— The Erimtan Angle —

Archive for the ‘Science’ Category

The Tablet known as Plimpton 322

Plimpton 322

Maev Kennedy, a special writer for the Guardian, puts forward that “[m]athematicians have been arguing for most of a century about the interpretation of the tablet known as Plimpton 322, ever since the New York publisher George Plimpton bequeathed it to Columbia University in the 1930s as part of a major collection. He bought it from Edgar Banks, a diplomat, antiquities dealer and flamboyant amateur archaeologist said to have inspired the character of Indiana Jones – his feats included climbing Mount Ararat in an unsuccessful attempt to find Noah’s Ark – who had excavated it in southern Iraq in the early 20th century”.1


The Professor of Ancient Near Eastern History Eleanor Robson explains that “Plimpton 322 is the modern label given to a cuneiform tablet written in the ancient Iraqi city of Larsa in the mid-18th century BCE. Old Babylonian (OB) mathematics, the oldest known body of ‘pure’ mathematics in the world, derived from two separate traditions in early Mesopotamia: an orally-based ‘surveyors’ algebra’ and a bureaucratic accountancy culture. The ‘surveyors’ algebra’ is heavily based on riddles concerning cut-and-paste geometry and has its origins outside the literate scribal tradition in the late third millennium . . . Scribes, on the other hand, had been directly concerned with the quantitative control of goods, time, and labour since the advent of writing at the end of the fourth millennium . . . Their complex system of metrology,work norms,andother technical constants also reached its apex at the end of the third millennium, under the so-called Third Dynasty of Ur III . . . The two traditions coalesced into the mathematics of the OB humanist scribal schools of the early second millennium, where education appears to have comprised far more than the acquisition of professionally useful skills”.2 Professor Robson goes on to say that “[a]lthough the archaeology of Old Babylonian schools is not clear-cut and the large majority of OB mathematical tablets known are completely unprovenanced, [she is] convinced that virtually all of the OB mathematical corpus as we have it should be interpreted as the products of scribal training, or, at the very least, as the products of a scholastic milieu”.3 And, going down to the nitty-gritty, she postulates that “Plimpton 322 is, physically at least, a typical product of OB mathematical culture . . . It is a clay tablet, measuring some 12.7×8.8 cm as it is preserved, ruled into four columns. It was excavated illegally sometime during the 1920s, along with many thousands of other cuneiform tablets, not from Babylon but from the ancient city of Larsa (modern Tell Senkereh, 31◦140 N, 45◦510 E)”.4


The mathematician Daniel Mansfield relates that the “huge mystery [of Plimpton 322], until now, was its purpose – why the ancient scribes carried out the complex task of generating and sorting the numbers on the tablet. 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. It is a fascinating mathematical work that demonstrates undoubted genius. The tablet not only contains the world’s oldest trigonometric table; it is also the only completely accurate trigonometric table, because of the very different Babylonian approach to arithmetic and geometry. This means it has great relevance for our modern world. Babylonian mathematics may have been out of fashion for more than 3,000 years, but it has possible practical applications in surveying, computer graphics and education. This is a rare example of the ancient world teaching us something new”.5 The mathemtician Norman Wildberger, for his part, adds that “Plimpton 322 predates [the Greek astronomer] Hipparchus by more than 1,000 years. It opens up new possibilities not just for modern mathematics research, but also for mathematics education. With Plimpton 322 we see a simpler, more accurate trigonometry that has clear advantages over our own”, also explaining that a veritable “treasure trove of Babylonian tablets exists, but only a fraction of them have been studied yet. The mathematical world is only waking up to the fact that this ancient but very sophisticated mathematical culture has much to teach us”.6 Mansfield and Wildberger have published their fiindings on the Babylonian tablet in an article published in the journal Historia Mathematica.

Historia Mathematica

1Maev Kennedy, “Mathematical secrets of ancient tablet unlocked after nearly a century of study” The Guardian (24 August 2017). https://www.theguardian.com/science/2017/aug/24/mathematical-secrets-of-ancient-tablet-unlocked-after-nearly-a-century-of-study#img-2.

