Display:
I only know a few things.  You have started digging up many things!  This is good! :D  

A.  

I am glad you dug up that part about the seven years.  There is a lot about this poem that I DON'T know.  Seven years was a standard unit of human life in Mideval times, seven years of childhood, seven years of apprenticeship, and so on.  In the US we have adulthood coming at 21 years, and you have to be of 35 years to qualify for president.  The Mideval analogy compared a human life to the twelve months of the year, from winter through spring and summer to autumn and then back to winter.  Each month was worth seven human years.  What month are you in now?  

So the seven years Thomas spends with the Elf Queen is one whole phase of his life.  But I sense there is also a deeper meaning, though I have not caught it.  

But you are veering away from her horse, which is a key clue--specifically, the fifty-nine silver bells.  

B.  

2340 is nine tzolkins...the time between the conjunction of Venus and Mars  

Yes.  You have it.  

Every nine tzolkins--2340 days--Mars and Venus return to their places in the sky (with respect to the Sun).  This is three rounds of Mars and four rounds of Venus.  3:4--This is something like the fifth best (most precise) harmony in the sky.  It is good to within half a day.  

And that is why Ares (Mars) and Aphrodite (Venus) are lovers.  

The nine lords of the night.  . . .  I couldn't get nine.

The Lords of Night do not belong to our culture, and I am far from getting their spiritual meaning.  Their numerical function is to make the calendar work--to combine with the tzolkin to mark the harmony of Mars and Venus.  

For the Americas, Mars and Venus have quite a different mythological import than for Europe and west Asia.  But they lie at the center of several religious and astronomical systems, not just that of the Mayans.  In fact it was a description of the Pawnee of the North American plains that made me realize what the Mayans were doing.  

I was reading this evening about animism, how anthropomorphism is in fact a very useful tool...it is a way of getting closer to the nature of something....so giving animals human characteristics  

When we anthropomorphize, we are giving a thing our full attention.  When we anthropomorphize correctly, we are giving our best attention.  

So generally, I count animism a good thing.  

(Even engineers do it.  Watch them talk about bugs and gremlins!)

the tzoltin is place specific.  It works for Mexico and regions close by.

In practice, yes, but you could use it anywhere, just as our Gregorian Calendar is used all over the world.  

C.  

I thought: one quarter of a lunar cycle  

A red herring.  The 28-day month is wrong.  This is a perfect example of what happens when knowledge is lost:  People make up something plausible to stick in.  An average lunar quarter is indeed 7 & 3/8 days.  But because of the Babylonians' planetary hours I KNOW that is NOT why we have a seven-day week.  

The Elf Queen's horse is the next step here:  What are those bells?  

I can only think of "light pollution" of some kind  

Too true:  Not lot long ago there was a power blackout in Los Angeles, and some people were in a panic--seeing stars in the night sky for the first time in their lives!  

...and so the fourteen and the seven...I don't know enough...  

This is a hard point.  I was both surprised and very happy to find the myth of Niobe.  Surprised because a myth is not an esoteric technical mannual, and yet the information pointed to is now known only to astronomers--amateur or professional--and not even all of them!  

Happy, because clues about ancient knowledge are very hard to come by, and each time, it is a delight.  

In modern terms, the Moon's orbit is eccentric, and this means that the length of the month can vary several hours from its average value.  Worse, the phases of new- and full- Moon vary up to + or - 10 hours from their average time, and the phases of first- and last- quarter vary up to + or - 15 hours.  You have to care about this if you are going to predict eclipses correctly--as many ancient people did.  Fortunately, these variations in the Moon form a regular pattern--which is (part of) what the myth of Niobe is about.  

D.  

The unexpectedly frequent appearance of Venus with the Pleiades.  

The reappearance is certainly unexpectedly frequent the first time it happens--it is stunning!  And I say that PERSONALLY! ;D  But it turns out that it is completely regular, and for the ancients, part of the World's harmony.  

great models of other cultures in other times.  

You describe what I am (have been) trying to do:  Starting from my own upbringing and perspective--which is modern and Western--try to understand the mind of other cultures, including those which may be sustainable.  In studying the ancient perspective of cycles, I begin to enter a mind that has a very different FEEL than the mind that travels along a path.    The mind that looks for a beginning, a middle, and an end is very different from the mind that dances to an ongoing rhythm and harmony.  

I have gradually been building this into my life.  Each time I celebrate the turn of season, it overlays and joins with all of the other years I have celebrated the same turning.  Each time Venus returns in the spring in the evening--as it is doing this year--it overlays and joins with the other years when this has happened.  This is Oneness.  

Buddhism can be very austere (especially zen).  Emptying the mind of chatter is hard work--and the harder we try, the harder it seems!  But with the story of the bodhi tree, and Venus at sunrise, we have the enlightenment being connected in a delightful way to the harmony of the World.  It is natural, and mythology can help, rather than hinder.  

For those who are arithmetically inclined (I am) numbers are part of that mythology.  Or, to return to the riddle:  What is that eight?  What is ninety-nine?  (Both numbers are part of the same thing).  

