Some mostly math-related books

I've just made a few purchases of math-related books:


Edward Frenkel's phenomenally good book Love and Math: The Heart of Hidden Reality is out in paperback, and I wanted to have it on hand. I interviewed Frenkel about a year ago, after reading a library copy of the hardcover. I'd certainly add this if I were doing a new version of my 10+ most influential books, as it got me into learning and writing about math on an ongoing basis.

One of the first things I did in that direction, after reading Frenkel's book, was take Jo Boaler's class How to Learn Math: for Students, which was valuable for thinking about math education (the course had only a limited sampling of math), which I'm interested in as a personal and political matter. I've now ordered her book Mathematical Mindsets: Unleashing Students' Potential through Creative Math, Inspiring Messages and Innovative Teaching, and may review it at some point here.


Also ordered: Patterns of the Universe: A Coloring Adventure in Math and Beauty, which certainly looks interesting.

Recently finished reading: Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers, by Amir Aczel, which is a nice blend of math, history and travelogue, and involves searching for the first zero through South and Southeast Asia.

Current non-math reading: Destiny and Power: The American Odyssey of George Herbert Walker Bush, by Jon Meacham. Quite interesting thus far (I'm up to around 1960) and elegaic, with much of the world described seeming not quite as distant as the ancient civilizations described in the zero book above, but pretty distant nonetheless.

How I became interested in math decades after studying it [updated and moved to top]

I've recently taken a strong interest in math, a subject in which I was not a particularly distinguished student decades ago. Math is highly relevant to many economic and science topics I've covered as a journalist; and has become a growing political issue involving how it should be taught (or in some misguided arguments, whether it's really much needed); and it's a personal issue for those of us with school-age children. I've come to a growing sense of all of that, as well as of what a fascinating, fast-changing, extensive, profound and, I think, socially under-appreciated field math is in itself.

A key factor in inspiring this outlook was an excellent book I recently read, Love and Math: The Heart of Hidden Reality, by Edward Frenkel. I've been in touch with Frenkel and hope to write about his views soon in a professional capacity. Another factor was reading the Simons Foundation's magazine Quanta, which provides much absorbing coverage of math and its diverse intersections with science.

Moreover, we live in the time of MOOCs, or massive open online courses. I've now taken Jo Boaler's online course "How to Learn Math: For Students," which I found interesting and helpful, and have signed up for Keith Devlin's "Introduction to Mathematical Thinking." While I surely will not be making a mid-career shift to mathematician, I do hope to become progressively better at thinking and writing about topics in and around math. I have nothing to lose except the sour and befuddled feeling that I took away from calculus long ago.
Originally posted 1/20/15.

UPDATE 3/2/15: My interview with Frenkel, geared for an audience of financial advisors, is in Research magazine: "How Math Will Shape Wall Street's Future."

Also, now that I'm a few weeks into Keith Devlin's "Introduction to Mathematical Thinking" course, I can confirm that it's extremely interesting and will not be the last math MOOC I take.

UPDATE: More on Devlin's course here, and a bad idea noted here.

Dark sides of math and data

Recommended reading: Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy, by Cathy O'Neil. This eye-opening book is about what the author calls "the dark side of Big Data"--how algorithms are used in sinister or negligent ways, in matters ranging from mortgage lending to for-profit prisons. It may be uncomfortable reading for people (like me) who love math, but as O'Neil puts it "math deserves much better [than to be used in such ways] and democracy does too."

Some related things to read: Edward Frenkel's great book Love and Math: The Heart of Hidden Reality, which though it is essentially a love letter to his subject, opens with a warning about how math can be misused, by Wall Street and others. I interviewed Frenkel about that and related matters for my former employer Research magazine.

Thinking back, I've been edging into such topics for a long time. I recall writing an article for U.S. Banker magazine in the early '90s about how data mining was becoming an important new technique in the financial industry. The banks were claiming it would help them have "relationships" with their clients, a claim for which I think I had some skepticism (but the article doesn't seem to be online). I also wrote around that time about how financial "rocket scientists" were using derivatives, in a piece for Insight magazine (also not online, at least not for free), but true to my conservative allegiances of the time, regrettably, I downplayed the potential problems.

Finally, I recommend reading this: "Revealed: how US billionaire helped to back Brexit," by Carole Cadwalladr in The Guardian. The billionaire is Robert Mercer, who played a key role in Trump's rise to power. Mercer will be remembered as a man who used data to damage democracy, in the U.S. and Britain. That damage can only be limited by more people knowing the math and computer science that's being used to undermine our freedom.

