Friday, February 05, 2016

3.37 Degrees of Separation


This is pretty interesting: Facebook has a tool that estimates the average number of intermediate people needed to link you, via the shortest path, to anyone else on Facebook. Mine is 3.37, which means the average path length (number of links) to me is 4.37, or that the average number of people in a shortest chain connecting others with me (including me and the person at the end) is 5.37.

What's yours?

An interesting aspect of this is that they use the Flajolet-Martin algorithm to estimate the path length. The paper of Flajolet-Martin deals with a certain correction factor φ, which is defined as follows: φ = 2 eγ α-1, where γ = 0.57721... is Euler's constant and α is the constant Πn ≥ 1 (2n/(2n+1))(-1)t(n), where t(n) is the Thue-Morse sequence, the sequence that counts the parity of the number of 1's in the binary expansion of n.

The Thue-Morse sequence has long been a favorite of mine, and Allouche and I wrote a survey paper about it some time ago, where we mentioned the Flajolet-Martin formula. The Thue-Morse sequence comes up in many different areas of mathematics and computer science. And we also wrote a paper about a constant very similar to α: it is Πn ≥ 0 ((2n+1)/(2n+2))(-1)t(n). Believe it or not, it is possible to evaluate this constant in closed form: it is equal to 2 !

By contrast, nobody knows a similar simple evaluation for α. In fact, I have offered $50 for a proof that α is irrational or transcendental.

Friday, January 29, 2016

Yet More Bad Creationist Mathematics


It's not just biology that creationists resolutely refuse to understand. Their willful ignorance extends to many other fields. Take mathematics, for example.

At the creationist blog Uncommon Descent we have longtime columnist "kairosfocus" (Gordon Mullings) claiming that "a set of integers that spans to infinity will have members that are transfinite", showing that he doesn't understand even the most basic things about the natural numbers.

And we also have Jonathan Bartlett asking "can you develop an effective procedure for checking proofs? and answering "The answer is, strangely, no."

Actually the answer is "yes". A mathematical proof can indeed be checked and easily so (in principle). This has nothing to do with the statement of Bartlett that follows it: "It turns out that there are true facts that cannot be proved via mechanical means." Yes, that's so; but it has nothing to do with an effective procedure for checking proofs. Such a procedure would simply verify that each line follows from the previous one by an application of the axioms.

If a statement S has a proof, there is a semi-algorithm that will even produce the proof: simply enumerate all proofs in order of length and check whether each one is a proof of S. The problem arises when a true statement simply does not have a proof. It has nothing to do with checking a given proof.

Can't creationists even get the most basic things correct?

Saturday, January 09, 2016

Our Car's Fibonacci Odometer


Been waiting for this for 11 years, and it finally happened!

Saturday, January 02, 2016

You Don't Have to Be a Sociopath to Become a Theist....


...but apparently it helps, at least judging from this video.

Several things come to mind when I watched this. First, if David Wood's story is largely true, then he's clearly a sociopath and why should we believe anything he says? He could just be manipulating us for some sick purpose. On the other hand, if his story is largely false, then he's clearly a pathological liar, and why should we believe anything he says? Of course, his story could be partly true and partly false (my guess), but then the same conclusion holds.

Second is how persuasive even a terrible design argument like the one proposed here can be for a diseased or weak mind. Don't bother studying any mathematics, or computer science, or biology. Just assert that there is no evidence for the scientific world view, and voilĂ !

Third is what an ignorant bastard the guy is for someone who thought he was the greatest person in the world. He thinks shingles are caused by vitamin deficiency, fer chrissake!

Oh well. I am comforted by the fact that there's lots of decent people who are religionists. They're not all sociopaths like David Wood.

Monday, December 21, 2015

10th Blogiversary!


Ten years ago, this blog, Recursivity, was born.

I've had a lot of fun with it, even though I never really had very much time to devote to it. A thousand posts in ten years sounds like a lot, but I wish I could have written a thousand more.

Generally speaking, my readers have been great. In ten years, I think I only had to ban two or three commenters, including one Holocaust denier. Thank you to everyone who read what I had to say, and even more thanks to those who took the time to comment.