E.  

Also encircling Stonehenge itself is a ring of fifty-six pits known as the Aubrey Holes, named after their discoverer, James Aubrey.  

Aubrey Holes!  Thank you!  

Hawkins also sets up a complex fifty-six year lunar eclipse cycle in which the Aubrey Holes are postulated as holding posts for movable counters

Last I looked, there was no fifty-six year eclipse cycle:  You have to watch archaeologists like a HAWK; sometimes their astronomy is just no good.  (Sorry about that.)  After I post this, I will have to look into what Hawkins is doing.  

I asked:  What returns for the third time, after fifty-six years?  

If you know, and if you have answered D, then it should look like this makes an eclipse cycle.  But you do have to worry about drift as well--one of those esoteric issues that muddies the neatness of ancient astronomy--and after fifty-six years the Moon has drifted some ten days out of position.  Have to come back after I see what Hawkins is up to.  

a) to the underlying beat--which for the Mayans beats in 13.  They had a subdivision as well, with eight being auspicious and ten being inauspicious.  ONE two three, ONE two three four ONE ONE two ONE two three....well, are there variations or are there specific divisions?  And I'm presuming that there is hidden...in the puzzle...the idea that this beat impacts directly on human life, in crop cycles, or planetary temperature changes, or eclipses which kill food or...or something huge...I don't know.  Something huge that modern science can't see because it can't or won't or has forgotten how to scientifically (via observation and measurement etc...) analyse the comings and goings of these events and how they relate to our environment--and us ?
 

You are on the threshold:  That is exactly what is out there.  I think it is subtle more than it is huge, but even so, important.  We are trying to learn how to enter it.  

A friend of mine once spent some time in Haiti.  He had the very strange experience that everyone seemed to move to a rhythm--a rhythm they all shared but that he was outside of completely.  Yet he could see it and feel it.  

Are there "longest cycles of interest"?  The Venus Mars nine tzoltin is about seven years.  Why would this relationship hold an interest?  

Longest cycles? A good question!  I deduce that the Babylonians knew of the eclipse cycle of 54 years--they would have had to discover it before they could have found the 18-year cycle.  (It's really 18 years and 10 & 1/3 days).  And there were longer cycles than that that were of esoteric interest.  

The longest cycle the ancients might have known about is the precession of the equinoxes.  I am still looking for evidence of this 25 800 year cycle.  By late Roman times the precession was certainly noticed (the Mithraic Cult).  This is definitely proving hard to track down.  I expect the Mayans knew it, but again, no proof yet.  

The Venus/Mars harmony is a fully 3/5 of a year shorter than seven years.  So seven years is something else.  Among other things, it is 22 rounds of Mercury.  Is that its import?  I don't know.  

Then again if you use a 365-day year (obvious right?), then each year starts on a different day of the week in an endless cycle of seven.  But that means letting the year "drift"--the solstices and equinoxes move.  So I still don't know about this.  

The interest of the Venus/Mars cycle is not so strange if the sky is available to you.  (That darn light pollution, again).  Both are very bright, and once you realize it is a recurring pattern  . . .  

By the way, it is 79 months--almost perfectly!  A triple harmony.  That means the Moon returns too.  

so what's been lost?    

Well, we are like archaeologists, digging up fragments, and doing reconstruction.  But restoration is risky--how do we know we are restoring correctly?  We do it anyway.  

Thanks.  

More later.  

The Fates are kind.

by Gaianne on Thu Apr 19th, 2007 at 01:04:22 AM EST
[ Parent ]
Not lot long ago there was a power blackout in Los Angeles, and some people were in a panic--seeing stars in the night sky for the first time in their lives!

So the psychological premise of Asimov's Nightfall is actually correct...

"It's the statue, man, The Statue."

by Migeru (migeru at eurotrib dot com) on Thu Apr 19th, 2007 at 05:51:28 AM EST
[ Parent ]


The Fates are kind.
by Gaianne on Thu Apr 19th, 2007 at 06:42:29 AM EST
[ Parent ]
Hokkay...

A - I've had no joy searching for "59".  I'm assuming they're stars relating to a constellation, but which constellation the horse might be and which 59 stars might hang from the horse's mane...I don't know.

That's a great short poem, btw.  I also read an allegory to liberty caps in there...the wee folk...the fairies, the elves...  (That may just be me ;)

There are forty days and forty nights where neither the sun nor the moon showed through... (sounds like christian symbolism.)

And he is told to take the hard road, not the smooth meadow, which looks so inviting (lovely agriculture?)

"O see not ye yon narrow road,         45
  So thick beset wi thorns and briers?  
That is the path of righteousness,  
  Tho after it but few enquires.  

"And see not ye that braid braid road,  
  That lies across yon lillie leven 5?         50
That is the path of wickedness,  
  Tho some call it the road to heaven.  

"And see not ye that bonnie road,  
  Which winds about the fernie brae?  
That is the road to fair Elfland,         55
  Whe[re] you and I this night maun gae.

