How Many Decimals of Pi Do We Really Need?

Earlier this week, we received this question from a fan on Facebook who wondered how many decimals of the mathematical constant pi (π) NASA-JPL scientists and engineers use when making calculations:

.. by cutting pi off at the 15th decimal point, we would calculate a circumference for that circle that is very slightly off. It turns out that our calculated circumference of the 25 billion mile diameter circle would be wrong by 1.5 inches.

.. We can bring this down to home with our planet Earth. It is 7,926 miles in diameter at the equator. The circumference then is 24,900 miles. That’s how far you would travel if you circumnavigated the globe (and didn’t worry about hills, valleys, obstacles like buildings, rest stops, waves on the ocean, etc.). How far off would your odometer be if you used the limited version of pi above? It would be off by the size of a molecule.

.. How many digits of pi would we need to calculate the circumference of a circle with a radius of 46 billion light years to an accuracy equal to the diameter of a hydrogen atom (the simplest atom)? The answer is that you would need 39 or 40 decimal places.

Five Years Later, Cutting Through the Fukushima Myths

At the site of the earthquake, stress had been building up in the Earth’s crust for decades. When it released, that stress caused one of the most damaging quakes on record. The earth moved more than 20 meters over a 500-mile zone and the resulting earthquake released as much energy as a 45-megaton hydrogen bomb (to put this in perspective, this is 30,000 times more powerful as the bomb that leveled Hiroshima). It was the fourth-strongest earthquake recorded since 1900 and the strongest earthquake to strike Japan in recorded history. The quake shifted the Earth’s axis by somewhere between 4 and 10 inches ..

.. For example, it’s true that radioactive cesium (Cs-134 and Cs-137) was measured in tuna caught in the Pacific Ocean. But it’s not true that this cesium posed any risk to people eating this tuna. I interviewed the scientist who made these measurements and he pointed out that the radioactivity of the cesium was lower than the radioactivity content of the natural potassium in the fish.

.. This shouldn’t surprise anyone who has studied the impact of the Chernobyl accident. While there was significant short-term impact in the areas close to the Chernobyl reactors—and the area right around the ruined reactor remains a forbidden zone where you just don’t want to go—further afield the impact was fairly low. Numerous studies (summarized by the International Atomic Energy Agency in this 2006 report) concluded that the ecosystem in the exclusion zone around the Chernobyl site is among the richest ecosystems in Europe, teeming with large game as well as smaller animals, partly because there aren’t any people there.

A Big Little Idea Called Legibility

Scott calls the thinking style behind the failure mode “authoritarian high modernism,” but as we’ll see, the failure mode is not limited to the brief intellectual reign of high modernism (roughly, the first half of the twentieth century).

Here is the recipe:

  • Look at a complex and confusing reality, such as the social dynamics of an old city
  • Fail to understand all the subtleties of how the complex reality works
  • Attribute that failure to the irrationality of what you are looking at, rather than your own limitations
  • Come up with an idealized blank-slate vision of what that reality ought to look like
  • Argue that the relative simplicity and platonic orderliness of the vision represents rationality
  • Use authoritarian power to impose that vision, by demolishing the old reality if necessary
  • Watch your rational Utopia fail horribly

Central to Scott’s thesis is the idea of legibility. He explains how he stumbled across the idea while researching efforts by nation states to settle or “sedentarize” nomads, pastoralists, gypsies and other peoples living non-mainstream lives:

.. The state is not actually interested in the rich functional structure and complex behavior of the very organic entities that it governs (and indeed, is part of, rather than “above”). It merely views them as resources that must be organized in order to yield optimal returns according to a centralized, narrow, and strictly utilitarian logic.

.. The book begins with an early example, “scientific” forestry (illustrated in the picture above). The early modern state, Germany in this case, was only interested in maximizing tax revenues from forestry. This meant that the acreage, yield and market value of a forest had to be measured, and only these obviously relevant variables were comprehended by the statist mental model. Traditional wild and unruly forests were literally illegible to the state surveyor’s eyes, and this gave birth to “scientific” forestry: the gradual transformation of forests with a rich diversity of species growing wildly and randomly into orderly stands of the highest-yielding varieties.

High-modernist (think Bauhaus and Le Corbusier) aesthetics necessarily lead tosimplification, since a reality that serves many purposes presents itself as illegible to a vision informed by a singular purpose. Any elements that are non-functional with respect to the singular purpose tend to confuse, and are therefore eliminated during the attempt to “rationalize.”

.. If my conjecture is correct, then the High Modernist failure-through-legibility-seeking formula is a large scale effect of the rationalization of the fear of (apparent) chaos.

.. And no, the currently popular “pave the cowpaths” and behavioral-economic “choice architecture” design philosophies do not provide immunity against these failure modes. In fact paving the cowpaths in naive ways is an instanceof this failure mode (the way to avoid it would be to choose to not pave certain cowpaths).

.. For the technologists among you, a quick (and very crude) calibration point should help: we are talking about the big brother of waterfall planning here. The psychology is very similar to the urge to throw legacy software away. In fact Joel Spolsky’s post on the subject Things You Should Never Do, Part I, reads like a narrower version of Scott’s arguments. But Scott’s model is much deeper, more robust, more subtly argued, and more broadly applicable.  I haven’t yet thought it through, but I don’t think lean/agile software development can actually mitigate this failure mode anymore than choice architecture can mitigate it in public policy

 

Are the Constants of Physics Constant?

So far, they seem to be—but nobody really understands why

.. Born was after a unifying theory to relate all the fundamental forces of nature. He also wanted a theory that would explain where these constants came from. Something, he said, to “explain the existence of the heavy, and light elementary particles and their definite mass quotient 1840.”
.. But the weird thing about such constants is that there is no theory to explain their existence. They are universal and they appear to be unchanging. So is the case with the masses of protons and electrons. But time and time again, they are validated through observation and experiment, not theory.
.. Paul Dirac, wondered in a Nature paper whether the constants were indeed constant if one were to look at the entire history of the cosmos. Measurements on earth are useful but it is a tiny blue dot in the vast universe. What Dirac asked decades ago is what physicists continue to ask today. Is it a constant everywhere in the universe? Why is it a constant? How constant?
.. The mass ratio, they write, varies less than 0.0005 percent, not enough to call it a change. This is based on telescope observations going as far as 12.4 billion years back in time when the universe was only 10 percent of its current age.
.. Even a small change of a few percent in the value of the ratio would mean a different universe. A smaller mass ratio could mean a wimpier proton, and possibly a weaker pull for the electrons orbiting the nucleus, leading to different kind of matter.
.. No theory in physics can explain the constant mass ratio, the steadfast shepherd of science. It just is, *shrug*.
.. The experimental search for a varying constant will likely continue as long as there is no theory to back its existence.