The Black Swan by Nassim Nicholas Taleb: A review

The short: I enjoyed the book and found it hard to put down. It challenged some of my thinking and changed the way that I look at things.

What I didn’t like: the book was very inefficient; he could have conveyed the same message in about 1/3 of the pages.
But: the fluff/padding was still interesting; the author has a sense of humor and writes in an entertaining style.

What is the gist of the book? Well, the lessons are basically these:

1. Some processes lend themselves to being mathematically modeled, others don’t. Unfortunately, some people use mathematical models in situations where it is inappropriate to do so (e. g., making long term forecasts about the economy). People who rely too much on mathematical modeling are caught unprepared (or just plain surprised) when some situation arises that wasn’t considered possible in the mathematical model (e. g., think of a boxer getting in a fight with someone who grabs, kicks and bites).

2. Some processes can be effectively modeled by the normal distribution, others can’t. Example: suppose you are machining bolts and are concerned about quality, as, say, measured by the width of the bolt. That sort of process lends itself to a normal distribution; after all, if the specification is, say, 1 cm, there is no way that an errant bolt will be, say, 10 cm wide. On the other hand, if you are talking about stock markets, it is possible that some catastrophic event (called a “black swan”) can occur that causes the market to, say, lose half or even 2/3′rd of its value. If one tried to model recent market price changes by some sort of normal-like distribution, such a large variation would be deemed as being all but impossible.

3. Sometimes these extremely rare events have catastrophic outcomes. But these events are often impossible to predict beforehand, even if people do “after the fact studies” that say “see, you should have predicted this.”

4. The future catastrophic event is, more often than not, one that hasn’t happened before. The ones that happened in the past, in many cases, won’t happen again (e. g., terrorists successfully coordinating at attack that slams airplanes into buildings). But the past catastrophic events are the ones that people prepare for! Bottom line: sometimes, preparing to react better is possible where being proactive is, in fact, counter productive.

5. Sometimes humans look for and find patterns that are really just coincidence, and then use faulty logic to make an inference. Example: suppose you interview 100 successful CEO’s and find that all of them pray to Jesus each day. So, obviously, praying to Jesus is a factor in becoming a CEO, right? Well, you need to look at everyone in business who prayed to Jesus and see how many of them became CEOs; often that part of the study is not done. Very rarely do we examine what the failures did.

I admit that I had to laugh at his repeated slamming of academics (I am an academic). In one place, he imagines a meeting between someone named “Fat Tony” and an academic. Taleb poses the problem: “suppose you are told that a coin is fair. Now you flip it 99 times and it comes up heads. On the 100′th flip, what the odds of another head?” Fat Tony says something like “about 99 percent” where the academic says “50 percent”.

Frankly, that hypothetical story is pure nonsense. In this case, the academic is really saying “if I am 100 percent sure that the coin is fair, there is a Black Swan even that has 100 heads in a row” though, in reality, the academic would reject the null hypothesis that the coin is fair as the probability of a fair coin coming up heads 99 times in a row is which is way in the rejection region of a statistical test.

Taleb also discusses an interesting aspect of human nature that I didn’t believe at first..until I tried it out with friends. This is a demonstration: ask your friend “which is more likely:
1. A random person drives drunk and gets into an auto accident or
2. A random person gets into an auto accident.

Or you could ask: “which is more likely: a random person:
1. Is a smoker and gets lung cancer or
2. Gets lung cancer.

Of course, the correct answer in each case is “2″: the set of all auto accidents caused by drunk driving is a subset of all auto accidents and the set of all lung cancer cases due to smoking is a subset of all lung cancer cases.

But when I did this, my friend chose “1″!!!!!!

I had to shake my head, but that is a human tendency.

One other oddity of the book toward the end, Taleb discusses fitness. He mentions that he hit on the perfect fitness program by asking himself: “what did early humans do? Ans.: walk long distances to hunt, and engage in short burst of high intensity activity”. He then decided to walk long, slow distances and do sprints every so often.

Well, nature also had humans die early of various diseases; any vaccine or cure works against “mother nature”. So I hardly view nature as always being optimal. But I did note with amusement that Taleb walks 10-15 hours a week, which translates to 30-45 miles per week! (20 minutes per mile pace).

I’d say THAT is why he is fit.

Poincare’s Prize by George Szpiro: a review

The short: I enjoyed this book; I can recommend it to either mathematicians who aren’t topologists but want to understand a little bit about the Poincare Conjecture with a minimum of effort and to the interested lay-person. There is enough here about the history and the characters involved for even an expert to learn something.

Disclaimer: my research area was (is?) knot theory which is a subset of low dimensional topology. I also have met many of the people that the book talks about; in fact one of them, John Thickstun, was on my dissertation committee. I also had a class from one of them (R. H. Bing).

Longer: the book takes you through the start of topology (called analysis situs at first) and traces the origins of the Poincare conjecture. It talks about the various approaches to solve it, what happened with the various approaches and, just as interestingly, what was going on in the lives of those working on the conjecture and its many spin off problems. Along the way you’ll learn (at a superficial, pop-science level) about homotopy groups, homology groups, homology spheres, Heegard surfaces, Dehn’s Lemma (and who ended up proving it!), R. H. Bing’s partial solution, property P for knots, Thurston’s geometrization conjecture, Smale’s work and, yes, Whitehead manifolds!

Of course, the story ends with the introduction of the Ricci flow, Yau’s work and Pearlman’s proof along with the controversy of some of the published proofs of the Poincare conjecture (e. g., the proof that fills in details that got published in a Chinese mathematics journal).

