Science

This just in: there are absolute, logical limits to the ability of any method (including the scientific one) for acquiring knowledge to produce a comprehensive theory of the world

Well, call off the search for a theory of everything. Physicist David Wolpert, in an article published in the prestigious Physica D (vol. 237, pp. 1257–1281, 2008), has shown that — at best — we can achieve a theory of almost everything. Wolpert’s work is very technical, but its implications are spectacular. Unlike the above mentioned limits to knowledge, which come out of empirical disciplines, Wolpert used logic to prove his point, following in the steps of the famousincompleteness theorem demonstrated by Kurt Godel in 1931. (An accessible summary of Wolpert’s discovery can be found in an article by P.-M. Binder in Nature, 16 October 2008.)

Basically, Wolpert — building on previous work by Alan Turing — formalized a description of “inference machines,” i.e. machines capable of arriving at inferences about the world (human beings are one example of such machines). Wolpert focused on what he calls strong inference, the ability of one machine to predict the totality of conclusions arrived at by another similar machine. Wolpert then logically proved the following two conclusions: a) For every machine capable of conducting strong inferences on the totality of the laws of physics there will be a second machine that cannot be strongly inferred from the first one; b) Given any pair of such machines, they cannot be strongly inferred from each other.

Of course, the article ends with the obligatory sideswipe at creationists.

Reference to original paper:

Physica D: Nonlinear Phenomena, Volume 237, Issue 9, 1 July 2008, Pages 1257-1281
David H. Wolpert

Wired has an excellent article on an optimal memorization algorithm developed by Piotr Wozniak. The technique has been embodied in a software program called SuperMemo and an open-source alternative called Mnemosyne

I’m somewhat skeptical that spending more time on memorizing facts is that useful but given that a few months ago I could barely remember the equation for the roots of a quadratic perhaps I should be more open-minded.

The algorithm is straightforward:

1. Split the knowledge into smallest possible items.
2. With all items associate an E-Factor equal to 2.5.
3. Repeat items using the following intervals:
   I(1):=1
   I(2):=6
   for n>2: I(n):=I(n-1)*EF
   where:
   I(n) – inter-repetition interval after the n-th repetition (in days),
   EF – E-Factor of a given item
   If interval is a fraction, round it up to the nearest integer.
4. After each repetition assess the quality of repetition response in 0-5 grade scale:
   5 – perfect response
   4 – correct response after a hesitation
   3 – correct response recalled with serious difficulty
   2 – incorrect response; where the correct one seemed easy to recall
   1 – incorrect response; the correct one remembered
   0 – complete blackout.
5. After each repetition modify the E-Factor of the recently repeated item according to the formula:
   EF’:=EF+(0.1-(5-q)*(0.08+(5-q)*0.02))
   where:
   EF’ – new value of the E-Factor,
   EF – old value of the E-Factor,
   q – quality of the response in the 0-5 grade scale.
   If EF is less than 1.3 then let EF be 1.3.
6. If the quality response was lower than 3 then start repetitions for the item from the beginning without changing the E-Factor (i.e. use intervals I(1), I(2) etc. as if the item was memorized anew).
7. After each repetition session of a given day repeat again all items that scored below four in the quality assessment. Continue the repetitions until all of these items score at least four.

There is a website called Memverse which has implemented this algorithm for memorizing popular bible verses. I’ve been using the site for about 3 months now and it is very impressive how much you can retain using the algorithm.

I’ve heard before that walking a mile emits more carbon than driving a mile so decided to investigate for myself.

A 190lb human walking at 3 miles per hour would expend 302 kCal. Therefore, covering a mile would take 20 mins and approximately 100 kCal. Apparently it takes 7-10 kCal of fossil fuel to produce 1 kCal of food. The upper end of the range assumes a diet of highly processed food and meat being transported long distances. The lower end of the range assumes a more vegetarian-centric diet and locally produced food.

Therefore,  a 1 mile walk requires 700 – 1,000 kCal of fossil fuel energy.