I'm just reading in, though.  Fixing maps randomly.  There's also a christian ref with the bread and the wine rather than the fruits of "this countrie"...

...and once things turn too esoteric (The Knights Templar!), well, Robert Anton Wilson...Illuminatus (I couldn't get more than twenty or so pages into that book...I don't have that strong a fascination for counter-theories, unless there's something less esoteric to back it up--something like the tzolkin--esoteric to us, but in fact an accurate calculator...?)

How little I know and why do I hear Marek grinding his teeth?  Or...no no!  Noises in ma heed.  Were (I ask, leaping ahead) eclipses of agricultural/plant importance, or were they of religious/mystic significance?  I mean, they had clever systems for judging when conjunctions of various kinds would occur, but we too have (different) systems for anticipating the same (kinds of events.)  We don't have a sense of awe, which may be a cultural failing, and maybe it affects mental health negatively not to have such a sense, but...but...in terms of information...were they tracking something we aren't?

So, no, 59 I cannae get.

B - (Putting on my sober hat--my hat, yes, is sober!)  I don't get why Mars and Venus are lovers if they meet so rarely...why not enemies who occasionally fight?  Or old friends--maybe a sister and a brother who have been exiled and meet once every nine tzolkins to discuss matters of great import...I mean, I can invent a story around a once-in-a-while-yet-regular conjunction, but beyond cultural myths...(I'm also thinking of the long-time-length [relative to the day] and how this meant they could keep track of larger periods of time--a life span might be ninety tzolkins etc...] is there any other--non-one-culture specific import to this?

Oh, my bad phrasing!

The nine lords of the night...was a nine day cycle?  Not being good with numbers, I don't see the connection to thirteen or twenty...

C - Well, PhD knowledge required!  Or detailed astronomical knowledge...so the 59 are not stars...the horse is the moon...no, it cannae be...not that I'd know ;)  Apart from a religious significance, I don't see why eclipses were important unless they had an effect on, say, crop cycles, but wouldn't something like "When you see a hundred bees, it's time to plant potatoes" be as effective, as the bees are also responding to the sun etc... as well as temperature, so if what is needed is a system to know when to plant...ach...do we know what they used their astronomy for?  I see the two reasons:

  1. For agriculture
  2. For a sense of balance--Z will happen in exactly X days after Y...

...but then you mentioned babylonian hours...coz days and nights change in length though they cycle one-one-one-one (day/night)...

D - Any links for why the reappearance of Venus is unexpected (what would we expect it to do and why?) and yet simply explicable (we know why Venus does what she does)?

Nothing about 99 here...I don't see how it connects to eight.  Is the Buddha idea your very own, Gaianne?  Eight could be so many things (eight alone, seven plus one, six plus two, and etc...)  It ties to Venus.  Is it an annual recurrence--something people would have known about because they saw it each year (an ancient version of, say, New Year's Day, which we know about because it happens every year and every year people celebrate, even if we don't know the whys of the whats...we know a year has passed again...sommat like that.)

And to return to the riddle: this is a riddle about ONE event, have I got that right?  All the different tales pointing to one specific astronomic phenomenon?  Which happens...yearly?

E -

On February 14, 1835, Oliver B. Huntington recorded in his diary that Joseph Smith had said that "God had revealed to him that the coming of Christ would be within 56 years."47  

;)  There be the number, but I don't think that's your ref.

And...hmmm....something that comes back for the third time after 56 years...and resets its cycle clock?  Because it must also have come back a first time after X (<56) years and a second time after Y (> X < 56) years.

So...a small astronomical event linked to the irregular orbit of the moon, but which is relevant because various different cultures knew of it (the clues), though maybe it has no great relevance to current culture (because we solve our problems in different ways and also have different problems?  "Hydroponics" suddenly pops into my head...)

And...this ties in to the thirteen?  No.  Or yes?  At any rate, pulses that are longer than one day/night, shorter than 260 days (growing season/gestation period) or 365 and a bit days (one trip round the sun), but also...hmmm...something that is erratic and reoccurs over long time periods, counted out against the moons erratic orbit around the earth as the earth moves around the sun...and those three linking to mars and venus (our nearest planets, so I suppose that's why they were of greater importance historically--they were brighter and their orbits were more specifically related to our own--and each others...)

Well, you blew off the top of my head, have introduced me to astronomy--though there's too much light pollution here, and 'tis cold on the hills of an evening (perfect for DoDo but too chilly for me--I remember my dad taking me out to see the stars; I remember thinking: Is it over yet?  I was cold.)

Well, I must off out into the sunshine.

I'm looking forward to your "more later".

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Thu Apr 19th, 2007 at 06:06:46 AM EST
[ Parent ]
but you will notice I am more concerned here with how the planets move than with the precise shape of the constellations.  (That is interesting too, but it is a different interest.)  

Maybe alchemy will get you there faster?  Silver is one of the "seven metals:"  gold, silver, iron, mercury, tin, copper, and lead.  

There are forty days and forty nights where neither the sun nor the moon showed through... (sounds like christian symbolism.)

