God and Reason, Lecture 6: Who Was Jesus?

I attended Lecture 6 in the God and Reason short course given by Christian professors at my university. Once again, attendance was down signficantly since Lecture 3. Once again I had to leave at 5:20 PM, so I missed most of the question and answer sessions. Today's lecture was given by Civil Engineering professor Wayne Brodland, and was entitled "Who Was Jesus and Did He rise from the Dead?" Prof. Brodland has won a teaching award at UW and his presentation was (like others in the series) well-done and easy to follow. However, it was very heavy on the Christian evangelism and quite light on the reason, in my opinion. As usual, my comments are in brackets.

He started by comparing his method for ascertaining truth in the laboratory with how he ascertains truth in his faith:
In his lab:
1. start with data (theory, experiments, computer simulations)
2. Sometimes he doesn't like the data and struggles to explain it
3. Employs "circularity" and seeks the best fit for jigsaw-puzzle pieces
4. Strives to constantly update his understanding
5. Submits his understanding to peer review
6. Tries to advance knowledge
7. Prefers simple closed-form answers.

In his faith:
1. start with data (Bible, experience, personal conversations)
and then 2 through 7 are the same.

Prof. Brodland claims he uses the same approaches to ascertain truth in the lab and his faith. [I don't think this is the case at all. For one thing, in science we try very hard to disprove our hypotheses, by setting up experiments to test them. What are the corresponding experiments Prof. Brodland has done to try to disprove his faith? None that he spoke about; if anything he seems extremely willing to take personal experiences as confirming of his faith, even if they are quite tenuous; see below. For another, "peer review" means submitting your work to reviewers that are often hostile, not just talking about your faith with friends who share the same opinion. Where is the evidence that Prof. Brodland has explored Buddhism, Hinduism, Judaism, Islam, and so forth with equal research that he has done on Christianity?]

Prof. Brodland went on to discuss the tools used for data collection and analysis. He divided these tools into three parts, which he called "body", "soul", and "spirit". By the "body", Prof. Brodland means the five sense and scientific instruments that detect physical phenomena. By the "soul" Prof. Brodland means "logic to organize ideas and make inferences" [which seems like a very strange definition of "soul" to me]. And in the last category, "spirit", Prof. Brodland refers to "communication from the supernatural realm". Naturalists or Deists, he claimed, only recognize the first two. whereas Christians are more "broad-minded" because they allow another kind of information, namely information from the supernatural realm, to influence them. [Prof. Brodland could be even more broad-minded by allowing information from Zeus, Bigfoot, and extraterrestrials to influence him. In other words, it's not clear to me that being "broad-minded" in this sense is a virtue.]

He then compared Jesus to Einstein, Fourier, and Pasteur. They all risked their credibility and changed the world with their ideas. For Einstein, it was relativity; for Jesus it was "love your enemies" and "I am the truth and the life". He then presented many passages from the New Testament that showed that Jesus claimed to be the son of the Christian god.

Who was Jesus? Prof. Brodland claimed he is the son of the Christian god and the only other possibilities are that he was (a) self-deluded (b) a liar (c) just a good teacher or (d) just a legend. He dismissed (d) as implausible by saying that there are "lots of extra-Biblical sources" proving Jesus' existence. [This is false or misleading. There are a handful of extra-Biblical sources, and not one is contemporary. Some of these extra-Biblical sources are widely acknowledged to be Christian fabrications, such as certain passages in Josephus. And these extra-Biblical sources are clearly just reporting what they have heard from others and are not first-hand, independent sources.]

He dismissed (c) by saying that if Jesus was not the son of the Christian god and yet taught that he was, he could not be a good teacher. [This also seems quite unreasonable. Has Prof. Brodland never been mistaken in something he taught? Then I guess he is not a good teacher, either, by this criterion. On the contrary, it is perfectly possible to be a good teacher and still be mistaken, even about fundamental claims.]

Prof. Brodland dismissed (a) and (b) by saying that Jesus' claims are validated by his resurrection. [He did not consider the other obvious possibilities: Jesus was misquoted, or Jesus was misunderstood, for example.]

Prof. Brodland gave three claims he felt were good reasons to believe in the resurrection:
1. The disciples were despondent and a triumphal re-appearance of their leader was not on their minds.
2. They were feeling defeated and not likely to have hallucinated his return.
3. In ancient times it was believe that the soul was good but the body weak or corrupt, and hence resurrection was not part of their thinking.

[None of these seem like even slightly good reasons to me. On the contrary, if the disciples were despondent they would be very quick to grasp any way to be less despondent. All they needed was one person who claimed to see Jesus and many followers would be quick to glom on to this as a "miracle". Furthermore, it is simply not true that resurrection was not in the minds of people of the ancient world. Some say Asclepius was resurrected by Zeus after being killed by him, for example.]

Did Jesus rise from the dead? Prof. Brodland said we could test this hypothesis against the null hypothesis by considering data in 3 areas:
- the empty tomb
- reports by witnesses to his being alive
- change in the witnesses' attitude after resurrection

The tomb: all 4 gospels report an empty tomb, some written only 30 years after the event, when eyewitnesses were still around. The eyewitnesses would have complained if inaccurate reports had circulated. Since they didn't, the reports must be accurate. [How does Prof. Brodland know there were not eyewitnesses who took issue with these reports? There could well have been, but since we have so few documents from that time and place, how would we know? Furthermore, there would have been great pressure at early church meetings to suppress any such documents, if they existed.]

Also, secular sources don't challenge the fact that the tomb was empty; instead they put forward alternative explanations for it. [Well, one alternative explanation is that the disciples went to the wrong tomb. So the "real" tomb might not be empty.]

No body was ever produced and no shrine was built. If there a body, there would be a shrine there. [Prof. Brodland seems to have inadvertently supported the most obvious explanation: the body was removed by enemies of early Christianity, fearing that the resting place would become a shrine.]

Reports by witnesses: there were over 500 witnesses that reported seeing Jesus. [This is quite misleading. There were not 500 individual witness reports; instead there is a claim by Paul to that effect, a claim that is not substantiated by the existence of the supposed reports.]

Changes in Jesus' followers: disciples "suddenly" started appearing in public; many died horrific deaths because of their beliefs. If they had just made it up they would not be so willing to die. [Again, this is very misleading. Most of the people "willing to die" probably did not experience the resurrection themselves but were simply told about it by others, and believed it. Many people died willingly as followers of cult leader Jim Jones, but that doesn't make Jim Jones's claims true.] The Church grew quickly, even where the government wanted it suppressed. Today, many report personal experiences of Jesus. [Yes, and many report other kinds of extraordinary experiences, but it doesn't follow that these experiences correspond to reality. Does Prof. Brodland believe in Bigfoot, extraterrestrials, and Elvis still being alive?]

Prof. Brodland concluded by telling about his personal experiences. He suffered from deafness and stated that doctors said he had nerve damage and would be deaf for life. However, after he started praying and asking for friends to pray for him, "Jesus healed me". An audiologist confirmed that his hearing improved. "Those are the facts. When I asked Jesus to heal me, he did. This is powerful personal evidence that Jesus is alive and he did respond. I have the records to show. This is such a strong piece of evidence and you can test my claims." [How does he know it was Jesus? This is a classic case of the post hoc, ergo propter hoc fallacy. A scientist should know better.]

I had time to ask one question. I said that I too, have suffered from hearing problems. I too visited doctors and had tests and the doctors said there was nothing they could do. But the problem has largely resolved itself with time, and my hearing is much better -- all accomplished without prayer. I said that I had not prayed, but if I had (say) prayed to Zeus and gotten better, would this be evidence of the existence of Zeus?

Prof. Brodland did not really address my question. To paraphrase his answer, he said that he had his story and he was sticking to it. That well may be, but it is not very good evidence for Jesus when there are spontaneous improvements in nerve damage all the time. It even happens in hearing loss, although apparently it is rare (I don't claim to be an expert). This page, on the other hand, claims spontaneous remission is common! Prof. Brodland certainly should understand the extremely weak status of personal anecdotes as evidence. Good evidence would be to test many people, each with similar conditions, some of which pray (or have friends pray for them) and some don't. That would be an example of the scientific method that Prof. Brodland claims to follow. Unfortunately for Prof. Brodland, studies of intercessory prayer do not provide much confirming evidence at all.

All in all, this was just another exercise in Christian evangelism, full of fallacies and incorrect claims. It does not surprise me, though: the case for Christianity always has been extremely weak.

Allouche Special Issue Published

A special issue of the Journal of Integer Sequences has just been published in honor of Jean-Paul Allouche's 60th birthday. There is also a brief introduction written by Valérie Berthé and me.

Creationists Live in Bizarro World

Sometimes I think creationists live in Bizarro World, where everything is backwards.

