Why is a minute divided into 60 seconds, an hour into 60 minutes?
scientificamerican.com
scientificamerican.com
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).
Relevant picture I found on twitter: https://pbs.twimg.com/media/Bdp2YLFCIAAM1Dy.png
The world would be an easier place without that headache.
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).
Also, I haven't read GP's post, but I find Fahrenheit degrees easier to work with primarily because they're smaller; differences in temperature are easier to express in whole numbers.
Gallons, cups, tablespoons, quarts can go DIAF; I have to convert between these all the time, and it drives me batty!
Also all physics and engineering formula are designed to get and return metric values. When I see K = 0.5mv^2, I know v is supposed to be m/s and m is in kilograms and the result would be in Joules. If it's E = m*c^2, the same thing could be inferred about it.
I'm curios with all different units of measurement, how do you know when to use which. Is there a convention to always e.g. use ft/s or is it different in each formula?
E.g. in italy you refer to a glass of 200ml, 100 grams of pasta and two hectograms of parmigiano, while in hungary they routinely use deciliters and decagrams, which I'd never seen outside of school.
On the other hand I don't understand for examples why in the US they still use measures like "cup", "oz" "pint" in cooking. Should I buy a specifically sized "cup" to cook a us recipe? :)
By watching UK television it seems that even they are using kilograms, liters and also Celsius for oven temperature, and some weeks ago there was a UK famous baker talking with some US guest and saying almost the same thing.
disclaimer: I'm Italian
Thank goodness no one seems to use Pecks / Bushels / Dry Gallons (the dry volume versions of Pints / Quarts / Wet Gallons). The only time I ever hear of "Pecks" is in the Tongue Twister.
Not to mention, having everything in metric and by weight allows you to easily figure out ratios of ingredients, making scaling recipes much easier and quicker.
On "the line" where food is cooked, measurements are mainly by hand and by eye.
Yes, during service you're not busting out scales, and a lot of things aren't precisely measured. But anything where precision is necessary, you weigh it. Where it isn't, you don't.
Good luck ever finding a cup measure, or a measuring teaspoon in a professional kitchen though...
In which case, it matters little if you use metric or not...
Well, you still will measure things, most cooks will do a stint in the pastry kitchen, plus in the higher end restaurants a lot of pastry techniques transfer over to the savoury side (ie. a lot of what we think of as "molecular gastronomy").
While metric vs imperial doesn't matter for accuracy (whereas weight is more accurate than volume if you're measuring anything that's not liquid, and even with liquids it's easier to measure volume incorrectly), metric is just easier.
Historically: 1 Minute of Great Arc = 1 Nautical Mile
Great Arc = Earth circumference
1 Minute of Great Arc = Great Arc / (360 * 60)
Fun Fact:
Earth Circumference = 4 times great circle distance Pole to Equator historically defined as 10000km or 10 Million Meters (They were that serious about being decimal)
That also explains why the earth radius can still approximately be expressed as 10000km/(π/2) = 6366.2km (just 4.8km off the current mean radius defintion of 6371 km)
How often do you need to do this in reality? Most people in their day-to-day have no need to these conversions.
of course perception of a metric also plays a tremendous role here. I don't have a 'feel' for how long it is 12-feet for example but I can eye-ball a distance and tell how many meters it is pretty accurately. I guess this perception is the main issue that prevents imperial system to be abandoned in favor of SI - people are too much used to it.
I also hate the left driving lane of UK btw. It screws up with my head every time I rent a car in London...
stupid metric-ism ;)
This doesn't mean metric is more accurate over imperial, it just means that on a day-to-day, conversion is easier. Also, you can work out the relationship of units simply by their name.
deci = tenth, so decimeters means there is ten of them in one meter. deciliters means ten in one liter. so on and so forth. centi = hundred... milli = thousand...
etc.
[1] Except for years BCE which the scheme doesn't treat.
