Another Crazy Journal Solicitation

Dear Shallit, Jeffrey,

With great sincerity, we are writing to you today.

We happened to have the opportunity to read your paper titled "On NFAs where all states are final, initial, or both" recently and are impressed by your research work in this field. Given that you share the same research interest with our journal Progress in Nanotechnology and Nanomaterials (PNN), we are writing to sending you our earnest invitation for paper submission.

No, you morons, nanotechnology has basically nothing to do with nondeterministic finite automata.

Denial Has Many Forms

Recently I spent about a week in Virginia, North Carolina, and Tennessee. I ate a lot of good food (I can recommend Parker's Barbecue in Greenville, NC) and met some genuinely nice people, including some distant cousins.

But some things I saw reminded me that the states of the former Confederacy are, in some ways, very, very different, even today, from the North. It's not just the statues of the confederate soldiers (here, from Windsor, NC):

(When I was in Colerain, NC in the summer, I met a guy with a Glock on the passenger seat of his pickup who told me to visit this statue in Windsor before "the niggers" got it taken down. He told me that the gun was to "put the fear of God" into anyone who would try to take it away from him.)

In Richmond I visited the Museum of the Confederacy. There were two men out in front, waving Confederate flags and handing out literature. The current museum location is scheduled to join forces with the American Civil War Center and move to a much larger venue elsewhere in Richmond. The protesters complained that the new sites are not "Confederate-friendly" and are "all about slavery".

I pointed out to one of the men protesting that slavery was obviously an important cause of the Civil War, but he denied this.

I find it a little surprising that 150 years later, there are still people fighting this war. In order to do so, they have to deny the words of the secessionists themselves. For example, here's what Mississippi wrote (in part):

Our position is thoroughly identified with the institution of slavery-- the greatest material interest of the world. Its labor supplies the product which constitutes by far the largest and most important portions of commerce of the earth. These products are peculiar to the climate verging on the tropical regions, and by an imperious law of nature, none but the black race can bear exposure to the tropical sun. These products have become necessities of the world, and a blow at slavery is a blow at commerce and civilization. That blow has been long aimed at the institution, and was at the point of reaching its consummation. There was no choice left us but submission to the mandates of abolition, or a dissolution of the Union, whose principles had been subverted to work out our ruin.

Here's what Texas wrote (in part):

In all the non-slave-holding States, in violation of that good faith and comity which should exist between entirely distinct nations, the people have formed themselves into a great sectional party, now strong enough in numbers to control the affairs of each of those States, based upon an unnatural feeling of hostility to these Southern States and their beneficent and patriarchal system of African slavery, proclaiming the debasing doctrine of equality of all men, irrespective of race or color-- a doctrine at war with nature, in opposition to the experience of mankind, and in violation of the plainest revelations of Divine Law. They demand the abolition of negro slavery throughout the confederacy, the recognition of political equality between the white and negro races, and avow their determination to press on their crusade against us, so long as a negro slave remains in these States.

And so forth.

I certainly concede that Lincoln didn't believe in the equality of races. I certainly concede that there were major issues other than slavery that contributed to secession. I certainly concede that the Civil War took a huge toll on both Confederate and Union lives, and had disastrous consequences for the South. I'll even concede that war might possibly have been avoided if Lincoln had attempted to simply buy the freedom of all slaves in the South. But to claim, as the men protesting outside the Museum of the Confederacy tried to do, that slavery was not an essential cause of the Civil War, is either dishonesty or lunacy. The seceding states themselves admitted it in detail.

When I came out of the museum, the protesters were gone. I saw a guy standing outside the museum, smoking a cigarette and walked over to him. It turned out to be S. Waite Rawls, CEO of the museum. In response to my question about the protesters, he rolled his eyes and said, "You can't reason with those folks." And I think he's right. The zeal of those protesters and their willingness to ignore the evidence reminds me of Holocaust deniers and evolution deniers. They have invested so much of their own identity in believing a falsehood that nothing could possibly convince them of the truth.

