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.
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.
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
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.
> 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.
I think the coolest thing from an experience perspective as far as a built environment with this is the opportunity to have spaces with different ratios and spacing.
I’m reminiscing about realizing from an American perspective why buildings in Europe felt so different. Old buildings sure, but new buildings feel weird! It finally dawned on me that the difference between imperial and metric had made its way to the build environment in subtle but pervasive ways that once seen could not be unseen. Case in point, European doors are wider, switches are lower, door handles are lower, rooms are just slightly off. Of course the reverse would be also be true. But contractors rounding to whole units for simplicity had standardized on a set of ratios that made things feel odd.
Would be cool to have an installation that embodied this. It’s subtle but talk about driving people crazy.
Anywhere between 28" and 30" is in the accepted range, though 28" will feel a little low to most people. I had a table at 31" once, and every time I sat at it, I felt like a kid sitting at the grown-up table.
A good reference for stuff like this is Human Dimension and Interior Space:
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 Guédelon 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.
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.
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.
"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."
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),
They certainly did! Fun fact: the first 1941 British combat drop of the newly formed Parachute Regiment was the Bruneval raid on the French coast whose purpose was to capture a German Wurtzberg radar.
Many years ago I spent some time working at an Army base in Finland. They had a small museum on site which had some German radar kit. It looked surprisingly modern (e.g. satellite dish type aerials) and was virtually unique because elsewhere in Europe the same hardware had all been destroyed
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.
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.
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.
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.
While I am frustrated by freedom units sometimes, the truth is that the US simply started too late and the transition costs are too high.
It is a different story to change measuring units in a still-mostly-rural society with relatively few engineers and engineering projects - which describes Europe in the late 19th century.
>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.
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.
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.
Avogadro's number is for making calculations including weight simpler. If I have x grams of carbon how many grams of oxygen I need to burn it all. And then how many grams of carbon dioxide I end up with.
Value is somewhat arbitrary. And could also be tied to some other isotope. It is really about the ratios between all the elements including their isotopes. Picking carbon and there of isotope C-12, and saying this is exactly 12 grams is not unreasonable selection.
Where did you get the A_oxygen and A_carbon in first part?
Take the same calculation, use 12,01 for carbon and 16,00 for oxygen. Values in one reference book, get 2,66444629475 or the 2,644.
Avogadro's number is just number of atoms in the mole. Making atomic masses sensible numbers.
Carbon dioxide is actually relatively bad example as both values are close to integers. Chloride with atomic mass 35,45 starts to be more reasonable example where you have pretty simple number.
As shown dealing with very small numbers like counting together masses of neutrons, protons and electrons and then removing binding energy gets very tiny numbers. Which make calculations more error prone or even complex to do by hand. Using atomic masses which include Avogadro's number makes it much simpler process.
Those are the mass numbers from the periodic table which are exact integers and chemists probably know in their heads.
If you have to look up a 4-digit number, it's not easier to look up or use 12.01 u instead of 19.95 yg, especially with higher atomic masses where they're less integer-like, as you say. But using u involves more conceptual complexity because you're mixing two different mass units (u and g) in the same calculation. That's the part that's hard to do in your head. Chemistry students often struggle with this whole concept, which comes with a whole parallel collection of formulas and quantities to work with the alternative mass unit. They more easily understand SI prefixes which is just reusing an existing well-known concept.
You don't need to struggle with doin math on very tiny numbers any more than electrical engineers have to struggle with picofarads and nanoseconds.
Avogadro's constant or number makes things relatively simple as you can treat 1 gram as 1 u and just work in moles. You have 100 grams of something, divide that by u or g and get number of moles of stuff. If you need to add something to react with, just multiply the number you just calculated with u of other stuff and get a minimum amount you need in grams.
It really doesn't matter that you have 6.02214097×10^23 things of something. Moles, grams and atomic units really only matter. You never go to yoctograms(btw defined in 1991). But instead deal with numbers above 1. Which is doable calculating by hand even. Avogadro is there just to tie 1 atomic mass unit to 1 gram.
Technically you could do it all on kilo, hecto, deka, deci, milli, micro moles... Depending on scale you work. As long as you keep it constant... In the end it is just moving the deciman point in the weight.
Can you write out a specific calculation using Avogadro's number/moles/u/etc. so I can do the same without those and see if it's actually any easier?
"treat 1 gram as 1 u and just work in moles"
Surely that's no easier than treating 1 gram as 1 yocto-gram and just working in yotta-things.
> You never go to yoctograms
You can and it's both as easy as moles to work with and conceptually simpler. That's why I'm saying we don't need all the Avogadro's number stuff since we do already have yg even if nobody uses it.
Just to be clear, I'm talking about how it could be done. You seem to be talking about how it is done. I'm not denying how people actually use it, just pointing out that it's a giant needlessly-complicated historical legacy.
