How did ancient peoples know "so much"?

What is a human being? What is life? Can science give us reliable answers to such questions? The electricity of life. The meaning of human consciousness. Are we alone? Are the traditional contests between science and religion still relevant? Does the word "spirit" still hold meaning today?

Moderators: MGmirkin, bboyer

How did ancient peoples know "so much"?

Unread postby altonhare » Sun Dec 21, 2008 8:06 pm

Many are amazed at the ability of ancient peoples to accurately estimate when certain celestial events would occur. The purpose of starting this thread is to explain how, with essentially 0 technology and mathematics only through trigonometry, a clever and inquisitive people could learn and "predict" a great deal.

Find a straight stick and ram it into the ground in a relatively flat area (one with a clear view of the horizon). This is all you need. Track the length of the shadow at sunrise, during the day, and at sunset. Also track its path from day to day. You will notice that, two days per 365, the shadow at sunrise points in exactly the opposite direction that it points at sunset. These two days are the fall and spring equinoxes. On two other days out of the same 365 you will notice that the noontime shadow is shortest on one and longest on the other. These are the summer and winter solstices, respectively. Additionally, you'll notice that the rise/set points for the sun will creep north of the east-west path after the spring equinox, then stop, then creep south again, rinse and repeat (this is for the northern hemisphere, opposite for the southern). We have now identified the 4 cardinal points on a compass and the 4 days per year that mark the change in seasons. I would be curious to know if 4 is special somehow to JL.

A simple hourglass will reveal that the time from one sunset to the next is not precisely the same from sunset to sunset, but averages out to the same value after 365 days sunsets, and we term this averaged value a "solar day". Actually, to be honest it won't be quite perfect, the moon's gravitational tug on the Earth's oceans slows Earth's rotation a bit.

Now, establish a line of site from the tip of your stick to a spot on the sky. Wait for a familiar star from a familiar constellation to pass over this spot. Use the hourglass and see how long it takes the star to realign with the stick from one night to the next. This interval is called the "sidereal day" and is constant from night to night and its value happens to be 99.72685% of the solar day. This slight mismatch creates the impression on the observer that the sun is migrating across the patterns of background stars, visiting the stars in one constellation after another throughout the year.

Now let's try something more interesting. Every day mark where the tip of the stick's shadow falls at noon (half a solar day after sunrise, called "clock noon", not when the shadow is shortest, called "local noon"). Each day's mark will fall in a different spot and, after 365 days, you will have a figure 8 pattern. A clever person or people will conclude that the earth is tilted towards the sun, this is what gives rise to the figure 8 that emerges as the sun migrates back and forth across the celestial equator. Additionally, a scientific society will conclude that earth's orbit is not perfectly circular. Because the earth's rotation remains rock-steady but the orbital velocity of the earth increases as we approach the sun and decreases as we recede from it, the sun doesn't always reach its highest point in the sky at exactly clock noon every day. The sun gets to its highest point as much as 14 minutes late on one day and 16 minutes early on another. Four days a year local noon is equal to clock noon, corresponding to the top, bottom, and the middle crossing of the figure 8. These days fall, in our modern calendar, on April 15, June 14, September 2, and December 25th.

Even more interesting. Send another scientist a ways south and tell them to take careful measurement of how far they go. Each of you measure the length of your sticks' shadows at the same time every day. If the shadows are the same length there are two possible conclusions. 1) You live on a flat earth or 2) The size of the earth is so large that the distance between you and your friend is too small to observe any local curvature. Notice that one could *never* decisively conclude on a flat earth, since there is always the possibility of a "supergigantic" earth. On the other hand if the shadows are different lengths one can decisively conclude on a "not flat" earth. If one invokes the assumption that the earth is spherical then this difference in lengths combined with the distance between you and your friend yields an estimate for the earth's diameter.

