[timey (OP)]

What exactly is so 'great' about the metric system?

In that the number 10 can only be divided by 1, 2, 5, and 10...

And the number 12 can be divided by 1, 2, 3, 4, 6, and 12...

... Indeed what are the benefits of a metric system?

Considering that the phenomenon of time is measured in divisions and multiples of 12's, where clearly there is 'also' a reference to divisions of 10 - presumably for those who can only count on their fingers - and also considering that distances that were once matched to time, (via speed), in feet and yards that use the same divisions or multiples of 12 that time does - when converting to the metric, why was the metric conversion not extended to clocks?

Surely this non compatibility between divisions of 12 regarding time, and the metric divisions of distances into blocks of 10, is unnecessarily complicating the measure of distance, relative to time...
Where it would be clear to work out, just based on ones ability to make use of times tables:

4 yards (4yards*3ft =12ft) distance, covered at a speed of 1 minute per yard (60sec/3ft=20sec per ft) is equal to 0.6 inch per second.
(12ft*12inch=144inch) and (12ft*20 sec=240secs) can be worked out as(2*12*10=240)
so (144inch/240sec=0.6inch per second)
...and it's only that I'm not so good at maths that I had to use a calculator for 144/240.
...But more to the point, 0.6 of an inch is an easy number to go on to use for whatever reason one calculated it for...
(Clearly I could have just calculated as:
36inches/60second=0.6 inches per second
...but I wanted to show use of times tables)

When converting 4 metres at a speed of 1 metre per minute:
4*60*100=240/400=1.6666667
or:
100cm/60=1.6666667cm per second

Comprehensive?
Well yes, of course, ... but we are left with this idiotic number to work with!

... Also of significant consideration, when building to architectural design, clearly it would be of paramount usefulness to employ a system who's base number is 'able' to be easily and comprehensively divided by 6 numbers, rather than a system who's base number can only be divided by 4?

[evan_au]

why was the metric conversion not extended to clocks?

It was. I have seen a dual-standard clock from after the French Revolution showing both decimal (10 hours) and duodecimal (12 hour) time.
See: https://en.wikipedia.org/wiki/Decimal_time#France

It was also extended to the calendar, but with less success, since no whole number divides exactly into 365.25 days.
See: https://en.wikipedia.org/wiki/French_Republican_Calendar

And the number 12 can be divided by 1, 2, 3, 4, 6, and 12..

If you struggle to do division manually (as I think all generations have), then you could do worse than follow the Babylonians, who used Base 60.
60 has lots of divisors (more divisors than 12 does), and is the historical reason we have 60 seconds in a minute, and 60 minutes in an hour.

But today we have computers that can divide, multiply and do more complex operations far more accurately and far faster than humans can, so the number of divisors of the number base becomes irrelevant (computers use Base 2, which has only one divisor: 2).

... Indeed what are the benefits of a metric system?

If you can represent a quantity as a a single number in scientific notation, then you can manipulate it in a formula very easily.
However, if you represent it as a number of different bases, eg a certain length = x miles, y yards, z feet and a inches, then it gets very complicated to use it in a formula, since you need to:

• Carry the inches after 12 (base 12)
• Carry the feet after 3 (Base 3)
• Carry the yards after 1760 (Base 1760)

The computer programs to add, subtract, multiply and divide these quantities get mind-bogglingly complex! Trying to do it on a decimal or duodecimal calculator would be impossible.
So in practice, the computer converts these mixed units into binary, does all the arithmetic in binary and then converts them back into mixed units (if needed).

The beauty of the metric system (or the SI version used by scientists) is that you can represent a length in meters, no matter how large (eg 1.23456x10⁵⁴m) or small (eg  9.87654x10^-20m) it is. Doing calculations on a scientific calculator is quite straightforward.
 
The USA has achieved partial metrification by:

• Replacing the English currency of Pounds, shillings and pence by dollars
• replacing the English system of measuring weights in tons, stone and pounds
• by just measuring weights in pounds (even quite large weights, like jet aeroplanes); this avoids the problem that US & UK tons are different units.
• but the US still suffers from using mixed liquid measures of pints and gallons (not helped by the fact that US & UK gallons are different units).

At least with SI units, an international committee creates an unambiguous definition. In the last century, they have also attempted to ensure that this can be measured anywhere in the universe, without having to refer to physical objects stored in a safe in Paris.

