Tuesday, December 30, 2014

Periodic Table with {wildly inaccurate} EMPHASIS

Studies show that scientists and those interested in science are susceptible to misinformation contained in memes.1 In 1976, William Sheehan published an article entitled "Periodic Table with EMPHASIS".2 This publication remained virtually undiscovered for 36 years until a series of events appears to have brought this obscure document to the forefront of chemical (mis)information. A Google investigation suggests that a Tumblr user posted a periodic table graphic with the caption "Totally in love with this image". The Radiolab Tumblr reposted the illustration, and finally io9 posted the image on its website. The unique version of the periodic table has been tweeted, retweeted, shared, +1 and liked into viral status,3 which would be quite a coup except that no one in the initial series of postings appears to have investigated or critically analyzed the veracity of the science this periodic table purports to illustrate. 


Two versions of the "Periodic Table with EMPHASIS". The version that appeared in 2012 and was subsequently went viral (top), and the original version from the article (bottom).

Take a look at the graphic (top). Anyone with sufficient background in rare elements will immediately spot problems with this periodic table (more on that later), but it's easy to see why this caught people's attention. You could get a contact high from the vintage LSD that the previously normal periodic table dropped before having its picture taken. This is probably what Salvador Dali would have produced if the periodic table commissioned him to paint its portrait. As my good friend and frequent co-author Brett mused "It looks very retro...You can smell the early 70s from the unshaven armpit between Y and Zr." After explaining on twitter for the umpteenth time that the information in this graphic was terribly wrong, I ordered the source paper through interlibrary loan.4 The original version of the picture is less striking as it lacks the color scheme (bottom), which as an aside does not correlate exactly with any normal categorization of elements.5 While it is unclear exactly who modified the original, the tie-dyed version was the one posted on Tumblr in 2012. 

To defend Sheehan, I don't believe he intended this to be anything other than a thought experiment to stimulate interest in the periodic table with children. The "paper" contains almost no information on how it was constructed. The only citations are to papers on other artistic versions of the periodic table from the educational literature. The article is 1 1/2 pages long. The bottom half of the 2nd page contains two poems 
written by high school students – one a ballad on Mendeleev and the other an ode to chemical bonds. The page also contains two separate lists of chemical puns. Not exactly the material you find in most scholarly journals, but a staple of internet science. I am unsure of what kind of publication Chemistry was, but the Sheehan "paper" has never been cited according to Scifinder. The composite evidence suggests that the article is from a magazine targeted toward a more general audience, not a peer reviewed journal.

So, what are the most egregious errors in this table? 
Tc (Technetium, element 43), At (Astatine, element 85), and Fr (Francium, element 87) are the most striking. At occurs naturally as a product of uranium and thorium radioactive decay, however, the half-life of all At isotopes are so short that less than 30 g of the element exists at any time on earth. A similar amount of Fr exists for analogous reasons. Their neighbors Po (Polonium, element 84) and Rn (Radon, element 86) exist at approximately 10-10 and 10-13 mg/kg in the earth's crust respectively. Small numbers certainly, but still 7 orders of magnitude greater than the estimates for At or Fr. The element boxes in the image are roughly the same size, not 10 million times larger.6

I discussed the table's problems with my friend Brett. His musings:
"Did I say that that table was actually impossible to display on a computer monitor correctly? I checked the math. It's amusing:

For argument's sake, let’s say that naturally occurring Tc is 10-10 the amount of U (Uranium, element 92). There are about 6 orders of magnitude less U in the earth’s crust (at least) than O (Oxygen, element 6) or Si (Silicon, element 14) the 2 most abundant elements. So there is 10-16 less Tc than O in the earth. I think this overestimates the amount of Tc, but 10-16 is bad enough.

To have a visible block for Tc requires how many pixels? If you want to read the "Tc" symbol, you need at least a 6×6 pixel square by my estimate. 36 pixels for the smallest element "block" on this hypothetical table. That means the largest block (O) would have (roughly) 3.6×1017 pixels. I don't have the motivation to figure out the exact size of all the other element blocks, but the earth's crust is dominated by just a few elements, so let's say that the total pixels required for the table would be about 2×1018 pixels (this is the worst estimate in this calculation, but it would take longer to calculate exactly and it's not off by more than an order of magnitude).