Virginia Heffernan Exemplifies What is Wrong With Journalism

Both my parents were journalists. In fact, in 1939, my mother was the first woman reporter at the Florence Evening Star in South Carolina -- a newspaper started by Melvin Purvis, the FBI agent who helped capture Pretty Boy Floyd and John Dillinger. My mother was a good writer who wrote about many topics, but she didn't write about science or mathematics. She never wrote about those topics because she didn't know anything about them. In fact, she never mastered long division. But she could write emotional and moving stories that would bring tears to your eyes. So I have great affection for journalism and its practitioners.

But my mother, and the editors who hired her, understood her limitations. They wouldn't have sent her to cover a science story because they all knew what her areas of competence were. Reporters were expected to know the basics of the area they covered.

That doesn't seem to be true for much of modern journalism. I hear over and over from scientists that whenever they read a popular article that touches on their area of competence, the writer gets everything wrong. And it's often true, in my experience, for articles discussing my own areas of mathematics and computer science.

This also seems to be the affliction of Virginia Heffernan, a writer who "came out" as a creationist earlier this year. According to Wikipedia, Heffernan has no advanced training in science or technology at all. Yet she happily wrote about technology and was described as an "Internet guru".

In her widely criticized Yahoo article, she claims to have read Darwin, but summarizes his argument incorrectly as "Whatever survives survives". (Has she been reading Michael Egnor?). She confuses evolutionary psychology with evolutionary biology; she doesn't understand the difference between "hypothesis" and "theory"; yet she feels competent to comment on evolution. Likewise, she characterizes the Big Bang theory as "something exploded". Maybe she confused the scientific theory with the TV show.

In her article, she cites Yann Martel for justification as follows: "1) Life is a story. 2) You can choose your story. 3) A story with God is the better story."

No, Virginia, science doesn't work like that. The universe isn't a story you can just "choose". The virtue of the scientific method is that it gives a way to distinguish between stories that make you feel good and the real state of affairs, using hypothesis testing, strong skepticism, and peer review. Despite her Harvard education, Heffernan doesn't show any sign of understanding this. You'd think that would make her question the value of her Harvard Ph. D., instead of questioning the science that allows her to post drivel on Yahoo.

Heffernan reminds me of another journalist: Malcolm Muggeridge. Muggeridge didn't understand or care very much about science either; he once wrote, "It is true that in my lifetime more progress has been made in unravelling the composition and the mechanism of the material universe than previously in the whole of recorded history. This does not at all excite my mind, or even my curiosity." Muggeridge's lack of interest in science had consequences: he once confused a good photographic film with a miracle. That's the kind of nonsense that happens when you think the universe consists of stories whose truth you can just choose at your whim.

Heffernan willingly exposed the limits of her competence and discredited herself. (In another example, she recommended a denialist blog here; it didn't seem to raise many alarm bells at the New York Times.) In the future, no responsible editor should hire her to cover science and technology. The real issue now is whether editors get the message Heffernan conveys, and do a better job assigning reporters to cover stories in their competence.

More Philosophical Silliness

While reading this moral argument against Darwinism by Doug Groothuis, keep in mind that the author reminds us, whenever possible, that he holds a Ph. D. degree.

Arguments like these convince me that a lot of philosophy is a kind of cargo cult mathematics. Practitioners don't do actual reasoning; they construct assemblages of words that mimic mathematical arguments, but fall far short of what a mathematician would consider acceptable.

Let's look at some of the techniques Groothuis employs:

1. Reliance on vague terms that one cannot possibly measure, test, or verify, such as "essential nature", "intrinsically valuable", and "human dignity". (If you have no argument at all, then you can always decry some practice you don't like by claiming it offends "human dignity"; it's a favorite ploy of Robert George.)

2. Quotation fabrication: Darwin never spoke of "less favored races", as Groothuis claims, and the term "favored races" that appears as a subtitle in On the Origin of Species actually refers to what biologists now call "varieties". If you google the phrase "less favored races", you find that it appears largely in creationist websites and a Republican congressional candidate.

3. An incoherent argument that concludes "But (4) is false, because of (5)" and "Therefore (6) is false because of (5)" But the terms (5) and (6) refer to nothing at all!

