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.
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 ‘lobotomized’ neural 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.
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 ‘protonradius puzzle’: the measurements disagreed if you probed the proton with ordinary hydrogen, or with exotichydrogen 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.
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.
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.
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.
(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 firstname.lastname@example.org.
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?
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.
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?