Take a look at this creationist letter to the editor by Terry Scambray, a retired college English instructor. It's in response to this perfectly reasonable opinion piece by Chemistry prof emeritus George B. Kauffman.

Even as you begin to read, the creationist clues are there. An English professor commenting on science? Surely he is a bit out of his depth. And indeed, the start of his letter is not so auspicious: "it's disappointing to read George Kauffman assert last week in The Bee that everyone should accept Darwin's "creation" story because a Quaker, physicist congressman had a House Resolution passed saying that we should!" But Kauffman never said any such thing. It's surprising to see an English professor with such poor reading comprehension, but maybe he taught English at Bizarro College.

Scambray goes on to huff, "Animals and plants appear in the fossil record fully formed and remain unchanged through millions of years. No knowledgeable individual denies this." The first assertion is pure creationist babble. What would it mean to be not "fully formed"? And, of course, species have not remained unchanged through millions of years. We know that each individual is likely to carry mutations and differ from its ancestors. Similar phenotypes do not imply lack of genotypic change. Furthermore, we have excellent examples in the fossil record of significant phenotypic changes. Is Scambray ignorant or a liar? That's too harsh; perhaps he just lives in Bizarro World.

Scambray claims, "Over millions of generations of laboratory testing, fruit flies, as one example, when subjected to genetic changes have not changed into anything but mutated, crippled fruit flies." Really? At my university, we have access to articles that say something different. Maybe at Bizarro College, they don't.

Mr. Scambray, if he has ever visited the Galapagos, must have visited a parallel Galapagos, because he claims, "Thus the [Galapagos] finches changed a little, adapted, while remaining fundamentally unchanged." He doesn't seem to understand that there are 15 different species of finches, all descended from a common ancestor that colonized the Galapagos millions of years ago. Things must be different in Bizarro World.

Mr. Scambray is not alone, however, One of his good buddies is - surprise! - creationist Cornelius Hunter. Hunter has biological training, but was he able to spot the flaws in Scambray's article? Apparently not, because he thinks Scambray "destroy[ed]" Kauffman's arguments. They have a good time together there in Bizarro World, as Scambray himself favorably reviewed Hunter's books back in 2009.

That's the end of today's tour of Bizarro World. Have a safe return to planet Earth.

Dembski Repeats the Same Tired Nonsense

Here's a video of Bill Dembski repeating the same old nonsense about intelligent design. Want to know why intelligent design is dead? Because even its leading proponents have nothing new to say.

- "specified complexity" and "complex specified information": incoherent, useless concepts that have been debunked long ago by me and many others

- the movie Expelled shows how intelligent design advocates get discriminated against (see here for the real story)

- same grotesque slurs against legitimate researchers, implying they've done something underhanded by "smuggling in" information

- same martrydom about how his career has been damaged by evil Darwinists.

- same mystical view of "information", without understanding how it can be created by any random process.

- same claim about prime numbers implying intelligence, even though there is evidence that natural processes that can generate them (e.g., cicada periodicity to avoid predation).

And he still doesn't understand that evolution doesn't have a goal and that evolutionary fitness landscapes come from the environment.

My Review of Chaitin

My review of Gregory Chaitin's book, Proving Darwin: Making Biology Mathematical, has finally appeared here.

Bottom line: Chaitin has an interesting idea, but it's a small idea expressed poorly, and will likely have very little impact on either biology or mathematics.

How Did This Guy Ever Get Elected?

The spectacle of George Galloway, British MP, walking out of a debate because his opponent was an Israeli, is appalling. How did he ever get elected?

Woodworth: If You Didn't Support My Motion, It's Because of "Ideology, Political Bias, or Personal Interest"

According to a letter in our local newspaper, our local MP, Stephen Woodworth thinks that the only reason people didn't support his Motion 312 was "ideology, political bias or personal interest": "[Trudeau's] opposition to the evidenced-based study of a law denying the equal worth and dignity of same human beings, in the Motion 312 vote a few short months ago, was a triumph of ideology, political bias or personal interest over policy creation based on evidence, fact, and sound principle."

I guess it couldn't possibly be that most MP's viewed Woodworth's motion as a transparent ploy to head down the road to outlaw abortion. I guess it couldn't possibly be that Woodworth, as a devout Catholic, subscribes to any "ideology" himself.

(And I don't know what "same human beings" means.)

New Online Journal Publishes Tripe about Gödel

A new online journal, Sententias, has published its first issue. It claims to be devoted to "philosophy, theology, and science", but its real goal can be deduced by clicking on the tab labeled "ministry tools". Why, all academic journals come with "ministry tools", don't they?

The first issue is not promising at all. One article is entitled "The argument from reason and incompleteness theorems" by Ryan Thomas. The author writes about Gödel's theorems, but it's clear he doesn't understand them. Too bad Thomas did not read Torkel Franzén's book, Gödel's Theorem: An Incomplete Guide to Its Use and Abuse; he might have saved himself some embarrassment.

Thomas thinks that Gödel proved that "within a consistent and complete set of axioms there will be at least one statement that is improvable within the system" and "a consistent and complete set of axioms cannot demonstrate its own consistency". Leaving aside the strange use of "improvable" instead of "unprovable", and leaving aside that one does not usually talk about being "within" a set of axioms, Thomas misses the point. The important thing is not that a logical theory has statements that are unprovable -- after all, we'd be unhappy if false statements had proofs in our theory. The interesting facet is the existence of true statements that have no proofs in the theory. Furthermore, Thomas doesn't seem to know that Gödel's theorem does not apply to all axiom systems, but only ones that are sufficiently powerful. There do indeed exist logical theories that can prove their own consistency.

Thomas thinks that Gödel's theorem has some profound consequences for understanding the human brain -- but this is a common misconception. Gödel's theorem is about logical deductions from axioms; but this is only one small and relatively unimportant facet of human reasoning. Most of our reasoning - even down to the level of assigning meanings to words and connecting those words to the physical world - seems probabilistic in nature. We use probabilistic reasoning all the time without being excessively worried about proving its "completeness" or "consistency"; why should logical deduction be any different?

Judging from Thomas's contribution, this journal has an inauspicious debut.

Callan Bentley is My New Hero

The Discovery Institute requests the right to us a photo by geology prof Callan Bentley. Bentley replies, and hilarity ensues.

Hey, they don't call it the "Dishonesty Institute" for nothing.

God and Reason - Week 4

I didn't get a chance to attend the "God and Reason" course, Week 4, so you can head over to Jeff Orchard's blog to find the answer to "Doesn't the church produce hypocrites and injustices?"

Happy Darwin Day!

Today is the 204th birthday of Charles Darwin, one of the greatest scientists of all time, and the person who contributed most to our understanding of human origins.

Think you know a lot about Darwin? Then, without using Google try this Darwin trivia quiz and report your score. You can answer in the comments, but all comments will be held for 24 hours today.

1. Who was the naturalist on board the Beagle?
2. What other famous person was born the same day as Darwin?
3. What denomination of UK currency has a picture of Darwin?
4. What common household item is associated with Darwin's wife?
5. What is the correct full title of Darwin's 1859 book? (Even Dawkins got it wrong recently.)
6. What is the name of Darwin's house in Kent?
7. Name a single species named after Darwin.
8. What occupation did Darwin originally plan to pursue?
9. What, as a young man, did Darwin spend his time collecting?
10. Where is the largest city named after Darwin located?

Minnesota Moose Misery

From Greg Laden, here's the sad story about the decline of the Minnesota moose.

The Advantage to Living in Canada

I will miss the penny, I really will. And Canadians are sometimes too subservient to authority. But I have to say that one clear advantage to living in Canada is that reasonable societal changes like this one (and the metric system, and gay marriage, and the adoption of OHIP) are not routinely derailed by breathtakingly insane opposition that resorts to rhetoric like "lies from the pit of hell".

God and Reason 3 - After the Course

After the third lecture in the "God and Reason" course I fell into conversation with someone I assume is a Waterloo undergraduate. Intelligent and articulate, he asked me some questions about my worldview and made a number of questionable claims. I don't know his name, but I'll refer to him as "M".

M has a pre-scientific view of the world and believes in spirits, souls, and so forth. I have done my best to reconstruct his claims, but if I am wrong in any particular I would be happy to correct it.

M does not accept the theory of evolution. He agrees that "microevolution" takes place, but does not accept "macroevolution". [See here and here for brief responses.] He asked me, "Were you there?" in response to my listing some of the evidence for evolution; this is a typical ploy of the creationist Ken Ham. However, M has never taken a course in evolutionary biology. (Here is how paleontologist George Gaylord Simpson would respond: "If a sect does officially insist that its structure of belief demands that evolution be false, then no compromise is possible. An honest and competent biology teacher can only conclude that the sect's beliefs are wrong and that its religion is a false one. It is not the teacher's duty to point this out unnecessarily, but it is certainly his duty not to compromise the point.")

