Alan Cobham

Alan Belmont Cobham (b. November 4 1927, San Francisco) is a mathematician and theoretical computer scientist. He was an undergraduate at Oberlin College and the University of Chicago, and later went on to do graduate work at both Berkeley and MIT, although he never got a Ph. D. He worked at IBM Yorktown Heights, and for a while was chair of the computer science department at Wesleyan University in Middletown, Connecticut. He still lives in Middletown. I recently had a chance to talk briefly with Alan Cobham at his home, and took the picture above.

He is known for several achievements. He was one of the first people to bring attention to the complexity class P, in a paper entitled "The intrinsic computational difficulty of functions", where he proposed studying the functions computable in polynomial time.

In 1969, he wrote the first of two papers on what are now called "automatic sequences" (he called them "uniform tag sequences"). An automatic sequence (a_n) is one in which the nth term can be calculated by expressing n in some base k, feeding it into a deterministic finite automaton, and then looking at the state reached at the end. An output function converts the state name into (a_n). In this paper Cobham proved a subtle and beautiful result: if a sequence is generated by two automata that accept inputs expressed in multiplicatively independent bases, then it is ultimately periodic. There is still no really simple proof of this result.

In 1972, he wrote a very influential paper entitled "Uniform tag sequences", where the theory of automatic sequences was developed in great detail. This paper has led to hundreds of others exploring the theory of automatic sequences and generalizing them.

I Won't Be Going to This Cafe

Two women sharing a kiss got told off by the owner of the 1842 Cafe in Waterloo, Ontario. Well, I guess I won't be buying anything from that place when I return to KW from my sabbatical.

Protons, Proteins - What's the Difference?

NPR's science reporter Nell Greenfieldboyce just now (2 PM EST, March 30) referred to the Large Hadron Collider sending "beams of proteins whizzing around a 17-mile circular tunnel, then smash[ing] them together at high speed, creating a shower of debris". I sure hope that was just a slip of the tongue. Any science journalist who doesn't know immediately what the difference between a proton and protein is, and why the LHC would be smashing the former and not the latter, doesn't deserve a job.

Economist is the New Messiah, Cult Says

Here's a funny article about Raj Patel, an economist who appeared on the Colbert Report and is now being proclaimed as the new Messiah by a religious cult.

I thought the Brits knew that Eric Clapton is god?

Freedom of Expression: Canada vs. Texas

The president of Tarleton College in Texas has a stronger commitment to free speech than the vice-president of the University of Ottawa.

This is one of the worst things about living in Canada.

Mathematical Genealogy

The Mathematics Genealogy Project records Ph. D. mathematicians and their thesis supervisors. Recently they've relaxed the "thesis supervisor" to include advisors of various sorts, which allows them to extend their records back to the Middle Ages.

Of course, I couldn't resist looking at my own record. (It's incomplete; they don't list 2 of my Ph. D. students.) Some of my supervisory ancestors include:

Saunders MacLane - 3
Hermann Weyl - 4
David Hilbert - 5
Felix Klein, Georg Frobenius, Lindemann - 6
Kummer, Weierstrass - 7
Jacobi, Dirichlet - 8
Fourier - 9
Gauss, Lagrange, Laplace - 10
Euler - 11
Leibniz - 14
Huygens - 15
Mersenne - 17
Copernicus - 23

Here the numbers indicate the number of links it takes to get to that person. Assuming that each student has shaken the hand of their supervisor, I find it neat to think that only 23 handshakes separate me from Copernicus. Of course, I'm not very special in this regard, as lots and lots of mathematicians have illustrious forbears. The database, for example, currently lists 53,775 descendants for Copernicus, or about 38% of all the people listed.

My wife's tree might even be more prestigious. She's got Newton at level 14, and Galileo at 17.

Everything in its Proper Place

Tony McManus sent along this picture from the Chapters bookstore in Waterloo, Ontario, showing that at least some bookstores recognize a charade when they see one.

Take That, Bob Dylan!

