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Equation of time

by rg Wed Apr 25th, 2007 at 06:53:07 AM EST

From the diaries - whataboutbob


The equation of time is the difference, over the course of a year, between time as read from a sundial and a clock.

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

Science and the garden.  Clockwork compared to organic growth.

The equation of time is the difference, over the course of a year, between the time as read from a sundial and a clock.

How Do They Compare?

I'm sure some of you know all this--the science grads learned astronomy, I think.  The basics at least.  It seems (to moi) that geometry, trigonometry, all the maths sciences must come from astronomy.

Or, taking the organic approach:

Stand up and look around.  Which way is north?  Which way is east?

Face the east; the direction in which you find the sun in the morning.

Make your first bow: you are moving....

The sundial can be ahead (fast) by as much as 16 min 33 s (around November 3) or fall behind by as much as 14 min 6 s (around February 12).

It's about regularity, exactitude of one action as it reacts--with exactitude--to others.  Action?

It results from an apparent irregular movement of the Sun caused by a combination of the obliquity of the Earth's rotation axis and the eccentricity of its orbit.

"irregular movement of the Sun"--compared to the movement of a model sun, a mechanical few-dimensional model in which many observable effects are absent.

Observation

The equation of time is visually illustrated by an analemma.

Analemmas

Due to the earth's tilt on its axis (23.45°) and its elliptical orbit around the sun, the relative location of the sun above the horizon is not constant from day to day when observed at the same time on each day. Depending on one's geographical latitude, this loop will be inclined at different angles.

Plotting the analemma with the width exaggerated shows that it is slightly asymmetrical due to the misalignment of apsides and solstices.

See equation of time for an in-depth description of the horizontal characteristics of the analemma.

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

The equation of time describes the horizontal characteristics of an analemma.

Apparent Time versus mean time

The irregular daily movement of the Sun was known by the Babylonians, and Ptolemy has a whole chapter in the Almagest devoted to its calculation (Book III, chapter 9). However he did not consider the effect relevant for most calculations as the correction was negligible for the slow-moving luminaries. He only applied it for the fastest-moving luminary, the moon.

Until the invention of the pendulum and the development of reliable clocks towards the end of the 17th century, the equation of time as defined by Ptolemy remained a curiosity, not important to normal people except astronomers. Only when mechanical clocks started to take over timekeeping from sundials, which had served humanity for centuries, did the difference between clock time and solar time become an issue. Apparent solar time (or true or real solar time) is the time indicated by the Sun on a sundial, while mean solar time is the average as indicated by clocks.

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

So...the world was running on "apparent" time until the clocks became accurate enough, in Europe, in the period 1660-1700, to take over.  Before then, the equation of time--as a problem--was only seen by astronomers.

But here comes the clock.  Tick tock.

No more sundials.  We're on mechanical time now.  Mean time.

(A vision of the well-tempered harpsichord...and the evenly tempered pianoforte.)

Until 1833, the equation of time was mean minus apparent solar time in the British Nautical Almanac and Astronomical Ephemeris. Earlier, all times in the almanac were in apparent solar time because time aboard ship was determined by observing the Sun. In the unusual case that the mean solar time of an observation was needed, the extra step of adding the equation of time to apparent solar time was needed. Since 1834, all times have been in mean solar time because by then the time aboard most ships was determined by chronometers. In the unusual case that the apparent solar time of an observation was needed, the extra step of adding the equation of time to mean solar time was needed, requiring all differences in the equation of time to have the opposite sign.

(You're with me...we're hanging in there...)

No one needed mean solar time.  Correction: at least someone needed, wanted, or both needed and wanted mean solar time.  And it came, with ships' clocks.  The clock was the time source; they could now begin to forget about the sky--unless it interested them.  It was no longer necessary, and because of flips here and twists there, the sky can sometimes be wrong, compared to clock time.

As the daily movement of the sun is one revolution per day, that is 360° every 24 hours or 1° every 4 minutes, and the sun itself appears as a disc of about 0.5° in the sky, simple sundials can be read to a maximum accuracy of about one minute. Since the equation of time has a range of about 30 minutes, clearly the difference between sundial time and clock time cannot be ignored. In addition to the equation of time, one also has to apply corrections due to one's distance from the local time zone meridian and summertime, if any.

The sun dial is waaaaay out!  Well, by up to fifteen minutes either way.  Only at certain times, though.  Over the course of the year it hits two points where it is spot on--to within a minute.

How a Sundial  Works

Equatorial or Equinoctial sundial

The simplest sundial is a disk mounted on a bar. The bar must be parallel to the Earth's axis of rotation. The disk forms a plane parallel to the plane of the Earth's equator. The disk is marked so that one edge of the shadow of the bar shows the time as the Earth rotates. Usually noon will be at the bottom of the disk, 6AM on the western edge, and 6PM on the eastern edge. In the winter, the north side of the disk will be shaded, and hard to read. In the summer, the south side will be shaded.

http://en.wikipedia.org/wiki/Sundial#Garden_sundial

Garden Sundial

The classic garden sundial uses the same principle, except the lines of the disk are projected, using trigonometry, onto a face that is parallel to the ground. The advantage of the garden sundial is that it keeps time all year, and its face is never completely shaded in the daytime (as vertical sundials are). For use in a public area, this sundial can be made visible by placing it in a square, or making the face of frosted glass, elevated high in the air, and visible from underneath. The top edge of the gnomon is parallel with the axis of the Earth's rotation. The shadow will cross time markings on the face.The markings of each edge are aligned with the edge of the gnomon that produces the shadow. The angle of the face markings from the root of the gnomon (the substyle) are calculated from the formula:

face-angle = arctan(sin(latitude)*tan(hour-angle))
The angle of the style:

style height = latitude
(See Logo programming language for a sample program to draw a garden sundial)

Here come the tech guys and gals with their calculations.  We can work this out!

But our problem wasn't that the sundial in the square wasn't accurate.

The high priests of where we've been, where we are, and where we're going.  They need accurate measurements.

As though the siesta were a bad thing if its length varied by up to, what?  Ah, yes.  Up to thirty minutes over a given hour.  (Spread over the year, and on either side.)

The Sun

That big ball of love that keeps radiating us with life-giving rays...

Someone calculated how long large mammals would survive if the sun were suddenly switched off.  The measurements were in months; not days, not years, certainly not decades.

The sun!  Stare at it and you'll go blind.

Whereas clocks.  Tick tock.  The sun.  Wander wander.  Too bright to observe directly with the naked eye.  But there are ways....of observing it without the naked eye.  Such as a sundial.

The sun does not move along the celestial equator but rather along the ecliptic. At the equinoxes part of the yearly movement of the sun appears as a component in the change in declination, leaving less for the component in right ascension. The sun slows down by up to 20.3 seconds every day. At the solstices, on the other hand, all yearly movement is in right ascension only, but at this declination, 23.4°, the meridians are closer together, which speeds up the sun by the same amount. The inclination of the ecliptic results in the contribution of another sine wave variation with an amplitude of 9.87 minutes and a period of a half year to the equation of time. The zero points are reached on the equinoxes and solstices, while the maxima are at the beginning of February and August (negative) and the beginning of May and November (positive).

The maths can be done to approximate this living system, by which I mean it is happening now and we're part of it, and we're alive, yeah!

But the maths of clockwork is easier, and therefore...

...I wanted to say cheaper.

More manageable?

What terrible things would happen if we all worked on solar time?

Well, everyone on the planet would have a different time...there would be no common time.

No easy means of communicating the time, or...clocks create an easier method of communicating time and can be calibrated more accurately, from which fact more accurate observations of the world around us can be made.

The clock separates time from the sun.  Time is local, but "time"...the tick tock...the tick and the tock are universal constants?

That tock follows tick.

The exact shape of the equation of time curve and the associated analemma slowly changes over the centuries due to secular variations in both eccentricity and obliquity. At this moment both are slowly decreasing, but in reality they vary up and down over a timescale of hundreds of thousands of years. When the eccentricity, now 0.0167, reaches 0.047, the eccentricity effect may in some circumstances overshadow the obliquity effect, leaving the equation of time curve with only one maximum and minimum per year.

Yes, time will outlive us.  But without us: who cares about mechanical time?  Not the sun.  Not our galaxy.

It is a human invention to replace, for various practical reasons, solar time as measured on sundials, to mark out the passing of a day.

Months are funky as you like.  Twenty eight days, thirty days, thirty one days.  Thirty days hath September; April, June, and November.  All the rest hath thirty one, except for February alone, which has twenty eight.

I'm remembeing that badly, I'm sure.

Back To The Equation of Time

Practical use

If the gnomon (the shadow casting object) is not an edge but a point (e.g., a hole in a plate), the shadow (or spot of light) will trace out a curve during the course of a day. If the shadow is cast on a plane surface, this curve will (usually) be the conic section of the hyperbola, since the circle of the Sun's motion together with the gnomon point define a cone. At the spring and fall equinoxes, the cone degenerates into a plane and the hyperbola into a line. With a different hyperbola for each day, hour marks can be put on each hyperbola which include any necessary corrections. Unfortunately, each hyperbola corresponds to two different days, one in each half of the year, and these two days will require different corrections. A convenient compromise is to draw the line for the "mean time" and add a curve showing the exact position of the shadow points at noon during the course of the year. This curve will take the form of a figure eight and is known as an "analemma". By comparing the analemma to the mean noon line, the amount of correction to be applied generally on that day can be determined.

You want to know the time?  Buy a watch!

Or a mobile phone.

Sundials are too clumsy to fine tune.  Or: their tune is too fine and it is too clumsy to turn them into clocks.

(He types, looking at the clock.  I'm sure it's accurate to within five minutes or so, but more or less it reads: "Evening".)

And, with a flurry of maths signs, the article finishes in a list of links to helpful sources.

Water Clocks

Around 1400 B.C. (about 3,400 years ago), water clocks were invented in Egypt. The name for a water clock is clepsydra (pronounced KLEP-suh-druh). A water clock was made of two containers of water, one higher than the other. Water traveled from the higher container to the lower container through a tube connecting the containers. The containers had marks showing the water level, and the marks told the time.