But it might be Babylonian.  Thirteen times 40 days is 520 days, which is three half-dragons.  If you were going to create a calendar for the Dragon, this would be the way to do it.  I am still looking for proof though--I would like to find 13 and 40 occuring together:  That might settle it.  

I love those three stanzas you quote.  

Robert Anton Wilson is fun, but I don't feel I can trust him.  He has recently started a big thing about the number 23.  Well, I would love to see the number 23 turn up for real--it is not only useful in eclipse prediction--which the Mayans knew--but for calculating the Moon's drift.  But I need evidence that it was actually used for that purpose.  

Eclipses are certainly awesome, but there is more.  If we are too modern, we shut it out, and don't get it.  Birds and animals DO get it--and you can see that they do.  Eclipses create an altered bit of time.  

B.  

Well, I didn't say they were married! :)  But I think the point really is the perfection--a simple ratio of three to four, and it is the fifth most perfect (precise) harmony in the sky.  

other--non-one-culture specific import  

The Mayans had it.  The Pawnee had it.  The (pre-classical) Greeks had it.  That's cross-cultural.   Agreed:  There are differences in religious meaning.  

The thing about nine and thirteen and twenty is that they are all relatively prime.  This is good.  It means that when you let these cycles run concurrently, you get no repetition of  lord + day-number + day-name until the 9 x 13 x 20 = 2340 th day--when Venus and Mars return to where they were when you started.  

Same lord + day-number + day-name = Same positions in sky.  This is how we make cycles of numbers map on to cycles of planetary positions.  The Mayans were masters of this.  I believe the Babylonians were too, but the proof comes harder.  

C.  

Speaking of Babylonians, I hope the planetary hours do not prove too hard.  I admit they are intricate.  But if we can show this elaborate scheme actually DOES something, then we are home.  

The change in length of daylight is not my concern here.  My concern is whether the phase of the Moon comes early or late.  Plus or minus ten hours amounts to nearly a day--If there were a lunar eclipse, it could happen while I am on the wrong side of the Earth, in daylight, or it might come in the middle of the night and I would see it.  Those ten hours of variance from average Moon could make all the difference.  So I need to know.  (The Babylonians needed to know, and did.)

D.  

Is the Buddha idea your very own, Gaianne?  

:D  

Standard Buddhism, actually, except for my last remark about World harmony and Oneness.  And the problem of turning off mental chatter is not unique to me.  Though it is true that Buddhists do not say WHY the Eightfold Way is eightfold.  They wouldn't.  But my approach is, if the mythology fits, wear it!  With their story about the rising of Venus, they have left themselves wide open, as you will see.  

One riddle about one event, yes.  Actually, it is NOT yearly.  

E.  

That Huntington quote is amazing.  A friend of mine does straight mythology--he is looking for structural patterns--and routinely comes up with things like that.  The numbers are magical, but the author seems to have no idea what it means.  It just sounds cool.  Sometimes I help my friend--I know what it means.  Sometimes not--I don't.

I hope I am not misleading you because of the way these two things align:  Three sidereal periods of the Dragon is 56 years, but so is 59 synodic periods of the Dragon.  Which were the Stonehenge people paying attention to?  The latter, I think, because I can see how they could have used it.  The former?  Not so sure.  Either way, this is about the year and the Dragon.  

Careful of that thirteen.  Thirteen shows up in many places, including some I have not mentioned.  But it does not show up EVERYWHERE.  It would not be useful if it did.  

Once I came across a paranoid site where he was proving how everything in the universe was based on 13.  Took me a while to figure out he was not okay.  Even then I would not say everything on his site was wrong.  But you have to be careful.  

out to see the stars; I remember thinking: Is it over yet?  I was cold  

Sorry about your bad experience.  Enjoy the Sun!  

Later.  

The Fates are kind.

by Gaianne on Thu Apr 19th, 2007 at 08:24:54 AM EST
[ Parent ]
Lovely sun, a bit chilly out.  I was round a bloke's flat.  His daughter, he said, had described the smell in his flat as being like "the inside of a hamster's cage."  Judging by our hamster (who has chosen to sleep in a climbing tube rather than her bed), his flat smells a lot worse.

So, back to the puzzle.

A - The Queen of Elfland is the moon.  The 59 bells are the fifty nine--somethings--that make up the 59 synodic periods of the dragon (hey, you told me!)  I looked up dragon and came up with the draconic month.  I also read that the chinese banged pans to scare away the dragon...not sure how that fits in with it being auspicious...but I haven't had time to investigate further.  So that's A.

B - The conjunction of Mars and Venus once ever nine tzolkins (I worked out that 9 x 260 = 2340, though your explanation of how they never had to repeat...that the idea is to have a single counting system with no repetition of terms...I think I understand that now.)

C - The week.  7 days running against a fourteen cycle.  14 x 7 = 98.  Hmmm.  I'm still stuck on that one.