What about gravitation? Tilt the stick and tie a rock to it. Set the rock swinging back and forth. Count how many times it swings in a pre-set unit of time (such as a turn of an hourglass). You'll find that the number of swings depends very little on the width of the arc and not at all on the size/mass of the rock, but rather only on the length of the string. With a simple equation one can deduce earth's inherent acceleration (what we call gravity). On the Moon the rock will move much more slowly.

How can we demonstrate that the earth itself rotates, though? Until now we've only shown that the sun and stars revolve at regular, predictable intervals. Well, if we take a particularly long stick (like 30 feet), a long thin string, and a heavy rock, we can set them in motion and observe the pendulum. We will notice that the plane in which the pendulum swings slowly rotates. In fact, at geographic north or south the plane of the pendulum's swing makes a full rotation in exactly one solar day! An exact measure of the rotational speed of the entity beneath it, the earth. The plane turns more and more slowly as you move toward the equator and, in fact, one can use the speed of the plane's rotation as a measure of one's geographic latitude.

So it's no wonder that ancient peoples were able to build monuments such as Stonehenge where several of the stones in concentric circles align precisely with sunrise on the summer solstice. Other stones align precisely with the extreme rising and setting points of the moon. Construction took about half a millennium. With 500 years to build it, regardless of how far they chose to drag their bricks, did they really need extraterrestrial intervention?

The point here is that the astronomy embodied in Stonehenge and practically all other ancient astronomical constructs is not fundamentally deeper than what can be discovered with a stick. All that is required is some basic math, patience, and an inquisitive mind.
Physicist: This is a pen

Mathematician: It's pi*r2*h
altonhare
 
Posts: 1212
Joined: Sun Oct 12, 2008 9:54 am
Location: Baltimore

Re: How did ancient peoples know "so much"?

Unread postby Grey Cloud » Mon Dec 22, 2008 6:45 am

Alton,
There is a great deal more to ancient knowledge than line-of-sight surveying and marking the solstices and equinoxes, so before you give us another demonstration of your ignorance, have a read of this and explain how the Maya knew the maths.
http://www.infinitelymystical.com/essay ... part1.html
When you've done that you can explain how the ancients moved stones which modern technology can't; how they worked granite with copper tools; how they employed phi and pi in the construction of buildings and a whole lot more.
You might want to read up on the subject rather than just regurgitate your prejudices.
Oh yes, and how does one make 'simple hour-glass' when one doesn't manufacture glass?

Other stones align precisely with the extreme rising and setting points of the moon. Construction took about half a millennium. With 500 years to build it, regardless of how far they chose to drag their bricks, did they really need extraterrestrial intervention?
How do you know that construction took about half a millenium? If it took that long then the edifice would no longer accurately mark whatever it was supposed to be marking, due to the effects of precession. Who mentioned extraterrestrial intervention? There are no bricks in Stonehenge, see my question above about moving the huge pieces of stone.
If I have the least bit of knowledge
I will follow the great Way alone
and fear nothing but being sidetracked.
The great Way is simple
but people delight in complexity.
Tao Te Ching, 53.
Grey Cloud
 
Posts: 2477
Joined: Sun Apr 13, 2008 5:47 am
Location: NW UK

Re: How did ancient peoples know "so much"?

Unread postby altonhare » Mon Dec 22, 2008 8:22 am

Grey Cloud wrote:Oh yes, and how does one make 'simple hour-glass' when one doesn't manufacture glass?


I'll be reading the link. In the meantime, it doesn't have to be made of glass. The term "hourglass" just refers to anything constructed of two vessels with a small hole between them, carrying some fine particulate matter. It's some unfortunate root of etymology that puts the word "glass" in there. It could have been made from stone.
Physicist: This is a pen

Mathematician: It's pi*r2*h
altonhare
 
Posts: 1212
Joined: Sun Oct 12, 2008 9:54 am
Location: Baltimore

Re: How did ancient peoples know "so much"?

