As an American with a physics background, a while ago I casually reviewed how bad our non-metric system is -- http://joshuaspodek.com/metric-system-isnt -- and found it not nearly as bad as people treat it. Among other things, when I build things it's useful to divide in half a few times, which is easier with inches and feet. And I've found no benefit to Celsius's 0 and 100 coinciding with water's state changing.
I bring that up here because I've never heard even the staunchest metric proponents use kiloseconds or megaseconds or hesitate to use hours, minutes, days, and so on. I know people experimented with decimal times, especially around the French Revolution, but it didn't stick. It's funny when someone talks about the value of using base ten and then switches to base 60, base 12, and base 24 in the next sentence.
I should say that in physics experiments people used seconds only (which is where I learned that to within about a percent a year is pi times ten to the seventh).
As a European living in America I disagree. The one value of metric vs imperial is that you (for the most part) don't have to do any math when converting between units.
If I have 1.73 miles, I have to do the math to figure out how many feet that is, 1.73*5280~=9134, which is not something that's easy for me to do in my head.
However, 1.73 km is 1730 meters, which is way easier (at least for me, but that might be my bias).
Imperial system is bad, even for you who grown up with it, it should be obvious how inconvenient it is. As for temperature, while F is not telling me anything useful, C is always telling me if it will rain or snow, actually when it snows it is always closer to 0 (or 32).
As article mentioned, we got time from Babylonians, who got it from Summerians. Time and calendar are one of the weirder things we deal with. I used internet time for a while, you know the Swatch thing. It looks weird in the beggining, but very quickly you get it and it works well and it is convenient that it is not time-zone dependant. And that was just a marketing gimmick from Swatch.
I think the whole idea that we somehow manage to create bridges and build buildings despite weird measures we use, is more testament to our ability to overcome difficult obstacles.
Similarly, people will claim it makes no sense that American M/D/Y dates are neither monotonically increasing nor decreasing, but then they'll find it totally natural to use "D/M/Y H:M:S" or "H:M:S D/M/Y" and not even notice that they share that same alleged flaw.
> when I build things it's useful to divide in half a few times
Fahrenheit adjusted his earlier scale, changing from 30° to 32° for freezing, and 90° to 96° for body temperature, in order to simplify constructing thermometers by bisecting between the calibration points.
It is extremely inconvenient that time is base-24 and base-60 while everything else in the metric system is base-10; it leads, for example, to a difficult conversion between the "meters per second" of the physics class and the "km/hr" of the highway. One surprisingly frustrating thing is that if you view a day as a million "instants" then an instant is actually a very human number, about the human reaction time or so; and a kiloinstant is a very human timescale too; 86.4 seconds or just shy of a minute and a half. We already know that when someone says "be there in five minutes" they mean 7-8; if they said "be there in five ki" they would be more accurate.
Fun things:
1. I wrote an HTML5 base-10 clock here with some togglable layers. Try out base-10 time: http://drostie.org/time/ . It's actually much easier than reading a normal clock because it's a digital readout, "8, 5, 6" rather than "two past a quarter after 8, that's 8:17." (It might not seem that way at first -- but that's because we spent long hours learning to tell time.)
2. For the exactly opposite view, that the number system should be base-12, see http://www.dozenal.org/ . It's actually a good way to work with numbers, and I've used the "counting on the joints/pads of your proper fingers" trick a number of times; sometimes you only have one hand free and want to count to something that's less than 48 (you can encode 2 extra bits with "hand facing up, hand facing down, hand facing up again, hand facing down again"; I've found it gets confusing after 4 or 5 of these though.)
3. I am very sympathetic to Feynman's "we don't need more units!" claim, but the reason we use various units is because we have different interests -- masses in eV/c^2 for example reflect someone who is interested in the atomic interaction energies (eV) of relativistic particles (c^2); energies in Kelvin reflect someone who is interested in how much they need to cool their experimental apparatus to see certain effects; energies in inverse centimeters reflect people who have spectrometers. Following this, I've tried to think whether the base-10 clock could be used to construct a set of "rational units" which would try to get the "human scale things" right while making all of these other units amount to a power-of-10 difference. I've not condensed these speculations to a final form yet but the speculations are themselves at: https://github.com/drostie/essay-seeds/blob/master/misc/rati... .
As someone who bakes, I loathe imperial measurements. For one, measuring by weight instead of volume is just much easier and more precise. (I'm looking at you "cups of flour.") For two, it's a lot simpler to scale recipes given in metric amounts.