M thinks there is no problem of pain for animals because animals don't have souls. (Theologian William Lane Craig has made some related claims, to which you can see good responses here.)

M thinks that the historicity of Jesus is the "most well-supported of any figure in the ancient world". He believes there are secular references to Jesus as early as 15 years after his death. This is not so. I gave him my e-mail address and asked for an example. So far nothing has come.

M tried a version of Plantinga's evolutionary argument against naturalism, but he wasn't quite sure where he was going and he eventually gave up with that.

M thinks that his god sets an absolute standard of right and wrong. He is completely fine with the slaughter of the Midianites (even the children), as depicted in the Bible. Although M believes that the Ten Commandments set this absolute standard (and prohibit murder), he also stated that if his god told him to kill someone, he would.

In many ways M seems typical of the hundreds of Christian evangelicals I've talked with in my life. I hope that a university education will broaden his horizons a bit and he will learn more about the theory of evolution and the evidence for it before he rejects it.

God and Reason - Lecture 3 - John North - The Problem of Pain

I attended the third lecture in the "God and Reason" short course given by Christian professors at my university. (This time I was also able to stay for the question-and-answer period, since my son's soccer schedule has a week break in it. I probably won't be able to do that in the future.)

This week's lecture was delivered by Prof. John North of the English department. I have known John North for 20 or so years, back to when our university had a weekly staff and faculty newspaper edited by Chris Redmond, the Gazette. He wrote good letters to the editor about the importance of the library for the University and the importance of scholarship. He is a scholar of some repute in his own field, too. And I learned some other impressive things about him that I didn't know before (more on this below).

Once again the talk was well-delivered (not a big surprise since Prof. North has won a teaching award) and easy to follow. Despite this, I would say that the emphasis was much more on the "god" and hardly at all on the "reason". And despite it supposedly being about "the problem of pain", more time was devoted to a summary of the dogma believed by most Christians. As usual, my comments are in brackets.

Prof. North started with answers to the argument that "a good God would not allow pain". (He gave as examples tsunamis and animal suffering.) He gave the following answers:

Answer 1: "because I cannot see the value in pain, there must be none" is unwarranted self-confidence, cf. God's answer to Job. [This is only relevant if one assumes that there is a god that has some plan that involves pain. But if one is simply trying to decide if a god's supposed attributes fit the evidence we see, then this answer doesn't really address the evidence.]

Answer 2: "to be free is to be free to choose evil with its consequences". Not to be free is to be an automaton. [I found this extremely unsatisfying. The best rejoinder I have heard is from the physicist Stephen Weinberg: "It seems a bit unfair to my relatives to be murdered in order to provide an opportunity for free will for Germans, but even putting that aside, how does free will account for cancer? Is it an opportunity of free will for tumors?"]

Answer 3: C. S. Lewis, "They say of some temporal suffering, 'No future bliss can make up for it,' not knowing that Heaven, once attained, will work backwards and turn even that agony into a glory." [Assumes facts not in evidence. We have no evidence of "Heaven", or backward causality. Are we supposed to accept this just because C. S. Lewis says so? How can C. S. Lewis possibly know with any certainty about this supposed glory? It reminds me of Ambrose Bierce's classic definition of faith: "belief without evidence in what is told by one who speaks without knowledge, of things without parallel."]

Why pain? He gave two answers: protection for our body, and protection for our soul.

He discussed his work as a volunteer chaplain at our local hospital, where he is on class for 2 shifts from 7 PM to 7 AM to help comfort dying people. He estimates that he has helped over 800 people on their deathbeds, by comforting them through prayer and Bible reading. [This is an impressive commitment to people who are suffering.]

The rest of the talk was an exposition of what many Christians believe, in an evangelical mode. I tried to write down some of it but the parade of Bible quotes was too familiar and boring. Here are a few things:

"unless you are converted and become as little children, you will by no means enter the kingdom of heaven." --- Matthew 18.

[Here we have Christian exclusivity -- only Christianity has the answer and you won't enter heaven unless you accept everything Christians say as gospel. And we also have the denial of intellect and reason -- you must think like a child, not as an adult.]

"Love the Lord your God with all your heart and with all your soul and with all your mind and with all your strength. The second is this: 'Love your neighbor as yourself.' There is no commandment greater than these." -- Mark 12:30-31.

[This kind of stuff disgusts me. Here we have the spectacle of a god commanding everybody to love him -- the kind of megalomaniacal behavior we would rightly shun or laugh at if it came from a friend or family member. Yet we are supposed to view god as some cosmic Mafioso and rejoice in it. I find that sick.]

The Apostle's Creed: "I believe in God, the father almighty..."

Christians are guilty: "For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven. (Matthew 5:20)

"For whoever keeps the whole law and yet stumbles at just one point is guilty of breaking all of it." (James 2:10)

[Here we have a clear violation of the principle of proportionality - a basic principle of law recognized in almost all human societies, namely, that punishment should be proportionate to the crime. Another example of how Jesus' teachings are not models of ethical behavior.]

"If anyone, then, knows the good they ought to do and doesn’t do it, it is sin for them."

"Confession, repentance, and forgiveness is the only hope
- between myself and God - between myself and every other person."
This, Professor North asserted, is the ultimate solution to the problem of pain.

[Of course, it is no solution at all. "Confession, repentance, and forgiveness" did nothing for my relatives who were murdered by their Christian neighbors in the Holocaust. "Confession, repentance, and forgiveness" did nothing for my father who died of Alzheimer's. And it does nothing for the millions of people who lived throughout time before the supposed revelation of Jesus and nothing for the millions of people alive today who have never heard the message of Christianity. This is just a cop-out.]

"Only Jesus Christ, God become man, is big enough to forgive me. Forgiveness costs. Ever tried it? Accusing is more common. "The Accuser" is one of the names of Satan."

"Jesus is the creater and sustainer of the universe, the stars, galaxies, insects, and every person."

[So then, Jesus is also the creator and sustainer of killer tsunamis, the Black Plague, and all the mass murderers that have ever lived, including Hitler. Nice guy!]

"Jesus died for me, rose again for me, ascended into heaven. He sees every sparrow that falls."

[He may see every sparrow fall, but he doesn't help them. Isn't it strange that Jesus can do parlor tricks like turn water into wine, but he can't stop world hunger?]

"200,000 Christians are martyred every year." [Probably exaggerated; searches reveal many different such claims, with no really definitive source or account of methodology.]

"Why are people killing Christians?" [For most of them, probably the same reason they kill Muslims and atheists: for personal gain, because of ethnic tensions, because they are "different", and because their religion and culture tells them they should.]

At that point the floor was opened for questions. I asked about the millions of people who lived before Jesus and the millions of people who live today without ever having heard of Jesus. If the "solution to the problem of pain" is "confession, repentance, forgiveness" then all those millions cannot have any solution for their pain. (This is one of the reasons I abandoned Christianity long ago.)

I know that some Christians respond to the effect that the Christian god's existence is obvious to everyone and therefore no one has any excuse to not believe. Of course, this isn't so; monotheism is a relatively recent invention and polytheism was a common belief for thousands of years. Prof. North answered somewhat differently: that in the future all time, both past and future, will become present. And, further, that everyone walks around with a hole in their hearts that only the Christian god can fill. Finally, he said there are some things that he doesn't understand about his god, but he believes nevertheless.

[You can see here how reason has been abandoned. There is no evidence that in the future 'all time will become present time'; this is just meaningless verbiage concocted out of thin air.]

Now, here is my solution to the problem of pain: pain is an evolved response that is present in people, just like every other mammal. The effect of pain is to help an animal avoid harm in the environment, such as extreme heat, extreme cold, bodily damage, and so forth. As social animals, we have also evolved standards of behavior that we share with other primates (see, e.g., the work of Frans de Waal) and many of us can feel pain if we do not live up to these standards. We can also feel pain if life goals (such as love and reproduction) are stymied. Pain systems are not perfect and sometimes go wrong, causing people to feel pain even in the absence of harmful stimuli (e.g., phantom limb pain). Pain is not divine retribution and needless suffering does not enoble you. There is no inherent "meaning" in suffering, although some people may find their own personal meaning through it, and some people may learn empathy through it. Through science we have found methods for alleviating pain (e.g., anaesthesia, antidepressants). I feel acutely grateful to scientists like Crawford Long and William Morton for their discoveries, which work for everyone, not just members of the same sect.

To me that is a much more satisfying explanation of pain, and it is in accordance with the facts that we see. It doesn't require positing an involved theology with magical beings for which there is no evidence. If the Christian god really wanted to alleviate pain, he could have revealed the recipe for diethyl ether in the bible. He didn't.

