8 ms·

The 39th Root of 92

217 points by bit-player 10y ago

deleted 10y ago
[deleted]
ysleepy 10y ago
I continue to be baffled by the arcane units in the US. This uses a measure on the completely wrong abstraction level. An accidental production process now defines a wire unit instead the end result the consumer/engineer/technician wants to know (mm^2 or inch^2 oh no no it's pica^2 ?). There must be some sociological phenomenon going on that keeps the US from adopting modern units. Maybe can't admit a shortcoming and fix it?
- kevhito 10y ago
  If you have never wired a house for electrical, then sure, the units seem arbitrary. But if you do, then the units seem very comfortable. 12ga for most typical 20a circuits, 14ga for light, 10ga or thicker for some heavy-duty circuits. Hey boss, we seem to be all out of 3.31mm^2 romex, all I got left is 2.08mm^2. And why did you mention cross-sectional area? Why not radius? or diameter? Or better yet, circumference? I'll take awg12 and awg14 please.
  - HCIdivision17 10y ago
    That's the trick. In a sense, the units follow the application, and hence English units always feel a bit natural. They have a tendency to have integer multiples and simple fractions. And when I say natural, I don't mean elegant. They often tend to be thoroughly arbitrary. But they match the needs, which is usually reasonably pragmatic. For example, 360 degrees is ideal for simple in-head directional geometry, but radians are by far simpler in algebra or very precise measurements (because Pi can often be neatly factored out). Once you start using enough decimal points, all units are lousy. I remember using angstroms in astronomy because it fit better into the optics theory and the distances are already absurd it didn't matter. So you may as well use the units that are convenient, and just get good swapping. (PS: glass sheets are sold by the square foot, but in thicknesses measured in millimeters. Turns out to be pretty convenient that way.)
    - sn41 10y ago
      The Sumerians divided the circle into 360 degrees because the Sun's annual path took 360 days to come around a full circle. It's no wonder that 360 degrees feel natural for directions. Another thing I've encountered: in South India, there is a measure of distance & time called a "nazhika". It is 24 minutes. 2 1/2 nazhika is one hour, 60 nazhikas make a day. A nazhika is also roughly the time taken for a normal person to walk 1 mile. Hence a nazhika is also used as approximately one mile. Seems a bit weird until you remember that light-years involve the same identification of time and distance. Non-metric units like these and others ("foot") have probably very good reasons behind them, and they could be used by people in their day-to-day activities while not carrying measuring instruments with them. Metric System is more systematic, but people "lose touch" with intuitions of quantity.
      - einhverfr 10y ago
        I assume that the Sumerians were observant enough to realize that there were still a few days missing, and that 360 was better because it was a more divisible number actually. The Sumerians did, in fact, periodically insert intercalary months in order to offset the difference, which suggests that this is in part close approximation and on the other part nice for application.
        sn41 10y ago
        I did not know this. Thanks.
        HCIdivision17 10y ago
        I feel like unit debates often result from a misunderstanding between sides of "is perfect the enemy of good?" I thought it suspicious that they would have miscounted the days, but you're right: it's so dang useful that it's worth a little error (with occasional corrections) for such convenience. Of course, at some point it becomes a huge pain and you buckle down and choose something just as arbitrary but easier to handle. And that's why we don't count angles in the milliseconds since 1970. Or days in a year; though we do sometimes measure 3D angles in solid minutes, which seems like a metaphor taken too far :)
  - Hondor 10y ago
    Your example of mm is not true at all. There's no need for 3 significant figures for electrical wire size. Where I am, it's 2.5mm^2 for 10 A circuits, 1.0mm^2 for lighting, etc. The 2nd digit is always a 0 or a 5 so it's even simpler than it looks.
  - toomanybeersies 10y ago
    In New Zealand, I'm fairly sure that the standard is to use diameter to measure wire. It's something like 2 mm for a 10 Amp circuit.
  - e2e8 10y ago
    awg14 or whatever isn't exactly the perfect gauge for whatever application it is used for. It is somewhat arbitrary. A nice metric system of gauges would have 2 mm, 2.5 mm, 3 mm, etc. and there would be still be a nice round number gauge for each application.
    - Turing_Machine 10y ago
      For some value of "nice round number". What really matters with most wires is the current carrying capacity, which largely depends on the cross-sectional area, not the diameter. Equally-spaced diameters don't give you equally-spaced areas.
      - jacobolus 10y ago
        If you have an industrial production process which is going to produce a set number of wire sizes, and you want them to be maximally useful for a wide variety of applications, you want a logarithmic scale. Responding to commenter e2e8: Using 2mm, 3mm, etc. would be substantially less functional. Once you have a log scale, it hardly matters whether you measure diameter or area, that’s just a constant factor. In the ideal case, the log scale would have a slightly easier to compute definition for the dilation at each step than the 39th root of 92 (~1.1229). Perhaps they could use the 6th root of 2 instead (~1.1224). Then every 6 steps you’d get a factor of two. Size 0 could be defined as 1mm diameter (or size 0 could be 1 millimeter squared cross sectional area, with 3rd root of 2 as the step each time). In practice if you’re wiring a house, it doesn’t much matter. * * * One of the reasons the metric system built on a base ten number system is so frustrating for practical purposes is that powers of ten are entirely arbitrary and indivisible, and tenth roots of ten or numbers expressed in terms of natural logarithms are even worse. We’d be much better off with a general-purpose base twelve number system, plus log scales uniformly designed around the twelfth root of 2. [Western music scale, ISO paper sizes, etc. would fit right in.]
        e2e8 10y ago
        You can plot out the wire gauges you want on a log scale and then round them to nice whole (metric measurement) numbers. That is in fact what is done for things like fasteners.
  - stdbrouw 10y ago
    Same deal for metric, though. I know I need 0.75mm2 for small appliances, 1.5mm2 is your run-of-the-mill cable for up to 10A (equal to 20A at 110V), 2.5mm2 and 4.5mm2 for heavy-duty circuits. I've sometimes heard the same remark about temperatures: jeez, how do you guys manage to work with something as unintuitive as degrees celcius? But really, you just get used to whatever it is you're using.
    - continuational 10y ago
      Wait, is there a temperature measurement out there that's mire intuitive than "water freezes at zero and boils at 100"?
  - int_19h 10y ago