Here are 25 of my favorite posts from the last ten years:

  1. Why We Never Lied to Our Kids About Santa: my absolute favorite, and still appropriate. You can criticize atheism and religion, but if you really want to get a reaction, just criticize the myth of Santa Claus.
  2. Robert J. Marks II refuses to answer a simple question: still waiting, more than a year later.
  3. Hell would be having to listen to Francis Spufford: Damn, he was boring.
  4. By the Usual Compactness Argument: for mathematicians only.
  5. Ten Common LaTeX Errors
  6. I defend a conservative politician's right to speak on campus
  7. Science books have errata. Holy books don't
  8. No Formula for the Prime Numbers?: Debunking a common assertion.
  9. In Memory of Sheng Yu (1950-2012): my colleague - I still miss him.
  10. Another Fake Magnet Man Scams AP
  11. William Lane Craig Does Mathematics
  12. Why Do William Lane Craig's Views Merit Respect?: Nobody gave a good answer, by the way!
  13. Stephen Meyer's Bogus Information Theory
  14. Religion Makes Smart People Stupid
  15. Test Your Knowledge of Information Theory
  16. David Berlinski, King of Poseurs
  17. Graeme MacQueen at the 9/11 Denier Evening
  18. Mathematics in a Jack Reacher novel
  19. The Prime Game: This appeared in my 2008 textbook, too.
  20. Debunking Crystal Healing
  21. Nancy Pearcey, The Creationists' Miss Information
  22. Academic Vanity Scams
  23. Time Travel: my second favorite, which nobody seemed to like that much.
  24. Janis Ian Demo Tape: the best part was that Janis Ian herself stopped by to comment!
  25. The Subversive Skepticism of Scooby Doo: my third favorite.
Happy Holidays to everyone, and may 2016 be a great year for you.

Sunday, December 20, 2015

Merry Kitzmas!


It's been ten years since the landmark decision of Kitzmiller v. Dover was handed down, the case that exposed the religious fraud of that absurd pseudoscience, "intelligent design". The ID movement, and especially its "think tank", the Discovery Institute, has never recovered.

I had the honor of meeting the lead plaintiff, Tammy Kitzmiller, a few years ago at one of the trial reunion parties. (I played an extremely minor role in the case, meeting with the lawyers for the plaintiffs and preparing as a possible rebuttal witness, but I never appeared in court because one person on the other side never testified.) A more pleasant and modest (yet determined!) person you can't imagine. In fact, all the people involved in the case in various ways, including Eric Rothschild, Nick Matzke, Steve Harvey, Kenneth Miller, Wes Elsberry, Genie Scott, and Lauri Lebo are about the nicest and most interesting people I've ever met. The contrast with the other side couldn't be more stark.

Ten years later, what's happening? Well, the Discovery Institute and their friends continue to churn out lies pretty much unabated, but nobody's listening any more. Even the "academic wing" of intelligent design seems to have given up. Bill Dembski just threw in the towel. At the same time Casey Luskin tries to boast about all the scientific work published by ID advocates, the flagship scientific journal for the movement has only published a single paper in calendar year 2015, despite getting a new editor and having an editorial board with 29 members.

There's just so long you can keep up this charade.

Meanwhile, the same nasty, deplorable tactics that renamed the Discovery Institute the "Dishonesty Institute" continue unabated. When one of the Kitzmiller team recently got a paper accepted to Science, one of the world's most prestigious scientific journals, all the Discovery Institute (and their slavering friends) could do is make ridiculous and groundless insinuations about misconduct. Truly, they have no shame at all.

Why do the ID folks behave so reprehensibly, over and over again? Of course, it has nothing at all do with science. They behave this way because they are motivated solely by their conservative religious beliefs. Recently a window opened on the ID world view, when one creationist was so disillusioned by their behavior that he posted a private e-mail message from ID advocate Barry Arrington that clearly revealed their motives. Arrington wrote

"We are in a war. That is not a metaphor. We are fighting a war for the soul of Western Civilization, and we are losing, badly. In the summer of 2015 we find ourselves in a position very similar to Great Britain’s position 75 years ago in the summer of 1940 – alone, demoralized, and besieged on all sides by a great darkness that constitutes an existential threat to freedom, justice and even rationality itself."

When you view your opponents this way, then no tactic is off limits. Lying is permissible because otherwise the "great darkness" will win. Insulting, making insinuations, likening your opponents to Nazis or Communists or fascists are all perfectly fine tactics, because your opponents constitute "an existential threat to freedom" and "justice". Treating your opponents as subhuman is ok, because after all, they threaten "rationality itself". And of course, they never, ever, admit they were wrong about anything.

I feel sorry for the ID folks today, I really do. Ten years after Kitzmiller, ID advocates are like the Millerites on October 23 1844, when their predicted triumphal ascent into heaven didn't happen. They are wandering around feeling puzzled and alone, and it's natural that they will lash out against any available target in an effort to cure their misery. It won't work, I'm afraid. Intelligent design is, for all practical purposes dead. Prop up the corpse all you want -- it won't work.

Meanwhile, science and evolutionary theory continue unabated. Those of us who enjoy and respect science (and there are lots!) continue to think about and solve interesting problems. The joy of discovery is genuine for us. May you find it, too.

So, to you and yours, I wish you a very merry Kitzmas.

Friday, December 18, 2015

Polish Immigrants a German Problem?


Only if the immigrants are moose.