(More on this later, if I have time!)

Physicists combine this sort of reasoning with basic physics to quickly get a feel for the contours of complex phenomena, without going through detailed calculations.

Fermi was famously good at this. He estimated the yield of the Trinity test from his vantage point 16 km away, by dropping little pieces of paper and watching how they moved as the pressure wave passed. He was running estimates as his nuclear pile in Chicago went critical.

By which I mean: There are about 3 million families in Chicago, and maybe 4 people per family-sized unit, and one actual piano (not a keyboard) out of every 20 family-sized groups. Probably they need tuning one a year or so, and I’d guess a tuner can handle two tunings per day? That gets us to around 50 tuners in Chicago.

That may be off, but hopefully by no more than a factor of 10. It should be a good order-of-magnitude estimate.

Physicists refer to these sorts of questions as “Fermi Problems."

Perhaps the most famous one – it's often used as an example of the genre – is “how many piano tuners are there in Chicago?”

The answer is almost certainly different than it was back in the 40s or 50s, but you can imagine various ways of arriving at an estimate.

3x10⁶ 👤
x 1👨👩👧👧 / 5👤
x 1🎹 / 20👨👩👧👧
x 1 tuning / 300📅
x 1 tuner x 📅 / 2 tunings
~ 50 🎹 tuners in Chicago

But Fermi was also famous for asking students and colleagues questions that seemed, at first, to require complex physics or information they did not have access to.

On a road trip he once asked: How thick will dust pile up on the windshield if we’re driving at 60 mph?

A precise answer wasn’t the point. His questions were exercises in approximation. You chain together a bunch of estimates to arrive at an answer that gives you an order-of-magnitude result. You’d be surprised what you know!

Fermi is perhaps best known as the first person to initiate a controlled and self-sustaining fission reaction. Chicago Pile-1 went critical on December 2, 1942, under the stands of the University of Chicago’s Stagg Field.

Image: Melvin Miller/Argonne

Enrico Fermi, one of the foremost physicists of the 20th century, was born #OTD in 1901. While most physicists focus on either experiment or theory, Fermi excelled at both.

Now, estimate how many new physicists will be born today.

Image: New York Public Library

@sciencewrighter I don’t know! I imagine it’s probably symbolic, but maybe it’s a literal reference.

Anyway, that 1746 paper by Maupertuis is probably the oldest work that I have cited in one of my own publications. (7/7)
https://arxiv.org/abs/0803.1485

He later tried to apply his principle in other fields including biology, theology, and psychology (he proposed a principle of pleasure and pain). Those efforts didn't meet with quite as much success!

Lagrange and later Hamilton would generalize and refine the principle in important ways, but we usually credit Maupertuis with originating the Principle of Least Action. (6/n)

In 1746 Maupertuis presented his paper “Laws of Movement and Rest” to the Berlin Academy of Sciences, applying his principle to the motion of point masses.

In his subsequent essay “The Laws of Rest and Motion Deduced from the Attributes of God,” Maupertuis gave a statement of the principle of least action that is often quoted or paraphrased. (5/n)

(Leonhard Euler proposed a very similar idea around the same time, but ceded priority to Maupertuis. Konig claimed they both swiped the idea from Leibniz, who probably came up with the same principle decades earlier. But Leibniz only discussed it in private letters, so how were Euler and Maupertuis supposed to know?)

By 1744, Maupertuis extended this idea to the motion of material objects.

He defined an object's “action" as the integral of momentum along its path, or the time integral of its "vis viva" (2 x kinetic energy) from start to finish.

Maupertuis proposed that Nature acts to minimize this quantity.

Maupertuis originally formulated his principle to explain the motion of light, arguing that the integral of its velocity along the path it follows is minimized.

This allowed him to recover Snell's Law for the refraction of light as it passes between different materials.

Astronomer and mathematician Pierre-Louis Moreau de Maupertuis, exact date of birth unknown, was born around this time in 1698 and baptized #OTD.

He was among the first to articulate the Principle of Least Action, one of the most beautiful ideas in physics.

Image: Wellcome Trust

Anyway, of all the important results Einstein published in his "miracle year" of 1905, the astounding and unexpected equivalence between mass and energy is the one that lodged itself in the popular consciousness.

Happy E = mc² day!

The rate at which the energy was radiated as gravitational waves was not uniform — there was a peak and then it fell off.

But if we estimate most of it being radiated over the last 10ms or so of the merger, that’s a power output of around 2 x 10⁴⁹ Watts.

That’s about 10 times the luminosity of all the visible stars and galaxies in our universe!

During the GW150914 black hole merger, between 2.5 and 3.5 solar masses were converted to energy that was radiated as gravitational waves.

One solar mass is about 2 x 10³⁰ kg, and the speed of light is 3 x 10⁸ m/s. So 3 solar masses is mc² = 1.8 x 10⁴⁷ J.

Image: NASA

Still, there are some examples of fantastically large masses being converted into an equivalent amount of energy! Just not in ways that we can harness.

My favorite examples are the binary black hole mergers observed by @LIGO and the EGO Virgo collaborations.

These mergers rapidly radiate so much energy in the form of gravitational waves that they are briefly more luminous than all the stars in our universe, combined.

@johnefrancis Thanks! I'll add it to the list.