Water clocks were very popular in Greece, where they were improved many times over the years. Look at the picture below. Water drips from the higher container to the lower container. As the water level rises in the lower container, it raises the float on the surface of the water. The float is connected to a stick with notches, and as the stick rises, the notches turn a gear, which moves the hand that points to the time.

http://www.arcytech.org/java/clock/clock_history.html

Water clocks worked better than sundials because they told the time at night as well as during the day. They were also more accurate than sundials.

Joost Bürgi, or Jobst Bürgi (February 28, 1552, Lichtensteig, Switzerland - January 31, 1632, Kassel, Hesse-Kassel) was a Swiss clockmaker and mathematician. He invented logarithms independently of John Napier, since his method is distinct from Napier's. Napier published his discovery in 1614, and this publication was widely disseminated in Europe by the time Bürgi published in 1620, at the behest of Johannes Kepler.

There is evidence[1] that Bürgi arrived at his invention as early as 1588, six years before Napier began work on the same idea. By delaying the publication of his work to 1620, Bürgi lost his claim for priority in historic discovery.[2]

Bürgi was also a major contributor to prosthaphaeresis, a technique for computing products quickly using trigonometric identities, which predated logarithms.

The lunar crater Byrgius is named in his honor.

http://en.wikipedia.org/wiki/Joost_B%C3%BCrgi

He made the first clock to have a minute hand.  It was not very precise.

And they were off!  Inventing clocks!

Here's an atomic clock.

Katori uses six laser beams to create a pattern of standing electromagnetic waves. This creates a series of energy wells, each of which supports one strontium atom, in much the same way as each dimple in an egg box holds an egg (see Diagram). This prevents the electromagnetic fields of individual atoms interfering with those of their neighbours, and allows the oscillating signals of many atoms to be measured at once.

Previous attempts to make clocks this way failed because the trapping lasers themselves interfered with the atoms' oscillation frequency. Katori's group has got round this by tuning the frequencies of the lasers so they alter the upper and lower transition energy levels of strontium by exactly the same amount, so the oscillation frequency remains unaltered. Katori claims that this "optical lattice clock" will keep time with an accuracy of 1 part in 10^18.

(Ed: That means it is probably out at any one moment by no more than 1 part in 1,000,000,000,000,000,000)

http://www.newscientist.com/article.ns?id=dn7397

I feel I have wandered into someone's subject!

As Gaianne wrote:

The problem is not with the science as science, but with how science supports a particular philosophical/economic/political agenda.  When the goal of harmony is replaced by the goal of progress, the sustainable is explicitly abandoned in favor of exploitation.

http://www.eurotrib.com/comments/2007/4/16/18483/2608/23#23

Yet there be cycles in them thar subatomic devils.

Hope you enjoyed the trip!

Display:


"Dieu se rit des hommes qui se plaignent des conséquences alors qu'ils en chérissent les causes" Jacques-Bénigne Bossuet
by Melanchthon on Tue Apr 24th, 2007 at 07:35:37 PM EST


Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Tue Apr 24th, 2007 at 08:03:16 PM EST
[ Parent ]
Brilliant, rg.

Now I reckon there's a good Diary to be made pulling together 2012, the end of the Mayan "Long Count" and the "End of Days" beloved of fundamentalists of all religious stripes.

Maybe Gaianne would be up for that?


"The future is already here -- it's just not very evenly distributed" William Gibson

by ChrisCook (cojockathotmaildotcom) on Wed Apr 25th, 2007 at 02:04:17 AM EST
It's been a long, tiring 52,000 years labouring in the Dark. I am looking forward to the Age of Light. ;-)

2012 is, of course, when Planet Earth will enter the giant cosmic beam that will change the clock speeds of all living cells and thus cause the mass mutation of all carbon-based life. We are about to go one more rung up the evolutionary ladder.

Seriously, speaking as a Tellurian (and don't bother to look it up - it's so secret that it certainly won't be in wikipedia), I am amazed how little the human race understands of the big cycles. Everything is measured only in human scale: our weight is what defines things as heavy or light, our lifespan is a stupid unit of time, what our retinas can detect is called light, even though it is a narrow band in a continuous range of radiation. etc

We Tellurians always like to point out what a stop-motion movie of the earth would look like if we took only one frame every 1 year (25 frames make one second of screen time). Human beings (as all creatures) would disappear. Instead we would see the explosive organic growth of habitation, forests dancing across the landscape, and the sea rising and falling like a global tide.

But I think I need another latte to wake up properly...

You can't be me, I'm taken

by Sven Triloqvist on Wed Apr 25th, 2007 at 03:33:10 AM EST
[ Parent ]
by Colman (colman at eurotrib.com) on Wed Apr 25th, 2007 at 04:56:48 AM EST
[ Parent ]
Weren't they on Dr Who once?
by ThatBritGuy (thatbritguy (at) googlemail.com) on Wed Apr 25th, 2007 at 05:21:03 AM EST
[ Parent ]
I thought he was referring to this lot.

And, not that it'll change anyone's mind about anything...

Inscriptions beyond 2012

Maya stela occasionally show dates beyond 2012. Most of these are in the form of "distance dates", where a Long Count date is given with a distance date to be added. For example, on Tikal Stela 10 we find the following Long Count date: 9.8.9.13.0 8 Ahau 13 Pop (24th March 603 AD Gregorian) with a distance date of 10.11.10.5.8. The resulting date is given as 1.0.0.0.0.8 5 Lamat 1 Mol,[8] or 21st October 4772 AD - a 2,000 years into the future.

Summary

Despite the publicity generated by the 2012 date, "we have no record or knowledge that [the Maya] would think the world would come to an end" in 2012.[9]

"For the ancient Maya, it was a huge celebration to make it to the end of a whole cycle," says Sandra Noble, executive director of the Foundation for the Advancement of Mesoamerican Studies in Crystal River, Fla. To render Dec. 21, 2012, as a doomsday or moment of cosmic shifting, she says, is "a complete fabrication and a chance for a lot of people to cash in."[10]

http://en.wikipedia.org/wiki/Mayan_long_count#Inscriptions_beyond_2012



Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 06:05:17 AM EST
[ Parent ]
2012/Maya/etc was invented by Jose Arguelles, following a tried and tested formula:

Pick an exotic ancient culture, preferably one with pyramids

Hint at either an apocalypse, an ascension, or both.

Arguelles got extra points because he also incorporated DNA and the I Ching into his ramblings.

(Nice work if you can get it.)

by ThatBritGuy (thatbritguy (at) googlemail.com) on Wed Apr 25th, 2007 at 07:15:35 AM EST
[ Parent ]
I agree. I incorporated into the Bonk Busines Inc. comic mythology for this reason.

But, on the other hand, I find all fiction fascinating. Especially when it oscillates around peoples' ill-informed perceptions - which is basically what life is about ;-)

You can't be me, I'm taken

by Sven Triloqvist on Wed Apr 25th, 2007 at 09:17:42 AM EST
[ Parent ]
Bonk Business!

Ah!  I needed that.

Ill-informed perceptions.  Ouch!

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

by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 11:55:48 AM EST
[ Parent ]
Where did you find it? We took everything off the web in '93! It was the first HTML website in Finland for Tele (then the state telecoms company)

We still have a site for our museum in Uusikapunki http://www.bonkcentre.fi/p2_eng.htm - so I guess you found it there ;-)


You can't be me, I'm taken

by Sven Triloqvist on Wed Apr 25th, 2007 at 12:11:02 PM EST
[ Parent ]
I googled bonk business, clicked images, and there it was.

You are part of that?  KEWL!

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

by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 12:48:49 PM EST
[ Parent ]
I co-founded it, with the painter of the picture above. The project took nearly 7 years of my life more-or-less full time, and we still have 15000 visitors a year to the museum ;-)

You can't be me, I'm taken
by Sven Triloqvist on Wed Apr 25th, 2007 at 01:26:15 PM EST
[ Parent ]
Great diary BTW. I am only sad that the TV series is taking so much of my TIME that it is hard to be here. But I try to check in every day - if only to read.

Tomorrow we have the first preview for journalists. You don't have a McCain critic-proof vest about your person, perchance?

You can't be me, I'm taken

by Sven Triloqvist on Wed Apr 25th, 2007 at 01:29:43 PM EST
[ Parent ]
Do you have to be there?  Man of Mystery...never turns up.

Or wear a ridiculous hat and keep a straight face...

Surely they wouldn't criticise it while you're there though?  That's what their articles will be about.

So...avoid buying newspapers while the moon swims between the dolphin and the newt.

(rg astrology services.)

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

by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 01:32:27 PM EST
[ Parent ]
I had considered that option, but I got the news today at 13.30 that one of our stars had a heart problem and was in fairly intensive care. I may be partly responsible, because I decided to continue with an outdoor shoot on Monday evening in +2 degress and cold drizzle. So I shall have to turn up tomorrow to handle that.

It was not an easy decision. It was the last night of the funfair where I had got permission to shoot, before they go up north on tour and become inaccessible to our budget.

Our actor was the leading figure in This rock band of the Seventies. The name of the band means 'Mad John'. You can understand why I would be attracted to them ;-)

You can't be me, I'm taken

by Sven Triloqvist on Wed Apr 25th, 2007 at 01:52:51 PM EST
[ Parent ]
It's a TV series, have I got that right?  When's it going out?  And when are the (hopefully subtitled) youtube clips going to appear?

(Boo hoo!  No flash chez rg.  No youtube.  No videos.  The most moving my computer gets is a .gif animation.)

(Especially annoying when now is the time I could watch great videos of the various cycles of earth, moon, sun, stars...)

(Luckily I have sun-venus-moon doing their dance outside my window at the moment, though it's more like the end of a friendship...the moon arriving ever later...Venus going ever earlier...until next time round...which will be over a year, I think--my astonomical calculating device--YE NOGGIN--need oiling.)

(Sip...ah.)

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

by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 03:45:00 PM EST
[ Parent ]
I think you are as sceptical as I am: but unlike others, you are prepared to juggle with decent alternative explanations until such time that they are proved truly fallacious - though they would still exist as a product of some sub-group of humans' imagination. Thus just as real, IMO, as anything else.

