6 ms·

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

by 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 :)
      - einhverfr 10y ago
        How many kiloseconds will you spend working next week? Even in metric-using countries, nobody uses it for time. For actual applications of spherical trig though degree, minute, second makes a lot of sense, primarily because the earth rotates about one arc second every 4 minutes, and if you know this then you can do manual navigation via the stars and many other things. However for many things I do use metric time, just not for the human aspect of it. For example, for one customer (admittedly in the sciences), we had to help them estimate how much hardware they needed for additional load. So you do the work in seconds because at that point the math is easiest, and convert to ratios following.
        10y ago
- einhverfr 10y ago
  One of the neat things about degrees and plane geometry is how regular polygons you can have without partial degrees. The number of sides depends on the divisiblity of 360 by the number of angles so: 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 30, and so forth. For angle measurement where you want a closed geometry figure at the end, degrees are extremely elegant, and 360 is 2^3x3^2x5
  - goldenkey 10y ago
    360 is arbitrary I hope you know. https://en.wikipedia.org/wiki/Degree_(angle)#History https://en.wikipedia.org/wiki/Degree_(angle)#History
- disc 10y ago
  Wouldn't a much more natural unit for angular measurements be 1/(2*pi)? That way angular measurements are represented as their fraction of a circle (which is pretty easy to visualize; 180 degrees becomes 1/2.)
  - Hondor 10y ago
    You'd lose the definition of angle as arc length / radius, which would make your proposed unit just as arbitrary as degrees - most formulas involving angles would need to contain a conversion factor. You'd also lose the small-angle approximations sin(theta)=tan(theta)=theta which in my field are used extensively to convert nonlinear to linear equations. Nonetheless, your proposed unit already exists and is called tau. Or write it as 2pi if you want to be more easily understood.
    - majewsky 10y ago
      The most relevant point here is that the natural choice of units is very subjective and depends on the task at hand. For example, particle physics uses "natural units" where all units are powers of gigaelectronvolts: https://en.wikipedia.org/wiki/Natural_units#.22Natural_units.22_.28particle_physics_and_cosmology.29 https://en.wikipedia.org/wiki/Natural_units#.22Natural_units...
- function_seven 10y ago
  Regarding your PS: The most baffling measurements to me are tires. The diameter is expressed in inches, the width in millimeters, and the sidewall thickness is given as a percentage of tread width. So you get 255/40R17 to describe a 17” tire that's 10” wide with 4” sidewalls. (Or a 430mm tire that's 255mm wide with 100mm sidewalls)
  - woliveirajr 10y ago
    And try to replace your wheel, for example, for one that has 16 or 18 inches, and calculate the size of the tire to have the same final size...
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?

by kevhito 10y ago

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 :)
    - einhverfr 10y ago
      How many kiloseconds will you spend working next week? Even in metric-using countries, nobody uses it for time. For actual applications of spherical trig though degree, minute, second makes a lot of sense, primarily because the earth rotates about one arc second every 4 minutes, and if you know this then you can do manual navigation via the stars and many other things. However for many things I do use metric time, just not for the human aspect of it. For example, for one customer (admittedly in the sciences), we had to help them estimate how much hardware they needed for additional load. So you do the work in seconds because at that point the math is easiest, and convert to ratios following.
      - 10y ago
einhverfr 10y ago
One of the neat things about degrees and plane geometry is how regular polygons you can have without partial degrees. The number of sides depends on the divisiblity of 360 by the number of angles so: 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 30, and so forth. For angle measurement where you want a closed geometry figure at the end, degrees are extremely elegant, and 360 is 2^3x3^2x5
- goldenkey 10y ago
  360 is arbitrary I hope you know. https://en.wikipedia.org/wiki/Degree_(angle)#History https://en.wikipedia.org/wiki/Degree_(angle)#History
disc 10y ago
Wouldn't a much more natural unit for angular measurements be 1/(2*pi)? That way angular measurements are represented as their fraction of a circle (which is pretty easy to visualize; 180 degrees becomes 1/2.)
- Hondor 10y ago
  You'd lose the definition of angle as arc length / radius, which would make your proposed unit just as arbitrary as degrees - most formulas involving angles would need to contain a conversion factor. You'd also lose the small-angle approximations sin(theta)=tan(theta)=theta which in my field are used extensively to convert nonlinear to linear equations. Nonetheless, your proposed unit already exists and is called tau. Or write it as 2pi if you want to be more easily understood.
  - majewsky 10y ago
    The most relevant point here is that the natural choice of units is very subjective and depends on the task at hand. For example, particle physics uses "natural units" where all units are powers of gigaelectronvolts: https://en.wikipedia.org/wiki/Natural_units#.22Natural_units.22_.28particle_physics_and_cosmology.29 https://en.wikipedia.org/wiki/Natural_units#.22Natural_units...
function_seven 10y ago
Regarding your PS: The most baffling measurements to me are tires. The diameter is expressed in inches, the width in millimeters, and the sidewall thickness is given as a percentage of tread width. So you get 255/40R17 to describe a 17” tire that's 10” wide with 4” sidewalls. (Or a 430mm tire that's 255mm wide with 100mm sidewalls)
- woliveirajr 10y ago
  And try to replace your wheel, for example, for one that has 16 or 18 inches, and calculate the size of the tire to have the same final size...

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?