## Book Review: Stuff Matters

When I watched the BBC documentary series Connections (which I recommend to everybody), one of the main takeaways was how important materials science and engineering are to the modern world. No matter the impressive high-tech features of some modern product, buried in the background is likely a need for highly-pure materials unavailable, save in maybe small quantities, to our ancestors. And so I picked up Miodownik’s popular-level Stuff Matters to get a materials fix.

A different material is explored in each of the main chapters, and we are led on a tour of

• Steel
• Paper, of various kinds
• Concrete, including steel-reinforced concrete
• Chocolate
• Aerogels
• Plastics, particularly celluloid
• Glass
• Carbon, including graphite, diamond, carbon fiber, graphene, and nanotubes
• Ceramics, particularly porcelain
• Biomaterials, including plaster, amalgams for tooth-fillings, and titanium

There’s a concluding chapter that moves quickly between the different length scales involved in materials and tries to end pointlessly romantically.

This is not a systematic approach to understanding materials, but rather essentially a collection of popular-level essays on various materials of interest. I don’t mean that as some sort of pointed criticism; the book is what it is. Some materials I might like to have included (there’s always a question of space) are aluminum, hydrocarbons, and textiles.

When posed with the question of what one piece of knowledge would we want to pass down if all of our scientific civilization were to crumbled, the most useful might be “all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another.” I had that in the back of mind as Stuff Matters regularly delves into how the arrangement of atoms determines the macro-scale properties of different materials. Arrange them one way and you get diamond; arrange them in another and you get pencil graphite.

Posted in Chemistry, Reviews

## Human race 2015 Kardashev score

Armed with 2015 data (found on page 40 here, for “Total World”), we can calculate the latest Kardashev score for human civilization. Further, the new data slightly revises previous years estimates, and so I’ll calculate the values for the past few years (while also taking the additional leap days into effect).

$\displaystyle K_{2015} = 0.727 \\ K_{2014} = 0.727\\ K_{2013} = 0.726 \\ K_{2012} = 0.725$

While there was a 1.0% increase in total world primary energy consumption in 2015 over 2014, that wasn’t enough to tick over the Kardashev score giving my three decimals of precision standard.

I guess I haven’t addressed issues with this score yet, so now is as good a time as any. The main problem with the Kardashev scale is the same with all other simple measures of civilization, like GDP or HDI: what you want to know might not be and probably isn’t exactly what you’re measuring. Imagine two civilizations; each produces the same amount of stuff and each happens to produce the same cultural output (same songs, same movies, etc). The only difference is that one uses twice as much energy as the other. We would conclude that the more energy-efficient civilization is the more advanced, right? But the more wasteful civilization would have a higher Kardashev score.

It’s therefore worthwhile to note while the energy consumption of Earth is still increasing, there is another trend where the energy intensity (the amount of energy needed to produce one unit of GDP) is decreasing.

Source: EIA

Posted in Energy, Science (general), Technology | 1 Comment

## Animated Kronig-Penney band structure

In our recent paper, my supervisor and I developed a method for generating the electronic band structure of one-dimensional periodic potentials using matrix mechanics. We used the Kronig-Penney model, which has known analytical solutions, as our benchmark and then extended the approach to potentials that had no analytical solutions.

Recent I made use of MATLAB’s ability to quickly generate animated GIFs by repeatedly writing new figures as frames. So now I can make animations like this:

This is the band structure of the Kronig-Penney model as you gradually turn on the potential (the black rectangles) and see the colored bands begin to split. The horizontal axis is in K-space, not real space, so the spacing of the barriers and wells isn’t meaningful in an absolute sense and is merely for decoration. The height of the barriers in terms of the vertical energy scale is correct, as well as the relative sizing of the barriers and wells.

Posted in Physics

## The Great Courses, organized

A really useful resource for being introduced to new subjects are the Great Courses series from The Teaching Company. If you haven’t heard of them, they’re first- or second-year university-level lecture courses on hundreds of different subject areas, with each lecture typically lasting 30 minutes and usually comprising multiples of 12 lectures. There are a number of sample lectures available on YouTube and on Audible they have a landing page dedicated to the Great Courses.

One difficulty is that with dozens or hundreds of courses it can be difficult to sort through the heap if you don’t already know exactly what you’re looking for. I had this problem when I was trying to see if they had an Introduction to Sociology or an Understanding Sociology series (I’m in the boat Robin Hanson describes here where as an outsider it’s not clear to me what the difference is between economics and sociology) and came up with nothing. At the same time I became interested in how the various academic disciplines relate to each other. Wikipedia was very helpful here.

So I put two and two together and began mapping various Great Courses series as best I could to the academic disciplines. It could never be done perfectly, since the academic disciplines have fuzzy boundaries, compete for different subject matters (is anatomy more a part of biology or medicine?), and the courses themselves don’t bother to follow clear boundaries. I found out as I was doing it (in stages) that there were many more courses than I had initially supposed and I kept discovering areas with dozens of courses that I had hitherto overlooked.

I did my best and the result is now a top-level page on this humble blog, found here. Every time I look at it I end up making small changes and I add to it as The Teaching Company produces new series so it’ll be a living document. I hope others find it useful.

Posted in General

## Book Review: Approaching Infinity

Approaching Infinity by Michael Huemer

“Infinity” is a concept that, if you’re not careful, can really bite you in the ass. In his latest book, Approaching Infinity, the philosopher Michael Huemer attempts to sharpen our idea of infinity to address two areas of concern.