Unless one is prepared to learn to jump effortlessly between so-called 'reality' and so-called 'fiction', I think the chances of finding love and happiness in this world are rather slim. ;-)

We've both found that, don't you agree? Not together, of course. I couldn't co-habit with someone who decorated all the time ;-)

You can't be me, I'm taken

by Sven Triloqvist on Wed Apr 25th, 2007 at 12:24:43 PM EST
[ Parent ]
I may be wandering into...well...

Is the following simple fiction?

There have been various methods proposed to allow us to convert from a Long Count date to a Western calendar date. These methods, or correlations, are generally based on dates from the Spanish conquest, where both Long Count and Western dates are known with some accuracy.

The commonly-established way of expressing the correlation between the Maya calendar and the Gregorian or Julian calendars is to provide number of days from the start of the Julian Period (Monday, January 1, 4713 BCE) to the start of creation on 0.0.0.0.0 (4 Ajaw, 8 Kumk'u).

The most commonly accepted correlation is the "Goodman, Martinez, Thompson" correlation (GMT correlation). The GMT correlation establishes that the 0.0.0.0.0 creation date occurred on 3114 BCE September 6 (Julian) or 3114 BCE August 11 (Gregorian), Julian day number (JDN) 584283, the number of days since the start of the Julian Period. This correlation fits the astronomical, ethnographic, carbon dating, and historical sources. However, there have been other correlations that have been proposed at various times, most of which are merely of historical interest, except that by Floyd Lounsbury, two days after the GMT correlation, which is in use by some Maya scholars.

Today, 14:54, Wednesday April 25, 2007 (UTC), in the Long Count is 12.19.14.4.13.

(My emphasis)

As they counted using astronomical events and were interested in cycles, it's not surprising that one of their cycles will end at an astronomical event.

Maybe I'm just getting some sparks in my brain, but ancient cultures with pyramids and other astronomical features have an interest because, among other things, they show the ancient culture's astronomy and, by inference, tell us something of how the culture viewed its movement through time and space (D'où venons-nous ? Que sommes-nous ? Où allons-nous ?.)

I'm sure some over-doped people have invented theories from this...who among us has never been over-doped and invented a crazy theory?

Oh...cough cough.

And maybe some people write their theories in books and sell a lot and make money.

But I don't see the "crazy theory" types as subtracting from analysable historical artifacts (eg. pyramids, both egyptian and mesoamerican, but not just pyramids...have a looksee at this...)

Which, when polished up might have looked like this.

...they think.

The Antikythera Mechanism  

I see the crazy theories as...well...crazy theories.  More entertaining than the ones told in religious buildings and maybe with a few more shafts of something real sneaking through...

...may just be sparks in my head...

(...and may I just add that when I think of "gullible people" I don't think of hippies being conned by ancient stories, I, more depressingly, think of people turning up to these meetings...

Eight million and counting!  Quick!  I need...something funky!



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

by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 11:46:33 AM EST
[ Parent ]


You can't be me, I'm taken
by Sven Triloqvist on Wed Apr 25th, 2007 at 12:42:08 PM EST
[ Parent ]
It sure isn't the End (according to the mythology: reconstructed or invented). It is a transformation.

You can't be me, I'm taken
by Sven Triloqvist on Wed Apr 25th, 2007 at 09:21:28 AM EST
[ Parent ]
What is the astronomical meaning of the year 2012? I can discern two interpretations. They are both related to precession of the equinoxes (or equinoctial cycle, the Platonic year, or Great year). It is the cycle of approximately 25800 years for one woble of the Earth axis around the ecliptic north pole. Equinoxes move as well, through the ecliptic. The Platonic year can be subdivided into 12 "months" by the Zodiac sign of the vernal equinox. Astrologically, the "months" are astrological ages.

Haven't you wondered why the 4 equinoxes & solstices roughly coincide with boundaries of Zodiac signs? Did you assume the coincidence by design? Think again... The Sun is leaving Pisces and entering Aquarius on vernal equinoxes. We are entering the Age of Aqarius. (Do a Google search of what that means.)

By some versions, the year 2012 is the moment of astrological age change.  But boundaries of Zodiac constellations are debatable. If you follow official boundaries of International Astronomical Union, the Aquarius age starts in 2595 or so.

By other version, the mystical date of December 21, 2012 is a coincidence of the winter solstice point (obviously) and the galactic center. This detailed (though maybe somewhat erratic) astrological source states that what Maya called "the Sacred Tree" is the intersection of the ecliptic and the Milky Way (galactic equator). At noon of December 21, 2012 the Sun sits "right" on the Sacred Tree.

by das monde on Thu Apr 26th, 2007 at 05:39:37 AM EST
[ Parent ]
I might be getting more crazy than anyone before, but... what about this coincidence?

The distance to the galactic center is 8 kiloparsecs, or 26000 light years. The Platonic year is about 26000 years long...

Does there have to be a straight correlation between axis precession of livable planets and their distance to the galactic center?

by das monde on Thu Apr 26th, 2007 at 05:47:56 AM EST
[ Parent ]
By other version, the mystical date of December 21, 2012 is a coincidence of the winter solstice point (obviously) and the galactic center. This detailed (though maybe somewhat erratic) astrological source states that what Maya called "the Sacred Tree" is the intersection of the ecliptic and the Milky Way (galactic equator). At noon of December 21, 2012 the Sun sits "right" on the Sacred Tree.
Wow, that is a cool coincidence.

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Thu Apr 26th, 2007 at 05:48:55 AM EST
[ Parent ]
by ThatBritGuy (thatbritguy (at) googlemail.com) on Thu Apr 26th, 2007 at 05:28:29 PM EST
[ Parent ]
What a great link!

Check out the article on the precession of the equinoxes.

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

by rg (leopold dot lepster at google mail dot com) on Thu Apr 26th, 2007 at 07:12:07 PM EST
[ Parent ]
Thanks! Now back to work :-)
by das monde on Thu Apr 26th, 2007 at 08:33:05 PM EST
[ Parent ]
Read more about the different measures and concepts of time in my earlier Central European Time diary.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Wed Apr 25th, 2007 at 07:18:07 AM EST
So...the world was running on "apparent" time until the clocks became accurate enough, in Europe, in the period 1660-1700, to take over.  Before then, the equation of time--as a problem--was only seen by astronomers.

Wiki sounds a bit imprecise here. It wasn't just clocks, but also star time (time as measured by the progression of stars on the firmament) that was off solar time. And one more profession could notice this: ship navigators.

The clock was the time source; they could now begin to forget about the sky--unless it interested them.

No, no, no! Both together were needed to give geographical location! The ships' clocks ran on Greenwich time (well -- most did, including all British), while the Sun's passage of the North-South line in the sky + the correction from Nautical Almanach, resp. certain stars' position and some formulas gave the local mean solar time -- and the difference gave longitude relative to Greenwich.

*Lunatic*, n.
One whose delusions are out of fashion.

by DoDo on Wed Apr 25th, 2007 at 07:30:10 AM EST
I remember R. Buckminster Fuller's unique (? for anyone who has read it...cough cough cough!  Though I'll admit to loving it) theory, in his book Critical Path, about how any mariner with a sail will see the stars or the sun or the moon moving relative to the mast...and start calculating accordingly.

Somehow--may have been drugs!--I was getting a sense of clock time as...losing flexibility...losing time = losing money = growth of Empire's needs...

My thinking was: mariners already knew how the sun and the stars went together.  So, the clock added specific accuracy--to what end?  Was it to avoid reefs, or other nautical perils, or was it because larger boats could drift more, or were harder to steer once danger beckoned?

One more thing: you say star time was off solar time.  I'm not sure what you mean by "off".

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

by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 07:56:28 AM EST
[ Parent ]
Star time has to do with the rotation of the earth about its own axis, and the [sidereal] day. From [sidereal] day to [sidereal] day, the sun will change where it rises and sets, its zenith, and how long it takes betweeen rising, setting ans rising again. Sundials have lots of problems.

Since this is all rather complicated and dependent on latitude [and if you're on a ship, changes in longitude, too] you need something more regular. The clock is as regular as star time, with the added benefit that you can use it regardless of dailight or atmospheric conditions.

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

by Migeru (migeru at eurotrib dot com) on Wed Apr 25th, 2007 at 08:02:42 AM EST
[ Parent ]
It was rail that mandated accurate national time. It's very difficult to run a national timetable without a central reference.

You can still find antique timetables which aren't corrected for GMT. The guard would have either have to keep adjusting his watch, or add and subtract a certain time offset in his head.

Central standardised time - and it might as well be mean time, to make life simpler - becomes inevitable once people start travelling faster than a horse does.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Wed Apr 25th, 2007 at 09:09:54 AM EST
[ Parent ]

I was sure I'd read that it wasn't so complicated for ancient mariners.  After all, they were crossing the seas thousands of years before the clock.

Have you heard of this?

Avoiding Chrichton Miller's theories about whatever he theorises about, do these technological explanations sound feasible?

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

by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 11:23:05 AM EST
[ Parent ]
I was sure I'd read that it wasn't so complicated for ancient mariners.  After all, they were crossing the seas thousands of years before the clock.

True. Before they had accurate clocks on board, they'd just sail on a parallel (a set latitude) and just wait until they'd arrive at destination. They'd just check the maximum height of the sun to remain at the set latitude. They didn't know their longitude E or W.

I have a question (Mig or DoDo ?) : is it possible to calculate some value of time just by sun / moon / stars observations ?

by balbuz on Wed Apr 25th, 2007 at 12:25:18 PM EST
[ Parent ]
I have a question (Mig or DoDo ?) : is it possible to calculate some value of time just by sun / moon / stars observations ?

How much time do you have to make the observations?

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

by Migeru (migeru at eurotrib dot com) on Wed Apr 25th, 2007 at 12:41:58 PM EST
[ Parent ]


You can't be me, I'm taken
by Sven Triloqvist on Wed Apr 25th, 2007 at 12:43:33 PM EST
[ Parent ]
There was an alternative technique for fixing longitude based on moon phase and position, but the maths was too scary to make it practical.

Galileo also proposed used the positions of Jupiter's moons as a very distant clock.

For obvious reasons, neither of these ideas was as useful as having an accurate timekeeper.