    The "it's more natural" argument, fielded by both sides, is largely a myth - take it from someone who lived in several countries and struggled with different units. Pretty much the only reason why something feels natural to you is because that's what you are accustomed to using. There's nothing more natural about an inch than a centimeter, and nice, round, easy-to-remember numbers can be had on both scales for "natural", commonly found distances. Ditto for pounds and kilograms, Celsius and Fahrenheit, acre and hectare etc. Objectively, metric wins because it uses the same decimal scale as our number system, and because the units are designed to establish the most straightforward relations between different quantities. Yes, using 12 for a base has some advantages due to more divisors, but not being consistent with decimal wipes them all out (and traditional units don't consistently use 12, either - consider units of volume, for example). In an ideal world, we'd have 6 fingers on each hand, and use base-12 everywhere; alas...
    - dancek 10y ago
      I don't know what's natural, but I live in Finland where we use the metric / SI system extensively. Some people don't even know how long an inch is, let alone a foot. Recently I was building a roof with an old, very experienced builder. Turns out that on construction sites, nails and planks are always discussed in inches, even when they're actually metric. So a 60mm nail would be "a two point fiver" ("kakspuokki" or such in Finnish).
      - Hondor 10y ago
        The reverse is true for metric pipe threads. They're named with mm but are actually the same dimensions as the inch threads. Luckily the inch numbers have only an arbitrary relationship to any dimensions of the thread anyway so nobody will get confused trying to measure them.
      - exDM69 10y ago
        The sizes of lumber and other construction materials are inch based, rounded to mm, even in Finland. Instead of 1/4", 1/2", and 3/4" we have 6.5mm, 12mm and 18mm. Note the inconsistency in 1/4".
    - 10y ago
  - oxymoron 10y ago
    In Sweden, when running wiring we'll refer to the dimensions by monikers like "one and half squared", "six squared" and so on, corresponding to "1.5mm^2" etc. It has never felt very bulky to me, and doesn't seem like more effort than saying 14-gauge (or at least close enough). If you're going to knock the other way, wouldn't t be far to at least check what that it is rather than making something up as a strawman?
- ycombinatorMan 10y ago
  Have you considered how much it would cost to change units, and how absolutely little would be gained?
  - xlayn 10y ago
    Maybe can be re-framed as how much has been lost? If the change is performed, the time gained by absolutely everyone making use of more saner unit system could offset the cost? maybe just by avoiding errors? This are ideas that has to be transformed in order to be shared with mostly everyone else. Shameful confession, I do use pounds for weight.
    - ubernostrum 10y ago
      more saner unit system The general idea in most of these arguments is that "more sane" is a very hard thing to define. There are cases for which metric is more useful. There are cases where it's less useful. Yet the argument is almost never actually made that way; metric tends to be presented as an ideally perfect system not susceptible to even the most trifling criticism, and any case presented in which it's disadvantageous compared to an alternative is dismissed with an ad hominem attack implying the person making the case is just too much of a stupid American to grasp the heavenly best-in-all-possible-cases-for-all-people perfection of metric. Truth is it's an arbitrary system optimized for a particular set of use cases. The traditional-ish units used in the US are a different arbitrary system, optimized for a different particular set of use cases.
      - Sean1708 10y ago
        > Truth is it's an arbitrary system optimized for a particular set of use cases. Actually it's an arbitrary system optimised for calculations.
        pandler 10y ago
        > Actually it's an arbitrary system optimised for calculations. Which is a particular set of use cases.
- MikeTLive 10y ago
  The English system of measure is based on offsets to make retooling factories easily done in house. It's very similar to metric paper sizes. Look into the history it's actually quite logical.
  - MikeTLive 10y ago
    Appelbaum: So the people blocking adoption of the metric system weren't backward-looking traditionalists, but cutting-edge industrialists? Mihm: That's correct. While the anti-metric forces included outright cranks, including people who believed that the inch was a God-given unit of measurement, the most sophisticated and powerful opponents of the metric system were anything but cranks. They were engineers who built the industrial infrastructure of the United States. And their concerns, while self-interested, were not entirely off base. Whatever the drawbacks of the English units, the inch was divided in ways that made sense to the mechanics and machinists of the era: it was built around "2s" rather than "10s," with each inch subdivided in half and in half again—and so forth. This permitted various sizes of screw thread to have some logical correspondence to all the other increments. The same was true of the sizes of other small parts that were essential modern machinery. http://www.theatlantic.com/technology/archive/2015/06/whos-afraid-of-the-metric-system/395057/ http://www.theatlantic.com/technology/archive/2015/06/whos-a...
    - rz2k 10y ago
      The philosophy seems to be reversed with the ISO 216 paper size standards like A4. Anyway, the main advantage of metric seems to be its universality between different markets, rather than the somewhat silly idea of ideal relationships such as water in one arbitrary form having a certain weight and volume replacing a system that was derived from a hundreds of years process resembling a genetic algorithm.
      - einhverfr 10y ago
        I wonder if it is an internal/external optimization. The whole point of metric is that it is built around the number system, leading to easy conversion between units. The whole point of the American unit system is that they are optimized for specific use, but definitely not for conversion. ISO paper sizes are a great counterexample, actually, because they took an application, rather than a conversion-centric approach. I.e when you print a signature you do so on a larger piece of paper, and then you fold, crop, and bind. Each fold cuts the paper size in half. So ISO paper sizes are much more like American units than American paper sizes are.
- empath75 10y ago
  They took an existing system and standardized it with as few changes as possible. It's the equivalent of continuously updating the same code base instead of rewriting from scratch.
- sgk284 10y ago