D - Eight and ninety nine.  I know it has something to do with Venus.  Venus plus the pleiades = eight.  But the moon comes in (you said the moon was the eighth planet so I'm all conked on this one.)  Plus, Venus in the Pleiades this year is the beginning of spring (the age of Aquarius!  Cough cough!  You caught me with the precession of the equinoxes)...but beyond that....I'm still lost.

E - The fifty six stones are the sidereal as opposed to the synodic fifty nine (the Church of England synod!)...whats?  I realise I'm getting confused with periods, days, cycles, and years.

I would love to solve this before I go to the pub this evening, because I will see my friend and would like to tell him the whole tale not just three quarters...but that might just be you giving me the answers...hehehheh...as if you weren't going to have to anyway...coz i nose nuffink.

;)

A supplementary question for yez.

The tzolkin counted 260 days.  There were 105 left over (or so) to make an earth year.  Counting in tzolkins would therefore mean there would be TWO tzolkin counts, the one that start at the relevant zenith, and the other ticking through to count out (eg?) the conjunction of Mars and Venus.

So my conclusion: something specific happens when Venus meets the moon in spring (?) every (?) period of days (or years?)....maybe a special kind of eclipse?

You comment about "an altered bit of time"....it's not about time standing still.  The lunar eclipse lasts about an hour (it changes length--is that important?)  Was it that specific hour that was "an altered bit of time"?  Was there something ELSE they could see during that hour?  I dunno, but I'm enjoying the puzzle immensely Gaianne!

Right, I must rush out under the sun again.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Thu Apr 19th, 2007 at 09:55:22 AM EST
[ Parent ]
Umm . . . you have a clean hampster!  

A.  

There's a lesson for me!  This subject is FULL of pitfalls.  The Elf Queen's 59 is not the Dragon's 59.  It is easy to get wrong-footed this way!  That is why Stonehenge's 56 was so surprising:  It is neat and clean.  It has to be 56 years; there just isn't anything else in the sky.  

Fifty-nine is a number that gets around a bit more.  So you need more information to pin it down.  

The Draconic month is a good find.  From the Draconic month it is possible to calculate (there is a techy bit in there, the conversion from sidereal periods to synodic periods, that is actually standard astronomy, but it's finicking) both the synodic period of the Dragon--346.62 days for the Dragons Head to climb out of the Sun up in the morning sky toward midnight (opposition) and climb down the evening sky back toward the Sun (conjunction); and the sidereal period--18.6 years for the Dragon to move retrograde through the stars and return back to the starting constellation.  

I find the synodic period (the Dragon round) of 346.62 days generally easier to use.  

Indeed synodic periods are easier to observe and measure than sidereal periods, and were the natural choice in ancient reckoning.  They also give simpler, cleaner harmonies in most cases.  

Skipping to the Church of England--yes, just the other week a friend pointed out to me that it is the same word "synod" meaning conjunction.  In this case, conjunction with the Sun.  

Three Dragon rounds is 1039.86 days--VERY nearly four tzolkins.  Did the Mayans know this?  Yes, that is part of what the tzolkin is meant for.  Did the Babylonians make use of this?  Maybe.  I am still looking for proof that they used cycles of two tzolkins to keep track of the Dragon.  

Hey!  It was right there on the same page!  Don't overlook the synodic month!  Could be useful.  

B.  

Good.  

The approach of the Alexandrian Greeks would have been:  A round of Mars is 780 days; a round of Venus is 584 days (but 585 is close enough)

780:585 = 4 x 3 x 5 x 13 : 9 x 5 x 13 = 4:3  

C.

Soon.  

D.  

Well, you have created a new hint by asking your supplementary question. See below.  

E.  

Oops.  Time to stop and regroup!  A year is 365.2422 days (that's a tropical year, which follows the seasons.  We're not going to worry about the other kind.)  A Dragon round is 346.62 days.  Fifty-six years is fifty-nine Dragon rounds:  

56 x 365.2422 = 59 x 346.62    +  2.98  days

That 2.98?  That's three days of error.  Nothing in astronomy is perfect!  But really, this is very good.  

SUPP Q.  

One hundred five days excess?  Yes indeed, the tzolkin does not keep track of the year at all--the Mayans had another method for that.  In turn, that means that the harmony of Venus and Mars does not fit the year either--at least not very well.  Eventually though, Venus, Mars and the year do (sort of) come back together.  Twenty rounds of Venus is fifteen rounds of Mars, and this is 45 tzolkins:  

45 x 260 = 11700 days  

How many years is that?  

32 x 365.2422 = 11687.7504 days  

It is 32 years (plus 12.25 days).  

The 12 and a quarter days discrepancy means we have some imperfection here.  

But despite imperfection, this might relate Venus (583.92 days) to the year.  Time to check.  

You comment about "an altered bit of time"....it's not about time standing still.  The lunar eclipse lasts about an hour  

From a physicists point of view, time continues as it always does.  But inside that hour the EXPERIENCE of time can be very different.  

