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#151
07-16-2018, 02:07 PM
 Nava Guest Join Date: Nov 2004 Location: Hey! I'm located! WOOOOW! Posts: 38,568
Quote:
 Originally Posted by rat avatar No, a pound is 16 oz, a nautical mile is 1/60 of a degree of arc, so you can represent the subordinate number as an exact finite number. There is no rounding needed to represent a nautical mile or an ounce.
There is no rounding needed to represent 0.1 nautical mile, but there is to represent 0.1km? Refuckingally?
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#152
07-16-2018, 02:07 PM
 watchwolf49 Guest Join Date: Dec 2009 Location: State of Jefferson Posts: 8,353
Quote:
 Originally Posted by rat avatar Are you claiming that the SI system isn't decimal, and doesn't use prefixes that are multiples or powers of 10? ... [snip]
It's said that if we brought together the world's most intelligent people and tasked them with designing the most confusing system of time keeping imaginable, this would still be easier to understand than the system in use today ... just saying ...
#153
07-16-2018, 02:10 PM
 rat avatar Member Join Date: Dec 2009 Location: Seattle, Wa Posts: 3,835
Quote:
 Originally Posted by Nava There is no rounding needed to represent 0.1 nautical mile, but there is to represent 0.1km? Refuckingally?
No there is NO INTRINSIC REASON TO USE DIVISION BY 10 in these systems. Division by 10 may need to be done but....

The ENTIRE metric system is based on division by a number that is not representable in binary floating point. DIVISION and multiplication BY powers of 10 IS THE ENTIRE BASIS OF THE METRIC SYSTEM.

Please to not change my point from that, and I should just quit responding to these posts as I am just adding to thread drift.

I apologize to the board.

Last edited by rat avatar; 07-16-2018 at 02:12 PM.
#154
07-16-2018, 02:42 PM
 Lemur866 Charter Member Join Date: Jul 2000 Location: The Middle of Puget Sound Posts: 21,821
There is a reason to use division by 10 in a traditional measurement system if you ever write down or input a number as a decimal. If you ever input 7.3 miles, or 1.2 feet, then you have just input a number that doesn't have an exact binary representation.

The only way around this is if your system is constrained to only accept inputs with fractions in the form of x/(2^y). But your system probably just accepts decimal inputs, and doesn't reject inputs like 7.3 miles, or 4.71 pounds. So then what?

Yes, if you accepted inputs, not in decimal but in hexadecimal, then you'd get exact representations of every finite input. But while this is easily possible to imagine and implement, the problem is that your human users will have to be trained to input hexadecimal numbers, and this is a very difficult thing to force them to do. If you're trying to avoid floating point errors this is one way, but then you're introducing the problem of input errors when they make mistakes when converting their inputs to hex.

In the real world, we use decimal numbers even for traditional measures like feet, miles, pounds, and hogsheads.
#155
07-16-2018, 04:31 PM
 Chronos Charter Member Moderator Join Date: Jan 2000 Location: The Land of Cleves Posts: 77,448
If you use single-precision floating point numbers, then the fact that none of your numbers has an exact binary representation results in an imprecision of about one part in a million. Usually, this doesn't matter at all, no matter what the cause of that one PPM error. But in the off chance that it does matter, you can instead use double precision floating point numbers (which are the default nowadays anyway, just because computing is so cheap), in which case your error is about one part in a trillion. I defy you to come up with any application at all where that's not good enough. And even if you are working in the one singular application (yes, that's meant literally) where even that much precision isn't enough, you can get higher-precision floating-point packages that will still work.
#156
07-16-2018, 07:00 PM
 Sunspace Member Join Date: Jun 1999 Location: Near the GT eeehhhh... Posts: 27,573
Quote:
 Originally Posted by bob++ Hopefully beowulff and rat avatar have gone out into the playground to fight it out. Yes, of course 12, 16, 60 etc have more whole number sub-multiples, but the metric system is a darn sight easier for kids to learn, especially since we count in tens. Maybe it would be different if we all had six fingers on each hand...?
I think the greatest missed chance with the metric system is that we originally didn't base it on a multiple of 12... and adjust all our arithmetic, etc, to also be in base 12.

That way you get all the convenient divisors of 12 (halves, thirds, fourths, sixths, twelfths), plus 200 years ago, there was a lot less math and science to convert to base 12.
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#157
07-17-2018, 11:28 AM
 Lemur866 Charter Member Join Date: Jul 2000 Location: The Middle of Puget Sound Posts: 21,821
Quote:
 Originally Posted by Chronos If you use single-precision floating point numbers, then the fact that none of your numbers has an exact binary representation results in an imprecision of about one part in a million. Usually, this doesn't matter at all, no matter what the cause of that one PPM error. But in the off chance that it does matter, you can instead use double precision floating point numbers (which are the default nowadays anyway, just because computing is so cheap), in which case your error is about one part in a trillion. I defy you to come up with any application at all where that's not good enough. And even if you are working in the one singular application (yes, that's meant literally) where even that much precision isn't enough, you can get higher-precision floating-point packages that will still work.
I think the point isn't the precision of the answer. The problem is doing comparisons between values. Like, you take a floating point variable, do some operations on it, and then compare the new value with the original value. Is it exactly the same? If you carefully limited your operations to ones that resulted in an exact binary representation, then you can be confident that A' will exactly equal A. If you haven't, then A' might be every so slightly different than A, and your (IF A'==A) statement will return false when you expect it to return true.