4. Rewriting history to claim that "our moral intuitions and the history of Western law" provides support for believing that "every human being, irrespective of race" possesses "intrinsic human dignity". Really? Whatever happened to slavery in the history of the US? How about all the Christian Southerners who claimed that slavery was ordained by God? How were black people treated in the US Constitution? In what year were women allowed to vote? If the history of Western law shows us anything, it shows us that our "moral intuitions" are not precisely fixed and are subject to change.

5. Pretending rigor by explaining grade-7 concepts like "modus tollens" and "reduction ad absurdum". Bad arguments don't get better when you use Latin.

But the silliest thing of all is the attempt to defeat a scientific theory, the theory of evolution, using moral reasoning. This makes no sense at all; it's like trying to justify a claim about chemistry by appealing to political theory.

I feel sorry for Groothuis's students.

The Southern Confederacy Arithmetic

Here is an interesting piece of mathematical Americana: The Southern Confederacy Arithmetic by the Reverend Charles E. Leverett, published by J. T. Patterson & Co., Augusta, Georgia, 1864.

Probably not too many Northern mathematics texts had questions about bales of cotton (p. 140):

Example 1. — A factor sells 25 bales of cotton at $100 per bale : what is his commission at 2½ per cent. ?

Similarly, a Northern text would probably not have an example of an order from Jefferson Davis (p. 209), or helpful explanations such as "In some States there is no capitation tax, and the sum to be raised for the expenses of the Government is collected from each individual, in proportion to his property. In South Carolina, this is on land and negroes, and is called the general tax." (p. 142)

You can also find questions such as (p. 13)

(19.) From the creation of the world to the flood was 1656 years ; from that time to the building of Solomon's Temple, 1336 years; thence to the birth of our Saviour, 1003 years : in what year of the world was our Lord born ?

I suppose it's not as bad as it could be. There are no questions like "Nathan Bedford whipped 3 slaves every day of the week except the Lord's day. How many slaves did he whip in total?"

Value of Personal Knowledge - The Answer

Here's the answer to yesterday's quiz.

1910 was a different world.

Homeopathy Kills

I have a lot of sympathy for Tamara Lovett, whose child Ryan recently died, apparently because she tried to treat his serious illness with worthless homeopathic remedies.

I'm not sure she's the real culprit here. By all accounts so far, she was a good mother who cared about her child. But she was misled by homeopathic and naturopathic propaganda to believe that plain water constituted medical treatment. When homeopathic remedies are sold openly in Canada's drugstores and natural food stores, what is an uneducated person to think? To them, it certainly seems that this kind of nonsense is legit medicine. After all, the government doesn't prohibit it, and a place calling itself a "homeopathic medicine clinic" looks a lot like a real clinic.

Shutting down homeopathic clinics wouldn't necessarily prevent deaths like Ryan Lovett's. But it would go a long way.

The Value of Personal Knowledge

This is part of an advertisement from a magazine in 1910. Can you guess what the key to "achievement of the highest excellence is"? (Answer tomorrow).

Creepy Deal Creating Public Religious School Finally Ends

I only live 20 minutes away from this school, but I never knew about it. Believe it or not, there's a Canadian public school that

• has Bible reading
• recites the Lord's Prayer every day
• only allows Mennonite children to enroll
• has no sex education
• has no teaching of evolution.

Thankfully, the school --- which is about the best example of illegitimate Christian privilege I've ever seen --- is about to close. Just imagine if there were a public school that allowed only Buddhists, or Muslims, or atheists to enroll!

But why has it taken so long?

Why Are There so Few Famous Dutch Composers?

I know little about classical music, but I have no problem listing, off the top of my head, German composers (Bach, Beethoven, Handel, Brahms, Mozart,...), French composers (Berlioz, Ravel, Messiaen, ...), British composers (Britten, Dowland, Elgar, maybe Handel counts again, ...), Italian composers (Verdi, Puccini, Corelli, Vivaldi, ...), American composers (Copland, Gershwin, Glass,...) and so forth.

But I can't name a single Dutch composer.

Here's Wikipedia's list, and I'll be damned if there's a single name I recognize.