If I find the time I will talk about my experiences after the talk.

How I Spend My Time

I bought a desktop task timer and have been using it this year to keep track of my activities at work. Just for fun, here's how I spent last week:

12 hours: Teaching CS 365 (includes teaching, preparing for teaching, making up problem sets, making up solutions, office hours, and answering student questions)
16 hours: Teaching CS 462 (same list as above, plus marking)
5 hours: answering e-mail
3 hours: talking with graduate students
5 hours: editorial duties for the journals I edit
1 hour: miscellaneous organizational tasks
1 hour: research

Total this week: 43 hours (we are paid for 35). During a non-teaching term, I spend much less time teaching and much more time on research, refereeing, and so forth.

More Silliness about Infinity

Once again we have someone claiming that infinity does not exist in the real world, and giving Hilbert as proof. The last time it was William Lane Craig and Kirk Durston. Now it's Uthman Badar, Australian Muslim advocate:

Start watching at 1:08:12. He says,

"I agree there's no problem with infinity in mathematics or in physics or in other studies. That's not the point. There's a difference between infinity, the potential infinity as an idea and actual infinity in the real world. Don't take my word for it, here's what the mathematicians say. David Hilbert ... is a renowned mathematician of the, or was, of the 20th century after whom Hilbert spaces and Hilbert operators that are prevalent in quantum mechanics is used, he said, "The infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought. The role that remains for the infinite to play is solely that of an idea."

Kasner and Newman, contemporary renowned mathematicians: "The infinite certainly does not exist in the same sense that we say there are fish in the sea. Existence in the mathematical sense is wholly different from existence of objects in the physical world."

...
There's no way in the real world, within our sensorially perceivable naturally world within space time that infinity can exist. If it does, you end up with a whole host of contradictions. If we had an infinite number of people in the room and five have left, how much do we have? An infinite number of people! But five have left! So, there's a distinction between the idea of infinity and the ontological reality of infinity in the real world."

Krauss's response is good. First, Hilbert was not a physicist, but a mathematician; his opinion about physical reality was not definitive back in 1926, when his article was written, and it is certainly not definitive now. Hilbert provided no empirical evidence that the infinite cannot exist in nature, and these days, physicists routinely consider the possibility of various aspects of infinity in nature. Does it or doesn't it? We don't know for sure, but we can't rule it out by Hilbert-style thought experiments alone.

Second, Uthman starts with a premise like `you can fit an infinite number of people in a finite room' (not an exact quote), which nobody is asserting. Then he asserts a contradiction where none exists. Yes, it's true that if you remove a finite number of items from an infinite set, the resulting set is still infinite. Why is this a contradiction? The answer is, it's not. Infinite quantities don't behave like finite ones, so they may not match the average person's intuition, but that's not the same as a "contradiction".

God and Reason - Lecture 2

I attended the second lecture in the "God and Reason" short course given by Christian professors at my university. It was entitled, "Does God exist?" I had to leave after 50 minutes, so it is possible that I missed something important. Again, my comments in brackets below.

Once again, the lecture was given by Prof. Robert Mann of Waterloo's physics department, and again was entertaining and comprehensible. (My only criticism of the delivery concerns the misspelling and mispronunciation of the word "verisimilitudinous", which was both displayed on the screen and pronounced without the first "i".)

Prof. Mann started by talking about three aspects of belief, which he classified as credulity ("other things being equal, things probably are as they seem"), simplicity ("other things being equal, the simplest explanation is probably the most likely"), and testimony ("other things being equal, things probably are as other people report").

He backed this up with a quote from philosopher Richard Swinburne, namely, "The rational person is the credulous person who trusts experience until they find it misleads them, rather than the skeptic who mistrusts experience until they find it does not mislead them." (not sure if an exact quote)

[I don't agree with either Prof. Mann or Richard Swinburne. We know that eyewitness testimony is remarkably unreliable; humans are just not good reporters of events that they witness, especially after a long period of time has gone by. There is a huge literature on this; I just mention one paper here. It is certainly rational to be very skeptical of eyewitness testimony, especially if it is about extraordinary events.]

Prof. Mann then talked about a "knowledge bootstrap". In a "hermeneutic circle", "to understand we must first believe; to believe we must first understand". In an "epistemic circle", "knowledge is controlled by Nature; Nature is revealed by knowledge". As an example of "hermeneutic circle", he gave quarks. There is no direct observation of fractional charge, yet quarks are useful to explain sub-nuclear phenomena.

As an example of "epistemic circle", he gave wave-particle duality. Understanding, he said, requires "a mutual conformity between the act of knowing and the object of study". Strict skepticism is a limited and unfruitful strategy.

Understanding God: we need to be firm enough in our thinking so that God doesn't mean anything we want, but open-minded enough to be receptive to the counter-intuitive character of the Divine.

Attributes of God: Wikipedia lists 26, but he can boil them down to 4: God is
- ultimate, infinite
- holy
- personal, loving
- agential

[What does it mean to say a god is "infinite"? Infinite in what sense? Infinite in extent in the universe? Infinite in time? How would a loving god consign people to hideous and prolonged deaths through earthquakes, tsunamis forest fires, and so forth? Here is an example where "things probably are what they seem" points to either multiple gods, or a god that hates people.]

What kinds of proof of God could there be?
- mathematical: deduction from premises
- legal: inference from testimony
- scientific: induction from observation

Proving things in science:
Paradigm (Kuhn) - normal science means solving problems within an established framework
Falsification (Popper) - science can only rule out what is false
Anarchy (Feyerabend) - science uses whatever methods work
Research Program (Lakatos) - science proceeds by core foundations surrounded by auxiliary hypotheses

Challenge: what is at the core? what is at the periphery?

Proofs of God's existence
- cosmological argument: causes imply a causer
- intelligibility argument: nature's comprehensibility implies designer
- ontological argument
- aesthetic argument
- regularity argument
- moral argument

[Here, however, Prof. Mann just speeded through what I would consider the core part of an answer to the question "Is there a God", taking only a few seconds. More argument is needed! And you would never know that these arguments are considered extremely weak by many philosophers.]

Who or what set the boundary conditions of the universe. We have a cosmic beginning - is that suggestive of a cosmic originator?

Are we special? Is our universe a typical specimen? Are the special features the thumbprint of a Designer?

Fine tuning of physical constants: if the neutron were just 0.2% lighter, all protons would decay, so there would be no atoms. If the neutron were just 0.2% heavier, no element beyond hydrogen could form. This "fine tuning" suggests a designer.

[This kind of argument doesn't seem remotely convincing to me. We have no idea currently how universes form. Maybe there is only one universe; maybe there is only one possible universe. Maybe there are infinitely many universes. Maybe there are uncountably many universes. Maybe the constants are linked. Maybe it is possible to have life just from hydrogen alone. It seems premature to make any conclusions at all when our knowledge is so incomplete.]

It's difficult to be objective about the search for God. He quotes Thomas Nagel: "I want atheism to be true."

[Speaking only for myself, I don't have much emotional investment in whether there is a god or not. I'm not sure the concept is even coherent! I was raised as a Christian, and haven't changed my attitude on ethics very much since I discarded it. Confucius and Hillel the Elder advocated the essential ethical core before Jesus.

Having a person that you can always rely on in terms of need, who would comfort you or help you solve your problems, is certainly attractive, and I think it might be nice. But on the other hand, the Christian god as depicted in the Bible seems to me so completely depraved that the world would be a horrid place if he existed as depicted there.]

[To sum up, while the talk was entertaining, I think it would have been better to simply go through the six "proofs" he mentioned, giving their strong and weak points.]

God and Reason Course: The Dilemma

I mentioned before that four Christian professors at my university are giving a non-credit course entitled "God and Reason". I attended the first session and wrote about it here.

In thinking about this course more, I think there is a big dilemma for the instructors. All four of them are respected and accomplished researchers and scholars. But a scholar, by definition, must explore the literature both for and against any point of view. If there are arguments with some merit against your thesis, you must address them.

On the other hand, a Christian evangelical usually feels no such obligation. Their primary goal is to convert you to their belief, not to explore themes with scholarly detachment.

So, which will it be in this course? So far I am not very optimistic that scholarship will win out over Christian apologetics. For one thing, the textbook is Timothy Keller, The Reason for God: Belief in an Age of Skepticism which, at least judging from the reviews, is not an academic or scholarly text that addresses the other side fairly. Second, no opposing point of view is given as recommended reading. Third, the whole exercise is sponsored by "Power to Change Ministries". And finally, no one associated with the course is a skeptic, non-believer, or even non-Christian.

