Kirk Durston Does Mathematics!

Kirk Durston is a local evangelical Christian who likes to construct unconvincing arguments for his faith. Every few years he trots them out at my university.

Here is one of his more recent attempts, a discussion of infinity. Not surprisingly, it is a confused mess.

Durston's argument is based, in part, on a distinction that does not really exist: between "potential infinity" and "completed infinity" or "actual infinity". This is a distinction that some philosophers love to talk about, but mathematicians generally do not.* You can open any contemporary mathematical textbook about set theory, for example, and not find these terms mentioned anywhere. Why is this? It's because mathematicians understand the subject well, but -- as usual -- many philosophers are extremely muddled thinkers when it comes to infinity.

Here is how Durston defines "potential infinity": "a procedure that gets closer and closer to, but never quite reaches, an infinite end". So, according to Durston, a "potential infinity" is not a set but a "procedure". Yet the very first example that Durston gives is "the sequence of numbers 1,2,3, ... gets higher and higher but it has no end". The problem should be clear: a "sequence" is not a "procedure"; a (one-sided infinite) sequence over a set S is a mapping from the non-negative integers to S. From the beginning, Durston is quite confused. His next example is "the limit of a function as x approaches infinity". But a "limit" is not a "procedure", either. Durston also doesn't seem to understand that limits involving the symbol ∞ can be restated to avoid it entirely; the ∞ in a limit is a shorthand that has little to do with infinite sets at all.

He defines "actual infinity" or "completed infinity" as "an infinity that one actually reaches", which doesn't seem to have any actual meaning that I can divine. But then he says that "actual infinity" or "completed infinity" is "just one object, a set". Fair enough. Now we know that for Durston, an "actual" or "completed" infinity is a set. But what does it mean for a set to "reach" something? And if we consider the set of natural numbers, for example, what does it mean to say that it "reaches" infinity? After all, the set of natural numbers N contains no number called "infinity", so if anything, we should say that N does not "reach" infinity.

But then he goes on to say "First, a completed countable infinity must be treated as a single ‘object’." This is evidently wrong. For Durston, a "completed infinity" is a set, but that doesn't prevent us from discussing, treating, or thinking about its members, and there are infinitely many of them.

Next, he says "it is impossible to count to a completed infinity". That is true, but not for the reason that Durston thinks. It is because the phrase "to count to a set" is not defined. We never speak about "counting to a set" in mathematics. We might speak about enumerating the elements of a set, but then the claim that if we begin at a specific time and enumerate the elements of a countably infinite set at, say, once a second, we will never finish, is completely obvious and not of any interest.

Next, Durston claims "one can count towards a potential infinity". But since he defined a "potential infinity" as a procedure, this is clearly meaningless. What could it mean to "count towards a procedure"?

He then goes on to discuss four requirements of an infinite past history. He first asserts that "the number of seconds in the past is a completed countable infinity". Once again, Durston bumps up against his own claims. The number of seconds is not a set, and hence it cannot be a "completed infinity" by Durston's own definition. Here he is confusing the cardinality of a set with the set itself.

Next, he claims that "The number of elapsed seconds in the future is a potential infinity". But earlier he claimed that a potential infinity is a "procedure". Here he is confusing a cardinality with a procedure!

Later, Durston shows that he does not understand the difference between finite and infinite quantities: he claims that "the size of past history is equal to the absolute value of the smallest negative integer value in past history". This would only be true for finite pasts. If the past is infinite, there is no smallest negative integer, so the claim becomes meaningless. So his Argument A is wrong from the start.

At this point I think we can stop. Durston's claims are evidently so confused that one cannot take them seriously. If one wants to understand infinity well, one should read a basic text on infinity and set theory by mathematicians, not agenda-driven religionists with little advanced training in mathematics.

* There are certainly some exceptions to this general rule. The "actual"/"potential" discussion started with Aristotle and hence continues to wield influence, even though mathematicians have had a really good understanding of the infinite since Cantor. Cantor met with resistance from some mathematicians like Poincaré, but today these objections are generally regarded as groundless.

Yet Another Dubious Journal Solicitation

This one was spammed to almost everybody in our School of Computer Science here at Waterloo on Wednesday:

Dear Dr. ,

Greetings from the Journal of Advances in Robotics and Automation!

Hope you are doing well!

The Journal is in need of your fortitude. We would like to invite you to send us your valuable contribution (research article, review article, Opinion article, Editorial or short communication), to publish in our journal and improve it for indexing.

It would be highly appreciable if you could submit the article before or till 30 th November. You can visit our journal website for any details http://omicsgroup.org/journals/advances-in-robotics-automation.php

Please submit the article to the below link https://www.editorialmanager.com/engineeringjournals/default.asp or you can mail to the below link.

Please help in this Regard.

With Regards,

Rachle Green

Editorial Assistant

E-mail: editor.ara@omicsonline.org

All the warning signs are there:

1. Spam sent to everybody without discrimination, including those (like me) who have nothing to do with robotics or automation.

2. Bizarre capitalization like "Regard".

3. Bizarre word choice like "fortitude" and "highly appreciable".

4. Ridiculously rapid deadline for submission.

5. A likely bogus name for the "Editorial Assistant". The first name "Rachle" is extremely uncommon.

I do not recommend having anything to do with this journal.

Alan Cobham: An Appreciation

This year, 2014, marks the 50th anniversary of a talk by Alan Cobham that is often regarded as the birth of the class P, the class of polynomial-time solvable problems.

Cobham's invited half-hour talk took place during the Congress for Logic, Methodology and Philosophy of Science at the Hebrew University of Jerusalem, which was held from August 26 to September 2 1964. His paper, which he delivered on the last morning of the conference (September 2), was entitled "The intrinsic computational difficulty of functions". It later appeared in the proceedings of that conference [1], which were published in 1965.

The paper introduces a number of fundamental ideas and questions that continue to drive computational complexity theory today. For example, Cobham starts by asking "is it harder to multiply than to add?", a question for which we still do not have a satisfactory answer, 50 years later. Clearly we can add two n-bit numbers in O(n) time, but it is still not known whether it is possible to multiply in linear time. The best algorithm currently known is due to Fürer, and runs in n(log n)2^{O(log* n)} time.

Cobham then goes on to point out the distinction between the complexity of a problem and the running time of a particular algorithm to solve that problem (a distinction that many students still don't appreciate).