It's strange, because there are so many famous Dutch people in other walks of life: scientists (Leeuwenhoek, Huygens, de Waal,...), mathematicians (de Bruijn, Lenstra,...), artists (Rembrandt, Hals, Vermeer,...), and so forth.

Where are all the great Dutch composers hiding? Or am I just that ignorant?

Got Moose?

From longtime reader D. S. comes this story about the UN encouraging the production of moose milk.

Moose cheese is already produced in small amounts in Sweden. It's my dream to try that someday.

Full of Hot Air

Stephen Woodworth, our local Conservative MP, is back with a new motion about the definition of "human being". He's also published this bizarre allegory that he thinks explains why.

It explains a lot. The engineer in his allegory doesn't like balloons. Stephen Woodworth doesn't like abortion.

The engineer in his allegory can't convince anyone to outlaw balloons. (Maybe that's because, at least in the allegory, not a single argument against balloons was offered.) So he tries an end-run around the issue by suggesting a bogus study of "aviation principles".

Then, despite his irrational hatred of balloons, the engineer is surprised that people see through his ploy and "accuse the aviation engineer of being a ballooning-hater whose only motive was to destroy the ballooning industry". Well, in the allegory, that was true, wasn't it? In the first paragraph, we learned that "He actively spoke and wrote against ballooning, penning letters to the editor and articles in professional journals to express this opposition to ballooning." So these accusations are perfectly justified, aren't they?

That allegory doesn't mean what Woodworth thinks it means. Somebody's full of hot hair.

50 Years Ago Today

When I was a child, I had this issue of My Weekly Reader on my bulletin board for many years.

Government Behaving Badly

There are so many stories of people in government behaving badly lately, it's hard to know what to pick out. Here are just a few:

• Health Canada torpedoes a cool magnetic pen for ridiculous reasons.
• Canada's Justice Minister Peter MacKay is all upset that Justin Trudeau talked about marijuana legalization in front of teenagers, because we have to keep the phony war on drugs no matter what, or something.
• US House Speaker John Boehner hosts extremist anti-gay group.
• Toronto mayor Rob Ford wants to sue former staffers who revealed his misconduct to investigators, despite no legal ground to stand on. Oh, and he also discusses his sexual practices in detail.
• Wisconsin Republicans restricted early voting because, you know, early voters tend to be Democrats.

Friday Not Quite A Moose Blogging

Here's a video of an elk on a trampoline. Not quite a moose, but close.

Hat tip: reader D. S.

Good Environmental News from Utah

Good news from Utah: a federal court has struck down the Bureau of Land Management's insane plan to designate over 4000 miles of Utah trails as suitable for off-road vehicle travel. Unrestricted ORV use tends to destroy streams and and soil and plants. The BLM's plan would have destroyed some beautiful wilderness areas. The decision will likely be a precedent for overturning similar plans elsewhere.

Hell Would Be Having to Listen to Francis Spufford

Some atheists are really boring, such as R. Joseph Hoffmann. But I've got to admit, I'd much rather have dinner with Dr. Hoffmann than Francis Spufford. Spufford, a Christian, an author, and a teacher of creative writing at Goldsmiths College, makes the history of NASCAR seem fascinating by comparison.

Take this Spufford piece, for example. It just rambles on and on, with paragraphs the size of the Himalayas, saying not very much at all, and doing so in the most supercilious and insufferable manner imaginable. This man actually teaches creative writing? Students of Spufford: run, don't walk, to the nearest exit, and learn writing from someone who can write, not someone who uses the phrase "bizarre category error" twice in the same essay. (Even using "category error" once by itself merits a big horselaugh -- R. Joseph Hoffmann is fond of it, too.)

Spufford starts with a healthy dollop of religious persecution complex; he thinks that being a Christian means there will be atheist "voices ... getting louder and louder" and "shouting right in ... [the] ear" of his daughter, telling her she's wrong. Funny, the only voices I hear shouting when I walk around my town are drunk people, insane people, and fundamentalist preachers. I'd really like to visit Spufford's town to see all these shouting atheists; it must make quite a show.