Review: Birth of a Theorem

I almost did not bother to read most of Birth of a Theorem: A Mathematical Adventure, by Cédric Villani. After reading several chapters, it was clear that I wasn't going to understand the mathematics in this book, and via Twitter I came across some negative reviews that emphasized the book's inclusion of incomprehensible material. Moreover, in keeping with my recent hobby of studying math, I've been very much in the mode of wanting to actually do math, rather than just observe it in some vague way. But I plowed ahead with Villani's book, and I am certainly glad I did.

Birth of a Theorem gives a compelling and personal picture of what it is like to do math at an extremely high level; for example, to think you've solved a longstanding problem and then find that you haven't, or to wake up with a momentous realization that "You've got to bring over the second term from the other side, take the Fourier transform, and invert in L²"--and then write a note on a scrap of paper before rushing to get the kids dressed and onto the school bus.

Some pages of the book are laden with equations, and a note on translation at the end states: "No attempt has been made to expand upon, much less to explain, fine points of mathematical detail, many of which will be unfamiliar even to professional mathematicians. The technical material, though not actually irrelevant, is in any case inessential to the story Cédric Villani tells in this book."

I would have preferred it if, at some point, there had been a diagram with annotations summarizing, term by term, what a key equation means. As it was, though, I had some fun picking out the symbols I did understand--an ∈ here, an ∀ there, a sup somewhere (all of which I learned fairly recently), and I agree that this book tells a valuable story even while displaying so much unexplained math. The only pages that I didn't find interesting were ones devoted to a long listing of musicians and bands the author likes. (Some readers may like this part, however, especially if they were attracted to the book by Patti Smith's blurb on the back cover.)

So, Birth of a Theorem is recommended. It is a very different offering from Edward Frenkel's Love and Math: The Heart of Hidden Reality, which strives to make some very difficult math comprehensible to a lay audience. Still, I suspect that some people will pick up Villani's book and end up being drawn further into mathematics, as well.

Stop teaching math?

A dreadful article at Bloomberg View: "Want Kids to Learn Math? Stop Teaching It." Via Twitter, I called it to the attention of Edward Frenkel and Keith Devlin, whose reactions were as negative as mine. (The thread is here.) However bad things are in math education currently, one shouldn't underestimate how much worse they could become, and conveying to kids that math beyond some basic arithmetic is something that only a small segment of the population ought to concern itself with is surely a fast track to a dystopia populated primarily by mentally enfeebled Morlocks.

I speak as someone who, even though not exactly lacking intellectual self-confidence growing up, decided too early and too easily that developing mathematical abilities was not where my talents lay. My efforts to rectify that, which I wrote about recently, are ongoing and, oddly enough, fun.

Progress report on learning math online [updated and moved to top]

3/25/15: I've been studying math lately, as noted in the post below. I'm now in the 6th week of Prof. Keith Devlin's "Introduction to Mathematical Thinking," which runs either 8 or 10 weeks depending on whether you stop after the Basic Course or continue through the Extended Course. The latter is described in the course description as being particularly difficult:

Students who struggle with the Basic Course are likely to find the additional two weeks of the Extended Course extremely difficult, if not impossible. Note also that the final two weeks of the Extended Course are more intense than the Basic Course, being in part designed to give students a sense of the pace of a university-level course in pure mathematics. Moreover, in Week 10 there is a series of fairly tight deadlines you must meet, with 48 hour turnaround times. [Emphasis in the original.]

Me: We'll see how that goes, as I've been hoping to make it through the Extended Course and get the Statement of Accomplishment With Distinction that comes from passing it. I've found the course highly interesting and will have learned a great deal regardless of how far I get. The overall course emphasizes logic and proofs, and is designed to give a sense of how mathematicians think (in contradistinction to the emphasis on following instructions that characterizes much K-12 math). At times, I have struggled with the concepts, though my weekly test results have been generally decent (with one exception), with scores equivalent to about 87, 87, 41 (oops), 96 (comeback) and 86.