So here is a suggestion to the organizers. Live up to your obligations and reputations as scholars, and, for each session, list some suggested readings for "the other side". For example, for the next lecture, you might mention Jordan Howard Sobel's recent book, Logic and Theism: Arguments for and Against Beliefs in God, which is available here for free if you are a student or faculty member at the University of Waterloo. I could list many more.

After all, "who ever knew Truth put to the worse, in a free and open encounter?"

Weird Maple Bug

I've found a few Maple bugs over the years, but this is one of the weirdest. The same weirdness occurs in very old versions, too.

    |\^/|     Maple 15 (X86 64 LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2011
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
> (2 &^ 0) mod 3;
                                       1

> (3 &^ 0) mod 2;
                                       1

> (2 &^ 0) mod 2;
Error, 0^0 is undefined
 
> (3 &^ 0) mod 3;
Error, 0^0 is undefined

Silly Journal Accepts Silly Paper

Over at That's Mathematics! we read that another computer-generated piece of silliness has been accepted by the Journal for Algebra and Number Theory Academia. Good job, JANTA! You are now officially a Silly Journal™.

Science Books Have Errata. Holy Books Don't.

I mentioned before that four Christian professors at my university are offering a non-credit course on "God and Reason". I won't be able to attend most of the talks, because the time often conflicts with my son's soccer games, but I did get to go to the first one. Here are a few notes. You can read a different perspective here. If others blog about it, send me links!

The first surprising thing was that I arrived at the room, PHYS 150, only to find the venue had been moved to MC 4020. You'd think the organizers would have updated their flyer, but no, today it still says the old room.

After walking to the new room, I was also surprised to see the number of people there for the lecture. By my estimate, there were about 120 people, including about 20 people standing.

The first lecture was entitled, "Doesn't science disprove Christianity?", by Prof. Robert Mann of the physics department. He is a good speaker, and his talk was frequently humorous and largely easy to follow (with the exception of his strange pronunciation of "analogous"), but didn't really address the question in much detail. I summarize below, with my comments in brackets.

He started by giving an example of the question "Why is the sky blue?" as something both science and religion could answer. A scientific answer might be something like "Rayleigh scattering". A religious answer might be "God made it that way", but he doesn't find that a useful answer.

Science is about "what is", Prof. Mann claimed. It is about how things work and constitutes public knowledge. It is objective, having nothing to do with emotions or political predilections. It is about measuring and quantifying things, and constitutes an "I-it" relationship with the universe.

Faith, Prof. Mann said, is about "what ought to be". How can things be different from what they are now? It is about "why" questions, not "how" questions. For example, "Why do I have feelings of awe when I stand in front of a mountain?" It constitutes private knowledge, is subjective, and is not concerned with measuring things. It is about quality vs. quantity. It is about an "I-Thou" relationship with the universe. All religions are concerned with, "What is of ultimate value?" and "What should be the rules of how we live our lives?"

[Here Prof. Mann contradicted himself right away. On the one hand, he claimed science could not answer "why" questions; on the other, he gave as his very first example the question "Why is the sky blue?", to which he then proceeded to give a scientific answer! Furthermore, one of the most famous Christian books is Francis Schaeffer's "How Should We Then Live?" -- a question that, despite its first word, presumably is intended to be religious and not scientific in nature. I sat in on a course Prof. Mann taught some time ago, where I pointed out that this "how/why" dichotomy is almost childishly simplistic and wrong, but he continues to use it.]

[Furthermore, I would contest the claim that faith represents "knowledge". It represents "belief", to be sure, but "knowledge" seems overstating the case. How exactly can such "knowledge" (claimed to be "private" and "subjective") be tested in any meaningful way? When it is tested, we find it is wrong. Christians frequently claim, for example, that intercessory prayer is effective; yet the tests of this claim return negative or inconsistent results.]

Science and theology, Prof. Mann claimed, are cousins. They are both concerned with rationality, contingency, novelty, and incompleteness.

Rationality: why is the world rationally transparent? [I know from previous experience that Prof. Mann finds the arguments of intelligent design creationist and physicist Guillermo Gonzalez intriguing. Gonzalez's thesis is that the universe is specially designed for scientific inquiry, and the Earth is in a privileged position to make scientific inquiry possible - hence god.]

[Personally, I don't think the world is "rationally transparent". If anything, it is largely "rationally opaque" or at least "rationally translucent". Here is one example from Prof. Mann's own field. One of the very simplest physical interactions we can think about is the problem of mutual gravitational attraction among three bodies. Yet there is no closed form known for the solution to the three-body problem! We do not even know whether the solar system is stable or unstable.]

[And here is another example. Suppose, at the beginning the lecture, I introduce a single molecle of Oxygen-18 at the very center. Dividing the lecture hall into four equal sized square sections, which section will the Oxygen-18 molecule be at the end of the lecture? What could be simpler? Yet we can't answer this very basic kind of question with any certainty, because there are just too many interactions. How does that make the universe - a far more complicated system - "rationally transparent"?]

Science, Prof. Mann said, is about "reason and experiment", but faith is about "reflection and revelation". Science is about "increasing complexity" as we dig deeper. Religion is about "increasing depth". The "universe appears to be structured for endless possibilities". [I find it odd for a physicist to claim that, when the heat death of the universe is one fate that might await us -- so much for "endless" possibilities.]

Religion is about novelties - why do little things "surprise us by joy?".

Wigner spoke about the "unreasonable effectiveness of mathematics". [I'm not convinced at all by this. It seems to me that physicists are trying to model the universe, and it is not very surprising that some models work better than others. If dance turned out to be better, we'd all be exclaiming about how wonderful it is that ballet is so effective at modelling the universe. And, as above, even in the most simple cases, we quickly find limits to our mathematical description of physical situations.]

Prof. Mann claimed that when scientists worked on nuclear weapons, "most did so without considering the consequences" because it was a good scientific problem. [Not really. For one thing, it was more an engineering problem than a science problem. I've read a number of books about the Manhattan Project, and his claim does not seem to be accurate. Oppenheimer, for example, had serious misgivings about the A-bomb.]

Prof. Mann claimed that "suicide bombers are not scientifically illiterate". [Actually, I'd bet they are. Most probably could not state, for example, any of the basic results in evolutionary biology. They might have some engineering knowledge, but engineering is not the same as science.]

[Prof. Mann spent a lot of time talking about the commonalities between religion and science. But to me, it is the differences that are starker and more important. One of them I can sum up in 7 words: "Science books have errata. Holy books don't." By this I mean the following: If, let's say, we discover an error in Newton's Principia, we don't go on teaching it as if nothing happened. We correct it. If errors occur in books or papers, we routinely admit them and correct them. But when has a Christian ever said, "Well, we used to believe x in the Bible, but now we realize the Bible was wrong about x?" I'd be curious to know if Prof. Mann can name a single thing in the Bible he thinks is simply wrong.]

[Here's another important difference between science and religion. Science has accomplishments. Not only that, but scientists are largely in agreement with what those accomplishments are. Ask any scientifically literate person about the great breakthroughs of the last 100 years, and you'll get largely the same list. In physics, relativity and quantum mechanics, for example. In biology, the structure of DNA and its role in genetics. In geology, the theory of plate tectonics, and so forth. But what are the great religious breakthroughs of the last 100 years? Can Prof. Mann name even one?]

Let's hope the remaining lectures are more serious.

Open Problems

One of the nice things about teaching an upper-level undergraduate course at a university is the opportunity to mention problems at the edge of our current knowledge. For example, in my course CS 462, Formal Languages and Parsing, I currently mention 15 open problems and offer an automatic 100 in the course for anyone who can solve any one of them.

The Mathematics of Intelligent Design

Here we have a classic example of why it's hard to take intelligent design seriously.

The flagship blog of intelligent design presents a worthless piece of software, not even at the level of a bad junior-high-school science project, as an accomplishment. It `tries to answer questions like this: “a random process generating sequences of length L from an alphabet of S symbols in T trials of t seconds each, involving c chemical reactions, does exceed the resources of the universe (age, max number of chemical reactions, universal probability bound)?”'. We are told that this silly exercise "may give an idea of the numbers involved in scenarios as origin of life, production of biopolymers, binary and character text generation, and so on." Right.

The author clearly doesn't know what "random process" means (hint: it doesn't necessarily mean uniform probability). And his program doesn't take into account anything interesting about chemistry at all. It's just worthless number pushing.

Garbage in, garbage out. Come to think of it, that's pretty much the description of intelligent design.

Addendum: they've already removed the page. I guess there are some things that are so stupid, even Uncommon Descent can't get behind it. But you can still see the software here.

Addendum: it's now back again. Not much different than before, except they added a few English mistakes.

More Creationist Credential Inflation

I've written at least once before about the propensity of creationists for credential inflation.

Here is yet another example: V. J. Torley, one of the most longwinded creationists at Uncommon Descent, refers to "Dr. David Coppedge".