Driving a 30 mile per gallon car for one mile at 60 mph takes 1 minute and 1/30th of a gallon of gas. One gallon of gasoline contains approximately 30,000 kCal of fossil fuel energy.

Therefore, a 1 mile drive requires approximately 1,000 kCal of fossil fuel energy.

Depending on where you source your food and what you eat, it doesn’t make much difference in terms of carbon emissions. Driving a car one mile is far cheaper than walking a mile. But the health benefits of walking a mile far outweigh the cost.

The Wall Street Journal had an article a few days ago about the unreliability of some of the numbers behind global warming. The article goes on to say:

The fear of a sudden loss of ice from Greenland also makes a lot of news. A year ago, radio and television were ablaze with the discovery of “Warming Island,” a piece of land thought to be part of Greenland. But when the ice receded in the last few years, it turned out that there was open water. Hence Warming Island, which some said hadn’t been uncovered for thousands of years. CNN, ABC and the BBC made field trips to the island.

But every climatologist must know that Greenland’s last decade was no warmer than several decades in the early and mid-20th century. In fact, the period from 1970-1995 was the coldest one since the late 19th century, meaning that Greenland’s ice anomalously expanded right about the time climate change scientists decided to look at it.

Warming Island has a very distinctive shape, and it lies off of Carlsbad Fjord, in eastern Greenland. My colleague Chip Knappenberger found an inconvenient book, “Arctic Riviera,” published in 1957 (near the end of the previous warm period) by aerial photographer Ernst Hofer. Hofer did reconnaissance for expeditions and was surprised by how pleasant the summers had become. There’s a map in his book: It shows Warming Island.

The mechanism for the Greenland disaster is that summer warming creates rivers, called moulins, that descend into the ice cap, lubricating a rapid collapse and raising sea levels by 20 feet in the next 90 years. In Al Gore’s book, “An Inconvenient Truth,” there’s a wonderful picture of a moulin on page 193, with the text stating “These photographs from Greenland illustrate some of the dramatic changes now happening on the ice there.”

Really? There’s a photograph in the journal “Arctic,” published in 1953 by R.H. Katz, captioned “River disappearing in 40-foot deep gorge,” on Greenland’s Adolf Hoels Glacier. It’s all there in the open literature, but apparently that’s too inconvenient to bring up. Greenland didn’t shed its ice then. There was no acceleration of the rise in sea level.

Finally, no one seems to want to discuss that for millennia after the end of the last ice age, the Eurasian arctic was several degrees warmer in summer (when ice melts) than it is now. We know this because trees are buried in areas that are now too cold to support them. Back then, the forest extended all the way to the Arctic Ocean, which is now completely surrounded by tundra. If it was warmer for such a long period, why didn’t Greenland shed its ice?

This prompts the ultimate question: Why is the news on global warming always bad? Perhaps because there’s little incentive to look at things the other way. If you do, you’re liable to be pilloried by your colleagues. If global warming isn’t such a threat, who needs all that funding? Who needs the army of policy wonks crawling around the world with bold plans to stop climate change?

It seems to me that we should have thought about this before we starting using our corn to power our cars. Because that’s the kind of stupidy that leads to food riots around the world.

[Update: If anyone has a link to the video/audio transcript please post in the comments]

Last night I attended the debate at Stanford between Christopher Hitchens and Jay Richards. The topic was “Atheism vs Theism and the Scientific Evidence of Intelligent Design” which I felt was a little too broad for a meaningful debate.

My heart at first sank when I saw Jay Richards. He has hair reminiscent of an early Abba member or a really blonde version of the BeeGees. He looked as though he had just put away his surfboard and strolled into the debate. Christopher Hitchens came slouching in making every effort to look like a disenchanted intellectual who is angry with the world but is sustained daily by his special breed of cynicism.

Christopher Hitchens opened for the first 14 minutes and unleashed his standard diatribe against ‘religion’. He seemed a little unprepared but is clearly a gifted rhetorician and quite capable of thinking on his feet. He didn’t say much new and his style was well captured by a later comment from Jay Richards: “A sneer is not an argument and insults do not constitute evidence”. His main argument was that if the world was designed by a creator, it was not a benevolent creator. He frequently resorts to this argument despite it clearly not belonging in a debate on Atheism vs Theism. (Just because one doesn’t like God, doesn’t mean God doesn’t exist).

