The frontispiece from Differentiable Germs and Catastrophes by Theodore Brocker:
When the Greek goddess Hera wanted to know who enjoys sex more, men or women, she had the good sense to ask Tiresias, who had lived as both. (She did not, however, have the good sense to accept Tiresias’s answer).
When sociologist Kristen Schilt wanted to know why men and women succeed differently in the workplace, she had the good sense to ask workers who have lived as both. I’ve read only a fraction of Schilt’s book, but I learned a little about it from Jessica Nordell’s thoughtful writeup in the New Republic. The upshot seems to be that when women become men, they feel that they’re taken more seriously, whereas when men become women, they feel the opposite.
As Nordell points out, this really is a cool idea because a change in gender doesn’t change your skills or education, so when we track people’s experiences before and after their crossings, we’re holding a lot of relevant variables constant.
On the other hand, as Nordell also points out, there’s at least one important variable that’s not being held constant, and that’s testosterone level. When you go from female to male, you acquire a lot of testosterone; when you go from male to female you give up a lot. That opens up a lot of possibilities. Maybe testosterone makes you more effective at work, which leads to better treatment. Or maybe the treatment doesn’t change at all, but your testosterone level leads you to perceive it differently. (Likewise, of course, for a variety of other hormones.)
I do, however, trust Per Krusell and Tony Smith to have given it a fair reading, because Krusell and Smith have long track records as diligent and thoughtful scholars. And their analysis appears to devastate both Piketty’s model and his prediction that income inequality is destined to grow explosively over time.
All of Piketty’s predictions depend on his assumptions about how much people save. The simplest respectable model (that is, a model that economists generally feel comfortable using for many purposes, and which fits fairly well with observations) says that we save a fixed percentage of our incomes — say 30%. (There are also more sophisticated models in which this percentage can change as economic conditions change.)
Piketty, by contrast, assumes that our net saving is a fixed percentage of our net incomes, where “net” means “after subtracting depreciation of our assets”. That’s a very different assumption, and, according to Krusell and Smith, not at all a plausible one. It’s implausible first because it has extremely odd implications. Most notably, it implies (though this is not immediately obvious) that if economic growth slows to zero, we will eventually choose to save 100% of our incomes(!!). Beyond that, Krusell and Smith argue in considerable detail that, compared to the more traditional models, Piketty’s does a poor job of fitting the last seventy years’ worth of data.
According to Krusell and Smith, Piketty demonstrates correctly that under his assumptions, slowing economic growth must lead to massive inequality over time. But under the far more plausible assumptions found in modern textbooks and modern research papers, that conclusion goes away. In fact, after substituting those assumptions, Piketty’s arguments yield something like the opposite conclusion — as growth slows down, changes in inequality become pretty much negligible.
If this analysis is right — and given the identities of the authors I’ll be very surprised if it’s wrong — then there appears to be very little reason to buy into Piketty’s story. That doesn’t mean he’s wasted his time. We learn a lot by making a variety of different assumptions and figuring out where they lead us, even when the assumptions are ultimately unsupportable. But a serious intellectual exercise is not the same thing as a serious prediction.
Max Tegmark is a professor of physics at MIT, a major force in the development of modern cosmology, a lively expositor, and the force behind what he calls the Mathematical Universe Hypothesis — a vision of the Universe as a purely mathematical object. Readers of The Big Questions will be aware that this is a vision I wholeheartedly embrace.
Tegmark’s new book Our Mathematical Universe is really several books intertwined, including:
As I work my way through Robert Caro’s monumental four-volume biography of Lyndon Johnson, I’m repeatedly astonished by Caro’s gargantuan appetite for detail on the one hand, and his near total incuriosity about the big picture on the other.
Case in point: We get almost 40 densely packed pages on the appropriations (eventually totaling $25 million) for the Marshall Ford Dam and another 30 or so on what a dramatic change the dam (and the electricity it brought) made in the lives of Texas Hill Country farm families. But unless I overlooked it, we’re never told how many of those farm families were affected — and are thus left with absolutely no basis for thinking about whether this dam was a good investment.
At another point, we’re told of a $1.8 million expenditure to bring electric lines to 2892 Hill Country farms. (This is, of course, over and above the cost of the dam, which presumably benefited many more than just these 2892.) This time, thankfully, we are at least told how many families are affected. But since the expenditure comes to $622 per family in a time and place when one dollar a day was a good wage, where there was no running water and very little communication with the outside world, and where the soil was bad and getting worse, this raises the question of whether that $622 could have been better spent relocating that family to a better place. (All the moreso if we top off that $622 with the family’s pro rata share of the dam cost.) Caro never even acknowledges the question, pausing simply to celebrate the benefits of electricity, which, he seems to imply, were great and therefore (!) justified the expenditures.