Later in the paper, Cobham points out that many familiar functions, such as addition, multiplication, division, square roots, and so forth can all be computed in time "bounded by a polynomial in the lengths of the numbers involved". He suggests we consider the class "ℒ", of all functions having this property. Today we would call this class P. (Actually, P is usually considered to consist only of the {0,1}-valued functions, but this is a minor distinction.)

He then goes on to discuss why P is a natural class. The reasons he gives are the same ones I give students today: first, that the definition is invariant under the choice of computing model. Turing machines, RAMs, and familiar programming languages have the property that if a problem is in P for one such model, then it is in P for all the others. (Today, though, we have to add an asterisk, because the quantum computing model offers several problems in BQP (such as integer factorization) for which no polynomial-time solution is known in any reasonable classical model.)

A second reason, Cobham observes, is that P has "several natural closure properties" such as being "closed in particular under ... composition" (if f and g are polynomial-time computable, then so is their composition f ∘ g).

He then mentions the problem of computing f(n), the n'th prime function, and asks if it is in P. Fifty years later, we still do not know the answer; the fastest algorithm known runs in O(n^½+ε), which is exponential in log n.

He concludes the paper by saying that the problems he mentioned in his talk are "fundamental" and their "resolution may well call for considerable patience and discrimination" --- very prescient, indeed.

Like many scientific ideas, some of the ideas underlying the definition of the class P appeared earlier in several places. For example, in a 1910 paper [2], the mathematician H. C. Pocklington discussed two different algorithms for solving a quadratic congruence, and drew a distinction between their running times, as follows: "the labour required here is proportional to a power of the logarithm of the modulus, not to the modulus itself or its square root as in the indirect process, and hence see that in the case of a large modulus the direct process will be much quicker than the indirect."

In 1956, a letter from Gödel to von Neumann discussed the possibility that proofs of assertions could be carried in linear or quadratic time and asked specifically about the number of steps required to test if a number n is prime. Today we know that primality can indeed be decided in polynomial time.

About the same time, Waterloo's own Jack Edmonds was considering the same kinds of ideas. In a 1965 paper [3], he drew a distinction between algorithms that "increases in difficulty exponentially with the size of the" input and those whose "difficulty increases only algebraically". He raised, in particular, the graph isomorphism problem, whose complexity is still unsolved today.

For some reason I don't understand, Cobham never got much recognition for his ideas about P. (Neither did Edmonds.) Stephen Cook, in a review of Cobham's paper, wrote "This is perhaps the best general discussion in print" of the subject. But, as far as I know, Cobham never got any kind of award or prize.

Cobham did other fundamental work. For example, a 1954 paper in the Journal of the Operations Research Society on wait times in queues has over 400 citations in Google Scholar. In two papers published in 1969 and 1972, respectively [4,5], he introduced the notion of "automatic sequence" (that is, a sequence over a finite alphabet computable, given the base-k expansion of n, using a finite automaton) and proved most of the really fundamental properties of these sequences. And in a 1968 technical report [6] he discussed proving transcendence of certain formal power series, although his proofs were not completely correct.

Alan Belmont Cobham was born on November 4 1927, in San Francisco, California. His parents were Morris Emin Cobham (aka Emin Maurice Cobham) (October 2 1888 - February 1973), a silk merchant, and Ethel Carolina Rundquist (June 24 1892 - Nov 1977), an artist. He had a older sister, Claire Caroline Cobham (June 18 1924 - November 29 2000), who worked for Boehringer-Ingelheim Pharmaceuticals. In the 1940 census, Alan was living in Palm Beach, Florida, where his father was a hotel manager.

Cobham's parents in 1920.

Sometime between 1940 and 1945, Alan's family moved to the Bronx, where Alan attended the Fieldston School. Below is a picture of Alan from the 1945 Fieldston Yearbook.

Alan attended Oberlin College. In the 1948 Oberlin College yearbook, he appears in a photo of the Mathematics Club (below). He is in the front row, 3rd from the right.

Later, Alan transferred to the University of Chicago. He worked for a time in the Operations Evaluation Group of the United States Navy in the early 1950's. He went on to do graduate work at both Berkeley and MIT, although he never got a Ph.D. He also worked at IBM Yorktown Heights from the early 1960's until 1984. One of his achievements at IBM was a computer program, "Playbridge", that was, at the time, one of the best programs in the world for playing bridge; it was profiled in an October 7 1984 article in the New York Times. In the fall of 1984, Alan left IBM and became chair of the fledgling computer science department at Wesleyan University in Middletown, Connecticut, a post which he held until June 30 1988.

I interviewed Alan Cobham in 2010. I was hoping to find out about the reception of his paper in 1964, but unfortunately, he was clearly suffering from some sort of mild dementia or senility, and could not remember any details of his work on P. When I asked him what he did to keep himself busy, he said, "I watch a lot of TV."

Alan passed away in Middletown, Connecticut, on June 28 2011. As far as I can tell, he never married, nor did he have any children.

References

[1] A. Cobham, The intrinsic computational difficulty of functions, in Y. Bar-Hillel, ed., Logic, Methodology and Philosophy of Science: Proceedings of the 1964 International Congress, North-Holland Publishing Company, Amsterdam, 1965, pp. 24-30.

[2] H. C. Pocklington, The determination of the exponent to which a number belongs, the practical solution of certain congruences, and the law of quadratic reciprocity, Proc. Cambridge Phil. Soc. 16 (1910), 1-5.

[3] J. Edmonds, Paths, trees, and flowers, Canad. J. Math. 17 (1965), 449-467.

[4] A. Cobham, On the base-dependence of sets of numbers recognizable by finite automata, Math. Systems Theory 3 (1969), 186-192.

[5] A. Cobbham, Uniform tag sequences, Math. Systems Theory 6 (1972), 164-192.

[6] A. Cobham, A proof of transcendence based on functional equations, IBM Yorktown Heights, Technical report RC-2041, March 25 1968.

This is a draft of an article I am preparing. I would appreciate feedback and more information, if you have it, about Alan Cobham.

Mormon Church Leaders Come Clean? Hardly

A new article in the New York Times suggests that the Mormon Church is suddenly becoming transparent about the more ridiculous and appalling aspects of its history.

As evidence they point to an essay, published on the Church's website, admitting that the Church's founder, Joseph Smith, had as many as 40 wives.

Well, I suppose it's a start, but the reporter is far too generous to the Church. I wonder if we can hope to see some forthright admission that Joseph Smith was a known and convicted conman; that some of the Egyptian documents he claimed to have "translated" are not even remotely what he claimed; that large sections of Mormon holy texts are evidently plagiarized; that DNA evidence clearly shows that the Church's claims about native Americans are without foundation, and so forth.