  Just like with software, backwards compatibility is a double-edged sword. You can look at almost any land assignment, building or commercial sale ever in the history of the United States and be able to compare / modify / extend it without any conversions. If my great-great-grandfather claimed 160 acres from the Homestead Act, any documentation from that time is just as easily understood today without any conversions. Differing units only become an issue when globalization factors in (which is a fairly recent phenomenon). Many fields in the states, such as the sciences, have indeed chosen interoperability over backwards-compatibility, but these decisions are done on a field-by-field basis. I'm in the camp that it'd generally be better to just rip the band-aid off and switch everything, but in general I value interoperability over backwards compatibility with software too. That said, who am I to tell Microsoft that they shouldn't worry about Windows backwards-compatibility? Who am I to tell farmers that they should measure their land in hectares?
  - ysleepy 10y ago
    Who says people should collectively forget what an inch is? Every other country made unit conversions. The people will use old units for some time to buy cheese at the counter and all is well.
    - einhverfr 10y ago
      Yeah, right up until your car lease contract limits you to 2000 Swedish Miles per year. (Note, these are about 6x longer than American miles). Or you buy fruit at the supermarket in Indonesia in ounces and kg (an ounce is an hg).
      - reitanqild 10y ago
        I guess anyone who knows what Swedish mil is will specify kilometres instead. I cannot remember a single time I have seen a contract specifying mil instead of km. ("Mil" == 10km == 10 000m is used here as well only not in formal or scientific contexts that I can think of but maybe that is a difference between Sweden and here.)
- jonahx 10y ago
  > There must be some sociological phenomenon going on that keeps the US from adopting modern units. Maybe can't admit a shortcoming and fix it? There's a sociological phenomenon at play here all right... a deeply pathological form of envy that Freud called "denial of USA-number-one-ness."
  - engi_nerd 10y ago
    Okay, I'll play devil's advocate here. There's a huge (but not insurmountable) lock-in effect behind wire gauges. All the wire I can buy is sized in it. All the wire strippers, crimpers, pins, sockets, plugs, jacks, terminal strips, insert/removal tools and clamps I can buy are sized around the AWG standards. Bulkhead passages in ships and aircraft are sized for carrying certain numbers of wires of certain gauges in bundles. Tens of millions of engineering drawings specify wire sizes in AWG. So why should we in the US change all of this? Just for the sake of being "modern"? I'll need a more persuasive argument than that.
    - rm445 10y ago
      Yes, that's the core of the issue. The US is a big monobloc, an economic superpower with not only the most advanced economy but also a lot of the history tied to developing the world's industries. Other places saw more benefit to adopting SI units either because they were smaller and closer to lots of other places with a need to harmonise, or playing catch-up. My own country, Britain, falls in the first group - though the population still uses some everyday old units, it didn't manage to be a hold-out despite its historic position and industrial heritage. It's hard to see the position being static in the longer term though, particularly if world economic growth gradually leaves the USA with a relatively smaller slice (in absolute terms much bigger, but a smaller proportion) of the larger future world economy.
      - engi_nerd 10y ago
        I agree. The only way things in the US will change with regards to standards like this will be if it becomes excruciatingly painful to continue being different.
- pacaro 10y ago
  The thing that always gets me about this is how incomplete it is (at least in most people's experience) What is the unit of mass smaller than an Ounce? Some people know that this is a Grain (7,000 in a pound, which means the awfully convenient division of 437.5 per oz - assuming avoirdupois of course) What if anything is smaller than an inch? Power of two fractions until 1/64 then "thous" - 15.625 thous in 1/64" - although I do like how biblical (KJV) it looks to be writing "thou"
  - dragontamer 10y ago
    > What if anything is smaller than an inch? Then we use Pica and Points. You know, like 12-point font. Which is 1/6th of an inch tall. 72-points to an inch, 12-points to a pica. Get with the program man!
    - saghm 10y ago
      Too bad we had to go and make displays with different pixel densities...
  - deleted 10y ago
    [deleted]
  - Turing_Machine 10y ago
    Most people never use units smaller than can be accounted for by fractional inches and ounces in their daily lives, and never did. The only people who ever used grains were pharmacists, jewelers, and the like. The only people who ever had to resort to thous were precision machinists and the like.
    - int_19h 10y ago
      Open Amazon, and search for something as mundane as plastic bags or trash cans. Notice that their thickness is specified in "mils". How many people make purchasing decisions on those products, for use in their daily lives?
      - 10y ago
- einhverfr 10y ago
  I am not sure. American units usually focus on divisibility and factoring of integers, while metric units focus on quick base-10 math. So they are different concerns and this is why, I think, people from elsewhere in the world have so much trouble understanding American units. If you are brought up with metric units, the units are built around the number system. A good way to understand the problem by for the HN audience is the problem of using IEEE floats where precise numbers matter in programming. The problem with IEEE floats is that we usually think about them in base 10 but they represent something in base 2, and no lossless conversion across the domain is possible. American units bridge that sort of gap much better than metric ones do because they usually focus on divisibility than on quick representation and conversion. There are certain areas where metric makes sense. If I have prices in kg and I want to know how many g I can buy for a certain amount of money, because the money and weight systems coincide we are well optimized for that problem. But, imagine calculating the angles of a triangle or a hexagon if your degree system was base 10. In other words, American units are abstracted around actual application. There is of course a happy medium. We could change to duodecimal numbers and come up with a duodecimal metric system. Then everyone would get what they want, right? ;-)
  - rm445 10y ago
    Shout out to another base-12 fan. If only we had 12 fingers it might have happened. Arbitrary divisions of angle aren't very interesting, since the radian is so fundamental. But there is an angle system using multiples of 100: gradians. 100 is a quarter-turn and the internal angles of a triangle add up to 200. A lot of electronic calculators still offer them (the DRG button = degrees, radians, gradians).
    - jacobolus 10y ago
