Education and “The Three-Body Problem”

The brilliant math-watcher, Ian Stewart, says of this classic physics problem, the Three-Body Problem:

Newton’s Law of Gravity runs into problems with three bodies (earth, moon, sun, say).

In particular, the gravitational interaction of a mere three bodies, assumed to obey Newton’s inverse square law of gravity, stumped the mathematical world for centuries.

It still does, if what you want is a nice formula for the orbits of those bodies. In fact, we now know that three-body dynamics is chaotic–so irregular that is has elements of randomness.

There is no tidy geometric characterization of three-body orbits, not even a formula in coordinate geometry.

Until the late nineteenth century, very little was known about the motion of three celestial bodies, even if one of them were so tiny that its mass could be ignored.

(Visions of Infinity: The Great Mathematical Problems, Ian Stewart, Basic Books, 2014, page 136)

Henri Poincaré, the great mathematician, wrestled with this with tremendous intricacy and ingenuity all his life:

Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as “The Last Universalist,” since he excelled in all fields of the discipline as it existed during his lifetime.

Born: April 29, 1854, Nancy, France
Died: July 17, 1912, Paris, France.

We now think of applying in an evocative and not a rigorous mathematical way, the unexpected difficulties of the three-body problem to the n-body (i.e., more than three) problems of sociology or economics or history itself, and sense that social life is always multifactorial and not readily pin-downable, since “everything is causing everything else” and extracting mono-causal explanations must be elusive for all the planetary and Poincaré reasons and beyond.

This suggests to the student that novels are one attempt to say something about n-body human “orbits” based on “n-body” stances and “circumstances” with large amounts of randomness governing the untidy mess that dominates human affairs.

Words are deployed in novels and not numbers as in physics, but the “recalcitrance” of the world, social and physical, remains permanent.

Education and meta-intelligence would be more complete by seeing how the world, as someone put it, “won’t meet us halfway.” Remember Ian Stewart’s warning above:

“There is no tidy geometric characterization of three-body orbits…” and you sense that this must apply to human affairs even more deeply.

Essay 89: Physics AI Predicts That Earth Goes Around the Sun

from Nature Briefing:

Hello Nature readers,

Today we learn that a computer Copernicus has rediscovered that Earth orbits the Sun, ponder the size of the proton and see a scientific glassblower at work.

Physicists have designed artificial intelligence that thinks like the astronomer Nicolaus Copernicus by realizing the Sun must be at the center of the Solar System. (NASA/JPL/SPL)

AI ‘Discovers’ That Earth Orbits the Sun [PDF]

A neural network that teaches itself the laws of physics could help to solve some of physics’ deepest questions. But first it has to start with the basics, just like the rest of us. The algorithm has worked out that it should place the Sun at the centre of the Solar System, based on how movements of the Sun and Mars appear from Earth.

The machine-learning system differs from others because it’s not a black that spits out a result based on reasoning that’s almost impossible to unpick. Instead, researchers designed a kind of ‘lobotomizedneural network that is split into two halves and joined by just a handful of connections. That forces the learning half to simplify its findings before handing them over to the half that makes and tests new predictions.

Next FDA Chief Will Face Ongoing Challenges

U.S. President Donald Trump has nominated radiation oncologist Stephen Hahn to lead the Food and Drug Administration (FDA). If the Senate confirms Hahn, who is the chief medical executive of the University of Texas MD Anderson Cancer Center, he’ll be leading the agency at the centre of a national debate over e-cigarettes, prompted by a mysterious vaping-related illness [archived PDF] that has made more than 2,000 people sick. A former FDA chief says Hahn’s biggest challenge will be navigating a regulatory agency under the Trump administration, which has pledged to roll back regulations.

Do We Know How Big a Proton Is?

A long-awaited experimental result has found the proton to be about 5% smaller than the previously accepted value. The finding seems to spell the end of the ‘proton radius puzzle’: the measurements disagreed if you probed the proton with ordinary hydrogen, or with exotic hydrogen built out of muons instead of electrons. But solving the mystery will be bittersweet: some scientists had hoped the difference might have indicated exciting new physics behind how electrons and muons behave.

Contingency Plans for Research After Brexit

The United Kingdom should boost funding for basic research and create an equivalent of the prestigious European Research Council (ERC) if it doesn’t remain part of the European Union’s flagship Horizon Europe research-funding program [archived PDF]. That’s the conclusion of an independent review of how UK science could adapt and collaborate internationally after Brexit — now scheduled for January 31, 2020.

Nature’s 150th anniversary

A Century and a Half of Research and Discovery

This week is a special one for all of us at Nature: it’s 150 years since our first issue, published in November 1869. We’ve been working for well over a year on the delights of our anniversary issue, which you can explore in full online.

10 Extraordinary Nature Papers

A series of in-depth articles from specialists in the relevant fields assesses the importance and lasting impact of 10 key papers from Nature’s archive. Among them, the structure of DNA, the discovery of the hole in the ozone layer above Antarctica, our first meeting with Australopithecus and this year’s Nobel-winning work detecting an exoplanet around a Sun-like star.

A Network of Science

The multidisciplinary scope of Nature is revealed by an analysis of more than 88,000 papers Nature has published since 1900, and their co-citations in other articles. Take a journey through a 3D network of Nature’s archive in an interactive graphic. Or, let us fly you through it in this spectacular 5-minute video.