And now that we actually know how big particles are, we could work the other direction [if restandarizing an industrialized civilization wasn't impossible] -- pick an arbitrary number of particles that is a nice number for some reason or another (eg, 4!!), take the simplest thing that has mass (monatomic hydrogen), and declare your unit of mass to be equal to 4!! hydrogen atoms.
Sure, it's not easy for a primitive scientist to take a box of an exact number of hydrogen atoms and weigh them, but any advanced civilization should know exactly what a hydrogen atom masses.
That system would last only as long as nobody wanted any more precision than you could get from measuring hydrogen atoms. Then they're do what they've always done and redefine it to something uglier but which can be measured more accurately.
> any advanced civilization should know exactly what a hydrogen atom masses.
Nobody can know that exactly. Just giving it a name isn't the same as knowing it. We already have a name for it - "the mass of a hydrogen atom".
There's a validity to your criticism that I'm not enough of a domain expert to really dismiss, but also --
We're already like, really good at measuring the mass of atoms. We know the hydrogen atom's mass to ten or eleven significant figures, something like one part in ten billion. It's not the most precise measurement we have, those are at around one part in a trillion or so, but it's still pretty darn good.
Are you suggesting we're already good enough at measuring the mass of atoms and no further precision will ever be needed? Otherwise, your statement would have been equally valid 100 years ago by just taking some significant figures off.
By the way, 4!! ~= N_A was a funny surprise! If you were starting from scratch though, you could make it even simpler and define the unit of mass to be 1e27 times the mass of a hydrogen atom which is 1.7 kg. But again, you might find some other more accurate way and have to redefine it to include an ugly conversion factor just to get practical work done in some high-precision future world.
Factorials are a base-independent way to make large numbers. You could go 10^27 or 10^25 or some other random power of ten, but why powers of ten over powers of two? And then once you choose a base, why 10^27 versus 10^25 versus 10^24? Which makes one the more natural choice than another?
On the other hand, once you choose factorials over exponents, and furthermore, double-factorials, there's really only one option. 3!! is is 720, which is not really much of anything, in the grand scheme of things. 5!! is something like 7e198, which is probably more than there is of anything in the universe, or at least, in the known universe. 4!! is the only double-factorial which is a useful number of particles.
The more annoying thing is that mass and electric charge are so far apart. If you were starting from scratch, it'd be really cool to have 1 number-unit of something be the mass unit, and 1 number-unit of electrons be the charge-unit. But 4!! electrons is like 100,000 coulombs, which is just a lot. 2^64 electrons is more like 3 coulombs, which is more workable, but 2^64 daltons is only around 30 migrograms, which is a helluva mass unit if roughly human-sized is the scale of most intelligent life forms.
(Incidentally, powers of two have an even closer coincidence to Avogadro's number -- 2^79 is within half a percent of N_A. But 79 is such an ugly number -- there's nothing particularly elegant about 10^1001111.)
Re: measurement, we're presumably going to get better at measuring the mass of a hydrogen atom over time. We might even eventually be able to calculate it from first principles (which is really just saying we might be able to establish an exact relationship between the mass of a proton, electron and various physical constants; according to a random search, a 2008 paper was able to calculate the mass of a nucleon within about 3% of experimental results, which isn't great accuracy wise but is still pretty interesting).
(Aside #2: You could also pick a larger particle to try to bridge the gap between mass and charge. The Higgs Boson, for instance, masses around 130x the hydrogen atom.)
Good point about being natural rather than tied to base 10. Though natural conflicts with human convenience and ultimately is is for humans. Even more natural could be using the same unit for mass and energy, and make it dimensionless!
2^64 daltons (30 micrograms) is already about 2 gigajoules.
4!! photons -- specifically the 21cm photons corresponding to the hydrogen line [which, speaking of precision, we have the frequency of that down to around 1 part in ten trillion] -- is about 0.6 Joules.
So 4!! hydrogen atoms gets you about 1 gram, 4!! H-I photons gets you about 0.6 Joules, and the wavelength of the H-I photon is around 21 cm.
It all seems a bit marginal. Nobody actually uses the definitions to measure anything anyway, least of all by hand or memory, so it's not going to make anything more convenient having fewer digits in the still-arbitrary conversion factors.
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)
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.
"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.
these are great. geometry is culture. there are some mythical proportions measured in cubits, handbreadths and other units of measurement (pillars of the first temple at jerusalem, etc) that put reading the old testament in perspective, where they were writing about physical objects we can use those measurements to reason about today.
I hope there are more editions of these rules and related ones in the future.
It's neat that the Egyptian measure was subdivided in an increasing fashion, almost logarithmically. I wonder what the error bound is if you use the Egyptian rule as a slide rule.
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.
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.
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...
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)
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...).
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.
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?
> 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)
Kitchen appliances and furniture basically work on multiples of feet. 1 foot = 30cm, so the reason the standard appliance is 60cm is because that’s the metric equivalent of 2 feet
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?
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)
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.
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.