I had a nice time with Celtic guitar superstar Tony McManus last night. Tony revealed that two of his pieces will be in the new Neil Jordan film, Ondine.

He also told the following story: a guitarist he knew recently died and was buried in a Jewish cemetery in Newton. His epitaph reads, "Times were sometimes tough, but at least I never made a Christmas album."

Boehner's Ridiculous Rhetoric

I have mixed feelings about the healthcare bill, but Boehner's hyperbolic rhetoric on the House floor last night was simply ridiculous:

"Today we stand here amidst the wreckage of what was once the respect and honor that this House was held in by our fellow citizens."

And just when was the House viewed with "respect" and "honor"? Was it when Joe Wilson yelled "you lie!" during Obama's speech? Or, for a bipartisan example, was it when disgraced federal judge Alcee Hastings was elected to that august body?

"We have failed to reflect the will of our constituents."

Duh - there's a reason why we elect our representatives instead of deciding everything by referendum. It's so that our representatives can do what they think is right, not what will appeal to the emotions of the moment. Besides, polls show wide support for the main provisions, even if people think they oppose the bill as a whole.

"They’re disgusted, because they see one political party closing out the other from what should be a national solution."

Actually, the bill had over 200 Republican amendments. It's not the Democrats' fault if the Republicans are bent on opposition and obstruction at all costs.

"Around this chamber, looking upon us are the lawgivers – from Moses to Gaius, to Blackstone, to Thomas Jefferson.

By our action today, we disgrace their values.

We break the ties of history."


Providing healthcare to more people disgraces the values of Moses? Who knew?

"It is not too late to begin to restore the bonds of trust with our Nation and return comity to this institution."

Yeah, and it's not too late for Republicans - like Randy Neugebauer (R-Texas) - to stop yelling "baby killer" at Stupak.

When to Doubt the Science Bashers

Former DI flack Jay Richards has a piece over at the American Enterprise's "journal", giving 12 reasons why you should stick your fingers in your ears and say "Na, na, I can't hear you!" when there is strong scientific consensus. So, in the spirit of that piece, let me offer a few reasons why you should doubt the doubters:

1. When the deniers have little or no scientific training. Richards has "a B.A. with majors in Political Science and Religion, an M.Div. (Master of Divinity) and a Th.M. (Master of Theology), and a Ph.D. (with honors) in philosophy and theology from Princeton Theological Seminary."

2. When the deniers worked for groups, such as the Discovery Institute, who have a history of prevaricating, dissembling, and just flat out lying.

3. When the deniers publish their supposedly scientific books with publishers devoted to far-right political screeds.

4. When the deniers have held appointments at so-called universities that advertise "biblically centered education" and offer courses in scientific apologetics designed to "demonstrate the harmony between science and a biblical worldview".

5. When the deniers claim that the very existence of a scientific consensus is a reason to doubt the consensus.

6. When the deniers are well-funded by groups that stand to lose a lot of money when action is finally taken.

7. When the deniers post their claims on web pages that don't allow comments.

8. And finally, when the evidence is strongly against the deniers.

Turkey!

This is the turkey I met walking down the street today - here in Newton, Massachusetts, a suburb of Boston. Any resemblance to a Discovery Institute fellow is purely coincidental.

The 2010 Bernoulli Trials

Here's a copy of the 2010 Bernoulli trials, a contest held annually at the University of Waterloo and open to all undergraduates. The students were given 13 statements and had to decide the truth or falsity of each one. Two incorrect answers and you're out. (For some previous years, see here.)

I like many of these questions, and a couple of them made me think for a while. How many can you do? Go ahead and post solutions in the comments, if you feel like it.

Loftus vs. Wood: An Atheist-Theist Debate

Here's a link to a debate entitled "Does God Exist?", featuring David Wood (theist) versus John Loftus (atheist).

I wasn't impressed at all with Wood's argument, which went roughly as follows:

1. He claimed that "Atheists have held that the Universe is eternal ... Much to the horror of atheists, research in the 20th century showed that the Universe is expanding, and we can therefore trace its development back to a beginning."

