Check out this post by Phil Plait in Slate, showing a marvelous photo by the Cassini spacecraft of two moons of Saturn. Talk about photo composition!
The pursuit of beauty and economic theory: friends or enemies?
I read this post on Aeon by Frank Wilczek this morning. I posted about it on Facebook but doing so did not make me stop thinking about it. I want to put some of these thoughts down here, as they relate to economic theory, what draws me to it, and whether the draw of beauty in the mathematics used in economic theory detracts from the theory’s value to society. First of all, I invite you to follow the link above and come back to read the rest of my thoughts.
Wilczek has published a book recently, A Beautiful Question: Finding Nature’s Deep Design (Google Play link, Amazon link). I have not read it to the end yet, but I hope I will over the winter break. His discussion in the Aeon post immediately made me think about the art of mathematics and how it motivates me (and many others) to do economic theory and guides our attempts to do it.
Empires built on math
In my early years studying for my doctorate, I thought of math as a collection of empire-building tools for empires of the mind (castles in the sky might be another apt name). Economic theory, heavily math-laden, becomes in this view a galaxy far, far away where each theorist builds an empire (or at least a few starships) to impose order on the universe. Once you have laid down your assumptions, you then have a solid foundation for building and you are the emperor of your theoretical creations, as long as you can write down your mathematical arguments correctly.
This view is not far from Asimov’s galactic empire fiction. Indeed, Asimov himself thought that some sort of social physics exists, and if we can discover its laws, we could predict the unfolding of societies over vast, even galactic, scales. For economics, this perspective explains at least some of the psychological attraction theorists feel towards their castles in the sky. This attraction is particularly prominent for me when I am working on general equilibrium theory, which most of the profession has left behind.
Ethereal but irrelevant?
Good question! Let me first tell a story about logic and the demise of the Hilbert program in mathematics. Then I will talk about the fragmentation of economic theory, this one brought about by the confrontation of the theory with empirical tests, such as they are (famously much harder in the social sciences than in physics).
Hilbert was a prominent German mathematician. His famous and eponymous program was an attempt to make all mathematics utterly rigorous by putting it on a formal basis and to prove within that framework that mathematics is consistent. (Perhaps the best way to understand “formalization” in this sense, besides the obvious which is that it should be totally understandable to a computer, is by thinking about something von Neumann said: “Young man, in mathematics you don’t understand things. You just get used to them.” —source)
Hilbert’s program came undone when Kurt Gödel came up with his stunning, deep, and worldview shattering (for mathematicians) Incompleteness Theorems. The gist of these theorems is that if you build all of mathematics on a finite list of axioms, then you cannot prove by using this list of axioms all true theorems of mathematics and you cannot prove that the mathematics you have founded on these axioms is consistent (contains no contradictions).
Coming as it did in 1930, this devastating development seems to be a symptom of the fragmentation of European culture, which was soon to produce a horrible war. But what does it have to do with economic theory? Well, it tells us that the theoretical castles are indeed based on air, not stone foundations.
What’s worse, that’s not all that ails theoretical empire-building in economics. While there are plenty of valid criticisms to aim at empirical research in economics, its basic import is that grand, unified economic theories perform badly. This has led to the growth of “behavioral economics”. (Once again, let me point out how silly this name is: isn’t all economics behavioral? — I prefer psychological economics). However mainstream this field has become, it does have a shattering impact on beautiful theory-building that aims at wide applicability.
We contain multitudes and that can be beautiful too!
Well, it was good enough for Walt Whitman. How about we apply it to the entire society, whose functioning is the domain of study of economic theory, broadly conceived? Does the fragmentation I just talked about make further theory development ugly?
Many social scientists have written on this issue. To me, it seems that a fragmented field of theories can still be an object of beauty in the mind of the theorist. Think of it as a kaleidoscope (a word that literally means “a device for showing beauty”). This is how I attempt to keep my motivation up when I am struggling with long, messy arguments trying to prove something in complicated mathematical models of society that invariably leave my head spinning after only a couple of hours of effort.
Another good thing to say about the fragmented collection of models that constitutes modern economic theory is that it has produced some quite literally life-saving innovations (kidney exchanges, which came from a deeply mathematical field of economic theory called mechanism design theory). A good and easily readable account is Al Roth’s recent book Who Gets What — and Why.
Some others to read on related matters
In conclusion, here are some thoughtful works to read carefully that I constantly feel guilty for not having time to read carefully enough.
Dani Rodrik has a recently published book in which he “argues that economics can be a powerful tool that improves the world―but only when economists abandon universal theories and focus on getting the context right”, as the book description on Amazon states. Another book I have started — so I really should wrap this post up now and get back to reading, even without having convinced myself that this gigantic post is as well written as possible! Of course it’s not. But I move on anyway. Ars Longa, Vita Brevis. Or, in the original language of Hippocrates, taken from the last link:
Ὁ βίος βραχύς, ἡ δὲ τέχνη μακρή, ὁ δὲ καιρὸς ὀξύς, ἡ δὲ πεῖρα σφαλερή, ἡ δὲ κρίσις χαλεπή. In English: Life is short, and art long, opportunity fleeting, experience perilous, and decision difficult.
