The Anthropocene

The Annual Review is a pretty good magazine for review articles. The Concept of the Anthropocene (Malhi, 2017) is written by a proponent of the concept of the anthropocene.

At its core, the Anthropocene is an encapsulation of the concept that modern human activity is large relative to the basic processes of planetary functioning, and therefore that human social, economic, and political decisions have become entangled in a web of planetary feedbacks.

Or, "Actually, the earth is small, and the ocean is not an infinite garbage dump."

How it started

The modern use of the term Anthropocene began in 2000 with Crutzen & Stoermer's paper in the Global Change Newsletter, simply entitled “The Anthropocene.” This was followed in 2002 by Crutzen's high-profile piece in Nature (“Geology of Mankind”), which gained much wider circulation and attention.

Crutzen is a 1995 Nobel Laureate for research on the ozone hole.

A pivotal event in terms of gaining wider scientific acceptance and adoption was the publication of a thematic issue of Philosophical Transactions of the Royal Society in 2011. This issue covered a range of perspectives, including conceptual and historical antecedents (6), biosphere transformation (10), sediment fluxes (11), and the geological case (12).

That issue is 13 March 2011, Volume 369, Issue 1938. It's a very fun issue, plenty to read!

How to find the (projective) inscribed circle in a quadrilateral

This post answers a question raised in Extraordinary Conics: The Most Difficult Math Problem I Ever Solved (CodeParade, 2020).

Consider the following quadrilateral, completed by extending some of its edges:

It can be regarded as a perfect square, drawn in perspective. The "undistorted" square, along with its two points at infinity, are drawn below:

Harmut Rosa explains why modern societies keep accelerating

SPEEDCORE for proper mood!

This post started when I felt exhausted after reading Scale, especially after that chapter describing how modern cities are speeding up the bigger they get, rather than slowing down. So I looked around for explanation of why, and found

Of course, I watched it on 2x speed while playing an idle game at the same time. The game is World Idle (2015), and I actually think it's a good way to get a visceral feel for this. In this game, you play as the sole controller of a country's economy, and you are constantly pushed to keep the numbers in the green. But keeping the numbers in the green only means people reproduce and the country keep growing, and you are clicking frantically only to keep in the same place (just above starvation), all the while the economy grows.

This post mostly follows Appropriation, Activation and Acceleration: The Escalatory Logics of Capitalist Modernity and the Crises of Dynamic Stabilization (2017).

Let's Read: Scale (Geoffrey West, 2017)

Scale (Geoffrey West, 2017) has the full title of Scale: The Universal Laws of Life, Growth, and Death in Organisms, Cities, and Companies, and it's a beautiful book. To get an overview, watch

Note

Geoffrey West has his own opinions which are largely orthogonal to what the book is actually about. Here I collect them. When you read the book, feel free to subtract these opinions from the book. It would not affect your understanding of the central point of the book, which is the scaling theory.

• No scientific field is complete without some simple theories. All fields should be like physics. Big data, model-free theory, mere collection of data... those are not enough.

"All science is either physics or stamp collecting." -- Ernest Rutherford

• 21st century is the century of biology.
• Reductionism to the fundamental theory of everything is not enough. Because it is impractical to derive complex phenomena, like life, from the fundamental theories of particles, it is wrong to pay too much attention to it. A full theory of the universe needs several layers, all equally important.
• Most biologists are too interested in "stamp collecting". There are easy discoveries are missed because not enough biologists are thinking like physicists. The physicist way of science is to pick a few key ingredients, make a mathematical model out of those, that can successfully predict a lot. Once that's done, they add more ingredients ("perturbation theory", "second-order theory", etc), making the model more precise but less elegant.

How to talk to dragons

Dragons would have two types of vocalization: high and low. Low voices are slow to make but travels long distances. High voices are fast to make but travels short distances. Thus, they can call out to each other with a low, droning sound generated in their chest. These long-distance calls would be generic messages like "Stay out!" "Want to hunt together?" and "Lemme smash".

When they are close, they use the high voice generated entirely in an organ called the voicebox. The voicebox is very small compared to the dragon chest. It is probably located somewhere on the backs of their necks, to protect it against the elements, impact damage (A dragon's life is hard. Frontal assaults are common.), and from fire and smoke damage (which is why it's not in the throat of the fire-breathing dragons).

The voicebox has its own, little "second lung" to pump air through.

Kolmogorov complexity is Turing equivalent to the halting problem

This post describes several Turing equivalent problems to the halting problem: the busy beaver problem, the busy beaver runtime problem, the minimal program problem, and the Kolmogorov complexity problem.

But really, only one part of the proof is hard, and that is proving that the halting problem can be Turing-reduced to the problem of calculating Kolmogorov complexity.

The core of the argument is this: there exists short strings with short minimal programs, whose runtime is insanely long. That's really it.

Aitken's trick for calculating decimal expansions of rationals

Aitken's Method

Professor Aitken was both a mental calculator and a master mathematician, and a detailed account of his mental math abilities is found in An exceptional talent for calculative thinking, (IML Hunter, 1962)

I'd just like to sketch out one amazing trick, which is illustrated thus:


The proof is  $x = 5/23 = 15/69$, then, $x = (15 + x) /70$, so the trick is to calculate $15/70$ by short division, to generate the digits of $x$ one at a time, then immediately feed to the top to continue. A kind of "just-in-time" algorithm!