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The 39th Root of 92

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Re: The 39th Root of 92

#91

Post by olau »

einhverfr wrote: post #28
ysleepy wrote: post #3

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…

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 audi…

I can see what you are trying to say, but I really don't think you're right. Yes, fractions are sometimes nicer with other subdivisions than decimal, but e.g. angles of a triangle: right-angled with 90 deg + 2 x 45 deg would be 50 + 2 x 25 deg. Works fine. Ultimate precision isn't necessary in everyday use.

The real reason why the US hasn't switched is that it is really painful to change something like this.

Re: The 39th Root of 92

#92

Post by pandler »

Sean1708 wrote: post #78
ubernostrum wrote: post #50

Earlier quoted context omitted.

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 disadva…

> Truth is it's an arbitrary system optimized for a particular set of use cases. Actually it's an arbitrary system optimised for calculations.

> Actually it's an arbitrary system optimised for calculations.

Which is a particular set of use cases.

Re: The 39th Root of 92

#93

Post by rhaps0dy »

rm445 wrote: post #51
einhverfr wrote: post #28

Earlier quoted context omitted.

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 audi…

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).

We have 12 non-thumb-finger visible divisions, though!

http://www.garywallace.net/wp-content/uploads/NF-SCI-0001-P0...

Each finger has three numbers, starting with the index and ending in the pinky, and you count pointing to the relevant division with your thumb.

Re: The 39th Root of 92

#94

Post by strictfp »

ycombinatorMan wrote: post #4
ysleepy wrote: post #3

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…

Have you considered how much it would cost to change units, and how absolutely little would be gained?

Have you considered how much it costs to keep them?

Re: The 39th Root of 92

#95

Post by protomyth »

rm445 wrote: post #51
einhverfr wrote: post #28

Earlier quoted context omitted.

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 audi…

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).

One of the Native American tribes went with base-8 because they counted the areas between the fingers because you can haul bottles with those.

I too wish base-12 were used more. Given how much a penny is worth, getting rid of decimal money and substituting a base-12 coin would solve a lot of pizza / dinner cost split problems.

Re: The 39th Root of 92

#96

Post by protomyth »

ycombinatorMan wrote: post #4
ysleepy wrote: post #3

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…

Have you considered how much it would cost to change units, and how absolutely little would be gained?

It would be a serious cost. Saw cost estimates on changing the letterhead for a US State and that was obscene. Changing units makes that look like a pittances.

Besides, what are we saying to a future Martian colony with conversion to an Earth-centric unit? The metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. Do we think our Martian brethren will be ill educated in history? Would Mars demand its own metre? Are we sending a message of Earth's lasting dominance over the colony?

Perhaps, if we convert, we do the simple change of 1 foot being defined as the distance light travels in one nano-second. Its pretty damn close to that already, and then we don't have issues with Mars.

/s

Re: The 39th Root of 92

#97

Post by _greim_ »

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.

Re: The 39th Root of 92

#98

Post by wglb »

ysleepy wrote: post #3

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…

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.

Re: The 39th Root of 92

#99

Post by runarberg »

jacobolus wrote: post #64
rm445 wrote: post #51

Earlier quoted context omitted.

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).

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…

> I personally like just writing fractions of a full turn

Well just multiply your fraction with τ = 2π and you get radians. E.g. a whole revolution is τ radians (or 360°), half a revolution is ½τ radians or (180°), etc.

Re: The 39th Root of 92

#100

Post by hatsunearu »

ysleepy wrote: post #3

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…

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?!"
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