First unit of time: the day. Division: day and night.
(For the astronomer with lots of time: place a stone on top of a wall where the sun comes up. Repeat for 230 days. The sun will then, (sort of), go back down the stones, then back up, then back down)
Second unit of time: the year. Division: into four. (the central stone in the row of stones divides them into two and the sun passes up and down the row, so four divisions)
Add the moon.
Start watching when the moon is just visible after the sun has gone down. (Crescent moon.) Note that each day the moon arrives later. It is lagging behind the sun. It lags more and more until the moon is only just getting up when the sun is going down. Then the moon is only visible at night, then it is only visible late at night, then it is lit by the almost-rising sun, then it is hidden by the sun and then you don't see it for a bit, and then it reappears, in the evening, just after the sun has gone down (crescent moon.)
Third unit of time: one mo(o)nth.
Now become a keen mathematician. Realise that you can divide the sky up into "moon chunks". The moon moves a certain distance away from the sun each day and finally comes back to where it was: a circle. Divide the circle into moon chunks. How long does it take the moon to go all the way round and back to where it started? 29.5 days, more or less. let's say 30 and you can divide your cicle into thirty chunks.
Plant some sticks in the ground in a circle. Each stick stands straight up but is in the direction of one of those moon chunks.
Now: you have four fingers on each hand. Splay out your fingers and measure off roughly equal measurements between each stick.
Next time the sun comes up it creates shadows on the sticks. As the shadows interact, work out a pattern.
Fourth unit of time: I have no idea whatsoever what I have just created!
Here's how ancient civilisations have divided up the day:
http://en.wikipedia.org/wiki/Hour
Circles can be divided into two, then four, then eight, then sixteen, then thirty two, then sixty four, then one hundred and twenty eight, then two hundred and fifty four, then five hundred and eight...
You could use those numbers to measure time.
Now...which values of time would you like to use ;)
We have sixty seconds and sixty minutes (minute as in tiny as in the smallest discernable measurement on a sundial--well, that's what the article says), twenty four hours...
Now...you have some timeframes. Day night. Month. They'll do for now. We don't have to work, we live in a land of plenty and make love when we can.
So...we are bored with making love one evening. We sit outside and stare at...the stars. We watch the moon going past them. ????? The moon is moving relative to the stars. We become mathematicians again, divide up the sky. Well, there are all those stars...why not make up some patterns and then, given that we know the sun comes up and goes down and the moon goes slower than the sun and given that we know we're drawing a circle...we could use our sticks! We could build large screens at the stick points and watch the stars we can see from our now-blinkered site. Note some of the brighter ones, draw some imaginary shapes to remind us of them...
...and then we'd notice that each month there's a difference...
...between the type of moon and the stars behind it. The moon is moving relative to the stars over its monthly course! It gets back to the same stars after 27 days, but it isn't the same kind of moon (full, crescent) until 29.5 days!
Enough! Build an atomic clock! Hold on. The sun...is atomic...
...I think it all depends what you wish to measure. If you wish to have an abstract measure...but how? Time must tick relative to something... How about
;)
(All errors my own; all corrections appreciated. The sun and the moon relationship--I've been watching it develop for the past six days...) Don't fight forces, use them R. Buckminster Fuller.
Arithmetical: 12 has a larger number of divisors (1,2,3,4,6,12) than any other number smaller than 18.
Geometrical: it is trivial to divide a circle into 12 equal sections, as you don't even need a variable-girth compass. "It's the statue, man, The Statue."
For the non-mathematical among us (or the non geometrical)--who would be me--I had to look it up.
Here's what I got.
To draw a circle you need a compass of some kind. The point is the centre and the line you draw is the circumference. Take the same compass, put it's point somewhere on the circumference and then draw another circle, which will bisect the orginal circle in two places. Move the compass to one of these bisection points and repeat. You will now have...three marks on your circle, because...because your new circle will bisect the circumference at a new point and also at the old point...keep going until you have...six divisions.
Now look at the circles you have drawn. They meet. Draw lines from where they meet to the centre of the original circle...voila! The circle is divided into twelve!
Did I get that right?
(And I'm presuming it is slightly out because the circumference is the diameter times pi, or the radius times pi times two...?
And lo....maths!
(Thing is, as I understand it the greeks weren't inventors of this knowledge; they learnt it over in Alexandria, and so I am assuming it is ancient knowledge, far pre-dating the greeks, but we call them the discoverers because...well, a reason I can think of: the destruction of the library in Alexandria.)
And as this all started, for me, with Gaianne's comment about knowledge being destroyed, how about this gem?
We found a large number of books in these characters and, as they contained nothing in which were not to be seen as superstition and lies of the devil, we burned them all, which they (the Maya) regretted to an amazing degree, and which caused them much affliction.
Only three Pre-Columbian "books" of Maya hieroglyphics (also known as a codices) and fragments of a fourth are known to have survived. Collectively, these works are known as the Maya codices.
http://en.wikipedia.org/wiki/Diego_de_Landa
The famous Library of Alexandria was created by Ptolemy I Soter and its first librarian was Zenodotus of Ephesus.
BTW, the second librarian was Eratosthenes of Cyrene, who was the first to measure the Earth's cicumference... "Dieu se rit des hommes qui se plaignent des conséquences alors qu'ils en chérissent les causes" Jacques-Bénigne Bossuet
My mind acheth.
So...I have read up on the library and have some questions.
1) Why were the greeks running a library in Alexandria?
My initial assumption: because the Pharaoh stumped up the cash.
After Ptolemy I Soter, on of Alexander's successful generals, secured the kingship for himself of conquered Egypt, Theophrastus turned down the Pharoah's invitation in 297 B.C.E to tutor Ptolemy's heir, and instead recommended Demetrius, who had recently been driven out from Athens as a result of political fallout from the conflicts of Alexander's successors
http://www.perseus.tufts.edu/GreekScience/Students/Ellen/Museum.html#RTFToC3
Oh, intrigue! Greek generals bashing about, establishing a centre of learning in Egypt. Why Egypt?
Well...was it a historic centre of learning? Or was it...opportune?
So. It was founded by a greek dictator exile, another greek declared himself king of Egypt, and soon enough the dictator was translating, starting with the Old Testament.
Sounds to me as though the greeks had the cultural and economic clout to set up a "world library" and had greeks as librarians, and the works of greeks such as Aristotle and Plato; but the idea was to collect the world's knowledge which, for me, pre-supposes a world of knowledge they wanted to capture, for many reasons but I assume at least some were scientific.
But Ikernov nussink! I'm just following a thread...in my head...
...What about the vedic traditions?
I can't see that knowledge was unshared. My guess: the various knowledge bases were seeking to coalesce under the shadow of power-battles among the rich and powerful.
So I'd expect some greek bias in the library, but I'm only interested in...what? In the capacities of human thought and invention I suppose. And also (look around us!) at the power of...human power...to break knowledge, to destroy information deleterious to the human power...that would seek to break it.
I must thank you, Melanchthon, and you too, DoDo! Don't fight forces, use them R. Buckminster Fuller.
You can make that crop circle with a single piece of string, a stick and a plank. "It's the statue, man, The Statue."
