Detecting mercury in PPM concentrations

One problem with me and my brain trust is that we are all a bit old. When it comes to trying to detect low concentrations of mercury (i.e. contact with a bowl from two thousand years ago,) the best we can think of is gas chromatography. This is about one step up from swabbing with reagents and hoping to see a color change.

A little back and forth with an actual archeologist reveals that the current art is portable x-ray fluorescence.  The instrument is the size of a hand-drill, and looks a bit like a Star Trek phasor. Some more back and forth with an XRF/pottery expert confirms this is the right tool. Now I just need to find one in New York.

P.S. These blog posts are lagging realtime by a couple of weeks. I'm trying to keep the chronology roughly straight rather than posting up-to-the minute results.

Molcajetes

Those are molcajetes: traditional mortars (the actual bowls) and pestles (the clubs.) They are typically made of basalt and used to grind chilies, etc, to make salsa.

Unfortunately, although "molcajete" means "grinding bowl" in the Nahuatl language, it also seems to be the term of choice for all legged shallow pottery bowls from Mesoamerica, even if the bowl is not a grinding bowl. This annoys my wife: over the second course at Le Bernardin, she mentions that people need to get an ethnoarcheologist to show the bowl around Oaxaca villages, asking people what is really called.

I'm pretty sure the pottery bowl I have was never designed for grinding food. In fact, I'm pretty sure almost none of the pottery molcajetes were designed for grinding. Naturally, I am pointed to a counterexample:

But most are not grinding bowls. Here's candidate number 3:

It's sitting in the Walters Art Museum in Baltimore.

Oh, and those bulbous legs are called "mammiform." Which just means breast-shaped. That concludes today's lesson.

That bowl in the Metropolitan Museum of Art?

I almost forgot. The day after I got back from Belize, I took a taxi up to the Met, paid my $25 suggested donation, and snapped a few pictures of the bowl in question. Apologies for the quality of the image - all I had on me was my ancient iPhone.

Anyway, the inside of the bowl is a nice, smooth curved surface. Almost too nice to get a real sense of depth and the overall curvature.

Torsion and Rotation

I haven't done any physics in a while, but a bowl suspended from a twisted length of thread shouldn't be too hard.

A twisted thread provides the force that spins the bowl. It should obey Hooke's law: . This just says the torque (twisting force) is opposite to the direction of the twist, and equal to the amount of twist (theta) scaled by a constant (k) that is a property of the thread. Interestingly, the force does not depend on the force the bowl is exerting on the thread (i.e. the weight of the bowl,) nor does it depend on the length of the thread.

Given the torque, we can derive the angular acceleration using Newton's laws:   This says the acceleration equals the torque divided by the moment of inertia of the bowl. I estimated the moment of inertia as 2 kg at 10 cm from the center of the bowl, or .02 kg-m^2. Of course, it's really not a constant, because it will increase as the mercury rotates and moves outwards from the center.

Integrating the acceleration over time gives the angular velocity. The plot above gives a sense of how the velocity of the bowl changes over time. Note that the shape of the curves should be reflective of reality, but the actual values (e.g. revolutions per minutes) should not be trusted at all: they are based on a complete guess for the term k / I. Unluckily, I can't find values for k for types of twine online. Luckily, if we actually put a bowl on a string, it should be easy to experimentally derive this term for the system.

Anyway, the system does spend a good portion of the time at a relatively constant velocity (the flatish peak in the velocity plots.) That's good, but I have an idea for how to get a much flatter, longer  peak in the rotational velocity...

I buy a bowl

The Guardian article on Teotihuacan creates a a lot of low level noise on the internet.  An article on Slashdot generates over a hundred comments and probably hundreds of thousands of page views.

The statistician in me worries that even an outre hypothesis (e.g 1 in 10000) exposed to 100,000 people may result in someone else exploring the same idea and buying up any candidate precursor bowls that can be found on-line. Because I am eventually going to want to test candidate bowls for mercury residue, I don't want the risk of them all vanishing into unknown private hands.

I decide to buy one bowl online. The bowl pictured above is the one I choose. My reasoning is:

1. It's got a good functional feel, no decoration, bulbous legs and slots like the Met bowl.
2. It's a bit of a mess, definitely not a museum quality piece because the legs don't match. This reduces the chance it is an outright fake.
3. It's been it the USA for decades, so the ethical issues with buying artifacts are reduced. I figure I can give it back to the country of origin once I'm done (if the country can even be identified) for further ethical transgression minimization.
4. It's not too expensive.

