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Subtitle: how a modern physicist is liable to misunderstand Aristotle. This post was inspired by a very interesting post by Edward Feser here.

I have tried. What follows is my attempt to give full expression of my own ignorance. One of the conclusions I have drawn from my forays into Ancient and Medieval philosophy is that these are great thinkers.

Here is the standard illustration for Aristotle’s four causes. Consider a marble statue. The statue has four causes. The material cause is the marble, the material out of which the thing is made. The formal cause is the arrangement of the statue, its geometrical shape. The efficient cause is the “doer”, the sculptor, who arranges the material into the desired shape. The final cause of the statue is the purpose for which the sculptor has created the statue, e.g. to look beautiful in the garden.

Aristotle and Newton

Right, I think. My physicist training naturally has me try to cast my Newtonian (occasionally Einsteinian, sometimes quantum) view of the world in these categories. (This might be a bad idea, I think, given the discontinuity between Aristotle and Newton. Still, I’ll give it a go. Also, I’ll worry about relativity and quantum mechanics later, if at all.) So,

  • Material cause – the particles of matter out of which physical things are made.
  • Formal cause – the arrangement of those particles. Mathematically, a list of the position and velocity of each particle at some time (x_i(t), v_i(t))
  • Efficient cause – Newtonian forces, which move particles around.
  • Final causes – an emergent, higher-level property of minds, who can make and execute plans.

(This is not the correct way to understand Aristotle, so stay tuned.) So far, so good, I think. The “Newtonian” material, formal and efficient causes give all the information one needs to solve Newton’s laws of motion. But now the confusion starts.

A lecturer giving an introduction to the history of science talks about Plato’s theory of forms as a realm of abstract but still “really” existing ideas. He later seems to suggest that the formal cause of a chalk circle drawn on the board is the idea of the circle in the mind of the lecturer. I ask, “For the circle on the board: is the formal cause the idea in the mind, or the idea of a circle floating out there somewhere in Plato’s realm?”. “Uh … have you been reading the Scholastics?”, he replies. “Nope”. I can’t remember the rest of his answer – it was rather vague. I’ve had a chance to ask a few other philosophers about formal causes since, and their reply usually starts with a grimace.

Enter Feser

So it was that I came to Edward Feser’s Aquinas (A Beginner’s Guide). His exposition is admirably clear, and it is obvious that I must change my understanding of the four causes. In particular, final causes are more than just intentions of minds. There are natural final causes. When a match is struck and fire is created, the efficient cause of the fire is the match. At the same time, the final cause of the match is the fire. The properties of the match “point to” or “are directed at” the creation of fire. Fire is what matches do. The match isn’t just a generic efficient cause that could cause any old thing but just happens to cause fire every time. Its ability to do something is controlled by fire as its final cause. I picture this as the efficient cause being the engine, and the final cause as the steering wheel. The efficient cause does the causing, and the final cause directs the efficient cause towards the production of its effect.

The shocking thing about this, as Feser points out, is that the scientific revolution, despite its PR, didn’t get rid of final causes. Final causes are how Aristotelian metaphysics explains the orderliness of nature. The fact that things keep doing the same kind of things – trees grow, the sun shines, fire burns, dropped stones fall – is because the efficient causes in the world are conjoined (is that the right word?) to final causes, ensuring that they produce consistent effects. The “laws of nature”, to use an slight anachronism, are more about final causes than efficient ones. But that is a topic for another day.

Despite Feser’s clarity, formal causes now get even more confusing. Feser argues that things can be imperfect instantiations of their form. Their form isn’t just how their parts are arranged. It is, in some sense, how they should be arranged, what their essential arrangement is. For example, when a person loses a leg, they don’t take the form of a one-legged person. Their true, two-legged human nature is still there in the person, but it is instantiated imperfectly.

Note that Aristotle differs from Plato in locating the form of a thing in the thing itself, not in some ideal external realm of forms. It isn’t just that the person fails to replicate the ideal of a  two-legged Platonic person “up there”. The one-legged person still has the form of a  two-legged human. Two-legged-ness is still in there, somewhere. (more…)

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Thanks to GGDFan777 for the tip-off: Jeffery Jay Lowder has weighed in on my posts (one, two, three, four) about Richard Carrier. It’s in the comments of this post over at The Secular Outpost. Keith Parsons even drops in with a few comments. [Edit:] More details here: The Carrier-Barnes Exchange on Fine-Tuning.

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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…)

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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.

Krauss asserts:

“[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.

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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.

I’ll try to tweet some highlights – so follow me or watch the hashtag #PhilosophyCosmology.

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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.)

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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.”

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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.

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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:

\hbar c = \sqrt{10} \times 10^{-26}

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).

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