Thursday, February 15, 2007

Flight of the Navigator, Part IV

And now back to our somewhat irregularly scheduled programming.

Cue music:
Procol Harum
"We skipped the light fandango, turned cartwheels 'cross the floor,"


The circumference of a circle is the basis of many forms of measurement of both time and distance (and, as a byproduct, speed). The odometer and speedometer in a vehicle use it. Navigators and cartographers use it, too. So do engineers, architects, and rocket scientists.

So did the ancients.

More Archemedes
(from Wikipedia)

Archimedes exceeded any other European mathematician prior to the European Renaissance. In a civilization with an awkward numeral system and a language in which "a myriad" (literally "ten thousand") meant "infinity", he invented a positional numeral system and used it to write numbers up to 1064. He devised a heuristic method based on statistics to do private calculations that we would classify today as integral calculus, but then presented rigorous geometric proofs for his results. To what extent he actually had a correct version of integral calculus is debatable. He proved that the ratio of a circle's circumference to its diameter is the same as the ratio of the circle's area to the square of the radius. He did not call this ratio pi but he gave a procedure to approximate it to arbitrary accuracy and gave an approximation of it as between 3 + 10/71 (approximately 3.1408) and 3 + 1/7 (approximately 3.1429).

Apart from general physics, he was also an astronomer, and Cicero writes that the Roman consul Marcellus brought two devices back to Rome from the ransacked city of Syracuse. One device mapped the sky on a sphere and the other predicted the motions of the sun and the moon and the planets (i.e., an orrery). He credits Thales and Eudoxus for constructing these devices. For some time this was assumed to be a legend of doubtful nature, but the discovery of the Antikythera mechanism has changed the view of this issue, and it is indeed probable that Archimedes possessed and constructed such devices. Pappus of Alexandria writes that Archimedes had written a practical book on the construction of such spheres entitled On Sphere-Making.

Archimedes's works were not widely recognized, even in antiquity. He and his contemporaries probably constitute the peak of Greek mathematical rigour. During the Middle Ages the mathematicians who could understand Archimedes's work were few and far between. Many of his works were lost when the library of Alexandria was burnt (twice) and survived only in Latin or Arabic translations. As a result, his mechanical method was lost until around 1900, after the arithmetization of analysis had been carried out successfully. We can only speculate about the effect that the "method" would have had on the development of calculus had it been known in the 16th to the 17th centuries.

In other words, Archemedes understood the motions of celestial bodies (having learned from his father) and invented his own math to describe it. A feat unmatched until Newton the better part of two millennia later. But more to the point, Archemedes also developed instruments that other, simpler minded folks could use to predict those motions.

Also germane to this discussion, Archemedes was a contributing and respected member of the royal house of the greatest maritime power of that period in antiquity, Carthage. He designed ships, too. One of his designs that was actually commissioned, built and sailed, the Syracusia, was the largest ship seen on the Med in antiquity, dwarfing all others by several to one. One tale has it that Archemedes' screw (a type of water pump) was developed to remove bilge water from this immense vessel. However, Archemedes received his education at Alexandria and he referred to the device as the "Egyptian screw", so one may speculate that he didn't invent it at all, but merely adapted it to a different use, having seen it in use for irrigation in Egypt.

So there we have one man who had a background in astronomy, shipbuilding, instrument making, had travelled much of the then known world, developed calculus from scratch, and had the resources of one of the major ruling houses of antiquity. Is it such a stretch to speculate that he could have adapted his astronomical instruments to maritime navigation?

On to slightly less esoteric navigation / surveying aids:
Plumb bobs

Two out of those three are the basis of the most common symbol of Freemasonry.

Cue music:

O that old rugged cross, so despised by the world,
Has a wondrous attraction for me

The Old Rugged Cross," one of the world's best loved hymns, was composed in Albion, Michigan in 1912 by the Reverend George Bennard (1873-1958)

Adding to the list

Last time I talked about the "Antikythera Device" and the Kimal. This time I want to discuss more devices, the Celtic or "wheel" cross and the "Coba" device (not to be confused with Cabo Wabo), and the gold chain.

