PSA Submissions Are a Go

The Philosophy of Science Association is holding its biennial conference in November, in Montréal, QC. Many of you were frantically preparing your manuscript for submission before midnight last night. Phew! Done and done.

Now you can start looking forward to your upcoming trip to Montréal! A few facts of interest:

• Montréal is the second largest city in Canada. It's slightly smaller than Phoenix, AZ and slightly larger than Marseille, Fr.
• Nearly 2 out of 3 people in the city are native French speakers.
• The weather in November is usually 28° to 50° F (-2° to 13° C) and rainy.
• The conference is at the Hyatt Regency in Old Montréal, which dates back to the 17th century. The nearby hill, called "Mont Royal" (hence Montréal) was previously inhabited by the Mohawk Nation.

For a quick view of the city, try this "Montréal in 2 Minutes" video.

Hopefully I'll see you there. And don't forget to share your freshly prepared manuscript on PhilSci Archive before you go!

Announcement: Meet Me in North Carolina

*Beeeeeeeeep* (Is this thing on?) Ahem.

Are there any philosophers of science out there who, on the weekend of February 27th, will be either (a) attending the NCPS/SCSP annual meeting, or (b) interested in skydiving near Charlotte? Weather permitting, I'll be doing both, and would welcome company. The conference and the dropzone are about an hour apart:



View Larger Map
If this means you, feel free to contact me so we can meet up!


I'm always interested in checking out new corners of philosophy departments I haven't seen before. And February seems like a nice time to migrate South for a few jumps. Charlotte just seemed like the perfect opportunity to kill both birds with one stone! Maybe I'll see some of you there.

AMFPVNP9M895

Visualize a Wave Function

Can you visualize a normalized wave function on spacetime?

Let's try with a simple example. The role of a wave function is to assign a complex number to each point (x, t) in spacetime. This is central to a quantum description of the world. The complex number at each point is interpreted as an amplitude, which determines a probability -- the probability of measuring some physical quantity (like position or momentum) at that point.

But in the end, it's just a complex number, of unit length.

Now, a complex number lives on the complex plane -- a plane with the vertical axis representing a complex value, and the horizontal axis representing a real value. And the complex numbers of unit length live on a circle around the origin. So you can think of these numbers as readings on a circular meter -- like a speedometer or an altimeter -- except that the meter reads amplitudes instead of speeds or altitudes.

That means you can visualize the wave function ψ(x, t) as assigning a meter-reading to each point in spacetime. And if I fix a point in space -- like a spot on my kitchen floor -- then I can trace through the history of this wave function over time. The result will be a smoothly changing meter reading. For example, the meter arrow might just spin around clockwise over time.

Then it would look something like the following.

(Click to enlarge)

Challenge Question: How would you characterize the "time-reverse" of this description of the world? Tune in next post for a discussion...

Edit: The above account is not quite right -- see the post comments for more.

How Time Really Passes

We all experience the passage of time. This is not an illusion. We agree on the serial delivery of moments, and it is very hard to dislocate us from this agreement. However, the core of this experience can be located as a feature of our physical theories. These theories do not replace our notion of passage. Rather, physics provides a reliable account of the regularities underlying our common experience of time passing. It does this by providing us with a concrete relationship between any given now, together with its future and past.


1. We Experience Time Passing

We can apprehend the passage of time through the succession of three mental states, in this order:

1. the expectation of an event;


2. the experience of the event; and


3. the memory of the event.

We prepare for lunch, we eat lunch, and we remember how tasty it was afterward. Moreover, we all agree that this is the way it works -- the order doesn't change.

This is an account of passage that John Norton has proposed. As John suggests, this agreement shows all the signs of not being an illusion. There's no known procedure that eradicates the experience of passage. There's no obvious underlying mechanism that reduces passage to an artifact of our perception. The best explanation of the reliable succession of these three mental states is that they reflect an objective regularity in the world. Passage is real. It produces the serial delivery of moments to our minds. We become aware of it through the succession of these three identifiable mental states.


2. Physical Theories Describe Passage

In a physical theory, passage appears as a relationship between matter at any given moment (the 'now') and its future and past developments. This relationship is determined by Cauchy evolution. The regularities appearing in Cauchy evolution correspond precisely to the regularities we experience with passage. This gives us good reason to suspect they reflect the same objective feature of reality.

We have said that the core feature of passage is the serial delivery of moments: a future event becomes present, and then recedes into the past. Another way to describe this situation is to say that, once a now has been specified, we are guaranteed a definite future and a definite past. These categories never get mixed up: the past cannot arrive after now; the future cannot arrive before now. There is some real regularity that guarantees future, present, and past will be delivered to us in the right order.

