The 39th Root of 92 • Hacker News Board

Re: The 39th Root of 92

#71

Post by Hondor » Sun, Aug 07, 2016, 10:09 AM UTC

dancek wrote: post #63

int_19h wrote: post #60

Earlier quoted context omitted.

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 "natur…

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…

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.

Re: The 39th Root of 92

#72

Post by Hondor » Sun, Aug 07, 2016, 10:24 AM UTC

disc wrote: post #62

HCIdivision17 wrote: post #20

Earlier quoted context omitted.

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 ra…

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.)

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.

Re: The 39th Root of 92

#73

Post by exDM69 » Sun, Aug 07, 2016, 10:27 AM UTC

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…

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.

Re: The 39th Root of 92

#74

Post by exDM69 » Sun, Aug 07, 2016, 10:33 AM UTC

dancek wrote: post #63

int_19h wrote: post #60

Earlier quoted context omitted.

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 "natur…

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…

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".

Re: The 39th Root of 92

#75

Post by exDM69 » Sun, Aug 07, 2016, 10:43 AM UTC

adrianratnapala wrote: post #37

sgk284 wrote: post #13

Earlier quoted context omitted.

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.…

As much as I hate the metric system myself, I don't think it's true that U.S. measuring culture is a self-consistent system that avoids unnecessary conversions. For example the energy content of fossil fuels tends to be measured in BTU per (whatever), while electrical energy is measured in kilowatt hours. On the other hand, automobile engines are often rated in horsepower. I find this sort of thing is ubiquitous in e…

In imperial vs. metric, I don't think the actual units are as big of a difference as the convention of using fractions vs. decimals.

When doing manual work, e.g. woodworking or metalwork it's pretty convenient to use fractions. You tend to divide things in half or quarters.

With most things not made by hand any more, using fractions and inconsistent units like inches, feet, yards and miles is a nuisance for engineers.

Re: The 39th Root of 92

#76

Post by fennecfoxen » Sun, Aug 07, 2016, 11:15 AM UTC

billforsternz wrote: post #6

ycombinatorMan wrote: post #4

Earlier quoted context omitted.

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

I would imagine the gains would be extraordinary - the deadweight cost of interacting with the metric world must be huge. The needlessly complicated calculations involved in dealing with things like fractions of inches impose their own subtle tax on productive effort. And let's not forget the avoidance of occasional catastrophes like space probes doomed by a conversion miscalculation or an airliner running out of gas…

"Extraordinary gains?"

Ordinary gains are about 4% a year (long-term returns of broad investments in the stock market, adjusted for inflation). If you buy a piece of equipment for $100 it should return $4/year (on top of maintenance costs, depreciation, and the like) otherwise you'll do better by buying a stock-market index fund.

How much do you think it would cost an arbitrary manufacturing company to switch over all their tools and equipment to metric measures, update and test all their designs and schematics, run them through any applicable regulatory agencies, and such? Include the cognitive up-front cost of switching, maintaining dual toolchains and inventories for any gradual transition, the opportunity cost of the profitable projects you would have to postpone while your company experts see to the metric switchover, and everything else. Consider adjusting the return downward a little to account for appropriate risks in this process.

Do you see savings substantially in excess of 4% a year? If so, that's extraordinary, and a worthwhile investment! If not, the company would do better for itself and its shareholders by spending money elsewhere, or returning that money through dividends or stock buybacks so it can be put in a stock market index fund.

Re: The 39th Root of 92

#77

Post by junofan » Sun, Aug 07, 2016, 11:20 AM UTC

jonahx wrote: post #16

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…

> 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."

I think you're making some assumptions. When I was coming up through the school system in the 90s, I thought metrication was a federal government thing (since it is). I doubt my parents are aware of the origins of the metric system. Things may have changed for the youngest generation though.

Re: The 39th Root of 92

#78

Post by Sean1708 » Sun, Aug 07, 2016, 11:34 AM UTC

ubernostrum wrote: post #50

xlayn wrote: post #5

Earlier quoted context omitted.

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.

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.

Re: The 39th Root of 92

#79

Post by arielb1 » Sun, Aug 07, 2016, 11:38 AM UTC

jacobolus wrote: post #67

e2e8 wrote: post #59

Earlier quoted context omitted.

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.

And then when you try to scale your whole design up, whoops, all the rounding changes and you need to redo everything. Anyway, neither way here is right or wrong. One optimizes for uniformity of scaling, the other optimizes for intelligibility with a base ten number system.

It's not like you are making tight fits with wires anyway, a millimeter here or there won't matter.

However, using something like the E12 series would work pretty well.

Re: The 39th Root of 92

#80

Post by pessimizer » Sun, Aug 07, 2016, 11:47 AM UTC

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).

Little Twelvetoes

https://www.youtube.com/watch?v=_uJsoZheTR4