It is the non-metric units for volume that really turn into a shitfest.
I grew up in America, went to public schools, learned to cook from American cookbooks, and still can't keep all of them straight.
Pints in a gallon? Quarts in a gallon? Quarts in a pint? Teaspoons in a cup? Cups in a pint? Who fucking knows? The best I can do is a pint is roughly how much beer you get at a bar (but that changes from region to region!) and milk comes in a gallon while other beverages do not.
I think the main problem isn't the quality of the system of measurement used by the US, but more that it is one of only three countries still not using the metric system.
The world would be an easier place without that headache.
IMO the reason why Americans prefer Farenheit to Celsius is that the 0 and 100 points correspond to roughly the limits of common outdoor temperatures, rather than water's state changes.
Pretty much the same argument for miles per hour vs kilometers per hour - 100 mph is all anyone's ever going to go during a normal day.
That's an interesting point about being able to divide by half more than once for feet/inches, though - I hadn't thought of that before.
In theory I'd prefer a timekeeping system that had its base unit in terms of the smallest discrete unit of time (basically planck time) and let everything else arise naturally from that. Sure, days may not be a perfectly XX kilo-mega-ultra-plank times (I'm unsure of the Metric nomenclature going from a power of -44 to a power of around +4) but I am always peeved we have designed our timekeeping, temperature, pressure, etc measurements bound to arbitrary properties of things on the surface of our planet than on the fundamental properties of the universe.
It is going to make space travel a much bigger hassle, to say the least.
On the topic of metric vs. otherwise, you may enjoy Matt Parker's "Guide to the Imperial Measurement System." [0] Matt Parker is an eminent stand-up mathematician, often featured on James May's excellent Number Hub series
12, 24, 60 are all used because they are cipherable using one's fingers.
To cipher on 12, pick a hand and assign the values 1 to 12 to each finger joint so that the tip of the index finger is one, the middle joint of the index finger is 2 ... the base joint of the little finger is twelve. Use the thumb as pointer to a number. Add and subtract by moving your thumb as you count.
Cipher on 24 by using each joint on both hands.
Cipher on 60 by using one hand to cipher on 12. The other to cipher on 5 in the traditional way but value each finger as 12. Example: Base joint of pinky on right hand and ring finger of left hand is 48.
To get the full Babylonian number system allow the exponent to float based on context. It's really just an extension of the move from ciphering on 12 to ciphering on 60.
Exercises:
1. [M05] Where are the indexes after adding 13 and 8?
2. [10] Change the system to use natural numbers.
3. [50] Is abandoning sexigisimal ciphering for decimal ciphering the oldest case of changing a computational system so as to make it easier for beginners at the expense of vastly reduced expressive power?
"Although it is unknown why 60 was chosen, it is notably convenient for expressing fractions, since 60 is the smallest number divisible by the first six counting numbers as well as by 10, 12, 15, 20 and 30."
Regarding the 12 hours division, they do suggest it is from "the number of finger joints on each hand (three in each of the four fingers, excluding the thumb)".
Interesting history lesson about the Egyptian's use of the duodecimal system.
I believe the last argument is understated: one big advantage of base 12 over base 10 is division by 3. This offers many ways of dividing a time interval into several sub-intervals of identical duration.
For base 60, this intensifies: as mentioned in the post, 60 is the smallest number divisible by 2, 3, 4, 5, and 6. This gives tremendous flexibility for dividing a time interval.
"Germanic languages have special words for 11 and 12, such as eleven and twelve in English, which are often misinterpreted as vestiges of a duodecimal system. However, they are considered to come from Proto-Germanic ainlif and twalif (respectively one left and two left), both of which were decimal."
After the french revolution there was a short period (3 years) when the French had decimal time. It didn't catch on because that meant the workers had 10-day workweeks instead of 7.
Base 12: 12 is a number that can be divided by 2, 3, 4 and 6. This makes it a much better fit than base 10, which can only be divided by 2 and 5.
Base 60: As good as base 12 is, it misses division by 5. So what do you do to make it divisible? You multiply 12 x 5 = 60.
Now you can divide an hour in 2 parts of 30 minutes each, 3 parts of 20 minutes, 4 parts of 15 minutes, 5 parts of 12, or 6 parts of 10 minutes. This also means that if for example you want to divide a job in 3 shifts, every shift will be 8 hours, not 3,3333333 hours or similar, what you would get in a base10 system.
I mean, the stars and the gods and the tip or our fingers might be also a justification, but I think those were rationalized after the fact. I find it difficult that the guys that came with base12/60 didn't realize the particular properties of those numbers.