      Gradians are absolutely terrible. For everyday use, radians are also pretty impractical. I personally like just writing fractions of a full turn, but degrees/minutes/seconds aren’t too bad. There are two cases where linear divisions of arclength-measured angles make sense: (1) the angles to make regular polygons of low numbers of sides, (2) repeated binary divisions, whose cartesian coordinates can be computed easily because we can just add two vectors and renormalize using an inverse square root which we know how to efficiently compute, and which are then nice for fixed point representations using binary integers in computers. For the first case, I think rational fractions of a turn work best; for the second case, I like binary angles (“brads”) https://en.wikipedia.org/wiki/Binary_scaling#Binary_angles https://en.wikipedia.org/wiki/Binary_scaling#Binary_angles ; losing the ability to precisely represent a thirds of a full turn is just one of those trade offs you sometimes need to make. Otherwise, treating angle as a linear quantity with precise measurements (instead of some kind of approximations) is for most problems less useful than just using a cartesian coordinate representation for an angle (possibly keeping track of the coordinates squared if we want to stick to rational arithmetic.) Radians are only really useful for solving calculus problems by hand, or writing academic math/science papers where it’s important to stick to established conventions. For practical computation radians are almost always an inferior choice, more computationally expensive and less precise (they’re built into lots of existing libraries, so can often be convenient despite the inefficiency).
- Turing_Machine 10y ago
  I strongly suspect that it was anything but "accidental", but was rather related to just how much you could draw down the diameter of a wire in one step without breaking it. If you can make a B&S Gauge X+1 wire from a B&S Gauge X wire in one drawing step, while making a metric size N wire from a size M wire requires two drawing steps, that actually matters. The article alludes to this, but doesn't actually explicitly state it.
- ArkyBeagle 10y ago
  The derivation isn't all that interesting; the use is. Everybody who cares already knows what 12 ga. wire is. People in general don't give a [ expletive deleted ] about the source code; they just want the answer.
- exDM69 10y ago
  You know what is worse than imperial units? Measurements that were traditionally inches but converted to millimeters, inconsistently. I do woodworking in a metric country. It's terrible. My "quarter inch" chisel is 6mm but my "quarter inch" plywood is 6.5mm so it won't fit in a groove made by the chisel. 3/4" chisel is 20mm but plywood is 18mm. All the measurements are inch based but converted to metric arbitrarily rounding up or down. 3/4" is the only measurement that works well, it's 19.004mm. But a 19 mm drill bit isn't a part of any standard set. Some automotive applications are similar. The Toyota Hilux pickup truck has an indestructible reputation because it was cloned by the Japanese from a US truck. They rounded every measurement up to nearest millimeter. It's beefier than the original while having a smaller and less powerful engine. You do need some exotic sized wrenches to work on it, though.
- wglb 10y ago
  This is a bit of a middlebrow comment that we tend to unfortunately find at the top on HN. What measure of time do you use? Hour, minute, second, month, day year? Those are pretty arcane. The first four are pretty arbitrary, and existed way before America.
- hatsunearu 10y ago
  Maybe, but knowing mm^2 doesn't really help either. This AWG system has the benefit of discretization of wire thickness, so manufacturers can optimize their processes for only ~30 gauges instead of answering "what do you mean you don't have 3.1415mm^2 wires?!"
- danny8000 10y ago
  I remember when reading "Napoleon: A Life" by Andrew Roberts, Napoleon wasn't a big fan of the base-10 metric system, but he figured it would be the best way to break with the hundreds of different measuring systems in place in France at the time, and enforce an empire-wide standard. I much prefer base-12 or base-16 systems, especially when measuring and hanging drywall! On the other hand, the British waited way to long (until 1971) to decimal-ize their currency. Before that the pound was made up of 240 pence.
deleted 10y ago
[deleted]
imglorp 10y ago
Hugged to death. http://webcache.googleusercontent.com/search?q=cache:http://bit-player.org/2016/the-39th-root-of-92 http://webcache.googleusercontent.com/search?q=cache:http://...
_greim_ 10y ago
As a guitar player I'm glad the article also mentioned equal temperament tuning. The frets of a guitar for example are spaced using the 12th root of 2. Musical theory is a tangled rat's nest, but at least that part is easy to understand.
weinzierl 10y ago
> It’s worth noting that instruments were being tuned to this scale well before the invention of logarithms. I assume it was done by ear or perhaps by geometry, not by algebra. Well temperament wasn't known before 1681, there were predecessors that came close but none used the the twelfth root of two. Logarithms were introduced by John Napier in 1614 [1], the twelfth root of two was first calculated by Marin Mersenne in 1636 [2], well temperament was introduced by Werckmeister 1681 [3]. > Around 1600 Simon Stevin did attempt to calculate numerical values for the pitch intervals by decomposing 12th roots into combinations of square and cube roots; his results were not flawless. He had the right idea but not the right math. [1] https://en.wikipedia.org/wiki/John_Napier https://en.wikipedia.org/wiki/John_Napier [2] https://en.wikipedia.org/wiki/Twelfth_root_of_two https://en.wikipedia.org/wiki/Twelfth_root_of_two [3] https://en.wikipedia.org/wiki/Well_temperament https://en.wikipedia.org/wiki/Well_temperament
- bit-player 10y ago
  (I'm the OP here.) My source for the statement that "instruments were being tuned to this scale well before the invention of logarithms" is an article by Edward Dunne and Mark McConnell, "Pianos and Continued Fractions," Mathematics Magazine, Vol. 72, No. 2 (Apr., 1999), pp. 104-115. They write: "Guitars in Spain were evenly tempered at least as early as the fiftheenth century, two hundred years before Bach. And Hermanus Contractus, born 18 July 1013, invented a system of intervalic notation that anticipated equal temperatment." My source on Simon Stevin's work is a Rudolf Rasch, "Tuning and Temperament," published as Chapter 7 in The Cambridge History of Western Music Theory." Rasch gives an interesting account of the state of root extraction before the advent of logarithms. He attributes the errors to "Stevin’s sometimes rather reckless rounding of digits after the decimal period, which are often truncated rather than rounded."
jeremysmyth 10y ago
"In metric, one milliliter of water occupies one cubic centimeter, weighs one gram, and requires one calorie of energy to heat up by one degree centigrade—which is 1 percent of the difference between its freezing point and its boiling point. An amount of hydrogen weighing the same amount has exactly one mole of atoms in it. Whereas in the American system, the answer to “How much energy does it take to boil a room-temperature gallon of water?” is “Go fuck yourself,” because you can’t directly relate any of those quantities." - Wild Thing, Josh Bazell