Spufford claims that "belief ... involves the most uncompromising attention to the nature of things of which you are capable." Really? You mean so uncompromising that you don't actually address the fundamental question of whether your beliefs are true or not? Spufford seems to think that his religious beliefs are justified because (a) they're normal (b) they're part of his imagination and (c) they make him feel good. Most of us have grown up enough to realize those aren't particularly compelling reasons.

He then spends a quarter of his essay attacking a London bus ad which said, "There’s probably no God. Now stop worrying and enjoy your life." Spufford apparently thinks the ad means that "enjoyment" is the sole goal of life and that the ad will be poor consolation for people with lives stricken with poverty, disease, or personal tragedies. But that's not what it means and not whom the ad is directed to, as anyone with connected brain cells can figure out. Hey, why not attack "Coke - Life begins here" instead? How limited must a man's Weltanschauung be if it has to commence with a carbonated beverage!

Like many North American atheists, I used to be a Christian. I ceased to become a Christian because the fundamental claims of Christianity -- which involve a unique all-powerful god, who is actually three different gods, that raped a woman to conceive a son, which is one of those three gods, who then died (but did not really die) to remove sin from me which is only sin because he decided it would be so, and which is not my sin, but rather the sin of a nonexistent ancient ancestor, and I must believe this or be consigned to a fiery hell, and he knows the future and hence everything I will do (but I also have free will) and he also loves me and cares about me, but if I put my hoohah in someone else's doohickey, I'm toast -- are simply not believable to anyone who spends 5 minutes thinking about it. Only someone who was propagandized from birth that this load of puerile nonsense is plausible could fall for it. For me it makes no logical sense, but also no emotional sense. A grotesque fable of one person's sin "redeemed" (whatever that is supposed to mean) by the execution of another, probably mentally deranged, has no emotional resonance at all for me.

What I find more interesting are the reactions to Spufford's piece in Salon. Thirty years ago, the comments would have been largely supportive. Those pesky atheists, they're juvenile, and stupid, and they miss the big picture... how right you are! Now, though, there's a sea change. The vast majority of comments are negative, pointing out the deficiencies in Spufford's reasoning (if one can call it that) and writing style. Now that is progress.

I really think that "Spufford" should be a verb: "to bore with ponderous incoherence". We went to the lecture, but the guy was just spuffording, so we left early. Now, where's that history of NASCAR?

More Bad Math in a Jack Reacher Novel

This is getting to be a series! In 2007 I criticized Lee Child's Jack Reacher hero for suddenly gaining the ability to perform lightning mental calculation, and for treating boring problems as if they were mathematically significant. Last year, I pointed out that (at least in one edition) Jack computed the decimal expansion of 1/81 incorrectly.

Well, happy 53rd birthday to Jack, who was born on October 29 1960. But I can't help complaining about yet another mathematical error, this time in Child's latest book, Never Go Back. On page 379 of the Canadian edition, Reacher muses,

"His ears had the center whorls intact like any other guy, but the flatter parts around them had been cut away, probably with scissors, very tight in, so that what was left looked like pasta, like uncooked tortellini florets, shiny, the color of a white man's flesh. Not exactly hexagons. A hexagon was a regular shape, with six equal sides, and Shrago's stubs had been trimmed for extreme closeness, not geometric regularity. They were irregular polygons, more accurately."

Sorry, but a hexagon is not necessarily a "regular shape"; that would be a regular hexagon. A hexagon is any polygon with 6 sides; there's no symmetry implied.

Eric Hehner Replies

Eric Hehner apparently could not figure out how to post this reply to my blog because of some character limit, so he asked me to post it. Here it is. I'll reply below.

---

Wow! I merit a tirade by Jeffrey Shallit. Thank you, Jeffrey. I hope your blog piques interest in my upcoming lectures. You have kindly included links to the work in question, so I hope people will read the work and judge for themselves, rather than accept your opinion.