Then dig deeper into what scientists learnt from analyzing tens of millions of scientific articles for this project.

150 Years of Nature, in Graphics

An analysis of the Nature archive reveals the rise of multi-author papers, the boom in biochemistry and cell biology, and the ebb and flow of physical chemistry since the journal’s first issue in 1869. The evolution in science is mirrored in the top keywords used in titles and abstracts: they were ‘aurora’, ‘Sun’, ‘meteor’, ‘water’ and ‘Earth’ in the 1870s, and ‘cell’, ‘quantum’, ‘DNA’, ‘protein’ and ‘receptor’ in the 2010s.

Evidence in Pursuit of Truth

A century and a half has seen momentous changes in science, and Nature has changed along with it in many ways, says an Editorial in the anniversary edition. But in other respects, Nature now is just the same as it was at the start: it will continue in its mission to stand up for research, serve the global research community and communicate the results of science around the world.

Features & Opinion

Nature covers: from paste-up to Photoshop

Nature creative director Kelly Krause takes you on a tour of the archive to enjoy some of the journal’s most iconic covers, each of which speaks to how science itself has evolved. Plus, she touches on those that didn’t quite hit the mark, such as an occasion of “Photoshop malfeasance” that led to Dolly the sheep sporting the wrong leg.

Podcast: Nature bigwigs spill the tea

In this anniversary edition of BackchatNature editor-in-chief Magdalena Skipper, chief magazine editor Helen Pearson and editorial vice president Ritu Dhand take a look back at how the journal has evolved over 150 years, and discuss the part that Nature can play in today’s society. The panel also pick a few of their favorite research papers that Nature has published, and think about where science might be headed in the next 150 years.

Where I Work

Scientific glassblower Terri Adams uses fire and heavy machinery to hand-craft delicate scientific glass apparatus. “My workbench hosts an array of tools for working with glass, many of which were custom-made for specific jobs,” says Adams. “Each tool reminds me of what I first used it for and makes me consider how I might use it again.” (Leonora Saunders for Nature)

Quote of the Day

“At the very least … we should probably consider no longer naming *new* species after awful humans.”

Scientists should stop naming animals after terrible people — and consider renaming the ones that already are, argues marine conservation biologist and science writer David Shiffman. (Scientific American)

Yesterday was Marie Skłodowska Curie’s birthday, and for the occasion, digital colorist Marina Amaral breathed new life into a photo of Curie in her laboratory

(If you have recommended people before and you want them to count, please ask them to email me with your details and I will make it happen!) Your feedback, as always, is very welcome at

Flora Graham, senior editor, Nature Briefing

Essay 1: Unnoticed Dimensions of Knowledge

Let’s “get down to cases” right now:

  1. You learn decimals and fractions in school. You see that 1/2 can be written as 0.5 or 0.50 or with as many zeros as you like. That seems “clean.”

But 1/3 is equal to something more complex (i.e., 0.3 recurring or repeating, like 0.3333 and so on infinitely).  If you divide 1 by three you keep getting three.

Imagine you want to experiment a bit, and multiply the fraction 1/3 by three and the 0.3 recurring by three, thus not affecting things since you’re doing the same thing to both sides of the equation.

You get:  1 = 0.9 recurring or repeating.

You’re suddenly puzzled: How can 1 be obtained by adding “slices of 9 fractions” (i.e., 9/10 + 9/100 + 9/1000) to infinity. How do you get to the end? What end? 

It turns out that it’s not that simple to get a grip on all this.  A person who allowed themselves to become fascinated by this specific conundrum would enter a “beautiful ocean” of mathematics beginning with so elementary a phenomenon.

This shows you a deep connection between a part (e.g., the fraction and decimal 1/3 and 0.3 recurring) and the wider world or domain or universe of numbers.

How can it be that such a simple elementary “thing” becomes so intricate, deep and elusive?

  1. Let’s jump over to an entirely different kind of example. Think of Dinesen’s novel Out of Africa. Remember the movie with Meryl Streep and Robert Redford.

Suppose you turn the movie “inside out” and “upside down” and ask: is this movie about coffee and coffee bushes, coffee markets and coffee growing, in a colonial context?  The coffee plantation is near Nairobi (today’s Kenya) and involves plantation economics, colonial relations with Kikuyu peoples, German-British colonial tensions around World War I.

Suppose I take the “backstory” and make that the “frontstory”.

The story of “economic botany” (coffee growing is one case) and colonial tensions between and among Europeans as well as Europeans and Africans is the deeper and larger story while the “musical beds” of the Westerners is a colorful footnote.   

We have the perennial question of “parts and wholes” which is one theme of this book.       

  1. Why does science “orbit” some numbers such as π (pi) (i.e., 22/7)?

You learn in school that there’s a ratio called π (pi) which is 22/7. Think of π (pi) as some kind of essence of circularity. Remember πr2 and 2πr in grade school.

Why does it keep appearing in almost every equation of physics? Why would “circleness” “haunt” science and math? Probability and statistical theory are dependent on π (pi) as a variable. Why?

You could peruse:

A History of Pi is a 1970 non-fiction book by Petr Beckmann that presents a layman’s introduction to the concept of the mathematical constant π (pi)

Why does science “orbit” some numbers such as π (pi)?

This is an example of this quest for connectedness.