217 points by bit-player 10y ago

deleted 10y ago

[deleted]

I continue to be baffled by the arcane units in the US. This uses a measure on the completely wrong abstraction level. An accidental production process now defines a wire unit instead the end result the consumer/engineer/technician wants to know (mm^2 or inch^2 oh no no it's pica^2 ?). There must be some sociological phenomenon going on that keeps the US from adopting modern units. Maybe can't admit a shortcoming and fix it?

kevhito 10y ago
If you have never wired a house for electrical, then sure, the units seem arbitrary. But if you do, then the units seem very comfortable. 12ga for most typical 20a circuits, 14ga for light, 10ga or thicker for some heavy-duty circuits. Hey boss, we seem to be all out of 3.31mm^2 romex, all I got left is 2.08mm^2. And why did you mention cross-sectional area? Why not radius? or diameter? Or better yet, circumference? I'll take awg12 and awg14 please.
- HCIdivision17 10y ago
  That's the trick. In a sense, the units follow the application, and hence English units always feel a bit natural. They have a tendency to have integer multiples and simple fractions. And when I say natural, I don't mean elegant. They often tend to be thoroughly arbitrary. But they match the needs, which is usually reasonably pragmatic. For example, 360 degrees is ideal for simple in-head directional geometry, but radians are by far simpler in algebra or very precise measurements (because Pi can often be neatly factored out). Once you start using enough decimal points, all units are lousy. I remember using angstroms in astronomy because it fit better into the optics theory and the distances are already absurd it didn't matter. So you may as well use the units that are convenient, and just get good swapping. (PS: glass sheets are sold by the square foot, but in thicknesses measured in millimeters. Turns out to be pretty convenient that way.)
  - sn41 10y ago
    The Sumerians divided the circle into 360 degrees because the Sun's annual path took 360 days to come around a full circle. It's no wonder that 360 degrees feel natural for directions. Another thing I've encountered: in South India, there is a measure of distance & time called a "nazhika". It is 24 minutes. 2 1/2 nazhika is one hour, 60 nazhikas make a day. A nazhika is also roughly the time taken for a normal person to walk 1 mile. Hence a nazhika is also used as approximately one mile. Seems a bit weird until you remember that light-years involve the same identification of time and distance. Non-metric units like these and others ("foot") have probably very good reasons behind them, and they could be used by people in their day-to-day activities while not carrying measuring instruments with them. Metric System is more systematic, but people "lose touch" with intuitions of quantity.
    - einhverfr 10y ago
      I assume that the Sumerians were observant enough to realize that there were still a few days missing, and that 360 was better because it was a more divisible number actually. The Sumerians did, in fact, periodically insert intercalary months in order to offset the difference, which suggests that this is in part close approximation and on the other part nice for application.
      - sn41 10y ago
        I did not know this. Thanks.
      - HCIdivision17 10y ago
        I feel like unit debates often result from a misunderstanding between sides of "is perfect the enemy of good?" I thought it suspicious that they would have miscounted the days, but you're right: it's so dang useful that it's worth a little error (with occasional corrections) for such convenience. Of course, at some point it becomes a huge pain and you buckle down and choose something just as arbitrary but easier to handle. And that's why we don't count angles in the milliseconds since 1970. Or days in a year; though we do sometimes measure 3D angles in solid minutes, which seems like a metaphor taken too far :)
- Hondor 10y ago
  Your example of mm is not true at all. There's no need for 3 significant figures for electrical wire size. Where I am, it's 2.5mm^2 for 10 A circuits, 1.0mm^2 for lighting, etc. The 2nd digit is always a 0 or a 5 so it's even simpler than it looks.
- toomanybeersies 10y ago
  In New Zealand, I'm fairly sure that the standard is to use diameter to measure wire. It's something like 2 mm for a 10 Amp circuit.
- e2e8 10y ago
  awg14 or whatever isn't exactly the perfect gauge for whatever application it is used for. It is somewhat arbitrary. A nice metric system of gauges would have 2 mm, 2.5 mm, 3 mm, etc. and there would be still be a nice round number gauge for each application.
  - Turing_Machine 10y ago
    For some value of "nice round number". What really matters with most wires is the current carrying capacity, which largely depends on the cross-sectional area, not the diameter. Equally-spaced diameters don't give you equally-spaced areas.
    - jacobolus 10y ago
      If you have an industrial production process which is going to produce a set number of wire sizes, and you want them to be maximally useful for a wide variety of applications, you want a logarithmic scale. Responding to commenter e2e8: Using 2mm, 3mm, etc. would be substantially less functional. Once you have a log scale, it hardly matters whether you measure diameter or area, that’s just a constant factor. In the ideal case, the log scale would have a slightly easier to compute definition for the dilation at each step than the 39th root of 92 (~1.1229). Perhaps they could use the 6th root of 2 instead (~1.1224). Then every 6 steps you’d get a factor of two. Size 0 could be defined as 1mm diameter (or size 0 could be 1 millimeter squared cross sectional area, with 3rd root of 2 as the step each time). In practice if you’re wiring a house, it doesn’t much matter. * * * One of the reasons the metric system built on a base ten number system is so frustrating for practical purposes is that powers of ten are entirely arbitrary and indivisible, and tenth roots of ten or numbers expressed in terms of natural logarithms are even worse. We’d be much better off with a general-purpose base twelve number system, plus log scales uniformly designed around the twelfth root of 2. [Western music scale, ISO paper sizes, etc. would fit right in.]
      - e2e8 10y ago
        You can plot out the wire gauges you want on a log scale and then round them to nice whole (metric measurement) numbers. That is in fact what is done for things like fasteners.
- stdbrouw 10y ago
  Same deal for metric, though. I know I need 0.75mm2 for small appliances, 1.5mm2 is your run-of-the-mill cable for up to 10A (equal to 20A at 110V), 2.5mm2 and 4.5mm2 for heavy-duty circuits. I've sometimes heard the same remark about temperatures: jeez, how do you guys manage to work with something as unintuitive as degrees celcius? But really, you just get used to whatever it is you're using.
  - continuational 10y ago
    Wait, is there a temperature measurement out there that's mire intuitive than "water freezes at zero and boils at 100"?
- int_19h 10y ago
  The "it's more natural" argument, fielded by both sides, is largely a myth - take it from someone who lived in several countries and struggled with different units. Pretty much the only reason why something feels natural to you is because that's what you are accustomed to using. There's nothing more natural about an inch than a centimeter, and nice, round, easy-to-remember numbers can be had on both scales for "natural", commonly found distances. Ditto for pounds and kilograms, Celsius and Fahrenheit, acre and hectare etc. Objectively, metric wins because it uses the same decimal scale as our number system, and because the units are designed to establish the most straightforward relations between different quantities. Yes, using 12 for a base has some advantages due to more divisors, but not being consistent with decimal wipes them all out (and traditional units don't consistently use 12, either - consider units of volume, for example). In an ideal world, we'd have 6 fingers on each hand, and use base-12 everywhere; alas...
  - dancek 10y ago
    I don't know what's natural, but I live in Finland where we use the metric / SI system extensively. Some people don't even know how long an inch is, let alone a foot. Recently I was building a roof with an old, very experienced builder. Turns out that on construction sites, nails and planks are always discussed in inches, even when they're actually metric. So a 60mm nail would be "a two point fiver" ("kakspuokki" or such in Finnish).