Coppedge, according to his profile on Linkedin, has no doctorate at all. He has a bachelor of science, secondary education, from the august institution, "Bob Jones University", in 1972, and a B. S., Physics, from California State, Northridge, 1995.

Update: Torley has now corrected his claim.

French Bigots

From today's anti-gay-marriage demonstration in Paris:

Professors Teach "God and Reason" Course at Waterloo

Reader HG points out that four professors at my university, the University of Waterloo, are teaching what is described as a "free not for credit course" at Waterloo, entitled "God and Reason".

It seems likely that this is not really an inquiry-driven enterprise, but more an evangelical one. Some evidence is that the poster says it is sponsored by "Power to Change Ministries", and the fact that there does not seem to be a single non-Christian or skeptic involved with the course. Probably students will be hearing a very one-sided presentation.

There is more detail here. I do hope the course is prepared with more care than this syllabus, which -- judging from the reference to "Shrum Science K building" which is at Simon Fraser, not Waterloo -- appears to have been copied wholesale from some evangelical boilerplate.

It would be great if some skeptical students could attend and blog about it.

The Canadian Milk Cartel

One of the really obvious differences between the US and Canada is the price of milk. In the US, you pay $3.30 or less for a gallon (3.79 liters); in Canada the price is usually something like $4.60 for 4 liters or even more.

Why? Because of a crazy marketing system controlled by the dairy industry, with government backing, that regulates how much milk you can produce. You even have to pay for the right to produce milk!

When we lived in Boston, we enjoyed Chobani Greek yoghurt. Chobani was going to build a plant in Ontario, but has been prevented from doing so by Canada's ridiculous quota system.

Canada should dump these stupid marketing boards that drive up prices for consumers and prevent innovation.

If I Had a Quadcopter

I might be tempted to do this.

Conspiracy Nuts

From reader Rob, a couple of years ago (!), an old xkcd cartoon.

Now that hardly anybody takes the 9/11 truthers seriously, it's time for them to move on to the claim that the Sandy Hook school shootings were a government plot.

The depths of insanity lurking inside the minds of crackpots is a terrifying thing.

A Spectacular Student Opportunity

The Dishonesty Institute is once again soliciting students for their summer bible camps on intelligent design.

Maybe if they get enough students, they can find some to write articles for ID's flagship journal. It's looking a bit thin these days.

I have some suggestions for article titles, but feel free to suggest more:

Why the Ducky is Different from the Horsie
C. S. Lewis or G. K. Chesterton: Which Was the Better Scientist?
Isaac Newton: the William Dembski of Physics

Another ID Icon: G. K. Chesterton

If you're an ID advocate, you have to swallow a lot of outlandish claims uncritically. I'm thinking about claims like "William Dembski is the Isaac Newton of information theory, and since this is the Age of Information, that makes Dembski one of the most important thinkers of our time".

You also have to believe that C. S. Lewis is a respected philosopher of science.

And finally, it seems that you have to believe that G. K. Chesterton had something profound to say about miracles and how those materialist scientists are just too dogmatic to accept them:

The believers in miracles accept them (rightly or wrongly) because they have evidence for them. The disbelievers in miracles deny them (rightly or wrongly) because they have a doctrine against them. The open, obvious, democratic thing is to believe an old apple-woman when she bears testimony to a miracle, just as you believe an old apple-woman when she bears testimony to a murder. The plain, popular course is to trust the peasant’s word about the ghost exactly as far as you trust the peasant’s word about the landlord. Being a peasant he will probably have a great deal of healthy agnosticism about both.
Still you could fill the British Museum with evidence uttered by the peasant, and given in favour of the ghost. If it comes to human testimony there is a choking cataract of human testimony in favour of the supernatural. If you reject it, you can only mean one of two things. You reject the peasant’s story about the ghost either because the man is a peasant or because the story is a ghost story.
That is, you either deny the main principle of democracy, or you affirm the main principle of materialism — the abstract impossibility of miracle. You have a perfect right to do so; but in that case you are the dogmatist. It is we Christians who accept all actual evidence — it is you rationalists who refuse actual evidence being constrained to do so by your creed.
But I am not constrained by any creed in the matter, and looking impartially into certain miracles of mediaeval and modern times, I have come to the conclusion that they occurred. All argument against these plain facts is always argument in a circle. If I say, “Mediaeval documents attest certain miracles as much as they attest certain battles,” they answer, “But mediaevals were superstitious”; if I want to know in what they were superstitious, the only ultimate answer is that they believed in the miracles. If I say “a peasant saw a ghost,” I am told, “But peasants are so credulous.” If I ask, “Why credulous?” the only answer is — that they see ghosts.

Chesterton apparently believed that you have to "trust the peasant’s word about the ghost", and if you don't, then you "deny the main principle of democracy". It looks like Chesterton knew even less about democracy than he knew about science.

For one thing, in democratic societies we don't usually talk about "peasants". But even if you replace "peasant" with "average person", there's no principle of democracy that says we need to "trust the average person" when the average person makes an outlandish claim. Democracy is about letting people elect their own government, not assuming that the average person is necessarily extraordinarily competent when it comes to evaluating scientific evidence or witness testimony. Would Chesterton have insisted that we need "trust the peasant" when he walks into the operating room or the cockpit and takes over?

Those dogmatic scientists have looked into miracles and other claims of the paranormal. Over and over, it turns out that those events had completely rational explanations. Perhaps not every claimed paranormal event will be resolved definitively, but there certainly is a pattern.

We know that the average person is a poor eyewitness, and that eyewitness testimony is not reliable. We know that people lie, especially when there are motivations like profit, personal image, and religion. We know that pure democracies are subject to the whims of the moment and to mob rule, which is why the US's Founding Fathers chose to establish a republic with elected representatives, and not to decide every issue by popular vote.

And finally, we know that Chesterton is a good icon for the ID movement: bloated, pompous, science-ignorant, but full of misplaced confidence that he's "impartial" and that he can reason better than those stupid materialists.

No Formula for the Prime Numbers?

I have seen the assertion "there is no formula for the prime numbers" over and over again mathematics books. To give just a few examples, here is p.235 of Charles Hutton's A Philosophical and Mathematical Dictionary, Volume 2, from 1815:

The Encyclopaedia Londinensis, from 1820, gives a discussion of the sieve of Eratosthenes, and then proceeds to deny it gives a formula:

It's not just old books that make this claim. For example, in Bello et al., Topics in Contemporary Mathematics, 2007, the authors state

Of course, there are formulas for prime numbers; for example, there is Willans' formula from 1964: Let F(n) = [ cos² π ((n-1)! + 1)/n ] where [ ... ] denotes the greatest integer function. Then for n ≥ 2, F(n) = 1 iff n is a prime.

Why this doesn't constitute a legitimate formula is anyone's guess, since it uses fairly standard and familiar functions from number theory. But then "formula" has no rigorous definition in mathematics and hence the claim about "no formula for the prime numbers" can't really be addressed until the definitions are made more precise.

Other books refine the claim, saying instead that there is no useful formula for the primes. Of course, the term "useful" is not defined, either. For example, David Wells writes in his 2011 book, Prime Numbers: The Most Mysterious Figures in Math

Well, how could one prove that "a formula is impossible" without giving a more rigorous definition? Yes, it's true that no nonconstant univariate polynomial can take only prime values, but is that really the only kind of formula one would allow? In that case, there is no formula for sine or cosine or exponentials, either!

Writers from the 18th century didn't know about Turing and computability theory, and modern computational complexity theory, so they have an excuse. More modern writers don't. If a "formula" for something means anything at all, it means that the something is computable and the prime numbers are certainly that. (Although I once had the strange obligation of convincing an author of popular math books that it was possible to write a program to compute prime numbers. This author initially denied it was possible, but after an exchange of three or four letters he finally agreed.)

And if a "useful formula" means anything at all, it means what Herb Wilf said it means: that the time to compute the nth object by your useful formula should be an asymptotically negligible fraction of the time to list all n of them. In that sense, also, there is a "useful formula" for the primes -- Lagarias, Miller and Odlyzko showed quite a while ago that the nth prime can be computed in about n^½ time.

Can it be done in time polynomial in log n? Nobody knows. Now that's an interesting question. Let's use the language of modern complexity theory to address the really interesting questions about primes and computation, and finally put to rest the silly and embarrassing "no formula for the prime numbers" claim.

The Strangest McDonald's

This has got to be one of the strangest McDonald's I've ever been in: the McDonald's at Praça da República 13-14 in Coimbra, Portugal.

Partially hidden behind the staircase is a large anti-capitalist mural by local artist Vasco Berardo, depicting the rich being trampled underfoot (you can see their champagne glasses dropping out of their hands) by virtuous peasants and miners.