I'll pass over the parts where you ridicule me by associating me with fraudulent archaeology and people who think 1>2 and circle-squarers. Your first direct volley is aimed at my paper “Beautifying Gödel”. The title comes from the fact that the paper was a contribution to a book titled Beauty is our Business. I set out to write the simplest, most elegant presentation that I could of one of Gödel's theorems. The paper does not suggest that there is anything wrong with Gödel's theorem. The simplifications come from our modern familiarity with the character string data type (so we don't have to encode programs as integers) and with programming language interpreters; these were unknown to Gödel. My presentation has been used by various authors and textbook writers (e.g. What Computing is All About, a textbook used at CalTech).

I am a fan of Torkel Franzén and his wonderful book Gödel's Theorem: an Incomplete Guide to its Uses and Abuses. His criticism of my paper was very mild (especially compared to his pointed criticisms of almost everything else). It seems to arise because he, like most mathematicians, is a platonist (he believes mathematical objects exist, independent of people; we just try to find out some truths about them) whereas I am a formalist (I believe mathematics is a formal language created by people to describe some aspects of the world). In particular, soundness is stated differently. Perhaps formalist mathematicians are “fringe”; if so, it's an august group that I am happy to be part of.

You cite my paper “the Size of a Set” as fringe mathematics. You say I deny “that it is reasonable to say that a set A is the same size as set B if A is equipollent with B”. Then a few sentences later, you say “But who cares what Prof. Hehner thinks is “reasonable”?”. When you quote the word “reasonable”, you are quoting yourself, not me; the word “reasonable” does not appear in the paper. You say “There are other problems with Hehner's paper”. First, I “present the minor technicality of some numbers having two different base-k representations as something that has to be “repaired”, when in fact this problem simply does not occur in Cantor's proof when correctly presented”. Your comment is entirely unfair. I first present the popular form of the proof, point out the problem, and repair it. I agree that the problem does not occur when the proof is correctly presented.

The next problem, you say, is that I “claim the proof is informal when in fact formalizing it is trivial”. The wordy proof is informal, and I formalize it. How is that a problem?

Finally, you say I “confuse the notions of cardinality and computability”. I most certainly do not. I present two analogous arguments, and point out the important difference that one talks about “having” a list, and the other about “generating” a list. Your criticisms are false and unfair.

Here is the conclusion of my paper; judge it, remembering that I speak from a formalist point of view: “It is popularly believed that Cantor's diagonal argument proves that there are more reals than integers. In fact, it proves only that there is no onto function from the integers to the reals; by itself it says nothing about the sizes of sets. Set size measurement and comparison, like all mathematics, should be chosen to fit the needs of an application domain. For all application domains that I know of, Cantor's countability relation is not the most useful way to compare set sizes.” How does that conclusion draw such ire?

Now let's get to the papers that upset you most: my claim that Turing's proof of the incomputability of the Halting Problem has serious flaws. You say: “If Prof. Hehner claims that this proof is flawed, then he must point to the exact line of the proof that he disagrees with.”. Yes! That is precisely the content of the paper (although it's not just a single line that I find fault with). Continuing, you say “Instead, what he does is translate this simple proof into his own private language in a flawed way, and then raise several objections to his own translation.”. By “translate” you mean formalize the proof. The “own private language” is the assignment statement, if-then-else, and while-loop. They are the basis for all current popular languages. I chose the language because it is standard. As for “in a flawed way”, formalization makes clear one's understanding of an informal, English-language proof, and one can never be sure that one has formalized correctly. After I had done my formalization, I read the formalization in Boyer and Moore's paper “a Mechanical Proof of the Unsolvability of the Halting Problem” JACM 31, 3, 441-458, 1984. I was delighted to see that they had formalized the problem the same way I had (except that they used LISP). That gave me confidence in my formalization. I added a section on the Boyer and Moore formalization and proof to my paper.

You say I “seem a bit confused” about what the computability hierarchy is. The paper begins with a very clear construction of the hierarchy. [Dear reader: judge for yourself.]

You cite a paper by Huizing, Kuiper, and Verhoeff, “which generously takes his work seriously and points out the flaws. If Prof. Hehner has a response, I have not seen it.”. So here is my response. I was the (one and only) referee for this paper; I accepted it. It makes good, valid points, and does not invalidate my paper, although they thought then that it did. I spent some time talking with them at the Turing100 celebration in Manchester last year. They suggested another way I could present my case; it became the paper “Reconstructing the Halting Problem”, which you cited.