2Eleanor Robson, “Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322” Historia Mathematica 28 (2001), 167–206.

3Eleanor Robson, “Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322”.

4Eleanor Robson, “Neither Sherlock Holmes nor Babylon: A Reassessment of Plimpton 322”.

5Maev Kennedy, “Mathematical secrets of ancient tablet unlocked after nearly a century of study”.

6Maev Kennedy, “Mathematical secrets of ancient tablet unlocked after nearly a century of study”.


Human Extinction ahead and the End of the World as we Know it


The eminent Australian scientist Frank Fenner, who passed away in late 2010, made some surprisingly unsurprising predictions right before his death. Writing on the web-based science, research and technology news service Phys.org, Lin Edwards put forward that Professor Fenner “predicts humans will probably be extinct within 100 years, because of overpopulation, environmental destruction and climate change”.[1] As such, this apparently shocking statement should not come as a surprise to anybody . . . given that estimates indicate that the availability of drinking water will become problematic by the year 2040 and that the supply of foodstuffs will arguably falter in about ten years from then, or by 2050 . . . underpinning such dire estimations are the prospects of the sustained growth of the human population in the coming century. The world’s leading resource for events, research, and insight into the global agricultural investment sector Global AgInvesting (or GAI) released a report in 2012 (entitled simply, World Population Growth in the 21st Century) that put the population increase into perspective: “[t]he world’s human population does not grow linearly, but rather geometrically, (i.e., 1, 2, 4, 8, 16…, etc.) which explains the five-fold increase in population from 1.2 billion to 6.1 billion during the 20th Century. Rapid population growth is predicted to continue for the first half of the 21st century, with rates of growth declining during the latter half of the century. World population is projected to stabilize at just over 10.1 billion by 2100”.[2] More than 10 billion people without easy or even direct access to either drinking water or food, to be precise. That is, as things stand today.



Edwards continues her piece by stating that Professor Fenner has “said [that] homo sapiens will not be able to survive the population explosion and ‘unbridled consumption’, and will become extinct, perhaps within a century, along with many other species. United Nations official figures from last year [i.e. 2011] estimate the human population is 6.8 billion, and is predicted to pass seven billion next year. Fenner told The Australian he tries not to express his pessimism because people are trying to do something, but keep putting it off. He said he believes the situation is irreversible, and it is too late because the effects we have had on Earth since industrialization (a period now known to scientists unofficially as the Anthropocene) rivals any effects of ice ages or comet impacts”.[3] The report World Population Growth in the 21st Century puts it like this: The “rapid growth [of the human population] is expected [to occur] in the next 40 years, and will likely place a huge burden on global resources and the agriculture sector in particular”.[4] Professor Fenner himself told the press that “We’ll undergo the same fate as the people on Easter Island, there will be a lot more wars over food”,[5] aka resource wars-in-the-extreme. Lin Edwards then goes on to explain Fenner’s analogy: the “Easter Island is famous for its massive stone statues. Polynesian people settled there, in what was then a pristine tropical island, around the middle of the first millennium AD. The population grew slowly at first and then exploded. As the population grew the forests were wiped out and all the tree animals became extinct, both with devastating consequences. After about 1600 the civilization began to collapse, and had virtually disappeared by the mid-19th century. Evolutionary biologist Jared Diamond said the parallels between what happened on Easter Island and what is occurring today on the planet as a whole are ‘chillingly obvious'”.[6]