I'm typing this on a screen with 1920×1200 pixels, or about 2.3 million pixels. At the same resolution as my monitor, to be able to SEE the Tc element block, the monitor would be 8.68×1011 times larger. Yes, the screen would need to be 868 BILLION times larger.

I think there MAY be enough pixels on all the monitors in the world to do this. Especially now that there are so many smartphones around. Right? A little Googling reveals that in March 2014 Apple sold the 500 millionth iPhone. Let's be generous and assume that all iPhones to date had the large high-res screen size available at that time, 1136×640 pixels (A slightly bad assumption, but since each iPhone has outsold its predecessors, not a terrible assumption). So each iPhone has 727,040 pixels. The block for oxygen would require 495 BILLION iPhones to display. The entire table would require about 3 TRILLION iPhones to display.

Yikes. Looks like smartphones are still a growth market."

So just like every other meme and viral post, take things shared on the internet with a grain of salt until you do some research. Fortunately, Google has a better version of the periodic table by relative abundance. Not as groovy as the Sheehan table, but more accurate. Our analysis of the problems with the graphic are by no means comprehensive. I would encourage readers to highlight their pet peeves about the table in the comments, so this post can be a resource to educate people about the true natural distribution of the elements.

Update: 7:32 PM 12/31/14
Here are a couple of other representations of the periodic table showing abundances. These cartograms are both aesthetically appealing and informative. This one by geochemists is also interesting if not all that artistic.

Update: 3:47 PM 1/2/15
Here is an in memorium from the Santa Clara University website on William Sheehan that references his periodic table graphic. Further updates or a new blog will be posted if/when I can track down further information.

Update: 11:25 AM 1/3/15
EUREKA! After doing a lot more digging and coming up with very little from Santa Clara University, I found a J. Chem. Ed. paper from 1993 by Kathleen Carrado at Argonne. It's copyrighted material and behind a paywall. The article discusses using a black and white version of the Sheehan table as a coloring book exercise with elementary-aged students. The paper also references a 1978 calendar by Instruments for Research and Industry that used Sheehan's graphic. Confirmation pending, but this seems like where the colored graphic originated, and further proof that this table was not intended to be an absolute representation of relative abundance.

Update: 11:34 AM 1/4/15
Another calculation analogy from Brett:
A properly scaled table would cover an area of about 3×1012 × ((58.6/1000)*(123.8/1000)) m2, or 21764 km2 or 8403 square miles. That’s an area about 7 Rhode Islands or 80% of the size of Massachusetts. Kind of hard to carry around or print out 

_________________________________________________________________________________
1. This is an anecdotal observation made by one blogger, which seems to be sufficient evidence of validity in the internet age.
2. W. F. Sheehan. Chemistry. 197649, 17-18.
3. What counts as viral in the chemistry world anyway.
4. I would post the paper in total, but this would probably violate copyright law. How about a link to the pdf in Google drive instead?
5. Colors correspond to relative electronegativity. This has been clipped off of some of the images being circulated. Also, the colors do not accurately represent electronegativity. See here. For example, Kr and Xe have approximately the same electronegativity as their halogen neighbors. 
6.  The Sheehan graphic has the disclaimer "To accommodate all elements some distortions are necessary. For example, some elements shown do not occur naturally", but does not provide details. The transuranium elements fit the latter characterization, nevertheless 7 orders of magnitude seems like a broad interpretation of "some distortions."

4 comments:

  1. I suppose you checked this but I'll ask anyway to double check. The elemental area illustrated isn't simply a function on the log of the abundance is it?

    ReplyDelete
    Replies
    1. Definitely not a log function. This was a freehand illustration for children to use like a coloring book page. There's no mathematical algorithm applied. It was just meant to be fun.

      Delete
  2. The rare earths aren't well represented either. Ce is about as common as Cu but not as well known.

    Using a log scale would be a great improvement. Oxygen would then be only ~18 times the area of Tc.

    ReplyDelete