Unread postby altonhare » Mon Dec 22, 2008 8:27 am

http://www.infinitelymystical.com/essays/2012-part1.html wrote:I intentionally have my title reflecting both the solid science of 2012 and also its mystical aspects in order to let people know that I am not going to “squeeze the wonder and awe out of the event” by “explaining it” with science.


The author is going to intentionally refrain from scientific explanations in order to make it all sound more exciting and mystical for us?
Physicist: This is a pen

Mathematician: It's pi*r2*h
altonhare
 
Posts: 1212
Joined: Sun Oct 12, 2008 9:54 am
Location: Baltimore

Re: How did ancient peoples know "so much"?

Unread postby junglelord » Mon Dec 22, 2008 9:51 am

I am waiting for the answer as to how the Mayans knew the spin domains of such great distances?
Your answer should be exciting. Forget all the modern hype, tell me how these dudes in the jungle knew the precession?
If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.
— Nikola Tesla
Casting Out the Nines from PHI into Indigs reveals the Cosmic Harmonic Code.
— Junglelord.
Knowledge is Structured in Consciouness. Structure and Function Cannot Be Seperated.
— Junglelord
User avatar
junglelord
 
Posts: 3693
Joined: Mon Mar 17, 2008 5:39 am
Location: Canada

Re: How did ancient peoples know "so much"?

Unread postby altonhare » Mon Dec 22, 2008 10:02 am

Grey Cloud wrote:How do you know that construction took about half a millenium? If it took that long then the edifice would no longer accurately mark whatever it was supposed to be marking, due to the effects of precession.


It's an estimate I've often read, I don't "know". Do you have better evidence for the construction time?

With regards to precession, the events people typically associate with stonehenge, eclipses and solstices, are insensitive to precession.

Grey Cloud wrote:When you've done that you can explain how the ancients moved stones which modern technology can't; how they worked granite with copper tools; how they employed phi and pi in the construction of buildings and a whole lot more.


Loop enough ropes/vines/whatever around a block and employ an army of humans, you can drag almost anything.

Could you work granite with... granite tools? A sharpened axe of some material can cut something of a similar material.

What's so difficult about pi or phi? If some ancient person wrapped a vine around around their neck, marked it, then extended the vine along their neck and marked it, they'd end up with a ratio somewhere around 314. The same goes for any remotely circular object. An astute observer measuring many circular objects would find that the more constant a circular object's diameter is the closer the ratio of its circumference to its diameter is to some value around 314. 3.14 and 1.62 are just numbers/ratios anyone with the concept of a number can measure.

Most people who draw polygons inside a circle and measure their perimeter would conclude that they could draw polygons incessantly and keep getting new perimeters. Why not? I can imagine drawing higher order polygons incessantly, although I can't imagine a reason to actually do it.
Physicist: This is a pen

Mathematician: It's pi*r2*h
altonhare
 
Posts: 1212
Joined: Sun Oct 12, 2008 9:54 am
Location: Baltimore

Re: How did ancient peoples know "so much"?

Unread postby altonhare » Mon Dec 22, 2008 10:06 am

junglelord wrote:I am waiting for the answer as to how the Mayans knew the spin domains of such great distances?
Your answer should be exciting. Forget all the modern hype, tell me how these dudes in the jungle knew the precession?


The pendulum I described. If there were no precession then the number of times the pendulum swings back and forth at a single location before the plane of the swing rotates a full turn should not change, ever. However it does. All the Mayans had to do was hang a rock from a tall stick and swing it back and forth, count the number of swings before the plane of the swing rotates a full turn, and repeat. Eventually a small but significant difference will be observed. This difference corresponds to the rate of precession.
Physicist: This is a pen

Mathematician: It's pi*r2*h
altonhare
 
Posts: 1212
Joined: Sun Oct 12, 2008 9:54 am
Location: Baltimore

Re: How did ancient peoples know "so much"?

Unread postby junglelord » Mon Dec 22, 2008 10:09 am

Prove it.