I think this misrepresents the case. Some physicists supported a steady-state universe (and some few still do), and some opposed it. But I see no evidence that atheists came down overwhelmingly on one side or the other. And I see no evidence today that atheists regard the Big Bang theory with "horror". Why should we? The Big Bang doesn't imply a magical creator.

2. He claimed that "Either the Universe began to exist as the result of some cause, or the Universe sprang into existence uncaused. The second alternative is obviously absurd - out of nothing, nothing comes."

Not much of an argument. First, we see apparently uncaused events all the time in radioactive decay. When a particular Americium atom decays in your smoke detector, what causes that one to decay rather than some other one? Nothing that we know. Second, even in a vacuum, virtual particles come into existence all the time and are measurable. So appealing to naive folk wisdom like "out of nothing, nothing comes" when modern physics contradicts this --- it's not intellectually honest.

3. He gave an argument about fine tuning. "These numbers [constants of physics] could have had a wide range of values, and yet the values they actually have fall into the extremely narrow range that makes biological life possible."

How does Wood know that the constants of physics "could have had a wide range of values"? Answer: he doesn't - it's just an assertion. Maybe because of something about physics we don't know, only a narrow range of constants is possible.

How does Wood know that tweaking the constants would usually result in an unlivable universe? Answer: he doesn't. Vic Stenger has modeled universes where the constants can change, and found that a relatively wide range of constants still allowed interesting physics.

How does Wood know that tweaking the constants couldn't result in some other completely different form of life? Answer: he doesn't.

4. He argued that the complexity of biology implies a Designer: "Where did Earth's diverse biological complexity come from? The most obvious explanation is design."

Yes, that may have been true before 1859, back in the day when our ideas about biology were so primitive that many physicians rejected the germ theory of disease. But a lot has happened since then, much of it due to another D-word: Darwin. We now have a strongly-supported theory that can account for biological complexity -- the theory of evolution -- so to pretend that we must stick with the "obvious explanation" 150 years later is dishonest.

5. He claimed that consciousness requires a "soul". "I can have a thought about a grilled cheese sandwich - I can't have a pattern of molecules about a grilled cheese sandwich".

Why not? I see no logical or physical problem in maintaining that I can have a thought about a grilled cheese sandwich and that this thought ultimately reduces to matter and energy in my brain. Much of Wood's argument seemed like this: pure assertion.

"If a scientist examines my brain he might learn all kind of things about my brain that I don't know, but he'll never learn more about my mind than I know."

Why not? What logical or scientific principle would prevent us, for example, from being able to access the subconscious through a physical examination of the brain, resulting in knowledge of (say) a repressed memory that you don't "know" consciously?

6. "We know scientifically that the mind can function even when the brain stops working. There are numerous cases in medical journals of people who are clinically dead, showing no brain activity at all, being brought back to life and reporting that they had conscious experiences while they were dead."

Near-death experiences typically occur during medical crises, when (for example) the brain might be starved of oxygen. If we don't consider the testimony of drunk people reliable, why should we consider the testimony of oxygen-starved brains as reliable? Claims about near-death experiences have been exaggerated and research has been plagued by poor experiment design; see the chapter by Hövelmann in the Skeptic's Handbook of Parapsychology.

7. Naturalism must be able to account for the coherence of human reason: "According to John, our ability to reason is the product of natural selection acting on random mutation ... Does this give us any basis for trusting our reasoning ability when it comes to questions of theology or philosophy or science?"

Here he's stealing - without attribution - C. S. Lewis's argument against naturalism, which has also been argued by Plantinga and others. I find this argument one of the dumbest around. Study after study shows that humans are not always good reasoners: we routinely mishandle basic probability, we make snap judgments based on appearances, and we have unconscious biases. But there's also good empirical evidence (like the existence of spaceships and toasters) that we somehow manage to muddle along and figure things out much of the time. We're simply stuck with the reasoning ability we have, and the heuristics -- known as science -- we've deduced over thousands of years to make sure that our conclusions are correct. It's not like religion comes up with conclusions that we can have confidence in. Which would give you more confidence in a plane never flown in the air before: calculations and simulations by trained engineers, or the blessing of a priest?

