Category Archives: Book Review

Having no internet for four half weeks isn’t necessarily all bad

I moved to the UK to begin a postdoc with John Cremona at the University of Warwick. And for the last four weeks, I have had no internet at my home. This wasn’t by choice — it’s due to the reluctance of my local gigantitelecom to press a button that says “begin internet service.” I could write more about that, but that’s not the purpose of this note.

The purpose of this note is to describe the large effects of having no internet at my home for the last four weeks. I’m at my home about half the time, leading to the title.

I don't talk about it, but I do know *exactly* where I can get other's wifi in my place. Sadly, no linksys.

 

I have become accustomed to having the internet at all times. I now see that many various habits of mine involved the internet. In the mornings and evenings, I would check HackerNews, longform, and reddit for interesting reads. Invariably there are more interesting seeming things than I would read, and my Checkout bookmarks list is a hundreds-of-items long growing list of maybe interesting stuff. In the middle times throughout the day, I would checkout a few of these bookmarks.

All in all, I would spend an enormous amount of time reading random interesting tidbits, even though much of this time was spread out in the “in-betweens” in my day.

 

I still remember modem sounds. This is a defining aspect of my generation. My postdoc advisor was telling me about the difference between 100 and 300 baud teletypes. Things change, you know?

 

When I didn’t have internet at my home, I had to fill all those “in-between” moments, as well as my waking and sleeping moments, with something else. Faced with the necessity of doing something, I filled most of these moments with reading books. Made out of paper. (The same sort of books whose sales are rising compared to ebooks, contrary to most predictions a few years ago).

I’d forgotten how much I enjoyed reading a book in large chunks, in very few sittings. I usually have an ebook on my phone that I read during commutes, and perhaps most of my idle reading over the last several years has been in 20 page increments. The key phrase here is “idle reading”. I now set aside time to “actively read”, in perhaps 100 page increments. Reading enables a “flow state” very similar to the sensation I get when mathing continuously, or programming continuously, for a long period of time. I not only read more, but I enjoy what I’m reading more.

As a youth, I would read all the time. Fun fact: at one time, I’d read almost every book in the Star Wars expanded universe. There were over a hundred, and they were all canon (before Disney paved over the universe to make room). I learned to love reading by reading science fiction, and the first novel I remember reading was a copy of Andre Norton’s “The Beastmaster” (… which is great. A part telepath part Navajo soldier moves to another planet. Then it’s a space western. What’s not to love?).

I have also been known to open hackernews, think there's nothing interesting on the front page, close the tab, and then go immediately to hackernews to see if there's something interesting. There isn't. This reminds me of opening the fridge, hoping for tastier food to have appeared since I last didn't put anything in there.

 

My primary source of books is the library at the University of Warwick. Whether through differences in continental taste or simply a case of different focus, the University Library doesn’t have many books in its fiction collection that I’ve been intending to read. I realize now that most of the nonfiction I read originates on the internet, while much of the fiction I read comes from books. Now, encouraged by a lack of alternatives, I picked up many more and varied nonfiction books than I would otherwise have.

As an unexpected side effect, I found that I would also carefully download some of the articles I identified as “interesting” a bit before I headed home from the office. Without internet, I read far more of my checkout bookmarks than I did with internet. Weird. Correspondingly, I found that I would spend a bit more time cutting down the false-positive rate — I used to bookmark almost anything that I thought might be interesting, but which I wasn’t going to read right then. Now I culled the wheat from the chaff, as harvesting wheat takes time. (Perhaps this is something I should do more often. I recognize that there are services or newsletters that promise to identify great materials, but somehow none of them have worked better to my tastes than hackernews or longform. But these both have questionable signal to noise.).

The result is that I’ve goofed off reading probably about the same amount of time, but in fewer topics and at greater depth in each. It’s easy to jump from 10 page article to 10 page article online; when the medium is books, things come in larger chunks.

I feel more productive reading a book, even though I don’t actually attribute much to the difference. There may be something to the act of reading contiguously and continuously for long periods of time, though. This correlated with an overall increase my “chunking” of tasks across continuous blocks of time, instead of loosely multitasking. I think this is for the better.

I now have internet at my flat. Some habits will slide back, but there are other new habits that I will keep. I’ll keep my bedroom computer-free. In the evening, this means I read books before I sleep. In the morning, this means I must leave and go to the other room before I waste any time on online whatevers. Both of these are good. And I’ll try to continue to chunk time.