Nope, we can't. For example, their article on DNA is full of excuses why the definitive results aren't really definitive after all.

Meanwhile, more and more people are leaving the Mormon Church because they can't get honest answers to their questions.

Mormon beliefs, like much of Christianity, are without foundation. The big difference is that Mormonism makes lots of claims that are subject to clear refutation and that the founding of the religion is so recent that its dubious origins are much easier to study.

Big Surprise: Wind Turbines Not Evil After All

Your tax dollars at work: Health Canada spent $2.1 million to test the wacky proposition that wind turbines have a negative effect on health.

The result should not surprise anyone who spent a few minutes thinking about it: no ill effects were found.

The only reason why they had to do this study at all is likely due to complaints from wacky wind turbine opponents, such as retired pharmacist Carmen Krogh.

Creationists Desperately Crave Respect - But They Don't Get It

When creationists have an event, they frequently try to have it at a university. The reason why is clear: they crave the academic respectability that a university would give them. If they can say they've had a conference at Cornell -- well, then, there must be something to it, or such a university wouldn't allow them to hold it, right?

If not a university, they can try to have their event at some famous scientific institution, like the Smithsonian. It's a win-win for creationists: if they succeed, they get respectability the famous name gives them; if they don't they can cry "censorship" and make a movie about how poorly they are treated. It feeds the martyrdom scenario that many fundamentalists seem to enjoy.

The latest bogus creationist event is the "Origin Summit", which they managed to hornswoggle Michigan State University into holding. According to Science magazine, subterfuge was used from the very start: "Creation Summit secured a room at the university’s business school through a student religious group, but the student group did not learn about the details of the program—or the sometimes provocative talk titles -- until later, says MSU zoologist Fred Dyer."

Dishonesty and illegitimately seeking academic validation: two of the major characteristics of creationism.

(By the way, if you want to be really appalled, read about Jerry Bergman, one of their illustrious speakers.)

P. S. If you look at this page, you'll see evangelical whack job Lee Strobel described as a "certified agnostic". I wonder where you get certified. Maybe they meant "certifiable" instead?

I See Berlinskis

Hey, there's a new science journal out. It's called Inference Review.

Sorry, I should have really said that it's a new "science" journal. That's because the weirdness is strong --- very strong --- with this one.

Just look at the first articles they published. One is by Michael Denton, the odd biologist who published an anti-evolution book called Evolution: A Theory in Crisis back in 1985. Needless to say, that book was filled with errors and misunderstandings. That ignorance, however, didn't prevent Denton from acquiring a big fan base among the intelligent design crowd (when does it ever?); Phillip E. Johnson and the laughable George Gilder counted themselves among Denton's fans. And Denton's new Inference Review article is touted by none other than that pathetic ID pipsqueak Casey Luskin.

Demonstrating yet another example of crank magnetism, a second Infererence Review article is by global warming skeptic William Kininmonth.

Are you beginning to get suspicious yet? Who's running the show here?

Well, we don't know. Unlike real science journals, nowhere on the website for Inference Review can one find a listing of the editorial board. I wonder why they want to hide...

A sharp-eyed commenter on a private mailing list points out, however, that the journal's twitter followers include, in addition to a few gullible science journalists, two different Berlinskis: Mischa and the eminently silly Claire Berlinski.

Hmmm. What would possess two Berlinskis to follow an obscure and mysterious "science" journal with intelligent design creationist and global warming denialist leanings?

Read some of the pages and you'll come to the same conclusion I did. That ol' poseur David Berlinski is surely involved somehow. All the signs are there: the Francophilia (why else would the grotesque caricatures be featured?), the pretension, the supercilious turns, the obsession with criticizing evolution, the solicitation for articles on mathematics topics dear to David, and the use of the word "irrefragable"; all are Berlinski hallmarks.

C'mon, David! Don't hide your light under a bushel. Come out into the open.

Most Philosophers Have Nothing Interesting to Say About The Brain

If you want to understand the brain, look to neuroscience. Most philosophers (unless they have some decent neuroscience training*) have simply nothing of interest to say. The reason why is that (a) their speculations were not tied to any physical models and (b) their claims were often so vague or incoherent they could not be verified and (c) when the claims were more precise, there was rarely an effort to prove or disprove through experimentation.

Instead, philosophers gave us time-wasters like the "Chinese room argument" (still taken seriously by some very smart people, which I find astonishing) and the silly and overblown early anti-AI claims of Hubert Dreyfus (who actually got awards for his work).

Of course, it's going to be really hard to understand how the brain works. That's because the immense complications of the brain did not arise through intelligent design -- which would have given us nice discrete subsystems that interact in controlled and efficient ways -- but rather through the rather higgledy-piggledy bricolage of billions of years of evolution.

Nevertheless, we're making some small progress in understanding the brain and the mind and the mind-body problem and perception and memory and awareness and "understanding" and consciousness and free will, and other conundrums that have baffled philosophers for thousands of years. For example, read Crick's The Astonishing Hypothesis. The tools philosophers used -- until recently -- were simply too puny to get anything reasonable done.

When you read a philosopher on the brain or the mind, look for the warning signs. Here's one: do they treat things like "consciousness" and "understanding" as a binary property -- that something either has or doesn't have? Or do they explicitly recognize that these could lie on a continuous (or at least variable) spectrum? If the former, beware.

If reading Crick is too much work, you can also show up today, at the University of Waterloo, to hear my colleague Jeff Orchard speak on "Computing Between Your Ears".

* For philosophers who really do have something to say, look at, for example, the Churchlands.

Calling all ID Advocates: Employment Awaits

One of the points of my long paper with Elsberry was that intelligent design (ID) advocates talk a big game, but don't actually accomplish anything.

They claim their methods are revolutionary. They claim that all sorts of fields, like archeology and forensic science, use "pre-theoretic" versions of their "design detection" methodology. Yet when it comes to actually applying their methods where they would potentially be useful, what happens?

Crickets chirping...

In fact, in 2003 we published a little paper, "Eight challenges for intelligent design advocates", where we asked ID advocates to prove their silly ideas useful in practice.

Needless to say, not a single ID advocate has come forward with an answer to any of our challenges.

Well, here's another. Recently archaeologists discovered what may be evidence of the earliest sign of humans in what is now Canada.

As the article says, researchers are not completely sure yet. They may have found a stone weir constructed to catch fish, or they may have found a natural, non-human-constructed formation: "A geologist will now study the images to ensure the rocks are not a natural formation..."