Jay Richards had the floor for the next 14 minutes and presented a rational, well-thought out argument for theism. He had 6 main points (and a seventh which he added later)

1. Moral truth – we all know what it is, the question is where did it come from and atheism has no answer to that. This issue was half-heartedly contested by Hitchens and a question from the audience regarding an evolutionary explanation for morality.
2. A finely tuned universe – basically a brief overview of the anthropic cosmological argument (every physical constant finely tuned for mankind and unlikely to have occurred by chance). Hitchens seemed to feel that the fact that the Andromeda galaxy will be obliterating earth in 5 billion years refutes this argument. Unfortunately his argument went along the lines of: “What kind of cruel god would allow this?”
3. A beginning to the universe in a finite past – therefore something caused the universe which must be God. He used the phrase “resting point” for the basis of a theistic belief and asked what the basis for atheism was. This is a fairly strong argument. Granted, there are theories which postulate an eternal universe but those seem to be less accepted these days.
4. Irreducible complexity - he didn’t get into details but cited the bacterial flagellum and asked why it’s obvious that Mt. Rushmore was ‘designed’. This argument obviously runs the risk of each instance of irreducible complexity being knocked down with subsequent research (a point which Hitchens noted). I spent many years doing research on genetic algorithms in computer science and this argument does accord with my experience of computer simulations.
5. Materialism – the atheist, materialist philosophers all conclude that consciousness is an illusion and feel that this is problematic. For most people, a purely material view of the world leads to a conclusion which seems incompatible with experience. Obviously this is not a proof for the existence of God but Richards’ point was that our subjective experience is more consistent with a theistic philosophy.
6. Free will – it’s incompatible with a mechanistic worldview. Hitchens’ bizarre response was that if free will was given to us then it can’t be free will.
7. The origin of biological information (added towards end of debate). They touched briefly on the direction of entropy but unfortunately nothing conclusive from either side. (I’d like to challenge some of the atheists who really know their biology to read this book and provide a rebuttal to the main thesis of the book in the comments below.)

Richards ended with the question: which worldview (atheism or theism) best accomodates all the above observations?

Hitchens then had 4 minutes to respond and, to my mind, did not answer one of the points that Jay Richards had made. For the rest of the debate he attempted to generalize from particular observations (how can we think Mohammad really made a midnight ride into the sky on his horse, how can anyone believe in a God who demands that we kill our children (Abraham/Isaac), genital mutilation in the name of religion, to his point that God does not exist. Along the way he attacked Mormonism, Islam, Catholicism, etc.

Jay Richards maintained his composure admirably, was exceptionally well-informed on every topic while still being likeable, charitable, and theologically rigorous. 

Hitchens’ hubris appears to know no bounds. When asked whether he thought he was more intelligent than everyone else who believes in God he said: “Yes. And the polls suggest that I am too” (!)

Basically there were two messages: one hopeful; and one of despair (he mentioned sex and schadenfreude as his two purposes for living), futility and constant railing against a God who doesn’t exist. Atheism, to my mind, has always been deficient on the inspiration front and it seems a shame to spend one’s allotted time fighting the God you don’t believe in.

First Things has a great article on the intersection of science and faith. Definitely a great read.

If you’re interested in the topic, I highly recommend the book: “The Anthropic Cosmological Principle“.

If you haven’t watched the documentary on Fermat’s Last Theorem you should set aside 45 minutes as soon as you can. The documentary is a splendid testament to what happens when passion and perseverance are coupled with a stunningly sharp mind. Here are some notes from the producer:

There is a brilliant genius from the past who solves an apparently impossible problem. He dies without revealing the solution. This becomes buried treasure, and every subsequent mathematician goes in search of it. There are heroes, villains, rivals, rich prizes, a duel at dawn, a suicide and an attempted suicide, but after 300 years the problem remains intact. The greatest minds on the planet failed to solve it. Undaunted, however, a young boy promises to devote the rest of his life to solving this notorious problem. After thirty years he suddenly identifies a strategy that might work. For seven years he works in secret. He reveals his proof, only to learn that he has made a mistake. He hides away again, humiliated and ashamed, but he returns a year later, this time triumphant. The problem has been solved. His journey is over.