    - Hondor 10y ago
      The reverse is true for metric pipe threads. They're named with mm but are actually the same dimensions as the inch threads. Luckily the inch numbers have only an arbitrary relationship to any dimensions of the thread anyway so nobody will get confused trying to measure them.
    - exDM69 10y ago
      The sizes of lumber and other construction materials are inch based, rounded to mm, even in Finland. Instead of 1/4", 1/2", and 3/4" we have 6.5mm, 12mm and 18mm. Note the inconsistency in 1/4".
  - 10y ago
- oxymoron 10y ago
  In Sweden, when running wiring we'll refer to the dimensions by monikers like "one and half squared", "six squared" and so on, corresponding to "1.5mm^2" etc. It has never felt very bulky to me, and doesn't seem like more effort than saying 14-gauge (or at least close enough). If you're going to knock the other way, wouldn't t be far to at least check what that it is rather than making something up as a strawman?
ycombinatorMan 10y ago
Have you considered how much it would cost to change units, and how absolutely little would be gained?
- xlayn 10y ago
  Maybe can be re-framed as how much has been lost? If the change is performed, the time gained by absolutely everyone making use of more saner unit system could offset the cost? maybe just by avoiding errors? This are ideas that has to be transformed in order to be shared with mostly everyone else. Shameful confession, I do use pounds for weight.
  - ubernostrum 10y ago
    more saner unit system The general idea in most of these arguments is that "more sane" is a very hard thing to define. There are cases for which metric is more useful. There are cases where it's less useful. Yet the argument is almost never actually made that way; metric tends to be presented as an ideally perfect system not susceptible to even the most trifling criticism, and any case presented in which it's disadvantageous compared to an alternative is dismissed with an ad hominem attack implying the person making the case is just too much of a stupid American to grasp the heavenly best-in-all-possible-cases-for-all-people perfection of metric. Truth is it's an arbitrary system optimized for a particular set of use cases. The traditional-ish units used in the US are a different arbitrary system, optimized for a different particular set of use cases.
    - Sean1708 10y ago
      > Truth is it's an arbitrary system optimized for a particular set of use cases. Actually it's an arbitrary system optimised for calculations.
      - pandler 10y ago
        > Actually it's an arbitrary system optimised for calculations. Which is a particular set of use cases.
MikeTLive 10y ago
The English system of measure is based on offsets to make retooling factories easily done in house. It's very similar to metric paper sizes. Look into the history it's actually quite logical.
- MikeTLive 10y ago
  Appelbaum: So the people blocking adoption of the metric system weren't backward-looking traditionalists, but cutting-edge industrialists? Mihm: That's correct. While the anti-metric forces included outright cranks, including people who believed that the inch was a God-given unit of measurement, the most sophisticated and powerful opponents of the metric system were anything but cranks. They were engineers who built the industrial infrastructure of the United States. And their concerns, while self-interested, were not entirely off base. Whatever the drawbacks of the English units, the inch was divided in ways that made sense to the mechanics and machinists of the era: it was built around "2s" rather than "10s," with each inch subdivided in half and in half again—and so forth. This permitted various sizes of screw thread to have some logical correspondence to all the other increments. The same was true of the sizes of other small parts that were essential modern machinery. http://www.theatlantic.com/technology/archive/2015/06/whos-afraid-of-the-metric-system/395057/ http://www.theatlantic.com/technology/archive/2015/06/whos-a...
  - rz2k 10y ago
    The philosophy seems to be reversed with the ISO 216 paper size standards like A4. Anyway, the main advantage of metric seems to be its universality between different markets, rather than the somewhat silly idea of ideal relationships such as water in one arbitrary form having a certain weight and volume replacing a system that was derived from a hundreds of years process resembling a genetic algorithm.
    - einhverfr 10y ago
      I wonder if it is an internal/external optimization. The whole point of metric is that it is built around the number system, leading to easy conversion between units. The whole point of the American unit system is that they are optimized for specific use, but definitely not for conversion. ISO paper sizes are a great counterexample, actually, because they took an application, rather than a conversion-centric approach. I.e when you print a signature you do so on a larger piece of paper, and then you fold, crop, and bind. Each fold cuts the paper size in half. So ISO paper sizes are much more like American units than American paper sizes are.
empath75 10y ago
They took an existing system and standardized it with as few changes as possible. It's the equivalent of continuously updating the same code base instead of rewriting from scratch.
sgk284 10y ago
Just like with software, backwards compatibility is a double-edged sword. You can look at almost any land assignment, building or commercial sale ever in the history of the United States and be able to compare / modify / extend it without any conversions. If my great-great-grandfather claimed 160 acres from the Homestead Act, any documentation from that time is just as easily understood today without any conversions. Differing units only become an issue when globalization factors in (which is a fairly recent phenomenon). Many fields in the states, such as the sciences, have indeed chosen interoperability over backwards-compatibility, but these decisions are done on a field-by-field basis. I'm in the camp that it'd generally be better to just rip the band-aid off and switch everything, but in general I value interoperability over backwards compatibility with software too. That said, who am I to tell Microsoft that they shouldn't worry about Windows backwards-compatibility? Who am I to tell farmers that they should measure their land in hectares?
- ysleepy 10y ago
  Who says people should collectively forget what an inch is? Every other country made unit conversions. The people will use old units for some time to buy cheese at the counter and all is well.
  - einhverfr 10y ago
    Yeah, right up until your car lease contract limits you to 2000 Swedish Miles per year. (Note, these are about 6x longer than American miles). Or you buy fruit at the supermarket in Indonesia in ounces and kg (an ounce is an hg).
    - reitanqild 10y ago
      I guess anyone who knows what Swedish mil is will specify kilometres instead. I cannot remember a single time I have seen a contract specifying mil instead of km. ("Mil" == 10km == 10 000m is used here as well only not in formal or scientific contexts that I can think of but maybe that is a difference between Sweden and here.)
jonahx 10y ago
> There must be some sociological phenomenon going on that keeps the US from adopting modern units. Maybe can't admit a shortcoming and fix it? There's a sociological phenomenon at play here all right... a deeply pathological form of envy that Freud called "denial of USA-number-one-ness."
- engi_nerd 10y ago
  Okay, I'll play devil's advocate here. There's a huge (but not insurmountable) lock-in effect behind wire gauges. All the wire I can buy is sized in it. All the wire strippers, crimpers, pins, sockets, plugs, jacks, terminal strips, insert/removal tools and clamps I can buy are sized around the AWG standards. Bulkhead passages in ships and aircraft are sized for carrying certain numbers of wires of certain gauges in bundles. Tens of millions of engineering drawings specify wire sizes in AWG. So why should we in the US change all of this? Just for the sake of being "modern"? I'll need a more persuasive argument than that.
  - rm445 10y ago