This plan does not sit well with my wife. She's ok with, say, private ownership of a Crimea war Minie ball, but not with a nondescript classic Greek potshard. I'm in her immoral camp for pursuing this.

Here's another view of the bowl:

Note how the nubs on the other two legs are horizontal rather than vertical. And they have no slots. And the foot pads are substantially larger.

A bowl suspended by forty feet of string?

Why not four feet? Or four hundred feet of string?

The longer the string, the better: a longer string can take more winding up, and so impart more spin to the bowl for a longer period of time. However, to prevent the wind from blowing the apparatus around, it needs to be inside a building or in a shaft in the earth, or similar.

Here's Scientific American on the shaft at Teotihuacan (it's near the center of this post's image, off a little towards the lower right.)

The tunnel itself was discovered when a heavy rainstorm exposed a shaft that led to a spot about halfway down its length. The shaft’s purpose remains a mystery but scientists believe the tunnel had a ceremonial purpose, and it is possible that the shaft was used for astronomical purposes.

That shaft was 14 meters (about 40 feet) deep. A number of other astronomical holes or shafts of about the same depth seem to have existed.  El Caracol looks to be about that height. I haven't found any location with a much deeper shaft, so 40 feet seems the best guess.

Assuming the user of the hypothetical telescope will be situated near the focal length of the telescope, then the minimum focal length is .2 meters (with the viewer near the bowl,) while the maximum focal length would be approximately the length of the string (with the viewer near the suspension point of the apparatus.)

In the long focal length case, the bowl would rotate at around sqrt(447/14) = 5.6 revolutions per minute.

Potttery and Paraboloids

Here's a bowl from Cenote. The picture comes from Arlen Chase's PhD thesis. I've aligned the image, added a grid, and plotted a parabola.

The fit is good out to a radius of 9 centimeters. That doesn't prove much, because pretty much any smoothly curved bowl will fit some parabola for some internal radius.

Working on the assumption of a 9cm radius of pool of mercury, with a y height of 1cm at that radius, the equation of the parabola would be approximately:

y = x*x / 81

a = 1/81

a = 1/(4f)

4f = 81

f is approximately 20 centimeters.

Given focal length of .2 meters, we can derive the required rotational velocity:

f * rpm * rpm = 447

rpm = sqrt(447/.2) = sqrt(2235) = 47

So, the bowl would be rotating at around 47 revolutions per minute.

These numbers are problematic for my theory. The focal length is too short assuming the goal is to reflect the image via a small mirror above the center of the bowl, then into some type of eyepiece that must be 9cm from the center axis (otherwise the viewer's head would obstruct the incoming light.) Secondly, 47 rpm is really fast: even with a forty foot string suspending the bowl, that would be 5 twists per foot of twine to get even five minutes of rotation. At 47 rpm, a forty foot string would be vibrating quite intensely, probably enough to ruin the optical surface of the mercury.

Of course, lower rotational speeds would be reasonable. The mercury would still form a parabola, it would just be deeper in the center of the bowl, and thus a less efficient use of the metal. The more scarce the mercury was, the more we would expect the rotational speed to conform to the parabola of the bowl.

I ran though the math for other similar bowls in the Cenote paper. They all produced numbers in the 40-70 rpm range.

Things get weird

So, my wife (actually, her name is Maya, but that will cause so much confusion that I'll try to avoid it,) has gone from thinking this whole telescope thing is complete idiocy to searching the web and asking why no one has noticed this before. In the movies, this would be a much more validating experience, like where she actually mentions I'm pretty smart or something.

Time warp a day or two ahead, and I'm back in New York and have laid out my speculation to six of my peers. Here's an idea that could have been kicked around anytime in the last one hundred years, but within two days, three of them send me a link to the same article:

Teotihuacan

It's frustrating how little information is there, but it links to an article about a one-stop Mayan optics shop. I figure I won't even need to write this blog because someone must see the obvious.

Rattle Bowl, Really?

Everybody likes rattles. The first pottery rattle was probably made twenty minutes after the first pot.