Waterloo Region from Space

Here's Waterloo region from space, courtesy of astronaut Chris Hadfield and the ISS.

Friday Moose Blogging

What to do when your moose population is too inbred? Why, set up a way for those single moose to mingle.

As Woody Allen once said, "The moose mingles. Did very well. Scored."

Hat tip: Anna.

The Evangelical Worldview is Very Fragile

So fragile that it can be challenged by a university education. That's why you have to read evangelical propaganda and study with Christian apologists.

I can guess the title of one book that's not on the curriculum in Doug Groothuis's courses: The Scandal of the Evangelical Mind, by Mark Noll.

Canadians are Breathing Easier

The US has Fort Knox. Canada has the strategic maple syrup reserve.

Canadians are now relieved that arrests have been made in the great maple syrup heist.

Wrong Mathematics in a Jack Reacher Novel

Lee Child is the author of the popular Jack Reacher thriller novels. He's probably going to get a lot more attention soon, now that the first Jack Reacher movie is headed for release next week.

Five years ago, I discussed some mathematics in Bad Luck and Trouble. I complained that suddenly, a new characteristic of Reacher was unveiled: he was a gifted mental calculator who could determine the primality of numbers quickly, and he was interested in properties like 'square root of n equals sum of n's base-10 digits'.

Now, in the new Reacher novel, A Wanted Man, Child returns to this numerological interest of his main character. First, Reacher is thinking about automorphic numbers: these are positive integers n such that n² ends in the same base-10 digits as n.

Then (on page 64), Reacher is thinking about 81, and he "muse[s] about how one divided by 81 expressed as a decimal came out as .0123456789, which then recurred literally forever, 0123456789 over and over and over again..."

The problem? That's not the decimal expansion of 1/81. It's actually 0.012345679012345679012345679012345679012345679012345679012345679 ..., where the period of the expansion is 012345679 and not 0123456789. The "8" is missing! The reason for this is not so surprising, and generalizes easily to the expansion of 1/(n - 1)² in base n.

A savant like Reacher, who can determine the closest prime to a randomly-chosen 6-digit number in a matter of a few seconds, would not have made such a silly mistake. Maybe Lee Child needs a mathematical consultant for his next novel. Hey, I'm available.

John Baird - Hypocrite

John Baird is a Canadian MP and the Minister of Foreign Affairs in the Harper government.

Back in May, he gave a speech at the "Religious Freedom Dinner" in Washington, DC, in which he decried persecution of religious people, but said not a single word about the very real persecution of atheists and other non-religious people around the world.

But it's even worse than that. He actually repeated the tired, old claim that "We know that freedom of religion does not mean freedom from religion."

But freedom of religion, if it means anything, must include the right to practice no religion at all.

Baird is a hypocrite.

A Christmas Song by My Father

Here's a Christmas song written by my father in 1966. The music was written by my brother, Jonathan Shallit, at age 14. Not surprisingly, my brother went on to become a professional violinist and music professor.

The Gift.

I guess my father liked the tradition of Christmas songs written by Jewish guys.

The Sterility of Intelligent Design

One thing that separates pseudoscience from science is fecundity: real science takes place in a social context, with an active community of scholars meeting and exchanging ideas. The ideas in one paper lead to another and another; good papers get dozens or hundreds of citations and suggest new active areas of study.

By contrast, pseudoscience is sterile: the ideas, such as they are, lead to no new insights, suggest no experiments, and are espoused by single crackpots or a small community of like-minded ideologues. The work gets few or no citations in the scientific literature, and the citations they do get are predominantly self-citations.

Here is a perfect example of this sterility: Bio-Complexity, the flagship journal of the intelligent design movement. As 2012 draws to a close, the 2012 volume contains exactly two research articles, one "critical review" and one "critical focus", for a grand total of four items. The editorial board has 30 members; they must be kept very busy handling all those papers.

(Another intelligent design journal, Progress in Complexity, Information, and Design, hasn't had a new issue since 2005.)

By contrast, the journal Evolution has ten times more research articles in a single issue (one of 12 so far in 2012). And this is just a single journal where evolutionary biology research is published; there are many others.

But that's not the most hopeless part. Of the four contributions to Bio-Complexity in 2012, three have authors that are either the Editor in Chief (sic), the Managing Editor, or members of the editorial board of the journal. Only one article, the one by Fernando Castro-Chavez, has no author in the subset of the people running the journal. And that one is utter bilge, written by someone who believes that "the 64 codons [of DNA are] represented since at least 4,000 years ago and preserved by China in the I Ching or Book of Changes or Mutations".

Intelligent design advocates have been telling us for years that intelligent design would transform science and generate new research paradigms. They lied.

Should Barbers Have the Right to Refuse Service to Women?

Should barbers have the right to refuse service to women?

Rex Murphy and George Jonas think so.

But it's not so clear to me. After all, discrimination in employment, housing, and even public accommodation like hotels is outlawed. Why should be it different for services like getting haircuts?

Does the reason for declining to cut the woman's hair matter? Would it be different if the barber pleaded incompetence at cutting women's hair, or if he did for the reason he stated: his Muslim beliefs prevent him from servicing women? How about if he refused to cut the hair of Jews, or blacks? Would that be more or less acceptable?

Tal Pinchevsky, "Breakway"

I'm a big fan of escape literature -- not escapist literature, but literature about clever escapes from prison camps and totalitarian regimes. So I approached Tal Pinchevsky's new book, Breakway, with some anticipation. It's the story of hockey greats from behind the Iron Curtain who gave up their homelands to play in the NHL: people like the Stastny brothers, Petr Klima, and Sergei Fedorov.

Of course, these players didn't have to endure anything like the conditions of World War II POW's, and the contracts they got when they arrived gave them unprecedented riches, which they sometimes squandered on alcohol. So I don't really have much sympathy for them to begin with.

Nevertheless, some of the stories are interesting and, not being a hockey fan, I hadn't heard any of them before. Unfortunately, the writing is not very good and the editor didn't bother to fix the problems: misspellings, sentence fragments, and run-on sentences can be found throughout.

Bottom line: 2.5 stars out of 5, suitable mostly for hockey fans.

Waterloo Ignorance Day

Today is Waterloo Ignorance Day!

No, it's not a day devoted to Michael Egnor: that would be Egnorance Year (or perhaps Egnorance Lifetime).

Instead, you'll hear 10 15-minute talks centered around the theme of "What I Wish I Knew about the Mind, Brain, and Intelligence".

One thing I can guarantee you won't hear is nonsense like this, from Ed Feser:

"Thoughts and the like possess inherent meaning or intentionality; brain processes, like ink marks, sound waves, and the like, are utterly devoid of any inherent meaning or intentionality; so thoughts and the like cannot possibly be identified with brain processes."

Only a creationist (like V. J. Torley)* could be so utterly moronic. While Feser and his friends are declaring it impossible, real neuroscientists and neurophilosophers are busy figuring it out.

* Feser seems to think I was calling him a creationist, and on re-reading I understand how he could think that. By "creationist" I intended to refer to the person who quoted Feser and thought Feser's claim deserved quoting. Clearly, though, I was wrong: there are people who are even more moronic than creationists. I apologize for the lack for clarity, and I apologize to creationists for this undeserved association with Feser.

Santorum Joins World Net Daily

As Ed Brayton would say, this is comedy gold: Rick Santorum is going to write a column for World Net Daily!

I can't think of a columnist and a website more suited to each other. We can look forward to four years of utter insanity.

My Unremarked Remarks at Eschaton

At Eschaton 2012, I was asked to appear on a panel about "skeptivism" - a word I'd never heard before, but apparently means "skeptical activism".

I don't know anything about being an "activist", but I prepared some remarks anyway. Then, when it came time for the panel, people were more interested in asking Sara Mayhew and me questions about our talks, so that's the way it went.

Since I prepared these, this is as good a place as any to record them:

1. It pays to complain. (title of a recurring column in Freethought Today): when you see church-state violations, or creationism in the public schools, or silly pseudoscience or outright scams, complain! Write a letter to the editor, or e-mail to the school board, or report scams to the police. You'd be surprised how much mileage you can get out of a single complaint.

2. Adopt your own style. You don't have to destroy a communion wafer to reach people. If you're comfortable with a more confrontational style, that's fine, but if you're not you can still have an effect.

3. Be scrupulous. You don't have to adopt the tactics of creationists. If you cite a quote, check it out first to make sure it's authentic. If you make a mistake, admit it. "Always do right," Mark Twain said, "This will gratify some people, and astonish the rest."

4. Ask hard questions. If your local elected representative has a meeting, go and ask how old he or she thinks the earth is. Ask their opinion of evolution and global warming. If they say something stupid, you can say "You are aware, I assume, that the scientific consensus is uniformly against you?"