Additionally, the point of doing it the other way round is that the most important thing is on the left, where we start reading, followed by less important things. If I need to know the time of day, the hour is the most important thing, once I know whether it's 4 or 6, I can look at the minutes and first then do I perhaps (and does one really ever?) care about the seconds. As a matter of fact, my old wristwatch only had hour and minute hands... The opposite is true for the date. It starts, again, with the most significant thing on the left: the day. This assumes that people will probably have it easier to remember the month or year they live in.
And a final example: I have an appointment on the 24/01/2014 at 10:15:00. The most important questions are: What day do we have? And if it happens to be the 24th, what hour of the day is it? Is it 5? Good, 5h left. Is it 10? Oh boy, better look at the minutes...
I think you mean 321 456. It's not monotonically anything.
> most important thing is on the left
See, I feel that the month is the most important part of the date. "My birthday’s in June" or "My birthday is on the eight of some month"? "The harvest is in October" or "The harvest is on the 30th of something?"
The hour. Is this supposed to be a trick question? 90% of the time, if I give the hour to quarter-hour resolution then I've done a good enough job of saying what time it is. I don't even think about minutes.
It is going to make space travel a much bigger hassle, to say the least.
I agree, I like how Fahrenheit degrees are smaller and therefore degrees in Fahrenheit are more exact.
That said, and as an European, if had to stop using one unit of measure it would certain be the Celsius scale.
In general, if I ask someone what the temperature is, it will be estimated as "low 70s" or "high 50s". Never have I met anyone who would feel the temperature and then declare that it is 72 degrees, as opposed to 71 or 73. This suggests that the granularity is greater than what people feel, and is unnecessary for day-to-day use.
> Nobody lives their life around freezing and boiling temperatures. I live my life around 50 to 90 degrees and if you live yours around 10 to 40, I don’t see the advantage.
The natural response is of course we live close to freezing! 0 °C is the temperature that differentiates frozen lakes from open lakes, snow from rain, slippery dangerous roads from regular.
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... .
Yes, some units are useful for particular interests. Create them as they're needed and useful. Base-10 time would make more sense. Celsius at least coordinates notable values with common materials.
Some units are just stupid. The lead article gives an unsatisfactory explanation of base-12/60 time (admitting near the end the reason for base-60 is unknown); trying to explain clocks to toddlers is proving annoying (I can't explain it if it doesn't make sense, and it doesn't make sense). Fahrenheit is just an arbitrary marking on a scale and seeing how reality happened to line up.
It turns out that Fahrenheit's reference thermometer was a bit... off... however.
I imagine it had something to do with the medium used for the thermometer?
http://antoine.frostburg.edu/chem/senese/101/solutions/faq/z...
That wasn't so reliable, and neither was using 100 for human body temperature, so when he discovered that water boiled at 212 he began calibrating with that.
A furlong is the distance a horse can plow in one day. This also gives a relationship between horsepower and furlongs. A chain is the distance you keep crops apart, and one chain by one furlong is an acre.
If you had 20 acres of land, you knew a horse could plow the land in 20 days.
The aging English system of Feet, Yards, Furlongs, Miles, Rods, Chains, Acres, Horsepower... they don't mean anything to non-farmers. So, we can replace these with a different system: the Metric system.
However, everyone uses the Point / Pica (1/72th an inch, and 1/6th an inch respectively) system for font measurement. As we are computer literate people today, font-size measured in "points" is quite important.
12-Point font (aka, font one pica in size) is a standard font size. No one cares that 12-points is really 4.233 mm. Hell, saying 4.233mm font means nothing to me.
But the day, night, moon, and sun cycles (approximated by day, month and year) is obvious to everyone. As such, an arbitrary 10-base system like Metric Time ignores the "reality" for most people... that the day, moon, and sun are related.
They would certainly never dream of using it for anything other than choosing how large they wanted their font, or possibly line.
The question then is, should we synchronize on the year, or on the day? The advantage of using the year is that it's a more stable unit of time; the length of a day is actually incredibly noisy and days are slowly getting longer every century as the Sun's and Moon's tidal forces deform the Earth, turning rotational energy into heat.
