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.

21 August 2010 rehabilitation

Shoulder I killed me last night; it woke me up at 1:30. By the time I went to bed, it settled down a bit; yes I used ice prior to sleeping. It didn’t hurt during the day though and didn’t bother me during my walk.

Knee: slight lateral pain last night; I forgot to ice prior to sleeping. Ice took it away nicely.

Piriformis: not a factor today but I had better stretch it out anyway.

Workout: 5.4 mile walk in 1:23:45 (15:31 mpm); I didn’t walk that hard but rather took it easy on a muggy, overcast but not-too-hot morning. The cemetery was nice:

I was going to do the lunchtime 5 miler but was blocked by the motorcycle parade. But this improvised route gave me a nice hill in the cemetery.

Pain: I thought about those with chronic pain. Personally, I’ve been dealing with night pains of various kinds since last October (knee, now shoulder). Ironically, I am NOT in pain during the day. And, I have confidence that the shoulder pain will eventually be resolved by therapy or medicine (shots or surgery, if necessary). But what do people do when their pain has no solution and it is constant? It must really suck.

I also thought about racing. Yeah, I miss it some, but I’ve replace the challenge of times/races with therapy goals. I thought that I might just give up racing all together; we’ll see. I sure as heck don’t want to give up working out though; I enjoy my workouts too much to do that.

This Homemade Ad is too Strident for me.

Bonus question: where did the music in this ad come from? (Song and artist)

21 August 2010 (am)

(and yes, I got calls from the DNC, DCCC, and two different campaigns. )

Science (public understanding) From Why Evolution is True: this talks about the surveys that ask “do you believe evolution”. The gist is that those who say that they believe in an evolutionary process that was guided by a deity really don’t understand the randomness” that goes into scientific evolution; the mutations that occur do so randomly; those that get passed along get passed because they either enhance or do not reduce the reproductive fitness of the recipient of the mutated gene.

Science (video)
I can’t get this to embed, but this is a spectacular video of time elapsed photos of a meteor shower from Joshua Tree National Park.

Science: piranhas Flesh eating piranhas and bikini clad women make for a blockbuster movie, but in reality, piranhas really aren’t a threat to humans (e. g., they don’t eat humans). Really. Watch a human get into a tank of piranhas.

Science/mathematics education Larry Moran talks about this: how many different professors does it take to give a good science education in a particular discipline? Here is a dirty secret: undergraduate math education (for the vast majority of mathematics undergraduates) consists of learning late 19′th century mathematics. Hence, in theory, ONE mathematics professor can give an undergraduate student an adequate mathematics education, though I don’t recommend this.

Seriously: most Ph. D. programs in mathematics require students to pass preliminary exams in algebra, analysis and topology, all well above the level that one can teach most mathematics undergraduates, and one needs at least a bit of knowledge in all these areas to do modern mathematical research.

Educational Issues: a school district in Florida told its teachers to unfriend their students. I can understand why.

Politics Paul Krugman talks about the lies and distortions that he commonly hears when he talks about the economy:

When you consistently irritate the hard right in the United States as I do, you quickly get used to the steady stream of accusations that you’re lying, simply because you didn’t present the facts in a way that suits the commenter. If I write, “The economy added 236,000 jobs a month under Bill Clinton,” the responses from conservatives will range from “That’s a lie! Krugman doesn’t mention the dot-com bubble!” to “That’s cherry-picking! What about Jimmy Carter?” [...]

Republican Mitch McConnell, the Senate minority leader from Kentucky, said in late July in an interview with CNN that during “the last year of the Bush administration, the deficit as a percentage of gross domestic product was 3.2 percent, well within the range of what most economists think is manageable. A year and a half later, it’s almost 10 percent.”

So where’s the deception? First, the Republicans are hoping that most people won’t know that standard budget data is presented in fiscal years, which start on October 1 of the previous calendar year. So what they’re talking about isn’t actually the “last year of the Bush administration” — they’ve conveniently lopped off everything that happened after the Lehman Brothers collapse —Troubled Asset Relief Program and all.

Krugman goes on to display a “quarter by quarter” graph of the data.

Evidently I am not alone

Yeah, I was a bit irritated when I wrote my previous post. Evidently the feeling is spreading among the blogs I regularly read:

Why Evolution is True:

Flash: many Americans are morons

. . . at least 18%, according to a Pew Research Center poll. [...]