The course is not particularly oriented toward visual thinking, but I have found some visualization helps in grasping the concepts. Here is what I drew and wrote for a homework problem. [Added: SPOILER: Don't read the image first if you want to answer the question yourself.] The question was: "Prove or disprove the claim that there are integers m, n such that m²+mn+n² is a perfect square." I drew and wrote the below, and posted it to a class discussion board (along with a question as to whether and to what extent "visual proofs" are acceptable):

A fellow student pointed out that my diagram doesn't match the algebraic expression m²+mn+n², which is true. If I were to do it over, I'd leave one of the mn boxes out or cross-hatch it or something. My basic idea that the claim is verified by making n zero seems to have some merit.

Here is a report from someone who took the same course a couple of years ago. I agree with many of the sentiments expressed, including about finding the course very interesting and enjoyable, and also about this:

Assignments are not submitted for marking (but a helpful feedback video is made available in the next week in which Devlin explains how to answer a selection of the questions). In the first few weeks of the course Devlin puts a very prominent amount of emphasis on the need for all students to discuss the course with others in an informally established study group. In my case I chanced on and joined a Google Group called “Mathematical Thinking UK Discussion Group”. This initially had about 40 members. About seven were helpfully active in the first three weeks, but the study group has seemingly since ceased to function. So I am on my own: it feels a bit late in the day to try to find another study group, nor to attempt to breath life into this one.

Me: That mirrors my experience very closely, as I was part of a weekly Google Hangout study group, which started off very promising and then progressively wound down into nothingness. I gather the dissolution of such groups has a lot to do with people quitting the course (considerably more that, I suspect, than with people finding the course easy and deciding they don't need a study group). The statistics posted by the professor weekly show that, while a large number of people are enrolled (over 38,000, from all over the world), they vary in activity or lack thereof; and those who actually hand in the weekly test, or Problem Set, are a small and declining subgroup (under 1,500 at last count).

In any case, I've become a big fan of online courses, a remarkable and unprecedented resource (and one that for now at least is often free). Edward Frenkel, who did much to inspire my newly heightened interest in math, has an upcoming (and seemingly not too time-consuming) class, which I've signed up for as well. Whatever limits I encounter in my online education, it's clear to me that I've learned much already, and that this has been time well-spent.

The above was originally posted 3/25/15.

UPDATE 4/28/15: I've completed the course, including the extended course, and am now awaiting my Statement of Accomplishment With Distinction, which I believe I earned. Someone pathetically tried to disrupt the peer-review portion of the extended course by placing numerous bogus "zero" reviews, but this was detected and deleted. I am now on to "Introduction to Mathematical Philosophy," which looks to have many fascinating concepts but also be less time-consuming (a good thing, given my schedule, though it also means it will involve less hands-on learning, as this course, unlike the previous one, does not involve handing in weekly problem sets for grading).

UPDATE 5/1/15: My SOA With Distinction. I was one of 275 students to get one of these; another 991 earned an SOA for completion of the Basic Course.

A few additional thoughts before closing this post:

1. "The only way to really learn math is by doing it." This is something one hears now and then, and I can affirm it based on my experience in this course. If I had only listened to the professor's lectures or read his book Introduction to Mathematical Thinking, without actually trying to solve the (ungraded) assignments and (graded) problem sets myself, I would not have gotten nearly as much out of this course.

2. "You don't really understand something until you've taught it." Another bit of repeated wisdom that I find has validity. In evaluating other students' work and trying to explain things to them, I found I had to learn the material better than I would have just from handing in my own work.

3. My final grade was 98.5%, which is of course good but needs some context. The numerical grades are described by the professor as "akin to the points awarded in a video game: significant within the game, but only within the game." Under the scoring system, it is possible for students to get more than 100%, which then gets normalized to 100%. My grade was boosted by certain features of the scoring, such as that it includes only your highest score out of three "evaluation exercises" (evaluating proofs and seeing how close your score is to the professor's; I did great on the third one); in general, the grades are a marker of progress and persistence more than performance.

4. A substantial portion of this course is about language and communication; such as in converting between natural language and symbolic logic, and in assessing the clarity of proofs. When I signed up for "Introduction to Mathematical Thinking," I wondered if I might be going too far afield in spending valuable time on something unrelated to my financial journalism day job, Erie Canal book project and overall writing career. I'm pleased to find the course was plenty relevant to writing.

UPDATE: More here.

