[rhelz]

> I'm failing to see what that has to do with the metric system

You are an apprentice house builder. Your boss hands you meter-stick, with 100 lines on it to mark out the centemeters, and asks you to cut him a piece of wood which is 1/3 meter long. This puzzles you, because you can't find a line on that stick which indicates 1/3rd of a meter.

So you go back to your boss, and he grumbles, but gives you another meter stick, with 1,000 lines on it. You still can't find a line on the stick which indicates 1/3rd of a meter....

[derekp7]

I'm assuming there is a reason for the 1/3 meter request, such as the board needs to fit in a specific spot. So you are saying that it is better to hand the worker a yard stick, so he can measure out 13.12322835 (approx) inches?

In reality, I would cut the board either 33.4 mm, or 13 1/8 inches (a bit long) then pound it in place (wood has a bit of give to it).

[friend_and_foe]

You're missing it entirely. If we weren't measuring using meters in the first place he wouldn't even be asked to cut 1/3rd of a meter. He'd be asked to cut 1/3rd of a yard, which is very easy on a yardstick. It only needs to fit in a specific spot that is a third of a meter because the structure around that spot was measured and built with the metric system.

[Jensson]

But they wouldn't ask for a third of a meter if they were using metric, just like you wouldn't ask for a firth of a yard if you were using imperial.

[mulmen]

The US customary system conventionally uses reciprocal powers of two. 1/3 is unlikely to be a specified distance. I rarely hear anyone speak in yards. If someone wanted “a third of a yard” they’d just say one foot. A third of a foot is just four inches. Or slightly less for clearance would be three and 7/8 inches, etc.

[friend_and_foe]

Yes they would, if they wanted something divided by 3.

[Ekaros]

I don't think they would ever ask to cut in 1/3rd... I can't imagine scenario where this happens in building. You always have things like wall thickness and such to consider also. You just don't make useless cuts.

Boss tells you to install 3 separate cabinets with shelves in 1 meter space. You measure that too to be sure it is. Then you see cabinet walls are 1 cm thick, you need 4 walls. 96 cm total shelve space. Actually this is nice 32 cm per shelve... And you even have some room to make extra cuts...

[rhelz]

Looking over the replies to this post, its pretty obvious that some of you have never really actually built anything requiring any amount of measurement.

"Why don't I just give my boss a 33mm piece?" -- and leave a 1mm gap in your house, where ants can come in, and heat goes out....

"Why would I ever need a board 1/3rd of a meter long?" -- sigh it could just as easily be a board 10/3 meters long, or 200/3 meters long. Because 3 is a small prime, and by the fundamental theorem of arithmetic, 3 is going to be a factor in a lot of integral lengths.

Say you are designing a switch with two buttons on it, "on" and "off". Well, the centers of those two buttons are going to be located at 1/3rd and 2/3rds of the length of the plate they are mounted on.

Say you design a crock pot with 3 buttons for the heat, "low", "medium", and "high". You don't want two of those buttons to be 1cm apart and the other 2cms apart!

If you look at countries like, say, Japan, or Germany, which really do use the metric system, you'll find that they measure things not in centimeters, but in millimeters. And the lengths they use are numbers like 48, or 120, which have lots of factors of 2 and 3 in them. Because you divide lengths into 2 or 3 parts all the time.

Which is to say, if you want to actually use the metric system in industrial design, you don't use a lot of lengths which are powers of 10. You use lengths which are divisible by 12 anyways.

There's a reason the U.S. never went off the English system, and why countries like Canada and the U.K., which actually make real efforts to try to go off of the English system still use a lot of English units in everyday measurements. And it's not just because of conservatism, or NIH syndrome.

[joshxyz]

i dont get it. just cut 33 and if my boss arses me about precision i either need to machine cut it or get a new boss?

[yongjik]

Why would my boss ask for a piece of wood which is 1/3 meter long, when everyone who ever learned the metric system knows it's base ten? It's the kind of thing that never happens in practice, just like an American boss would never ask a piece of wood 0.24 yard long.

[imtringued]

It's impossible to do this in any measuring system. The problem is that wood isn't dimensionally stable.

There is no way to machine, grind and then lap the wood to a perfect 1/3.

[VS1999]

I don't get it. You can't represent 1/3 in base 2 either, and even worse, now you can't represent 1/10.

[rhelz]

> now you can't represent 1/10

This is why 12-inch rulers commonly have the inches divided into 10 inches.

There is a line on that ruler for 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, and 1/10 of a foot. Uh, and 1/12th of a foot too, of course :-)

cf. with a 10-cm ruler, each cm divided into 10 mm. You've got a line for 1/2, 1/4, 1/5, 1/10, and 1/25, and 1/100th. That's it.

[lolinder]

But you can represent 1/3 cleanly in base 12, so inches don't have this problem.

Yeah, you can't represent 1/10, but why does that matter? When 1/10 comes up in practice it's almost always as a side effect of us using base 10, not a natural requirement to partition something 10 ways.