One is the nature of infinite regresses. A famous one is the Regress of Causes, where one event needs to be caused by another event, but that event needs to be caused, etc all the way down the line. Thomists’ attempt to to address this regress is to stipulate an uncaused “unmoved mover” that starts the whole process going. Note that this was a regress that people thought they needed to solve; Huemer calls it thus a “viscous regress”. Other regresses are classified as “benign” though, like starting from the postulate that some proposition P is true. Then it’s true that P is true. It’s also true that it is true that P is true. And so on. Nobody really complains about that regress.

The other area is a number of famous “paradoxes of the infinite”. Examples include Zeno’s paradox, Thomson’s lamp, Galileo’s paradox, and Hilbert’s hotel (there are 17 paradoxes discussed in all). In each case, there’s a paradox that occurs when we assume an infinity is involved. Take Galileo’s paradox (please!): which are great in extent, the natural numbers (1, 2, 3, 4, 5, …) or the perfect squares (1, 4, 9, 16, 25, …)? At first it seems like there should be more natural numbers, since for any finite list of numbers from 1 to n there will be both perfect square and non-squares like 7 or 18. But you can map every natural number to a square (just square the number!) so (1 ↔ 1), (2 ↔ 4), (3 ↔ 9), (4 ↔ 16), and so on. Since every spot on that ladder is filled, it looks as though there are just as many perfect squares as natural numbers. A paradox!

Huemer goes over two classical accounts of the infinite, that of Aristotle and that of Georg Cantor, and finds both wanting in various ways. There are multiple chapters of the philosophy of numbers, sets, and geometrical points that I think fairly present the views of the usual Cantorian orthodoxy before poking holes in them. Even if you ultimately disagree with Huemer’s account, I think it’s a very readable and enjoyable introduction to issues in the philosophy of mathematics.

We then come to Huemer’s own account: extrinsic infinities are allowable or at least possible, whereas intrinsic infinities are not. An extrinsic property is one that changes when you change the “size” of the object in question. So things like size itself, volume, mass, energy content, etc. If you double the size of a block of wood, you double its mass. An intrinsic quantity is one that is comparably scale-invariant; things like temperature, speed, color, etc. If you imagine one cup of boiling water and then bring another cup of boiling water together with it, the temperature of the water does not change.

With this theory of the infinite in hand, Huemer is able to (mostly) resolve the 17 paradoxes and give an account of viscous and benign regresses. For the case of the Regress of Causes, and infinitude of causes going back in time is an extrinsic one, and so in principle non-problematic. The Thomist proposal of an “unmoved mover” who is infinitely powerful fails on this account, though, since such an entity would involve infinite intrinsic magnitudes.

If you’re interested in understanding infinite quantities which if you’ve done any work in the STEM fields you’ll have come across, I wholeheartedly recommend Approaching Infinity.

Posted in Logic, Mathematics, Reviews

## Book Review: The Theory That Would Not Die

If you have a passing familiarity with statistics, you’ve probably come across the centuries old debate between frequentists and Bayesians. Most users of statistics and probability today are probably all too happy to avoid the debate and “just use what works” (though, that doesn’t prevent science from being really hard). The striking thing I learned from the book is just how heated and vicious the debate has gotten in the past (and present), so it’s no wonder that even if there is an Objectively True Outcome people would want to avoid the debate just to be able to get some work down.

I won’t give a lengthy synopsis of the book since Luke Muehlhauser already did a very thorough job some time ago. One of the big takeaways is that in a fairer world it would be called Laplacian statistics with Thomas Bayes credited with having an early inkling. One thing that McGrayne says is that English-speaking scientists grew up not knowing about Laplace and hence the preference for the English Bayes. At least in my experience if this is true it’s pretty outdated, since engineers and physicists (at the very least) learn about the Laplacian, Laplace’s equation, and the Laplace transform.

Two things I wanted from the book but didn’t get were the origin story and effects of Cox’s theorem and how ET Jaynes fits into modern Bayesian thinker, particular in regards to his acclaimed posthumous book Probability Theory: The Logic of Science. There’s no mention of Cox’s and there are only two mentions of Jaynes as basically a voice in the wilderness.

However, that was just my wishlist. My main complaint is that neophyte readers won’t come away with a deep understanding of what actually was being debated. I understand that it’s hard to explain statistical techniques without becoming a math-ridden textbook, but to a great extent many of the points of contention just sound like arcana if you don’t have prior experience with statistics. If you’re somewhat interested in statistics and want to know what all the controversy is about, I’m not sure that this book will clear things up for you. It’s mostly just historical anecdote light reading.

Posted in Mathematics, Reviews, Science (general)

## From a contradiction you can prove anything

Premise:
0. P ∧ P’
Theorem
1. P (simplification from 0)
2. P’ (simplification from 0)
3. P ∨ M (addition from 1)
4. M (disjunctive syllogism from 2 and 3) Q.E.D.

Or in words: P and not P are true. Therefore, P is true. Also, not P is true. Since P is true, P or some other statement M are true. But since not P is true, P or M must collapse into just M.

But we just made M up. It can be whatever we want. Let’s substitute in some actual sentences to see how this works:

P = It is raining
Not P = It is not raining
M = Earth is made out of cottage cheese

It is both raining and not raining. Therefore, it is raining. Also, it is not raining. If it’s raining, that means that we can say that it is true that it is raining or Earth is made out of cottage cheese. But it’s not raining, so in order for that to be true, Earth must be made out of cottage cheese.

The logic is valid (and fairly straightforward), but the conclusion is categorically wrong. Note that this relies on the logician’s use of inclusive as opposed to exclusive or. The latter is what we use in everyday language, but the former is what we mean by “or” in a deductive argument.

So if you’re ever examining your own beliefs and discover a contradiction, be warned!

Posted in Logic, Rationality