Skills for competing with robots

My latest at Research magazine is on robots, jobs, Wall Street and studying math online: "Will Robo-Advisors Be Good at Relationships?" Excerpt:

For advisors eager to understand what it takes to be competitive in the advice business (and other fields) as computers take on a growing array of tasks, I recommend a new book: "Humans Are Underrated: What High Achievers Know That Brilliant Machines Never Will," by Geoff Colvin, senior editor at large of Fortune magazine (the book is published under the imprint Portfolio/Penguin).

The skills that will be valued in the workplace increasingly will be those of human interaction, in Colvin's view — abilities to work in teams and to understand what other people are thinking and feeling. “Being a great performer is becoming less about what you know and more about what you’re like,” he writes.

Another excerpt:

An experience of mine early this year provided some insight into just how entwined personal and technical skills can be. I was taking a popular online course titled “Introduction to Mathematical Thinking,” taught by Stanford mathematician Keith Devlin. My fellow students numbered in the tens of thousands worldwide. The course's goal was to give a sense of how mathematicians think and work. 

While math might seem to epitomize a technical subject, interpersonal skills were crucial. The professor encouraged students to form and join study groups, which met online or off. The coursework put considerable focus on writing proofs and evaluating proofs written by other students — exercises in communication as well as analysis. 

I have taken some other math courses online that did not involve anything like the same degree of personal interaction, and I learned less in them.

Whole thing here.

Common Core math/politics

Subject to keep an eye on: Common Core and opposition to it. Some complaining about math problems got my attention online, and I'd already heard some grumbling face to face. Common Core's become a Tea Party issue, but one that won't necessarily be limited to them. I saw some poorly worded math problems in my brief research online, but will have to look into this further before forming a strong opinion. But I've seen enough to recognize a political issue that's likely to have resonance.

Advice on (not) being a journalist

In an excellent post at Bloomberg View, journalist Megan McArdle offers some career advice, under the paradoxical headline: "You Want Advice? Don't Ask Journalists." She comes down largely on Felix Salmon's dour side versus Ezra Klein's upbeat one in a debate over whether young people today should go into journalism. McArdle:

So when kids who are passionate about writing ask me how they can get a job doing this thing that they love, I don't tell them to follow their bliss; I tell them there are a lot of things they can love. I loved building computer networks. I loved business school. This is a fantastic job, and believe me, I count my lucky stars every day that I have it. But there are a lot of fascinating things in the world. Go get a job doing something in an industry that is not struggling so hard to get people to pay for their products. 

And if you find, in the end, that you have to write, you will be a better writer for actually knowing something about an industry other than the production and consumption of white papers. One of the biggest weaknesses of modern journalism, and modern politics, is that none of the people in them have any idea what it is like to work for a regular company. Organizations are very different from the inside than the outside, in ways that are not obvious to you until you've lived through a couple of executive bloodlettings and experienced the high-stakes tedium of the annual budget process. If you want to report on the military or global development or poverty programs or health care, go work for that industry and come back with some actual knowledge that you did not gain from earnestly asking insiders how they do their jobs. You'll not only be a better reporter, but you'll also have something to fall back on if your outlet folds.

Me: I could not agree more with the above. In fact, even before journalism's plague of financial difficulties in the past decade, it would have been good advice to spend at least some time immersing yourself in some industry or field other than journalism, so as to develop expertise that, besides its own merits, would also improve any journalism you might do at some point in writing about that area.

Not that being an expert outside of journalism is any guarantee against producing awful journalism even about one's area of expertise. I was genuinely shocked the other day by another Bloomberg View post, this one by economist Noah Smith, that went on at length based on a confusion of "billion" with "trillion" and thus made hash out of what could have been a cogent critique of something Rand Paul had said about the Fed. Smith's piece, now minus the Emily Litella paragraphs, is here.

As I wrote recently, I've been working lately on expanding my knowledge of math. One reason for this is that I want to be able to write more capably about math-related topics and about math itself, a vast field that in my view deserves more and better journalistic coverage than it tends to get. If I were giving advice to a young person considering a journalism career, I would include a suggestion that he or she get exposure to some technical subjects, and so know something journalism types don't tend to know.

Math novel: The Parrot's Theorem

Current reading: The Parrot's Theorem: A Novel, by the late Dennis Guedj. It's about what happens when a family in France receives a library of math books from the Amazon*, and also finds a parrot able to communicate sophisticated concepts. It contains more diagrams and equations than most novels, which is a big plus.