8. "Our reasoning is governed by certain logical truths ... we are presupposing that there are logical absolutes - rules of reasoning that cannot be violated... A statement cannot be both true and false at the same time. But what are logical laws? They are not material objects. We don't learn about them through the senses... Logical laws don't depend on human minds. The law of non-contradiction was true before there were any human beings, and if all human beings died tomorrow they would still be true. In fact, the laws of logic would be true in any universe, not just ours. So the laws of logic transcend time, space, matter, and all human minds - they're invariant, unchanging, and eternal."

Spoken by someone who has clearly never heard of multi-valued logic. And is the axiom of choice true or false? When Wood says "the laws of logic would be true in any universe, not just ours", how does he know this? Does he have intimate knowledge of other universes?

In the clever words of philosopher Tim Kenyon, there aren't laws of thought. It's more like "municipal by-laws" of thought.

I might add that Wood gave us no reason to believe that there aren't multiple gods, or even infinitely many.

Unfortunately, Loftus' performance was not very impressive either. Although he made a lot of good points, he read his opening presentation from notes, mumbled too much, stumbled over pronunciations (like "plate tectonics"), made too many joking asides that weren't funny and chuckled at them, sounded a bit patronizing, didn't really connect with the audience, and didn't consistently offer strong rebuttals to Wood's points.

Don't Cite Works You Haven't Read

It's something you teach your graduate students: Don't cite works you haven't read.

It's a rule with good reasons behind it. First, it's a bad idea to rely on someone else's summary of another work. Maybe they summarized it incorrectly, or maybe there is more there you need to consider. Second, as a scholar, it's your obligation not to spread misinformation. Maybe the page numbers or the volume are given incorrectly.

Like all rules, there are occasional exceptions. Maybe it's a really old and obscure work that you've tried to get a copy of, but failed. In that case, you can cite the work but mention that you haven't actually been able to find a copy. (I've done this.) That way, at the least the reader will be warned that you're relying on someone else's citation.

And now, from Paris, comes a spectacular case of why citing works you haven't read is a bad idea. The French philosopher Bernard-Henri Lévi has been caught citing and praising, in his new book De la guerre en philosophie, the work of the philosopher "Jean-Baptiste Botul". Only problem? Botul doesn't actually exist. He is the creation of journalist Frédéric Pagès.

Now, maybe Lévy did actually read Botul's book La vie sexuelle d'Emmanuel Kant. But if so, despite the big warning signs (Botul's school is called "Botulism") he failed to recognize it as a big joke, which raises even more questions about his perspicacity.

Maybe I need to tell my graduate students another rule: Don't cite works that you suspect may be a hoax.

Oh, and for the record? I haven't read Lévi's new book, nor Pagès's satire.

Reply to Paul Nelson

Glenn Branch has kindly pointed out that Paul Nelson thinks that my counterexample to the claims in Meyer's Signature in the Cell is a "fluffy confection" and "sophistry".

Recall that Meyer claimed that only minds can create information. I gave a simple counterexample: weather prediction. Meteorologists gather the information needed to make their predictions from the natural world - things like wind speed, wind direction, temperature, and so forth - and then use this information to make their predictions. Nelson is unconvinced. But his reply is unconvincing.

Nelson starts by claiming that you can't determine quantities like barometric pressure and temperature without looking at a measuring instrument. This is both (a) false and (b) not relevant. Nelson must spend all his time indoors, because I can (and do all the time) estimate the temperature quite accurately (typically within 2-3 degrees C) just by sticking my head out the door.

Next, Nelson claims that you can't predict the weather accurately without a complex analytical model. Again, this is both (a) false and (b) not relevant. Even the boy scout manual gives some basic techniques that can be understood by teenagers.

