Conversation with a "Cantor Crackpot"

As readers of this blog know, I'm fascinated by how people come to decisions about things and the various ways they can go wrong.

A few weekends ago, I got a chance to chat with a "Cantor crackpot". This is not pejorative; it is the term he used to describe himself. S, as I'll call him, is a pleasant and educated person, but he is convinced that Cantor's proof of the uncountability of the real numbers is wrong.

Here is what he recently wrote to me (paraphrased): Cantor's proof is wrong because the diagonal method that he used fails to produce a number not on the list. He illustrated this with the following example, in which S purports to give a 1-1 correspondence between the integers and the real numbers:

integer <-> real
23456 <-> 0.65432
23457 <-> 0.75432
23458 <-> 0.85432
23459 <-> 0.95432
23460 <-> 0.06432

This is a common misunderstanding among people when they first see Cantor's proof. I think this misunderstanding is essentially rooted in the following misconception: either that the only real numbers are those with terminating expansions, or that the set of integers contains objects with infinitely long base-10 representations. In this case, having talked with S, I know his misunderstanding is of the latter type.

In his example above of the purported bijection, we can ask, what integer corresponds to the real number 1/3? Its decimal expansion is 0.33333... where the 3's go on forever to the right. This must correspond to the integer ....3333333 where the 3's go on forever to the left. But this is not an integer!

So in this case the misunderstanding is really of a trivial nature. I would be interested in speaking to people who deny the correctness of Cantor's proof based on more elaborate misunderstandings.

Silly Barry

The ID creationist blog, Uncommon Descent, just gets more and more amusing now that lawyer and certified public accountant Barry Arrington has taken over.

For some comedy gold, read this post and enjoy the logical fallacies, straw man arguments, and misspellings. (Barry also doesn't seem to know what "antecedent" means.) It looks like it was written by an 8th grader, not a member of the bar.

Let's start with the first line: "Living things appear to be designed for a purpose. That statement is entirely non-controversial." Well, I dispute it. Living things don't really appear designed to me, much less designed for a purpose. Most of the designed things I know look like artifacts: the characteristic product of human activity. Mark Isaak even wrote a paper in which he tried to list commonalities among designed things. Living things don't fit very well.

As for "designed for a purpose", what purpose would that be? What is the purpose of the Ebola virus, Mycobacterium tuberculosis, the tick, the cockroach, and Celine Dion? A commenter tried to ask this, but didn't get any sensible answer.

Barry's post is called "Denying the Obvious". Lots of things which people used to think were "obvious" turn out to be not so obvious. It was "obvious" for many years that the earth was flat. It was "obvious" for many years that the earth was stationary. It was "obvious" for many years that witches were real, that slavery was the natural order of man, and so forth.

Barry thinks the denial of design is dishonest: "Dawkins and his ilk deny design, however, not because the evidence compels them to deny it, but because their a priori metaphysical commitments compel them to do so." Actually, they don't, at least not for me. I think it would be really mind-blowing if we discovered that life on earth (in general) or people (in particular) were part of an extraterrestrial engineering experiment. But since there is currently no evidence for this, pardon me if I am skeptical.

Barry thinks "Materialists must deny the existence of libertarian free will". Well, not this materialist. I don't deny it because I don't think anybody --- and certainly not Barry --- has a coherent definition of "free will". I do think that the folk and religious understanding of free will is very, very likely to be wrong, or at least wildly simplistic, as we are finding out from neuroscience. I think ultimately we will come to a scientific understanding of the various phenomena we currently lump under "free will". Progress is unlikely to come from philosophers and even more unlikely to come from theologians or certified public accountants.

Barry thinks "A man’s body is designed to be complimentary [sic] with a woman’s body and vice versa. All of the confusion about whether same-sex relations are licit would be swept away in an instant if everyone acknowledged this obvious truth." Well, no, it's not "an obvious truth", even if one uses the correct word "complementary". And even if it were, what does that have to do with whether same-sex relations are "licit", by which I assume Barry means "lawful"? After all, hammers are designed for hammering, but does that mean if I use a hammer as a doorstop I am breaking the law?

Barry illustrates the truth of William James' observation, "A great many people think they are thinking when they are merely rearranging their prejudices."

