Elegant Desktop ToDo List

A lot of people have been asking me about the Desktop ToDo list that appears in my last screencast. So, here's the scoop on this simple and elegant ToDo list system, which can be easily synchronized across multiple (Mac) computers.




Here's what you need to set this stuff up.

Mac OS X. I don't know of any good windows analogues for Quicksilver and Geektool. Let us know if you do!

Geektool. This beautiful little app is available for free from Tynsoe.org. For more on what it can do, try this tutorial. For our purposes, here's how to display a TXT file on your Desktop:

• Create a new Shell geeklet in the Geektool preference pane
• Enter the command: cat PathToYourList/YourList.txt
• To synchronize multiple computers, make sure the file is in a Dropbox folder.

Quicksilver. This is why I own a mac. It's free from Blacktree.com. If you're new to it, try this beginner's guide. To set up the 'Append' and 'Completed' functions seen in the screencast:

• On the Quicksilver > Plugins page, add the 'Text Manipulation Actions' plugin. Then make sure 'Append' box is checked on the Preferences > Actions page.
• Now you can append text to any .TXT file -- but only files with that extension.
• Download the Completed script.
• Open it with ScriptEditor and set the path to your Completed.txt file.
• Add the Completed.scpt script to the folder YourUsername/Library/Application Support/Quicksilver/Actions. Create this folder if it doesn't exist yet.

And that's it! As always, be sure to leave your thoughts, ideas or improvements in the comments below.

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The three-way duel

The late great Martin Gardner once posed this puzzle.

Suppose you're involved in a duel with two other people. You (Person A) shoot first, followed Person B, followed by Person C, then it goes back to you, and so on. Moreover, you know the following about everyone's shooting skills.

• You (Person A) will hit your target with probability 1/3.
• Person B will hit her target with probability 2/3.
• Person C is a perfect marksman, will hit his target with probability 1.

You get to go first. Who would you shoot at, and why? Best solution gets a free sheep.

(Note: your options are Person B, or Person C, or neither.)

Update:  Jonathan of Unshielded Colliders has been awarded a free sheep for his solution. Here you go, Jonathan:

In Memory of Bacon

Not the fatty breakfast-food, although you may remember that if you like. The great Sir Francis Bacon died 384 years ago today. And in memory of Bacon, here is your assignment:

THIS PASSAGE IS A FRANCIS BACON CIPHER WHERIN THE BOLD LETTERS REPRESENT B AND THE PLAIN LETTERS REPRESENT A

Cheers!

On Th' Electrodynamics O' Moving Bodies

What do you do when you come across an excellent English-Pirate translator? You immediately translate Einstein's presentation of Special Relativity into Pirate-speak:

't might appear possible t' overcome all th' difficulties attendin' th' definition o' "time" by substitutin' "th' position o' th' wee hand o' me watch" fer "time." An' in fact such a definition be satisfactory when we be concerned wi' definin' a time exclusively fer th' place 'ere th' watch be located; but 'tis nay longer satisfactory when we be havin' t' connect in time series o' events occurrin' at different places, or--what comes t' th' same thing--t' evaluate th' times o' events occurrin' at places remote from th' watch. (More)

Now that's physics even a scurvy bilge-rat can understand. The entire Pirate-speak translation of "On the Electrodynamics of Moving Bodies" can be viewed here. Enjoy!

Constructing the Ultimate Machine

The mathematician and engineer Claude Shannon kept a machine on his desk, which he called "The Ultimate Machine." As it turns out, there are a number of clever instantiations of Shannon's machine on the intertubes. Here are a few of the best ones.

The Classic Model. Large. Sumptuous. Classic.

The Elegant Two-Handed Version. Transparent so you can see the mechanism at work.

Lego Ultimate Machine. The ultimate application of your favorite building bricks.

Variant - The Unplugger. There seems to be a slippery slope from this to "The Exploder."

And now the craze over the Apple iUltimateMachine is just a matter of time. Not to mention the Ultimate iPhone App. You're welcome, Steve Jobs.

Get Started Handling Academic Citations Like a Pro

Using a Mac to do your academic work? Here's a brief tutorial on how to optimize your day-to-day dealings with academic citations, by integrating Bibdesk, Textmate, Quicksilver and Scholar. Below, you'll find instructions on how to set up all these neat little tricks.