Meanwhile, I'm continuing the MOOC "Paradox and Infinity," which this week is on "Orderings and the Higher Infinite." The course is interesting and sometimes harder to follow (as this week) than other times. Where's that parrot when you need him?

* - the rainforest, not the company.

Next MOOC: Paradox and Infinity

UPDATE 6/8: The course is about to start. Sign up here if interested (it's free to audit, as I'm doing), and if you're taking it, feel free to be in touch.

This course looks promising: "Paradox and Infinity," at EdX, by MIT philosopher Agustín Rayo, and I'm planning to take it as the next step in my online math education. It looks like it will be lively and interesting, for instance based on this earlier clip of some of the material, and I've gotten some assurance from course staff that there will be opportunity to build math skills.

 

I'm also, when I have a chance, going through the self-paced Calculus One at Coursera, taught by mathematician Jim Fowler of Ohio State University. That's a subject I studied long ago and never really understood. Down the road, I expect to take courses in statistics, probability and more; as an economics major, I learned some statistics, but that was never a strong point of mine either. Given the general level of mathematical interest and knowledge among journalists, I'm hoping to be an outlier.

Human capital transfer

Fareed Zakaria has an intelligent article on the silver lining of the crisis: "A More Disciplined America." Among other things, here's one major benefit: As the financial sector reels, a lot of math and science degree-holders who would otherwise be inventing incredibly complicated ways to lose money are now going to be doing something way more productive.

The financial industry itself is likely to shrink, and that's not a bad thing, either. It has ballooned dramatically in size. Curry points out that "30 percent of S&P 500 profits last year were earned by financial firms, and U.S. consumers were spending $800 billion more than they earned every year. As a result, most of our top math Ph.D.s were being pulled into nonproductive financial engineering instead of biotech research and fuel technology. Capital expenditures went into retail construction instead of critical infrastructure." The crisis will stop the misallocation of human and financial resources and redirect them in more-productive ways. If some of the smart people now on Wall Street end up building better models of energy usage and efficiency, that would be a net gain for the economy.

I suspect some of them are also going to do some real rocket science.

Book note: Finding Fibonacci

Reading a review copy of this currently: Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World. It's by Keith Devlin, whose math thinking MOOC I took and wrote about here and here. I may have more to say about the book when I finish it, but I'm already intrigued by its interdisciplinary nature (a "deft, engaging mix of history, math and travelogue," per Publishers Weekly) and that it discusses how important people are sometimes forgotten--and sometimes rediscovered--by history, with Leonardo Pisano (aka Fibonacci) having disappeared from the world's awareness for centuries, and with his true significance only emerging in recent years. The tendency of historical reputations to rise and fall (even when they don't disappear altogether) is a theme I've found in my own research on DeWitt Clinton, and I suspect it holds true in many cases.

Quantitative links

Here are some math/physics-related items I have found interesting:

"Dust Off Your Math Skills: Actuary Is Best Job of 2013."

"Physicist Proposes New Way to Think About Intelligence."

"A View From the Top."

Guest post: A dissenting view on Manzi's Uncontrolled

I recently gave a positive review to Jim Manzi's Uncontrolled: The Surprising Payoff of Trial-and-Error for Business, Politics, and Society at David Frum's Daily Beast blog. I then passed the book on to William S. Carter, Emeritus Professor, Environmental Safety and Health at the University of Findlay, who happens to be my father-in-law. Bill was less impressed by the book; his review is below. —K.S.


Jim Manzi's book Uncontrolled is a bold attempt to apply the scientific experimental model to public policy. To complete his application Mr. Manzi should first provide a more complete description of the scientific method. He fails to define the concept of hypothesis, but proceeds to intersperse the use of hypothesis and theory. The scientific method requires the developing of a hypothesis or several hypotheses and then testing those hypotheses with data. Most often in testing a hypothesis the experimenter describes two hypotheses, an affirmative hypothesis and a null hypothesis. The data collected is compared for the experimental group relative to a control group. Either random selected or otherwise carefully selected cohorts are selected to minimize the potential for bias. The results may demonstrate a difference, determined by a statistically significance test.

When determining whether the data sets are significantly different requires that the experimenter to determine, preferably beforehand, what level of significance is acceptable. A 99% significance level may be preferable to a 95% or 90% since there is a greater confidence in the statement that the outcomes are differences. In some situations, and often in pharmaceutical clinical trials, a 95% confidence levels is considered acceptable to proceed to make a professional judgement.