Chapter 7 talks about the conjecture itself. True, the author makes a few subtle errors here and there (e. g., once confusing simple connectivity with being contractible, confusing “one point compactification” with “deformation”, the Poincare space is called the only known homology sphere), but none are serious enough to really confuse the reader.

So, what is the Poincare Conjecture anyway?
I am going to lie simplify just a bit; hopefully someone who has had multi-variable calculus will understand a bit.

First of all, the classical 3-sphere is the set in 4 space. In practice, a topologist says that a space is a three sphere if there is a function that is continuous, one to one, onto and has continuous inverse that takes onto the classical 3-sphere. Such a function is called a homeomorphism.

A 3-manifold is a space that, at every point, locally “looks like” (traditional 3-space); that is, for each point in the manifold, there is a map from the unit “ball” in 3-space () that is a homeomorphism onto a small subset containing the point (e. g., you can parametrize every point in the space by a piece of 3-space). By the way, such a map is called a "chart" (and yes, most people like their manifolds to be second countable).

The n-th homotopy group is the group that is formed by talking all the maps from the n-sphere into the space ; by “group”, I mean the objects that you studied in abstract algebra. The group operation is function composition (we insist that all maps contain a common point called a “base point”), the identity element is the map that takes the n-sphere into a single point. For the group is Abelian (is commutative).

A manifold is said to be closed and compact if the manifold has no boundary and is compact (in the sense of your analysis class OR can be embedded as a closed, bounded subspace of a for some .

The n-dimensional Poincare conjecture (n > 1) says that an n-dimensional manifold that has trivial m-homotopy groups for all not equal to and n-homotopy group infinite cyclic is homeomorphic to the n-sphere.

This was proven a long time ago for n = 2, proven later (1960′s by Stephen Smale) for n greater than or equal to 5. The proof for n = 4 came even later (1980′s; solved by Michael Freedman).

The reviewed book talks about the n=3 case, which Grigori Pearlman solved.

How difficult was this theorem? Smale, Freedman and Pearlman all were awarded Field’s Medals for their work (Pearlman declined his). That is the highest mathematical prize.

22 August 2010 Rehabilitation

Workout notes Floodplain Trail at Wild Life Prairie Park in 55:53 (4 miles); It was wet, slightly muddy. Michelle caught up to me (I was looking for frogs) and we walked about 1/3 of the trail together. Note: a week ago it took me 60 minutes and on 31 July it took me 63 minutes (Olivia had to slow down for me). I am getting stronger.

Shoulder: less pain last night (surprising since I cut the grass) but I am icing it more.

Knee: I have to watch how I get into the car; If I put my right leg in first, I sometimes twist with my weight on it; not good.

Piriformis: not an issue over the past couple of days.

22 August 2010 post I

Some Sarah Palin Humor

Speaking of those who mangle the English language:

(more here)

Tell you what: I’ll join the English Only movement when those morons demonstrate a command of the English language. I am not holding my breath.

Science, Skepticism and tone
Jerry Coyne gives his reaction to Phil Plait’s “don’t be a dick” speech.
The speech is 31 minutes long and can be found here.

My reaction was a bit different; I saw it more as aimed at the “rank and file” (people like me) than at the better known people (e. g., people like Dr. Coyne). And to be honest, I have been called “strident” (and worse) by many who know me. I see it more as a reminder that saying “ok, why do you believe that; what makes you so sure?” opens more doors than “my goodness, that belief is idiotic” (which I am wont to say).

Or I can put it this way: my own family (wife, daughter) considers me to be too strident. They actually told me that I ought to look to Richard Dawkins as an example as to how to become less strident! (that is, they consider Dawkins to NOT be strident).

This type of BS sells in the Republican party

Republican candidate for the US House seat (FL-22)

Via Think Progress.

Of course, ALL religions have to accept that the US is a liberal democracy and has a secular government.

21 August 2010 Awesomeness

Ok, I exaggerated a bit. But these posts are cool.

From the Smithsonian Magazine: check out this article about the study of chimpanzee intelligence. A couple of highlights: the scientists wanted to find out if the chimps really “understood” what color was.
So consider the following experiment: Start the experiment by showing, say, red dots and blue dots. Ask a person to look at the dots and say what color they were. That would be easy. Now take some colored markers (say, red, blue, green black, etc.) and write the words for the colors in a different color example: blue , red . When you read the word, say the color that the word is written in aloud. Example, for the previous two words, you’d say “red” and then “blue”. Humans slow down when they do this; the brain sees the word blue and recognizes that the letters are red, but prior to saying “red” the human has to somehow block out the word “blue”.

Well, it turns out that chimps have a similar slow down when they are assigned a similar task that assigns colors to words that signify that color; the “get” colors.

It turns out that they don’t “get” math so well; for example they somehow “know” 4 is less than 5 but they don’t know that 5 is “one more” than 4.
There is a lot more in this article.

A few videos and photos
One way to respond obnoxious campus preaching:

There is more at this article at Friendly Atheist. For example, Brother Jed (a notorious campus fundie preacher) had a shirt that said “you deserve hell”; see how some students confronted him.)

And just for the heck of it, here is a repeat:

Religious tit-for-tat (hat tip: Invisible Pink Unicorn)

The Invisible Pink Unicorn: Team Mohammed Vs. T…, posted with vodpod

Awesome smack down on 9-11 site Mosque protest

Hat tip: Randazza.