Quicksilver Web Search. After you download Quicksilver (free) and open the preferences window, go to Plug-ins > All Plug-ins, and check the box next to "Web Search Module." Restart Quicksilver. Go to Catalog, click the "+" at the bottom-left, and select "Web Search List." A new pane should appear (if not, click the little i), in which you can add any number of web-search shortcuts by clicking the other "+" appearing above "Source Options" on the new pane. Just go to any search box (such as Google Scholar) and search for "***", and copy resulting page's URL. Paste it in the web-search shortcut you just created in Quicksilver under "URL." Under "Name," write something useful like "GoogleScholar." Finally, rescan your catalog by clicking the circular-arrow in the bottom right. That's it! To search for stuff, just invoke Quicksilver, hit "." (period) to enter text, hit Tab, start typing "Find with", hit Tab again, and start typing "GoogleScholar."

Even more useful -- if you want to use a secure remote access service (like VPN) to search for articles from home, just log into VPN before going searching for "***" in Google Scholar. When you first search for something, you'll have to enter your username and password. But in every search after that, you'll have your regular access to secure articles.

Bibtex Records on Google Scholar. You won't see these unless you actually set them up. Log into your Google account, go to Google Scholar, and click the "Scholar Preferences" link next to the search box. Click the dial that says, "Show links to import citations" and select "BibTex" from the drop-down menu. Now you'll see that useful BibTex link below all your search results.

Bibdesk. You can download this beautiful little app for free from Sourceforge. If you copy a bibtex citation record to the clipboard, you can add it automatically to Bibdesk by typing Command-Option-L.

Textmate Drop-down Menu. Make sure you've installed Textmate (trial available from Macromates) and Bidesk. To set up that neat little drop-down menu in Textmate, first download and unzip the "Completion.zip" package (available here or here). Second, double-click each of the .tmComand files. Next, copy the binary file "BibDeskTMCompletions" somewhere convenient, like a folder called "bin" in your home directory. Finally, open Textmate and go to Bundles > Bundle Editor > Show Bundle Editor. Click the newly-added bundle, "Build Cite With BibDesk." Find the line that begins "CMD = '"$HOME"...," and set it to the path of your binary file. If you chose the "bin" folder in your home directory, just change this line to the following:

CMD = '"$HOME"/bin/BibDeskTMCompletions

Do the same thing in the bundle, "Bibdesk DO Completion." While still in this second bundle, set a useful Activation key, such as the Tab-Trigger "cite". Close the editor and restart Textmate. Now, to make the drop-down menu work, you just need to open a Latex document with a bibliography set at the end -- for example, mine reads \bibliography{~/Documents/MasterBibliography.bib}. Now, whenever you type "cite" followed by the Tab key, you'll get a drop-down menu displaying all the references in you .bib-file.

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Galileo and the Physics of Skydiving

During a visit to Skydive, PA yesterday, I noticed jumpmaster Jim tightening a corset-like weight belt onto his abs. "Jim, your figure looks so refined," I commented. Jim sneered. "I've got to keep up with the big guy," he said, nodding toward the hulking student he was about to jump with.

True enough. But it sounded funny to me, having just re-read Galileo's Two New Sciences. Galileo doesn't fool around: he clearly states that your speed in freefall does not depend on your mass. His student Viviani famously reported that Galileo discovered this by dropping different weights off the Leaning Tower of Pisa, and observing that they hit the ground at the same time.

And yet, skydivers wear weight belts to fall faster. A slight person like Jim, I myself used to wear such a belt, when I was a student learning to fly with much bigger skydivers than myself. And it really helps. The reason is: even though your body mass doesn't affect your acceleration in a vacuum, it does affect how hard your body pushes against air.

A few seconds after stepping out of a plane, a skydiver's motion will begin to be slowed by the drag force of air -- the same force you feel when pushing your arm through the water of a swimming pool. The weight of the skydiver pushes back against the drag force, until the two forces become equal and a constant (terminal) velocity is reached. The heavier you are, the harder your body pushes back against that drag force -- and the faster your terminal velocity will be. In particular:

where K is a constant, m is your mass, and SA is the surface area that is facing the wind. In short: when you skydive, your surface area slows you down, and your mass speeds you up. That's why small skydivers sometimes wear weights.

Of course, Galileo still had the basic mechanics correct: when air resistance is neglected, mass doesn't matter. However, it does seem unlikely that he would have put much thought into the effect of mass on terminal velocity. After all, accurate measurements involving freefall were hard enough even at earthly speeds. As I've noted before, the difficulty of these experiments gave rise to much confusion about the nature of freefall in the early years of mechanics.

So. Galileo was right, but you may still need weights to keep up with your skydiving partner.

