Category Archives: Grit

Counterfactual History of Scientific Discoveries

Source: Nautilus, Dec 2016

think about the way science works: how ideas arise out of the context of their time and the contingencies and quirks of individual scientists.

Heliocentrism – Johannes Kepler

There are few great discoveries for which one can’t find precedents, and heliocentrism—the idea that the Earth revolves around the sun and not vice versa—is no exception. It’s such a pivotal concept in the history of science, displacing humanity from the center of what was then considered the universe, that anticipations have been well documented before the German-Polish astronomer Nicolaus Copernicus outlined the theory in his epochal De revolutionibus orbium coelestium, published as he lay on his deathbed in 1543.

Tycho’s protégé and Galileo’s correspondent, the German Johannes Kepler, would have done it first. He had access to Tycho’s excellent observational data, he was mathematically adept, but crucially he also had Copernicus’s dash of (to our eyes) mysticism that saw a sun-centered universe as appropriately harmonious. To dare to put the sun in the middle, you needed not just rational but also aesthetic motives, and that was Kepler all over.

Laws of motion – Christiaan Huygens

A single law of gravitational attraction was all you needed to explain the shapes of planetary and lunar orbits and the trajectories of comets.

All this was laid out in Newton’s Principia, published in 1687 after being instigated to eclipse Hooke’s reckless claim that he could explain the ellipse-shaped planetary orbits. Before he could deal with planets, Newton had to set down his basic laws of motion. The three that he described in Book I are the foundation of classical mechanics. In short: Bodies maintain their state of uniform motion or rest unless forces act on them; force equals mass times acceleration; and for every action there is an equal and opposite reaction.

They are concise, complete, and simply stated, almost heart-breaking in their elegance. Could anyone else have managed that feat in Newton’s day?

at least one genius among the Society’s many continental correspondents who might have risen to the challenge. Dutchman Christiaan Huygens was polymathic even by the
 ample standards of his day: a mathematician, astronomer (he made
 some of the first observations of 
Saturn’s rings), inventor, and expert
 in optics and probability. He was especially good at devising clocks and watches, which occasioned a priority dispute with the irascible Hooke. Huygens’ theorems on mechanics in his book on the pendulum clock in 1673 were taken as a model by Newton for the Principia.

Newton’s first law was scarcely his anyway: Known also as the law of inertia (a moving object keeps moving in the absence of a force), it was essentially stated by Galileo, and Huygens embraced it too. The Dutchman’s studies of collisions hover on the brink of stating the third law, while Huygens actually wrote down a version of the second law independently. He had what it took to initiate what we now call Newtonian mechanics.

Special relativity – James Clerk Maxwell

One reason why it is more than just fun to imagine alternative routes to discovery is that it can help to puncture myths. The story of Einstein imagining his way to special relativity in 1905 by conceptually riding on a light beam captures his playful inventiveness but gives us little sense of his real motives.

awarding that realization to a man who was dead in 1905, namely Maxwell himself. He died in 1879 aged just 48, and was very much active until the end. He had the kind of deep intuition in physics that was needed for the remarkable feat of adding electricity to magnetism and producing light. Given two more decades (and the seeds of doubt sown about the ether) I suspect he would have figured it out. You don’t need to take my word for it: Einstein said it himself. “I stand not on the shoulders of Newton,” he said, “but on the shoulders of Maxwell.”

General relativity – Hermann Minkowski

In 1916 Einstein unveiled a new view of gravity, which superseded the theory of Isaac Newton that had reigned for over two centuries. He argued that the force we call gravity arises from the curvature of space and time (the four-dimensional fabric called spacetime) in the presence of mass. This curvature causes the acceleration of bodies in a gravitational field: the steady speeding up of an object falling to Earth from a great height, say. This was the theory of general relativity, which is still the best theory of gravitation that exists today and explains the orbits of the planets, the collapse of stars into black holes, and the expansion of the universe. It is Einstein’s most remarkable and revered work.

Permit me again to bend the rules of the game here—for once more, Einstein might have been beaten to it if another scientist had not died first.

In 1908 Minkowski explained that the proper way to understand Einstein’s theory of special relativity—which was all about bodies moving at constant speeds, not accelerating—was in terms of a four-dimensional spacetime. Einstein was at first skeptical, but he later drew on the concept to formulate general relativity.

Minkowski was already alert to the implications, however. Crucially, he saw that whereas the path of an object moving at a constant speed in spacetime is a straight line, that of an accelerating object is curved. In three-dimensional space, the path of the moon orbiting the earth under the influence of their gravitational attraction is more or less circular. But the four-dimensional worldline of the orbiting moon is a kind of helix: It goes round and round in space, but returns to the same position in space at a different time.

There’s more to general relativity than that. It is mass itself, Einstein said, that deforms spacetime into this curving, so-called non-Euclidean (not flat) shape. But the idea of a non-Euclidean spacetime was Minkowski’s, and it’s quite conceivable that he would have fleshed out the idea into a full-blown gravitational theory, perhaps working together with the formidable mathematician David Hilbert at the University of Göttingen, where Minkwoski was based starting from 1902.