The Fates are kind.

by Gaianne on Thu Apr 19th, 2007 at 12:07:14 PM EST
[ Parent ]
All those numbers!  And they're getting "sort of exact", but because I haven't seen--haven't seen the map of the sky as it were, haven't followed it, the timescales are a bit arbitrary in my head.  I didn't read "56" as 56 years for some reason.  And there are sidereal years and synodal years.

It would make sense for me, if I were to make measurements, to measure the synodal year.  The sun will come up....there!

So, just some added bits of info for me to store here:

Around the year 130 BC, Hipparchus compared ancient observations to his own and concluded that in the preceding 169 years those intersections had moved by 2 degrees. How could Hipparchus know the position of the Sun among the stars so exactly, when stars are not visible in the daytime? By using not the Sun but the shadow cast by the Earth on the moon, during an eclipse of the Moon! During an eclipse, Sun, Earth and Moon form a straight line, and therefore the center of the Earth's shadow is at the point on the celestial sphere which is exactly opposite that of the Sun.

So...the importance of the lunar eclipse was as a measuring the device.  Or is that the theory?  If someone were calculating the next lunar eclipse, the question "why"? would be answered if they were using it as a checking device for, say, precession (all these terms I'm learning...)

I've also found the 8/99 link.

To determine when an embolismic month needs to be inserted, some calendars rely on direct observations of the state of vegetation, while others compare the ecliptic longitude of the sun and the phase of the moon.

On the other hand, in arithmetical lunisolar calendars, an integral number of synodic months is fitted into some integral number of years by a fixed rule. To construct such a calendar, the average length of the tropical year is divided by the average length of the synodic month, which gives the number of average synodic months in a year as:

12.368266...
Continued fractions of this decimal value give optimal approximations for this value. So in the list below, after the number of synodic months listed in the numerator, an integer number of tropical years as listed in the denominator have been completed:

  12 /   1 = 12           (error = -0.368266... synodic months/year)
  25 /   2 = 12.5         (error =  0.131734... synodic months/year)
  37 /   3 = 12.333333... (error =  0.034933... synodic months/year)
  99 /   8 = 12.375       (error =  0.006734... synodic months/year)
 136 /  11 = 12.363636... (error = -0.004630... synodic months/year)
 235 /  19 = 12.368421... (error =  0.000155... synodic months/year)
4131 / 334 = 12.368263... (error = -0.000003... synodic months/year)
The 8-year cycle (99 synodic months, including 3 embolismic months) was used in the ancient Athenian calendar. The 8-year cycle was also used in early third-century Easter calculations (or old Computus) in Rome and Alexandria.

http://en.wikipedia.org/wiki/Lunisolar_calendar

...but I don't know how this relates to Buddha's enlightenment or Venus.  The eight year cycle was a form of regulating calendar (I feel I'm re-typing--only worse--migeru's diary on the subject of calendars; worse because I'm probably getting it all wrong and am in a cloud of oh-so-very unknowing....;)

So: the transit of Venus across the sun?  Some other special astronomical event?  I don't know how I'd work out which one it is because I don't know of many.

Another question about the tzolkin.  I'd understood it to be for planting maize (among other things), so it started not when mars and venus conjoined, but at one of the sun's zeniths (I type that as if I knew what it meant.)  So as the "long" tzolkin worked out, there would be a new one each year, whose start date was calculated by a synodal event?

I'm baffled now as to why anyone would want to invent the "sidereal" time period.  The synodal one (it's back where it started) marks a pure cycle.  The sidereal relates to the "background of stars", the zodiac, the constellations, against which we are running anti-clockwise (? to the left?  I still don't have a good mental map of the earth in relation to the celestial sphere...I'm trying to find a good site to help me fix a picture, so I can get the rough layout of the major stars clear in my noggin...)

But, yes, the background "fixed" stars were used for..what, navigation?  So for navigators it would be important to know if each year was slightly slowed relative to previous years, otherwise a ten year off-shoot might mean missing the island...something like that?

So the lunar eclipse was a calibration device?

And I still don't know what fifty nine bells refer to, or how the alchemical metals relate to the eight year lunisolar calendar; and I don't have it clear in my head how the sun and the moon interact--there's some shift, I suppose...we can count off cycles of the moon (new - full - gone - new etc...) and roughly twelve cycles makes a year, but not quite, so they had to "refix" the year by letting one have thirteen lunar cycles, and after eight years (and three additions) it was more or less okay, with a give or take--always forward?  Always backward?  One or t'other?

But this doesn't seem to get me any closer to answering the puzzle which has, no?, to do with Venus?

So...using Venus to calculate the year...Venus has a synodal cycle of 584 days.  The synodal solar cycle is about 365 days?  120 days difference, or maybe it's closer to 118?  (I remember that number), which is twic fifty nine...but I'm buggered if I know if that all links up in some way, and I would have the first idea how they'd be measuring this in the sky--they'd be using moon events as a tick tock and at certain points either re-set their clocks, or check where certain planets and/or stars were in the sky?

Finally (I'm still looking forward to seeing how this all ties up), I thought this was amusing.