The documentary was about mathematics and mathematicians, but it was also about childhood dreams, ambition, obsession, passion, failure and triumph. Not surprisingly, there was a time when one of the Hollywood studios put in a serious bid to make a feature film, but somewhere along the line the project faded away.

The emotion of the documentary is clear from the first minute. The opening sequence shows Professor Andrew Wiles recalling the moment when he realised that he had solved Fermat’s Last Theorem and achieved his childhood dream. The memory is so moving that he begins to stumble over his words. He then pauses, takes a breath, tries to continue, but eventually he is overcome with emotion and turns away from the camera. There are other moments in the programme that are equally emotional.

I particularly like the final comments from Iwasawa, the Japanese mathematician who came up with the conjecture which was necessary to prove the theorem.

It is rare to read a book that has the potential to change one’s entire worldview. This weekend I read Genetic Entropy & the Mystery of the Genome. The author is John Sanford, a professor of genetics at Cornell University, inventor of the gene gun, and holder of 25 patents. His essential thesis is that a blind evolutionary process could not have produced humans from single cell organisms. He gives a multitude of cogent arguments why this is so.

Moreover, he makes a very compelling case that, in fact, mutation and natural selection are actually degrading the genome to such an extent that humans will eventually go extinct. The simple reason is that each generation introduces at least 100 mutations which are both deleterious (degrade the genome) and near-neutral (unlikely to be removed by natural selection). The cost of natural selection would have to be extraordinarily high to remove such a large number of mutations from the gene pool. In addition, the rare beneficial mutations are also near-neutral and consequently impossible to select for.

A lot of this resonates with my experience with genetic algorithms where the vast majority of the population has to be wiped out at each generation to prevent non-useful mutations from multiplying.

What I find fascinating, though, is that everyone I have spoken to about this book immediately dismisses it because it “sounds like Creationism”. Perhaps secularism really has risen to the level of a religion: steeped in dogma and unwilling to confront facts.

I have long held the theory that every conversation, if pursued long enough, naturally and necessarily ends with a discussion about the existence of God and our purpose on earth. A few years ago a long lunch conversation reached this point, and an engineer concluded with the statement: “My God is a set of equations.” To which I replied, “What do those equations describe?”

These days it is fashionable among the intelligentsia to declare with newly-discovered transcendence that religion is a good enough thing (if done in moderation) and science is self-evidently worthwhile but we should never, ever confuse the two. The intersection of science and faith, rationalism and mystery, is best left to the final pages of an epilogue in a serious book on science, or to footnotes in a book on faith.

And yet equations are merely an abstraction of the physical world and the Christian faith claims to worship a Jesus who walked in history and a God who created the physical. Why then, have the last few decades produced an intellectual movement so devoted to a separation of faith and science?

In 1931 Godel published a paper which challenged the basic assumptions underlying mathematics and became a milestone in the history of logic and mathematics. I believe that the world is still coming to terms with the philosophical implications of Godel’s Theorem of Incompleteness. Others have better summarized his theorem but it proscribes the limits of axiomatic logic and shows that provability is a weaker notion than truth; in short, there is Truth that we can’t logically prove.

Nagel and Newman, in their classic book on the subject, Godel’s Proof, conclude with the comment:

Godel’s proof should not be construed as an invitation to despair or as an excuse for mystery-mongering.

That might be. But it does, I believe, suggest that if God is a set of equations, those equations lie in a realm of mathematics about which we haven’t even begun to dream.

A scientist, Rupert Sheldrake, is claiming that he has proof of telephone telepathy. Maybe I’ve read too many fantasy books lately but the idea of telepathy has always resonated with me.