I am with Kevin on this 100%. Your limits to how they derived knowledge are your limits, not ours, or theirs.
If you only knew the magnificence of the 3, 6 and 9, then you would have a key to the universe.
— Nikola Tesla
Casting Out the Nines from PHI into Indigs reveals the Cosmic Harmonic Code.
— Junglelord.
Knowledge is Structured in Consciouness. Structure and Function Cannot Be Seperated.
— Junglelord
User avatar
junglelord
 
Posts: 3693
Joined: Mon Mar 17, 2008 5:39 am
Location: Canada

Re: How did ancient peoples know "so much"?

Unread postby Grey Cloud » Mon Dec 22, 2008 11:12 am

Hi Alton,
you wrote:
It's an estimate I've often read, I don't "know". Do you have better evidence for the construction time?

The result of two seconds research via google n wiki:
History
Stonehenge itself evolved in several construction phases spanning at least some 1500 years. However there is evidence of large scale construction both before and afterwards on and around the monument that perhaps extends the landscape's time frame to 6500 years.
http://en.wikipedia.org/wiki/Stonehenge
Of which 500 year chunk were you thinking?
You wrote:
Loop enough ropes/vines/whatever around a block and employ an army of humans, you can drag almost anything.
And how, pray tell, does one then manoeuvre the 100-ton stones into place such that one cannot get a razor-blade between them? Anyways, the
rope trick has been de-bunked by engineers. It is simply impossible to get enough rope and bodies around the stone given its relatively small size and huge weight. Where does one get 'an army of humans' from when one lives in smallish village-sized communities? And who does the hunting, farming and or fishing while everyone is off tugging on ropes?
You wrote:
With regards to precession, the events people typically associate with stonehenge, eclipses and solstices, are insensitive to precession.

The result of another two seconds' research via google and:
Stonehenge does exhibit alignments with the Sun and the Moon. In fact, the main axis of the monument faces the horizon where the Sun rises midsummer morning, the longest day of the year. But the axis really only lines up roughly. The Sun actually rises to the left of the Heel
Stone (the marker for the axis). And because of the Earth's precession, 4,000 years ago, the Sun would have risen even farther off the center axis. This failure to REALLY line Stonehenge up demands an explanation if these people were practicing exact astronomy. It is possible that since these people were only using such knowledge for ritual purposes, their standards of accuracy were different from our own.
http://www.windows.ucar.edu/tour/link=/ ... astro.html

Then you wrote:
What's so difficult about pi or phi?
Only that until very recently all you experts said that the ancients weren't smart enough to know either of them. Try reading one of
Schwaller De Lubicz's books and you may get a little understanding of how intelligent and subtle were the Egyptians (and all ancients).
And then:
The pendulum I described. If there were no precession then the number of times the pendulum swings back and forth at a single location in a unit time should not change, ever. However it does. All the Mayans had to do was hang a rock from a tall stick and swing it back and forth, count the number of swings in a turn of an hourglass, and do it again the next year. And again the next year. A small but significant change in the number of swings will be observed. This change corresponds to the rate of precession, again with the use of geometry and trigonometry.
So you do that for 25,920 years then? Are you seriously proposing, that from a scientific point of view, one could detect such a small change by measuring the swing of a string pendulum? Even if one could, then how does that explain the mechanism? Given that the Earth was allegedly flat and stationary and the constellations were the 'fixed stars' physically attached to a firmament. Would the Moon not influence the swing of the
pendulum, assuming the degree of accuracy you imply?
And where did these people get the geometry and trigonometry from? They are supposed to be primitive farmers.
If I have the least bit of knowledge
I will follow the great Way alone
and fear nothing but being sidetracked.
The great Way is simple
but people delight in complexity.
Tao Te Ching, 53.
Grey Cloud
 
Posts: 2477
Joined: Sun Apr 13, 2008 5:47 am
Location: NW UK

Re: How did ancient peoples know "so much"?