To end, I’ll note what I read in the last month, along with a few notes about each.

Fiction

From best to worse.

  • The best fiction I read was The Three Body Problem, by Cixin Liu. I’d heard lots about this book. It’s Chinese scifi, and much of the story takes place against the backdrop of the Chinese cultural revolution… which I know embarassingly little about. The moral and philosophical underpinnings of this book are interesting and atypical (to me). At its core are various groups of people who have lost faith in aspects of science, or humanity, or both. I was unprepared for the many (hundreds?) of pages of philosophizing in the book, but I understood why it was there. This aspect reminded me of the last half of Anathem by Stephenson (perhaps the best book I’ve read in the last few years), which also had many (also hundreds?) of pages of philosophizing. I love this book, I recommend it. And I note that I read it in four sittings. There are two more books completing a trilogy, and I will read them once I can get my hands on them. [No library within 50 miles of me has them. I did buy the first one, though. Perhaps I’ll buy the other two.]
  • The second best was The Lathe of Heaven by Ursula Le Guin. This is some classic fantasy, and is pretty mindbending. I think the feel of many books of Ursula Le Guin is very similar — there are many interesting ideas throughout the book, but the book deliberately loses coherence as the flow and fury of the plot reaches a climax. I like The Lathe of Heaven more than The Wizard of Earthsea and about the same as The Left Hand of Darkness, also by Le Guin. I read this book in three sittings.
  • I read three of the Witcher books, by Andzej Sapkowski. Namely, The Sword of Destiny, Blood of Elves, and Time of Concempt. These are fun, not particularly deep reads. There is a taste of moral ambiguity that I like as it’s different from what I normally find. On the other hand, Sapkowski often uses humor or ambiguity in place of a meaningful, coherent plot. The Sword of Destiny is a collection of short tales, and I think his short tales are better than his novels — entirely because one doesn’t need or expect coherence from short stories.

I’m currently reading Confusion by Neal Stephenson, book two of the Baroque trilogy. Right now, I am exactly 1 page in.

Nonfiction

I rank these from those I most enjoyed to those I least enjoyed.

  • How Equal Temperament Ruined Harmony, by Duffin. This was told to me as an introduction to music theory [in fact, I noted this from a comment thread on hackernews somewhere], but really it is a treatise on the history of tuning and temparaments. It turns out that modern equal termperament suffers from many flaws that aren’t commonly taught. When I got back to the office after reading this book, I spent a good amount of time on youtube listening to songs in mean tone tuning and just intonation. There is a difference! I read this book in 2 sittings — it’s short, pretty simple, and generally nice. However there are several long passages that are simply better to skip. Nonetheless I learned a lot.
  • A Random Walk down Wall Street, by Burton Malkiel. I didn’t know too much about investing before reading this book. I wouldn’t actually say that I know too much after reading it either, but the book is about investing. I was warned that reading this book would make me think that the only way to really invest is to purchase index funds. And indeed, that is the overwhelming (and explicit) takeawar from the book. But I found the book surprisingly readable, and read it very quickly. I find that some of the analysis is biased towards long-term investing even as a basis of comparison.
  • Guesstimation, by Weinstein. Ok, perhaps it is not fair to say that one “reads” this book. It consists of many Fermi-style questions (how many golf balls does it take to fill up a football stadium type questions), followed by their analysis. So I read a question and then sit down and do my own analysis. And then I compare it against Weinstein’s. I was stunned at how often the analyses were tremendously similar and got essentially the same order of magnitude at the end. [But not always, that’s for sure. There are also lots of things that I estimate very, very poorly]. There’s a small subgenre of “popular mathematics for the reader who is willing to take out a pencil and paper” (which can’t have a big readership, but which I thoroughly enjoy), and this is a good book within that subgenre. I’m currently working through its sequel.
  • Natures Numbers, by Ian Stewart. This is a pop math book. Ian Stewart is an emeritus professor at my university, so it seemed appropriate to read something of his. This is a surprisingly fast read (I read it in a single sitting). Stewart is known for writing approachable popular math accounts, and this fits.
  • The Structure of Scientific Revolutions, by Thomas Kuhn. This is metascience. I read the first half of this book/essay very quickly, and I struggled through its second half. This came highly recommended to me, but I found the signal to noise ratio to be pretty low. It might be that I wasn’t very willing to navigate the careful treading around equivocation throughout. However, I think many of the ideas are good. I don’t know if someone has written a 30 page summary, but I think this may be possible — and a good alternative to the book/essay itself.