At the end of 2010, I wrote a piece appropriately headlined “Easter Island as a metaphor” and in it I tried to come to terms with what had happened to the island and how these events appear to predict the fate of the planet as a whole: “[w]hen Europeans arrived on the island it was utterly treeless. Pollen analysis has revealed however that the island was ‘almost totally’ forested until about the year 1200. But now the island is barren. A volcanic crater on the island’s eastern plain, Rano Raraku, provided the source of the sideromelane (basaltic) tuff from which 95% of the statues were carved. Some 250 mo‘ai [or Easter Island statues] are found in an almost unbroken line around the perimeter of the island, while 600 others in various stages of completion are scattered around the island. It is hard to imagine that this now barren island was once covered with trees and forests, but as wood and other tree materials were needed to transport the mo‘ai, trees had to be cut down and forests subsequently disappeared. In view of this rapacious resource depletion executed in the space of two and a half centuries, the locals devised narratives that managed to minimize the role of humans destroying the island’s abundant forests. The environmentally concerned physicist Adam Frank, on the other hand, relates in a matter-of-fact voice that the ‘need for trees, rope, and food to maintain a population of laborers eventually led to the destruction of the very forests the islanders depended on. After the forests were gone erosion took the soil too. What followed was Easter Island collapsing into starvation, warfare and cannibalism. The chance of escape disappeared too as seafaring canoes require large trees for their hulls'”.[7] Edwards, for her part, adds that “many scientists are also pessimistic, [but] others are more optimistic”.[8] She cites Professor Stephen Boyden as an example of the latter and predictably, he has come out to state that “[w]hile there’s a glimmer of hope, it’s worth working to solve the problem. We have the scientific knowledge to do it but we don’t have the political will”.[9] The other side of the coin is represented by somebody like the English writer and erstwhile green activist Paul Kingsnorth, who spent about two decades striving to save the planet as an activist in the environmental movement. But once he turned 40, he had an epiphany of sorts and threw out the baby with the bathwater, some would argue . . . he wrote an essay that ended with the following words: “It’s all fine. I withdraw, you see. I withdraw from the campaigning and the marching . . . I am leaving. I am going to go out walking”.[10] Together with Dougald Hine, he penned UNCIVILISATION: The Dark Mountain Manifesto,[11]


“These are precarious and unprecedented times . . . Little that we have taken for granted is likely to come through this century intact.

We don’t believe that anyone — not politicians, not economists, not environmentalists, not writers — is really facing up to the scale of this … Somehow, technology or political agreements or ethical shopping or mass protest are meant to save our civilization from self-destruction.

Well, we don’t buy it. This project starts with our sense that civilization as we have known it is coming to an end; brought down by a rapidly changing climate, a cancerous economic system and the ongoing mass destruction of the non-human world. But it is driven by our belief that this age of collapse — which is already beginning — could also offer a new start, if we are careful in our choices.

The end of the world as we know it is not the end of the world full stop”.[12]




[1] Lin Edwards, “Humans will be extinct in 100 years says eminent scientist” Phys.org (23 July 2010). http://phys.org/news/2010-06-humans-extinct-years-eminent-scientist.html#jCp.

[2] World Population Growth in the 21st Century (23 March 2012), p. 3. http://www.globalaginvesting.com/downloads/files/World-Population-Growth-in-the-21st-Century-277F.pdf.

[3] Lin Edwards, “Humans will be extinct in 100 years says eminent scientist”.

[4] World Population Growth in the 21st Century, p. 3.

[5] Lin Edwards, “Humans will be extinct in 100 years says eminent scientist”.

[6] Lin Edwards, “Humans will be extinct in 100 years says eminent scientist”.

[7] C. Erimtan, “Easter Island as a metaphor: resource depletion, climate change and the word of God” Today’s Zaman (21 December 2010). http://www.todayszaman.com/op-ed_easter-island-as-a-metaphor-resource-depletion-climate-change-and-the-word-of-god-by-can-eri-mtan-_229397.html.

[8] Lin Edwards, “Humans will be extinct in 100 years says eminent scientist”.

[9] Lin Edwards, “Humans will be extinct in 100 years says eminent scientist”.

[10] Wen Stephenson ,”‘I withdraw’: A talk with climate defeatist Paul Kingsnorth” Grist 50 (11 Apr 2012). http://grist.org/climate-energy/i-withdraw-a-talk-with-climate-defeatist-paul-kingsnorth/.

[11] The Dark Mountain Project. http://dark-mountain.net/about/manifesto/.

[12] Wen Stephenson ,”‘I withdraw’: A talk with climate defeatist Paul Kingsnorth”.

