Pi, climate change denial and creationism


Right off, it may not sound like pi, climate change denial and young-Earth creationism have much in common. In fact, there is an important connection. Here is some background.

Credit: Michele Vallisneri, NASA JPL

Computing pi

Pi = 3.1415926535…, namely the ratio between the circumference of a circle and its diameter, has fascinated not only mathematicians and scientists but the public at large for centuries. Archimedes (c.287–212 BCE) was the first to present a scheme for calculating pi as a limit of perimeters of inscribed and circumscribed polygons, as illustrated briefly in the graphic to the right (see this Math Scholar blog for details). In the centuries following Archimedes, ancient mathematicians worldwide used this approach to calculate pi to increasing accuracy. Beginning in the 17th century, in the wake of the discovery of calculus by Newton and Leibniz, numerous new formulas by pi were found, some permitting even more digits to be computed. This culminated in 1874 with Shanks’ hand calculation of pi to 707 digits (alas, only the first 527 were correct).

In the 20th century, with the advent of the computer, pi was computed first to thousands, then to millions, then to billions, and, most recently, to trillions of digits. Facilitating these calculations are some remarkable new formulas for pi. For example, this paper presents a formula that permits one to calculate digits (in a binary or hexadecimal base) starting at an arbitrary starting position, without needing to calculate any of the digits that came before. Even more important was the discovery of some very clever computer algorithms applicable to computing pi. For example, in 1965 researchers found that the “fast Fourier transform” (FFT), a computational technique widely used in signal analysis and many other scientific fields, can be used to greatly accelerate high-precision multiplication.

The most recent record of pi, as of the present date, was to 31 trillion digits (actually 31,415,926,535,897 digits, to be exact, which happens to be the first 14 digits of pi), by a researcher at Google.

Pi denial

The subject of pi is dear to the present author, as he has published several papers and a book on this very subject. Thus it is with great sadness and consternation to see a growing number of writers (mostly lacking advanced mathematical training) who reject basic mathematical theory and the accepted value of pi, claiming instead that they have found pi to be some other value. For example, one author asserts that pi = 17 – 8 * sqrt(3) = 3.1435935394… Another author asserts that pi = (14 – sqrt(2)) / 4 = 3.1464466094… A third author promises to reveal an “exact” value of pi, differing significantly from the accepted value. For other examples, see this Math Scholar blog.

Needless to say, as any professional mathematician or, for that matter, any person who has at least completed a course in calculus will attest, such claims cannot possibly be correct. Tens of thousands of mathematicians, and hundreds of thousands of others who have been taught mathematics through the centuries, have derived many of these pi formulas for themselves, and have even calculated pi for themselves, checking their poofs and calculations very carefully. These proofs and calculations have also been checked by computer, in excruciating detail. It is also very well known that pi was proven to be transcendental by Lindemann in 1882 (and his proof has been carefully checked by countless mathematicians since). This means that pi cannot possibly be given by any finite algebraic expression, and most certainly not by a simple algebraic expression such as those mentioned in the previous paragraph.

In short, the fact that pi = 3.1415926535… (and not any variant value) is as certain as any assertion in all of mathematics, right up there with “the square root of two is not a rational number” and, for that matter, “two plus two equals four.”

So why do these and other writers insist pi is otherwise? In reading through some of their email messages promoting their views that they have sent to long lists of researchers (including the present author), two common themes emerge: (1) they are distrustful of the proofs of traditional results (such as Archimedes’ construction and Lindemann’s theorem), even though they scarcely understand them, and (2) they believe that the “professors” who object to their writings are deliberately ignoring or even colluding to repress these writings.

Credit: IPCC

Climate change denial

It is similarly distressing to see the fact of climate change, along with the very likely fact that humans are the leading contributor to climate change, widely discounted in the public arena.

At this point in time, the basic facts of climate change are not disputable in the least. Careful planet-wide observations by NASA and others have confirmed that 2018 was the fourth-warmest year in global average mean temperature in recorded history. The only warmer years were 2016, 2017 and 2015, respectively, and 18 of the 19 warmest years in history have occurred since 2001. Countless observational studies and supercomputer simulations have confirmed both the fact of warming and the very likely conclusion that this warming is principally due to human activity. These studies and computations have been scrutinized in great detail by a climate science community numbering in the thousands, from all major nations, as summarized in the latest report by the Intergovernmental Panel on Climate Change (IPCC).

At this point in time, at least 97% of climate science researchers agree with these conclusions. Further, this consensus is supported by official statements from the American Association for the Advancement of Science, the American Chemical Society, the American Geophysical Union, the American Medical Association, the American Meteorological Society, the American Physical Society, the Geological Society of America, the U.S. National Academy of Sciences and other scientific societies worldwide.

According to the latest report by the IPCC, impacts on natural and human systems are already occurring, and even a warming of 1.5 C, which at this point can hardly be averted, will have very serious consequences, including more extreme temperature events, more instances of heavy precipitation, more severe droughts, rising sea levels damaging cities and agricultural lands, as well as enormous stress on ecosystems worldwide.

And yet, although there has been some progress, large numbers of Americans in particular continue to deny this consensus. In a 2017 Pew Research Center survey, 23% denied that there is any solid evidence that the Earth has been warming, and of those who acknowledge warming, nearly half doubted that it is due to human activities.

So why are so many skeptical of the scientific consensus? In part, it is because that many in the public are simply not aware of the degree of consensus among scientists. According to a separate 2017 Pew Research Center survey, only 27% agreed that “almost all” scientists are in agreement; 35% said only “More than half,” and 35% said half or fewer. But even more disturbingly, only 32% agreed that the “best available scientific evidence” influences the climate scientists’ conclusions; 48% said only “some of the time”, and 18% said “not too often or never.” These results underscore a severe level of distrust of scientists in general and climate scientists in particular by the public.