How do you know who's going to fall faster? You can read the basic rules off the equation above. Someone the same height as you but heavier will have increased mass, and fall faster. Someone the same weight as you but taller will have increased surface area, and fall slower.

It's even easier if your partner is of your same proportions (that is, taller or shorter, but no more overweight or underweight than you are). Everyone has roughly the same body density, so mass is roughly proportional to volume. But volume is roughly proportional to surface area (SA) times height (h). So, if you're jumping with someone who's similarly proportioned, above equation reduces to:

For example, 9% taller (about a head) means 3% faster. For a typical terminal velocity of around 200 feet per second, that means: for similarly proportioned people, a head taller means about 6 feet per second faster.

Are skydivers ever in the kind of environment where these rules don't hold? Only in the absence of air. This seems to have happened just once, when Joe Kittinger jumped out of a balloon at 100,000 feet during the (1959) Project Excelsior study. That's well beyond the official edge of the earth's atmosphere, making it the only skydive from space. I'll leave you with the video for today. Blue skies -- I hope to see you up there!

How to Create a Closed Timelike Curve

Time along the vertical axis; space along the horizontal....





Voila! And now, how to travel to the past....

Soul Physics Meets Cosmic Variance

Sean Carroll of Cosmic Variance made his way to Pittsburgh on Friday. Sean and I managed to solve the problems of the Universe over lunch (more or less), before his visit to the Center for Philosophy of Science. We were joined by fellow Pittsburgh philosophers John Earman, Balázs Gyenis, Elay Shech, and Julia Bursten.

After lunch, Sean gave a very interesting lecture on why the early Universe might appear to have begun in a low-entropy state. His idea, stemming from a couple of his recent papers, is that the entropy of the Universe can increase without bound. Once the Universe has reached maximum entropy state (which Sean models as de Sitter spacetime -- empty but expanding), there is some quantum mechanism a la Farhi, Guth and Guven (1990) that can pinch off new 'baby' Universes, in which entropy can continue increasing. The process is symmetric in time, and can be continued indefinitely.


Pittsburgh was the first stop on Sean's tour for his new book, From Eternity to Here: The Origin of the Universe and Time. The book will be published by Dutton, is written for popular science audiences, is scheduled to be out this Fall (2009).

Visualize the Eversion of a Sphere

It is famously possible to continuously deform a sphere until it's inside out. You have to imagine the sphere is something like a bubble, which can 'pass through' itself. This transformation is called an eversion.

The fact is established by a theorem due to Stephen Smale (1959 - JSTOR),
which is not constructive -- Smale was not able to tell us exactly how we can carry out this deformation. However, recent computer-minimization techniques have allowed us to describe many (constructive) ways to turn a sphere inside out.

The process is difficult for most of us to visualize. Fortunately, three University of Illinois mathematicians have made a 7-minute computer animation that illustrates how it's done. (Warning: this video is trippy.)


Smale's theorem says that any two immersions of a sphere a real n-dimensional manifold are regularly homotopic. Thus, in particular, it follows that a sphere sitting in 3-space according to the immersion,


is regular homotopic to the same sphere turned inside out (that is, to inverse immersion). Smale is also well known for having proven higher-dimensional versions of the Poincaré conjecture in the 60's.

Quantum of Solace

What does quantum mean? With a new Hollywood blockbuster just out, and containing the word "quantum" in the title, it seems we'd better get to the bottom of this.

The word "quantum" was substantively introduced into atomic physics by Einstein, in his 1905 paper (PDF) on the thermodynamics of radiation. (Einstein won the 1921 Nobel Prize in physics for this work.) The meaning of "quantum" in this paper is clear: Einstein describes heat radiation as behaving thermodynamically as if it were made up of "energy quanta" -- discrete chunks of energy of exceedingly small size size hf (where f is frequency and h is Planck's constant, the latter being equal to about 0.0000000000000000000000000000000006). In other words:

    Meaning #1: quantum = very small chunk.

However, when someone refers to a "quantum theory" today, it almost always means much more than Meaning #1. As I've mentioned before, we can point to three categories of phenomena that can be tested in a laboratory, which in large part form the empirical basis of quantum theory. They are:

(1) particle diffraction;
(2) superposition; and
(3) discrete energy spectra.

Einstein's original use of the word "quantum" was an instance of item (3). But today, when one often refers to a "quantum particle," "quantum tunneling," "quantum teleportation," and the like, what is meant (broadly speaking) is:

    Meaning #2: quantum = exhibiting properties (1), (2) and (3).