Another Moose Tragedy

This time, in Connecticut.

James Keegstra Dead

Most people, if they think of Red Deer, Alberta at all, think of famous native sons like actor Jacob Blair or hockey player Ron Anderson. For me, however, Red Deer is (in)famous as the home of James Keegstra, who died last month.

As a public school teacher in nearby Eckville, Keegstra spread his anti-Semitism to a captive audience in the Eckville public schools for years with hardly any complaints. When his lies were exposed, many in the community came to his defense. He was even Mayor for a time.

Keegstra was the classic fundamentalist Christian anti-Semite. He learned his anti-Semitism from crackpot Christian tracts like The Talmud Unmasked. Keegstra taught his students all sorts of nonsense, from the claim that John Wilkes Booth was Jewish, to Illuminati conspiracies, to the claim that Jews killed Franklin Roosevelt and that they were behind all kinds of world disasters, to Holocaust denial --- and his students duly repeated these claims in their essays. (One student essay contained the line "we must get rid of every living Jew so that we can live in peace and freedom.")

It was only when some courageous parents finally spoke out against Keegstra that the school board took action. It was actually his anti-Catholicism that got initially got him noticed; echoing today's crackpot claims of Rebecca Bynum and Jody Hice about Islam, Keegstra claimed that Catholicism was not a religion but a "humanly created ideology". In 1982 he was finally suspended from teaching. Later, he was prosecuted under Canada's hate speech laws. (Personally, I think the prosecutions were misguided; they only served to make Keegstra more of a martyr. He should not have been teaching his pernicious lies in the public schools, but neither should he have been convicted for believing them.)

If you would like to know more about Keegstra, a good source is Bercuson and Wertheimer's book A Trust Betrayed: The Keegstra Affair.

Believe it or not, there are people who praised Keegstra. For example, Joshua Blakeney, a former Alberta graduate student who was actually awarded a Queen Elizabeth II graduate scholarship for his bizarre "investigations", tweeted a recommendation of this Press TV article eulogizing Keegstra. (Warning: you're likely to want to wash your hands after clicking the link.) In case you didn't know, Press TV is a propaganda arm of the Iranian government. Blakeney is, by the way, also heavily into 9/11 conspiracies. Blakeney was a student of Lethbridge professor Anthony Hall, whose reasoning ability can be gauged from this article.

More praise from Keegstra comes from Arthur Topham who was (you guessed it) a recent guest on Blakeney's podcast.

Creationists Don't Understand Evolution

Creationists don't understand evolution. There may be a few rare exceptions to the rule, but this is largely true.

Here is an example, from the Princeton Alumni Weekly. The writer, one Mr. S., is hopelessly confused about what evolution is:

Evolution is the transition from one species to another...

No, that's not what evolution is. Evolution is the change in allele frequencies in a population over time.

To support his mistaken belief, he quotes from a PBS website:

"The evolutionary process of speciation is how one population of a species changes over time to the point where that population is distinct and can no longer interbreed with the ‘parent’ population."

But that is evidently a definition of "speciation", not "evolution". How confused do you have to be to not understand that?

Mr. S. goes on to

• use the hoary old "finches remained finches" argument
• claim that microevolution is not evolution (which is about as silly as claiming that a microcomputer is not a computer, or micromotion is not motion)
• claim that "the change of one species to another — is assumed and has not been observed" (which can be easily refuted by consulting any textbook on evolution, or here or here).

An Ivy League education is wasted on some.

Yet Another Gullible Reporter Snookered

Used to be that reporters were skeptical, hard-nosed investigative journalists. Not any more. Is there anyone more gullible than an AP or Canadian Press stringer?

Here we have the spectacle of reporter Laura Kane being snookered by a woman who claims to be a "psychic medium". Kane says, "During the recent interview in Toronto, Baird delivered messages to a Canadian Press reporter from deceased family members that were at times eerily significant and, at other times, completely inexplicable. In all, about two-thirds of her suggestions hit the mark."

In one respect, I feel sorry for poor Laura Kane. She doesn't seem to know anything about cold reading, the technique used by phony psychics and fortune-tellers for ages to persuade the gullible. But why does Laura Kane's ignorance merit an article in my local paper?