Unread postby nick c » Mon Dec 22, 2008 3:10 pm

Grey Cloud wrote: ...explain how the ancients moved stones which modern technology can't;

An ancient picture showing how the ancient Egyptians moved a "Colossus" which was made of alabaster and probably weighed about 60 tons (weight estimate from, I.E.S. Edwards, The Pyramids of Egypt, p266 Penguin Books):
http://books.google.com/books?id=RTiTQS ... utput=html
That the ancient Egyptians were well acquainted with practical mechanics, is evident from the vast masses of stone which they managed to transport to distances of hundreds of miles from quarries. Thus the obelisks of Thebes and Heliopolis, measuring from 70 to 93 feet long, were dragged the whole way from Aswan on sledges by forced labour, in the manner shown in the illustration. The largest of these which stands at Karnak, weighs 300 tons, and traversed a distance of 138 miles; [...]
Our illustration exhibits the transport of a colossus of a grandee ("Tehuti-hotep, beloved of the king"). It is fastened on a sledge with double ropes, twisted together, and kept taut by inserted pegs. (Compresses of leather or some other substance are placed between the ropes and the statue, to obviate damage from friction. Hieroglyphics state that the statue is 13 cubits, or 22 feet 2 1/2 inches high. It is being dragged by 172 men, in four rows of 43 each, some of whom are Egyptian convicts, others foreign captives, wearing their own distinctive dress. Behind the fourth row are some carriers of grease for oiling the track. Behind these again three men carry a piece of cogged timber for placing, when necessary under the sledge; and after these walk three taskmasters, stick in hand. The four rows of men at the back of the statue are mer or superintendents of the work. A man is pouring grease on the track from the plinth of the statue; and another, standing on its knees, is beating time to the chant of the labourers, to insure all are pulling together. In front of the statue a priest is offering incense (arit sentra). A detachment of soldiers, unarmed, and carrying branches of trees, is seen marching towards the statue, beside the first row of labourers.
http://books.google.com/books?id=RTiTQS ... 0PZA&hl=en

This is how the Egyptians pictured it. If you go to the next page of that link the author has another picture and detailed text dealing with the moving of a large Assyrian (colossus) statue by similar means. The ancients accomplished this by themselves in a simple and straightforward manner. No levitation, no anti gravity device, no aliens, and...not even wheels. (Though they, no doubt, used the wheel for other things.) They used planning and coordination... ropes, a sled, grease, water, maybe a barge, and lots of manpower.
I don't know, could a couple of hundred men do this today?

And how they carved a statue:
http://books.google.com/books?id=RTiTQS ... #PPA113,M1

Grey Cloud wrote:how they worked granite with copper tools

You cannot effectively work granite with copper or bronze tools, common sense tells me that the cutting tool has to be harder than what is being cut. Logically then, the Egyptians must have used iron tools, and not wrought or meteoric iron because it is too soft. They must have used steel tools.
A piece of iron was found in the Great Pyramid by Colonel Howard Vyse:
Vyse's second �great discovery� was a flat iron plate, 12' by 4' and 1/8'thick. The plate was removed from a joint in the masonry at the place where the southern airshaft of the king's chamber exits to the outside. Experts conclude that it was left in the joint during the building of the pyramid and couldn't have been inserted afterwards. This is highly significant since the date for Iron Age in Egypt is around 650 B.C., though some believe it was in some use earlier and the accepted date for the building of the great pyramid is 2589 B.C. to 2566 B.C. (Colavito 2002)
http://www.mnsu.edu/emuseum/information ... chard.html
highlight added

