Author: cogiddo

On Karush of the Karush-Kuhn-Tucker theorem

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People like Paul Krugman would call this type of post “wonky”. You have been warned.

In preparation for teaching Mathematics for Economists I for graduate students tomorrow, I decided to see what the Web has on Karush, of the Karush-Kuhn-Tucker theorem. I should have done it earlier! Even though I had been writing Karush-Kuhn-Tucker in my lecture notes almost from the first time I taught mathematics for economists, I did not have much to offer my students on the mystery of why Karush’s work was never published. Why I never searched online about it before I do not understand. Nevertheless, I hit a goldmine in my search today: a paper by R.W. Cottle that offers a lot of fascinating details on Karush and Kunh-Tucker, along with photos of the protagonists and excerpts of letters between Kuhn and Karush, when Kuhn belatedly discovered Karush’s master’s thesis, which pretty much anticipated the Kuhn-Tucker theorem, and hastened to give credit to Karush to fix the historical record. And how did Kuhn discover that Karush had done this? By reading Akira Takayama’s massive 1974 book on Mathematical Economics.

Call me a hopeless nerd, but I find this fascinating. A bit of human interest to liven up all the constrained maximization we do for our work, in one way or another, every day.

The URL where I discovered the paper is
http://www.math.uiuc.edu/documenta/vol-ismp/41_cottle-richard.pdf

Criticizing economics

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Critics of economics abound. The criticisms have become more pointed since the financial and economic disaster that started in 2007 and promises to trouble us for years to come yet. But the critics often take unproductive approaches. I came across an excellent post by Diane Coyle today, on exactly the topic of how to criticize economics. In it, I also noticed a link to a previous good post by Chris Dillow.

All in all, I spent a rewarding period of time in reading these posts today and following their links, so I wanted to note this here. I am also looking forward to the review by Coyle of Mirowski’s new book, which she promises in her post is forthcoming soon.

RIP Ronald Coase (1910–2013)

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I am late to the commemoration of Ronald Coase’s contribution to economics, on the occasion of his death yesterday at the age of 102 years. You will find a large number of online posts about this with a simple search. The New York Times publishes its obituary here. The Economist points to its article published two years ago on the occasion of Coase’s 100th birthday.

After reading a number of other posts on Coase’s legacy, I decided to offer here this fantastic piece by Kevin Bryan. I heartily recommend a careful reading of it and the links it offers. In the Toolbox for Economic Design there are several cautions against taking the “Coase Theorem” seriously. After studying Bryan’s post and the links he offers in it (especially that to McCloskey’s article), you will have a better idea why this nomenclature (Stigler’s baby, Coase proclaimed no theorems) is wrong and misleading, while Coase’s contributions to institutional economics, stemming from his 1960 article The Problem of Social Cost, are important.

Let us also not forget Coase’s 1937 (!) article The Nature of the Firm, an early and fundamental contribution to the way economists ought to view the limits of the efficacy of markets.

On “Time Reborn” by Lee Smolin

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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.