Nelson also fails to recognize that answering a simple question like "Is it warm enough to go around without a coat?" gives you information about the weather. If the answer is yes, you can be pretty damn sure that it is not going to snow in the next hour. That's not a lot of information, perhaps, but it certainly constitutes information.

Third, Nelson claims that "there is complexity aplenty in the data, but, as SITC explains, that complexity is unspecified". This is the standard creationist ploy: admit that weather observations constitute "information", but just claim it is not the right kind of information. Never mind that this "right kind of information" is not recognized by anybody who actually studies information theory for a living - we should listen to Nelson because of his great credentials in mathematics.

However, weather observations do constitute information according to Meyer's own definition in Signature in the Cell, because these data are images of the underlying physical systems that cause the weather.

Finally, Nelson claims that the raw data (which he claims is not "specified information") suddenly becomes "specified" after it passes through an algorithm that does weather prediction. Nelson scores it in his own goal, because according to Dembski, computer algorithms cannot produce specified complexity. Even if Nelson is going to claim that the "specification" is contained in the algorithm, that doesn't explain how weather prediction algorithms can go on, day after day, producing weather forecast after weather forecast, each forecast with its own new amount of "specified information", from only the input data and a finite program.

Nelson's response is completely without merit. Look for more similar creationist attacks in the future, because this simple example of weather prediction is so devastating to their bogus claims.

When Faith Healing Kills

Via Hemant Mehta (the Friendly Atheist), here is the sad story of Neal Beagley, a 16-year-old killed by his parents' failure to seek adequate medical care, and their choice to rely on prayer instead.

Their son died, and the Beagleys have been sentenced to 16 months in jail. Yup, nothing fails like prayer.

I have a slightly different take on the case than Hemant does. I don't see any reason to doubt that the parents were sincere in their beliefs that they were doing what was best for their kid. And we don't always criminalize actions (or failure to act) that result in death: look at all the people that die during surgery - or perhaps, in a better parallel, look at all the people that died in the early history of medicine from the mistaken belief that being "bled" would help cure them. I don't see any "mens rea" in the Beagley case. Stupidity isn't a crime, and the parents have already paid a heavy emotional and genetic penalty for their stupidity.

The real criminals in this case are not the Beagleys, who were just doing what they had been told by authority figures would work. The real criminals are the religious leaders who make the bogus claim that "prayer heals", despite the fact that there is no good evidence that this is the case. Reportedly their church, the Followers of Christ, has a long history of letting children die by treating them with prayer instead of modern medicine.

I'll concede that we need laws against what the Beagleys did -- but purely for their deterrent, and not their punitive value. If people who rely on prayer alone to cure serious illnesses in children know that their failure may result in prison time, maybe they'll be less likely to rely on prayer alone. I'd definitely like to see a repeal of all religiously-based exemptions of child abuse charges for faith-healing deaths.

But more importantly, I'd like to see a law that makes it a crime for someone who is not a medical professional to counsel someone to withhold medical care for seriously ill children where there is a well-established and safe remedy known for the condition. Such a law could be very narrowly written and still have a beneficial effect.

Looking for an Honest Creationist

There's a new blog, Diogenes' Lamp, that takes on creationism, intelligent design, and similar foolishness. Worth a look - but, like Diogenes, if he's looking for an honest creationist, he's going to have a long wait.

Justice Isn't Blind

The Berkman Center for Internet & Society at Harvard University has been hosting a really interesting series of talks. Video is available on the internet, too.

Here's one: Leslie Zebrowitz, a professor at Brandeis, has been doing research on how people's appearance governs how they are treated in court. The results are a little scary: if you have a "baby face", you are more likely to win your case in Small Claims Court when you are denying intentional wrongdoing. If the defendant is "maturefaced", and the plaintiff is "babyfaced", the plaintiff is more likely to get larger monetary damages.

This is just one in a series of results showing that people's unconscious biases strongly color their decision-making.