(precession)

The discovery of precession is usually attributed to Hipparchus of Rhodes or Nicaea, a Greek astronomer who was active in the 2nd century BCE. [...]  [though] Various claims have been made that other cultures discovered precession independent of Hipparchus.

[...]

claims have been made that precession was known in Ancient Egypt prior to the time of Hipparchus. Some buildings in the Karnak temple complex, for instance, were allegedly oriented towards the point on the horizon where certain stars rose or set at key times of the year. A few centuries later, when precession made the orientations obsolete, the temples would be rebuilt. Note however that the observation that a stellar alignment has grown wrong does not necessarily mean that the Egyptians understood that the stars moved across the sky at the rate of about one degree per 72 years. Nonetheless, they kept accurate calendars and if they recorded the date of the temple reconstructions it would be a fairly simple matter to plot the rough precession rate. The Dendera Zodiac, a star-map from the Hathor temple at Dendera from a late (Ptolemaic) age, supposedly records precession of the equinoxes (Tompkins 1971). In any case, if the ancient Egyptians knew of precession, their knowledge is not recorded in surviving astronomical texts.

I don't know why I enjoyed the image of the egyptians knocking down their temple and rebuilding it pointing...a couple of degrees to the west (or east...I is so confused!)  Maybe it was the idea that they didn't know why their buildings were off.  "Bloody hell, we got it wrong again!  Right!  Knock it down."


Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Thu Apr 19th, 2007 at 01:18:24 PM EST
[ Parent ]
But you are digging up all KINDS of good stuff!  

But it can be confusing if you don't give yourself time to put it together.  

You have stumbled into sidereal periods.  I have been trying to avoid them--there is nothing wrong with them--just, I have been hoping to keep down complications.  

I like eclipses for other reasons, but yes, until you have modern high-precision instruments, eclipses are absolutely the cleanest and most accurate way of astronomical measurement.  Very useful, technically.  

The passage you found on 8/99 is good:  The heart of comparing the Moon against the year.  A LOT of information is implicit in that passage.  Of all those ratios, the only one that connects to Venus though, is 99/8.  

99 months is 8 years is ____ rounds of Venus.  Once you fill in the blank you are home.  

So: the transit of Venus across the sun?  Some other special astronomical event?    

Yes, though this wasn't part of my puzzle.  Very important in modern science:  It was the basis for deducing planetary distances (such as that the Earth is 93 million miles--I forget how many kilometers--from the Sun) which was a major problem of the 18th century.  Telescopes and filters are needed to make the observations.  Not ancient.  

I'm baffled now as to why anyone would want to invent the "sidereal" time  

Yes.  I feel that one doesn't do it until one has to.  This too is modern.  It takes time to explain.  Fortunately for the ancients, they didn't need it.  

But, yes, the background "fixed" stars were used for..what, navigation?    

Yes, but this too lies outside my puzzle.  It is a whole study.  Maybe a semester course to become  proficient.  I never learned this.  

So the lunar eclipse was a calibration device?

Yes, in ancient times and modern.  Right into the 20th century it was the only way to do many things.  

That piece on the Egyptian temples was a find.  I had no idea about that.  

Maybe it was the idea that they didn't know why their buildings were off.  "Bloody hell, we got it wrong again!  Right!  Knock it down."

:D It seems strange, for sure.  

Meanwhile, go back and look at the synodic month:  This is the month as we mean it in common usage--new Moon to new Moon.  How many days?  

The pieces are all nearly there.  

Putting together the Babylonian planetary hours may entail more than I thought.  Maybe we pause for breath first.  We'll see.  

The Fates are kind.

by Gaianne on Thu Apr 19th, 2007 at 02:11:43 PM EST
[ Parent ]
Hokkay.  A lunar month is about 29.5 days.  99 x 29.5 = 2920.5.  That's the number of days in eight years.  Venus's cycle is 584 days (to get back to where it started in the sky.)  So when Venus gets back to where it started for the fifth time (5.000856), that's the end of the eight year lunar cycle.

So: eight years
is the same as ninety nine lunar cycles
is the same as five Venus cycles

Not sure about the dragon.  I couldn't find any pages about it--I'll have to keep looking.

And I don't know how the seven days fit in.  I asked my friend last night; he didn't know.  Why seven days?  And how does it fit?

So...

A - 59
B - Venus and Mars meet every 9 tzolkins, but I don't know how that relates to the year/moon
C - ?
D - 8/99 see above
E - Something to do with lunar eclipses?  But I don't know how eclipses fit in to Venus / eight year....

Am I getting warmer?

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Fri Apr 20th, 2007 at 05:04:37 AM EST
[ Parent ]
Oh, I meant

A - 59  Still don't know!

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Fri Apr 20th, 2007 at 05:05:51 AM EST
[ Parent ]
What is 2 x 29.5 ?  

Why do this?  They just wanted a whole number--no fractions.  

More later.  

The Fates are kind.

by Gaianne on Fri Apr 20th, 2007 at 01:03:39 PM EST
[ Parent ]
Do you have a night sky where you are?  