That the Egyptians(and others, such as the Mesopotamian civilizations) worked hard rock such as granite and the even harder diorite a thousand years or more before the accepted dates for the "iron age" is an anomaly. Either the conventional understanding of metalurgical chronology is off, and (at least some) ancient civilizations had the ability to make steel tools long before the accepted dates for the discovery of that technology or the chronological location of those civilizations are off and they belong in the "iron age."
It also must be remembered that choice of tools would also depend on economic considerations, that is the cost of the tool in relation to the task. People used bronze and stone tools in Egypt until modern times, because they were cheaper. So many or most ancient jobs would have been done with stone, copper, or bronze tools; the more expensive steel tools being reserved for special or demanding work.

nick c
Last edited by nick c on Mon Dec 22, 2008 3:24 pm, edited 1 time in total.
User avatar
nick c
Moderator
 
Posts: 2459
Joined: Sun Mar 16, 2008 8:12 pm
Location: connecticut

Re: How did ancient peoples know "so much"?

Unread postby bboyer » Mon Dec 22, 2008 3:23 pm

Grey Cloud wrote:Alton,
There is a great deal more to ancient knowledge than line-of-sight surveying and marking the solstices and equinoxes, so before you give us another demonstration of your ignorance, have a read of this and explain how the Maya knew the maths.
http://www.infinitelymystical.com/essay ... part1.html
When you've done that you can explain how the ancients moved stones which modern technology can't; how they worked granite with copper tools; how they employed phi and pi in the construction of buildings and a whole lot more.
You might want to read up on the subject rather than just regurgitate your prejudices.
Oh yes, and how does one make 'simple hour-glass' when one doesn't manufacture glass?

Other stones align precisely with the extreme rising and setting points of the moon. Construction took about half a millennium. With 500 years to build it, regardless of how far they chose to drag their bricks, did they really need extraterrestrial intervention?
How do you know that construction took about half a millenium? If it took that long then the edifice would no longer accurately mark whatever it was supposed to be marking, due to the effects of precession. Who mentioned extraterrestrial intervention? There are no bricks in Stonehenge, see my question above about moving the huge pieces of stone.


From the Cymatics thread: viewtopic.php?f=10&t=38&st=0&sk=t&sd=a&hilit=pyramids&start=60#p183

From the above post: http://www.materials.drexel.edu/Pyramids/
(be sure to view Prof. Barsoum's webcast seminar presentation of his testings here - requires Microsoft Silverlight, installation link available at the site: http://media.irt.drexel.edu/mediasite/v ... 08a26de747 - downloadable pdf's of the presentation available at the first link)

http://www.youtube.com/watch?v=znQk_yBHre4 How the pyramids where (sic) built in Egypt

It may not address all ancient megalithic/monumental structures but, then again, I don't think any of them outside the Great Pyramid have been tested for the possibility yet either. If this was, perhaps, the technology/craft/methodology used by our ancestors I see it in no way detracting from their ... stature ... particularly when even today we still have not duplicated what may have been their advanced knowledge of dealing with cast material precision/technology/art/craft. Tho' we do produce some nice home driveways, decorative borders and such. :lol:
There is something beyond our mind which abides in silence within our mind. It is the supreme mystery beyond thought. Let one's mind and one's subtle body rest upon that and not rest on anything else. — Maitri Upanishad
User avatar
bboyer
 
Posts: 2410
Joined: Thu Mar 13, 2008 10:50 pm
Location: Upland, CA, USA

Re: How did ancient peoples know "so much"?

Unread postby altonhare » Mon Dec 22, 2008 10:12 pm

junglelord wrote:Prove it.

I am with Kevin on this 100%. Your limits to how they derived knowledge are your limits, not ours, or theirs.


So instead of adopting the simplest explanation, you insist on imposing your own?