Of course, this characterization is perhaps heavy on the side of the experimentalist. The theoretician might prefer to think of "quantum" as referring to the structure of a typical quantum theory. Unfortunately, it's not that easy to say precisely what that structure must be like. For example, it's certainly not a simple matter of casting one's theory in terms of bounded operators on Hilbert space, since Koopman and von Neumann showed that this is also possible for classical theories. But I think it's fair to ask that, in order for a theory to be "quantum," it must admit:

(5) a unitary representation of the Canonical Commutation Relations; or
(6) a unitary representation of the Canonical Anticommutation Relations.

Since the theories typically described as "quantum" all tend to admit at least one of these two properties, we now have available:

    Meaning #3: quantum = characterized by (5) or (6).

There's one last meaning for "quantum" that I should mention. It's a unique (and, for the moment, inescapable) feature of all our current quantum theories, but perhaps an undesirable one. Namely, quantum theories describe the world in terms of the following two kinds of processes. The first, called unitary (Schrodinger) evolution, is continuous through time. The second, called state reduction (or for von Neumann (1932), "wave function collapse"), is discontinuous. So, according to quantum theory, the typical lifetime of an entity in a particle physics lab consists in a sequence of successive evolutions and "jumps." A system evolves continuously, until a measurement interaction occurs. It then undergoes a discontinuous transition to a new point, and then begins evolving continuously again. (The nature of these jumps is a matter of debate among interpreters of quantum theory, but let's bracket that.) We thus have:

    Meaning #4: quantum = discontinuous transition.

This meaning seems most closely related to the use of the word in popular jargon. Indeed, my dear friend and fellow blogger Justin over at My Mind is Made Up thinks that the main way people use the word is in phrases like "a quantum leap." If this simply means a severe, discontinuous jump, then I'd say "the folk" have picked up on Meaning 4. Interestingly, Justin tells me that Hollywood has managed to pick up on something more like Meaning #1, which would be more historically accurate. But of course, I'm no expert on Hollywood, or the folk -- so check out what Justin has to say!

Special: What's With the Economy.

I'm a philosopher of science, not an economist. So I decided to write a story that explains what's with the economy, using small words and Disney characters. The first 5 parts explain the background. The last two parts explain what's actually going on. So here it goes.

PART 1: SECURITIES. There's a hamburger joint on your street called BurgerBee, and they do pretty good business. But they need some extra cash up front (say, to get a new grill). You have cash up front. So the two of you strike a deal: you will give BurgerBee some money (say, 1000 bucks or so). In return, BurgerBee will give you a little certificate, which says that every day, you get 1% of the money that BurgerBee makes. That sounds pretty good to you, because eventually, the money that BurgerBee gives you will add up to much more than 1000 bucks.

The certificate that BurgerBee gave you is called a security. It is a promise that you will get some money, although you will generally get it over an extended time period.

PART 2: MORTGAGES. Every month, BurgerBee (or anyone else who owns a building or a home) pays an expense called a mortgage. The reason for this goes back to when BurgerBee first became a restaurant. They wanted to buy a building to make and sell burgers in. The wealthy Scrooge McDuck had enough money to buy buildings. So they struck the following deal.

McDuck gave BurgerBee the money to buy a building for their burger joint (say, $100,000). In return, BurgerBee gave McDuck a little certificate, which says that BurgerBee will pay McDuck MUCH MORE than the original amount (say, $200,000). But the payments are made in small amounts, every month, over the course of 30 years. (Actually, the extra amount paid is interest, but let's not complicate this story.)

That payment is called a mortgage.

PART 3: PRE-PAYMENTS & FORECLOSURES. In order for the deal with McDuck to be fair, there's one exception about those mortgage payments. Imagine that, one week after McDuck gave BurgerBee the money for the restaurant building, BurgerBee came into 100,000 bucks all by themselves. (Let's say they owned another store elsewhere, and were able to sell it.) BurgerBee wants to pay back McDuck. But should they really have to pay him back the entire $200,000 dollars, after only 1 week? That doesn't seem fair! That extra money was meant to compensate for the fact that it would take 30 years to make the payment.

So BurgerBee and McDuck added the following exception to their deal: if BurgerBee pays McDuck back EARLY, then they don't have to pay as much. So after a week, they might only have to pay back $100,001 dollars. And after 15 years, they might only have to pay 150,000 dollars. And so on. (Again, what really happens is that each payment has interest added to it, but we're setting aside that complication.)

And it is exactly the same situation if the burger business goes bad, and BurgerBee can't keep making the mortgage payments to McDuck. In that situation, the two agree that McDuck takes the building away from BurgerBee as a payment. But remember, the building is only worth $100,000. So McDuck won't get his full $200,000 in that case either.