The regularity underlying our experience of passage reflects the same reality as the regularity underlying the way physics describes change. In physical theories, this change is called evolution. Here is how the regularity appears.

By specifying a matter configuration 'now' (indicated as a gray circle), we determine a local past and a local future.
We can input a configuration of matter representing 'now' into a physical theory. These are called (local) initial conditions. Once now has been specified, the theory determines (in the most common physical situations^1.) a definite future and past. The equations of motion of our theory determine the moments in the past from which our matter evolved, as well as the moments in the future to which it will evolve soon. This separation into past, present, and future states of matter matches the key feature of passage: the serial delivery of moments is fixed once we specify our 'now.'

For example, I might input my 'now' to be 10am this morning. My matter configuration at 10am is determined (according to some hypothetical theory) to have evolved out of my bed at around 7am, and is determined to evolve to eat lunch at noon. When I set my 'now' to be noon, then everything changes in a regular way. I am determined to have evolved from my 10am configuration, and determined to wash my dishes soon. And so on.

This is a striking match of our experience of the serial delivery of moments. At 10am, I am in a state of remembering my bed, and a state of expecting to eat lunch. This is followed by my noon state of remembering my 10am state, enjoying my lunch, and expecting to do the dishes.

Craig Callender (2000) argues that Cauchy evolution is what makes time informative. Here, we have reached a simpler conclusion: Cauchy evolution is how physics reflects time's passage.


3. Experience and Theory Reflect the Same Thing

The human mind apprehends the passage of time through a change of state: we expect, we experience, and then we remember. This is a fact about our human experience. The steadfastness of this experience suggests it reflects an objective feature of the world.

Physical theory describes passage by describing a state's evolution: given an initial state, we determine the past states as well as the future ones. This is a fact about our physical theories. The empirical confirmation of these theories suggests that they too reflect something objective about the world.

This does not mean that our apprehension of passage can be reduced to the physical description of passage, or vice versa. Rather, our conclusion should be that both the experience and the physics are very likely reflective of the same phenomenon. Physics is not devoid of passage. It is even more evidence for its existence.

-----------------
1. This is not to ignore the difficult problem of specifying, and justifying, the conditions under which the Cauchy problem is well-posed. There are many well-known cases in which initial conditions fail to settle future/past evolution. However, it is sufficient for us to note that in a great many cases, and in almost all common applications, initial conditions can be chosen so as to guarantee a well-posed Cauchy problem.

Get Started Reading Blogs on the Philosophy of Science

Want to read some nice raw philosophy of science? Here are twelve options that I highly recommend.

1. It's Only a Theory is a new blog on the philosophy of science, which appears very promising. Otávio Bueno (Miami), Gabriele Contessa (Carleton), Marc Lange (UNC), and Chris Pincock (Purdue) are currently running the show. Guest posts are being invited.


2. Honest Toil is Chris's other very interesting blogue on the philosophy of mathematics.


3. My Mind is Made Up is run by my fellow Pittsburgher Justin Sytsma. He produces some nice work on the philosophy of mind here on this generally amusing blog.


4. Words and Other Things is run by another another fellow Pittsburgher, Shawn Standefer. WAOT has recently received a facelift, and is a great resource on logic, the philosophy of math, early analytic philosophy, and other philosophico-logical delights.


5. Obscure and Confused Ideas contains Pitt-graduate Greg Frost-Arnold's thoughts on logic, early analytic philosophy, and the philosophy of science.


6. The Statistical Mechanic (a.k.a. Wolfgang Beirl) has been producing some very interesting work lately on the philosophy of physics -- this blog really deserves to be more widely read.


7. The Truth Makes Me Fret is another very interesting blog that covers topics in the philosophy of physics, but also a wide range of philosophy of science issues.


8. Cosmic Variance is (Caltech physicist) Sean Carroll's frequent cyber-stomping ground. Apart from the general entertainment value of this blog, it is of special interest to for both its physical and its philosophical content.


9. Backreaction is one of my very favorite blogs. Sabine Hossenfelder and Stefan Scherer (Perimeter Institute) provide a lot of great updates on physics, but also some excellent contributions to the philosophy of physics.


10. A Mind for Madness ranges from very technical mathematical physics, to general philosophy of science, to music, and beyond.


11. The Blog of Noah Greenstein produces a lot of very original philosophy, and takes its occasional jaunt into the philosophy of science.


12. Philosopher's Anonymous. Ok, this isn't really philosophy of science. But it's hilarious. Especially if you are (or are on your way to becoming) a professional philosopher.

That's all the philosophy of science blogs for today. Enjoy!

