As readers of GM/BM at the old site know, one of the things that I love to shred is trashy numerology. I also have a great dislike for the tendency of many modern pseudo-researchers to insist that ancient people were hopelessly naive or stupid.

I've found a delightful little article about Stonehenge that combines these two themes.

Stonehenge is quite an interesting construct. To the best of our knowledge, it was a sort of observatory: the patterns of stones and their arrangement are structured to allow a number of astronomical observations and predictions of astronomical events. This is a very cool thing.

Altie pseudo-researchers consistently insist that the people who lived around stonehenge when it was constructed could not possibly have built it. This is built on that naivety assumption that I mentioned above. For example, from the linked article:

Research has revealed that before the Sarsen Circle of upright stones was erected, a 285 foot diameter circle of 56 chalk holes, 3 feet in diameter, was created. (These are called the Aubrey Holes, in honor of John Aubrey).

A CBS TV program in the 1960's ran a computer analysis of the Aubrey circle. They declared that Stonehenge's location--latitude 51 degrees 11 minutes, was a very special location for eclipses of the moon. This location produces moon eclipses in the repeating sequence of 19 years, 19 years, and 18 years.

Adding 19+19+18=56. Thus if the white 3 foot diameter chalk holes were covered by a black stone, that was moved around the circle in synch with the passage of moon cycles, the black stone would arrive at the heal stone position, on the exact day when a moon eclipse would occur. (Eclipse computer.) (S.I.D.)

How could this stone computer have been created without the precise knowledge of the celestial mechanics of this unique geographic location? Certainly this was not the work of the early tribes that lived on this Salisbury Plain, thousands of years ago.

And why could it not have been the work of the people who lived there? Why, because it would have required careful observation of the skies by primitive people, and the recognition of simple arithmetical patterns in the repetitions of astronomical events. And obviously, things like repeated observations and arithmetic were *clearly* beyond the abilities of "early tribes".

But there's also something else quite interesting in the quote above - something that demonstrates the fundamental cluelessness of the writer. The author is corect that the geographic location of stonehenge *is* important. If you move it 100 miles north, it doesn't work so well anymore as an instrument of observation or prediction.

There are two ways that a location of an artifact like Stonehenge could have been selected. One is the approach that the author of the linked article takes: we believe that someone wanted an artifact that could observe and predict astronomical events; and so therefore, they computed the perfect position for making those observations. Doing that computation to select the location where the artifact should be placed would require a lot of knowledge, and some reasonably complicated math.

But there's another way that the location could have been chosen. Suppose you have a large number of people living on a relatively small island. Astronomical events like eclipses are very important to them. There is a location on the island where the pattern of events is clearest. Go north; things become less regular. Go south, things become less regular. But at the right location, you get the strongest pattern.

Now: add in a tradition where the people who do the astronomical observations/predictions are travellers.

Will the observers notice the pattern of astronomical events? Will they notice that in a certain location, the pattern becomes most regular?

If you don't assume that people a thousand or two years ago were stupid, *of course so!*

This S.I.D. (Stored Information Device) clearly displays enormous information about planet Earth's celestial relationships with the Sun, the Moon and the rotational speed of our planet.

Yes, that's true. Does that necessarily imply that the people who built it knew about the real structure of the solar system, and the sizes, distances, and velocities of the bodies in our solar system? No. It means that they were aware of *relationships*. As they point out, lunar eclipses occur in a regular pattern at this location. This fact is an implication of the relationships of the positions and motions of celestial bodies. But you don't need to know the positions and velocities of the bodies: you need to know *the observable relationships* between their motions. And *that* is something that is easily observable.

To give a simple example of this kind of thing: There's a right triangle whose sides have lengths 1, 2, and the square root of three. To draw a 1,2,sqrt(3) right triangle, you *could* start with a horizontal line 1 inch long, and then draw a vertical line whose height is sqrt(3) inches, and then draw the hypotenuse. To do this, you need to be able to compute the square root of three, which is not the easiest thing to do. You clearly need to be able to do something beyond simple arithmetic to be able to compute and measure the square root of three without using a geometric relationship. On the other hand, you *could* draw a horizontal line of length 1; then draw a long vertical line from its endpoint; and then take a ruler, and rotate it until the distance from the endpoint of the horizontal line to an intersection with the vertical line was 2 inches. The second way doesn't require you to be able to compute roots.

Following the stone computer, came the erection of the 30 upright stones that formed the Sarsen Circle, 100 feet in diameter. (My question was why 30? I divided 360 degrees by 30 and discovered the number 12. The number 12 is one of the most important numbers in the Anunnaki civilization...their Pantheon consisted of the Twelve Great Anunnaki gods, they declared 12 months in one year-2 twelve hour parts of each day, they created the 12 signs of the Zodiac. These Sarsen uprights are harder than granite and weigh 25 tons each. They were quarried at Marlborough Downs using tools not locally available at that time, and then transported these huge stones over 20 miles to this site.

And now we get the trashy numerology.

Why are there twelve months in a year in pretty much *every* calendar we know of? Why is the number of months equal to the number of signs of the zodiac? Could it be, perhaps, that the moon goes around the earth pretty darned close to twelve times a year? You know, the moon? That thing that's the most obvious thing in the night sky? That thing that's perfectly correlated with the tides?