A Renewable Future for the United States: Stanford Study


On 24 February 2014, Stanford’s Mark Shwartz writes that “Mark Jacobson and his colleagues have created a 50-state roadmap for replacing coal, oil and natural gas with wind, water and solar energy”.[1] As Director of the Atmosphere/Energy Program and Professor of Civil and Environmental Engineering, Jacobson seems well-placed to head such an ambitious undertaking, and he himself had this to say: “Drastic problems require drastic and immediate solutions. Our new roadmap is designed to provide each state a first step toward a renewable future”.[2] And the Jacobson plan was first unveiled at the annual meeting of the American Association for the Advancement of Science in Chicago . . . and as it turns out, the ‘2014 Annual Meeting theme—Meeting Global Challenges: Discovery and Innovation—focused on finding sustainable solutions through inclusive, international, and interdisciplinary efforts that are most useful to society and enhance economic growth’.[3]


Here is Professor Jacobson at the NASA Ames Research Center Director’s Colloquium on July 8, 2014 (in Moffett Field, California). Global warming, air pollution, and energy insecurity are three of the most significant problems facing the world today. The Jacobson talk discusses the development of technical and economic plans to convert the energy infrastructure of each of the 50 United States to those powered by 100% wind, water, and sunlight (WWS) for all purposes, namely electricity, transportation, industry, and heating/cooling, after energy efficiency measures have been accounted for.

Published on 27 Aug 2014

The 132-page report is freely available on the internet and presents the Jacobson plan in great detail, stressing that “[c]onversion to a 100% WWS [or wind, water and sunlight] energy infrastructure in the U.S. will eliminate energy-related air pollution mortality and morbidity and the associated health costs, and it will eliminate energy-related climate change costs to the world while causing variable climate impacts on individual states”.[4]


[1] Mark Shwartz, “Stanford scientist unveils 50-state plan to transform U.S. to renewable energy” Stanford News (26 Feb 2014). http://news.stanford.edu/news/2014/february/fifty-states-renewables-022414.html.

[2] Mark Shwartz, “Stanford scientist unveils 50-state plan to transform U.S. to renewable energy”.

[3] “Meeting Global Challenges: Discovery and Innovation (2014 Highlights)” AAAS. http://www.aaas.org/AM2014.

[4] Mark Z. Jacobson, Mark A. Delucchi, Guillaume Bazouin, Zack A. F. Bauer, Christa C. Heavey, Emma Fisher, Sean B. Morris, Diniana J. Y. Piekutowski, Taylor A. Vencilla and Tim W. Yeskooa, ” 100% clean and renewable wind, water, and sunlight (WWS) all-sector energy roadmaps for the 50 United States” Energy & Environental Science (2015), 8, pp. 2093–2117.

Inside Story: A new member of the human family?

‘Scientists say they have uncovered the remains of a new human-like species in South African cave. Patrick Randolph-Quinney, Ashley Kruger and Briana Pobiner talk about the newly discovered Homo naledi. Published on Sep 11, 2015′.

Electrosmog: How WiFi & other EMFs Cause Biological Harm

At the moment, Prof. Emeritus Martin L. Pall is a lone voice in the vast global desert of wireless connectivity . . . ‘Pall’s extensive research over recent decades (some of his peer-reviewed studies on this subject are listed in the final two minutes of this presentation) shows that: 1) Microwaves damage humans at levels far below present radiation limits, through mechanisms at the cellular level. 2) These biological mechanisms can – completely or partially – be behind growing “unexplained illnesses” like sudden cardiac death, ME, weakened immune system, fibromyalgia, post-traumatic stress, and increased DNA breakage, etc. 3) The effects can in principle affect all multicellular animals, and is proven, for example, in mussels. 4) You need neither New Age, tendentious science or conspiracy theories to justify this. The video is footage from Arne Naess seminar 18th October 2014 Oslo’.  