    Yes, that's the core of the issue. The US is a big monobloc, an economic superpower with not only the most advanced economy but also a lot of the history tied to developing the world's industries. Other places saw more benefit to adopting SI units either because they were smaller and closer to lots of other places with a need to harmonise, or playing catch-up. My own country, Britain, falls in the first group - though the population still uses some everyday old units, it didn't manage to be a hold-out despite its historic position and industrial heritage. It's hard to see the position being static in the longer term though, particularly if world economic growth gradually leaves the USA with a relatively smaller slice (in absolute terms much bigger, but a smaller proportion) of the larger future world economy.
    - engi_nerd 10y ago
      I agree. The only way things in the US will change with regards to standards like this will be if it becomes excruciatingly painful to continue being different.
pacaro 10y ago
The thing that always gets me about this is how incomplete it is (at least in most people's experience) What is the unit of mass smaller than an Ounce? Some people know that this is a Grain (7,000 in a pound, which means the awfully convenient division of 437.5 per oz - assuming avoirdupois of course) What if anything is smaller than an inch? Power of two fractions until 1/64 then "thous" - 15.625 thous in 1/64" - although I do like how biblical (KJV) it looks to be writing "thou"
- dragontamer 10y ago
  > What if anything is smaller than an inch? Then we use Pica and Points. You know, like 12-point font. Which is 1/6th of an inch tall. 72-points to an inch, 12-points to a pica. Get with the program man!
  - saghm 10y ago
    Too bad we had to go and make displays with different pixel densities...
- deleted 10y ago
  [deleted]
- Turing_Machine 10y ago
  Most people never use units smaller than can be accounted for by fractional inches and ounces in their daily lives, and never did. The only people who ever used grains were pharmacists, jewelers, and the like. The only people who ever had to resort to thous were precision machinists and the like.
  - int_19h 10y ago
    Open Amazon, and search for something as mundane as plastic bags or trash cans. Notice that their thickness is specified in "mils". How many people make purchasing decisions on those products, for use in their daily lives?
    - 10y ago
einhverfr 10y ago
I am not sure. American units usually focus on divisibility and factoring of integers, while metric units focus on quick base-10 math. So they are different concerns and this is why, I think, people from elsewhere in the world have so much trouble understanding American units. If you are brought up with metric units, the units are built around the number system. A good way to understand the problem by for the HN audience is the problem of using IEEE floats where precise numbers matter in programming. The problem with IEEE floats is that we usually think about them in base 10 but they represent something in base 2, and no lossless conversion across the domain is possible. American units bridge that sort of gap much better than metric ones do because they usually focus on divisibility than on quick representation and conversion. There are certain areas where metric makes sense. If I have prices in kg and I want to know how many g I can buy for a certain amount of money, because the money and weight systems coincide we are well optimized for that problem. But, imagine calculating the angles of a triangle or a hexagon if your degree system was base 10. In other words, American units are abstracted around actual application. There is of course a happy medium. We could change to duodecimal numbers and come up with a duodecimal metric system. Then everyone would get what they want, right? ;-)
- rm445 10y ago
  Shout out to another base-12 fan. If only we had 12 fingers it might have happened. Arbitrary divisions of angle aren't very interesting, since the radian is so fundamental. But there is an angle system using multiples of 100: gradians. 100 is a quarter-turn and the internal angles of a triangle add up to 200. A lot of electronic calculators still offer them (the DRG button = degrees, radians, gradians).
  - jacobolus 10y ago
    Gradians are absolutely terrible. For everyday use, radians are also pretty impractical. I personally like just writing fractions of a full turn, but degrees/minutes/seconds aren’t too bad. There are two cases where linear divisions of arclength-measured angles make sense: (1) the angles to make regular polygons of low numbers of sides, (2) repeated binary divisions, whose cartesian coordinates can be computed easily because we can just add two vectors and renormalize using an inverse square root which we know how to efficiently compute, and which are then nice for fixed point representations using binary integers in computers. For the first case, I think rational fractions of a turn work best; for the second case, I like binary angles (“brads”) https://en.wikipedia.org/wiki/Binary_scaling#Binary_angles https://en.wikipedia.org/wiki/Binary_scaling#Binary_angles ; losing the ability to precisely represent a thirds of a full turn is just one of those trade offs you sometimes need to make. Otherwise, treating angle as a linear quantity with precise measurements (instead of some kind of approximations) is for most problems less useful than just using a cartesian coordinate representation for an angle (possibly keeping track of the coordinates squared if we want to stick to rational arithmetic.) Radians are only really useful for solving calculus problems by hand, or writing academic math/science papers where it’s important to stick to established conventions. For practical computation radians are almost always an inferior choice, more computationally expensive and less precise (they’re built into lots of existing libraries, so can often be convenient despite the inefficiency).
Turing_Machine 10y ago
I strongly suspect that it was anything but "accidental", but was rather related to just how much you could draw down the diameter of a wire in one step without breaking it. If you can make a B&S Gauge X+1 wire from a B&S Gauge X wire in one drawing step, while making a metric size N wire from a size M wire requires two drawing steps, that actually matters. The article alludes to this, but doesn't actually explicitly state it.
ArkyBeagle 10y ago
The derivation isn't all that interesting; the use is. Everybody who cares already knows what 12 ga. wire is. People in general don't give a [ expletive deleted ] about the source code; they just want the answer.
exDM69 10y ago
You know what is worse than imperial units? Measurements that were traditionally inches but converted to millimeters, inconsistently. I do woodworking in a metric country. It's terrible. My "quarter inch" chisel is 6mm but my "quarter inch" plywood is 6.5mm so it won't fit in a groove made by the chisel. 3/4" chisel is 20mm but plywood is 18mm. All the measurements are inch based but converted to metric arbitrarily rounding up or down. 3/4" is the only measurement that works well, it's 19.004mm. But a 19 mm drill bit isn't a part of any standard set. Some automotive applications are similar. The Toyota Hilux pickup truck has an indestructible reputation because it was cloned by the Japanese from a US truck. They rounded every measurement up to nearest millimeter. It's beefier than the original while having a smaller and less powerful engine. You do need some exotic sized wrenches to work on it, though.
wglb 10y ago
This is a bit of a middlebrow comment that we tend to unfortunately find at the top on HN. What measure of time do you use? Hour, minute, second, month, day year? Those are pretty arcane. The first four are pretty arbitrary, and existed way before America.
hatsunearu 10y ago
Maybe, but knowing mm^2 doesn't really help either. This AWG system has the benefit of discretization of wire thickness, so manufacturers can optimize their processes for only ~30 gauges instead of answering "what do you mean you don't have 3.1415mm^2 wires?!"
danny8000 10y ago
I remember when reading "Napoleon: A Life" by Andrew Roberts, Napoleon wasn't a big fan of the base-10 metric system, but he figured it would be the best way to break with the hundreds of different measuring systems in place in France at the time, and enforce an empire-wide standard. I much prefer base-12 or base-16 systems, especially when measuring and hanging drywall! On the other hand, the British waited way to long (until 1971) to decimal-ize their currency. Before that the pound was made up of 240 pence.

