
| rameses from 3200 years ago, which contain multiple precisely
| measured statues constructed all over egypt (though i don't
| have references on what the tolerances were on the statues)
| fhars wrote:
| That is also why now country became industrialized before
| they gave up their ancient foot/inch/ounce measurement
| systems and became fully metric.
|
| Or something like this.
| jzxy wrote:
| "metric vs imperial" has very little to do with the idea of
| "standardizing measurements". A foot is just as well
| defined of a unit as a meter and is not the historical,
| ancient meaning of "just use your foot". In fact, the
| Imperial units system was standardized and enshrined in
| British law before the metric system got adopted in France.
| saalweachter wrote:
| It's a shame that we entered the era of precision a century
| or so before we got some good science.
|
| We could have chosen so many different, cooler distance units
| than "one ten-millionth the distance between the North Pole
| and the equator, on a line passing through Paris". We could
| have chosen 1 nano-lightsecond! We could have chosen the
| wavelength of the hydrogen line! We had options, but we
| didn't even know them in 1800.
|
| Avogadro's number is about 3% off from 24!. Instead of
| defining our mole as the number of carbon-12 atoms equal in
| weight to 12 cubes of water each one-billionth the distance
| between the North Pole and the equator, on a line passing
| through Paris, on a side, we could have defined it as 4!!!
| Imagine telling that to aliens when explaining our standard
| units, they'd be so jealous they'd convert on the spot.
| legitster wrote:
| More importantly, we missed a real opportunity to switch to
| a base-12 number system.
| BitwiseFool wrote:
| Now we have to wait for the French to have another
| revolution.
| dredmorbius wrote:
| _Liberte, egalite, duodecimilite!_
| EnigmaFlare wrote:
| Instead of having Avogadro's number at all, chemists could
| just count using numbers like we do for everything else. We
| already have the prefixes to make 10^+/-24 easy. No need to
| re-define it, just stop using it.
|
| It's nothing more than a conversion factor between two
| parallel unit systems that somehow both coexist within SI.
| btbuildem wrote:
| That's a great observation! Measuring with ruler / tape /
| string isn't the most reliable way to do it -- using a full
| length of something like a stick, is. This is the basis of the
| simplest of jigs: cut a piece, then cut all the other pieces
| you want to be like that piece, by using that piece as a guide.
|
| The need for specific measurements seems to have arisen
| alongside industrialization of building processes - in the
| times before that, measurements were relative (eg, piece A is
| 3x piece B, etc). It's telling that a lot of the "traditional"
| measurements we have (looking at you, metric system) refer to
| body parts. We used to measure things in relation to the human
| body.
| legitster wrote:
| Another fascinating tidbit I learned from the curator at an
| air museum - the transition from wooden airplanes to metal
| airplanes was not a material constraint! In many ways, wood
| continued to be a superior building material for airplanes
| even by the advent of WWII.
|
| The transition from wood to metal was driven primarily as a
| _manufacturing_ improvement. Wood changed and warped as you
| built the airplane, and it required a lot of expertise and
| knowledge of the properties of wood to properly tie together
| the structure.
|
| Metal weighted more and cost more - but you could step away
| from a production line and the piece would not have changed
| shape on you.
| throw0101c wrote:
| > _In many ways, wood continued to be a superior building
| material for airplanes even by the advent of WWII._
|
| A mostly-wood WW2 airplane:
|
| * https://en.wikipedia.org/wiki/De_Havilland_Mosquito
| UncleSlacky wrote:
| Also notably stealthy as a result of its wooden
| construction:
|
| From https://militaryhistorynow.com/2014/11/28/flying-
| under-the-r...
|
| "British aircraft designers got out to an early lead with
| the De Havilland DH. 98 Mosquito. Introduced in 1941, the
| twin-engine, fighter/bomber's airframe was constructed of
| radar absorbing plywood. While not specifically designed
| to be stealthy from the outset, the plane's low signature
| as well as its top speed of nearly 600 km/h (375 mph)
| made it a tough target to track for Axis radar
| operators."
| dredmorbius wrote:
| I didn't realise the Axis powers _had_ radar. Apparently
| they did, though Axis technology greatly lagged the
| Allied powers ':
|
| <https://en.wikipedia.org/wiki/German_Luftwaffe_and_Krieg
| smar...>
|
| Axis powers lead in other areas, notably in drones (V-1),
| rocketry (V-2), tank design, air-to-surface missiles, and
| audio technology (recording, public-address, playback,
| broadcast),
| saalweachter wrote:
| Growing up, I always heard "measure twice, cut once", but in
| almost every context I've actually had to measure and cut,
| "measure once, cut twice" [or more] is actually the way to
| go. Cut with a jig or a stop, stack your layers of fabric
| together and cut them at the same time -- any time you can
| avoid measuring the same length twice, the better your two
| pieces will match up.
| dredmorbius wrote:
| The human body was generally available to those making
| measurements, and (by the standards of the time) roughly
| sufficient for most purposes. An inch (of bronze or steel), a
| yard (of cloth), or fathom (of depth, measured by a sounding
| line) would have been immediately accessible to a tinker, a
| tailor, or sailor. (Units of measures applicable to spies are
| left as an exercise to the reader.)
|
| Metric measurements are _standard_ but not _convenient_ ,
| particularly in a world without rapid cheap communication or
| standardised industry. Virtually everything built was a one-
| off and fit-to-fashion on site.
| incognito124 wrote:
| That's a great title
| ne8il wrote:
| Brendan (the maker of these) is a fascinating, very smart guy.
| He's a very talented woodworker and wrote a great book on James
| Krenov. I was lucky to take a class he taught a few years ago,
| and I enjoy following his Instagram page to see the new projects
| he has going on.
| detourdog wrote:
| I'm excited to see others as focused on this sort re-evaluation
| of the correct balance between digital and analog tools and
| manufacturing. This is exactly the area I'm working but this guy
| is documenting it.
| heikkilevanto wrote:
| I have two anecdotes. One is a shipyard in Denmark, possibly in
| the 1700's, where the master builder would hammer a stake in the
| ground, walk as many steps as needed for that ship, and hammer
| another stake. The rest would follow geometrically.
|
| The other is a builder of harpsichords, late 1900's, who
| explained that when starting a new instrument, he would define
| the "inch" for that one, the width of the "white" keys. 8 of
| those would make the width of an octave, and the usual 5-6
| octaves would give the width of the keyboard. From that he could
| figure out the length of the instrument, and the curve of the
| side. All this with nothing more than a compass and a straight
| edge. He claimed it was the more historical way to do it, as they
| did in the 1600's. His instruments were well regarded by
| musicians today, and fetched a good price.
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