Needless to say, there is no sign these researchers are basing their decision on the research oeuvre of William Dembski to decide the question.

But why not? After all, detecting design is what ID advocates say they're really, really good at. Better than all those stupid "materialist" scientists.

So have at it, ID advocates! Volunteer your massive expertise here. Do your investigations. Create your specifications, prove they're independent, tell us what the "rejection region" is, and so forth. Write a paper with your decision about these possible stone weirs. Publish it in the peer-reviewed literature --- you know, a real journal like Science or Nature, not the creationist circle-jerk that is Bio-Complexity. (Try not to be fooled the way Dembski was about the so-called "bible codes".)

What are you waiting for?

Silly Barry. Have a Cookie.

Have you ever had this experience? You're having a technical discussion and someone you don't know well is listening. Then they enter the conversation, and from the first thing they say, you realize they have absolutely no idea what's going on, but they think they do. At this point, the only thing to do is to give the poor fellow a cookie and move on.

Person 1: "So, you see, since the derived subgroup is not supplemented by a proper normal subgroup, it follows that the group is imperfect..."

Very Silly Person: "Wait a second, the rock group Brand New split off from The Rookie Lot, and they're pretty perfect."

Person 2: "Umm... yes... Here, have a cookie and go play outside."

That's why it's usually a waste of time having a discussion with intelligent design (ID) advocates. The vast majority of them have absolutely no idea what people like William Dembski claim; they just know that ID is in agreement with their religious beliefs, so they support it.

I was reminded of this when I saw the response of certified public accountant Barry Arrington to my my post pointing out his misunderstandings.

Now, maybe in some universes certified public accountants are the people to go to when you want to understand the basics of information theory. But not in the one I live in. Christians like Barry go on and on about how humble they are, but when someone takes the time to explain a basic mistake like the one Arrington made, how do they behave? With arrogance and ignorance.

I'll briefly summarize Arrington's mistakes and misrepresentations.

1. "Correction, I [Arrington] routinely ban trolls, who then claim they were banned for dissenting." A lie. All one has to do is look at this page, which has example after example of Mr. Arrington's intolerance of criticism. Then there was the famous agree with the laws of logic or be banned episode. One poster said it best: "The only firm rule at UD seems to be, Thou Shalt Not Make Barry Arrington Feel Inadequate".

2. Showing he can google a phrase just as well as the next fellow, Arrington brings in a quote from Steve Ward about pseudorandom numbers. It has pretty much nothing to do with what we are discussing, but Silly Barry doesn't understand that. Silly Barry could attend my current course CS 341, where we discuss the generation of pseudorandom numbers in Lecture 11.

3. Arrington tries to distract from his mistake by claiming "The issue is whether – as with the CD player in Ward’s illustration – it is random enough for the purposes for which it is employed." No, the issue is, was string #1 more or less random than string #2? Barry implied it was more random. I showed why he was wrong.

4. Arrington says "Shallit believes he has achieved some great triumph of argumentation by demonstrating that the first string is not truly, completely and vigorously random...". Actually, what I showed was that string #1 was actually less random than string #2.

5. "So, according to Shallit’s calculations an excerpt from Hamlet’s soliloquy is “more random” than a string of text achieved by randomly banging away on a keyboard. That is a sentence only a highly educated idiot could have written." Ahh, the traditional ploy of the scientifically illiterate: your conclusion (about evolution, global warming, the roundness of the earth, scientific theory of disease) disagrees with my preconceptions. Therefore you are the idiot! Very Silly People have used this ploy for hundreds of years. So far it's not working so well for them.

6. "The larger point – and here Shallit gives the store away – is his admission that he detected the design of the first string using rigorous statistical methods." Poor Silly Barry. I said nothing about "design" at all; the word doesn't even appear in my post. I didn't say anything about "statistical methods", either. The method I used is based on information theory, not statistics. (But Barry knows little advanced mathematics, it's clear.)

Barry, and all ID advocates, need to understand one basic point. It's one that Wesley Elsberry and I have been harping about for years. Here it is: the opposite of "random" is not "designed".

I'll say it again. Just because an event E is not "random" (more precisely, that it deviates from uniform distribution with equal probabilities) does not mean it was "designed" by some natural or supernatural agent. There are many possible explanations. It could have arisen from a uniform random process with unequal probabilities, like (in the case of string #1) a stochastic process biased towards the letters "a", "s", and "d". It could have arisen from a nonuniform random process like a Markov model. It could have arisen from some deterministic process -- basically, an algorithm -- that could have arisen naturally or with human agency. There are lots of possibilities. Silly Barry doesn't understand that.

7. "Jeffery Shallit has spent years denying the basic formulation of ID: Some patterns are best explained by the act of an intelligent agent." I'll overlook the spelling incompetence of Mr. Arrington (although it is basic politeness to spell a man's name correctly). Nobody denies human agency or the ability of scientists to detect it in many cases. What ID critics point out, though, is that those who detect human agency aren't detecting "Design" with a capital "D". They are detecting artifacts: the characteristic product of human activity. For a good look at why capital-D "Design" is basically a charade, read the fine article of Wilkins and Elsberry published in Biology and Philosophy. When Mr. Arrington gets his Very Silly views published in a philosophy journal, give me a call.

8. Yet here he is yelling from the rooftops: "That first string of text only appears to be random; I have demonstrated rigorously that it was in fact designed." This is a manufactured quote by Mr. Arrington. (Using fake quotes is a disease of ID advocates in general and Mr. Arrington in particular.) I didn't say that at all. I said string #1 was not as random as string #2 (in the sense of being more compressible), and then I guessed how it came to be constructed, a guess that is based on what I know of Mr. Arrington and keyboards and the typical behavior of certified public accountants.

9. "In ID theory the “specification” of a strnig of text, for instance, is closely related to how compressible the description of the string is. In other words, whether a given string of text is “specified” is determined by whether the description of the string can be compressed. Take the second group of text as an example. It can be compressed to “first 12 lines of Hamlet’s soliloquy.” This is simply not possible for the first string. The shortest full description of the first string is nothing less than the string itself."

Once again Barry shows he doesn't understand anything. In Dembski's original formulation, there was no requirement that the "description" of a string be compressible. (Arrington seems even more confused, in that he talks about the "description of the string" as opposed to the string itself. Does he think the specification needs to be compressible or the string? Who can tell, with such shoddy writing?) And he makes the silliest mistake of all when he says "The shortest full description of the first string is nothing less than the string itself". That hilarious misunderstanding gives away the store: Arrington has understood nothing of what I wrote. The experiment using gzip shows that string #1, just like string #2, can indeed be compressed; it shortest description is indeed shorter than itself.