For a while I lived on Long Island, which is essentially a suburb of New York.  (It was awful, but that is not my point).  Between everything, including a shopping mall, the night sky was so bright with glare that the only celestial objects were the brightest three planets, the Moon, Arcturus (in Bootes), Spica (in Virgo), Vega (in Lyra), Antares (in Scorpio, and the seven brightest stars of Orion.  NOTHING else was visible.  

That was my starting point for learning the sky. A little sparce!  ;)  

Later, I would make trips to better skies and then compare what I had seen with a star map that I had.  

The Fates are kind.

by Gaianne on Fri Apr 20th, 2007 at 01:18:53 PM EST
[ Parent ]
As I look out of the window, at 20:31, I see a crescent moon and, below it and a bit to the right, Venus.

I'm seeing this (well, I'm a fraction of a degree to the west and south.)

http://www.fourmilab.ch/cgi-bin/Yourhorizon?lat=51.5000&ns=North&lon=0.000&ew=West&f ov=45.000&azimuth=270.000&z=2&elements=

It's a fascinating beast of a problem trying to capture a model which makes the realities (the various cycles) link together so that when I stare at that crescent moon...I know that it is being lit by the sun, but...I'm still stuck at the concept of the ecliptic: It is the path of the Sun against the background stars, yes.  But when we look at the Sun, we don't see the stars behind it.  We see the stars when we swing round and away from the Sun...where the Sun isn't.  So I find the concept of the movement of the Sun against the (inivisible) stars behind it...hard to visualise...

Re: 59.  So the 50 silver bells are the daily phases of the moon over two lunar cycles?  (And a lunar cycle means: the moon is back in the same place in the sky?  So, in 59 days, if I look out of the same window at the same time I'll see the moon in the same place and with the same size crescent of light?

Like I said, though, I need to get a...mental handle...on what I'm looking at.  Really, I want to find a way to sense my movement relative to the sky.  I want to get that sense of being on the panoramic deck of a huge ship, moving...(but in which direction relative to the celestial objects?)...and then, when I can sense that I am moving, really get that sense, then I think I'll be able to get how the celestial objects are also moving, relative to me and relative to each other.  

But I'm still stuck in that mind set of: "Here I am, sitting here, not moving, and there are those obbjects...moving and changing...there's no dynamic, no motion...

I remember hitting that motion point once, looking down into the sky, the objects far below me...you know the sensation, when you involuntarily grab some grass to stop from slipping or falling into space.

As I also said, I can't find any references for the dragon.  But I need to re-read what you wrote, coz I think you stated it in a side comment which I didn't read properly.

Anyway, Venus and the moon are at my window.  I'll see if and how far they move between now and...later this evening, relative to my viewing space (they are framed...'twill be easy to see if they move more than a few of my centimetres.  The moon is four fingers below the top window frame; Venus is four fingers below the moon...

...Gaianne, I have to thank yez!

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Fri Apr 20th, 2007 at 03:42:52 PM EST
[ Parent ]
So, in 59 days, if I look out of the same window at the same time I'll see the moon in the same place and with the same size crescent of light?    

Yes.  

That's what it's for.  

Really, I want to find a way to sense my movement relative to the sky.

One spring I walked every night up a local hill just after sunset.  I was lucky to have a stretch of clear weather. Each night the stars sank lower into the Sun.  (This was NOT on Long Island).  After a month the sky had sunk one entire zodiac sign.  The constellation of Gemini has a couple of bright stars (also, Procyon in Canis Minor is nearby) and their movement from roughly overhead down toward the Sun was very obvious.  After a while I could begin to feel it.  

Dope helps ;)  

The Fates are kind.

by Gaianne on Fri Apr 20th, 2007 at 06:01:59 PM EST
[ Parent ]
is just touching the silhouette of one of the houses opposite, it's moved down and to the right, a finger distance in not too many minutes.  They were so much brighter than the other stars (I could make out a few others, but I had no reference points...I need to learn the maps a bit, and then look up and out.

But the thing is, I realised as the moon went down...see, I'd be wondering how we could ever see Venus, as it's closer to the Sun than us, to look at it we have to look towards the sun.  But then I realised that we must be looking acrossVenus, that it is moving away because I am spinning away from it.  And I realised I was looking in the rear-view mirror, that the moon and Venus were moving away into the distance.  I want to see the stars I'm moving towards, I'll have to check it out.  My "east" looks out over the town, so there'll be a lorra light down below bleeding out a lot of stars above.  I'll have to go see.

And the puzzle.  I need more clues or pointing back towards the right track.  Venus and the moon.  I saw them this evening, a very elegant relationship, relative to my window.  I thought of Islam and the crescent moon with its single star.

So, the moon.  It's cycles.  Then there are lunar eclipses, used to reset time systems.  And there is Venus...and there was Mars in B.  So Mars, too.  Something about their conjunction and how it relates to lunar eclipses?  ??????  I still can't get my head around the ecliptic.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Fri Apr 20th, 2007 at 06:24:29 PM EST
[ Parent ]

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