To see how complex a mixed-base system of lengths can get, have a look at:
See: https://en.wikipedia.org/wiki/English_units#/media/File:English_length_units_graph.png

[Bored chemist]

What has 12 got to do with it?
OK, 12 inches in a foot but 3 feet in a yard (3 is prime)
22 yards in a chain,
So the chain (also 100 links or 4 poles) is 66 feet- or 11 fathoms if you prefer
And there are 10 chains to the furlong and 8 furlongs  a mile.

So the mile (5280 feet or 63360 inches) is evenly divisible by 2,3,4,5,6,8,9, 10,11,12,
Cut to the  chase- it doesn't divide by 13 or higher primes.
So what?
Who wants to remember all those factors- the 11, for example, is half the number of yards in a chain.

Similarly there are 16 ounces  (each composed of 16 drachms) in a pound then we have 14 pounds in a stone, (which is handy- as often as you need to divide by 7) and 2 stone in a quarter.
4 quarters make a hundredweight (which isn't a hundred of anything- it's 112 Lbs if you have been keeping track) and then there are 20 hundredweight in a ton (that's 2240 Lbs)
Don't get me started on units of volume.
As long as you enjoy memorising all these damned silly units and the conversion factors you can do the divisions more easily.
Or, you can pretend it's the 20th centruy and use a calculator

[timey (OP)]

Great information Evan!

I particularly enjoyed a book called "All Done with Mirrors) by John Neil.  Which, despite its lengthy allusions to pyramids, has bog all to do with any new age mumbo jumbo, and everything to do with metrology.

Having made measurement world wide, he concludes with a basis for a connection between such measurements, but the exact reason for there being a connection escapes him, other than from a view of common sense.
Common sense in that a master architect of any era would find more use in a measuring system that can be easily divided into 'reasonable' numbers, that blocks of stone may be  fashioned and installed by work forces under a supervisor who only requires a basic understanding of times tables.
(I haven't read his latest book, but fully intend to)

It is interesting to me though that you mention the Babylonian's in relation to time.
The Babylonian calendar is a lunisolar calendar, where each month begins with the crescent moon.

Here is a great explanation of the physics behind the derivation of why our units of time are split into the divisions that they are:

https://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/

Given that sun dials, and moon dials, were used to derive these divisions of the time period of days and night, clearly there is an intrinsic link between 'distance', ie: the amount the shadow moves in a certain time, in relation to how far away the light source is...
...and 'time', ie: how much time passes within a certain distance that the dial shadow moves by.

Basically, our derivation of these divisions of duodecimal time 'are' distance related - which is why a clock that runs decimal time cannot divide exactly into 365.25 days.
And remembering that 365.25 days is also a radius distance of orbit around the sun...
Similarly, decimal distance cannot be divided by duodecimal time into whole numbers either.

So really, the fact that duodecimal distance can be compatibly equated with duodecimal time is indeed some very very damn clever stuff!

[timey (OP)]

For a more precise Babylonian reference to time:

http://www-history.mcs.st-and.ac.uk/HistTopics/Babylonian_mathematics.html

Quote:
"The Babylonians divided the day into 24 hours, each hour into 60 minutes, each minute into 60 seconds. This form of counting has survived for 4000 years. To write 5h 25' 30", i.e. 5 hours, 25 minutes, 30 seconds, is just to write the sexagesimal fraction, 5  25/60  30/3600. We adopt the notation 5; 25, 30 for this sexagesimal number, for more details regarding this notation see our article on Babylonian numerals."

[syhprum]

When I was at technical school in the forties we used the decimal system (cgs) in those days ! and was promised that by 1948 all the English measures would be fully converted.
Vain hope mothers still burble about the weight of their babies in pounds and ounces and fret about their own weight in stones, the only measures we  have adopted  are litres for petrol and Kgs for most groceries although we get kilo packs with only 908 grams in them and milk and beer still come in pints.
I expect if this Brexit nonsense goes thru we will go back to pounds ,shillings and pence

[timey (OP)]

... Pound and shillings?  Cor blimey mate!  It'll just be the pence for us peasants...

[evan_au]

these divisions of duodecimal time 'are' distance related - which is why a clock that runs decimal time cannot divide exactly into 365.25 days.

I think that this might be confusing two quite different things:

• We use hours to divide a day into an integer number of units
• We could divide the day into 24 hours of equal duration (ie 12 for the daytime, and 12 for the nighttime)
• We could (just as easily) divide the day into 20 hours of equal duration (ie 10 for the daytime, and 10 for the nighttime)
• We do not use hours to divide a year into an integer number of units
• We do (by various tricks and approximations) attempt to divide the year into an integer number of days, which is why we have the exception of leap years every 4 years (and the exceptions to the exceptions 3 times in 400 years...

And remembering that 365.25 days is also a radius distance of orbit around the sun.