We do know, from a lecture Minkowski gave at Göttingen in 1907, that he was already thinking about gravitation in the context of relativity and spacetime. But we’ll never know how far he would have taken that, had he not died suddenly at the start of 1909, aged just 44.

Structure of DNA – Rosalind Franklin

I’d love to think that Rosalind Franklin, the English crystallographer whose data were central to the discovery of the double-helical structure of DNA, would have figured it out if James Watson and Francis Crick hadn’t done so first in 1953. It was famously only when Watson saw the pattern of X-rays scattered from DNA and recorded by Franklin and student Raymond Gosling that he became convinced about the double helix. He was shown these data by Maurice Wilkins, with whom Franklin had a prickly working relationship at King’s College London—and Wilkins did not have Franklin’s permission for that, although any impropriety has been overplayed in accounts that make Franklin the wronged heroine. In any event, those data triggered Watson and Crick’s deduction that DNA is a helix of two strands zipped together via weak chemical bonds between the gene-encoding bases spaced regularly along the backbones.

I was worried, though, that Franklin—cautious, careful and conservative by instinct in contrast to the brilliant, intuitive Crick and the brash young Watson—wouldn’t have stuck her neck out on the basis of what by today’s standards is rather flimsy evidence. She knew that a female scientist in those days couldn’t afford to make mistakes.

So I was delighted when Matthew Cobb, a zoologist at the University of Manchester who delved deeply into the DNA story for his 2015 book Life’s Greatest Secret, confidently told me that, yes, Franklin would have done it. “The progress she made on her own, increasingly isolated and without the benefit of anyone to exchange ideas with, was simply remarkable,” Cobb wrote in The Guardian. Just weeks before Watson and Crick invited Franklin and Wilkins to see their model of DNA in March 1953, Franklin’s notebooks—studied in detail by British biochemist Aaron Klug, who won a Nobel Prize for his own work on DNA—show that she had realized DNA has a double-helix structure and that the two strands have complementary chemical structures, enabling one to act as a template for replication of the other in the way Watson and Crick famously alluded to in their discovery paper in Nature that April.

“Crick and I have discussed this several times,” wrote Klug in the Journal of Molecular Biology. “We agree she would have solved the structure, but the results would have come out gradually, not as a thunderbolt, in a short paper in Nature.” At any rate, her contributions to the discovery are undeniable. “It is clear that, had Franklin lived, the Nobel Prize committee ought to have awarded her a Nobel Prize, too,” writes Cobb.

The other contender for the discovery is American chemist Linus Pauling, who was the Cambridge duo’s most feared rival. Pauling had impetuously proposed a triple-helical structure of DNA in early 1953 with the backbones on the inside and the bases facing out. It made no chemical sense, as Watson and Crick quickly appreciated to their great relief. Unperturbed by such gaffes, Pauling would have bounced back. But he didn’t have Franklin’s X-ray data. “Pauling was a man with great insight, but not a magician who could manage without data,” wrote Klug.

Natural selection – ?

Sometimes discoveries or breakthrough ideas occur to different individuals more or less simultaneously. It happened with calculus (Leibniz and Newton), with the chemical element oxygen (Scheele, Priestley, and Lavoisier), and most famously, with evolution by natural selection, announced in 1858 by Charles Darwin and Alfred Russel Wallace.

That tells us something about this entire counterfactual enterprise. Science provides us with theories that are objectively useful in explaining and predicting what we see in the world. But that doesn’t deny the fact that specific theories generally have a particular style in terms of what they express or stress, or of what metaphors they use:

quantum electrodynamics could have been constructed without using the celebrated language of Feynman diagrams devised by Richard Feynman. It seems entirely possible that the way we conceptualize the world bears the imprint of those who first proposed the concepts. Scientists may be less replaceable than we think.

An 800-feet ladder between school & home

Source: The Guardian/UK, Nov 2016

Authorities in south-west China have come to the aid of schoolchildren who had to climb an 800m cliff to get to and from school – by installing a thin steel ladder at the site.

Left:  newly installed blue steel ladder
Right:  old wood+vine-based ladder

Close-up of students on the old ladder

How to be a Successful Scientist

Source: University of Waterloo website, 2005 &  Psychology Today, May 2010

1. Make new connections.

Broaden yourself to more than one field.
Read widely.
Use analogies to link things together.
Work on different projects at the same time.
Use visual as well as verbal representations.
Don’t work on what everyone else is doing.
Use multiple methods.
Seek novel mechanisms.
Find new ways of making problems soluble, e.g. by new techniques.

2. Expect the unexpected.

Take anomalies seriously.
Learn from failures.
Recover from failures.
Avoid excessive attachment to your own ideas.
Be willing to recognize and admit mistakes.

3. Be persistent.

Focus on key problems.
Be systematic and keep records.
Confirm early, disconfirm late.
Concentrate tenaciously on a subject.

4. Get excited.

Pursue projects that are fun.
Play with ideas and things.
Ask interesting questions.
Take risks.
Have a devotion for truth and a passion for reputation.
Have an inclination toward originality and a taste for research.
Have a desire for the gratification of discovery.
Have a strong desire to comprehend.
Never do anything that bores you.