There's a good overview here.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Wed Apr 25th, 2007 at 02:48:48 PM EST
[ Parent ]
The author has proved beyond reasonable doubt that Ancient mariners could determine longitude by the application of simple geometry[1] without the use of a time piece by utilise the retrograde action of the moon against the fixed stars.

http://www.crichtonmiller.com/longitude.htm

I don't have the tech. knowledge to know whether this guy is making things up or telling the truth, but I've been linking to his info.  He is claiming that there was, indeed, a simple way of measuring both latitude and longitude using a device based on the celtic cross.

Is he crazy?  Is it nonsense?  Certainly he is claiming that this was used thousands of years into the past.  I'm very interested in reading a tech person's view(s) of this guys tech. theories.

What I mean by that is: he has a lot of other theories too, but...does his device work?

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

by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 03:52:01 PM EST
[ Parent ]
Lattitude, yes, it was used as a primitive sextant, Longitude, not a hope in hell, unless you had a boat full of them and layed them end to end while you were sailing.

Any idiot can face a crisis - it's day to day living that wears you out.
by ceebs (ceebs (at) eurotrib (dot) com) on Wed Apr 25th, 2007 at 05:00:05 PM EST
[ Parent ]
Ceebs...indulge me.

Here is what I understand, tell me where I go wrong.

[edit]

How to mark a standard time reference before Greenwich and clocks?  What could be the same for all, yet different at different longitudes?

Well...nothing.  There has to be a reference point.  So, how about where you live?

[edit]

Ceebs!  My mind is blown again!

Look at draco (but you know all this!  Humour me!)  There it lies, at the centre of the ecliptic pole.  The true centre...is dark.  No star.

Well...

Maybe not....

The ecliptic pole.  I needed that.  Our celestial pole is at the bottom of Ursa Minor, the last star.  Polaris.  In the time of the Egyptians (have I understood this correctly?) our north pole pointed more or less directly at the third star in Draco's tail.

H - Upper position (in relation to the galactic
equator) of the North celestial pole.
L - Lower position of the North celestial pole.
G - Line of the Galactic equator.

http://www.pakhomov.com/duat.html

The galactic equator...

Another wheel!

It's like taking mushrooms, but it isn't.  How about learning all this, and then taking mushrooms?

Whoooosh!

Celestial north, south, east, west

(indulge me!_

Ecliptic north, south, east, west.

Galactic north, south, east, west.

The moon.

The planets.

Add psilocybin, a hill, a clear sky, no unwanted earth-light, warmth, soft grass, like back...

VOOOOM!

And the report back?

Hyperbolic trajectories!

Every year, about 4500 meteorite falls each drop at least 1 kg of extraterrestrial material on earth. Falls are more common in the afternoon than in the morning hours, and are about 10% above average near the spring equinox and a similar amount below average at the autumnal equinox. The influx rate also varies somewhat with latitude: at the equator, the yearly average meteorite rate exceeds the normal value for the entire earth by 5% while the geographic poles experience 90% of the mean rate.4

http://ourworld.compuserve.com/homepages/dp5/dust2.htm

Ach...I ramble.

...so...recapping.  Longitude is time from somewhere.  You look up.  There is Draco.  It marks out the spot above the sun.  There is the moon.  It measures time against the sun (in degrees--and therefore in minutes and seconds?)  There are the stars.  We don't point to the ecliptic pole.  We point to the celestial pole.  Polaris.  This difference is enough, if measured accurately, to work out where we are on the planet...because...

we know where the moon should be, relative to the stars.  And at two different points on the globe, the difference: moon, pole star, draco = movement?

The Method

The only way to navigate by the moon is to work out the angular differential from a star over time and motion with the help of an almanac reference
This requires tracking the moon along the ecliptic and using certain stars in known constellations that the Egyptians called a decan of which there were 36 in one complete Zodiac to make up 360 degrees.
But that knowledge is insufficient on its own, there is a crucial requirement, an instrument of sufficient accuracy
The moon tracks over the earth at 720 nautical miles per hour and moves against the zodiac (a great circle) 30 arc minutes in 60 minutes of time during which the position of the observer has spun through 900 nautical miles on a great circle.
To find a longitude position by measuring the angular difference requires an accuracy of observation of at least 1 arc minute to achieve a longitude accuracy of 15 nautical miles at the equator reducing in proportion by latitude.

http://www.crichtonmiller.com/longitude.htm

So the questions are:

1) Could humans many years ago have worked this out?

My answer: yes.  They had the sky.  They had time.  They had brains like ours.  Earth--axis.  Sun--axis.  Moon--relationship.

???

Did humans long long ago--thousands of years, counting 2,3,4, and beyond...beyond even the disappearance of..the ice...

During the most recent North American glaciation, the Wisconsin glaciation (70,000 to 10,000 years ago), ice sheets extended to about 45 degrees north latitude. These sheets were 3 to 4 km thick.

http://en.wikipedia.org/wiki/Ice_age#Recent_glacial_and_interglacial_phases

...did they know this more than 10,000 years ago?  I can't see why not.  (It's taken me about a week to start getting my head around it.)

2) Did they have the mechanical means to use this information for longitudinal navigation?  Did they have a sense of lateral time?  -- I am here now, and you are there now, but where you are, it is a different time...of day and, if you are in New Zealand, year.  But it is still Now.

So...now where am I?

Did they have measuring devices for that?  Which would have been useful to understand where on earth they were, relative to their home.  And I'm assuming everyone knew the earth was a globe.  (Well, I'm assuming those who had worked out the relationship of the celestial pole to the ecliptic pole knew the earth was a globe.)

The galactic equator!  The galactic north pole!

As I understand it, the argument comes down to: did they use snakeskin as an exponential device in order to calculate longitudinal movement?  Why would they need it?  Because they sailed across seas, I assume.  A nagivator's riddle.  Where am I?  Where am I going?  How far am I from where I started?

The skin of a snake is exponential and can be used with a plumbline to measure angles accurately to arc minutes when placed on a cross bar.

http://www.crichtonmiller.com/sophia.htm

Crazy theories!

But I learned about longitude, and the celestial equator, and...yes!  The ecliptic north pole!

Ah, the power of the internet...I ramble to this screen and get to see...the universe in pictures.

Cough cough!

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

by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 07:26:05 PM EST
[ Parent ]
I'm assuming everyone knew the earth was a globe.

There is no evidence for anyone at the time of Columbus thinking the world was flat. in fact the flat earth story was the invention of Washington Irvine,

The ancient Greek and Egyptians new that the world was round and calculated its size correct to within 1% and 5% respectively, and considering that they used people who paced out the distance between  Thebes and Cairo as a basline for the calculations that wasn't bad.

The timepeice is still the difficult step in calculating longitude, without complicated calculations. although if you wish to take on these calculations there is evidence of a variety of observatories in India, china and (I think)Iran. to work out the difference, you would have needed to combine the observations at these several sites to work out what was happening.

could they have done it thousands of years ago? that's hard to say, If you ask an Archaeologist, youll just get the answer of it being "Ritual" which is their get out line when they don't want to say "We don't know".

Any idiot can face a crisis - it's day to day living that wears you out.

by ceebs (ceebs (at) eurotrib (dot) com) on Wed Apr 25th, 2007 at 08:40:55 PM EST
[ Parent ]
I now chewed some more on this Crichton Miller's claims (your post actually helped to make more sense of them), so now I see the following problems and errors.

  1. A star clock "runs" on stellar time, that is one full rotation per the actual rotation period of the Earth, 23 hours 56 minutes 5.09 seconds. To determine solar time from that on a fixed location, you need to know the date, multiply by a factor, and know a reference moment.

  2. Crichton wants local midnight as reference moment, as determined by the position of the ecliptic pole-surrounding part of Draco and an almanach giving the angle of the Sun relative to it at a given date. That is less easy than it sounds. There is not one but four error factors: positions of the ecliptic and equatorial poles, that of the vertical line (the plumbline), and that of the almanach/resp. date. The last warrants its own separate point:

  3. if you want to use the star clock to determine local midnight, you face a recursive problem. To know the equatorial position angle of the Sun relative to Draco, you'd need a time data. You know the date, but the Sun moves c. 1° a day, so if say you can guess your geographical location and local time with a precision of 13 degrees and 50 minutes, that'll give a 3 arc second error.

  4. The Moon is close enough to the Earth for its position to the stars appear rather different from different geographical locations. To be precise, the variation is up to 61 arc seconds. Again, like in the previous point, in theory the ancient navigator would first have to guess his position and time, but in practice I don't think there were almanachs or calculation methods correcting for the Moon's apparent position.

  5. Also, the Moon has an elliptic orbit titled to the Eclyptic, complicating the job of almanach writers/calculating navigators.

  6. I didn't get what is the significance of the exponentiality of a snake's skin('s pattern). If it is to put it on a nautical cross, then the projection of even divisions on an arc onto a tangent to that arc (e.g. the scale beam of the cross) is, well, tangential, which is approximated by exponential at small angles.

  7. Though impractical, the basic idea makes more sense than I thought at first sight (and reading stuff like "Serpens constellation of Draco"), though he explains it rather clumpsily.


*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Thu Apr 26th, 2007 at 08:34:49 AM EST
[ Parent ]
I'm way out of my depth.

So...

  1. 2) 3).  They had time to work out the cycles: the lunisolar 18.6 year cycle, say.  So they could count from a solstice or an eclipse--something exact--around that cycle?   Re: equipment.  They had time to refine both the materials and their usage of them.  I'd assume there was no rush?  They were developing a technology but not necessarily under time pressure?

  2. 5) Maybe a question is: how accurate did they have to be?  In the same way that the sundial is fine for normal daily tasks, but not good for bringing a train in "on time" when the train has travelled fast from east to west or vice versa; so the question: how regular did they need their time pulse to be?  How accurate did their time-keeping have to be?  I'd guess: it depended.  They took advantage of any improvements in accuracy as they suited their needs.  (Maybe to travel across larger bodies of water in directions other than east-west?)  Would a daily reading be necessary, or a weekly reading, or a monthly reading?  Then they'd have their almanacs--or some other device(s)--to check against.

Migeru wrote it would not be possible to read off the necessary moon movement with the naked eye--even using the device.  I wouldn't know...

...the snakeskin is needed for the accuracy somehow...maybe to pinpoint and then to read off?  Because snakeskin was a finer measure (the tip of the scale--yet still visible to the human eye--than any manmade mark--at the reading end, not just for the tangential?

