What this ancient Babylonian tablet teaches us about the politics of discovery

Recent coverage of the Plimpton 322 has made inflated claims about the importance of its discovery – but does it hold up to scrutiny?
Artefact Plimpton 322 has been in the news lately – an ancient Babylonian clay tablet inscribed with numbers (now known as Pythagorean Triples) which has recently been hailed as a key unearthing in the existence of trigonometry. In a paper published by Dr. D. Mansfield from the University of South Wales, he calls it “a rare example of the ancient world teaching us something new”. The problem is that the artefact in question has been known to the archaeological and scientific world for decades, having been discovered in the 1920’s in modern-day Iraq. It may be the oldest example of trigonometry in human history, pre-dating Pythagoras by approximately 1000 years.

Picture of Plimpton 322, taken from: “https://scientificgems.files.wordpress.com/2013/11/plimpton_322-colorised.png”

So why the recent media attention? In short, because the paper’s authors are really good at publicizing their work. Most of the information reported has been known for a long time, and the University of New South Wales study isn’t even the first to suggest that the table contains trigonometric identities. Most of the hype, therefore, comes from the flat-out fraudulent claims made by one of the paper’s authors, Dr. D. Mansfield about the artefact, as well as mathematics itself.
For example, Mansfield claims “Our research reveals that Plimpton 322 describes the shapes of right-angle triangles using a novel kind of trigonometry based on ratios, not angles and circles” – which is unquestionably wrong, as any book about trigonometry will confirm. In addition to this, Mansfield claims that the base-60 numerical system used on the clay tablet is superior to the base-10 system we use today because it has many more “exact fractions”. By “exact fraction” Mansfield supposedly means fractions which, when expressed as a decimal, are rational numbers such as ¼ =0.25 , as opposed to ⅓ = 0.3333… He claims that our base-10 system only has two “exact fractions” while the base-60 system has many more that make it more advanced. This is also completely false because there are demonstrably more “exact fractions” in the base 10 system than he suggests. Disregarding that, his claim is also wrong because “exact fractions” aren’t useful, or even meaningful in mathematics. Irrational numbers (which have infinite decimal places) are common in mathematics, and they do not limit our ability to calculate anything – making Mansfield’s claims wrong on multiple levels. Evelyn Lamb pointed this out in her piece in Scientific American.
Trigonometric ratios, taken from: https://mathsteaching.files.wordpress.com/2008/04/trig-ratios-to-learn.jpg

We have to be careful not to view historical artifacts through the lens of our modern day understanding of science and mathematics, as Eleanor Robson, in “Neither Sherlock Holmes nor Babylon,” notes: “Ancient mathematical texts and artifacts, if we are to understand them fully, must be viewed in the light of their mathematical-historical context, and not treated as artificial, self-contained creations in the style of detective stories.”
Surprisingly science popularizers such as Popular Science and Big Think jumped on the hype-wagon and were eager to report on the paper, and it’s attention-grabbing claims. This is disappointing, in part because you’d expect more skepticism from otherwise respectable news sources.
There’s no doubt that the clay tablet is a fascinating artefact, which can teach us a lot about Babylonian mathematics. Inaccurate reporting and attention seeking publications not only take away some of its beauty but also add to the amount of misinformation circling around on the Internet. Let this be a reminder to be skeptical of all information we come across and are eager to share, even if we obtain it from a source we usually trust.

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