Base 60 has many advantages, but bare in mind that this is dated almost 4000 years ago. When people developed language and started counting, they would need something to keep track and help them go from one number to the other, so the finger tip theory is actually quite accurate.
Aside from previously discussed, the pendulum length is convenient, and water drop "clocks" are fairly reasonable at one drop per second.
Also people can count one digit per second pretty easily if the point is to cook or process something for 45 seconds or whatever. That would be tough if the second were 100 times smaller than it is.
Its a numerical base with two "digits" not just one digit. So its not just 60 sec/min its 60 min/hr and if you arbitrarily decided to use 2 for both, or 1000 for both, you don't get multiple levels that result in the second being useful. If you used 2 for both aka binary then each new-second would be 900 of our seconds long, thats useless. If you used 1000 for both then a new-second would be about 3 ms which might be handy for power EEs (not the RF guys...) but seems a bit inconvenient for the ancients.
One curiosity from the chem lab from decades ago was measuring to a milligram isn't all that challenging and a candle burned about a mg of wax per second (or was it a tenth?) anyway I'm well aware the gram is pretty recent, but the point is your stereotypical apothecary type in the ancient world should have been able to build a "mg capable" balance pan scale or at least approach it, so weighing a candle before and after would be a not too awful way to measure time and the least they could measure might have been around a second.
> Interestingly, in order to keep atomic time in agreement with astronomical time, leap seconds occasionally must be added to UTC. Thus, not all minutes contain 60 seconds. A few rare minutes, occurring at a rate of about eight per decade, actually contain 61.
Interesting, although I stopped reading at the end of page 1. It seemed the article already explained most of it and while I would've scrolled down to skim the rest of the article, waiting for a page load seemed too much effort.
The most interesting part of page 2, in my opinion, was the below quote:
Each degree was divided into 60 parts, each of which was again subdivided into 60 smaller parts. The first division, partes minutae primae, or first minute, became known simply as the "minute." The second segmentation, partes minutae secundae, or "second minute," became known as the second.
And why are multiplication tables in school typically taught up to 12x12? Historically in the UK, there were 12 pence in a shilling, 240 pence in the pound, 12 inches in a foot, etc, but I'm not sure of the value nowadays.
I asked this of a curator at the British Museum several years ago. And he replied that it was the Sumerians that first adopted the 24 hours in a day convention. But he didn't know who came up with 60 minutes in an hour.
[+] [-] spodek|12 years ago|reply
I bring that up here because I've never heard even the staunchest metric proponents use kiloseconds or megaseconds or hesitate to use hours, minutes, days, and so on. I know people experimented with decimal times, especially around the French Revolution, but it didn't stick. It's funny when someone talks about the value of using base ten and then switches to base 60, base 12, and base 24 in the next sentence.
I should say that in physics experiments people used seconds only (which is where I learned that to within about a percent a year is pi times ten to the seventh).
[+] [-] edvinbesic|12 years ago|reply
If I have 1.73 miles, I have to do the math to figure out how many feet that is, 1.73*5280~=9134, which is not something that's easy for me to do in my head.
However, 1.73 km is 1730 meters, which is way easier (at least for me, but that might be my bias).
[+] [-] manish_gill|12 years ago|reply
Relevant picture I found on twitter: https://pbs.twimg.com/media/Bdp2YLFCIAAM1Dy.png
[+] [-] desireco42|12 years ago|reply
As article mentioned, we got time from Babylonians, who got it from Summerians. Time and calendar are one of the weirder things we deal with. I used internet time for a while, you know the Swatch thing. It looks weird in the beggining, but very quickly you get it and it works well and it is convenient that it is not time-zone dependant. And that was just a marketing gimmick from Swatch.
I think the whole idea that we somehow manage to create bridges and build buildings despite weird measures we use, is more testament to our ability to overcome difficult obstacles.
[+] [-] raldi|12 years ago|reply
[+] [-] kps|12 years ago|reply
[+] [-] raldi|12 years ago|reply
But under the metric system, the score would have been 14.38 to -6. Completely awkward and out of touch with the human scale.
[+] [-] drostie|12 years ago|reply
Fun things:
1. I wrote an HTML5 base-10 clock here with some togglable layers. Try out base-10 time: http://drostie.org/time/ . It's actually much easier than reading a normal clock because it's a digital readout, "8, 5, 6" rather than "two past a quarter after 8, that's 8:17." (It might not seem that way at first -- but that's because we spent long hours learning to tell time.)