Phylogenetic tree for the Tktaalik fossil

Evolution denial

Darwin’s On the Origin of Species by Means of Natural Selection was first published 160 years ago. In the intervening years scientists have scrutinized every aspect of Darwin’s theory in extraordinary detail. For example, Darwin acknowledged that there were numerous gaps in the fossil record, but since Darwin’s time, most of these gaps and others have been filled by discoveries of remarkable transitional fossils. For example, the origin of the original four-legged creatures (tetrapods) remained murky until 2004, when the “Tiktaalik” fossil was found in the Canadian arctic — see graphic at right.

Technology for studying evolution has advanced far beyond Darwin’s wildest dreams. Radiometric dating produces extremely accurate and very reliable geological dates, amply confirming the fact that the geological ages are many millions of years old, and that the Earth itself is approximately 4.56 billion years old. Even more impressive is the enormous decline in price of DNA sequencing technology — by approximately a factor of 27 million since 2000. The DNA data obtained via this technology have dramatically confirmed the central tenets of evolution, including the common ancestry of all biological organisms in a phylogenetic family tree, in most cases exactly as had been previously reckoned based solely on similarities of physical forms and biological functions. Indeed, the data all but scream “evolutionary descent from common ancestors.” See DNA for an overview of the latest results.

Here is just one of many examples of how DNA data, in this case transposon (“jumping gene”) mutation data, can be used to determine the phylogenetic relationships (i.e., “family tree”) of various primates including humans. The columns labeled ABCDE denote five blocks of transposons, and x and o respectively denote that the block is present or absent in the genome of the given species. It is clear from this data that our closest primate relatives are chimpanzees and bonobos [Rogers2011, pg. 89].

						Transposon blocks
			Species		A	B	C	D	E
        /---------	Human		o	x	x	x	x
       /----------	Bonobo		x	x	x	x	x
      / \---------	Chimp		x	x	x	x	x
     /------------	Gorilla		o	o	x	x	x
-----|------------	Orangutan	o	o	o	x	x
     \------------	Gibbon		o	o	o	o	o

Sadly, a large percentage of the public also discounts the scientific consensus on evolution. According to a 2019 Pew Research survey, fully 31% of Americans assert that humans have existed in their present form since the beginning of time. According to a 2017 Gallup survey, 38% of Americans believe that God created humans in their present form within the past 10,000 years. Needless to say, such views are in severe conflict with the overwhelming majority (well over 99%) of qualified scientists in evolution-related fields, representing every major nation and religious movement on Earth — see Scientists on evolution.

Why the denial and distrust?

We are living at the apex of scientific and technological progress. Within the past few decades, our species has discovered the laws of relativity, quantum physics and the standard model; unraveled the structure of DNA; found that the universe’s expansion is accelerating; discovered thousands of extrasolar planets; began observing the universe via gravitational wave astronomy; increased worldwide life expectancy from 29 in 1880 to 71 today; developed space vehicles for travel to the Moon and Mars; developed computer technology that is one million times more powerful than just 25 years ago; linked the world with the Internet; placed a smartphone (or at least a cell phone) in the hands of 70% of the entire world population; dropped the price of genome sequencing by a factor of 27 million; and launched a new world of artificial intelligence and robotics whose impact we can only dimly foresee.

Instead, a large fraction of the public resist even the most basic and overwhelmingly confirmed scientific principles, such as the value of pi, the fact of global warming and the fact of evolution.

So what can be done to counter this dreadful public mindset, which in the case of climate change denial and vaccination denial threatens our very existence? To begin with, numerous first-world nations, and the U.S. in particular, need to upgrade their educational systems. The U.S., for instance, ranks only mediocre in international educational performance tests. Students who are better educated in school are less likely to be persuaded by science skeptics later.

Many of the public fear, some with good reason, that advanced technology will steal their jobs. Others fear technologies such as genetically modified foods, in spite of the fact that major scientific societies have overwhelmingly concluded that GMO foods are no more or less safe than conventional foods.

But for the most part, the hostility mentioned above appears to be a reaction to the public’s perception scientists as “elites” and out of touch with common people, due in part to scientists’ miserable failure to communicate the excitement of modern science to the public and to involve the public in scientific discovery.

Ellie Arroway (Jodie Foster) awe-struck at a galaxy in “Contact”

Winning the battle, but losing the war

We mathematicians and scientists have been very successful in our battles to prove theorems, make discoveries, analyze data, write journal articles and obtain grants. But we are losing the war for the hearts and minds of the public. What can we do? Here are some suggestions:

  • Start a blog.
  • Visit schools.
  • Give public lectures.
  • Write articles for science news forums.
  • Study creative writing, arts and humanities to sharpen communication skills.
  • Recognize those who do reach out in hiring, promotion, tenure and research funding decisions.
  • Promote interdisciplinary coursework and studies at universities that combine the arts with science, working in synergy rather than in competition or opposition to other fields.
  • Find ways to involve the public in research projects, for example by inviting the public to help with field studies or lending home computer cycles for data analysis.

In one memorable scene from the movie Contact, Ellie Arroway (Jodi Foster) views a galaxy from her spacecraft, and is so overcome with awe that she exclaims, “They should have sent a poet. So beautiful. So beautiful… I had no idea.” In a similar way, those of us involved in scientific research are often stunned by the beauty and elegance of science and the mathematics behind it, along with the remarkable (and quite mysterious) fact that we humans are able to comprehend these laws through diligent effort.

So why don’t we do more to share this wonder? Why don’t we write some poetry?

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