I’ve invited cosmology questions before, but I wanted to renew the call. I’ve got a Q&A article on cosmology coming out soon, so ask away!
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I’ve spent a lot of time critiquing articles on the fine-tuning of the universe for intelligent life. I should really give the other side of the story. Below are some of the good ones, ranging from popular level books to technical articles. I’ve given my recommendations for popular cosmology books here.
Books – Popular-level
- Just Six Numbers, Martin Rees – Highly recommended, with a strong focus on cosmology and astrophysics, as you’d expect from the Astronomer Royal. Rees gives a clear exposition of modern cosmology, including inflation, and ends up giving a cogent defence of the multiverse.
- The Goldilocks Enigma, Paul Davies – Davies is an excellent writer and has long been an important contributor to this field. His discussion of the physics is very good, and includes a description of the Higgs mechanism. When he strays into metaphysics, he is thorough and thoughtful, even when he is defending conclusions that I don’t agree with.
- The Cosmic Landscape: String Theory and the Illusion of Intelligent Design, Leonard Susskind – I’ve reviewed this book in detail in a previous blog posts. Highly recommended. I can also recommend his many lectures on YouTube.
- Constants of Nature, John Barrow – A discussion of the physics behind the constants of nature. An excellent presentation of modern physics, cosmology and their relationship to mathematics, which includes a chapter on the anthropic principle and a discussion of the multiverse.
- Cosmology: The Science of the Universe, Edward Harrison – My favourite cosmology introduction. The entire book is worth reading, not least the sections on life in the universe and the multiverse.
- At Home in the Universe, John Wheeler – A thoughtful and wonderfully written collection of essays, some of which touch on matters anthropic.
I haven’t read Brian Greene’s book on the multiverse but I’ve read his other books and they’re excellent. Stephen Hawking discusses fine-tuning in A Brief History of Time and the Grand Design. As usual, read anything by Sean Carroll, Frank Wilczek, and Alex Vilenkin.
Books – Advanced
- The Cosmological Anthropic Principle, Barrow and Tipler – still the standard in the field. Even if you can’t follow the equations in the middle chapters, it’s still worth a read as the discussion is quite clear. Gets a bit speculative in the final chapters, but its fairly obvious where to apply your grain of salt.
- Universe or Multiverse (Edited by Bernard Carr) – the new standard. A great collection of papers by most of the experts in the field. Special mention goes to the papers by Weinberg, Wilczek, Aguirre, and Hogan.
Scientific Review Articles
The field of fine-tuning grew out of the so-called “Large numbers hypothesis” of Paul Dirac, which is owes a lot to Weyl and is further discussed by Eddington, Gamow and others. These discussions evolve into fine-tuning when Dicke explains them using the anthropic principle. Dicke’s method is examined and expanded in these classic papers of the field: (more…)
Having had my appetite for the Middle Ages whetted by Edward Grant’s excellent book A History of Natural Philosophy: From the Ancient World to the Nineteenth Century, I recently read Edward Feser’s Aquinas (A Beginner’s Guide). And, on the back of that, his book The Last Superstition. If I ever work out what a formal cause is, I might post a review.
In the meantime, I’ve quite enjoyed some of his blog posts about the philosophical claims of Lawrence Krauss. This is something I’ve blogged about a few times. His most recent post on Krauss contains this marvellous passage.
“[N]othing is a physical concept because it’s the absence of something, and something is a physical concept.”
The trouble with this, of course, is that “something” is not a physical concept. “Something” is what Scholastic philosophers call a transcendental, a notion that applies to every kind of being whatsoever, whether physical or non-physical — to tables and chairs, rocks and trees, animals and people, substances and accidents, numbers, universals, and other abstract objects, souls, angels, and God. Of course, Krauss doesn’t believe in some of these things, but that’s not to the point. Whether or not numbers, universals, souls, angels or God actually exist, none of them would be physical if they existed. But each would still be a “something” if it existed. So the concept of “something” is broader than the concept “physical,” and would remain so even if it turned out that the only things that actually exist are physical.
No atheist philosopher would disagree with me about that much, because it’s really just an obvious conceptual point. But since Krauss and his fans have an extremely tenuous grasp of philosophy — or, indeed, of the obvious — I suppose it is worth adding that even if it were a matter of controversy whether “something” is a physical concept, Krauss’s “argument” here would simply have begged the question against one side of that controversy, rather than refuted it. For obviously, Krauss’s critics would not agree that “something is a physical concept.” Hence, confidently to assert this as a premise intended to convince someone who doesn’t already agree with him is just to commit a textbook fallacy of circular reasoning.
The wood floor guy analogy is pretty awesome, so be sure to have a read.
I’m currently at the Philosophy of Cosmology Summer School at the University of California, Santa Cruz. I’ve been invited to speak for an afternoon on the fine-tuning of the universe for intelligent life. I’ve given such talks a number of times, but never with so many of the people whose work I am discussing actually sitting in the room. The line-up is very impressive:
Anthony Aguirre (UCSC), Craig Callender (UCSD), Sean Carroll (Cal Tech), Shelly Goldstein (Rutgers), Anna Ijjas (Harvard/Rutgers), Tim Maudlin (NYU), Priya Natarajan (Yale), Ward Struyve (Rutgers), Tiziana Vistarini, (Rutgers), David Wallace (Oxford), Alex Pruss, Chris Smeenk, Fred Adams, Leonard Susskind, Matt Johnson …
At the moment, Sean Carroll is holding forth on cosmology, time, initial conditions and such. The talks are being placed on YouTube fairly quickly, and I encourage you to have a look through the list of talks.