So the answer is, don't do that. Don't make checks on floating point numbers where the value has to be an exact value, because if you ever once do division by a number that is not 2^n, you will not get an exact binary value.
#158
07-17-2018, 12:02 PM
 Ají de Gallina Guest Join Date: Dec 2007 Location: Lima, Perú Posts: 4,363
The great advantage of the US/UK system is that very few units get divided by 3 easily (feet, particularly. Aside from that, the numbers are incredibly arbitrary and have to be memorised. 1760 yard to a mile is ridiculous unless dividing by 11 is a common ocurrence. However, for everyday life, they are perfectly easy to use.
Here in Perú, an SI country, we still have non SI units in common use.

Gasoline is in US gallons (but LPG and LNG in liters and cubic meters)

Nails, pipes and such comes more frequently in inches than mm.

A few things are measured in "Arrobas" (Bushels).
#159
07-17-2018, 01:02 PM
 Kobal2 Guest Join Date: Mar 2008 Location: Paris, France Posts: 16,947
Quote:
 Originally Posted by Sunspace I think the greatest missed chance with the metric system is that we originally didn't base it on a multiple of 12... and adjust all our arithmetic, etc, to also be in base 12. That way you get all the convenient divisors of 12 (halves, thirds, fourths, sixths, twelfths), plus 200 years ago, there was a lot less math and science to convert to base 12.

But why ? We count in base 10 for intuitive reasons. We have 10 fingers, 10 toes and 10 testicles (what ? You don't ? ). Basing the metric system on that base feels so right, it's actually downright weird that so many traditional unit systems - not just the Imperial system mind you, but also the various currency and weight unit systems used in France circa 1789 - eschewed base 10 altogether.

I'm sure it all made sense at one point, but I can absolutely grok enlightenment thinkers being born in a world where 1 coin of this equal 240 coins of that each of which are equal to 3 and 4/18th of those going "WHAT THE HELL ?! No. Just no. Let's take it back from the top."

(FTR, a couple years ago I had to work on a 9th century document, a market/fair ordinance that ostensibly tried to set up standards for measures, weights and currencies and it was maddening. The fuckers almost had one separate measuring system per crop)
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#160
07-17-2018, 01:09 PM
 rat avatar Member Join Date: Dec 2009 Location: Seattle, Wa Posts: 3,835
Quote:
 Originally Posted by Ají de Gallina The great advantage of the US/UK system is that very few units get divided by 3 easily (feet, particularly. Aside from that, the numbers are incredibly arbitrary and have to be memorised. 1760 yard to a mile is ridiculous unless dividing by 11 is a common ocurrence. However, for everyday life, they are perfectly easy to use. Here in Perú, an SI country, we still have non SI units in common use. Gasoline is in US gallons (but LPG and LNG in liters and cubic meters) Nails, pipes and such comes more frequently in inches than mm. A few things are measured in "Arrobas" (Bushels).
The mile wasn't set at 1760 yards, but eight furlongs of 660 feet. The acre was based off the furlong too. 1 furlong by 1 chain (66 feet), the yard is a bit of an outlier post 16th century not that there was a lot of standards back then. A furlong was the typical distance a team of oxen could plough without resting which worked well under the feudal system. (taxation drove most standards, even the metric system)

Oddly he US considered the metric system, but before the French revolution it wasn't established enough and they adopted the UK system after being frustrated that the congress selected the troy oz for the mint as it was the only viable option at the time.

Last edited by rat avatar; 07-17-2018 at 01:13 PM.
#161
07-17-2018, 02:13 PM
 Lemur866 Charter Member Join Date: Jul 2000 Location: The Middle of Puget Sound Posts: 21,821
For most traditional measures there was no such thing as an official conversion factor between miles, chains, rods, furlongs, feet, inches, yards, or whatever, because each traditional measure was used in different contexts, and you'd almost never convert between systems. Along comes the 19th century and various national standards start to emerge, and you get official conversions between incompatible measures, and now for the first time we know how many teaspoons are in a hogshead. But of course that introduces additional problems because the standards set by one body don't match the standards set by another body, and so we have multiple definitions of the ton, we have the mile and the nautical mile, and crazy shit like that.