How can I know if I am a crackpot? On the one hand, a person whose work and opinions I respect, Jeffrey Shallit, tells me so. On the other hand, there's a wonderful book named the Experts Speak by Navasky and Cerf that has a long list of major scientific achievements that were ridiculed by the reigning scientists (the “experts”) of the time. Usually, one is not called a “fringe” scientist just for making a mistake (I don't think I have made a mistake, but I can't be sure). You call me “fringe” because I am challenging an established result of computer science. One way science is distinguished from religion, at least in principle, is by not having any sacred truths that must not be challenged. Unfortunately, I am discovering, some scientists treat some of their truths as sacred, and become quite upset when they are challenged. Challenging sacred truths can be dangerous to one's reputation and career: the priests who protect their truths will attempt to assassinate your character by writing insulting blogs. That's why I waited until retirement to pursue this topic. Here is the real danger: if challenging basic accepted results becomes too costly (it's not easy to bear the insults), science loses its self-correcting character that distinguishes it from religion.

“It is our unfortunate duty to host this nonsense at the University of Waterloo at 4 PM on Thursday, November 28, in DC (Davis Centre) 2585.” See you there!

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My reply:

Eric Hehner:

You seem confused. I didn't call your work "fraud" in my post, I did not use the word "crackpot" there, and I never said a word about your "character", much less "assassinate" anything. For all I know you're probably a nice guy who is kind to your pets. My post was about your work, not you. I think your work on the topic of Cantor and Turing is junk, and I said so.

I'm certainly uninterested in a long back-and-forth about this, but I will say a few things. Your work (and the venue you publish it in) speaks for itself, I think. You also confuse "ire" with "amusement"; I think your criticism of Cantor's work is trivial, silly, and is likely to be completely ignored for those reasons and others.

Your presentation of the proof of the unsolvability of the halting problem (on page 1 of "Problems with the Halting Problem") is not the one I present in class. It is also not the one in any standard textbook on the subject that I looked at (e.g., Sipser, Hopcroft and Ullman, etc.). You certainly do not take the standard proof and point to the exact line that you disagree with. That is your obligation, and you didn't fulfill it.

Blogs are not the place to reply to the Huizing et al. paper. If you contest their conclusions, publish a paper specifying exactly where they went wrong. That's the "self-correcting" nature of science you seem to think highly of.

the priests who protect their truths will attempt to assassinate your character by writing insulting blogs: oh, please. I'm not a priest, just a guy with a blog who is pointing out your silly claims and is sorry that my university is giving you a venue. I didn't say anything about your character. By the way, you forgot to compare yourself to Galileo.

science loses its self-correcting character: you're confused. The self-correcting character is precisely that you offered a bogus refutation of the standard proof, and I'm pointing out that your refutation is bogus.

Eric Hehner's Fringe Computer Science

Fringe science -- making claims, with little evidence, that nearly everyone who works in the field recognizes as wildly wrong -- is nothing new. In archaeology, fringe science includes promotion of artifacts like the Vinland Map (now completely discredited) and the Kensington Runestone (likewise discredited). There are two very good books discussing fringe archaeologists and their "methods": Stephen Williams, Fantastic Archaeology and Kenneth Feder's Frauds, Myths, and Mysteries: Science and Pseudoscience in Archaeology.

You would think that in a field like mathematics, it would harder to be fringe. People don't normally debate whether 1 > 2, or whether ½ is a rational number. Nevertheless, there is a surprising amount of fringy mathematics. I'm thinking, for example, of circle-squarers, who continue to try to construct π with straightedge and compass long after Lindemann's proof that it cannot be done. In 1977, the Journal für die reine und angewandte Mathematik published a fringy proof of Goldbach's conjecture that, needless to say, is not widely accepted.

While most people engaged in fringe mathematics are amateurs, there are a few professionals. It used to be pretty hard to publish fringe mathematics in journals, but with the rise of open access journals of questionable credentials, it has become a lot easier. Not all fringe mathematics is wrong, but most of it is.