Map of the Cosmic Acceleration Literature

Ten years ago, the physics community came to agree that the expansion of the Universe is experiencing a positive acceleration. The experts still disagree on why. Everything but the kitchen sink has been proposed (I've mentioned this twice before), but there is a paucity of experimental evidence to favor one proposal over another.

This situation strikes me as a gold-mine for philosophers physics. In particular, I would hope that we could learn something interesting about what kind of reasoning is allowed in such an empirically starved research program. In particular, what I'd like to know is:

What argumentative moves are licit in response to the cosmic acceleration problem?

As a first step toward figuring this out, I made a map of the most common arguments being made. To see my map, click the image on the left (or download the PDF). This map is inspired by a (much smaller) such diagram given by Sean Carroll (2003). Suggestions are more than welcome!

What is Interesting in the Philosophy of Physics?

Philosophers of physics may have experienced this problem. You know you're interested in a particular question about physics. You come face to face with the mountain of literature on the topic. And you immediately start digging furiously. Deeper and deeper you dig, until you've finally mastered a wealth of material, and at the same time completely lost track of what the hell you were doing in the first place

To avoid this problem, John Norton suggested that Elay Shech and I make a list of really successful tactics in the philosophy of physics. The idea is to characterize a few exemplary problems in the field in terms of a very broad methodology. That way, one can more easily stay focused on the really interesting problems. Here is the list the three of us came up with.

1. Correction of a standard history. Sometimes, everyone agrees that things went one way, and they all turn out to be wrong. Examples. For years, everyone thought that the Michelson–Morley experiment lead to the discovery of Special Relativity. It turns out that this experiment had little to do with it.


2. Explication of a concept in physics. A theoretical term might allow a non-standard interpretation, or might not have an obvious interpretation at all. Examples. The concept of gauge and of the simultaneity relation.


3. Traditional philosophy illuminated by physics. A particular physical theory might imply something about more traditional problems in philosophy. Examples. Claims about substantivalism, the persistence of objects, and the passage of time have all received arguments that draw on physical theories.


4. Characterization of a a theory's foundation. Something is suggested about the most basic elements of a theory. Examples. Realism, interpretations of GR or QM, or the conventionality of geometry.


5. Analysis of 'paradoxes.' The word 'paradox' is common in physics jargon, but it almost never means a logical paradox. Analysis of what's at the bottom of the problem is often illuminating. Examples. The black hole information paradox; the paradox of cosmic acceleration.


6. Synthesis of Philosophy and Science. One often seeks to understand how big-picture philosophical views can be combined with particular physical theories. Examples. The combination of reductionism with statistical mechanics.


7. Characterization of epistemic/metaphysical limitations. Sometimes physical theories seem to place sharp limits on what can in principle exist or be known. Examples. Indeterminism. Observationally indistinguishable spacetimes.

This list is certainly not exhaustive. But I have already found it to be surprisingly useful. Comments and additional suggestions are welcome!

Pittsburgh HPS Proves That P

Who knows where these came from, but I'm sure that they are not endorsed by the parties mentioned.

Earman. Start with plain vanilla Minkowski spacetime (in which obviously not p), and delete a point. Multiply the metric by a conformal mapping in a compact region around the deleted point, so that the length of every geodesic diverges as it approaches that point. Then, p.

Gotthelf. All we can learn from whoever really wrote Aristotle's Parts of Animals is p. Therefore, p.

Grunbaum. Many theistically inclined philosophers have quite wrongly confused themselves into thinking that not p. Therefore, p.

Lennox. For years, scholars used to think that not p. But when you actually look at what Darwin wrote in the manuscripts, it's pretty clear that p. Therefore, p.

Machamer. (Loudly): It's time to start breaking down the old dichotomies! Once we do that, p won't sound so strange! Therefore, p.

Machery. Surveys show that while 60% of American students say not p, only 40% of Chinese students say not p. Therefore, p.

McGuire. It's tempting to follow enlightenment scholars in thinking that for Newton, not p. On the contrary. For Newton, it was very much the case that p. Therefore, p.

Mitchell. While not p might be suggested on a top-down analysis, p clearly emerges on an integrative pluralist account. Therefore, p.

Norton. As you can see in this little animated GIF, p. Therefore, p.

Palmieri. Historians have argued about whether or not p is really true. However, recreation of the experiment suggests that p. Therefore, p.

Schaffner. Some suggest that not p. But there are certainly distinct theories that have the same formal structure, but for which p is true nonetheless. Therefore, p.

Levine & Mcintyre. Back in the good old days, it used to be that not p. But then the graduate students bought a scanner. Therefore, p.

Alternatives anyone?

Get Started Improving Your Philsci Archive Experience

You may already know that Philsci Archive is the way to stay updated on new developments in the Philosophy of Science. Here are three easy tricks to make your experience more pleasant.