Barry says that string #2 can be compressed to "first 12 lines of Hamlet's soliloquy". But of course, this is not a compression that anyone in information theory would regard as legitimate, because it does not allow one to reconstruct the string losslessly without reference to an external source: namely, a book of Shakespeare. Real compressions do not have external referents like that (except, perhaps, to the particular computational model of compression). We talk about this basic misunderstanding in my CS 462/662 course, given each year in the Winter term. Mr. Arrington is invited to attend.

Now one could consider that "design detection" takes place in a framework of "background knowledge". Then "first 12 lines of Hamlet's soliloquy" would be a specification, not a compression. But then someone raised in Mongolia would likely not have the same background knowledge. So their measure of the "specified information" or "specified complexity" of string #2 would differ from Barry's. This shows the weakness of the "background knowledge" component of ID claims, as we pointed out: quantities in mathematics and science are not supposed to differ based on who measures them.

10. And finally, here's the funniest thing of all. There are actually at least two different legitimate ways to criticize my analysis on a technical basis. I even gave a not-so-subtle hint about one of them! Yet the Uncommon Descent folks, harnessing all the power of intellectual heavyweights like Barry Arrington and Eric Anderson and Gordon Mullings, could not manage to find them. What a surprise.

Silly Barry. Have a cookie.

Eric Anderson is Silly, Too!

I really love Uncommon Descent!

Believe it or not, they have a whole thread devoted to how horrible I am.

Here's what silly nonentity Eric Anderson says:

As I pointed out, if Shallit’s bluff were true, he would be sitting on a Nobel Prize right now and would not be revealing the secret in some college computer science class."

My supposed "bluff" is my claim that we know what produces information. But it's not a bluff. Ask any mathematician or computer scientist if they know how to produce information in the normally-understood (Kolgomorov) sense of the word, and the answer is easy.

Randomness.

Any process generating truly random bits will generate strings with high Kolmogorov information with very very high probability.

Don't expect creationists to understand this, however.

Want to know more? Attend my CS 462/662 course starting in Winter 2015.

Barry Arrington's Silly Misunderstanding

Ever since the ID creationist blog Uncommon Descent was taken over by Barry Arrington, it's been a first-class show of the irremediable arrogance and ignorance of creationists. I don't post there because Arrington routinely bans dissenters, but I do sometimes enjoy the show.

I particularly enjoyed this post because it touches on the subject of my Winter 2015 course here at the University of Waterloo. Arrington displays two strings of symbols and says "the second string is not a group of random letters because it is highly complex and also conforms to a specification". By implication he thinks the first string is a group of random letters, or at the very least, more random than the second.

Here are the two strings in question, cut-and-pasted from Arrington's post:

#1:

OipaFJPSDIOVJN;XDLVMK:DOIFHw;ZD
VZX;Vxsd;ijdgiojadoidfaf;asdfj;asdj[ije888
Sdf;dj;Zsjvo;ai;divn;vkn;dfasdo;gfijSd;fiojsa
dfviojasdgviojao’gijSd’gvijsdsd;ja;dfksdasd
XKLZVsda2398R3495687OipaFJPSDIOVJN
;XDLVMK:DOIFHw;ZDVZX;Vxsd;ijdgiojadoi
Sdf;dj;Zsjvo;ai;divn;vkn;dfasdo;gfijSd;fiojsadfvi
ojasdgviojao’gijSd’gvijssdv.kasd994834234908u
XKLZVsda2398R34956873ACKLVJD;asdkjad
Sd;fjwepuJWEPFIhfasd;asdjf;asdfj;adfjasd;ifj
;asdjaiojaijeriJADOAJSD;FLVJASD;FJASDF;
DOAD;ADFJAdkdkas;489468503-202395ui34

#2:

To be, or not to be, that is the question—
Whether ’tis Nobler in the mind to suffer
The Slings and Arrows of outrageous Fortune,
Or to take Arms against a Sea of troubles,
And by opposing, end them? To die, to sleep—
No more; and by a sleep, to say we end
The Heart-ache, and the thousand Natural shocks
That Flesh is heir to? ‘Tis a consummation
Devoutly to be wished. To die, to sleep,
To sleep, perchance to Dream; Aye, there’s the rub,
For in that sleep of death, what dreams may come,
When we have shuffled off this mortal coil,

Needless to say, Arrington -- a CPA and lawyer who apparently has no advanced training in the mathematics involved -- doesn't specify what he means by "group of random letters". I think a reasonable interpretation would be that he is imagining that each message is generated by a stochastic process where each letter is generated independently, with uniform probability, from some finite universe of symbols.

Even with just a cursory inspection of the two strings, we see that neither one of them is likely to be "random" in this sense. We immediately see this about the second string because the set of reasonable English texts is quite small among the set of all possible strings. But we also see the same thing about the first because (for example) the trigram "asd" occurs much more often than one could reasonably expect for a random string. Looking at a keyboard, it's a reasonable interpretation that somebody, probably Arrington, dragged his hands repeatedly over the keyboard in a fashion he or she thought was "random" -- but is evidently not. (It is much harder to generate random strings than most untrained people think.)

If we want to test this in a quantitative sense, we can use a lossless compression scheme such as gzip, an implementation of Lempel-Ziv. A truly random file will not be significantly compressible, with very very high probability. So a good test of randomness is simply to attempt to compress the file and see if it is roughly the same size as the original. The larger the produced file, the more random the original string was.

Here are the results. String #1 is of length 502, using the "wc" program. (This also counts characters like the carriage returns separating the lines.) String #2 is of length 545.

Using gzip on Darwin OS on my Mac, I get the following results: string #1 compresses to a file of size 308 and string #2 compresses to a file of size 367. String #2's compressed version is bigger and therefore more random than string #1: exactly the opposite of what Arrington implied!

I suppose one could argue that the right measure of "randomness" is not the size of the compressed file, but rather the difference in size between the compressed file and the original. The smaller this difference is, the more random the original string was. So let's do that test, too. I find that for string #1, this difference is 502-308 = 194, and for string #2, this difference is 545-367 = 178. Again, for string #2 this difference is smaller and hence again string #2 is more random than string #1.