No. Not that. Couldn't be. Must be aliens.

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I was deeply impressed at the ability of numbers to be abused in this context by a TV program about Egyptian megaliths (one which name has eluded me for years). It was the usual combo of "lost knowledge of the ancients" and "had to be aliens" garbage. The showcase "expert" described in great detail how the Great Pyramid displayed all these magical characteristics quoting that it was so-many-feet by so-many-feet by so-many-feet, and since these numbers of feet and the ratios between them were "significant", it proved his point.

The the show then produced an actual scientist who said "it's all rubbish, the Egyptians didn't use the Imperial measure of 'feet' and in any contemporary Egyptian measure, these ratios don't exist." I remember laughing out loud at the insight.

Some modern people still haven't noticed the sun and you're expecting ancient civilizations to have noticed the moon!?

the ratio should be the same in any unit system.

e.g. 1 in : 6 in = 254 mm : 1524 mm == 1 mm : 6 mm

This is why a ratio is useful in many cases; its a pure relationship, independent of units.

pough:

I've not seen that quote before. That really takes the cake on the cretinist thermodynamics argument.

anonymous:

I suspect the kind of thing that Ken was talking about involved ratios based on specific units. It's like the article I posted: did the Celts of Britain use 360 degree angle measurements? If they didn't, and you have an argument based on the fact that 360 degrees divided by 30 = 12 degrees, and the number 12 degrees has some mystical significance - then you're right out of luck. Use grads and you end up with 400/30 = 13.3 grads. The fundamental ratio is the same: 13.3/400 = 12/360. But because of the units, one of the expressions of that ratio appears to have some kind of significance: a circle divided into 20 sections produces 12 degree angles, and 12 is allegedly special.

I've seen lots of arguments based on things like this where the units used in the ratio are important; things like using ratios of the angle of something measured in degrees to its length measured in yards to come up with some kind of special magic result.

Er, while I agree with the gist of the article, I feel I shoudl point out that a right-angled triangle with shorter sides of lenght 1 and 2 has a hypoteneuse of sqrt(5), not sqrt(3)!

Ollie:

You misread me. I probably should have included a picture.

The triangle I'm talking about has a

hypotenuseof length 2, and legs of length 1 and sqrt(3).The procedure I mentioned was draw a base of length one. Then try to draw a vertical of length sqrt(3). The hypotenuse will be length 2.

There's an even easier way to make that triangle. Just make an equilateral triangle and break it in half.

My favorite way of making equilateral triangles: Take three spherical stones of the same size. Cover them with soot. Place them on the ground so that each touches both of the others. Put a flat rock on top. Connect the dots.

You could then divide it in half with a level and a plumb bob. (Or a compass and a straightedge, but if you have those then you could make the equilateral triangle a bit more easily, too.)

You don't even have to be able to measure distances to make that triangle, let alone take roots.

I've always had a fascination for Stonehenge and followed some of the controversy when Gerald Hawkins published

Stonehenge DecodedThe arguments for and against the "observatory theory" fall into a number of interesting categories.On the "anti" side, have the "neolithic people were too stupid to have built an observatory so it's just a temple with accidental alignments." On the "pro" side you have the very-woo "wisdom of the ancients" people and the ultra-woo "they were too stupid so aliens did it." On the "anti" side you get people who are so put off by those two arguments that they couldn't be "pro" if they wanted to.

As you point out, it's perfectly possible through observation and simple stick-and-string geometry to design Stonehenge. It's sad that the "too stupid" and "too wise" camps distort this.

pough:

If you read the full usenet post that was the source of that quote, and then other things by the same poster, it becomes pretty clear that the poster is just a pseudonym someone uses to troll with the most bizarre creationist-ish stuff they're able to imagine. In short, while amusing, this isn't a heartfelt creationist delusion, but a sort of internet performance art in parody of creationists.

Good or Bad? (I'd just like someone else to do the maths for me!)

http://www.secretacademy.com/

Totally random interjection: I've noticed several times in the last week that people on the scienceblogs.com community seem to use "woo" as a shorthand for things connected to alternative medicine and related pseudoscience. I've never seen this term anywhere else before. What is the origin of this word?

Coin:

Orac did a great post explaining it:

http://scienceblogs.com/insolence/2006/08/reader_mailbag_what_is_woo_1…

Short version is: beliefs based on magical thinking.

Stonehedge ReconstructionContains

73 stones total and 5 trilithons(central archways) indicating a normal year as73 x 5 days (73 x 5 = 365).There are

33 lintels(stones hung upon rooted stones) in two groups, a group of28 lintels capping the circleand a group of5 lintels capping the trilithons.The solar calendrical significance of the lintels indicates a 33-year leap-day cycle where a 366th day is added 7 times (every 4 years) in 28 years and then the 8th leap-day of the cycle is added after 5 more years.

Credit:S. Cassidy, 1053 47th Street, Emeryville, Ca. 94608Excuse me. Who gives a damn? and if you knew what difference would it make? Numerology? A mark on a surface. How the hell will that make any difference to diddly quot?