(I think he's in wild speculation with the snakeskin...but I enjoy wild speculation!)

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

by rg (leopold dot lepster at google mail dot com) on Thu Apr 26th, 2007 at 10:06:04 AM EST
[ Parent ]
rg,

to even know that one can determine longitude through the apparent position of the moon against the fixed stars, one would have to have compiled accurate almanacs at two widely separated locations, and then compared them.

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

by Migeru (migeru at eurotrib dot com) on Thu Apr 26th, 2007 at 10:21:36 AM EST
[ Parent ]
An intriguing thought.

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Thu Apr 26th, 2007 at 12:01:20 PM EST
[ Parent ]
1)2)3) In general, what astronomers at a fixed location work out is one thing, what navigators on a moving ship apply is another. In particular, I don't follow you :-) What do you use the eclypse for? And what about equipment? If you meant my notes on precision, the issue is not the instrument but the person who holds them before the sky on the shaking ship.

4)5) Regarding how accurate, much more accurate than 61 arc seconds. That's about twice the Moon's apparent diameter, and the distance the Moon travels in the sky in 111 minutes! If we go from time to latitude, it is not nice at all.

Migeru wrote about measurement precision, e.g. you want to measure the position of the center of the moon, but you have a luminous object just below 30 arc seconds in diameter.

To emphasize what gave me for thinking about the snakeskin, it wasn't simply its use, but this:

The skin of a snake is exponential

I'm not sure what's exponential about it BTW, I tipped that the scales get bigger away from the head or something.

*Lunatic*, n.
One whose delusions are out of fashion.

by DoDo on Thu Apr 26th, 2007 at 10:27:02 AM EST
[ Parent ]
Oh, and to correct myself: those 61 seconds are half of the actual variation of the apparent angle of the Moon as seen from the Earth.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Thu Apr 26th, 2007 at 10:33:55 AM EST
[ Parent ]
The guy is probably thinking about geometric growth and the Fibonacci sequence (see this page for instance). And that's being charitable.

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Thu Apr 26th, 2007 at 10:34:54 AM EST
[ Parent ]
In particular, I don't follow you :-)

DoDo, I don't follow myself either!

Backing way up: all I (mis?)understand is:

It's possible (using specific events such as eclipses) to bring exactitude to our study of the earth-sun-moon-stars relationships.  We can measure different combinations, so I'm assuming that ancient peoples could in theory have known how to calculate movement west-east/east-west.

(And as Migeru said: why would they think there'd be any difference, unless they had travelled east-west/west-east, taking their almanacs, far enough to discover the differences--or else they met people from somewhere else who had almanacs...which didn't match?  I like this idea because either

a) two different groups came to the same conclusions re: rotation, position, etc...

or

b) the various groups were, in fact, connected--just maybe not at the speeds we imagine; maybe they communicated once a year or even less?  I have no idea.  I just like the concept.)

I can imagine that people who knew of other locations could work out their longitude relative to those other locations (did I read somewhere that the pyramids were an ancient equivalent of Greenwich?  Zero = the north south line between a pair of pyramids or somesuch.)

Then I can imagine someone attempting to do this on a boat--no success.  Maybe they would try different techniques, different devices.  This guy's device...has he tested it at sea?  Certainly it seems that holding something out at arms length while one gently or not so gently bobs up and down does not sound right.  So then my question about minimum useful measurements.  You're saying that the minimum feasible is the width of two moons, which is a useless measurement?

When it comes to degrees I get lost.

(I thought latitude wasn't a problem--you measure a star's height against the horizon or somesuch...I could well be wrong...I really am out of my depth at this point.)

With the snakeskin, I think he wanted his theory to match up to...all the signs.  I suppose it's possible to e-mail him and ask what he meant.  

And...bowing humbly...

I thank you again!

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

by rg (leopold dot lepster at google mail dot com) on Thu Apr 26th, 2007 at 12:26:04 PM EST
[ Parent ]
Who are these people you're talking about?

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Thu Apr 26th, 2007 at 12:33:22 PM EST
[ Parent ]
The ones who travelled around, you mean?  Who knows?  Maybe no one did, I just like the idea.

Certainly God doesn't like the idea that people once upon a time were sharing knowledge:

11:5  Yahweh came down to see the city and the tower, which the children of men built.

11:6  Yahweh said, "Behold, they are one people, and they have all one language; and this is what they begin to do. Now nothing will be withheld from them, which they intend to do.

11:7  Come, let's go down, and there confuse their language, that they may not understand one another's speech."

11:8  So Yahweh scattered them abroad from there on the surface of all the earth. They stopped building the city.

11:9  Therefore the name of it was called Babel, because Yahweh confused the language of all the earth, there. From there, Yahweh scattered them abroad on the surface of all the earth.

http://www.awitness.org/biblehtm/ge/ge11.htm

These are old pre-flood/post-flood myths, seen through the eyes of the Torah; I prefer myths that involve some happy humans somewhere communicating and getting along.  The stars...seem a useful, because obvious, point , which might be the same myth seen a different way (except for the God confusing everyone part.)  Certainly we have myths of before/after and the only cataclysmic before/after we have is the ending of the last ice age, which would confound all old social relationships...unless one were free from the effects--isolated.  Yet it seems that all communities have flood myths; which would make sense if there were a global connection network pre-melt...

...contact between disparate groups.  You mentioned that to understand the concept of longitude (or maybe I misunderstood!), one would have to have an almanac and then travel with it.

I don't know how far you'd have to travel west-east/east-west before the naked eye and memory pointed out that things had changed.  Maybe never?  See how little I know!  In my imagination I see a person far from home, staring up at the sky as the moon goes past and thinking, "Hold on.  That shouldn't be there, it should be over there."  His friend from the other faf-flung tribe pats his knee.  "Happened to me first time I came to where you live.  Here, have one of these.  It'll help," he adds, handing him a large mushroom...

*:R

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

by rg (leopold dot lepster at google mail dot com) on Thu Apr 26th, 2007 at 01:12:04 PM EST
[ Parent ]
That about latitude was a brain-typo, of course I meant longitude.

I now get what you mean with the eclypses, e.g. that the ancients could have been aware of the Moon's parallax and put that in almanachs. This is the case at least with the Greeks -- Hipparchos is credited with the measurement of the Moon's parallax using a soler eclypse (probably 129 BC).

But for a navigator to get the parallax at an unknown location, that's another thing. So if, say, we want to get the error under just 3' for the Moon anywhere in the sky, the guessed location must be precise by 320 kilometres, while the error of the final result will be around half of that or more -- not very efficient.

*Lunatic*, n.
One whose delusions are out of fashion.

by DoDo on Thu Apr 26th, 2007 at 05:00:09 PM EST
[ Parent ]
Maybe....just maybe...

it's the difference between landing at Standstead--miles from London!  Where to stay?

and landing in a country where they know of you and welcome you; and if you arrived a hundred miles (or whatever measurement you choose)...away from where you were heading...there wasn't a problem.

So I think the problem must have been aiming at small islands.  They are the things you can miss.

If it was a problem; and if they didn't have alternative navigational methods as adjuncts to--or even alternatives to--the sky.

If you ask the following question:

"That's north, that's south, that's east, that's west" pointing, "Are we moving?  And if we are, which way are we moving?"

If they look confused, you say, "The sun rises in the east and," drawing an arc, "it sets in the west.  Which way are we moving?"

I asked a colleague today.

"Clockwise," she said.  "I suppose we're moving clockwise."

But, for an hour or so she was as fascinated as me by the basic movements of planet (spin), sun (axis), moon (moooovement), and stars (tick tock)....

What was the measure of efficiency before those huge ice-sheets melted?  Because humans have been around for long before they melted.  I'm beginning to think...hmmm...who wouldn't have been inundated?  Who would'nt have had their life revolutionised.  Maybe some people in India, in China, the himalayas must have changed; but maybe they changed, and the inhabitants could change with the himlayas, which are still growing...

Bhutan has an "Annual Happiness Index"...or somesuch.  Was it Laurent who pointed out the ridiculousness of GDP?  It's ridiculous.  An overthrow, and overhang, of Empire.  "It's over there, grab it!"

The sun is our source of life.  If we harness the sun's powers...we still live on an unstable ball of energy, with fruity effects--us!

So risk is ever present.  But now people have no sense of solar risk, or lunar risk, or stella risk.  All the risks are human-created.  War.  Famine.  Destitution.

DoDo!

You got me rambling!

Thanks for all your input.  Very much appreciated!

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

by rg (leopold dot lepster at google mail dot com) on Thu Apr 26th, 2007 at 07:04:11 PM EST
[ Parent ]
You got me rambling!

And you got me thinking! Thinking about a hypothesis I would normally have dismissed out of hand (due to its bad wording). Soon I'll post a second summary as top-level comment.

*Lunatic*, n.
One whose delusions are out of fashion.

by DoDo on Fri Apr 27th, 2007 at 03:59:31 AM EST
[ Parent ]
Does (4) refer to the Moon's parallax or to the 1 degree per day shift in the "star time" due to the Earth's orbit around the sun?

If you're at the same latitude on the same night, there should be no parallax.

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

by Migeru (migeru at eurotrib dot com) on Thu Apr 26th, 2007 at 10:39:53 AM EST
[ Parent ]
Parallax. There is parallax between the position as observed by the almanach-makers and the position as observed by the ship navigator, and that both due to latitude and longitude.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Thu Apr 26th, 2007 at 10:44:35 AM EST
[ Parent ]
But if you observe at "local midnight" you cancel the longitudinal parallax.

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Thu Apr 26th, 2007 at 10:48:16 AM EST
[ Parent ]
No way, think it over.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Thu Apr 26th, 2007 at 11:15:39 AM EST
[ Parent ]
I got struck where he describes the establisahment of the "prime meridian". It doesn't make sense to me.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Wed Apr 25th, 2007 at 06:10:21 PM EST
[ Parent ]
As far as I can make out he's proposing to measuring longitude by measuring the the apparent position of the Moon at "local midnight".

15 degrees of latitude is one hour of difference in local time, during which the moon will move by 33 arc minutes (about one Moon apparent diameter). So that's the kind of accuracy we're talking about.