Anyone with access to google can find lots of information about Laura Kane (try googling "Laura Kane Canadian Press"): where she went to school, what she studied, and so forth. With a little more work you could probably find out information about her parents and grandparents -- and then obituaries in local papers or on the web. That's another trick used by "psychics".

Neither does Laura Kane do what used to be obligatory: interview someone, anyone, who might take issue with the claims of this "psychic". No, Laura Kane would rather just take dictation from the subject of the article. That's not journalism.

"Beyond Belief" by Jenna Miscavige Hill

Just finished reading Beyond Belief: My Secret Life Inside Scientology and My Harrowing Escape by Jenna Miscavige Hill.

I have already read other anti-Scientology books, like A Piece of Blue Sky by Atack and Bare-Faced Messiah by Miller. Hill's book is quite different: it offers a very intimate and personal account of what it was like to work, essentially as slave labor, in a large number of Scientology's different organizations starting from age 6. Hill recounts the abuses of the religion while recalling the details of being a young girl, growing up, and discovering love. Being David Miscavige's niece, she had access to the highest levels of the group.

Reading it brought home how similar Scientology is to other totalitarian belief systems, like the Communism of the Soviet bloc, and (to a lesser extent) Christian Science, Mormonism, and many forms of Christianity. Scientology uses all the classic mind control techniques, including indoctrination at an early age, a pervasive organization of spies and reporting, verbal and physical abuse, and so forth. It is very, very dangerous.

I also find it fascinating how Scientologists can rise to prominence in their organization without ever hearing the details of Scientology's completely insane theology. Of course, Christianity's theology is unbelievable, too, but there are different degrees of insanity. To use a mathematical analogy, Scientology is uncountably insane, while Christianity is only countably so.

I definitely recommend it for anyone interested in cults in general and Scientology in particular.

The Vastly Overrated C. S. Lewis: A Shallow and Sophomoric Thinker

C. S. Lewis, Christians tell us, is "the 20th century's most towering intellectual practitioner of the Christian faith". His thinking is "rich and deep". He is "amazingly influential" and his influence is "profound".

Well, bah to all that.

Lewis is vastly overrated. He was a shallow and sophomoric thinker. He knew virtually nothing about science. His children's books were twee crypto-Christian twaddle. (How old were you when you figured out that Aslan was Jesus? And how disappointed and misled did you feel?) His celebrated "trilemma" (not original with him) is so full of holes that a high-school student can spot the flaws. If this is the best that Christians can offer, the atheists win without even trying.

Recently I saw this passage of C. S. Lewis being extolled on a creationist web site:

In a way I quite understand why some people are put off by Theology. I remember once when I had been giving a talk to the R.A.F., an old, hard-bitten officer got up and said, `I've no use for all that stuff. But, mind you, I'm a religious man too. I know there's a God. I've felt Him out alone in the desert at night: the tremendous mystery. And that's just why I don't believe all your neat little dogmas and formulas about Him. To anyone who's met the real thing they all seem so petty and pedantic and unreal !'

Now in a sense I quite agreed with that man. I think he had probably had a real experience of God in the desert. And when he turned from that experience to the Christian creeds, I think he really was turning from something real to something less real. In the same way, if a man has once looked at the Atlantic from the beach, and then goes and looks at a map of the Atlantic, he also will be turning from something real to something less real: turning from real waves to a bit of coloured paper. But here comes the point. The map is admittedly only coloured paper, but there are two things you have to remember about it. In the first place, it is based on what hundreds and thousands of people have found out by sailing the real Atlantic. In that way it has behind it masses of experience just as real as the one you could have from the beach; only, while yours would be a single glimpse, the map fits all those different experiences together. In the second place, if you want to go anywhere, the map is absolutely necessary. As long as you are content with walks on the beach, your own glimpses are far more fun than looking at a map. But the map is going to be more use than walks on the beach if you want to get to America.