‘The conclusion to be drawn from Pall’s findings is that we face a new and increasingly present environmental pollutant. Some have called it the “21st century environmental bomb”, with implications for the environment, human health, construction of mobile towers, computers in schools, and handling of individuals presenting with symptoms of EHS. Martin Pall, Prof. Em. at Washington State University, has an impressive body of work. His first article on EMFs and their role in VGCC activation earned a place in the “Global Medical Discovery” list of the most important articles in medicine in 2013’.  

Climate Change is a Hoax: Ice melt, sea level rise and superstorms

Some time ago a research article entitled “Ice melt, sea level rise and superstorms” was published; its authors include such crazy climate luminaries like James Hansen and Eric Rignot: “Abstract. There is evidence of ice melt, sea level rise to +5–9 m, and extreme storms in the prior interglacial period that was less than 1 °C warmer than today. Human-made climate forcing is stronger and more rapid than paleo forcings, but much can be learned by combining insights from paleoclimate, climate modeling, and on-going observations. We argue that ice sheets in contact with the ocean are vulnerable to non-linear disintegration in response to ocean warming, and we posit that ice sheet mass loss can be approximated by a doubling time up to sea level rise of at least several meters. Doubling times of 10, 20 or 40 years yield sea level rise of several meters in 50, 100 or 200 years. Paleoclimate data reveal that subsurface ocean warming causes ice shelf melt and ice sheet discharge. Our climate model exposes amplifying feedbacks in the Southern Ocean that slow Antarctic bottom water formation and increase ocean temperature near ice shelf grounding lines, while cooling the surface ocean and increasing sea ice cover and water column stability. Ocean surface cooling, in the North Atlantic as well as the Southern Ocean, increases tropospheric horizontal temperature gradients, eddy kinetic energy and baroclinicity, which drive more powerful storms. We focus attention on the Southern Ocean’s role in affecting atmospheric CO2 amount, which in turn is a tight control knob on global climate. The millennial (500–2000 year) time scale of deep ocean ventilation affects the time scale for natural CO2 change, thus the time scale for paleo global climate, ice sheet and sea level changes. This millennial carbon cycle time scale should not be misinterpreted as the ice sheet time scale for response to a rapid human-made climate forcing. Recent ice sheet melt rates have a doubling time near the lower end of the 10–40 year range. We conclude that 2 °C global warming above the preindustrial level, which would spur more ice shelf melt, is highly dangerous. Earth’s energy imbalance, which must be eliminated to stabilize climate, provides a crucial metric”.[1]

Talking about this new research article in Rolling Stone, Eric Holthaus declares that “[h]istorians may look to 2015 as the year when shit really started hitting the fan. Some snapshots: In just the past few months, record-setting heat waves in Pakistan and India each killed more than 1,000 people. In Washington state’s Olympic National Park, the rainforest caught fire for the first time in living memory. London reached 98 degrees Fahrenheit during the hottest July day ever recorded in the U.K.; The Guardian briefly had to pause its live blog of the heat wave because its computer servers overheated. In California, suffering from its worst drought in a millennium, a 50-acre brush fire swelled seventyfold in a matter of hours, jumping across the I-15 freeway during rush-hour traffic. Then, a few days later, the region was pounded by intense, virtually unheard-of summer rains. Puerto Rico is under its strictest water rationing in history as a monster El Niño forms in the tropical Pacific Ocean, shifting weather patterns worldwide”.[2]  Holthaus then explains that “Hansen’s new study also shows how complicated and unpredictable climate change can be. Even as global ocean temperatures rise to their highest levels in recorded history, some parts of the ocean, near where ice is melting exceptionally fast, are actually cooling, slowing ocean circulation currents and sending weather patterns into a frenzy. Sure enough, a persistently cold patch of ocean is starting to show up just south of Greenland, exactly where previous experimental predictions of a sudden surge of freshwater from melting ice expected it to be. Michael Mann, another prominent climate scientist, recently said of the unexpectedly sudden Atlantic slowdown, ‘This is yet another example of where observations suggest that climate model predictions may be too conservative when it comes to the pace at which certain aspects of climate change are proceeding’. Since storm systems and jet streams in the United States and Europe partially draw their energy from the difference in ocean temperatures, the implication of one patch of ocean cooling while the rest of the ocean warms is profound. Storms will get stronger, and sea-level rise will accelerate. Scientists like Hansen only expect extreme weather to get worse in the years to come, though Mann said it was still ‘unclear’ whether recent severe winters on the East Coast are connected to the phenomenon”.[3]