Unfortunately, there are a bunch of disadvantages. There are a lot of calendars in effect today, and they don't always settle on the same definition of "year" -- for that matter, there are a lot of astronomical definitions of "year" -- since the Earth's axis doesn't point at the same stars eternally, do you mean orbiting the Sun once relative to the distant stars (ignoring the axis) or do you mean coming back to the same tilt relative to the Sun so we can start the seasons over again (including the axis)? Or do you just mean a full cycle of phases of the moon, as lunar calendars do it?
The best way that I can see is to settle approximately on a day with an atomic clock; and push the question of actually trying to keep dawn at the same time each day (correcting for the slowdown of the Earth) to the time zones, which already sometimes try that in the sense of Daylight Saving Time.
But then they would actually show up in 7-8 ki, meaning 10-12 minutes!
On the other hand, maybe this is just the cure for high-intensity fast-paced society that we need. ;)
But under the metric system, the score would have been 14.38 to -6. Completely awkward and out of touch with the human scale.
> when I build things it's useful to divide in half a few times
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.
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)
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.
The way to remember that is "pi seconds in a nanocentury"
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.
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.
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."
[1] http://en.wikipedia.org/wiki/Betteridge%27s_law_of_headlines
Personally, I wasn't upset at all. I really liked the article although it had a deceiving title.
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.
One interesting thing I heard once - a journalist was discussing the merits of counting in base 12 with someone whose society already adopted this method. When the journalist asked how we would teach kids to count with their fingers, the answer was simple - use the divisions created by your knuckles!
It would mess with everyone but I think there's a pretty strong argument for base 12.
edit: okay, i finished reading and it kind of says that already. But it's still cool!
I'm pretty sure my flatmate told me the story and he watches numberphile too so you're almost certainly right either way :P
Sorry to nitpick, but "exacerbate" is to make worse. It's like "ex-acerbate". It doesn't mean "even more so" in a good way. Just thought you'd like to know.
The verb "to exacerbate" comes from French verb "exacerber", which means "to make more intense or more acute".
My post has been edited to reflect your comment.
It's interesting to me that both duodecimal and decimal counting are recommended as being easy to calculate with.
The benefits of decimal come from our using base-10 for other purposes. I guess the best of all possible worlds would be to use duodecimal for all units (including our normal number system).
Then we'd get the ease of use of modern base-10 units plus the better factorisation of duodecimal.
(But we'd still have an impedance mismatch with the binary powers. The KB/KiB split wouldn't go away).
As an aside, I wonder how technology affects the units or systems we use. They had to rely on decimal or duodecimal systems for their units because they were doing all of their calculations manually (so did we until about 20 or so years ago btw,) but now that everyone* carries a computer on his/her pocket, what better systems could we design?
I guess binary might be an example of that. 2 values is not something that applies to everything, at least not naturally in the way the human mind works, but it is much more efficient for machines to process information, that makes sense.
How is base 10 more elegant than base 12?
1/64th might result from a binary, octal or hexadecimal system; duodecimal tens to favour things like 1/3, 1/4, 1/6, 1/9, 1/12 and so on. The elegant thing is that in duodecimal all of those are non-repeating fractions: .4, .3, .2, .14, .01 respectively. Interestingly, in duodecimal 1/5 and 1/10 are non-repeating (this is also true in binary...).
Base 12 is far more elegant than base 10, but the conversions cost make the conversion to French units look cheap--and then we'd need to convert all our units to some sort of French units mark II.
For day-to-day use, it makes sense to use a system where you can express your age (in years) in one or two digits rather than five to seven. Hence, a hexadecimal system might be preferable as a representation.
1/3 vs 0.3' ? Much elegance!