The rotation of the plane of the pendulum's swing depends on the rotation of the body beneath it. If the earth were a perfect sphere at all times the rotational rate of this plane at a single location would not vary. Further, if the earth were a spheroid whose curvature never changed, the rotational rate would also be constant. However, the curvature at any one location does change as the earth's orientation relative to the sun changes. The precession of the earth's rotation causes its degree of oblateness to change, which alters its curvature at any given location, causing the rate of rotation of the plane of the pendulum's swing to alter slightly. Since this change in plane rotation rate depends directly on the nearly circular precession of earth's rotation, the plane rotation rate change will also follow the algebraic expression of a circular path. The ancient Mayans noticed the change in the plane rotation rate of such a pendulum and either

A) Assumed it would change as a circle, since circles were so often revered as divine or significant in some way

B) Actually noticed a circular trend over time

Either way, by invoking a circular pattern, they could calculate how long it would take for the rotation rate to return to its original value.

This method does not even mention the observation that the stars' positions change slightly over time due to precession, and there's no reason not to believe the Mayans did not notice this also.

Grey Cloud wrote:Of which 500 year chunk were you thinking?


As I admitted, it's only an estimate I recall from some years back. In any event, the fact that it took thousands of years instead of hundreds only makes the structure less remarkable.

Grey Cloud wrote:And how, pray tell, does one then manoeuvre the 100-ton stones into place such that one cannot get a razor-blade between them?


You're saying it's difficult to put two stones next to each other so that they are touching?

Grey Cloud wrote:Anyways, the
rope trick has been de-bunked by engineers. It is simply impossible to get enough rope and bodies around the stone given its relatively small size and huge weight.


I distrust such a conclusion. I see no reason why ropes cannot be stacked on top of each other almost without end. Additionally I see no reason we cannot have people, row upon row, holding them. The ropes/bodies do not have to be crammed into a dense mass around the stone. Perhaps I am misunderstanding the argument here, do you have a dependable reference where I can read about it?

Grey Cloud wrote:Only that until very recently all you experts said that the ancients weren't smart enough to know either of them.


I hope by saying "you" you are not referring to me, since I have never made this assertion. There's no reason to believe any ancient people were any less "smart" than we are. Technology != science. As I am trying to point out in this thread, technology is not really a barrier to measuring/quantifying the major motions of earth. The barrier is an inquisitive and patient mind to pursue such activities as counting swings and measuring positions for years and possibly centuries.

Grey Cloud wrote:So you do that for 25,920 years then? Are you seriously proposing, that from a scientific point of view, one could detect such a small change by measuring the swing of a string pendulum?


As I pointed out, one only has to observe a change and then invoke a circular relationship. Circles are pretty popular, especially among ancient mathematicians. I'm not sure what the % error was on their pendulum, but the mean value from day to day would shift decisively in a direction. I doubt any change would be observable day to day, but over decades perhaps. The change in the pendulum's plane of swinging depends on where we are in the precessional cycle. If the earth's axis is pointed as much toward the sun as possible and just beginning to point away, the swinging rate will change very slowly. If the earth's axis is pointed as far away as possible and is just starting to point toward, the swinging rate will change very slowly. At points exactly in between these two the change in the rotational rate of the pendulum's plane of swing will change very fast. The variation will, in fact, by a sine function. However we do not need the modern notion of the sine function to model this pendulum. All we need is the notion of a circle. Specifically we need to have conceptualized the relationship R2 = y2 + x2. They could still determine the Great Year by measuring a change in the rotational rate of the pendulum's swinging plane per day/year/decade. This would tell them the rate of change, which would tell them "where they are" on a hypothetical circle. Extrapolation would yield the Great Year.

So they measure this rotational rate. Let's say it's x1 days per plane rotation right now. T0 years later it's x2 days per plane rotation. T0 years later it's x3. How long will it take before it returns to x1 days per plane rotation, assuming a circular relationship? What is T'?

Three points define a circle. Our three points are:

[(x'-x1)/x', 1] ; [(x'-x2)/x',(T'-T0)/T')] ; [(x'-x3)/x',(T'-2*T0)/T')]

X' and T' are the maximum rate of rotation of the pendulum's swing and the time for the rate of rotation to return to its measured value (the Great Year) respectively. T' is what we want to find!

