Wednesday, March 11, 2009

Génesis or the Biblical Origin of Q-Orders

C.A. Petri proposed that order (or sequence of events) should not be imposed or defined from outside but rather generated by more elementary properties and relations among events themselves. As candidate to start with, he saw the separation-relation , a relation that mathematically originates from the relation among four points on any simple curve independent whether it’s an open or closed curve.

There is however a natural first, that without any doubt gave origin to any of our current notions of time and space, order and orientation.

Almost all tales about creation begin as Genesis saying:

In the beginning God created the heaven and the earth. And the earth had no form. It was empty, covered with darkness and water.

Then the Spirit of God hovered over the water, and God said, "Let there be light," and there was light. God saw that the light was good.

Then He divided the light from the darkness. God called the light "day", and the darkness he called "night." And the evening and the morning were the first day.

We were given Day and Night, Morning and Evening: the very first perfect 4 pair:

These were in fact the very first precise observations we were capable to make.

Then God said, "Let there be lights in the heavens; and let them be for signs and seasons, and for days, and years." God made two great lights; the sun to rule by day and the moon to rule by night. He also made the stars.

And He set them all in the heavens to give light upon the earth; And God saw that it was good. And the evening and the morning were the fourth day.

We observe that in the Morning the Sun starts rising, but the Evening ends by setting. The next Day the sun reappears again rising. Somewhere during Day and Night there has to be a change of orientation: from rising to setting, from setting to rising. We name these changes noon and midnight and have a new pair.

Please note: Rising and Setting, Noon and Midnight are already abstractions. And note that specifically Midnight is a construction based on a hypothesis, as it can not be observed directly, reason probably why the Romans had no Midnight.

We split our Day in after morning but before noon and in afternoon but before evening, the night in after evening but before midnight and in after midnight but before morning. To summarize our findings, we draw a simple picture showing 4 changes between Day and Night, Rising and Setting of the sun, and the 4 sub-divisions of Day and Night. So do speak an elementary Theory of Day and Night.

We got a picture usually called Four Seasons, the smallest structure that satisfies all axioms. But I think there is better reason to call it Genesis: 4 seasons in nature don’t exist everywhere on earth and it requires already sophisticated measuring techniques to detect the equinoctials and solstices; a couple of tens of thousands of years or so of more observation and more reasoning, after creation and our initial discovery.

Then God said, "Let us make man in Our image, after Our likeness." And the Lord God formed man out of the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.

And God saw everything that He had made, and it was very good. And the evening and the morning were the sixth day.

What follows is human history: If we put just one additional 5th element on a circle with already 4 and count the possible configurations, we've got 12 of them. Another 6th element, we obtain 60 configurations, which the Sumerian used as the natural way to sub-divide the circle in 6 equilateral triangles, easy to fabricate with high precision and easy use to survey the lands and to observe the skies. A 7th element passing from triangle to triangle gives 360 configurations.

The heavens and the earth were finished so on the seventh day God ended his work.

God blessed the seventh day and made it holy.

Since those ancient times the day has two periods of 12 hours, the week 7 days and the full circle 360 degrees with 60 as base unit, hence the hour 60 minutes respectively 3600 seconds. Noteworthy the solar calendar of the Maya had also 360 good days -a complete circle- and 5 bad days in between.

Q-Orders try to put the initial idea in a mathematical language and to explore some of its consequences.

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