Hey, metric keeps one traditional unit, the second, which is 1/60th of 1/60th of 1/24th of one day. Nowadays the metric second isn't defined by the day but by the amount of time it takes for a certain number of vibrations of cesium at such and such conditions. If we were starting over from scratch we could have picked round numbers for this rather than some arbitrary number, but it doesn't really matter much because only people building atomic clocks have to know the number, and if they don't have that number written down then maybe they should change careers.
#162
07-17-2018, 02:23 PM
 Nava Guest Join Date: Nov 2004 Location: Hey! I'm located! WOOOOW! Posts: 38,568
Quote:
 Originally Posted by Lemur866 For most traditional measures there was no such thing as an official conversion factor between miles, chains, rods, furlongs, feet, inches, yards, or whatever, because each traditional measure was used in different contexts, and you'd almost never convert between systems.
Oh, yes you did! There's these things called "borders", and every time you crossed one your units of measure changed, you see, but often while keeping the same exact name! And border taxes were based on the local unit, of course. And you had to pay them in every border, and some of the realms which had their own units were smaller than a county - either UK or US.

Isn't geography fun! Now with taxes, yay!
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Last edited by Nava; 07-17-2018 at 02:24 PM.
#163
07-17-2018, 02:32 PM
 DPRK Guest Join Date: May 2016 Posts: 1,660
The answer to the original question of how people were able to convert with relative ease from the British system to the international standard system is that British law defined fixed conversion factors.
#164
07-17-2018, 02:39 PM
 Voyager Member Join Date: Aug 2002 Location: Deep Space Posts: 43,469
Quote:
 Originally Posted by Nava Is that supposed to be easier than "((C/5)*9)+32 gives you Farenheit" or "(((F-32)/9)*5) gives you Celsius"? Why include percentiles where all you need is basic arithmetic
And you don't even to memorize the formula. I derive it when needed by converting 100C to 212 F and back. The 32 falls out from freezing point. Trivial.
#165
07-17-2018, 03:13 PM
 naita Guest Join Date: Jun 2002 Location: Norway Posts: 5,548
Quote:
 Originally Posted by Kobal2 But why ? We count in base 10 for intuitive reasons. We have 10 fingers, 10 toes and 10 testicles (what ? You don't ? ). Basing the metric system on that base feels so right, it's actually downright weird that so many traditional unit systems - not just the Imperial system mind you, but also the various currency and weight unit systems used in France circa 1789 - eschewed base 10 altogether.
You need to check your assumptions. Yes, there is a link between our ten fingers and base ten, but there are a lot of languages out there not using base ten, and reminders of the non-dominance of base ten living on in indo-european languages as well.

Not just in words like score, dozen and gross, which can sort of be handwaved away as affectations, but in the fact that our base ten counting numbers start with twelve different numbers before going into what is clearly base ten. The etymology is apparently base ten, but different from the rest of the "tens".

Danish and French both have clear vigesimal counting numbers, and prior to the 15th century "hundred" in Germanic languages was what came to be known as a long hundred, namely ten dozen.

The "weird" measurement systems arose in that world of mixed base counting and adding/subtracting done mostly in your head, not in the modern world where everyone learns multiplication and division with arabic numerals in a solid positional base ten system.
#166
07-17-2018, 04:45 PM
 rat avatar Member Join Date: Dec 2009 Location: Seattle, Wa Posts: 3,835
Quote:
 Originally Posted by naita You need to check your assumptions. Yes, there is a link between our ten fingers and base ten, but there are a lot of languages out there not using base ten, and reminders of the non-dominance of base ten living on in indo-european languages as well. Not just in words like score, dozen and gross, which can sort of be handwaved away as affectations, but in the fact that our base ten counting numbers start with twelve different numbers before going into what is clearly base ten. The etymology is apparently base ten, but different from the rest of the "tens". Danish and French both have clear vigesimal counting numbers, and prior to the 15th century "hundred" in Germanic languages was what came to be known as a long hundred, namely ten dozen. The "weird" measurement systems arose in that world of mixed base counting and adding/subtracting done mostly in your head, not in the modern world where everyone learns multiplication and division with arabic numerals in a solid positional base ten system.
To add to this, simply counting touching the joints fingers with the thumb works for base 12, and just counting without the thumb leads to base 8. Or you can just ignore the innermost joint and count like you do with base 12. Consider with base 12, if you fold two of your fingers you can just count the remaining joints and get half.

The Sumerians and the Babylonians were base 60 thus our time, angles etc...

Base 10 just happened by chance, probably because of the Egyptians,

https://en.wikipedia.org/wiki/Rhind_...atical_Papyrus

Funny enough, 1,2,6,7,8 and 9 loaves of bread are divided among 10 men and how decimal base was a challenge for them too

Last edited by rat avatar; 07-17-2018 at 04:49 PM.

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