Well worth three minutes of your time is this video on sonic resonances in a 2D square board.
As the sound wobbles the board, standing waves are set up. Because these waves are 2 dimensional, the resulting pattern is more intricate than for standing waves in a 1 dimensional string.
The red dots are places on the string that do not move – called the nodes. For a 2D membrane, like the one above, these nodes will be lines, and salt sprinkled on the board will naturally follow these lines, since and grains not on the lines won’t sit still.
As well as being rather pretty, the video shows why drums are rhythmic instruments, rather than melodic (you wouldn’t ask the drummer to drum out the melody, and drummers don’t have to worry about key changes). When you pick a guitar string, you get a note determined by the length of the string (and its tension and line density). You also get, layered on top of that note, overtones. Because the string is essentially one dimensional, these overtones are related to the fundamental tone by simple fractions. Thus, the fundamental and the overtones all sound good together – the overtones harmonize with the fundamental. (I’ve written in more detail about the musical scale here.) A skilful (bass)-guitarist can use his finger at a node to excite only these overtones, creating the so-called harmonics. Jaco Pastorius‘ “Portrait of Tracy” is the classic example, and the technique has been expanded by Victor Wooten and others.
For the skin of a drum, however, there is no nice, neat relationship between the fundamental tone and the overtones. This is shown in the complexity of the patterns in the video above. The result is that there is no one pure “note” that a particular drum makes, but rather a somewhat atonal mixture of notes. Tuning a drum generally involves trying to eliminate the overtones, with the final result being a strong function of a drummer’s personal preferences about what sort of tone s/he wants.
(I have a half-written post titled “Drummers, Metronomes and the Tyranny of the Beat”, but I’ll save that for another day.)
A great post by Ted Bunn on the difference between Bayesian and frequentist approaches to probability, summarised in this marvellous plot:
Highlight: “Frequentism simply refuses to answer questions about the probability of hypotheses. … In frequentist analyses, all probabilities are of the form P(data | hypothesis), pronounced “the probability that the data would occur, given the hypothesis.” Frequentism flatly refuses to consider probabilities with the hypothesis to the left of the bar — that is, it refuses to consider the probability that any scientific hypothesis is correct.”
I have a rule: if I see an article by Frank Wilczek, I read it. Wilczek is a particle physicist and Nobel Prize Laureate, and recently wrote on “Why Does the Higgs Particle Matter?” for Big Questions Online:
The discovery of the Higgs particle is, first and foremost, a ringing affirmation of fundamental harmony between Mind and Matter. Mind, in the form of human thought, was able to predict the existence of a qualitatively new form of Matter before ever having encountered it, based on esthetic preference for beautiful equations.
A nice talk from Jeff Shallit from Recursivity on numerology. I’m going to forward it to a guy who keeps emailing me about his “Final Formula” of physics:
which has the same problem with units that Shallit’s marvellous Washington Monument example does.
That said, there have been a few episodes in physics where something that looks alarmingly like numerology proved successful, such as Gell-Mann’s 8-fold way. Murray Gell-Mann plotted mesons and spin-1/2 baryons on a plot with charge on a horizontal axis and strangeness on the diagonal. The particles formed an octagon with two particles at the centre. He also plotted the spin-3/2 baryons, which formed a triangle, but with the apex missing. Gell-Mann predicted the existence of the particle that would complete the triangle, together with its strangeness, charge and mass. Two years later, it was discovered.
Is this really numerology? I’m not familiar with Eddington’s argument, but my suspicion is that the difference is in predictive power. Gell-Mann predicted the existence of a particle, its properties and was ultimately led to the quark model, whereas the zero-predictive-power of Eddington’s ideas were displayed by his easy switch from pulling 136 out of a mathematical hat to producing 137.
The moral of the story seems to a combination of the following:
- While successful physical theories can predict relationships between physical quantities that would otherwise appear to be coincidences, searching for such coincidences in the absence of a deeper physical theory is not a good way to discover the laws of nature.
- The deeper we go into the laws of nature, the more remarkable simplicity we uncover. The applicability of group theory and symmetry to particle physics is a good illustration of this.
- The power of science comes not from its ability to make assumptions about nature, but the ability to test those assumptions and discard those that fail. That’s why this quote from Mark Twain about “wholesale returns of conjecture out of such a trifling investment of fact” only tells half the story of science. In particular, one must keep an eye on the relationship between the number of free parameters and the number of data points, so that we can tell the difference between prediction (where the data tests the model) and curve-fitting (where the data creates the model).
How much does the altitude at which a cricket (or baseball) match is played affect the flight of the ball? If you’re only interested in the answer to that question, then skip ahead. But there is a reason I am particularly interested in this question, and it has to do with a freakish cricket match played in 2006.
Every sport has its fables and epics, and nothing attracts a story like an outlier. In statistics, an outlier is an event that is way out on its own, deviating significantly from the rest of the population. In cricket, for example, the primary statistic that measures how good a batter is is the batting average, defined as the average number of runs per dismissal. The details aren’t required here; it will suffice to say that an average of above 50 in test cricket marks out one of the greats. Below (top) is a plot of the batting averages of all those who have played test cricket.
We see few players with an average greater than 50, and even fewer above 60. And then comes the outlier, way off to the right – Donald Bradman, with a career average of 99.94. His other career statistics are similarly off-the-scale. The premier achievement for a batter in a match is to score a hundred runs in a single innings, a century. Bradman did it 29 times in his career of 80 innings. Of the 7 batters who have scored as many or more centuries, all required at least twice as many innings. Cricket is one of the few sports in which the question “who was the greatest?” attracts little debate.
Cricket has also seen freakish matches. (more…)