I’m now reading Grit, by Angela Duckworth. Another side effect of reading more is that I find myself reading one fiction, one non-fiction, and one “simple” book at the same time.


Written while on a bus without internet to Heathrow, minus the pictures (which were added at Heathrow).

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Review of How Not to Be Wrong by Jordan Ellenberg

Almost 100 years ago as I write this, on 21 October 1914, Martin Gardner was born. He wrote a popular “Mathematical Games” column for Scientific American from 1957 to 1981, introducing a wide audience to fun and recreational mathematics. His influence and writing were so profound that many of his subjects are still popular today. Notable examples include:

Conway’s Game of Life

Gospers_glider_gun
After its first public appearance in Gardner’s Scientific American column in October 1970, Conway’s Game of Life grew to enormous popularity and interest.

Flexagons

The column “Mathematical Games” started with Gardner’s article on flexagons. The editor of Scientific American thought Gardner’s flexagons was engaging, and suggested that Gardner write a regular column. Fortunately, Gardner acceded.

Public Key Cryptography

The first major public key cryptosystem, the RSA system, first appeared in Gardner’s August 1977 column. (Their formal paper appeared in 1978 in Communications of the Association for Computing Machinery). Now, public key cryptography is used everywhere, all the time, mostly without the conscious thought of the user.

Martin Gardner was in constant contact with many mathematicians, and always looked for interesting recreational mathematics to share with his readers. He inspired an entire generation of mathematicians and math enthusiasts. He also inspired others to pursue popular mathematics writing (and blogging, and even youtubing, such as the excellent series produced by Vi Hart).

The current issue(October/November 2014) of the MAA Focus, a mathematical newsmagazine from the American Mathematical Association, features Martin Gardner. In addition to describing some of Gardner’s contributions and legacy, the article includes a quote from Gardner: “I’ve always thought that the best way to get students interested in mathematics is to give them something that has a recreational flavor — a puzzle or a magic trick or a paradox, or something like that. I think that hooks their interest faster than anything else.” Later, he is also quoted to say “It’s good to to know much about mathematics. I have to work hard to understand anything that I am writing about, so that makes it easier for me to explain it, perhaps, in a way that the general public can understand.”

(As an aside, the Doctor has noted the lack of recreational mathematics in school too)

It is in this noble succession that I consider Jordan Ellenberg’s recent book How Not to Be Wrong: The Power of Mathematical Thinking, for Ellenberg has made a significant effort to make an approachable, inspiring work (even though it’s not recreational math). After reading the book, it seems clear to me that Ellenberg’s beliefs about how to interest people in mathematics mirror Gardner’s. This book is full of paradoxes and magic tricks. Or rather this book is full of captivating stories each centered around a problem or misconception, and whose resolution comes through careful and explicit reasoning.

Ellenberg presents mathematics as “an extension of common sense by other means,” but I get the feeling that he means to blur what it means to be “common sense” and what it means to be “other means” as the book advances. Much as a textbook or college course eases students into the subject, starting simple and getting progressively deeper, Ellenberg starts with problems that are undeniably simple logic and ends with ideas that are truly profound.

The reader is engaged within the first five pages. After a quick justification about learning mathematics — mathematics is reason, and allows for deeper understanding of the world around us — Ellenberg demonstrates that this is not an abstract book about abstract mathematics, but is instead full of actual examples. And he begins with a tale about Abraham Wald, a mathematician and statistician considering where to reinforce the armor of planes during the Second World War. The writing is conversational, as though this were an oral history transcribed and kept safe in written word. To support the claim that mathematics is an extension of common sense, the book alternates between explaining and setting up problems and careful, but common sensical, analysis. And most of the time, he proceeds without overwhelming the reader with arithmetic details or a flood of equations.

