Book Review: Hidden Order

Hidden Order: The Economics of Everyday Life by David Friedman

Hidden Order is my favorite popular economics introduction, because, rather than being a sequence of interesting stories making a point, it has the logic and structure of a textbook: starting from simple beginnings, Friedman hones in on certain insights, and then gradually adds complexity to explain more and more.

This is not surprising, since before this book (published in 1997), Friedman had written an intermediate macroeconomics textbook called Price Theory (first edition in 1986, second edition in 1990). The chapter titles and subjects are almost word-for-word identical. The difference is a loss of mathematical detail and rigor and end-of-chapter problems; perfectly fair for a pop intro.

After an introductory Part I that introduces economics as it’s actually thought of by economists (as opposed to a naive laymen view that it’s all about money and the stock market, the far more fun stuff is things like the economics of war and the economics of driving), Part II logically constructs modern price theory in a very clean and ideal world. Part III adds a number of real-world complications, like the existence of firms (as opposed to single-person production), strategic behavior, and the uncertainties of time and chance. Part IV is subtitled “The Economist as Judge” and deals with efficiency, at least as economists define it. This is the section dealing with rent-seeking, public goods, and externalities. One simplification in this section that I wish he had done without was the assumption of constant utility of dollars (one dollar being worth the same to a rich man as a poor man) versus something more realistic like utility as a logarithmic function of dollars. The final Part V deals with some particular applications: the economics of crime, public choice theory, and the economics of dating and marriage.

In my experience (having convinced several people to read it), Hidden Order might need to be read “in waves”, as many paragraphs are dripping in insight and the reader might move too quickly and not be building on a solid foundation. Typically when revisiting a chapter the point sticks better having seen a bit where he’s heading. It’s definitely worth the effort though.

Posted in Uncategorized

Book Review: Square One

Square One: The Foundations of Knowledge by Steve Patterson

The first of a series of planned philosophy books by Steve Patterson, who runs the Patterson in Pursuit podcast that I listen to, Square One is about the ultimate grounding of human knowledge in necessary logic.

In the first chapter, Patterson lays out a tree analogy for one’s worldview, where the leaves are conclusions, the branches are premises, and the roots are the foundations. People spend most of their time on the leaves, when it’s the roots that matter most (if you get the foundations wrong, all your conclusions are in serious doubt). This is contrasted with the “web of knowledge” way of thinking where there are no foundations but instead all your beliefs consist of one interconnected layer. He argues that the roots of knowledge are the laws of logic, which are necessary and can be known for certain.

In the second chapter, Patterson addresses implausibility arguments against humans attaining such certain knowledge. Examples include the skeptical injunction to always be humble about what we can know, the evolutionary origins of the brain which emphasizes what works rather than what is necessarily true, and the implausibility of the universe needing to be sensible to humans. While these arguments have some persuasive power, they cannot establish that certain truths are unknowable. Impossibility arguments are addressed in chapter five.

Chapter 3 is the core of the book, where the laws of logic are laid down: the law of identity, the law of non-contradiction, and the law of excluded middle. Patterson hammers home that these are necessarily true and cannot be denied, for the denial of them assumes their truth. Chapter 4 extends these basic laws to some necessary consequences, such as how theory is prior to data and how we can be certain there exists the phenomena of awareness by a mind. This is not a textbook on logic, though, so he doesn’t demonstrate the formalization of propositional logic and how it can be used and manipulated (perhaps that could have made a short appendix? For people who want to explore this topic more and in particular how logical operations can be mechanized, try The Logician and the Engineer).

The final fifth chapter addresses “impossibility argument” counters to the claim that we can be certain about the laws of logic. Some major arguments that he addresses are the liar’s paradox (a misuse of language), quantum indeterminacy (whatever else, logic is prior to physics), and the “mere tautology” reply (mathematics can be thought of as a series of “mere tautologies”, but we sure as hell learn something new).

Short and readable, this makes for a good primer on logic and the rationalist worldview and I wouldn’t hesitate to recommend it to a logic neophyte or to somebody who claims that “we can never really know anything”. I look forward to Patterson’s subsequent books.

Posted in Logic, Rationality, Reviews

Book Review: Stuff Matters

Stuff Matters: Exploring the Marvelous Materials that Shape Our Man-Made World by Mark Miodownik

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