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.