365.25 days is a duration of time, which is measured in seconds in the SI system.

• 365.25 days is not a measure of radius or circumference; both radius and circumference are lengths, which are measured in meters in the SI system.

365.25 days is the duration of Earth's orbit around the Sun, which is determined by a number of factors, including:

• The current mass of the Sun (which changes slowly over time due to Solar Wind, infalling comets, etc)
• The semi-major axis of Earth's orbit (which changes slowly over time due to the influence of other planets, especially Jupiter)
• The rotational speed of the Earth (which changes slowly over time, due to the effect of the Moon and the tides)
• The mass of the Earth, which is so small that we can effectively ignore it
• The Gravitational constant G, which we assume is constant
• Different planets (and different Solar Systems) have different years and different days.

So there is nothing fundamental about a year being 365.2422 days (approximately) - it just happens to be the current value on Earth; it was slightly different 1,000 years ago, and it will be slightly different again in 1,000 years.

[timey (OP)]

365.25 days/speed of motion = distance of radial orbit.
(edit: (lol)... I gaffed that one up didn't I? !!! Let me try again...
...Speed of motion*365.25 days(time)= radial orbit distance.)

Presumably the Babylonian's divided their seconds, minutes and hours into divisions of a 24 hour day because this was the most precise division of the motions 'of distance' observed of the shadow of the sundial.
Remembering that distance/speed = time

Now recall that current physic states distance as variable in the face of the rate (which is a speed) of frequency, of wavelength of light, and time itself as variable in the face of distance from mass.

So - given that mass and distance changes are occurring over long periods of time, and that were we to take measurement of the Sun's motions in relation to the Earth today, our findings would be 'evolved' from say when the Babylonian's, or the Sumerians before them, measured.

Current physics would make statement that within the SI units used today, we now have the most precise rendition of time keeping ever recorded...

However, this view takes the position that time is not a reactive phenomenon mechanically inherent to the universe, but rather a measurement imposed upon it...
While both GR and SR strongly hint at the status of the phenomenon of time being otherwise!

[zx16]

Particles are the last refuge of a scientist.

[Bored chemist]

Particles are the last refuge of a scientist.

Perhaps you could expand on how that relates to the topic.
Or, perhaps you can't.

[jeffreyH]

Nonsense is the last refuge of the ignorant.

[alancalverd]

365.25 days/speed of motion = distance of radial orbit.

Except that planetary orbits are not circular.

Mixed units are a blessing. There's a lot of noise and mental arithmetic involved in flying an aeroplane, so it's very helpful to keep the numbers separated by units when talking on the radio. Feet means height, knots is speed, air distance is nautical miles, runway length in meters, and temperatures in celsius - at least in the UK. Flight rules are international and written in mixed units (visibility and horizontal separation are in meters)  even though Americans tend to use statute miles and Fahrenheit. Bloody SI committees insist that pressure is now reported in hectopascals, which nobody else uses but are conveniently exactly the same as the millibars on our old altimeters - except the US military still reports in inches of mercury, which is annoying as we also use inches for manifold boost pressure, and the numbers are very similar! 

As far as physics is concerned, the only measure of time is the second and the only measure of distance is the meter. Easy. Problems arise because the standard of mass is the kilogram, which is convenient for engineering but a pain when dealing , for instance, with pharmaceuticals, particularly as the SI committees insist that  we must use Latin and Greek prefixes, not scientific notation.  So a gram is, formally, 1 mKg. Which, though ridiculous, would not be dangerous if it were not for the fact that handwritten prescriptions make it difficult to distinguish between m, M and "mu" (please can we have the Greek character set back soon?).  And if you are involved in radiation protection, you should be able to convert picocuries (pC) in to Petabequerels (PBq) with some idea of just how large each quantity is.

[timey (OP)]

365.25 days/speed of motion = distance of radial orbit.

Except that planetary orbits are not circular.

And that sum is wrong!
(as I pointed out in the post)

So:

Speed of motion*365.25 days(time) = distance of orbital (elliptic)

But it is of interest that you mention that for physics the only measure of time is a second, and the only measure of distance is a metre...
This being because in this universe, according to GR and SR, neither are constant phenomenon, and the only constant of the universe, this being the speed of light, is held relative to these variables as 299 792 458 metres per second!

[chiralSPO]

distinguish between m, M and "mu" (please can we have the Greek character set back soon?).

yes, please do bring the extended alphabet back! But in the meantime: µ µ µ
You can use hotkeys to access many of the most useful greek letters (like π, ∆, Ω, µ etc.). On a mac, option+m is µ.