Well, there are two ways you can get the benefits of electricity. The electricity can come to you, or you can go to it. Sometimes one way is better; sometimes the other. When conditions are as Caro describes them — with the land essentially worn out, starvation rampant, and everyone too poor to get a fresh start in, say, Austin — there’s a pretty good likelihood that the guy who could have helped you move, but instead spends a bundle to bring you an electric line, has something other than your best interests at heart.
I’m not far enough along to be sure of this, but after a little peeking ahead, it’s beginning to look like this is how Caro’s going to treat the Great Society also — hundreds of pages on the details of the legislation, hundreds more on the good it (allegedly) did, and not a single inquiry into how much more good somebody could have done with expenditures of that magnitude.
And then there’s this passage, which I feel compelled to assure you I am not making up:
In yesterday’s post, I claimed to have refuted Richard Dawkins’s claim that everything complex must have emerged from something simple by citing the natural numbers, which are provably highly complex (in a very precise sense) yet did not emerge from something simple. Numerous commenters suggested that I’d been unfair to Dawkins, because he’d surely meant his claim to apply only to biological processes.
Here is a quote from Dawkins’s book “The God Delusion”:
Time and again, my theologian friends returned to the point that there had to be a reason why there is something rather than nothing. There must have been a first cause of everything, and we might as well give it the name God. Yes, I siaid, but it must have been simple and therefore, whatever else we call it, God is not an appropriate name….The first cause that we seek must have been the simple basis for a self-bootstrapping crane which eventually raised the world as we know it into its present existence.
I could provide additional quotes, but this one should suffice. Dawkins believes, unless I have misunderstood him completely, that he has a quite general argument, not tied in any way to biology (because the above quote, for example, has nothing to do with biology) to establish that complex structures must have simple causes. That argument, whatever it might be, cannot be correct because the natural numbers stand as a counterexample.
If Dawkins, or any of his defenders, wants to respond that his argument is not intended to apply to the natural numbers, it becomes incumbent on them to point to a hypothesis which is actually used in the argument which would rule out such an application. Absent such a hypothesis, the argument must be erroneous.
I claim to have explained in The Big Questions exactly how the first cause of our Universe could be a mathematical structure that is far more complex than the Universe itself; of course others, like Max Tegmark, have demonstrated this possibility in far more detail than I have. Whether or not Tegmark and I are correct in our beliefs, I claim we’ve at least demonstrated that (as far as we can tell) those beliefs could be true, which, once again, refutes Dawkins’s position.
An argument that leads to flat-out wrong conclusions cannot be a correct argument, even if some of its implications turn out to be true. So I stand by what I said both yesterday and in The Big Questions : Dawkins’s position fails for exactly the same reason that Michael Behe’s does — we have an explicit example that shows that complexity requires neither a simpler antecedent nor a designer.
The letter to the editor is a literary genre unique unto itself. Unlike the editorial or the op-ed, the letter typically allows its author only a couple of short paragraphs to make a single compelling point. A good blog post might ramble from one loosely connected idea to another, but a good letter proceeds directly to its target.
Don Boudreaux is, beyond any doubt, the modern master — no, the all-time master — of this underrated branch of literature. When a radio station interviews a Galveston resident who’s just topped off her gas tank in anticipation of Hurricane Ike — and who is furious to learn that gas prices have jumped 50 cents a gallon overnight even though “Ike hadn’t hit yet” — a blogger (or an Armchair Economist) might respond with a long-winded explanation of why it’s a good thing that supply, demand, and therefore prices respond quickly to a change in expectations. Boudreaux, instead, skips right to the heart of the matter:
Your reporter should have immediatedly asked this woman: “Well, why were you topping off your tank? Ike hadn’t hit yet.”
Edited to Add: These problems are fixed now! The electronic versions are correct. They are still advertised as November 2007 editions, but they are in fact the May 2012 edition. You can now trust the links at http://www.TheBigQuestions.com/buy .
Today (May 1) was the official publication date for the all-new revised edition of The Armchair Economist. (Read the preface here.) Unfortunately, we had a major communication screw-up and purchasers of the electronic editions (Kindle, Nook, etc.) are still receiving the 1993 edition (which is labeled the “2007 edition” because that’s when it was converted to an e-book). This will be fixed in a day or so. I’ll post to let you know when it’s safe to buy.