Universities have become too enamored with journal impact factors. These factors are supposed to indicate journal quality. They are used heavily in evaluating the research of scholars, espcially at the time when professors are evaluated for tenure and promotion. But the impact factor of a journal is a bad measure of its quality. This is quite obvious when one looks at distritbutions of citations of journals. This post has an excellent discussion. H/T to Joerg Fliege for posting this link on Google+, where I saw it.
Paul Romer has a new post about “mathiness”, this time in financial economics. Right at the top of the post, he includes two links to blog posts by Tim Johnson about how mathiness was used to obfuscate what the math says in finance, so that official investigations into the latest financial crisis, the one that started in earnest in 2007, would miss something. In Romer’s words, “People in finance used math to hide what they were doing.” The Johnson posts are rich in material from the beginnings of probability theory, incidentally, and surprised me with a connection to Aristotle and how thinking about money as a universal measure showed people the way to apply math to physics; Johnson also connects finance to a notion of justice. Fascinating stuff! I hope to carve some time out to delve in this more deeply.
H/T for the Paul Romer link: Mark Thoma, here.
I promise in the Hello World post at the top of this blog that the blog would be an attempt to gather at least some of my disparate posts online in one place. In this spirit, let me share here that I was intrigued by this review in the Economist and this post by Paul Romer enough to buy Hidalgo’s book. Since promising to blog about it here might help motivate me to read it soon (by creating some time carved out from my time on social media, which I know I should be doing much more), I hereby promise to blog about this book soon.
Another title for this post could be “Why people who talk about general equilibrium theory should always mention the Arrow-Debreu-McKenzie model, without omitting McKenzie”.
Prompted by a post by Joshua Gans, which I saw first on Google+, I recently bought the book Finding Equilibrium, as on the title of this post. The book contains an insightful discussion of the problem of assigning scientific credit in economics, as the book’s subtitle makes clear: Arrow, Debreu, McKenzie and the Problem of Scientific Credit. I finished the book today. It was published by Princeton University Press very recently, in 2014.
The authors continue an old project of the more senior of the two, Weintraub, that dates from the early 1980s. It has to do with why the Arrow-Debreu paper on the existence of general equilibrium gets more airtime in economic theory circles than McKenzie’s paper, even though the latter was submitted to Econometrica and published a bit earlier than the former.
I must disclose here that Lionel McKenzie was a member of my doctoral dissertation committee. I defended my dissertation at the University of Rochester in 1988 to earn my Ph.D. Furthermore, the professor responsible for my applying (and being accepted, I am sure) to the graduate program in economics at Rochester, Emmanuel Drandakis, was the second person to receive a Rochester Ph.D. in economics after McKenzie created the economics department and graduate program there in the late 1950s. Thus, I was immersed in the story of McKenzie’s unfair treatment in not receiving a Nobel Prize, unlike Arrow and Debreu. The story was “in the air” at Rochester, but I did not hear McKenzie himself talk about it, to the best of my recollection. This accords with my memory of McKenzie as a perfect gentleman; in the book I am talking about here, he is described as “classy” by one of the economists quoted there.
I enjoyed the book and read it in a couple of days, even as it came in the middle of a week that started with some worries in my personal life. It gave me the idea of writing a paper about the now ignored general equilibrium approach as it, I think, should be revived in conjunction with extensions to make it properly include collective goods and externalities (an approach that should proceed with techniques not only limited to the axiom-and-proof ones that were the hallmark of the emergence of general equilibrium in the 1950s). I have worked in this area before, myself, so I may have something new of interest to say by revisiting it. However, I did not want to wait to post here until I wrote a paper; that would mean quite a long wait!
Apart from the inclusion of some jargon from the sociology of science and (naturally) from economics, the book is very well written for a general audience. It flows well and is very instructive. The authors make the best of the fact that their topic allows them, by its very nature, to tell it as a story of people and their interactions. Readers always want stories (as we must remember every time we have to teach abstract ideas in the classroom).
As someone who is well versed in general equilibrium theory (although I’ve been neglecting it lately), I found the exposition of the theory’s inception in the book well done. Furthermore, it gave me a few perspectives and some context I did not already have. If I were to teach general equilibrium again, I would be sure to assign parts of this book to complement the rather dry and scary (for students) mathematics that dominate the theory.
Gans’s post that led me to this book concluded that, of the three main protagonists, Debreu emerges in the most unfavorable light. That is indeed my impression and it comes from documentary evidence of his behavior as a referee of McKenzie’s paper for Econometrica and also vis-a-vis his own co-author, Kenneth Arrow, from whom he kept secret his knowledge that McKenzie was already working on his own paper on pretty much the same topic. By contrast, McKenzie emerges clearly as the wronged party and Arrow as quite generous in giving credit to scholars who preceded him.
