Category Archives: Optimization

Kenneth Arrow and Formal Modeling as a Form of Criticism, Part 1


arrowKenneth Arrow died on Feb. 21 at the age of 95. I am not a scholar of Arrow’s work, per se, but inasmuch as I’ve studied him in the context of my broader work, I’ve always found him to be a thoughtful and intriguing person. My book, Rational Action, even gives him the last word.

My point, channeled through Arrow, is that the people who developed fields like operations research and decision theory and who formalized economics were not advocating an exotic, revolutionary, or naive concept of rationality and governance. Rather, they worked to understand and explicitly describe rationality as it exists in the world and to use and improve on that rationality so as to improve decision making and policy. In 1957, Arrow described building formal (i.e., mathematics and logic-based) models of decision making as striving toward a final destination that could never be reached. But, drawing on Goethe’s Faust, he regarded the very act of striving as offering a chance at intellectual salvation. (“He who ever strives, him can we save” / Wer immer strebend sich bemüht, Den können wir erlösen.)

But to what end was Arrow actually striving? I would argue that, certainly early in his career, it was not primarily toward more faithful descriptions of reality—his craft remained far distant from that destination. Rather, his paramount interest was to use models to build an improved critical understanding of cutting-edge concepts and ideas—their presuppositions and logical consequences, their possibilities, and their limits. In this, Arrow was not so different from the humanistic (literary, historical, or philosophical) critic. Yet, his methods were, of course, very different.

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Optimization and the Gulag: A brief tour of certain 20th-century intellectual anxieties

Optimized labor?

Optimized contruction? Prisoner laborers constructing the Baltic Sea-White Sea canal

In her recent New York Times Magazine essay, “A Sucker is Optimized Every Minute,” Virginia Heffernan posits that an increasing infatuation with “optimization” in our society is leading to cultural, economic, and political harms. Her themes and some of the topics she examines are very much in this blog’s wheelhouse, so I thought it would be useful to take a look at some of the ideas in her piece. First, I’d like to point out that, if we stand back and think about the various associations Heffernan draws, they should seem bizarre. A good example is her concluding line, “Right there in my Apple Watch: a mini Gulag, optimized just for me.” Suppose she chose a slightly different metaphor, say comparing Spotify music-selecting algorithms to Auschwitz. The obvious distastefulness of the comparison would make it immediately apparent that the former and the latter simply exist in totally different moral, intellectual, and institutional universes. Let’s leave aside the question of why it seems to be OK to rope Soviet forced-labor camps into clever cultural critiques. The fact is it is actually perfectly possible to follow Heffernan’s argument without undue bafflement. The reason has to do with our various inheritances from intellectual history. Continue reading

The Traveling Salesman Problem: How much computational efficiency do you really need?

This post is inspired by a blog post by analytics and software engineer Nathan Brixius concerning recent media interest in the Traveling Salesman Problem (TSP). The TSP, for the uninitiated, is to find a minimum-distance route between a set number of points; as the number of points increases, the problem of being certain one has found a solution becomes computationally formidable. Thus, the problem is really to find an efficient algorithm for finding solutions.

Randal Olson's minimum-distance road trip

Randal Olson’s minimum-distance road trip

Come out with guns blazing, or lay out the welcome mat?

Michigan State computer science grad student Randal Olson developed, and blogged about, an algorithm to solve the Traveling Salesman Problem for a 48-stop tour of the United States. This is almost the exact same version of the problem featured in 1954 in the first publication to use linear programming methods to address the TSP. Olson’s approach was picked up by blogs at the Washington Post and New York TImes websites as an interest story. Unfortunately, Olson also suggested that guaranteeing a solution is computationally impossible—for 48 stops it is actually very simple to prove optimality.

TSP expert Bill Cook, Professor of Combinatorics and Optimization at the University of Waterloo, quickly pointed out that the true shortest route—35,940 meters shorter than Olson’s—could be easily computed on an iPhone using his Concorde TSP app. Brixius writes that, good as it is to point out OR’s extensive work on the TSP, it was important to go gently on Olson’s misstatements so that the OR profession would not come out of the episode looking bad.

And it’s here where, as a historian of science who happens to study the history of OR, I find I recognize the issue from two complementary perspectives.

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