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

by Migeru (migeru at eurotrib dot com) on Wed Apr 25th, 2007 at 06:17:52 PM EST
[ Parent ]
So  about accurate enough so you could be standing in England or France and not know the difference from your observations.

Any idiot can face a crisis - it's day to day living that wears you out.
by ceebs (ceebs (at) eurotrib (dot) com) on Wed Apr 25th, 2007 at 06:28:50 PM EST
[ Parent ]
He does say
An instrument capable of sidereal measurement to 1 arc minute would result in an accuracy of 7.5 nautical miles at 45ºN
The problem is that he's assuming he can locate an object 31 arc minutes across to 1 arc-minute accuracy.

It is one thing to determine the distance between two (pointlike) starts to 1 arc minute by naked eye (with the aid of his instrument) but quite another to locate the moon to that accuracy.

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

by Migeru (migeru at eurotrib dot com) on Wed Apr 25th, 2007 at 06:36:03 PM EST
[ Parent ]
(oh so humbly!)

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:

The hour was originally defined in ancient civilizations (including those of Egypt, Sumer, India, and China) as either one twelfth of the time between sunrise and sunset or one twenty-fourth of a full day. In either case the division reflected the widespread use of a duodecimal numbering system. The importance of 12 has been attributed to the number of lunar cycles in a year, and also to the fact that humans have 12 finger bones (phalanges) on one hand (3 on each of 4 fingers). (It is possible to count to 12 with your thumb touching each finger bone in turn.) There is also a widespread tendency to make analogies among sets of data (12 months, 12 zodiacal signs, 12 hours, a dozen).

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...

The Ancient Egyptian civilization is usually credited with establishing the division of the night into 12 parts, although there were many variations over the centuries. Astronomers in the Middle Kingdom (9th and 10th Dynasties) observed a set of 36 decan stars throughout the year. These star tables have been found on the lids of coffins of the period. The heliacal rising of the next decan star marked the start of a new civil week, which was then 10 days. The period from sunset to sunrise was marked by 18 decan stars. Three of these were assigned to each of the two twilight periods, so the period of total darkness was marked by the remaining 12 decan stars, resulting in the 12 divisions of the night. The time between the appearance of each of these decan stars over the horizon during the night would have been about 40 modern minutes. During the New Kingdom, the system was simplified, using a set of 24 stars, 12 of which marked the passage of the night.

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

the duration of 429,228,004,229,952 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the strontium atom at rest at a temperature of 0°K.

;)

(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.

by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 01:57:32 PM EST
[ Parent ]
There are non-anthropomorphic reasons for a duodecimal number system.

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."

by Migeru (migeru at eurotrib dot com) on Wed Apr 25th, 2007 at 03:09:22 PM EST
[ Parent ]
it is trivial to divide a circle into 12 equal sections

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?

After hearing of Roman Catholic Maya who continued to practise "idol worship", he ordered an Inquisition in Mani ending with a ceremony called auto de fe. During the ceremony on July 12, 1562, a disputed number of Maya codices (or books; Landa admits to 27, other sources claim "99 times as many") and approximately 5,000 Maya cult images were burned. The actions of Landa passed into the Black Legend of the Spanish in the Americas. Describing his own actions later, Landa wrote that:

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



Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 04:33:52 PM EST
[ Parent ]
The Greeks established Alexandria.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Wed Apr 25th, 2007 at 05:55:54 PM EST
[ Parent ]
Alexandria was created by Alexander the Great

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

by Melanchthon on Wed Apr 25th, 2007 at 07:07:02 PM EST
[ Parent ]
Humble bow.

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.

Demetrius himself was a former ruler, no less than a ten-year tyrant of Athens, and a first-generation Peripatetic scholar. That is, he was one of the students of Aristotle along with Theophrastus and Alexander the Great.

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?

Scholars were invited there to carry out the Peripatetic activities of observation and deduction in math, medicine, astronomy, and geometry; and most of the western world's discoveries were recorded and debated there for the next 500 years.

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.

Aristeas, writing 100 years after the library's inception, records that Ptolemy I handed over to Demetrius the job of gathering books and scrolls, as well as letting him supervise a massive effort to translate other cultures' works into Greek. This process began with the translation of the Septuagint, the Old Testament, into Greek, for which project Ptolemy hired and housed 72 rabbis at Demetrius' suggestion. [Letter of Aristeas 9-10].

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.

by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 07:59:55 PM EST
[ Parent ]
While we're on the topic of crop circles and division by 12...

You can make that crop circle with a single piece of string, a stick and a plank.

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

by Migeru (migeru at eurotrib dot com) on Thu Apr 26th, 2007 at 05:57:04 AM EST
[ Parent ]
Slightly more challenging:

by ThatBritGuy (thatbritguy (at) googlemail.com) on Thu Apr 26th, 2007 at 05:38:38 PM EST
[ Parent ]
That one cannot be done with a compass and a straightedge.

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Thu Apr 26th, 2007 at 06:07:14 PM EST
[ Parent ]
Which time do you want? You get solar time just by determining North and sticking a stick in the ground, stellar time is stellar time, if you know your geographical location and count the date and have an almanach with star positions, you'll get local solar time, if you also have equation of time tables, then mean solar time.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Wed Apr 25th, 2007 at 05:53:37 PM EST
[ Parent ]
See balbuz;and ancient mariners did even less: they sailed by sight, never far from shore., or crossed rather narrow seas like the Mediterranean.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Wed Apr 25th, 2007 at 05:50:20 PM EST
[ Parent ]
So you will surely explain to us the presence of cocaine (or relevant alkaloids) and nicotine in the Egyptian pharoaic mummies...

....Not plants that were entirely indigenous to Africa.

Or alternatively the presence of large stone carved sculptures on the North East coast of South America, that have undeniably negroid features.

You can't be me, I'm taken

by Sven Triloqvist on Wed Apr 25th, 2007 at 06:36:59 PM EST
[ Parent ]
DoDo didn't say ancient mariners didn't cross oceans : I described how they navigated across oceans, and he added how they used local knowledge or dead reckoning to cross smaller bodies of water. That's all.

Actually, it's quite feasible to cross the Atlantic by dead reckoning (speed * time passed = distance, and direction by a corrected compass) alone, with reasonable accuracy. In the 70s and 80s, before everyone had GPS, quite a few sailors didn't want to bother with a sextant, and just crossed that way.

The error upon arrival depended a lot actually on the speed of the boat : the faster the boat, the less chances of small errors on boat/current speed/course building up to result in large errors upon arrival.

by balbuz on Thu Apr 26th, 2007 at 03:21:07 AM EST
[ Parent ]
Or even better, you could ride currents. However, I do remain sceptical of widespread travel over high seas in ancient times.

Regarding the mummies with nicotine and cocaine traces, that's still a matter of dispute -- contamination, chemical products during mummification, and African plants now gone are among the other possibilities. For the latter speaks that there is wild tobacco discovered somewhere in the South of Africa, and that the formation of the Sahara definitely must have caused some extinctions.

If there was regular trade with America, there is also the question of a trace in the historical record. There is one candidate, Punt, unfortunately the description doesn't fit America. It does fit India though, and the route there does involve one crossing of high seas (the Arabian Sea).

As far as I know, the "undeniably negroid features" of Olmec heads is something peddled by Mormons and some US Black nationalists, no more science.

*Lunatic*, n.
One whose delusions are out of fashion.

by DoDo on Thu Apr 26th, 2007 at 10:07:55 AM EST
[ Parent ]
Good visual coverage here:

http://www.crystalinks.com/olmec.html

You can't be me, I'm taken

by Sven Triloqvist on Thu Apr 26th, 2007 at 10:35:01 AM EST
[ Parent ]
The evidence seems solid.

I suppose it comes down to asking whether plants that might exist but have never been found and have left no trace are more likely than voyages that might exist and have never been found.

Olmec vs Egyptian tie-ins are a bizarre suggestion archaeologically. There's one big similarity - pyramid building - but not much else.

If the two cultures were closely related, you'd have expected some overlaps in imagery, writing (hieroglyphics, especially) and so on. But there's really next to nothing.

If you allow for some trade, it's possible Olmec visitors to Egypt might have seen the pyramids and though 'Good idea! Let's do that too!' But I think it's unlikely there was ever more of a connection than that.

So it remains a mystery. (And probably always will.)

by ThatBritGuy (thatbritguy (at) googlemail.com) on Thu Apr 26th, 2007 at 05:47:24 PM EST
[ Parent ]
Another thought: clocks would be useful for places or journeys where the sky was covered, by thick cloud--thick enough to hide the moon and the stars, for days at a time.

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 08:05:47 AM EST
[ Parent ]
The French, in particular, were mad about clocks that computed the equation of time. Here's a picture of one, by Janvier, in the Consevatoire des Arts et Metiers in Paris:

I picked out this example, out of thousands, because the kidney shaped cam which is used to calculate the difference between mean and apparent time is clearly visible. This cam rotates once per year. This clock has a fairly straightforward method of displaying the wierd minutes: An inner disk on the time dial has a duplicate set of minute markers, and it rotates back and forth for direct reading from the minute hand. More common, and more complicated, is a standard dial with two minute hands. Usually the mean time is blue steel and the solar hand is gilt. These two vary in their relative position by means of a complicated planetary gearing system.

The French were very serious about sundial time. I'm told that French railroad stations had sundials until WWI.

by dmun on Wed Apr 25th, 2007 at 08:02:37 AM EST
So, whe have to adopt a new definition for the second:
it is now the duration of 429,228,004,229,952 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the strontium atom at rest at a temperature of 0°K.

"Dieu se rit des hommes qui se plaignent des conséquences alors qu'ils en chérissent les causes" Jacques-Bénigne Bossuet
by Melanchthon on Wed Apr 25th, 2007 at 08:14:17 AM EST
...give or take a period.

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 12:03:48 PM EST
[ Parent ]
give a period to whom?

"Dieu se rit des hommes qui se plaignent des conséquences alors qu'ils en chérissent les causes" Jacques-Bénigne Bossuet
by Melanchthon on Wed Apr 25th, 2007 at 04:32:35 PM EST
[ Parent ]
To the great goddess of the infinite fraction.  Or take...