The Legal Satyricon:

And in related news, it is time for forced sterilization of a lot of people in this retard laden country

One in five Americans think that Obama is a Muslim. (source)

Before you bring out the surgery tools, this seems to be a Fox News focus group. So, really the headline should be “one in five abject fucking retards who get their ‘news’ from Fox think that Obama is a muslim.”

Millard Fillmore’s Bathtub:

Hallowed ground: Why other nations think we’re nuts

Scott Hanley at Angular Unconformities used Google Earth to see how other nations deal with the placement of potentially-offensive installations near the sites of their great national calamaties.

But Robert Reich knows why the rubes (the targets of our derision) are acting up: fear:

Americans who feel economically insecure may even become paranoid, believing, say, that the President of the United States is secretly one of “them.”

Economic fear is the handmaiden of intolerance. It’s used by demagogues who redirect the fear and anger toward people and groups who aren’t really to blame but are easy scapegoats.

It has happened before.

Economic crises animated the pre-Civil War Know-Nothings and Anti-Masonic movements, the Chinese exclusion acts, the Ku Klux Klan in the economically-ravaged South, and the anti-immigrant movements of the early decades of the 20th century.

In different places around the world, mass economic stress has had far worse results. At its most extreme it has spawned genocide.

We are far from that. But it’s important to understand the roots of America’s growing intolerance. And to fight the hate-mongers and cynical opportunists who are using the fears unleashed by this awful economy to advance their own sordid agendas.

Does that sentiment ring a bell?

I guess that the President was right all along? That is the charitable way to look at it. My view of “them” is far less charitable.

Why I have so little respect for many Republicans

I’ll be clear: I have no problem with policy disagreement. I happen to think that we need to withdraw from Afghanistan and that we need more stimulus spending and to increase taxes on the wealthy. Others disagree; I am happy to have that debate and I admit that I might be wrong about some or all of those positions (in terms of what will yield the best results).

I admit that my positions aren’t always the best and that I don’t know it all.

So where is my beef? It is simple: it lies in the growing “culture wars” between those who just “know” what it means to be an American and who think that others who aren’t like them are really not American.

Politico has a nice article on this:

Much of the right — including the noisy and influential tea party movement — sees greater and more immediate danger from this administration and Congress on issues related to the role of government and the very meaning of America than from the old “social issues.” For while Obama has avoided single-issue fights on issues such as gays in the military and federal funding of abortions — angering parts of his base, in the process — he has, in the minds of conservatives, pushed a comprehensive agenda, and that is far more threatening.

“His worldview is dramatically different than any president, Republican or Democrat, we’ve had,” said former Arkansas Gov. Mike Huckabee, a potential 2012 presidential candidate, who attributes conservative fear not just to Obama’s effort to expand the federal government but to the president’s overall governing philosophy.

“He grew up more as a globalist than an American,” Huckabee said. “To deny American exceptionalism is in essence to deny the heart and soul of this nation.”

See: Gov. Huckabee has the hubris to claim that HE decides on what is an American and what isn’t. HE describes what the proper American attitude is.

To Gov. Huckabee and all who think this way: Fuck You.

It is a large world out there. Yes, the United States of America has a place and we do lots of things well. We also have weak areas.
And we are not all alike. Yes, the “rural uneducated but thinks that they are smarter than everyone else” hick in rural Arkansas is an American.

But so is a Nobel Laureate who writes on economic issues for the New York Times.

Like it or not, though not all of us agree with him on all issues at all times, Barack Obama does represent many of us and he won the last Presidential election fair and square. He is black, intellectual and worldly and does not subscribe to some comic book caliber fundamentalist religion. He is one of America’s faces, like it or not.

Attack his policy decisions and priorities all you want. Attack mine too. Americans can disagree on policy. But spare me this “this is “real America” and this isn’t” bullshit. The scientist who came up with a vaccine or a medical cure that saved your life might well be an atheist. Millions of us who produce wealth live in big cities. Many of us have traveled around the word, thereby gaining an understanding that the United States, while currently the dominant country, is just one of many countries. And those of us who know history understand that our place on the perch is, in the great scheme of things, temporary.

Many Americans WANT us to get along with other nations and to not bully them.
Many have no desire to live in a small town nor to attend some brain-dead fundamentalist Christian church.
Many Americans like their Birkenstocks and granola.
Many Americans can spot the joke in this photo (but perhaps not that many in Huckabee’s America? )