Now, Theology is like the map. Merely learning and thinking about the Christian doctrines, if you stop there, is less real and less exciting than the sort of thing my friend got in the desert. Doctrines are not God: they are only a kind of map. But that map is based on the experience of hundreds of people who really were in touch with God-experiences compared with which any thrills or pious feelings you and I are likely to get on our own are very elementary and very confused. And secondly, if you want to get any further, you must use the map. You see, what happened to that man in the desert may have been real, and was certainly exciting, but nothing comes of it. It leads nowhere. There is nothing to do about it. In fact, that is just why a vague religion-all about feeling God in nature, and so on-is so attractive. It is all thrills and no work; like watching the waves from the beach. But you will not get to Newfoundland by studying the Atlantic that way, and you will not get eternal life by simply feeling the presence of God in flowers or music. Neither will you get anywhere by looking at maps without going to sea. Nor will you be very safe if you go to sea without a map.

Let's ignore all the hidden assumptions here and accept Lewis's analogy: theology is like a map. Well, then it is a very poor map indeed. If you compare two contemporary maps of the same place, you usually find lots of commonalities between them. Not so with theology -- even if you restrict yourself to Christian theology. Christians can't even agree if faith alone, or good works plus faith, are required for salvation! Remember that itsy-bitsy schism called the Reformation? Why wasn't Lewis a follower of Joseph Smith or Mary Baker Eddy or Ellen G. White? They had their own competing maps, after all.

Maps are supposed to render what is there, not what one imagines is there. It would be a poor map indeed if one went to visit the place mapped and found it did not exist. But this happens all the time with theology; even Mother Theresa strongly doubted her own theological map. But why? Wasn't it based on, as Lewis claims, "the experience of hundreds of people who really were in touch with God"?

If theology really is a map, then it's more like a malfunctioning GPS. It's the kind of map that, if you follow it, takes you off the road and into the water. A really bad theology will fly your jet into buildings. Sometimes you'd be lucky just to survive.

Some Towns Get All the Luck

Like this one, for example. In case you're wondering, that's in Sault Ste. Marie, Ontario.

Luke Schaeffer Wins Governor General's Gold Medal

Yesterday, my former master's student Luke Schaeffer was awarded the Governor General's Gold Medal for outstanding work in a master's program. Luke is now a Ph.D. student at MIT.

Congratulations, Luke!

Are You from Ontario?

If you are from Ontario, you've already seen this terrific short film "Blackfly", by Christopher Hinton, which is a kind of music video for Wade Hemsworth's song. They also used to show it on Air Canada flights.

You'll also know what "Little Ab" means.

If you're not Canadian, you have no idea what I'm talking about.

20 Questions for Donald Knuth

Here is an interesting and good* interview with Donald Knuth, in which he is asked twenty questions and he responds. This is to celebrate the electronic version of The Art of Computer Programming.

* Here I am using the Alf van der Poorten definition of "good". A "good" interview is one in which I am mentioned.

Do Not Approach the Goose

It's springtime here in Canada. Do not approach the goose.

Death is Not Final?

That was the subject of a recent debate between Eben Alexander and Raymond Moody, on the one hand (arguing the affirmative), and Sean Carroll and Steven Novella on the other hand (arguing the negative).

The good guys -- Carroll and Novella -- won handily here. Alexander came off like a charlatan and Moody like a new age babbler. Carroll and Novella came off like the serious scientists they are.

Moody -- described as a philosopher! -- babbled about a "higher dimension" and "higher domain of existence". He believes there are "new ways of thinking" and "new logical principles" that will let us understand the afterlife -- but of course, he doesn't say what these new ways and principles are! And he apparently also believes in ghosts, not just an afterlife. Then again, Alexander believes in "telepathy, precognition, remote viewing, out-of-body experiences, past-life memories in children" as well as "lower spiritual realms".

Alexander egregiously misrepresented the views of Carl Sagan at 1:26:30. He claimed "a very renowned skeptic and scientist, Carl Sagan, admitted that, past-life memories in children, the evidence for that is overwhelming" and justified this with an appeal to The Demon-Haunted World, p. 302. Well, here is what Sagan wrote on that page:

As you can see, Sagan describes the evidence as "at least some, although still dubious, experimental support". That is a very far cry from "overwhelming".