[dudul]

Wait what? Why is 1/3 so critical to represent but not 1/10?

[DemocracyFTW2]

for the reason it was used in the artificial example given above I guess. OTOH it should be expected that the fractions 1/2, 1/3, 1/4, 1/5, 1/6... appear more often than others in practical work, not sure about that

[rhelz]

> more often than others in practical work

Here is a thumbnail sketch of a reason for why they do:

1. Large structures tend to be build from smaller substructures. (E.g., a train is typically built of a number of cars, a 6-pack is built from 6 cans).

2. And large structures tend to be built from integral multiples of smaller substructures, because a fraction of a substructure is typically not as useful as a whole substructure. (e.g. a train car missing its wheels isn't as useful as an intact train car, and a partially drunk-up can of beer isn't nearly as desirable as a whole can of beer.)

3. The fundamental theorem of arithmetic says that every integer can be factored into prime numbers.

4. Small primes are more common factors of integers than large primes are. (e.g. you more often want twice of something than 37 times of something)

Ergo:

5. Most of the numbers involved in designing and building something are going to be divisible by 2 and 3--because the number of subsystems it contains will likely be multiples of 2 and 3. Prime factors of 5 and over are relatively rare.

6. Therefore, when you are measuring the larger system, it is handy to use units which are easily divisible by 2 and 3. (like a foot is 12 inches).

Its why donuts and eggs are sold by the dozen, and beer comes in 6-packs, and cases of 24. You are far more likely to divide up cans of beer or some donuts to a number of people which is divisible by 2 or 3, then by 5 or any higher prime factor.

[rhelz]

> Why is 1/3 so critical to represent but not 1/10?

TLDR reason: Every second number is divisible by 2. Every third number is divisible by 3.

So if you want to divide something (like donuts or cans of beer, or the length of a wood plank) by N, it's far more likely that N will have a factor of 2 or 3 than it will not have a factor of 3, but be divisible by 10. Which is to say, you are far more likely to need tick marks spaced by 1/2 and 1/3 than tick marks spaced by 1/10. Which is to say that a 12-inch ruler is preferable to a 10 cm ruler, Q.E.D.

That's why they sell donuts by the dozen, and beer in 6-packs. And why the US officially (and Canada and the UK unofficially) still use English units for everyday measurements. Its just more practical.

[Jensson]

> Yeah, you can't represent 1/10

You can't represent 1/5 either while base 10 can. You gain 3 but lose 5, it has the same number of primes.

[NikkiA]

Vernier guages are horseshit in anything but metric.

[rhelz]

Here is a vernier gauge for degrees--a non-metric unit, expressed in base 360 :-)

https://www.amazon.com/Universal-Stainless-Protractor-Precis...

[NikkiA]

Thanks, I hate it.

[timeon]

Are you implying that they are not able to build in most part of the world?

[rhelz]

That's a good question, actually. Surely, they can. But if you look at countries which really embrace the metric system, like Japan, or Germany, and look at the products they design, you'll find that the dimensions are not given in centimeters. The centimeter is, empirically, not a very useful length.

Instead, what you find is that they measure things in millimeters--and curiously, the lengths in millimeters tend to be numbers like 48, or 120, i.e. numbers which have lots of factors of 2 and 3 in them.

Don't just take my word for it!! Go browse Amazon.com and see what typical lengths of objects designed in those countries are, and what units they are stated in.

Which is to say, if you are really going to use the metric system, you are going to be using lots of lengths divisible by 12 anyways. Which means they are not powers of 10, and probably not divisible by 10, which means you've largely lost the biggest advantage of the metric system--easy arithmetic for numbers which are powers of 10 and divisible by 10.

Cf with a ruler, which is divided into 12 inches, and each inch into tenths. There is a line on that ruler for 1/2 a foot, 1/4 of a foot, 1/5th of a foot---and 1/3rd and 1/6th of a foot. All of the smallest and most commonly used prime numbers are present and accounted for.

cf with a 10-centimeter ruler, each cm divided into 10 milimeters. You've got lines for powers of 1/2 and 1/5--that's it. If you want to divide it by any other factor, you are squinting your eyes and guesstimating between lines.

[TraspSE]

You're missing the point. What I'm saying is that the metric system is built around base 10, not because of its properties, but because it's the base we use in general - and the simplicity of having one single system with seamless conversions.

Arguing in favour of base 12 systems would make sense if it seemed doable to introduce more numerals and replace base 10 altogether, in my opinion, but that's not realistic.

Besides, if you live somewhere where the metric system is used, and you're unable to manually measure and cut one third of a meter (0.333m/33.3cm/333mm/333333µm) with the same speed and precision as you would be able to using a yard-stick - then you probably shouldn't be allowed near the tools needed in the first place.

PS. In practice, the boss would've asked you for a piece that is either 3dm, 33cm or 333mm long, indicating the expected precision.

[seba_dos1]

Just wait until your boss asks you to cut a piece of wood which is π inches long.