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The Terror of Threes in the Heavens and on Earth

The terror of threes in the heavens and on earth | artistic

The Terror of Threes in the Heavens and on Earth
Physicists have long explored how phenomena in groups of three can sow chaos. A new three-body problem, they warn, could lead to not only global races for new armaments but also thermonuclear war.

By William J. Broad
June 26, 2023 | Updated 1:52 p.m. ET

Isaac Newton was baffled. He was already famous for discovering how gravity holds the universe together and for using that knowledge to predict the movements of celestial bodies, such as the moon’s path around the Earth. Now, by taking the sun’s gravitational tugs into account, he sought to improve his lunar predictions. Instead, it made them worse.

The setback, Newton’s friend Edmond Halley reported, “made his head ache, and kept him awake so often, that he would think of it no more.” Newton felt his defeat so keenly that he recalled it more than once in his old age.

Today it’s called the three-body problem. Famous in science and science fiction for orbital perturbations and chaotic phenomena, it’s recently become a concern of atomic experts and military planners. As Beijing rapidly expands its nuclear arsenal, they warn that the world of atomic superpowers is about to escalate to three from two. The outcome, they add, compared with the Moscow-Washington standoff, now 70 years old, could represent a dangerous new kind of unthinkable.

Three body problem

The looming era could encourage “states to resort to nuclear weapons in a crisis,” Andrew F. Krepinevich Jr., a senior fellow at the Center for a New American Security, recently warned. He cited the natural instabilities observed by physicists and astronomers as a portent.

Experts say the tripolar age could put human survival at risk. But they also cite a number of three-body lessons from nature — starting with Newton’s — that illuminate the issue and suggest possible ways forward. So far, however, no answer stands out. The world’s nuclear thinkers are finding the knotty topic to be as intractable as it was for Newton.

“We have a conceptual problem,”

Ernest J. Moniz

“We have a conceptual problem,” said Ernest J. Moniz, a physicist who as the secretary of energy in the Obama administration oversaw the U.S. nuclear arsenal. “We’ve got to change the traditional approach of equalizing weapons or strategic delivery systems, but how to do that is still unclear.”

“Things are changing very rapidly”

France A. Córdova

France A. Córdova, an astrophysicist and past director of the National Science Foundation, said the study of three-body phenomena in the natural sciences could nonetheless help reveal the military risks. “Things are changing very rapidly,” she said. “Anything that helps in understanding that is great.”

Security-minded hawks want to expand the American arsenal in response to China’s nuclear rise and the threat of Beijing’s closing ranks with Moscow. Doves see a window for three-body downsizing. They want to break the problem into smaller and more manageable parts. For instance, they argue that Washington should deal with the two superpowers independently and seek diplomatic bonds that reinforce two-body stability.

Recently, the Biden administration called for a further simplification. Jake Sullivan, the national security adviser, argued that the American response should focus less on the quantity of the nation’s nuclear arms than on their quality. To deter attacks successfully, he said in a speech, the American military has no need for arms that “outnumber the combined total of our competitors.”

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How to triple your memory by using this trick Ricardo Lieuw On TEDxHaarlem

Triple your memory | Tedx

Do you recall studying for your exams? You probably do. But do you remember how you studied, how you memorized French words or the year of the American civil war? Now, that’s probably harder. As a teenager, Ricardo Lieuw On was packing groceries when he knew what he wanted to study: he wanted to learn about learning. He picked up a study in psychology and learned how to reduce his learning time from 3 hours to 1 hour on the same piece of content. He gained the same knowledge in 200% less time. And specially for TEDxHaarlem, he shares the secret of his technique. This talk was given at a TEDx event using the TED conference format but independently organized by a local community. Learn more at

How to triple your memory by using this trick Ricardo Lieuw On TEDxHaarlem


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Fibonacci & Pythagoras Help save a beautiful discovery from oblivion

Pythagorean Triples

This is another brillian video from Mathologer. In 2007 a simple beautiful connection Pythagorean triples and the Fibonacci sequence was discovered. This video is about popularising this connection which previously went largely unnoticed. If you want more details go to the video on Mathologer.

Pascal’s Triangle

  • One of the most interesting Number Patterns is Pascal’s Triangle (named after Blaise Pascal, a famous French Mathematician and Philosopher). …
  • Diagonals. …
  • Symmetrical. …
  • Horizontal Sums. …
  • Exponents of 11. …
  • The same thing happens with 116 etc.
  • Squares. …
  • Fibonacci Sequence.

The Coefficients of the Binomia Theorem from Pascal’s Triangle

Pascal’s triangle formula is (n+1)C(r) = (n)C(r – 1) + (n)C(r). It means that the number of ways to choose r items out of a total of n + 1 items is the same as adding the number of ways to choose r – 1 items out of a total of n items and the number of ways to choose r items out of a total of n items.

The Fibonacci sequence with Pythagorean triples

The sum of the squares of consecutive Fibonacci numbers is another Fibonacci number. Specifically we have the following right triangle. The hypotenuse will always be irrational because the only Fibonacci numbers that are squares are 1 and 144, and 144 is the 12th Fibonacci number.

Pascal’s triangle is commonly used in probability theory, combinatorics, and algebra. In general, we can use Pascal’s triangle to find the coefficients of binomial expansion, the probability of heads and tails in a coin toss, the probability of certain combinations of things, and so on


About Mathologer

Enter the world of the Mathologer for really accessible explanations of hard and beautiful math(s). In real life the Mathologer is a math(s) professor at Monash University in Melbourne, Australia and goes by the name of Burkard Polster. These days Marty Ross another math(s) professor, great friend and collaborator for over 20 years also plays a huge role behind the scenes, honing the math(s) and the video scripts with Burkard. And there are Tristan Tillij and Eddie Price who complete the Mathologer team, tirelessly proofreading and critiquing the scripts and providing lots of original ideas. If you like Mathologer, also check out years worth of free original maths resources on Burkard and Marty’s site