Anyway, my wife, the museum conservator and part time archeologist, arrives for dinner. I give her the bad news about the rattle bowls I am finding. While she is unfailing polite with regards to the theories of her colleagues, she does manage to convey the absurdity of a Maya housewife serving a bowl of soup to her husband and telling him to give it a good shake. I'm forced to agree that having the brittle family cookware do double duty as a toy for the toddlers in the house is probably not reasonable either.

So, why do the hollow, bulbous, slotted legs in a telescope bowl have clay pellets inside them?

One possibility is that it's how you balance them so they rotate nicely: you make the coiled pottery paraboloid bowl. Let it dry. Then attach three or four hollow, slotted legs. Once those have dried, give the pot a trial hanging, and add small clay beads as needed until it hangs true. After firing, you can even add a little sand into the legs to fine tune the balance.

The Evolution of Functional Pottery

That's the bowl. But, of course, you knew that already from reading my previous posts.

It's sitting on display in he Metropolitan Museum of Art. This is the only picture of it that I can find: the shiny internal reflection is pretty awesome, but it's hard to tell if the bowl shape is actually parabolic. The legs are interesting: what are those slots?

I won't learn anything more about this bowl until I get back to New York.

But there are still avenues to explore. There should be precursor bowls, i.e. more primitive versions of this design. Of course, I have no idea why there are bulbous legs, or weird slots, but they are probably there for a reason. So I go searching for variations on this design in Mayan pottery. A number of possible hits turn up. Actually, because I am Bayesian, I also search Middle Eastern, Indian, Chinese, Roman, and Greek pottery: nothing like this appears. Good.

The annoying thing is that most of the hits are "rattle bowls": the hollow legs contain pottery beads that, well, rattle when the item is shaken. About half the candidates are possible telescope elements, but the other half are clearly household pots with rattle legs. Even assuming a functional design element transferred to an everyday item (with loss of function,) the whole rattling telescope bowl thing is looking to be a bit of a stretch.

An example of a functional design element making its way to an everyday item with total loss of function:

Stone Knives and Bearskins

So how do you spin a bowl of mercury?

Anything like a potter's wheel is out: there is no evidence of that sort of technology.

This is the sum total of Mayan technology: stone, flint, obsidian, wood, glue, gum, rubber, cloth, twine, paper, bone, sinew, water, fire, pottery, mirrors, mercury, digging holes, the arch.

And pretty good mathematics: knowledge of zero, a positional notation, plus, minus, multiply, and divide.

And zero science: no scientific method, no sign of designed machinery or scientific instruments.

But some strong astronomy/astrology. There are records of various planets and constellations. Solid tables of eclipses, etc. They may have known about the Orion nebula a thousand years before anyone else (vague Three Hearthstones stuff.)

But they had cities of 100,000+ people. They must have had pretty sophisticated civic management. And a population density that could support a large number of astronomers.

Maybe there was more, but the Spanish burned almost all the Mayan books. All that remain are four books:

1. The Dresden Codex
2. The Madrid Codex
3. The Paris Codex
4. The Grollier Codex

Anyway, how do you spin a bowl given this menu of technology?

It's actually quite simple: you put the bowl in a string basket, i.e put a loop around each leg. Suspend it on a long piece of string (say 40 feet.) Wind the string, then release it and let the torsion rotate the bowl.

The nice thing about this is that you don't need any science. Unlike, say, a glass lens where you have nothing until you've ground it to a precise shape. Here, you have mercury in a bowl (where else would you put it?) You swirl it around and see it does interesting optical things. You know about spindle whorls, so putting the bowl on a spinning string is obvious. 

Obviously, this still has problems. But it's better than trying to spin a bowl by hand.

One of these things is not like the others

So, I'm several beers into my research. The mercury looks fine. Now I just need to find the bowl that spins. I'm embarrassed to say that my mental image at this point was a simple paraboloid bowl that was basically whipped around by hand (maybe the bottom of the bowl would have circular scratch marks or something.)

I spend a few hours browsing images of Mayan pottery. Because I have little idea what I'm looking for, I figure I'll sample the space to get a sense of what is common, then look for bowls that are outliers (because there should only be 1 telescope for every 10000 cooking pots.) Bonus points if the outlier looks like a scientific instrument and seems amenable to spinning. I am so Bayesian.