In Mr. Manzi's discussion he fails to explain the difference between correlation and causality. Typically a single experiment only demonstrates a correlation. Additional data obtained from separate experiments are needed to develop a causal relationship. Mr. Manzi references John Mill and Sir Austin Hill on how to determine likely causality. In fact Hill outlines nine criteria that could be employed to determine whether statistical associations are indeed causal associations. Failing to discuss these important aspects weakens Manzi's argument. Regression analysis is a process of showing multiple relationships between possible independent variables and a single dependent variable. Again no causal relationship can be concluded based on the mathematical calculations, as implied by Manzi. Perhaps Manzi is too quick to jump to the same conclusions that imprudent readers jump to in reviewing well constructed scientific papers.

An example of the conclusion jumping occurs on p. 88 where Manzi discusses studies conducted in Ghana. In reviewing the hypotheses put forward as a result of the study, he concludes they are all false. The data does not appear to refute the null hypothesis and therefore no conclusions should be drawn. Researchers would have to either collect more data to demonstrate a statistical difference or reformulate the affirmative hypothesis. With the possibility of many confounding variables (what Manzi calls high causal density) the possibility of the outcome resulting in affirmation of the affirmative hypothesis becomes less likely.

Again on p.159 Manzi's statement "In science, theory precedes experiment" is false. In science initial data encourages development of hypotheses which then need to be tested. Science is a continuous iterative process of attempting to prove or improve on a hypothesis. When there is a large body of information that can be culled together to develop an over arching concept this information is pulled together to form a theory.

There is a limited discussion of the importance of blinding to limit or attempt to control bias. In clinical trials single blinding occurs when the patient does not know whether she is being treated or has received a control or placebo. In double blind, neither the patient nor the direct experimenter knows which cohorts are being treated. In triple blind experiments not only do the patient , experimenter, but also the person(s) doing the statistics not know who has been treated and who is a control.

When Manzi gets to Chapter 13 he wanders off into another world. It is not clear to me whether he chose to enter a political arena to sell the book or whether the gobbledegook that he writes is written to try to tie his arguments into the latter chapters. Whichever, the chapter seems totally irrelevant and leads to a weakness of his credibility in his final chapter 15 recommending "Sustainable Innovation."

Chapter 15 provides a reasoned set of recommendations to improve public policy. Manzi claims his argument is based on his previous chapters. In fact some of his suggestions seem to be disconnected from previous chapters. He states there is a need for decentralized innovation, however his examples argue for innovation with no justification for decentralization. In fact, he argues for strong oversight by a federal authority similar to the FDA for studying public policy issues such a medical delivery, education and criminal justice. Innovation requires some form of supervision of the studies to coordinate and evaluate the study results. All human studies require an Institutional Review Board so that we do not repeat unethical or illegal tragedies such as the famous Tuskegee syphillis study.

Some of the proposals he suggested have merit. He advocates increasing the number of students pursuing science and math. He recommends automatically issuing H-1B visa to international students graduating with appropriate math and science degrees.

However, others have problems. For instance, his suggestion to privatize schools are structured to benefit the stockholders. How is that an improvement over union contracts benefiting the teachers? Establishing a financial mutually funded institutions where the parents (or students) make the investment and reap the benefits. We need a common knowledge bases for upper level learning (high school or college) or else colleges will spend even more time than they do now in remediation education. Funding at a limited number of research institution will only exacerbate an already existing problem. Federal funding that funnels money to a limited number of "successful " institutions restricting innovative thinking. Many good ideas have sprung from smaller institutions and projects started on a shoe string. We need to be able to foster those innovative ideas with a spreading of federal funding, not shrinking the institutions who are considered to be "eligible."

Overall this book would have greater value if the political rhetoric (libertarian statements) would have been left out. A clearer statement of the scientific method and how it could be applied to public policy could turn this book into a useful and more widely read reference source.

— William S. Carter, Ph. D. CIH

Emeritus Professor Environmental Safety and Health
The University of Findlay
Findlay, OH 45840

Controversial messages to aliens

There's a discussion about seeking and contacting extraterrestrial intelligence this month at Cato Unbound: "Politics, Social Theory, and SETI." It includes some effort to connect the topic to libertarianism, this being a venue of the Cato Institute, but the main focus is on whether "active SETI" or "METI" (often called Messaging to Extraterrestrial Intelligence) is a good idea, with the balance of opinion so far being 'no' and Robin Hanson even throwing in a suggestion that we scale back radio astronomy as an activity that might send a relatively easily detectable message out inadvertently. David Brin's lead essay has a lot of interesting angles, though I'd tinker with his description of the math (the left side of the Drake equation is N).