Meanwhile, if you’ve recently purchased an electronic Armchair Economist, I encourage you to return it, wait just a day or two till you see the announcement that all systems are go, and then buy it all over again.
I cannot begin to tell you how sorry I am about this. There is at least one very particular head I’d like to see roll.
Thanks for bearing with the glitch, and watch this space for the big announcement that all systems are go.
FROM THE PREFACE:
One day in 1991, I walked into a medium sized bookstore and counted over 80 titles on quantum physics and the history of the Universe. A few shelves over I found Richard Dawkins’s bestseller The Selfish Gene along with dozens of others explaining Darwinan evolution and the genetic code.
In the best of these books, I discovered natural wonders, confronted mysteries, learned new ways of thinking, and felt I had shared in a great intellectual adventure, founded on ideas that are dazzling in their scope and their simplicity.
Economics, too, is a great intellectual adventure, but I could find, in 1991, not a single book that proposed to share that adventure with the general public. There was nothing that revealed the economist’s unique way of thinking, using a few simple ideas to illuminate the whole range of human behavior, shake up our preconceptions, and jolt us into new ways of seeing the world.
I resolved to write that book. The Armchair Economist was published in 1993, and attracted much critical praise along with a large and devoted following. But what I take most pride in is that The Armchair Economist is still widely recognized among economists as the book to give your mother when she wants to understand what you do all day.
Sometimes I think we should license economics writers.
Thomas Nagel is a prominent philosopher (author of the provocative and widely anthologized essay What is it Like to be a Bat?) who’s just reviewed Daniel Kahneman’s new (and excellent) book in The New Republic. (Fun fact: When I stepped off an airplane at Heathrow last week, the first thing I saw was a limousine driver holding a sign that said “Daniel Kahneman”. This, incidentally, was my final issue of The New Republic, due to their criminally evil subscription practices — more on that, perhaps, later this week. ) Here is how Nagel describes what he seems to think is orthodox economic theory:
Most choices, and all economic choices, involve some uncertainty about their outcomes, and rational expectations theory, also called expected utility theory, describes a uniform standard for determining the rationality of choices under uncertainty…
The standard seems self-evident: The value of a 50 percent probability of an outcome is half the value the outcome would have if it actually occurred, and in general the value of any choice under uncertainty is dependent on the values of its possible outcomes, multiplied by their probabilities. Rationality in decision consists in making choices on the basis of `expected value’, which means picking the alternative that maximizes the sum of the products of utility and probability for all the possible outcomes. So a 10 percent chance of $1000 is better than a 50% chance of $150, an 80% chance of $100 plus a 20% chance of $10 is better than a 100 percent of $80 and so forth.
AAAAGGGHHH! Even on the Internet, it’s rare to see quite so much ignorance packed into so few words. Where to begin?
In late 17th century England, there were no newspapers outside of London, and scarcely a printer outside of London, Cambridge and Oxford. The difficulty and expense of conveying large packets from place to place was so great that an extensive work took longer to reach Devonshire or Lancashire than it took, in Victorian times, to reach Kentucky. As a result, books and printed matter generally were largely unavailable outside of London — and London, for most rural Englishmen, might as well have been the moon.
I learned this from Macaulay’s History of England, which I just pulled up on my Kindle, which of course gives me instant — and searchable! — access to pretty much everything that’s ever been published. But the Kindle, and its brother e-readers, are more revolutionary than that. Not only do they give us easy access to existing literature; they call forth entirely new literary genres, such as the Kindle e-book, which brings to market extended essays that are too long to be magazine articles but too short to be traditional books — and are priced to sell.
All of which brings me to Alex Tabarrok’s Launching the Innovation Renaissance: A New Path to Bring Smart Ideas to Market Fast, which is both a product and a celebration of the innovation revolution, along with a recipe, or rather a set of recipes, for nurturing that revolution.
This is a great book. It’s fast-paced, fun to read, informative as hell, and it gets everything right. At first I wished I’d written it— until I realized I could never have written it half so well.