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 04:36:08 PM EST
[ Parent ]
And (whisper it): they say the give and take goes all the way down...

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 04:37:11 PM EST
[ Parent ]
..and up...

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 04:37:40 PM EST
[ Parent ]
At its 1997 meeting the CIPM affirmed that:

      This definition refers to a caesium atom at rest at a temperature of 0 K.

This note was intended to make it clear that the definition of the SI second is based on a caesium atom unperturbed by black body radiation, that is, in an environment whose thermodynamic temperature is 0 K. The frequencies of all primary frequency standards should therefore be corrected for the shift due to ambient radiation, as stated at the meeting of the Consultative Committee for Time and Frequency in 1999.

Gaah, this means the second is now defined in terms of unrealisable physical conditions!

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Thu Apr 26th, 2007 at 11:53:49 AM EST
[ Parent ]
I have always had problems with time equation especially when I am in the East. I forget which day of the week today, date and sometimes what part of the day. Here time flows discreetly from observers. That was probably reason behind absence of history sense (evolution etc) among South Asian nations, for example Hindus and Tibetans what in turn was responsible for development of peculiar religious beliefs like samsara and reincarnation.

Once in one fantasy novel I read about sense of time. It was said that the distance between corners of one room may be covered quickly or very slowly. The distance remains the same, the time is not. Thus all objects in this Universe have different sense of time.  

 

by FarEasterner on Wed Apr 25th, 2007 at 12:49:17 PM EST
Here time flows discreetly from observers. That was probably reason behind absence of history sense (evolution etc) among South Asian nations, for example Hindus and Tibetans what in turn was responsible for development of peculiar religious beliefs like samsara and reincarnation.

Are you saying it is a feature of the physical environment that time is perceived differently?

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

by Migeru (migeru at eurotrib dot com) on Wed Apr 25th, 2007 at 12:57:14 PM EST
[ Parent ]
To great extent the answer is yes. I think the environment was responsible in the beginning phase then other factors started working (joint family system, rigidity of social norms, religious beliefs etc).
by FarEasterner on Wed Apr 25th, 2007 at 01:03:07 PM EST
[ Parent ]
So what exactly was it about the physical environment in the West that led to the development of a shipborne chronometer?
by ThatBritGuy (thatbritguy (at) googlemail.com) on Wed Apr 25th, 2007 at 02:50:40 PM EST
[ Parent ]
It's mainly down to the introduction of large scale trading networks across water. With the trading networks being set up by European nations to the Americas you do have large featureless bodies of water that you need to navigate across. The Pacific generally does not have large enough populations at its periphery to set up these trading networks at that time.  the Indian ocean has trading networks that are set up either overland, or do not travel far enough out of sight of land for this item to be truely necessary.

Any idiot can face a crisis - it's day to day living that wears you out.
by ceebs (ceebs (at) eurotrib (dot) com) on Wed Apr 25th, 2007 at 03:42:42 PM EST
[ Parent ]
I can go for that, up to a point.

The Chinese were famously intent on developing trade, and according to one (very debatable) suggestion they discovered America before the Europeans did.

But they got so far - and then they stopped. In theory there's no reason why they couldn't have begun trading with Europe - the potential for trade was certainly there, and the routes were already available.

If they had established trade routes, they would inevitably have been involved in the American adventure, one way or another.

So possibly the question is really - was there something in the physical environment that turned the Europeans into aggressive explorers, and the Chinese into isolationist stay-at-homes?

Europe could easily have chosen not to explore at all. Nominally the driver was access to spices, but it seems like a lot of effort to go to to put some nutmeg and saffron on the king's table.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Wed Apr 25th, 2007 at 06:39:20 PM EST
[ Parent ]
<hammering on the table> Perceptions, perceptions!

 How am I going to ever get this into your skulls! ;-)

You can't be me, I'm taken

by Sven Triloqvist on Wed Apr 25th, 2007 at 01:55:33 PM EST
[ Parent ]
Or, taking the organic approach:

Stand up and look around.  Which way is north?  Which way is east?

Face the east; the direction in which you find the sun in the morning.

You will notice that the place on the horizon where the sun rises changes each day, so "East" is not well-defined.

The stars, on the other hand, always rise and set at the same points on the horizon, so you should use those for orientation.

The North pole is relatively easy to locate on the night sky. It is easiest to locate by taking a long photographic exposure overnight. The direction or North is the point of tangency of the horizon with the star trails that happen to pass tangent to it.

You can then turn 90 degrees right if you want to go East.

If you're on the Southern hemisphere there is no Polar star, but you still have star trails.

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

by Migeru (migeru at eurotrib dot com) on Wed Apr 25th, 2007 at 02:54:40 PM EST
Well if you have an entire day and three sticks

plant a stick to observe from, use a second stick to mark sunrise, come back that evening, and mark sunset with your third stick,

Bisect the angle between the sunrise and sunset stick from the observer stick and that direction is north. There will be some very slight deviation from true north,  butmuch less than you would get by looking at magnetic north, or grid north.

Any idiot can face a crisis - it's day to day living that wears you out.

by ceebs (ceebs (at) eurotrib (dot) com) on Wed Apr 25th, 2007 at 03:50:13 PM EST
[ Parent ]
Yeah.  I was assuming a prior knowledge of the direction of east.

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 03:56:47 PM EST
[ Parent ]
of the year, five miles from me.

Named, with typical enthusiast ingenuity and lateral thinking, The Sundial.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Wed Apr 25th, 2007 at 06:47:33 PM EST
Does it work?

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 08:02:11 PM EST
[ Parent ]
I'll try winding it up and see if it chimes.
by ThatBritGuy (thatbritguy (at) googlemail.com) on Wed Apr 25th, 2007 at 08:52:05 PM EST
[ Parent ]
A chiming sundial!

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Wed Apr 25th, 2007 at 09:30:17 PM EST
[ Parent ]
You know, the more I ponder crop circles the more I like them (not being a a farmer.)

You, mate, have an annual arts festival in your fields!  Free to view, every year something new...

The site from your pic told me how to design the crop circle.

http://www.cropcircleconnector.com/2007/oliverscastle/oliverscastle2007reconstruction.html

I see a connection between these works and the works of the guy who walks across dewey fields and photographs the results.  He built mats out of leaves and photographed them as they flowed downstream.  I'm not sure if he's the same guy who built a wall through a wood, using local stones and bending round trees and dipping down to a lake and reappearing at the other end.

Very enjoyable!  Did you see Migeru's pic?  Wot I wrote in one enjoyable image--in a field near you!  (No doubt.)

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

by rg (leopold dot lepster at google mail dot com) on Thu Apr 26th, 2007 at 07:04:39 AM EST
[ Parent ]
Great diary. Wonder what you think about the clock of the long now
by nanne (zwaerdenmaecker@gmail.com) on Thu Apr 26th, 2007 at 10:50:10 AM EST
I thought of that too.

The center of the clock will show a star field, indicating both the sidereal day, and the 26,000-year precession of the zodiac. Around this will be a display showing the position of the Sun and the Moon in the sky, as well and the phase and angle of the Moon. Outside this will be the ephemeral dial, showing the year according to our current Gregorian calendar system. This will be a five-digit display, indicating the current year as in a format like "02000" instead of the more usual "2000" (to avoid a Y10K problem).

Something for everyone!

I like the idea.

In the universe, pure information lives the longest. Bits last. Just before Jonas Salk died, I was lucky enough to sit next to him at a dinner. I didn't know him well, but in past conversations he had always encouraged my more mystical lines of thought. I was sure he would like the millennium clock.

I was disappointed by his response: "Think about what problem you are trying to solve. What question are you really trying to ask?"

I had never thought of the clock as a question. It was more of an answer, although I wasn't sure to what. I talked more, about the shrinking future, about the oak trees. "Oh, I see," Salk said. "You want to preserve something of yourself, just as I am preserving something of myself by having this conversation with you." I remembered this a few weeks later, when he died. "Be sure you think carefully about exactly what you want to preserve," he said.

OK, Jonas, OK, people of the future, here is a part of me that I want to preserve, and maybe the clock is my way of explaining it to you: I cannot imagine the future, but I care about it. I know I am a part of a story that starts long before I can remember and continues long beyond when anyone will remember me. I sense that I am alive at a time of important change, and I feel a responsibility to make sure that the change comes out well. I plant my acorns knowing that I will never live to harvest the oaks.

I have hope for the future.

-Danny Hillis

http://longnow.org/projects/clock/

It's a huge eye!



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

by rg (leopold dot lepster at google mail dot com) on Thu Apr 26th, 2007 at 12:48:33 PM EST
[ Parent ]
Ah, future... Here is how the year 2000 was imagined in 1900:

by das monde on Thu Apr 26th, 2007 at 09:03:13 PM EST
[ Parent ]
Okay, here it is.

Time is a human invention to measure motion.

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

by rg (leopold dot lepster at google mail dot com) on Thu Apr 26th, 2007 at 06:38:39 PM EST
Upthread, we considered the ideas of a certain Crichton Miller regarding how ancient mariners could have measured longitude, with the help of angle measurements on stars and the Moon. After thinking over it, I saw that there is some merit in the idea. Now I thought it over a second time, and summarize both the method and its error factors below.

  1. The basic idea is the same as in the modern era: longitude is derived from the difference of the local time of the ship and a fixed observatory that issues almanachs. (1 hour = 15 degrees.)

  2. Crichton posits the comparison at the ship's local midnight, though calculation would be possible at other times. The trick is to bring an almanach that gives the equatorial positions of the Sun relative to some stars (the "rectascension", which can be considered a stellar longitude), and then wait until the stars are at that angle from the Meridian (the North-South direction on the sky).

  3. To measure this angle, Crichton's navigator holds a cross in front of him with a plumbine hanging from one end of the crossbar. He must hold the bar so that the end of the crossbar is at the equatorial pole (so that the plumbine marks out the meridian), and the cross at the eclyptic pole (relative to which he knows the Sun's position from an almanach).

  4. Due to the swings of the ship, there is an irreducible angle error from the plumbine, which converts 1:1 into error in longitude. The positioning error for the two poles in debrees converts into an error in longitude c. 0.3 times that big. E.g. a 3' [' = arc second] swing of the plumbine or a 10' error in finding the poles would both result in 3' longitude errors. I note though that thinking more about it, at least the second error source could be much reduced by choosing two stars near the poles rather than the poles themselves, preferably in parallel direction.