Mathematics is not arithmetic. Yes, arithmetic is one tiny part of mathematics, but mathematics is much more. The typical student is overexposed to arithmetic and underexposed to mathematics. Stories like Abraham Wald seek to rectify this imbalance by demonstrating more mathematics. And later stories, like the chapter about challenges facing Netflix analytics — how does Netflix know what movies to recommend? — use equations and arithmetic to support the underlying mathematics.

It might seem like a delicate arrangement to go through so much mathematical reasoning with so little arithmetic, but Ellenberg succeeds. Part of this is certainly that this is a book full of what he calls “simple and profound” mathematics. The simple is what allows the conversational tone. The profound is what makes it interesting. But the larger part is that Ellenberg’s thesis, math is common sense and allows for deeper understanding of the world around us, is fundamentally true. And quite beautiful.

Ellenberg does truly get to some profound mathematics. Some of the chapter is common material for popular mathematics: survivorship bias, statistics lie, and the high likelihood of coincidence, for instance. But in many ways, he goes deeper, and more profound, than I would expect. He examines with great detail the divide in statistics between Fisher’s “significance testing” and Pearson’s “hypothesis testing,” and evidences deep dissatisfaction with the accepted standard in experiments and hypothesis testing of “Reductio ad unlikely.” He not only mentions and cautions misunderstandings about conditional probabilities, but also undertakes Bayesian inference as a decision-making model, perhaps even a good model for how we make our own decisions.

He makes a strong point that sometimes, mathematics does not have all the answers. Or more pertinently, sometimes the answer from mathematics is inaction. For this is action, this not being sure! Although Ellenberg never says it, he hints at the fact that saying anything meaningful about anything at all can be really hard, and sometimes even impossible.

Of course, the book is not without its flaws. Most chapters have their central players, central ideas, and a sort of take home message. But I found the last two chapters to suffer from a bit of indigestion. This might be because they concern the very idea of “existence.” Does public opinion exist as a measurable, or even well-defined quantity? Lurking beneath these two chapters is the problem of designing good, accurate voting systems. Though Ellenberg emphasizes Arrow’s paradox on the impossibility of having a rank order voting system that accurately reflects community opinion, this message is muddied.

And though Ellenberg confronts some of the common misunderstandings of mathematics, like thinking that all mathematics is simple arithmetic and boring, there is one more misunderstanding that I wish he tackled more explicitly, which is that there is room for more mathematics all the time. It is easy to read this book, look at how common sense and mathematics can feel so alike, and sleep comfortably under the sheets at night knowing that these mathematicians have solved all these hard problems for us. But really, more mathematics is needed in both academic and ordinary walks of life.

I think it should also be mentioned that Ellenberg’s rejection of the cult of genius, including the idea that it takes a genius to succeed in mathematics and the far worse idea that we depend on geniuses to progress the sciences, is both good and from an interesting position. Ellenberg was one of the child “geniuses” in the Study of Mathematically Precocious Youth, which found and followed high-performing children and followed them throughout their lives. In an article in the Wall Street Journal, Ellenberg wrote of the dangers of the cult of genius. He also wrote that we need more math majors who don’t become mathematicians. Math and the sciences are not only progressed by the top 0.01 percent, but instead are more often advanced by the hard work and determination of someone who pursued their interests and ignored the cult. For more, read his article. It’s not very long, and it rounds out the end of “How Not to Be Wrong” very nicely.

Ultimately, “How Not to Be Wrong” is a great read that I highly recommend, both to a mathematical and non-mathematical crowd. It’s an engaging and educational read that’s not afraid to do some real math. After finishing the book, part of me wondered if more mathematics should be taught against the history of the mathematicians themselves. Why is it that I learned the development and logic of chemistry along the lives of the chemists of the past while in middle and high school, but I heard almost no mathematician’s name until I began to major in college? This book is literally a tour-de-mathematical-force throughout recent history, and in the spirit of Martin Gardner. I look forward to reading more of his work.

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A Book Review of Count Down: The Race for Beautiful Solutions at the IMO

I read a lot of popular science and math books. Scientific and mathematical exposition to the public is a fundamental task that must be done; but for some reason, it is simply not getting done well enough. One day, perhaps I’ll write expository (i.e. for non-math folk) math. But until then, I read everything I can. I then thought that if I read them all, I should share what I think.

Today, I consider the book Count Down: The Race for Beautiful Solutions at the International Mathematics Olympiad, by Steve Olson. CDThe review itself can be found after the fold (more…)

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