In sixth grade, I did not read My Side of the Mountain, though it was assigned for class. In eighth grade, I did not read Little Women and in ninth grade I did not read Great Expectations and The Good Earth. As I passed through high school, I worked my way through much of the western canon, not reading The Scarlet Letter, Bartleby the Scrivener, The Return of the Native, and dozens more. In eleventh grade, we were assigned two books by Steinbeck, two by Hemingway, two by Sinclair Lewis and two by William Faulkner. I did not read the Steinbeck, Hemingway or Lewis but for some long-forgotten reason I violated years of established tradition by tackling the Faulkner — specifically As I Lay Dying and The Sound and the Fury.
As I Lay Dying went down pretty easily, but I remember many nights struggling my way through The Sound and the Fury, Cliff notes at my side. It felt like scaling Everest, and the vistas at the top were worth the climb.
A couple of weeks ago, as part of my ongoing project to read great novels, I decided to revisit The Sound and the Fury, and I’m more than glad I did; I finally have an answer to give the next time I’m asked what one novel I’d bring to a desert island. But what I’m flabbergasted by is this: How did this book ever get assigned to high school students in the first place? I ask for at least two reasons:
A few years ago, I discovered that reading on my Kindle is about 1000 times better than reading a book. This year, I discovered that reading on my iPhone is about 100 times better than reading on my Kindle. As a result (and also as a result of a lot of time spent on airplanes), I’ve been on a mad fiction-reading spree the past few months. Some mini-reviews:
In 1999, the journalist James K. Glassman co-authored a book called Dow 36,000. The eponymous prediction did not pan out. A couple of days ago, Glassman popped up in the Wall Street Journal, trying to explain where he went wrong. “The world changed”, explains Glassman. The relative economic standing of the U.S. is declining. Plus terrorists and economic instability made the world a riskier place.
But there’s a better explanation. Glassman’s story never made sense in the first place, for reasons Paul Krugman explained when the book first came out.
Glassman has a substantial history of confusion about how financial markets work. Ten years before he wrote Dow 36,000, he was explaining in The New Republic that stocks are better investments than real estate:
To understand the universe at the deepest level, we need to know not only how the universe behaves, but why.
- Why is there something rather than nothing?
- Why do we exist?
- Why this particular set of laws and not some other?
So say Stephen Hawking and Leonard Mlodinow in their book The Grand Design, and so say I.
The Big Big Question is the first one: Why is there something rather than nothing? Hawking’s answer: The laws of physics — and especially the form of the law of gravity — allow for the spontaneous creation of universes out of nothing at all. We live in one of those spontaneously created universes. But this, of course, only serves to raise a new Big Big Question, namely: Why are the laws of physics as they are? Hawking’s answer: The laws of physics must be consistent and must predict finite results for the quantities we can measure. It turns out that those criteria pretty much dictate the form of the laws of physics.
So unless I’ve misunderstood him, here is Hawking’s position: In order for us to be able to measure the things that we measure, the laws of physics must have a certain form, and in order for them to have that form, universes must be able to arise from nothing. Therefore our universe was able to arise from nothing. But this does not seem to answer the question of why things couldn’t have been very different. Why couldn’t there have been no us, no measurements, no laws of physics and no anything?
If you happen to be attending Harvard this semester, one of your course options is Greg Mankiw’s Freshman Seminar 43j, “The Economist’s View of the World”:
This seminar probes how economic thinkers from the right and left view human behavior and the proper role of government in society. Each week, seminar participants read and discuss a brief, nontechnical, policy-oriented book by a prominent economist. Regular writing assignments are also required. Students should have some background in economics, such as an AP economics course in high school or simultaneous enrollment in Social Analysis 10.
The ten books on tap for this semester are:
My treasured copy of the humor classic Science Made Stupid, copyright 1985, contains a Wonderful Future Invention Checklist. Who in 1985 would have thought that just 25 years later, I could check off a third or so of the entries?
65 years ago today, the world changed. In his magnificent World War II memoir Quartered Safe Out Here, George McDonald Fraser looks back on what might have been:
I led Nine Section for a time; leading or not, I was part of it. They were my mates, and to them I was bound by ties of duty, loyalty and honor… Could I say, yes, Grandarse or Nick or Forster were expendable, and should have died rather than the victims of Hiroshima? No, never. And the same goes for every Indian, American, Australian, African, Chinese and other soldier whose life was on the line in August, 1945. So [I'd have said]: drop the bomb.
And then I have another thought.