5. Don't pay any attention to foolish detractors, whether they're atheists or not. No matter what you do, there will be critics; the "old school" of atheists like R. Joseph Hoffman are sometimes the silliest of all. Listen to people that have something valuable to contribute and ignore the rest.

6. Learn to be a good speaker. Record yourself and watch it. Watch videos of good speakers, such as Christopher Hitchens, and try to learn from them.

7. Know what you're getting into. Depending on where you live, speaking up might cost you your friends, subject your to attacks on you and your property, or get you fired. Choose your battles wisely! Not everything is worth your job.

Eschaton 2012

Had a great time at the Eschaton 2012 conference in Ottawa this past weekend.

Larry Moran exposed the appalling stupidity of the Discovery Institute and everybody laughed at them.

P. Z. Myers gave a good introduction to incomplete lineage sorting and coalescent theory for a general audience, and he explained why it is not at all surprising that part of the gorilla genome is closer to humans and chimps than humans and chimps are to each other. Along the way, Casey Luskin was exposed as a fool or a liar. Everybody laughed again.

P. Z. Myers talked about Canada's "neighbor to the south", but little did he know that his hometown Morris, Minnesota is actually north of Ottawa!

And here's my talk on numerology, if you're interested.

Congratulations to the Watsons and to CFI for a well-run conference!

I'm Really Glad Steve Fuller is on Their Side

If you are having trouble sleeping, this video of Steve Fuller prattling on and on and on while not saying very much at all is just the thing for you.

Fuller thinks that what the intelligent design movement really needs is another creationist geology book. And he thinks that Dembski is updating Shannon on information theory. (That'll be news to everyone who actually does information theory.) I'm really glad that Fuller is the intelligent design movement's favorite philosopher. Imagine the damage he could do if he were on the side of science and reason!

"Says You" in Syracuse

I finally got to attend a taping of one of my favorite radio shows, "Says You", in Syracuse, New York. That's host Richard Sher at the top, and at the bottom you see panelists Tony Kahn, Lenore Shannon, and Tony Horwitz conferring on a question. The other panelists that night were Carolyn Faye Fox, Arnie Reisman, and Paula Lyons.

Although the show is one of my favorites, I have to admit it was not as good or funny as shows in the past. They sometimes play old shows or highlights from old shows, and you can hear the difference: they used to have lightning-fast wordplay and deductions, and lately they've been slipping a bit. Maybe they need some new blood: some younger panelists.

By the way, if you want to listen to the show, you either have to pay for it, or listen to it live on Saturday or Sunday on your local NPR station, or over the internet.

Do you have some favorite radio shows that you listen to over the internet? If so, give links in the comments.

I Definitely Do Not Recommend This "Book" About Me

On ebay, for only $86.08 you can buy this "book" about me. But I don't recommend it.

This is the usual scam where someone advertises a book that consists of nothing but reprints from freely-available web pages, and then prints a book on demand if someone is stupid enough to buy it.

The same "author" has written 6000 other books.

Monckton Spoke at U. Western Ontario ?!?

I don't know how I missed this.

Believe it or not, the Department of Applied Mathematics at University of Western Ontario, located in London, Ontario, invited the loony Christopher Monckton to give a prestigious invited lecture, the Nerenberg lecture, last March. Previous speakers included Roger Penrose.

In addition to being a pompous twit, Monckton is famous for global warming denial and, in his latest schtick, claiming that Obama's birth certificate is fraudulent.

My source tells me that the invitation to Monckton came from Chris Essex, professor of the department, and another global warming denier. Most of the Department boycotted the talk, I was told.

If anybody attended the talk, I would like to hear about it. This is really a disgrace.

Chili Colorado

I made chili colorado from this recipe tonight. It took about three hours. The sauce was too liquidy for my tastes; next time I will add some flour to thicken it. Do you have a better recipe?

The Kurt Mahler Archive

Thanks to the hard work of Jon Borwein, Yann Bugeaud, Michael Coons, and the late Alf van der Poorten, there is now an online archive of the works of the number theorist Kurt Mahler. This is a great resource for mathematicians and more initiatives like this are needed.

I'll just mention one open problem from Kurt Mahler's last paper: what are the positive integers n, not divisible by 7, such that n² has only digits 0 and 1 when expressed in base 7? The only examples known are n = 1 and n = 20. There are no other solutions with n < 1.67 · 10¹¹.

Waterloo's Dubai Campus Fails, As Predicted

In 2009, despite protests from faculty, the University of Waterloo opened a campus in Dubai.

Now, just three years later, it is closing. Big surprise there. Administrators were warned that it was unlikely to succeed, and if I remember correctly, our School of Computer Science voted against it. There was a lot of opposition to setting up a campus in a place with little protection for free speech and a free press, as well as violations of women's rights and gay rights.

By the way, the article in the Record I pointed to above is the typical shoddy job done by local reporter Liz Monteiro. There is nothing about how much this failure has cost the University (if anything), nor any interview with anyone originally opposed to the campus, nor any investigation of why the campus was set up to begin with. This is not good journalism.

Elections Past

A few buttons from our family collection.

Greedy Millionaire Loses

Last night a greedy millionaire lost an important election vote.

No, I'm not talking about Mitt Romney. I'm talking about a little-noticed ballot measure -- little-noticed, that is, if you don't live in Ontario or Michigan.

Believe it or not, one of the most important crossings between Canada and the United States -- Ambassador Bridge -- is privately owned by a guy named Matty Moroun. For years people have wanted another bridge, because the existing one can't support the traffic. Canada has even offered to pick up all the cost of the new bridge, so it will be essentially free for the US.

Moroun can't stand the competition, and he's tried in every possible way to block the new bridge. Who cares if the bridge will benefit millions of people on both sides of the border? The only thing that matters is Moroun's profit.

He spent $33 million to back a statewide ballot measure intended to block the bridge, but lost badly, 60% to 40%.

Maybe now this important bridge will get built.

Most Americans are Not Crazy

It was a good election. Serial liar Romney, a man completely devoid of honesty, principles, and integrity, was convincingly defeated. I wasn't completely happy with Obama, but he was so much better than the alternative.

Nearly all the crazies lost: Allen West, Connie Mack, Todd Akin, Joe Walsh, and Richard Mourdock. Unfortunately it looks like we are still stuck with Michele Bachmann. And Judge Roy Moore won election in Alabama. Alabama secures its reputation as the worst place to live in the US.

Elizabeth Warren, who was the subject of nasty attacks about her native American heritage, easily defeated Scott Brown. Brown was not nearly as extremist as depicted by Democrats, but he was in the wrong state. He would have been a decent candidate for a state like Indiana or Pennsylvania, but not Massachusetts.

Maine and Maryland legalized same-sex marriage. Minnesota turned down a bid to change its constitution to prevent same-sex marriage. And Washington voters have apparently approved a law allowing same-sex marriage.

Two states legalized marijuana. This may be the start of a sane drug policy.

The mathematical illiterates who were skeptical of Nate Silver were proven wildly wrong. Silver's predictions were basically completely correct.

As predicted, crazies like Doug Groothuis are apoplectic. Groothuis raves as follows: "American [sic] does not know how to think, has no moral or political principles worth having, is manipulated by images and slogans, does not fear the idol of the State does not give a rip about unborn children; we will be taxes [sic] for their murders, does not believe in its own God-given greatness."

The dishonest Charles Krauthammer was raving about the "nationalization" of health care under Obama. Krauthammer is a liar. If you want to see nationalized health care, go to Britain. Obamacare isn't even close to "nationalization"; it's a timid initiative that maintains the status quo in almost every health care aspect except insurance. Bush's prescription drug benefit was a much bigger change.

Americans proved that the majority was not racist and was not fooled by pandering. That's a very good sign.

My Talk at the APL@50 Conference

Yesterday York University hosted a 1-day conference entitled "APL@50", to celebrate the 50th anniversary of the publication of Kenneth Iverson's book, A Programming Language. This book, and the subsequent implementation of APL, eventually won Iverson the Turing award in 1979.

Here are my slides for the talk.

I said a lot of things that were not on the slides. In particular: "More foolish things have been said about APL than any other programming language, and Edsger Dijkstra was one of the biggest offenders."

In addition to the talks, there were some really nice displays from the collection of the York University Computer Museum. For example there was an IBM 5100 APL machine (one that I spend several years programming as an undergraduate), and an MCM APL machine.

We also saw a short film by Catherine Lathwell, who is working on a full-fledged documentary about APL.

At a panel we were asked to summarize what APL meant to us. I said something like the following: APL taught us that a good notation is half the battle. Computing is ultimately about insight, and a system that encourages experimentation and variation is one that can be used to treat mathematics almost as if it were an experimental science.

Thanks to Zbigniew Stachniak and Catherine Lathwell for organizing this.