Michael Mann is the climate scientist behind the famous hockey stick analogy: “The hockey stick is a famous historical temperature plot that shows for the past 2,000 years global temperatures moved up and down very slightly (hockey shaft) but in the past several decades the temperature has rapidly risen (hockey blade)”, as expressed by the meteorologist Scott Mandia.[4]  In response to Hansen et al.’s new research paper, Professor Mann e-mailed this missive to the Washington Post: the authors’ “case is most compelling when it comes to the matter of West Antarctic ice sheet collapse and the substantial sea level rise that would result, potentially on a timescale as short as a century or two”, adding however that “[t]heir climate model scenario wherein Greenland and Antarctic meltwater caused by warming poles, leads to a near total shutdown of ocean heat transport to higher latitudes, cooling most of the globe (particularly the extratropics), seems rather far-fetched to me”, nevertheless conceding that “[w]hether or not all of the specifics of the study prove to be correct, the authors have initiated an absolutely critical discussion”.[5]  Hansen himself then merely stated that “[y]ou can see a lot of different points in this paper, and it’s going to take a while for the community to sort them out, but actually, the story is clear”, namely that sea level rise is “the big impact of human made climate change”.[6]  And, taking into consideration that about 71 percent of the earth’s surface is covered by water, and that the oceans hold about 96.5 percent of all the earth’s water, Professor Hansen’s words may seem a bit trite but also alarmingly ominous.

[1] J. Hansen, M. Sato, P. Heart2, R. Ruedy, M. Kelley, V. Masson-Delmotte, G. Russell, G. Tselioudis, J. Cao, E. Rignot, I. Velicogna, E. Kandiano, K. von Schuckmann, P. Kharecha1, A. N. Legrande, M. Bauer, and K.-W. Lo, “Ice melt, sea level rise and superstorms: evidence from paleoclimate data, climate modeling, and modern observations that 2 °C global warming is highly dangerous” Atmospheric Chemistry and Physics (23 July 2015). http://www.atmos-chem-phys-discuss.net/15/20059/2015/acpd-15-20059-2015.html.

[2] Eric Holthaus, “The Point of No Return: Climate Change Nightmares Are Already Here”Rolling Stone (05 August 2015). http://www.rollingstone.com/politics/news/the-point-of-no-return-climate-change-nightmares-are-already-here-20150805.

[3] Eric Holthaus, “The Point of No Return: Climate Change Nightmares Are Already Here”.

[4] Scott Mandia, “BOOK REVIEW: The Hockey Stick and the Climate Wars” Planet3.0 Beyond Sustainability (10 February 2012). http://planet3.org/2012/02/10/book-review-the-hockey-stick-and-the-climate-wars/.

[5] Chris Mooney, “The world’s most famous climate scientist just outlined an alarming scenario for our planet’s future “The Washington Post (20 July 2015). http://www.washingtonpost.com/news/energy-environment/wp/2015/07/20/the-worlds-most-famous-climate-scientist-just-outlined-an-alarming-scenario-for-our-planets-future/.

[6] Chris Mooney, “The world’s most famous climate scientist just outlined an alarming scenario for our planet’s future “.

Human-Climate Interactions and Evolution — Past and Future

‘CARTA – Center for Academic Research and Training in Anthropogeny: This symposium presents varied perspectives from earth scientists, ecologists, and paleoanthropologists on how climate may have shaped human evolution, as well as the prospects for the future of world climate, ecosystems, and our species. Elizabeth Hadly begins with a discussion about A Tipping Point: Using the Past to Forecast Our Future, followed by Naomi Oreskes on Human Impacts: Will We Survive the Future?, and Veerabhadran Ramanathan on Climate Change Mitigation: In Pursuit of the Common Good. Recorded on 05/15/2015′.