You see, I have a feeling that if—and I know it’s an impossible if—but if, on that sunny August morning, Nine Section had known all that we know now of Hiroshima and Nagasaki, and could have been shown the effect of that bombing, and if some voice from on high had said: “There — that can end the war for you, if you want. But it doesn’t have to happen, the alternative is that the war, as you’ve known it, goes on to a normal victorious conclusion, which may take some time, and if the past is anything to go by, some of you won’t reach the end of the road. Anyway, Malaya’s down that way … it’s up to you”, I think I know what would have happened. They would have cried “Aw, fook that!”, with one voice, and then they would have sat about, snarling, and lapsed into silence, and then someone would have said heavily, “Aye, weel” and got to his feet, and been asked “W’eer th’ ‘ell you gan, then?”, and given no reply, and at last, the rest would have got up, too, gathering their gear with moaning and foul language and ill-tempered harking back to the long dirty bloody miles from the Imphal boxes to the Sittang Bend and the iniquity of having to do it again, slinging their rifles and bickering about who was to go on point, and “Ah’s aboot ‘ed it, me!” and “You, ye bugger, ye’re knackered afower ye start, you!”, and “We’ll a’ git killed!”, and then they would have been moving south. Because that is the kind of men they were.
I’ve just finished reading The Girl Who Played with Fire, the second book in the series that begins with The Girl with the Dragon Tattoo. I’m not giving away any significant plot point when I tell you that there’s a character who works on Fermat’s Last Theorem as a hobby, or that the book was clearly written (or perhaps translated) by somebody with no clue how mathematics works or what Fermat’s Last Theorem is about. I particularly liked the reference to Andrew Wiles using the “world’s most complicated computer program” to solve the problem. It’s my understanding that Andrew barely even uses email. And certainly if you understood anything about the nature of the problem and/or the solution, you’d recognize the absurdity of trying to tackle it with a complicated computer program.
Be that as it may, I finished the novel with a few hours left to spare, so of course I was inspired to work on Fermat’s Last Theorem, or at least on the simplest cases. The problem, if you’ll recall, is to show that there are no integer solutions to any of the equations x3+y3=z3 , x4+y4=z4 and so on, except for the so-called trivial solutions in which one or more variables take the value zero.
David D. Friedman’s The Machinery of Freedom, a classic of libertarian thought, has long been out of print and hard to find. (Well, it’s easy to find, actually. But hard to find for less than about a hundred bucks.) It is therefore a very good thing that David’s gotten his publisher’s permission to post the entire book on the World Wide Web, for free.
What does David get out of this? Well first, of course, he wants you to read his book. But second, he’s about to start preparing a third edition and welcomes reader feedback. If you post your comments here, I’ll make sure he sees them.
After six months of blogging nearly every weekday, I’m taking a four day weekend. This will give you a chance to browse through the archives for all the good stuff you might have missed. Or, if you’re looking for a good read to tide you over, I can recommend Chapter Two of my book Fair Play. Some of the examples are dated (Wal-Mart, as far as I know, no longer advertises that “we buy American so you can too”), but it makes a good companion piece to yesterday’s post.
I’ll be back on Tuesday with, I expect, something new to say.
Over at Overcoming Bias, Robin Hanson blogs about a science fiction novel that posits a world where people routinely sell shares in their future income. (I have not read the novel, which is called The Unincorporated Man.) Robin laments that while many reviewers have taken it for granted that we wouldn’t want to allow such contracts, none seem to have seriously engaged the idea.
I’m not sure if this counts as serious engagement, but I am reminded of the apparently little-known fact that the singer/actor/TV phenomenon Dean Martin did exactly this. In fact, he overdid exactly this. By the time he was 27 years old, Martin had sold 10% of himself to MCA Records, 20% to his manager DIck Richards, 35% to his other manager Lou Perry, and 25% to the mobster Frank Costello. That left him with 5% of himself—”$50 for every grand he made” in the words of writer Nick Tosches. A year later, he hired yet another manager and sold him another 10%. Having now sold 105% of himself, it became imprudent to earn money. Therefore, in need of something to live on, Martin sold yet another 10% of himself to nighclub owner Angel Lopez.
It’s a bit of an odd feeling to be reading a novel and stumble upon yourself as a character. Well, at least a well-disguised version of yourself. The novel is Victor Snaith’s The Yukiad, and the character is a large Scotsman named Pans who tugs at his earrings when he becomes agitated. I am neither Scottish, nor earringed, nor particularly large, but I suspect that Pans, viewed through the haze of poetic license, is I.