1. Use Google to search philsci archive. Google is a far superior search engine. Why use anything else?
   

   Enter your search keywords into Google, followed by this string: site:philsci-archive.pitt.edu

   
   This will return a Google search for your keywords, restricted to Philsci archive. Trust me, this is a real pain-reliever: for example, searching for "van fraassen" returns baloney on Philsci archive's search engine, while Google returns hundreds of items. For more options, use Google's advanced search to find what you want.


2. Browse by Category. Only look at the categories you're interested in.
   

   Go to Browse > Subject and select the category you're interested in.

   
   I recommend bookmarking several subjects for quick browsing. For example, here's Physics.


3. Get updates in selected categories by email. Three easy steps:
   

   Step 1: register if you haven't done so already, and login to the registered users area.
   Step 2: Select "Change your subscription options" and click the "New Subscription" button.
   Step 3: Follow the instructions to design your email subscription.

   
   You can even select how often (or how rarely) you want to have an update sent to you.
   

Enjoy!

A 4-Line Proof of the Isoperimetric Theorem in 3D

Here's an example of what might be called "biological proof" of a mathematical claim.

Proposition (The Isoperimetric Inequality). The solid that minimizes the ratio of surface area to volume (SA/V) in Euclidean 3-space is the sphere.

A Biological Argument. Consider the large class of animals capable of changing their ratio of surface area to volume. (And note that these animals live -- approximately -- in Euclidean 3-space.) What do these animals do when it's cold? They curl up into a ball! More precisely, they assume the closest approximation to a ball that they can manage. This is because any exposed surface area is a place where heat is lost, and curling up into a ball minimizes that surface area. So a spherical or "ball" shape keeps animals warmer. Now, here's how these ideas can be turned into a 4-line "biological proof" of the above proposition.

1. Animals overwhelmingly assume a spherical shape when they are cold.


2. If animals overwhelmingly assume some shape when they're cold, then it is because that shape is the warmest.


3. The warmest shape is the one that minimizes SA/V.


4. Therefore, the sphere is the shape that minimizes SA/V.

It's a pretty easy argument, and you can write it down in four lines. At the same time, there simply are no easy mathematical arguments for this proposition in 3-Dimensions (for a nice survey, see Osserman (1978).)

Now, here come the tricky questions: what's the status of an argument like the one that I've given here? What does it allow me to infer? And especially: how does it compare to an argument in which, say, the conclusion is produced by way of the calculus of variations?

And just to ratchet the trickiness up another notch: there are apparently many of these non-mathematical arguments for mathematical claims. For example, a lovely economic argument for a mathematical conclusion was recently described about by Kenny, which he calls part of the "unreasonable effectiveness of the sciences in mathematics."

But let me encourage a little caution. Arguments with correct conclusions are easy to come by. An example: Bibble, babble, blat, blit: therefore, the primes are infinite. We must not be mislead by the fact that this argument for the infinitude of the primes (which is drivel) ends with a correct conclusion.

The biological argument above is analogous, to an extent (though I hope not quite drivel). Suppose that premise (1) turned out to be wrong -- for example, our empirical data may have been poorly gathered, or we may have interpreted it incorrectly. Then this little "proof" would be just another bad argument for a correct conclusion.

This doesn't mean that non-mathematical arguments for mathematical claims can't lead to new knowledge. I think that they can, and in many cases they do (is this mathematical intuition?). But my suspicion is this: these non-mathematical tricks are instructive only insofar as they lead to good arguments.

Update, 2 July 08. I just found out that George Pólya (1954, 170) has already suggested this kind of argument could be made. But the difficulty of the exercise remains, as I suggest above, in how you work out the details.

When Philosophers of Science Go Practical

Here's a feature of philosophy of science that may have captivated many of us: the freedom to be shamelessly, wildly creative about science.

Philosophers of science love to think hard about difficult questions, so that our minds can run happily with possibilities. But we're interested in knowing what science says about these matters. So we dive into the neather-regeions of algebraic quantum field theory and differential geometry, or population genetics and probability -- or whatever part of scientific practice catches our interest.

What happens when that kind of carefree creativity and affinity for science are set loose on raw, practical problems? Nathan Myhrvold seems to have asked this question, and then systematically implemented an answer, in a company called Intellectual Ventures.

The first part of what I.V. does looks a lot like the Philosophy of Science. (An interesting note: Myhrvold did a PhD in early-universe QFT.) A bunch of interesting people get together, think about interesting stuff on which science bears, and then come up with ideas. The really good ones get refined and developed thoroughly, and written down. But then comes the second part: those ideas get patented. And then they get sold.

Read about it in the recent New Yorker Article.