Finally, one could argue that we're comparing apples and oranges because the strings aren't the same size. Maybe we should compute the percentage of compression achieved. For string #1 this percentage is 194/502, or 38.6%. For string #2 this percentage is 178/545, or 32.7%. String #2 was compressed less in terms of percentage and hence once again is more random than string #1.

Barry's implications have failed spectacularly in every measure I tried.

Ultimately, the answer is that it is completely reasonable to believe that neither of Barry's two strings is "random" in the sense of likely to have been generated randomly and uniformly from a given universe of symbols. A truly random string would be very hard to compress. (Warning: if you try to do this with gzip make sure you use the entire alphabet of symbols available to you; gzip is quite clever if your universe is smaller.)

By the way, I should point out that Barry's "conforms to a specification" is the usual ID creationist nonsense. He doesn't even understand Dembski's criterion (not surprising, since Dembski stated it so obscurely). String #2 can be said to "conform" to many, many different specifications: English text, English text written by Shakespeare, messages of length less than 545, and so forth. But the same can be said for string #1. We addressed this in detail in our long paper published in Synthese, but it seems most ID creationists haven't read it. For one thing, it's not good enough to assert just "specification"; even by Dembski's own claims, one must determine that the specification is "independent" and one must compute the size of the space of strings that conforms to the specification. For Dembski, it's not the probability of the string being generated that is of concern; it's the relative measures of the universe of strings and the strings matching the specification that matters! Most ID creationists don't understand this basic point.

Elsewhere, Arrington says he thinks string #1 is more complex than string #2 (more precisely he says the "thesis ... that the first string is less complex than the second string ... is indefensible").

Maybe Barry said the exact opposite of what he meant; his writing is so incoherent that it wouldn't surprise me. But his statement, as given, is wrong again. For mathematicians and computer scientists, complexity of a string can be measured as the size of the optimal compressed version of that string. Again, we don't have a way to determine Kolmogorov complexity, so in practice one can use a lossless compression scheme as we did above. The larger the compressed result, the more complex the original string. And the results are clear: string #1 is, as measured by gzip, somewhat less complex than string #2.

ID creationists, as I've noted previously, usually turn the notion of Kolmogorov complexity on its head, pretending that random strings are not complex at all. We made fun of this in our proposal for "specified anti-information" in the long version of our paper refuting Dembski. Oddly enough, some ID creationists have now adopted this proposal as a serious one, although of course they don't cite us.

Finally, one unrelated point: Barry talks about his disillusion when his parents lied to him about the existence of a supernatural figure --- namely, Santa Claus. But he doesn't have enough introspection to understand that the analogy he tries to draw (with "materialist metaphysics") is completely backwards. Surely the right analogy is Santa Claus to Jesus Christ. Both are mythical figures, both are celebrated by and indoctrinated in by parents, both supposedly have supernatural powers, both are depicted as wise and good, and both are comforting to small children. The list could go on and on. How un-self-aware does one have to be to miss this?

Record Coverage Fails Again

Despite the fact that Waterloo Region is the home to many scientific and technically-minded people and businesses, the coverage of science and technology by our local paper, the Record, is truly abysmal. I've written about it before.

Here's yet another example: this article about naturopathy didn't include a single skeptical voice. Couldn't the reporter have noted, for example, that homeopathy is regarded by most medical experts as a fake and worthless therapy?

Gelernter's Non-Response

Over the years, I've pointed out a number of times when Yale professor David Gelernter has misrepresented the truth... like the time he claimed that the US Supreme Court "outlawed prayer and Bible reading in the public schools" (they didn't; the decision he cited refers to ending teacher-led devotion and indoctrination only).

But Gelernter -- who apparently doesn't believe that academics have the duty to justify their claims and retract them when wrong -- has never replied.

Until recently, that is. My brief correction of Gelernter's wild misrepresentation of the reaction to Thomas Nagel's silly book elicited this reply from Gelernter:

Little needs saying to Jeffrey Shallit, except that I was not using "lynch mob" to suggest that Nagel’s opponents wanted him to be hanged or even gently murdered. "Nagel had some fundamental misunderstandings about science and biology" is a statement some people might possibly disagree with, especially those who care about what a person knows versus what degrees he holds. As Emerson would have said: Ph.D.’s, Mr. Shallot, are the hobgoblin of little minds.

This is preposterous in so many ways.

1. Gelernter dismisses his own misrepresentations by insinuating I interpreted "lynch mob" literally. Read my reply again, and my longer and more detailed one here. (I sent Gelernter a link.) It is clear I am objecting to Gelernter's exaggerations. Maybe Gelernter thinks describing Nagel's critics as "punks" and a "lynch mob" and "mass attack of killer hyenas" is accurate and appropriate. Does anyone else?

2. Gelernter fails to address my points, saying only "some people might possibly disagree". True enough, but does their disagreement have any rational basis?

3. Gelernter implies I am a person who doesn't "care about what a person knows versus what degrees he holds". Well, which group of people is likely to know more about evolutionary biology? Actual evolutionary biologists, who disputed Nagel's claims in detail, or Nagel and Gelernter, who have no expertise and no training in evolutionary biology? I challenge any fair-minded person to read Nagel's book (I have), Gelernter's praise of it, and the reviews by people like Orr and Elliott Sober and decide who has made the better case.

4. Finally, Gelernter can't even be bothered to spell my name correctly, even when his only task is to copy and paste it from the first line of his own reply.

All in all, it's a pretty poor performance for Professor Gelernter. But -- I am not surprised to see -- par for the course.

Meet David Gelernter, First Amendment Hypocrite

The whiny and porcine David Gelernter has a column where he makes fun of Muslim students at Yale who have objected to Ayaan Hirsi Ali speaking there.

I'm very glad that Gelernter is such a stalwart defender of the 1st Amendment of the US constitution.

But then, let's read what he says about atheists who have rightly objected to forcing nontheist schoolchildren to publicly acknowledge their belief in the Christian god: the children have a choice, Gelernter says, because they can just shut up.

Oops, I guess that 1st Amendment is just so much chin music.

The Robert J. Marks II Information Theory Watch, Day One

The illustrious Robert J. Marks II recent claimed that "we all agree that a picture of Mount Rushmore with the busts of four US Presidents contains more information than a picture of Mount Fuji".

I wanted to see the details of the calculation justifying this claim, so I asked Professor Marks to supply it. He did not reply.

So today I e-mailed him, as follows:

Dear Prof. Marks:

Here

http://humanevents.com/2014/08/19/biological-information-new-perspectives-from-intelligent-design/

you claimed

"we all agree that a picture of Mount Rushmore with the busts of four US Presidents contains more information than a picture of Mount Fuji".