Finally, I google for "classic Mayan shallow pottery bowl." The bowl shows up on the first page. I dismiss it at first because it has legs: no way will this thing spin nicely. But it's got a lot of things going for it: it's the right shape, it has no decoration, it's described as well-balanced, it even has a small vertical wall around its rim (just like the Large Zenith Telescope - nice to see a design choice repeated across 2000 years.)

I'm not sure how objective I'm being. So, when my kids show up, I ask each of them to find the pot that does not look like the others on the page of images. They both pick the target as their second choice.

I still don't know why the thing has legs, though. How does it spin?

Mercury

Back at the lodge, I retire to the bar where there is satellite internet. Research is a bit tough to do over a 56K connection that drops every few minutes. Still, I can't complain: many rainforests don't have any beer or internet.

The first topic is mercury. 684 grams were found at Caracol. At 13.5 grams per cubic cm, that's about 50 cubic centimeters. Assuming a depth of 5mm, that's a surface of 100 square centimeters, or a puddle with a radius of about 6 cm.

That's pretty cool. Enough mercury to make a 4 1/2 inch reflector. And it turns out that mercury was found at a number of Mayan sites.

Note that the Maya were a stone age civilization. That means no iron, copper, or even gold or silver. Luckily, they had local mercury deposits. Small quantities of liquid mercury could have be obtained either directly as a liquid dripping from certain rocks, or by burning cinnabar.

The lack of gold or silver means the Maya could not have used mercury for precious metal extraction. There aren't many other uses for mercury in a pre-industrial society. Maybe desperate medicine or an ill advised attempt at eternal life. Unfortunately, the absence of practical applications of mercury provides little support of my theory because the null hypothesis (as every science nerd will attest, liquid mercury is just a fun thing to have around and play with) cannot be rejected.

It looks like the Maya had decent quantities of liquid mercury. Enough for liquid mirrors, anyway.

Caracol, Belize

So we're at Caracol, looking at structure A6. The guide is telling us how the Maya used this as an astronomical observatory. He mentions that liquid mercury was found here, and how archeologists speculate that the Maya might have used it in a primitive spirit level sort of device.

The spirit level idea was absurd: mercury does nothing that plain water wouldn't do. But, if we're going to play "guess the use of an ancient object," I figure you put the mercury in a bowl, spin it to form a paraboloid reflector, and you've got the primary lens of a telescope. That's no more absurd than a spirit level, and at least it works in the idea of astronomy.

While the evidence for this theory was a bit on the thin side, and the guide didn't know how much mercury was found, I liked it enough to tell the guide his archeologists were wrong, the Maya had a telescope, and he was lucky to be the second person alive to know this. My wife looked at me witheringly.

Telescope Design

I don't have a complete design for a Mayan telescope, but here is a good start:

It's a Newtonian telescope

The primary mirror is a rotating liquid mercury paraboloid reflector, approx 7" diameter

As telescopes go, it's pretty primitive: it only points straight up.

Think of a telescope as doing two things: collecting light to make dim things visible, and magnifying small images to make them large. A big reflector does the first but not the second. We really need an eyepiece for the second.  

I don't have a good theory for the eyepiece. 

It is possible a light-enhancing, but non-magnifying, system could still be useful.

This is the total claim. If you find it totally implausible, stop now. If you find it merely louche, read the next post...

Introduction

Thesis: the Maya used telescopes.

The claim to be explored is that the Maya invented and used devices that allowed better than naked eye viewing of the sky.

Don't expect von Daniken weirdness here. There is not going to be aliens or lost technology or crystal skulls or strange interpretations of Pacal's sarcophagus.

Don't expect academic rigor. I had hoped this was going to be a simple argument with clear proof. I was wrong: an unassailable argument would require years of reading and physical experimentation in a number of fields.  It's better to throw out an inchoate idea now and hope someone makes something of it: I'm old enough to not care too much about the apportion of credit.

This is a blog. I'll probably talk about what I am thinking and doing rather than presenting a coherent narrative that directly supports my thesis.

Credits: I've had great help from archeologists, physicists, chemists, and other experts. My brain trust of strategists, generalists, and all round very smart people has been invaluable. Given the crackpot nature of this blog's claims, I will not mention anyone by name. Retroactive acknowledgement of contributions will of course be made if the contributor requests it.