Up until now, I hadn't seen too much fringe computer science. But now I have. And to make things worse, we have apparently asked the author of these fringe works to come speak at our university.

The work in question is that of Eric C. R. "Rick" Hehner, an emeritus professor at the University of Toronto. Hehner worked in what is called "formal methods", which concerns logical formalisms for computer science constructs, such as those in programming languages. On his web page, you can find a list of his publications.

Hehner seems to have done some reasonable work in the past, although I'm probably not the very best judge. Some other people apparently disagree. For example, Hehner lists a paper called "Beautifying Gödel" as among his very best; yet the late Torkel Franzen, an expert on Gödel's theorem who published an eponymous book on the subject, said that Hehner's paper "contains some odd misunderstandings" and exhibits "some standard confusion regarding the soundness condition needed".

Lately, however, Hehner's work can, I think, fairly be characterized as "fringe computer science". For example, he claims that our modern understanding of uncomputable problems, such as the halting problem is completely wrong and that the standard proof of unsolvability, taught in nearly every undergraduate course on the theory of computation, is bogus. (Another version of Hehner's claims is here.) As a result, Hehner denies the existence of something he calls the "computability hierarchy" (although he seems a bit confused about what that is). At the end of this piece, Professor Hehner reveals that his focus on the halting problem dates from the 1980's.

Prof. Hehner has recently branched out into another favorite of the fringe mathematician, Cantor's proof of the uncountability of the reals. Prof. Hehner's paper is not the worst anti-Cantorian work I have read --- it seems that, at least, Hehner does accept that Cantor's proof is correct. He just denies that it is reasonable to say that a set A is the same size as set B if A is equipollent with B. (There are other problems with Hehner's paper, such as (1) presenting the minor technicality of some numbers having two different base-k representations as something that has to be "repaired", when in fact this problem simply does not occur in Cantor's proof when correctly presented; (2) claiming the proof is informal when in fact formalizing it is trivial; (3) confusing the notions of cardinality and computability.) But who cares what Prof. Hehner thinks is "reasonable"? There's a lot of beautiful and interesting mathematics that arises from this definition, and mathematicians find it useful. If Prof. Hehner does not, he is free to make a case for a better definition. But he does not, not in any serious way. In this sense, his case is entirely a negative aesthetic one: he doesn't like Cantor's definition, and can't imagine why anyone else would. This is not a basis for good science.

The reception of Prof. Hehner's claims about computability and Cantor -- which would be revolutionary if accepted -- has been, I think it is fair to say, silent or negative. There are only a handful of citations of the relevant papers, mostly self-citations. One exception is this paper by Huizing, Kuiper, and Verhoeff (behind a paywall, probably, if you aren't at a university) which generously takes his work seriously and points out the flaws. If Prof. Hehner has a response, I have not seen it.

Professor Hehner seems unhappy that his work is not treated seriously, and that some people who object to it do not always point out specific problems with his reasoning. But I think he's got it exactly backwards. The uncomputability of the halting problem has a proof, and we teach that proof in most introductory courses in theoretical computer science. The proof doesn't have many steps, the steps are very simple, and it is accessible to any bright junior-high school student. If Prof. Hehner claims that this proof is flawed, then he must point to the exact line of the proof that he disagrees with. Instead, what he does is translate this simple proof -- as in this video -- into his own private language in a flawed way, and then raise several objections to his own translation. This tactic is well-known as the "straw man". It is not a serious scientific attack on our understanding of the problem.

It is our unfortunate duty to host this nonsense at the University of Waterloo at 4 PM on Thursday, November 28, in DC (Davis Centre) 2585. The public is welcome. If it had been up to me, I would not have extended an invitation to Prof. Hehner to speak on this topic because (1) I am not convinced, based on what I've read, that he has a deep understanding of the material and (2) I do not think, based on what I've read, that he has anything interesting to say. But a great feature of a university is that all kinds of ideas, from the well-supported to the fringe, can be discussed.

Sometimes, though, we pay the price.