I asked you there for the details of the calculation that would show this, but you did not reply on that page, so I'm asking again.

Could you please provide me with your calculation to justify this claim?

Regards,

Jeffrey Shallit

I'll let you know if and when he replies. Not holding my breath, though. ID advocates have a history of wild claims that they refuse to justify.

Answering a Baptist's Question

While on vacation in Wyoming, I saw this sign at the First Baptist Church of Thermopolis:

It says

Dear Atheist,

If you don't believe in God
Why do you care if I pray to him?

My guess is that Pastor Harvey Seidel is not really interested in an answer. If he were, he would just find some atheist and genuinely ask. Instead, it's probably intended as a "gotcha".

Nevertheless, I'm going to pretend that the question is an honest one and do my best to answer.

Dear Pastor Seidel,

You ask, if I don't believe in God, why do I care if you pray to him?

The simple answer is, I don't. Neither I, nor most of the atheists I know, give a damn one way or another. I personally wouldn't waste my time with that particular activity, but then there's a lot of activities that others enjoy -- such as stock car racing or listening to Celine Dion -- that I consider a waste of time and don't participate in. If prayer makes you happy and gives you some consolation, go right ahead. You don't need my or other people's approval to pray to your god -- be my guest.

It's not your prayer I'm concerned with. It's not even your beliefs, which I think are irrational. Lots of people have silly and irrational beliefs.

No, what I'm really concerned about is the actions your irrational beliefs might lead you to take. If your beliefs cause bigotry against black people, I'll oppose you. If your beliefs cause you to deny equal rights to gay people, then I'll oppose you. If your beliefs cause you to suppress the teaching of scientific theories like evolution in public schools, or deny the problem of global warming, then I'll oppose you. If your beliefs cause you to prevent sex education, and instill in young people an unhealthy view that sex is somehow "sinful", then I'll oppose you. If your beliefs result in anti-Semitism, I'll oppose you. If your beliefs cause you to work to further entrench Christian privilege in North America, then I'll oppose you.

I'm not saying you do any of these things. I know that Baptists are a very diverse bunch. Maybe you marched in solidarity with black people in Selma. Maybe you welcome gay people in your church. Maybe you conduct same-sex weddings. Maybe you acknowledge the truth of evolution and global warming. Maybe you warn your flock about the sin of anti-Semitism. If so, more power to you. We can join hands and work together.

Speaking of Christian privilege, I hope you're not one of those theists who think they can violate the separation of church and state by having teacher-led prayer in public schools, or forcing non-theists to listen to sectarian prayers at the beginning of government meetings. Not only is it not respectful of those whose beliefs differ (and there are lots of us), it's not constitutional, either.

Do I think we'd all be better off if you didn't pray? Probably. There are a lot of societal problems that won't be fixed by prayer. As a famous agnostic once said, "The hands that help are better far than lips that pray."

Still, I'll repeat myself: pray all you like. Neither I, nor most atheists, care. But we do care about your actions when your irrational beliefs take you down roads that adversely impact other people's rights, and create policies that are bad for non-Christians and bad for society. When you do that, suddenly we care. We care a lot.

Anti-Science Nuts are On All Sides of the Political Spectrum

There are so many anti-science nuts on the far right that I think we sometimes forget about the crazies on the left.

Here's an example I recently stumbled across: this radical feminist blogger thinks that women have "higher cognitive and sensory capacities than men" and "that compared to men, women simply seem to have a fully functioning brain (or far better functioning than men at least)" and "The mutation process clearly generates a deteriorated version of the original", thus showing she doesn't have much understanding of what a mutation is.

Of course, she also thinks that "some women do have the capacity to communicate with plants and trees and living beings in different ways, they ask the plant what kind of healing powers she has and the plant may reply, if she wants to". It's hard to understand someone whose world view is so distanced from reality.

The same blogger believes that all (literally all) sexual intercourse is rape and that sexual intercourse is somehow unnatural. When a commenter reasonably asks "Almost every mammal species reproduces this way, how can it be unnatural?", the blogger responds that "The purpose of PIV is to cause harm" (PIV, by the way, is the acronym for "penis-in-vagina sex") and "PIV isn’t natural, it’s an action done by men to us".

I feel very sorry for someone so filled with hate towards men, with such a warped worldview. Not filled with hate, you say? Read her December 12 comment here, where she advocates killing most or all men simultaneously: "The only way it could work without risking severe male retaliation is for all women to do it [kill men] at the same time, literally at the same time, so that the remaining males wouldn’t be sufficient in number and wouldn’t have enough time to organise repression harshly enough to terrorise women back into domestication." Honestly, this person sounds seriously dangerous to others. Let's hope her homicide fantasies don't become reality.

The Nonsensical Syllabus

Rebecca Schuman of Slate deftly summarizes what's happened to the course syllabus.

Needless to say, this disease of absurdity has already been happening at Waterloo for some time. For example, here's part of a message I recently received concerning my fall Algorithms course:

"It is now mandated by Senate that each offering of a course must provide a course outline that will be archived (those for CS will be archived on https://sharepoint.uwaterloo.ca/sites/cscourses/). Information that does not exist for the course, such as the names of the teaching assistants if there are none, may be omitted.

Course outlines should include the following basic elements: course number and title; class days, times, building, and room number; class instructor's name, office, contact information, office hours; TA's name, office, contact information, office hours (if applicable); course description; course objectives; required text and/or readings; general overview of the topics to be covered; expectations of the course, including requirements, deadlines, weight of requirements toward the final course grade; acceptable rules for group work; indication of how late submissions and missed assignments will be treated; indication of where students are to submit and pick up marked assignments; the institutional-required statements regarding "Academic Integrity", "Grievance", "Discipline", "Appeals", and the "Note for students with disabilities" (see https://uwaterloo.ca/secretariat/sites/ca.secretariat/files/uploads/files/courseoutline-requirements.pdf for the text of these statements);

The outlines are to be distributed to students electronically or on paper by the end of the first week of classes; and are required to be filed with the appropriate administrative authority."

Huckabee is a Moron

Caught Mike Huckabee on Fox News. (I never watch it at home, but when traveling sometimes you are forced to.) He was asked about the wisdom of arming teachers in schools. Needless to say, he was for it, comparing it to rich or powerful people who have armed guards.