5. Be sociable.

Find smart collaborators.
Organize good teams.
Study how others are successful.
Listen to people with experience.
Foster different cognitive styles.
Communicate your work to others.
Marry for psychological compatibility.
Tell close colleagues everything you know.
Communicate research results effectively.
Learn from winners.
Have people to fall back on when you get into trouble.

6. Use the world.

Find rich environments.
Build instruments.
Seek inspiration in nature.
Have good laboratory facilities and use them.
Observe and reflect intensely.
Perform experiments that rigorously test hypotheses.

Highly Creative People are Auto-Didacts

Source: PBS, Jul 2014

They teach themselves from an early age, have many deep interests, rather than just one. And they are very persistent, even in the face of rejection.

… many of these highly creative people are autodidacts. They are people who teach themselves. That makes them almost misfits in the educational system that they get put into. It would be nice if educators were aware of the existence of autodidacts and the need to give them slightly different education experiences, to nurture them.

Think Big – Nima Arkani-Hamed

Source: Wired, Oct 2015

… pursuing one’s own ideas with unbridled enthusiasm, politely disregarding naysayers and tackling obstacles head-on.

Life was good in Canada; only one thing was jarring. At that time, “there was a ceiling to the level of bigness and ambition with which people thought about things,” Arkani-Hamed said. He was particularly struck by how proud many Canadians were of having built the robot arms of NASA’s space shuttles. During news coverage of launches, he recalled, “there would be all these close-ins on the arm, on the ‘Canada’ on the arm, and I’d be, like, the space shuttle is a bigger deal!”

As radical as it sounds, many physicists now think that the spatiotemporal dimensions we seem to move around in are not fundamental, but rather emerge from a deeper, truer description of reality. And in 2013, anunexpected discovery by Arkani-Hamed and his studentJaroslav Trnka offered a possible clue to what the underlying laws of nature might look like.

They uncovered a multifaceted geometric object whose volume encodes the outcomes of particle collisions—beastly numbers to calculate with traditional methods. The discovery suggested that the usual picture of particles interacting in space and time is obscuring something far simpler: the timeless logic of intersecting lines and planes. Although the “amplituhedron” (as Arkani-Hamed and Trnka dubbed their object) initially described a simplified version of particle physics, researchers are now working to extend its geometry to describe more realistic particle interactions and forces, including gravity.

He believes that the interchangeability of points and lines in the geometry of the amplituhedron may be the origin of a mysterious mathematical duality between particles and strings, the basic building blocks of nature in string theory. And particle interactions are just “the baby version of the problem,” he said. His ultimate goal is to describe the entire cosmological history of the universe as a mathematical object.

Ultimately, he said, anywhere from 10 to 500 years from now, the amplituhedron and these cosmological patterns will merge and become part of a single, spectacular mathematical structure that describes the entire past, present and future of everything “in some timeless, autonomous way.”

How to Write Productively

Source: Psychology Today, Nov 2013

  1. Conform to your body rhythms.
  2. Have a daily quota
  3. Produce outlines
  4. Expect multiple drafts.
  5. Read “just in time”.
  6. Know your audience.
  7. Revise thoroughly.
  8. Backup your work.

Asking the Right Question – Einstein

Source: Quora, Sep 2016

Einstein didn’t take 7 years to find the answer to a question; instead, he took 7 years to ask the right question in the first place.

After special relativity, Einstein decided to find a way to incorporate gravity into his theory. Special relativity is all about inertial reference frames and observers traveling at constant velocities, but free-falling observers moving under the influence of gravity always accelerate, so how could he end up with a fully relativistic theory of gravity?

Answering such a question with the knowledge that he had is like trying to navigate a huge expanse of complete darkness. Somehow you’ve got to ask a series of new, important and relevant questions that are also solvable, to try to make sense of this new territory. Any question that you ask could be intractable, but more frequently they could also be irrelevant. Even if you’ve found the right question, you must still figure out how to attack the problem.

That Einstein unraveled this whole thing is nothing short of remarkable, because it must have been confusing as hell when it was first being stated. In fact, Einstein initially set aside what became ultimately the right approach for about 2 years before coming back to it and resolving his earlier confusion. Once he understood that the use of curvature tensors of the spacetime metric was the right way to go, the final answer ended up being very simple:

which basically says that the local curvature of spacetime is proportional to the energy/momentum content at that point. Framed correctly, this is pretty straightforward, and any mathematician working on Riemannian geometry, given the right way of thinking about the problem, could have come up with it. But the key point as I’ve been arguing is in the phrase in italics: you have to go from a physical picture of gravity, and draw the connection between that and something as mathematically abstract as Riemannian geometry before things start to make perfect sense.

Once you appreciate the process by which someone could have come up with this, a question like “was Einstein bad at math” becomes absolutely pointless. He wasn’t an expert at Riemannian geometry, but he was the first to see the connection between geometry and gravity, which in itself is a profound accomplishment. He then successfully learnt the material and put all of the very confusing pieces together, and published his full theory at the same time as David Hilbert, one of the preeminent mathematicians of the 20th century, who based his work on Einstein’s earlier realizations in the first place.