I really have to wonder, however, about the organizers of this debate. Why are they giving Eben Alexander's goofy claims any attention at all, considering that very very serious questions have been raised in Esquire about the truthfulness of his account? It certainly undermines their credibility. And I wonder why neither Carroll nor Novella explicitly brought up the Esquire article at all. Perhaps it was a tactical decision on their part.

Doug Groothuis on Transvestism

I have a not-so-secret sinful pleasure, which is reading Doug Groothuis's blog. The stupidity and lack of self-awareness of this "Ph. D." rarely fail to amuse. Here's his latest piece, which is about his displeasure on seeing a transvestite on TV.

Groothuis is disgusted by it, and finds it a "sinful sickness" that is "a sure sign of cultural decay, bone rot, disintegration and dissipation". But nowhere in his little rant does he explain why it drives him nutty.

Transvestism occurred and occurs in many different cultures; the idea that it is a "sure sign of cultural decay" doesn't seem supported by the historical record. It doesn't appeal to me, but then again, neither do tattoos, or heavy metal, or Christian fundamentalism. All in all, it seems pretty harmless -- certainly more benign than the dangerous nonsense that Groothuis routinely espouses.

I think Groothuis should examine his own feelings more closely. Why, precisely, is he so disgusted by the sight of a drag queen?

The Pierce Expansion Problem

I just posted one of my oldest open math problems to Math Overflow. Let's see if anyone can come up with a new idea for attacking this problem, which I thought of back in 1978, and only a little progress has been made in 36 years.

Just What Russia Needs

The Templeton Foundation, not content with its corrupting influence on American science, is branching out to encourage more theology in Russia.

What wonderful news! If there's anything that Russia needs now, it's more theology. I wonder what we can look forward to. Perhaps a "natural law" justification for putting gays in prison, or for the takeover of Crimea.

Moose and Drones

Any story about moose and drones deserves our attention. From reader D. S. comes this story about Alaska's decision to outlaw moose hunting with drones. That is, the hunting of moose, not moose doing the hunting. Moose actually doing the hunting, with drones, is still legal.

Yet Another Insane Conference Solicitation

Needless to say, I don't work on "polymer and composite materials".

Dear Shallit, J.,
This is Ms. Yin pan from 2014 Global Conference on Polymer and Composite Materials (PCM 2014) which will be held in Ningbo, China on May 27~29.

Considering your research titled On NFAs where all states are final, initial, or both may be relevant to our conference, We cordially invite you to present your new research at our conference. Accepted papers will be published in IOP Conference Series: Materials Science and Engineering (MSE) which is an open access journal indexed by CPCI (Conference Proceedings Citation Index), Scopus, Compendex and Inspec. Authors also have the option to publish papers in special issues organised by PCM2014 in SCI (Thomson Reuters ISI) indexed journals .

Keynote speech titles:
Mechanical and Tribological Aspects of Nanocomposite Coatings
Investigation of Controlled Migration of Anti-fog Additives in Thin Polyolefin Products
Injection of "Liquid Wood": Samples Microstructure and Properties
Some High Coordination Compounds of Lanthanides (III) Derived From Schiff Bases Derived From 4-aminoantipyrine and Their Application.
New Polymer Materials for the Potential of Optical, Electronic and Green Energy Applications.
Highly Efficient Polymer Solar Cells.

We are also calling for reviewers
Reviewer's papers can be published without publication fee in Open Access journals 'Progress in Nanotechnology and Nanomaterials' or 'Advances in Materials Science and Applications'.

Reviewer Benefits:
Free to visit the 2014 China (Ningbo) International Engineering Plastics and Modified Plastics Industry Exhibition
Free to tour around Ningbo after the conference
Enjoy a discount for your conference registration fee
Be a potential candidate of Technical Program Committee for the next PCM conference
If you want to join us as a reviewer, please send us your CV.

Best regards
Ms. Yin Pan
PCM 2014 Organizing Committee
Website: http://www.cpcmconf.org
Email: pcm2014@cpcmconf.org

Scott Vanstone (1947-2014)

Here is a good tribute to the life and career of my late colleague Scott Vanstone, written by my colleagues at the University of Waterloo.

Scott and I only wrote one paper together, on the analysis of a gcd algorithm, back in 1998.