So, for the very few of you who say “Arrow-Debreu”, please do remember to say “Arrow-Debreu-McKenzie” when talking about general equilibrium theory.
[Edited 2014-09-29 to correct some infelicities in my use of English.]
Reflections on Lee Smolin’s Time Reborn: From the Crisis in Physics to the Future of the Universe, Houghton Mifflin Harcourt, April 2013.
I want to react here to this book which apparently has the potential to create monumental change in the physical and the social sciences, including economics. This will take a lot of thinking and writing, so consider this post the first in a series.
If Smolin is correct, then a lot of what we teach in economics about dynamical systems will be found to be irrelevant. The origin of the so-called Black Swans will have found an explanation (but we will still not be able to predict them or prepare better for them). The prevalence of network and evolutionary thinking in economics will become ever greater.
What is Smolin saying in this book? Before I start giving my take, here is his own website about it and here is the lengthy review by James Gleick in the New York Review of Books. I also noticed a review of the book, together with two others on physics, in The Economist. Smolin’s website, linked above, has links to other reviews, as well, of which that of Alan Lightman is quite critical.
The book starts by a summary of the framework that the author built to change how we make theories about the universe. His major contention is that the universe is defined as a relation between events in it that evolves over time and that all objects we observe and their relations evolve over time. Everything marches to the beat of time. Time is absolute and everything is relative to time. Rather than imagining that the space-time continuum is the correct basis for understanding the world, we are to ascribe time, but not space, the property of being absolute. Space, being this evolving network of evolving objects, changes with time, and so do the laws of physics. So here we have it: Leibniz was right in his conception of the universe as a network, Newton was wrong in thinking of space as standing, like a Platonic ideal, outside of time and unaffected by the objects in it. Nothing is outside of time: nothing is timeless. (Believers in various religions will not like this aspect of Smolin’s framework.)
There is one problem to note with the book before I go on further. Smolin, an accomplished physicist, does not actually redo all of physics on the basis of the new framework he proposes. So, having said that physics has to be dismantled and rebuilt, he has not done the rebuilding yet; he has not even started. This point is made clear in Gleick’s review as well as in the review by Pedro Ferreira in Nature. Given how monumental this task is, I am willing to cut Smolin a lot of slack. Even if it turns out that this book is thought-provoking but leads nowhere in the end, the provocation will surely prove to have been worth it for making us gain a better understanding of what science is.
Join me here next time for my next post on Time Reborn, to appear once I have had time to read more of the book and reflect further.
UPDATE: Sorry about this, but I lost interest in this book shortly after I published this post. The more I thought about it, the less I saw any positive suggestions on how to alter the kind of mathematical modeling that we economists engage in. Do not expect another post from me on this book.
Software is eating the world. Despite a poor year, Facebook has a market capitalization of $65 billion. This little company with barely 2000 developers is worth as much as a car marker.
Students should take notice. I would expect countless students to come to college demanding top-notch software training. I would expect graduate students to focus on building gorgeous software programs.
Yet software produced in universities and colleges is awful, and it is not getting better. I have a few explanations:
(Via Daniel Lemire’s blog) Highly recommended. Read all about it at the link on the top.
OK, I am becoming obsessed with Lemire’s blog. One more post from there now, and back to my own work I go. Incidentally, the book by Michael Nielsen discussed below is sitting in my queue of e-books I really should be reading yesterday. (Once again, I have snipped most of the text of the post, for which I strongly recommend that you visit the source.) And before I go, let me obey Lemire’s injunction and repeat: scholarship is not a publishing business.
Thus, a much more significant vision is Nielsen’s open science. Michael Nielsen is arguing for a culture shift in science: from a science obsessed with individual performance (and publications) to a science culture resembling more that of open source software or wikipedia.
I fear however that despite all the (well deserved) press that Michael Nielsen’s latest book has been getting, too few people understand the importance of this shift. It is not about becoming hippies. It is not a socialist utopia. On the contrary, the system we have right now is akin to an highly regulated industry. All power is in the hands of the government and a few large organizations (universities, publishers) working in tandem. The barrier to entry is maintained artificially high. Open science is really about creating “open markets” with freer exchanges. It has the potential to boost our collective productivity by orders of magnitude through the removal of unneeded friction.
And we finally get a hint at why it is so hard it is to open up science: the business of science has become intertwined with businesses like the publishing business. ACM has to speak both as an association of computing professionals, and as a publishing house.
What should be a critical support service, the publication of results, ends up driving much of our culture. The journals become the science. The medium becomes the message.
In effect, we have too much organizational scarring tissue in science. It could be that we need to reboot the system. As a starting point, we should collectively recognize the problem. Repeat after me: scholarship is not a publishing business.
- Is Open Access publishing the solution? Really?
- ACM’s role in public policy
- Time for scholarly publishers to disavow the AAP
The ACM charges the authors of any conference for the publication of proceedings. However, they do not require payment for publishing in their journals: instead they request page charges.
(Via Daniel Lemire’s blog)