  5. A further error is recursive(ly reducible). The navigator took the rectascension of the Sun from an alamanach -- the angle is a function of time, as the Sun moves around relative to the stars. This would pre-suppose our knowledge of the local time of the almanach-making observatory. So in theory, if there would be no other error factors, we could reduce this error by starting with a guess of our longitude, then progress with the calculation, then use the end result in place of the previous guess, then repeat this over and over: e.g., reduce the error recursively. However, the longitude error from our initial longitude guess is a mere 1/366.25636th of the error of our initial guess, so I now see this error is not significant.

  6. The local time of the almanach-making observatory is to be determined by measuring the position of the Moon relative to the stars, and then looking up for what time the almanach gives that position. The rationale is that the Moon is the celestial object moving fastest relative to the stars, so there is good time resolution. (Today with precise instruments, you could do this with the planets.)

  7. A first error factor comes from the fact that the Moon appears as a disc a little under half a degree (30') across in the sky, so our navigator positions his instrument at its center with an error. The Moon-disc center positioning error converts to an error in longitude around 1/27.4th of that.

  8. The Moon is close to the Earth, and thus it appears at a different position relative to the stars when viewed from different locations at the same time. This is called parallax, and was measured by Hipparchos by comparing eclypse obervation records, most likely for an eclypse in 129 BC. The longitude part of this is another recursively reducible error. In theory, our ancient navigator can start with a guess of longitude. Parallax error is greatest when the Moon is near the zenith on the equator and is in perigeon, then the error of the lonngitude guess converts to a parallax (and thus Moon position error) 0.018 times that. But that converts to a rather brutal error in longitude merely reduced to 0.5 times that of the original guess! This is the chief problem for the method. And as soon as the non-recursive errors add up to something of similar magnitude, even recursivity won't help.

  9. There is parallax in latitude, too, which makes it difficult to make simple almanachs with the Moon's position given to stars appearing nearby: you go significantly further North or South than the obervatory, and those reference stars will no more be in the Moon's path, but above or below.

  10. The almanach-makers' job is further complicated by the fact that the Moon's orbit is elliptical and tilted to the equator: what they have to predict is not a simple linear progression, and the reference stars must change over time.

  11. I am also sceptical that ancient mariners could have got that precise almanachs about both the Sun's and the Moon's positions, not to mention the Moon's parallax, and that they even knew about the principle of recursive error reduction.

In summary, this method would have needed a guessed position as input, yet it could have only brought an insignificant improvement upon it, and ancient mariners might not have known all the relevant science needed for its application.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Fri Apr 27th, 2007 at 05:42:54 AM EST
8. The Moon is close to the Earth, and thus it appears at a different position relative to the stars when viewed from different locations at the same time. This is called parallax

But you are not observing at the same time, you are observing at the same local time. So, you trade off the longitudinal parallax error from (8) for the error in the rectascension of the sun (5).

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

by Migeru (migeru at eurotrib dot com) on Fri Apr 27th, 2007 at 05:56:51 AM EST
[ Parent ]
No, in the method as I described above, when observing the Moon, you want to derive the almanach-makers' local time at the same moment as the local time derived from measuring Draco.

Parallax wouldn't count if you compared local times at the differing absolute times when the Moon was in the same position in the sky. Then you also need the absolute time difference. That absolute time difference is (ignoring point 10) proportional to the longitude...

*Lunatic*, n.
One whose delusions are out of fashion.

by DoDo on Fri Apr 27th, 2007 at 06:30:34 AM EST
[ Parent ]
I thought the fixes stars look exactly the same if you are at the same latitude at the same local time on the same night, and that it's deviations in the position of the moon at that same local time that are being used.

"It's the statue, man, The Statue."
by Migeru (migeru at eurotrib dot com) on Fri Apr 27th, 2007 at 06:34:57 AM EST
[ Parent ]
In that case, longitude would be derived from the fifference between the apparent positions of the Moon in the sky. E.g., the Moon's position relative to the Meridian would have to be derived (that's no problem), then correct for the Moon's motion, then calculate time difference from angles (parallax is hidden in this), and then calculate longitude angle. I should think more about this to evaluate the involved errors.

*Lunatic*, n.
One whose delusions are out of fashion.
by DoDo on Fri Apr 27th, 2007 at 06:52:52 AM EST
[ Parent ]
So, upon re-reading, I see I was mis-reading it all along, unlike you.

I thought about the method's details. On one hand, it can be used to establish a first approximation of latitude without an initial guess: the apparent motion of the Moon between the moment of the observatory local midnight and the ship getting into the same position (relative to the stars) on the same day is roughly the same as the latitude difference per sidereal month in sidereal days. You don't even need to correct for the Sun's motion relative to the stars.

However, this time, we have another parallax, not because of differing observing positions, but because we aren't watching the Moon from Earth's center, but its surface. When the Moon is near the horizon at the equator, the distance from the Meridian exceeds the Moon's geocentric position angle from the same Meridian by those up to 61 arc seconds [somewhat less when the Moon is not in apogeon].

Once we have the more or less correct position angles (the Moon's changing distance from the Earth means an error of up to c. 10% in the parallax, up to 7'), we still have the bigger problem of the elliptic nature of the Moon's orbit. Near the perigeon and apogeon, the Moon's angular speed is more than 10% faster/slower, assuming constant speed can mean up to 1.5 degrees error [when the ship is at latitude 180°].

So, for precise position determination,
a) the almanach-makers should be aware of the elliptic nature of the Moon's orbit,
b) the navigator must be supplied with a data series or formula (epicycles?) giving the time differences corresponding to the Moon's location,
c) the navigator must be able to calculate parallax.

Realistically, I wouldn't expect a predicted Moon position precision for the ancients better than 15'. That would convert to 6.85 degrees precision in latitude, or 760 km at the equator.

*Lunatic*, n.
One whose delusions are out of fashion.

by DoDo on Fri Apr 27th, 2007 at 04:44:16 PM EST
[ Parent ]
Thanks DoDo.

Starting with number 7), tell me where I go wrong.

The moon is 0.5 of a degree wide (give or take) when seen from earth.  This means that if you drew a moon next to a moon next to a moon all the way around its orbital path you could draw 720 moons.

You say that the navigator necessarily has an error when finding the centre of the moon.  Could you expand on that?  If I had, say, a circle cut in a piece of metal that (give or take) represented the moon, then by positioning the moon within that circle, the plumb line would cut straight through the centre and down...so one could see the stars in another cut out, maybe one with degree markings--even a grid of some kind (fine hairs stretched tight?)

So you are saying that the human eye-moon relationship has a necessary innacuracy--error-of 1/27.4th of the width of the moon?

  1. and 10) I don't understand "Parallax error".  Would it help if the almanac ran through the entire sol-lunar cycle, so accuracy would remain constant as the moon made its various deviations from the hypothetical perfect globe moving in a perfect circle?  If one knows that on day X there will be a human-viewing error of Y%, then one could use that known error in the calculation (like sighting an inch above the target because you know that given the relationship of sight to barrel to bullet, you'll hit the target?  Am I way off?)

  2. had me thinking of ice ages again!  Before the last great melt, the ice came down to 45 degrees north, so we can imagine people working in a 45 degree area north (and south?)  Is that enough for serious problems to arise?

Would it also have helped these (mythical) mariners if they had had regular observatory points along the trip, land based observatories who knew their position relative to the observatories east and west...over a large area?  (eg: Egypt, Persia, India, China, and divisions thereof?)

Don't fight forces, use them R. Buckminster Fuller.
by rg (leopold dot lepster at google mail dot com) on Fri Apr 27th, 2007 at 08:00:53 AM EST
[ Parent ]
land based observatories

I'm thinking of a network of astronomers, spreading out from central points, so the mariner could arrive in a port and know "the time" at that port and how it related to their home port.

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

by rg (leopold dot lepster at google mail dot com) on Fri Apr 27th, 2007 at 08:02:05 AM EST
[ Parent ]
Provided stupendous measurement accuracy, longitude (or universal time) can be determined by Sun's position alone. Suppose we have an almanac that gives one of the following information for (say) London for each day:
  1. The position (relative to stars) of the Sun at the sunset;
  2. Zenith (sky) coordinates at the sunset;
  3. Zenith coordinataed exactyl one hour after the sunset (because stars are better observable "somewhat" later than at a sunset);
  4. Zenith coordinates at solar midnight;
  5. or similar.
The coordinates would form a discrete set of 365 (or 366) points on the ecliptic, about 1 degree apart from each other. If you measure the same moment at other point with London's lattitude, you will get an interpolated point between 2 almanac's dots, distanced proportionally by longitude difference. Whola! In how many parts can you instumentally subdivide 1 degree?

(For other lattitudes, almanac dots can be routinely adjusted.)

If you measure position of the moon at fixed solar moments, you are more lucky, since synodic month is 29.53 days long, so daily moon positions from a reference point (London) differ by 360/29.53 = ~12.2 degrees. You can be 12 times more precise. Better still, measure Moons position at a lunar moment (moonset or so) - sidereal month is 27.32 days, so you have ~13.2 degrees interpolation spans. Isn't this what Crichton tries to do?

Can the difference between sidereal and synodic months employed? I doubt it. It seems to me that you have to employ the fastest movement (discarding Earth's rotation) across the skies. Apart from Sun and Moon, we have Venus moving in 95.6 degrees span around the Sun in 224.7 days twice, Mercury moving in 56.6 degrees span in 88 days, and much slower planets. The average angular speed for Venus and Mercury (relative to the Sun) is 0.9 or 1.3 degrees per day, with fastest movement across Sun's disk unobservable - that's hopeless.

If our civilisation is about to collapse, with technology setback for long centuries, it would be smart to launch a couple of "bright" satelites with the lapse period of exactly 12 hours (or maybe better, half of sidereal day, 11 hours 58 minutes, 2 seconds), with the most conveninet orbit circular equatorial (or ecliptic, respectively).

by das monde on Fri Apr 27th, 2007 at 11:27:07 PM EST
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