The midpoints of lines drawn between these points:

[x'-((x1-x2)/2*x'),T'+(T0/2*T')] ; [(x'-(x2-x3)/2)/x',T'+T0/T']

Lines through these points perpendicular to the original lines pass through a common point that is the center of the circle:

T = (x*x')/T' * [(1+(T'-T0))/(x2-x')] + 1 - (x'/T') * [(T'-T0-1)/(x2-x1)]

T = [-T' * (x3-x2)/3*x' * T0] * x + (T'-T0)/T' + (T' * (x3-x2) * (x'-x2))/3*T0*x'^2

This is a linear pair of coupled equations that can be solved by standard algebraic methods. The answer is long and messy:

x = { [(T'-T0)/T'] + [T' * (x3-x2) * (x'-x2)]/(3*x' ^2*T0)] + (x'/T') * [(T'-T0-1)/(x2-x1)] } / [ (x'/T') * [(1+(T'-T0))/(x2-x')] + [(T' * (x3-x2))/(3*T0*x')]

Substituting this back in to the above equations yields a formula for T. We now have x(x',T') and T(x',T').

T0, x1, x2, and x3 are all known (measured). What about T' and x'? To determine these we take advantage of the properties of circles. In particular, T=0 x=x' and x=-x'. When x=0 T=T' and T=-T'. Again we have a pair of coupled equations that can be solved by standard algebraic methods. We solve it for T'(T0,x1,x2,x3). This yields the Great Year.

This is probably how the Mayans did it, with a stick, a rock, string, and good ol' fashioned geometry. It took some fortitude to grunt through all the algebra, but the algebra is not fundamentally deeper than what most of us learn by 10th grade. Many bright children discover this level of algebra largely on their own.
Physicist: This is a pen

Mathematician: It's pi*r2*h
altonhare
 
Posts: 1212
Joined: Sun Oct 12, 2008 9:54 am
Location: Baltimore

Re: How did ancient peoples know "so much"?

Unread postby flyingcloud » Tue Dec 23, 2008 7:36 am

altonhare wrote:



What's so difficult about pi or phi? If some ancient person wrapped a vine around around their neck, marked it, then extended the vine along their neck and marked it, they'd end up with a ratio somewhere around 314.


how do they get their neck diameter/ radius, sounds yucky

give them enough rope theory and they'll hang themselves
flyingcloud
 
Posts: 490
Joined: Fri Nov 07, 2008 2:07 am
Location: Honey Brook

Re: How did ancient peoples know "so much"?

Unread postby flyingcloud » Tue Dec 23, 2008 7:38 am

altonhare wrote:Find a straight stick and ram it into the ground in a relatively flat area (one with a clear view of the horizon).


I thought there weren't any straight lines in nature...
flyingcloud
 
Posts: 490
Joined: Fri Nov 07, 2008 2:07 am
Location: Honey Brook

Re: How did ancient peoples know "so much"?

Unread postby Grey Cloud » Tue Dec 23, 2008 11:59 am

Hi Arc,
I've come across the concrete theory before and find it intriguing. I wouldn't put it past the Egyptians. It doesn't address the granite issue though. Which brings us to cymatics. Cymatics or something similar would be my guess for the heavy blocks.
One can stick 'em on sleighs and tug away at ropes but at the end of the day the block has to be raised and fitted into postion. Once the block is approximately in position, one can only get so many bodies around it to get it into its final position.
One also wonders how one fares with sleighs and ropes in the Andes, across soggy British countryside or through Central American jungle.
If I have the least bit of knowledge
I will follow the great Way alone
and fear nothing but being sidetracked.
The great Way is simple
but people delight in complexity.
Tao Te Ching, 53.
Grey Cloud
 
Posts: 2477
Joined: Sun Apr 13, 2008 5:47 am
Location: NW UK

Next

Return to The Human Question

Who is online

Users browsing this forum: No registered users and 1 guest