When one Fox News host dared to ask the obvious question -- namely, isn't it reasonable to worry about the misuse of all those guns in schools? -- Huckabee merely dismissed this concern, saying something like 'If this ... if that ... you can waste your time worrying about scenarios like that'.

Huckabee is a moron. The chance that any particular school being attacked by an armed intruder is vanishingly small, and the chances that it occurs and an armed teacher is going to stop it successfully is even smaller. On the other hand, accidents with guns happen every day, and there is certainly a nontrivial probability that (a) an accident will happen (b) a teacher will misuse a gun or (c) the gun will be stolen and used against a teacher or other student.

If you are going to evaluate the wisdom of arming teachers in schools, you have to have some good estimates on the various probabilities. And if the school district is going to pay for all that teacher training, you also have to factor in the costs of doing the training instead of (say) installing higher-security doors or training students how to respond in the unlikely event of an attack. This sensible approach to deciding about the proposal was dismissed by Huckabee as "if this".

It's not just conservatives who are stupid in this way. Sometimes you hear liberals saying something like "if it saves just one life, it's worth it" about some new policy. Well, of course, it's not necessarily worth it. A law restricting the speed limit to 10 mph on US roads would probably save lives, but we deem it not worth it because of the inconvenience and extra time it would cost us.

Robert Marks Caught!

Here you can read the true story of the evil Darwinist censors, not the version of intelligent design creationist Bob Marks.

Nonsense from Marks

Intelligent design creationists love to write for conservative political magazines because they know most of their audience won't have the technical skill to spot their bogus claims.

Here's Robert Marks, writing nonsense in Human Events:

"Yet we all agree that a picture of Mount Rushmore with the busts of four US Presidents contains more information than a picture of Mount Fuji."

We do, eh?

"Since it is our uniform experience that elsewhere, information is only created by intelligent agents..."

Here Marks is just repeating the familiar lie of ID creationist Stephen Meyer, which I pointed out was wrong four years ago.

Repeating lies doesn't make them any more credible.

Addendum: Tom English points out that Marks's claims about the publication of their creationist volume are bogus. Big surprise.

A Probable Meteorite Hoax (or Prank)

There have been a number of articles in the popular press about Radivoje Lajic (sometimes rendered as "Radivoke"), a Bosnian man who claims his house has been hit six different times by meteorites.

By and large, press coverage of this guy has been completely credulous, referring to unnamed scientists at "Belgrade University" who have verified that the rocks are indeed meteorites.

In pictures he is shown holding a rock that doesn't look very much like a meteorite.

Here is what I think probably happened: either

• They're not meteorites, and he is confused, or
• This is a hoax perpetrated by Lajic himself. Perhaps the rocks aren't even meteorites, although it is easy to buy meteorites, even fairly large ones, at mineral shows or on e-bay. It is then simple to pretend to discover it after you claim it hit your house, or
• One of Lajic's neighbors is having a little fun with him in the same way.

It is worth noting that the meteorite database contains no mention of the meteorites supposedly found by Lajic. At least, searching for "Lajic" turns up nothing, and only two meteorites are listed as being discovered in Bosnia. Why can't reporters be more skeptical?

My New Book

Here is my new book, Neverending Fractions:

My co-authors, Jon Borwein, Wadim Zudilin, and the late Alf van der Poorten, wrote most of the book. I only contributed one chapter, a couple of sections, and some editing. I hope you'll enjoy it!

Avoid This Conference: CSNT 2015

I strongly recommend avoiding having anything to do with this conference: CSNT 2015.

Here is the solicitation I just got from them:

Dear Jeffrey Shallit,

I am the secretary of the 2015 International Congress on Computer Science and Network Technology (CSNT 2015). On behalf of CSNT 2015 Organizing Committee, we cordially invite you to be a member of Technical Program Committee of CSNT 2015.

CSNT 2015 will be held in Hong Kong, China, from February 10-11, 2015. The main objective of CSNT 2015 is to provide a comprehensive global forum for experts and participants from academia to exchange ideas and present results of ongoing research in the most state-of-the-art areas of Computer Science and Network Technology. More information about the conference, please visit the website:

http://www.as-se.org/conf/csnt2015/

As a leading authority of the field, your participation and support is essential to the success of the conference. And we believe your participation will bring more glory to this conference!

Note:

As a TPC member,

1.    Your paper or papers recommended by you can enjoy a discount on registration fee. -

2.    Your name will be shown on conference website and hardcopy of proceedings.

If you are interested in being a member of TPC, please attach your CV in your reply. Thank you for your consideration, and we look forward to hearing from you!

Best regards,

Yours Sincerely,

CSNT 2015 Organizing Committee

Email: icsnt2015@hotmail.com

Website: http://www.as-se.org/conf/csnt2015/

Notice everything wrong with this:

• They invited me to be on the program committee, even though I have never published a thing on "network technology"
• The solicitation does not mention a single person on the program committee
• The solicitation is unsigned

All these are major warning signs.

Must Pop Science Writers Know What They're Talking About?

Is it too much to ask that a pop science writer knows what they're talking about?

On the one hand we have the Denyse O'Leary school of journalism, blending lousy writing with an even lousier understanding of her subject matter.

On the other hand we have Carl Zimmer, whose books are praised by scientists knowledgeable in the areas he covers.

In between, we have books like The Violinist's Thumb by Sam Kean. Kean seems like a nice fellow, not at all like the know-nothing harridan O'Leary. But a master's degree in library science doesn't exactly inspire confidence that he knows what he's talking about. Nevertheless, his books have garnered some positive reviews, so I thought I'd take a look.

I was disappointed. Just to name four howlers:

• On page 107, Kean reveals that he thinks that Mitochondrial Eve is the "oldest matrilineal ancestor of everyone living today". No, she's the youngest (most recent) matrilineal ancestor. The distinction is absolutely crucial.
• On page 159, Kean states that he thinks the name "junk DNA" has "haunted [scientists] as an embarrassment ever since". Not so.
• On page 255, Kean claims that Paganini was not a composer. Even I, a classical music dilettante, know that Paganini wrote many works.
• On page 267, Kean translates the French idiom "étrangler le perroquet" as "strangling the parakeet". But "perroquet" mean "parrot", not "parakeet", in French. The word for "parakeet" is "perruche".

Kean is not the only one at fault. I also blame the publisher (Little, Brown). Didn't this book get any fact-checking at all?

What the World Needs

Market Street, Philadelphia, August 2014.

Maine Moose Mishap

Title says it all: Maine State Trooper Responding to Moose-Car Crash Hits Moose.

Hat tip to R. M.

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?