1/3+1/3+1/3==1 vs 0.3'+0.3'+0.3'==0.9'==1 or something.
ten, eleven, twelve | thirteen, fourteen, fifteen, sixteen
zehn, elf, zwölf | dreizehn, vierzehn, fünfzehn, sechzehn dix, onze, douze, treize, quatorze, quinze, seize | dix-sept, dix-huit, dix-neuf diez, once, doce, trece, catorce, quince | dieciséis, diecisiete, dieciocho, diecinueveвосемь (8), девять (9), десять (10) | одиннадцать, двенадцать, тринадцать, четырнадцать, пятнадцать, шестнадцать, семнадцать, восемнадцать, девятнадцать.
As for dix-huit and dix-neuf, the Romans counted down from twenty; duodeviginti (two-down-from-twenty) is eighteen and undeviginti (one-down-from-twenty).
So it probably made more sense to the early French to say dis-huit and dix-neuf instead.
But one interesting thing about French numbers that you have missed is that it possess a vestigial remnant of the vigesimal (base-20) number system of the Celtics, where 80 is quatre-vignts (four-twentys) to the French, and 90 is quatre-vignts-dix.
70 is sixty-ten (soixante-dix), then 71 is sixty-eleven... and so on, up to 99: four-twenty-nineteen. Indeed, 80 is 4 times 20, hence "four-twenty" (quatre-vingt, without the "s" at the end).
Interestingly enough, French-speaking Belgians use the regular forms: 70 is "septante", 80 is "octante", and 90 is "nonante".
http://en.wikipedia.org/wiki/French_Republican_Calendar
As a result, decimal clocks from that era are very rare and highly sought after!
And later, with the calendar came a simpler version with 100 minutes in an hour, 100 seconds in a minute, and so on (Article XI of the "Décret de la Convention Nationale concernant l'Ere des Français" [1]). It was only official (and mandatory) for a few months, however [2].
Edit: the one with 1M seconds a day was only an earlier draft version that never made it into law.
[1]: http://www.gefrance.com/calrep/decrets.htm (in french)
Also, the weird thing was that, although they decided that an hour is divided in ten "parts", and each one of those in ten, and so one... they gave the name "minute" to the part of the part of the hour (so that 1 hour == 100 minutes), and the same for the second vs the minute.
I wonder how people managed to get a hang of this mess...
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.
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.
And thus, the programmer's nightmare begins...
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.
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)
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)
http://www.amazon.com/Universal-History-Numbers-Georges-Ifra...
More on topic, the book makes a good point how base 60 came to be. It appeared when two natural bases merged: base 12 and base 10. Base 12 is natural, because you can conveniently count to 12 using fingers of one hand. To do that, you use the thumb. Notice that each of your remaining fingers consists of 3 segments. 4 fingers left * 3 segments = 12.
Base 60 allows cultures using bases 12 and 10 to coexist. It's the least common multiple. Naturally, it ALSO made it easier to avoid fractions.
you can divide it by 10, 5, 4, 3, 2, etc.
[1] http://physicsfaq.co.uk/General/BlueSky/blue_sky.html Section: Why not violet?
This makes no sense. For this to be true, it implies that the ancient Greek already had knowledge that the Earth is round, 1600 years before Galileo.
https://en.wikipedia.org/wiki/Eratosthenes#Measurement_of_th...
What makes no sense is the perpetuation of the myth that spherical earth is "new" concept.
The concept of a spherical Earth dates back to ancient Greek philosophy from around the 6th century BC -- http://en.wikipedia.org/wiki/Spherical_Earth
http://scienceblogs.com/startswithabang/2011/09/21/who-disco...
Secondly, the idea that people believed in a flat earth before Columbus is entirely a 19th Century conceit: https://en.wikipedia.org/wiki/Christopher_Columbus#Geographi...
In fact, the fact that the earth is (essentially) spherical was well-known to basically everybody since ancient times. For example, any sailor could have told you that when approaching land, the tops of mountains appear first over the horizon.
Well, "encountered" would probably be more accurate. Discovery -- even rediscovery -- requires recognition, and Columbus insisted he had reached the East Indies.