2. For the exactly opposite view, that the number system should be base-12, see http://www.dozenal.org/ . It's actually a good way to work with numbers, and I've used the "counting on the joints/pads of your proper fingers" trick a number of times; sometimes you only have one hand free and want to count to something that's less than 48 (you can encode 2 extra bits with "hand facing up, hand facing down, hand facing up again, hand facing down again"; I've found it gets confusing after 4 or 5 of these though.)
3. I am very sympathetic to Feynman's "we don't need more units!" claim, but the reason we use various units is because we have different interests -- masses in eV/c^2 for example reflect someone who is interested in the atomic interaction energies (eV) of relativistic particles (c^2); energies in Kelvin reflect someone who is interested in how much they need to cool their experimental apparatus to see certain effects; energies in inverse centimeters reflect people who have spectrometers. Following this, I've tried to think whether the base-10 clock could be used to construct a set of "rational units" which would try to get the "human scale things" right while making all of these other units amount to a power-of-10 difference. I've not condensed these speculations to a final form yet but the speculations are themselves at: https://github.com/drostie/essay-seeds/blob/master/misc/rati... .
[+] [-] js2|12 years ago|reply
[+] [-] Crito|12 years ago|reply
I grew up in America, went to public schools, learned to cook from American cookbooks, and still can't keep all of them straight.
Pints in a gallon? Quarts in a gallon? Quarts in a pint? Teaspoons in a cup? Cups in a pint? Who fucking knows? The best I can do is a pint is roughly how much beer you get at a bar (but that changes from region to region!) and milk comes in a gallon while other beverages do not.
[+] [-] aerique|12 years ago|reply
The world would be an easier place without that headache.
[+] [-] drewblay|12 years ago|reply
I agree, I like how Fahrenheit degrees are smaller and therefore degrees in Fahrenheit are more exact.
[+] [-] ArbitraryLimits|12 years ago|reply
Pretty much the same argument for miles per hour vs kilometers per hour - 100 mph is all anyone's ever going to go during a normal day.
That's an interesting point about being able to divide by half more than once for feet/inches, though - I hadn't thought of that before.
(From another American with a physics background)
[+] [-] zanny|12 years ago|reply
It is going to make space travel a much bigger hassle, to say the least.
[+] [-] jhanschoo|12 years ago|reply
Using SI, 1 J = 1 N * 1 m = 1 W * 1 s.
You can't do the same with calories, miles, horsepower, and other Imperial units.
[+] [-] elspecial|12 years ago|reply
If you find it easier to work with base 12 than base 10, you are not like most of the people.
"And I've found no benefit to Celsius's 0 and 100 coinciding with water's state changing."
So the fact that pure water freezes at 0 and boils at 100 is of no benefit to you?
I don't buy it.
[+] [-] wikwocket|12 years ago|reply
0: http://www.youtube.com/watch?v=r7x-RGfd0Yk
[+] [-] Someone|12 years ago|reply
The way to remember that is "pi seconds in a nanocentury"
[+] [-] brudgers|12 years ago|reply
To cipher on 12, pick a hand and assign the values 1 to 12 to each finger joint so that the tip of the index finger is one, the middle joint of the index finger is 2 ... the base joint of the little finger is twelve. Use the thumb as pointer to a number. Add and subtract by moving your thumb as you count.
Cipher on 24 by using each joint on both hands.
Cipher on 60 by using one hand to cipher on 12. The other to cipher on 5 in the traditional way but value each finger as 12. Example: Base joint of pinky on right hand and ring finger of left hand is 48.
To get the full Babylonian number system allow the exponent to float based on context. It's really just an extension of the move from ciphering on 12 to ciphering on 60.
Exercises:
1. [M05] Where are the indexes after adding 13 and 8?
2. [10] Change the system to use natural numbers.
3. [50] Is abandoning sexigisimal ciphering for decimal ciphering the oldest case of changing a computational system so as to make it easier for beginners at the expense of vastly reduced expressive power?
http://en.m.wikipedia.org/wiki/Babylonian_number_system
[+] [-] treenyc|12 years ago|reply
"Although it is unknown why 60 was chosen, it is notably convenient for expressing fractions, since 60 is the smallest number divisible by the first six counting numbers as well as by 10, 12, 15, 20 and 30."
[+] [-] svantana|12 years ago|reply
[+] [-] sushirain|12 years ago|reply
[+] [-] nmc|12 years ago|reply
I believe the last argument is understated: one big advantage of base 12 over base 10 is division by 3. This offers many ways of dividing a time interval into several sub-intervals of identical duration.
