June 26, 2009
Why are There 60 Minutes in an Hour?
Gary Wallace at Scienceray:
To understand the units of time we need to investigate the number systems of ancient civilizations. How did the Sumerians count to 12 on one hand and to 60 on two? What advances did the Babylonians make and how did they use this number system for measurement? And what refinements did the Egyptians make to time measurement to give us the system we still use today?
It is easy to see the origins of a decimal (base 10) number system. Our hands have 10 digits to count on, so a decimal system follows naturally. With the addition of the toes on our feet a vigesimal (base 20) number system, like that of the Maya, also makes sense. But understanding a sexagesimal (base 60) number system, as used by the Sumerians, takes a little more thought.
A quick glance at a hand shows us four fingers and a thumb that can be used for counting. But the human hand is a complex machine consisting of 27 bones...
Some of these features are evident externally, especially in the fingers. By using the thumb as a pointer, and marking off the distal phalanx, middle phalanx and proximal phalanx of each finger, we can count up to 12 on one hand, as shown [in the photo].
More here.
Posted by S. Abbas Raza at 09:11 AM | Permalink
Comments
Take a compass and draw a circle. Without changing the width of the compass, step off chords around the perimeter of the circle. With a straightedge, draw lines conecting the center of the circle to the endpoints of the chords.
Hey, presto! -- you've divided a circle into six equal pieces, and have done it using the simplest kind of geometry and the kind most available to the ancients.
Now that you have six arc segments, and given that you have ten fingers ...
Posted by: joel hanes | Jun 26, 2009 10:10:09 PM
This brings to mind Buckminster Fuller's Numerology.
Because of its utterly pragmatic bias,
The Roman culture had no numerical concept
Of "nothing"
That corresponds to the abacus's empty column__
That is, the idea of "no sheep"
Was ridiculous. Humans cannot eat "no sheep."
When the Europeans first adopted the Arabic numerals
in 700 A.D.
As "shorthand" for Roman numeral aggregates,
They of course encountered the Arabic cypher,
But they had no thinkably identifiable experiences to
associate with it.
"Nothing" obviously lacked "value."
For this reason, the Mediterranean Europeans
Thought of the cypher only as a decoration
Signifying the end of a communication
In the way that we use the word "over"
In contemporary radio communication.
The cypher was just an end period,
Just a decorative terminal symbol.
It was not until 1200 A.D.
Or five hundred years later,
That the works of a Persian named Algorismi
Were translated into
Latin and introduced into Europe.
Algorismi lived in Carthage, North Africa.
He wrote the first treatise explaining
How the Arabic cypher functioned calculatively
By progressively moving leftward
The newly attained tenness
By elevating one bead at the bottom
Of the bottom section
Of the next leftwardly adjacent column in multiplication
And next rightwardly in division.
Thus complex computation could be effected
Which had been impossible with Roman numerals.
The Arabic cypher had been used
For several millenniums
In the computational manner,
First in the Orient,
Then in Babylon and Egypt.
But such calculations had never before been made
In the Roman Empire's Mediterranean world.
No matter how intuitively
A man might have felt
About the probable significance
Of the principle of leverage
Or about the science of falling bodies,
Previous to the knowledge
Of the cypher's capabilities to position numbers,
He could not compute
Their relative effectiveness values
Without "long" multiplication and division.
That's but a snip. Go to the link which is awash with insights from Fuller's fertile mind.
Posted by: John Ballard | Jun 27, 2009 8:10:21 AM
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