The Celtic cross has been examined off and on for many decades as to possible meanings beyond Christian burial markers. Some very in-depth research was conducted by Crichton Miller. Adaptations and transmutations of the original meanings have become symbols for various groups and political activists, but Mr. Miller has concentrated on the ancient meanings and has hypothesized a purpose of the device, as a practical navigational tool. His case was compelling enough to win a British patent on his claim for a simple wheeled cross to act as a tool for navigation with an accuracy of 3 arc minutes of longitude.

The patent does not prove that the ancients used this tool or some form of it to navigate the high seas, but it does prove that they could have. For the "how it works" details, please see Crichton's website.

No slight to Crichton or anybody, but most other folks in the British Isles have stumbled around these things for some 1200 or 1300 years and never made that connection definitively. Though several others speculated that it might somehow be related to measuring angles, only Crichton, to my knowledge, has proven it as a practical device and supported the claim.

Another person who has devoted much time, travel, and effort in researching evidence of ancient navigation is William "Mark" Smith from south western Ohio. He and his Yahoo group, THOR, of which I am a member, have investigated and continue to investigate various ancient artifacts and discuss the possible use in navigation or mapping. Mr. Smith is a retired engineer in the automotive industry and applies a lifetime of engineering tools and skills towards these riddles. Several "classes" of artifacts have been identified as probable navigation aids. The one I want to spotlight here is the "Coba device" and how William (and I)
interpreted it.

But first, a little background on the actual artifact: The actual inscribed stone panels with the depiction of the "device", found near Coba, Mexico in the late twenties or early thirties disappeared in Germany during or shortly after the second World War. All we have to go on is one black and white photograph. From that, William built a model and tested it. It works.

I will let William explain it and other devices in greater detail during the Blogtalkradio Oopa Loopa Cafe program coming up on March 1st.

The last device I want to describe in this post is the chain. More specifically, the engineer's chain. Although nowadays, engineers' apulets depict gears, they once were represented by a chain (somewhat similar to the emblem of the International Order of Odd Fellows). Also, the "chief engineer" is called the "cheng" in print, but it is most often pronounced "chain". Some in the engine room might sometimes refer to that officer as "ball and chain", but not the good engineers.

Naval traditions die hardest. Why would the engineer be identified by a chain? Because sighting through the links of a chain is a quick, reliable means of measuring lunar distances. The link diameter is matched to the diameter of the moon when the chain is held at arms length. The engineer centers one link on the moon, slides the other hand to hold a different link in line with the other celestial body chosen for that sighting, then merely counts the links. Comparing this distance against the almanac allows the engineer to calculate the angular displacement (longitude) from the prime meridian. It also enables derivation of local time (Luna as chronometer).

I can't direct you to any website that discusses this application of chains as navigation aids because I haven't set one up and I don't think anybody else has considered this. However, an example of lunar distances measurement using cell phone cams then counting pixels can be found by registering at If you do that, you can see the basis of my hypothesis regarding engineers' chains.

Last item for this post

February 22, this coming Thursday, at 6 Central, will mark the first podcast of Oopa Loopa Cafe on

This call-in talk show centers on the evidence supporting
pre-Columbian contact, ancient technologies and sciences, and diffusion.
This show and will feature scheduled guests with predefined subject
matter and a family listening environment. It will be a companion to the written blog -- where I intend to
recap shows. Also, all the shows will be archived for later listening.

The first show will "air" on 22 Feb. '07 at 7 pm Eastern, 6 Central.
CORRECTION: 02/21/07 8PM
Got a call from the nice folks at this evening. They requested and I agreed to move back tomorrow's show one hour. So now it starts at 8 eastern, 7 central. So far, the March 1st and subsequent shows are still scheduled for 7 eastern and 6 central. If any of this changes, I will post again.


Find it at

or go to

type "Oopa" in the search box and it will take you to my host page.
Scroll down to the show description for segment details. The call in
number is near the top of the page for guests and listeners to call in.
When the show is on live, there is an icon next to the segment description
("Listen Live" or similar). Afterwards, listeners can click on the
archived shows, but there are none yet.

Holy signposts, Batman, how will we know they were here?

Tune in next time to find out.

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