For base 60, this intensifies: as mentioned in the post, 60 is the smallest number divisible by 2, 3, 4, 5, and 6. This gives tremendous flexibility for dividing a time interval.
[+] [-] justwrote|12 years ago|reply
[+] [-] lunchbox|12 years ago|reply
http://en.wikipedia.org/wiki/Duodecimal#Origin
[+] [-] nmc|12 years ago|reply
[+] [-] dirktheman|12 years ago|reply
[+] [-] dirktheman|12 years ago|reply
http://en.wikipedia.org/wiki/French_Republican_Calendar
As a result, decimal clocks from that era are very rare and highly sought after!
[+] [-] eloisant|12 years ago|reply
[+] [-] abgv|12 years ago|reply
Base 12: 12 is a number that can be divided by 2, 3, 4 and 6. This makes it a much better fit than base 10, which can only be divided by 2 and 5.
Base 60: As good as base 12 is, it misses division by 5. So what do you do to make it divisible? You multiply 12 x 5 = 60.
Now you can divide an hour in 2 parts of 30 minutes each, 3 parts of 20 minutes, 4 parts of 15 minutes, 5 parts of 12, or 6 parts of 10 minutes. This also means that if for example you want to divide a job in 3 shifts, every shift will be 8 hours, not 3,3333333 hours or similar, what you would get in a base10 system.
I mean, the stars and the gods and the tip or our fingers might be also a justification, but I think those were rationalized after the fact. I find it difficult that the guys that came with base12/60 didn't realize the particular properties of those numbers.
[+] [-] fjcaetano|12 years ago|reply
[+] [-] VLM|12 years ago|reply
Also people can count one digit per second pretty easily if the point is to cook or process something for 45 seconds or whatever. That would be tough if the second were 100 times smaller than it is.
Its a numerical base with two "digits" not just one digit. So its not just 60 sec/min its 60 min/hr and if you arbitrarily decided to use 2 for both, or 1000 for both, you don't get multiple levels that result in the second being useful. If you used 2 for both aka binary then each new-second would be 900 of our seconds long, thats useless. If you used 1000 for both then a new-second would be about 3 ms which might be handy for power EEs (not the RF guys...) but seems a bit inconvenient for the ancients.
One curiosity from the chem lab from decades ago was measuring to a milligram isn't all that challenging and a candle burned about a mg of wax per second (or was it a tenth?) anyway I'm well aware the gram is pretty recent, but the point is your stereotypical apothecary type in the ancient world should have been able to build a "mg capable" balance pan scale or at least approach it, so weighing a candle before and after would be a not too awful way to measure time and the least they could measure might have been around a second.
[+] [-] mVChr|12 years ago|reply
And thus, the programmer's nightmare begins...
[+] [-] dsego|12 years ago|reply
[+] [-] sdfjkl|12 years ago|reply
[+] [-] mdisraeli|12 years ago|reply
Each degree was divided into 60 parts, each of which was again subdivided into 60 smaller parts. The first division, partes minutae primae, or first minute, became known simply as the "minute." The second segmentation, partes minutae secundae, or "second minute," became known as the second.
[+] [-] petercooper|12 years ago|reply
[+] [-] icebraining|12 years ago|reply
[+] [-] headbiznatch|12 years ago|reply
1) The Measure of All Things - http://www.kenalder.com/measure/ (science history goodness)
2) Frink - http://futureboy.us/frinkdocs/ (one of my first discoveries on HN and still one of the most fun to return to)
[+] [-] yardie|12 years ago|reply
http://www.amazon.co.uk/gp/product/0747597162/ref=oh_details...
The book author declares the Babylonians had a base 60 system. some native cultures have none at all. (well 1 and many)
[+] [-] jakub_g|12 years ago|reply
http://www.amazon.com/Universal-History-Numbers-Georges-Ifra...
[+] [-] auvrw|12 years ago|reply
[+] [-] chiph|12 years ago|reply
[+] [-] carsonreinke|12 years ago|reply
[+] [-] jokoon|12 years ago|reply
you can divide it by 10, 5, 4, 3, 2, etc.
[+] [-] netcan|12 years ago|reply
[+] [-] squirejons|12 years ago|reply
[+] [-] nmc|12 years ago|reply
[1] http://en.wikipedia.org/wiki/Rayleigh_scattering
[+] [-] unknown|12 years ago|reply
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