deleted 10y ago

[deleted]

imglorp 10y ago

Hugged to death. http://webcache.googleusercontent.com/search?q=cache:http://bit-player.org/2016/the-39th-root-of-92 http://webcache.googleusercontent.com/search?q=cache:http://...

_greim_ 10y ago

As a guitar player I'm glad the article also mentioned equal temperament tuning. The frets of a guitar for example are spaced using the 12th root of 2. Musical theory is a tangled rat's nest, but at least that part is easy to understand.

weinzierl 10y ago

> It’s worth noting that instruments were being tuned to this scale well before the invention of logarithms. I assume it was done by ear or perhaps by geometry, not by algebra. Well temperament wasn't known before 1681, there were predecessors that came close but none used the the twelfth root of two. Logarithms were introduced by John Napier in 1614 [1], the twelfth root of two was first calculated by Marin Mersenne in 1636 [2], well temperament was introduced by Werckmeister 1681 [3]. > Around 1600 Simon Stevin did attempt to calculate numerical values for the pitch intervals by decomposing 12th roots into combinations of square and cube roots; his results were not flawless. He had the right idea but not the right math. [1] https://en.wikipedia.org/wiki/John_Napier https://en.wikipedia.org/wiki/John_Napier [2] https://en.wikipedia.org/wiki/Twelfth_root_of_two https://en.wikipedia.org/wiki/Twelfth_root_of_two [3] https://en.wikipedia.org/wiki/Well_temperament https://en.wikipedia.org/wiki/Well_temperament

bit-player 10y ago
(I'm the OP here.) My source for the statement that "instruments were being tuned to this scale well before the invention of logarithms" is an article by Edward Dunne and Mark McConnell, "Pianos and Continued Fractions," Mathematics Magazine, Vol. 72, No. 2 (Apr., 1999), pp. 104-115. They write: "Guitars in Spain were evenly tempered at least as early as the fiftheenth century, two hundred years before Bach. And Hermanus Contractus, born 18 July 1013, invented a system of intervalic notation that anticipated equal temperatment." My source on Simon Stevin's work is a Rudolf Rasch, "Tuning and Temperament," published as Chapter 7 in The Cambridge History of Western Music Theory." Rasch gives an interesting account of the state of root extraction before the advent of logarithms. He attributes the errors to "Stevin’s sometimes rather reckless rounding of digits after the decimal period, which are often truncated rather than rounded."

jeremysmyth 10y ago

"In metric, one milliliter of water occupies one cubic centimeter, weighs one gram, and requires one calorie of energy to heat up by one degree centigrade—which is 1 percent of the difference between its freezing point and its boiling point. An amount of hydrogen weighing the same amount has exactly one mole of atoms in it. Whereas in the American system, the answer to “How much energy does it take to boil a room-temperature gallon of water?” is “Go fuck yourself,” because you can’t directly relate any of those quantities." - Wild Thing, Josh Bazell