I've long been interested in this overall subject, as with this review (which originally was planned for Reason but perhaps didn't have enough of a libertarian angle for them). I'm no enthusiast of METI, which strikes me as having less upside than downside; I would prefer that such activity be delayed until some time when we know more about what might be out there (but what that knowledge might consist of and how much of it we need is hard to say). Still, restricting METI, let alone radio astronomy that might reveal our presence, requires some very murky risk assessment. For all we know, it's only if aliens do know we're here that they won't use this solar system for some sterilizing experiment or such. If, notionally, the risk of extermination by aliens who pick up our signals is anywhere near one in a billion, then unlike Hanson I'd be happy to shrug off that risk.

College major advice

My latest at Research magazine: "Which College Majors Are Solid Investments?" With some ideas relevant to the target readership (financial advisors) and others, including journalists and the occasional Secretary of Defense. Excerpt:

What was your major in college? Ask that question and you’re likely to find out something interesting about a person—regarding their areas of interest, habits of thought, and past or present ambitions. 

Often a major matters greatly in determining a career path, and not necessarily in a predictable way. Consider Secretary of Defense Ashton Carter. He has written of how, as a Yale undergrad, he took a double major in the disconnected subjects of physics and medieval history. Their appeal lay in being so different. Moreover, in his words: 

“As far as course choice was concerned, I had no interest in between the extremes of medieval history (history, language, philosophy) on the one hand, and science (physics, chemistry, mathematics) on the other…. I have taken exactly zero social science courses in my entire life. My arrogant view at the time was that life would eventually teach me political science, sociology, psychology, and even economics, but it would never teach me linear algebra or Latin. It seemed best to get my tuition's worth from the other topics and get my social science for free!”

Whole thing here.

My own majors at NYU were economics and history, which both have served me reasonably well and been frequent subjects of my writing. Still, if I were doing things over, I would have a different mix with significantly more math and science than I was willing to try back then.

NASA to help Muslims feel good

I've long thought that promoting scientific rationalism is an important way in which the West should be engaging the Islamic world, including through celebration of historic Islamic achievements in science and math. But for the head of NASA to say that his mandate from the president is "perhaps foremost" to "engage much more with dominantly Muslim nations to help them feel good about their historic contribution..." is surely the strangest statement from a NASA official I can remember. The fact that the other things Obama apparently tasked Bolden with (reinspiring children and building international relationships) are also ancillary to anything that actually happens in space is a disturbing indicator of what the Obama-era space agency is up to, or not up to.

UPDATE: In Twitter-based discussion, Julian Sanchez contended that the three objectives Bolden stated were new, or additional, priorities for NASA, not that they're the top priorities. Whether or not that's so, it still reflects some muddled thinking on Bolden's part, as two of the objectives surely aren't new. None of the above, however, means I endorse the reactions of the lathered-up simpletons here.

Some free-will links

In a study, some students were primed to think there's no such thing as free will, and became more inclined to cheat on a math test. Ronald Bailey is skeptical about assumptions that justice and morality depend on free will. So am I, though in addition I'm skeptical about assumptions that there is no free will. I wrote about it here, as well as here, here and here. A mention of how I started caring about the subject is here, though for the record, the snowstorm was in Queens, not Manhattan.

Book note: A Numerate Life

I read an advance copy of this: A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours, by John Allen Paulos. It's an eclectic book, mixing math, autobiography and reflections on memory, storytelling and more.


One intriguing section explains why "Despite Normal Appearances, We're All Strange" by imagining a higher-dimensional hypercube in which people's preferences on various matters are charted. The result:

...if each of us has a score along each of the very many dimensions in a hypercube, then almost all of us will find ourselves to be a point along the edges of the hypercube; that is an extreme, abnormal point. Nobody except the hopelessly boring and banal live in the moderate, normal interior of the human hypercube.

Me: I'd be interested in constructing such a hypercube based on stated positions of the Republican candidates. Perhaps the upshot would be that George Pataki is "edgy" and could win. In any case, no one will accuse this book of being banal or normal, and I think it offers much of interest accordingly.