When we meet Pans, he is hovering over a glass contraption—a perpetual motion machine, really—consisting of a circular tube containing several colored beads, which travel around the tube, some clockwise, some counterclockwise, all at the same speed, bouncing off each other in perfectly elastic collisions whenever they collide. Pans is currently tugging at his earrings so hard as to cause some concern for the integrity of his earlobes, as he ponders the following question:
But wull tha’ aver gut bark to weer tha’s started, at a’, at a’?
Well, okay, maybe I’m not Pans. Maybe I’m the character Sherloch Humes, a “trim but rather wrinkled gentleman in worsteds”, who calculates for Pans’s benefit that “the configuration of beads is guaranteed to have exactly replicated itself by the year two thousand and nineteen”. I believe that I am the inspiration for one of these characters and that the mathematician Leonid Vaserstein (who is neither Scottish nor wrinkled) is the inspiration for the other, and here is why:
Tyler Cowen started a blogospheric whirlwind recently when he posted the list of books that had influenced him the most and called on other econ bloggers to do the same. In short order, we got entries from Peter Suderman, E.D. Kain, Arnold Kling, Michael Martin, Niklas Blanchard, EconJeff, Bryan Caplan, Matt Yglesias, Jenny Davidson, Will Wilkinson, Matt Continetti, Ross Douthat, Mike Konczal, Kieran Healy, Ivar Hagendoorn, Scott Sumner, and no doubt others. [Update: Some of these links were wrong; I think they’re all fixed now.]
I’m late to the party, but here’s my list:
For some decades now, at more or less random times and in more or less random places, I’ve been asking people “Why would you care if your baby’s name reads the same upside down as rightside up?”. I have never gotten an answer that rang true.
One of the various unsatisfactory answers I keep getting is something like: “Umm. You wouldn’t care.” But I know that’s wrong, because I’ve read Clown Town.
Professor Joseph Weiler, who is facing criminal charges in France for posting a mildly negative book review on a web site he edits, has asked supporters to search out and email him copies of even more negative reviews (presumably of academic writing), to submit to the court as evidence that this sort of thing happens all the time.
The review I’ll be emailing is a classic of the genre. It was written by Andre Weil, one of the most influential mathematicians of the twentieth century, and possibly the most erudite person who ever lived. Here’s how I described Weil shortly after his death:
On June 25, 2010, Professor Joseph Weiler, editor of the European Journal of International Law, will stand trial in a French criminal court for running a mildly negative book review on a journal-associated website.
The book in question is The Trial Proceedings of the International Criminal Court by the Israeli law professor Dr. Karin N. Calvo-Goller. According to the reviewer the main part of the book “simply restates the…relevant parts of the ICC Statute.” This rehashing, he adds, is particularly unproductive since a large part of the volume consists of a reprint of the Statute itself.
This is a genre that thrived back before the Internet (mostly between 1930 and 1960) when connoisseurs of weirdness and misinformation had only bound books to turn to. Its heroes include Osmond P. Breland (author of the classics “Animal Facts and Fallacies”, “Animal Friends and Foes”, and “Animal Life and Lore”) and Alan Devoe (who gave us “Speaking of Animals” and “This Fascinating Animal World”).
Here’s a six-question quiz I compiled from these books.
Is mathematics invented or discovered? In my experience, applied scientists often think of mathematics as a human invention, while actual mathematicians (with a few notable exceptions) feel sure that mathematics was always there to be discovered. (Of course, it’s sometimes hard to tell how much of this is genuine disagreement and how much is a language barrier.)
I’ve just finished reading an excellent book by Mario Livio which is entirely about the invention/discovery question, though he’s chosen the (somewhat unfortunate) title Is God a Mathematician? Much of the book is a lively romp through mathematical history, with a well chosen mix of biography and exposition. Although he parts company with them in the last chapter, Livio gives a more than fair hearing to the many great mathematicians who have insisted that they are discoverers, from Pythagoras through Galileo, G.H. Hardy, Kurt Godel, and the contemporary Fields Medalist Alain Connes (among others). Here, for example is Connes:
Steve Levitt and Steve Dubner, the SuperFreakonomics guys (formerly the Freakonomics guys) have raised a lot of temperatures with their chapter on global warming. The backlash began with Paul Krugman, who in turn was neatly skewered by several authors, but most effectively by the journalist Ari Armstrong.
The critics have raised two objections that come perilously close to contradicting each other: First, Levitt and Dubner are accused of minimizing the problem. Second, they are accused of overeagerness to solve the problem, as opposed to, say, demonizing the responsible parties. Of these, only the first deserves to be taken seriously.