If BurgerBee completes their mortgage early, it is called a pre-payment.
If BurgerBee stops making payments and McDuck takes the building, it is called a foreclosure.

PART 4: MORTGAGE-BACKED SECURITIES. Now, McDuck is a pretty clever investor. So he decides to use his mortgage certificate to get some immediate cash. Suppose that McDuck does mortgages for a lot more people besides just BurgerBee. In total, let's say that he gave away $2 million for people to build restaurants. McDuck feels pretty good about this, because he expects to eventually get $4 million in return -- he just won't see all of it for 30 years.

But now imagine that McDuck needs some cash up front. (Let's say he wants $3 million to build a skyscraper.) The Bank has $3 million up front. So the two decide to strike a deal. The Bank will give McDuck the money for his skyscraper. In return, McDuck will give the Bank all of his mortgage certificates. These certificates are worth $4 million. But the Bank won't see all of it for 30 years.

McDuck's mortgage certificates are called mortgage-backed securities.


PART 5: RISK. The Bank just gave $3 million in cash to McDuck, and received $4 million in mortgage certificates in return. This seems like a pretty good deal: with a little patience, the Bank makes a million bucks. However, there is also a risk involved in the deal. Remember, if BurgerBee pays its mortgage back early -- or if it stops making payments -- then it won't pay back the entire $200,000 -- it might pay back much less than that. If this happens, then the Bank won't receive the full $4 million dollars.

Now, the Bank is still generally willing to take that risk. Even if BurgerBee pre-pays or forecloses on its mortgage, the Bank can still make a nice profit -- say, $900,000 instead of a million. But if EVERYONE payed back their mortgage too early -- or stopped making payments -- then the mortgage certificates could actually bring back less than $3 million total. Then the Bank will have gotten screwed: it gave McDuck $3 million, and got back less than $3 million in return. But it's pretty unlikely that EVERYONE pre-pay or foreclose. So the Bank is generally willing to take that risk, in order to make some money.

PART 6: OUR PROBLEM. The problem is, some of the most important banks and McDucks in the US got screwed in exactly this way. But not out of a million dollars -- we're talking about losing billions each, sometimes over the course of just a few months.

There were a lot of things that led to this. Here's the basic idea. Consider poor Mickey Mouse, who was struggling to make a living this decade. McDuck decided to lend him some money anyway, to buy a nice house (let's say, $100,000). This was a very risky idea. After all, poor old Mickey was struggling just to get by, let alone make regular mortgage payments. So to make up for the risk, McDuck asked Mickey to pay MUCH more than the original price of the house -- say, $500,000 over the course of 30 years. McDuck was betting that he had a chance to make a lot more money, because $500,000 is a lot more than $100,000. But it was a risky bet.

That kind of risky mortgage is called a sub-prime mortgage.

As it turned out, starting last year, millions of Mickey Mouses around the country stopped making their payments, and their houses were foreclosed. And so thousands of McDucks lost their bets.

This had a kind of domino effect. Think about the skyscraper that McDuck built. He payed the bank in mortgage certificates (mortgage-backed securities). So when all those Mickey Mouses stopped paying, the "unlikely" actually happened -- those mortgage certificates lost most of their value, and the banks got screwed.

In the news, they are calling these kind of mortgage certificates bad or toxic mortgage backed securities.

The dominos kept falling, because almost everyone was connected to those bad certificates somehow. For example, the banks also made payments using those certificates. And even worse, they themselves took out new loans ON THE BASIS of those certificates. (This kind of thing is called a derivative, and it gets very complicated.) A good analogy is a tower (i.e., US borrowing practice) with a very risky foundation (i.e., bad mortgage backed securities). So when the foundation fell out, the whole building started to wobble almost uncontrollably.

On Wallstreet, this meant that nobody knew how much anything was worth. It started with all those houses that foreclosed. Nobody's really sure how much those houses are worth. So lots of banks are invested in lots of houses of questionable value. So nobody's sure how much the banks are worth -- or all the elaborate derivatives -- all the way up. Now, when people on Wallstreet don't know how much something is worth, they often do one of two things: they do nothing, or they sell. They did both last week. And so the stock market fell dramatically.

PART 7: THE PLAN THIS WEEK. The main strategy of the US Government is now to try to restore confidence in those investors, so that the stock market doesn't fall so badly. Paulson, the Bush administration's treasury secretary, proposed a plan for the US government to buy up a lot of those bad mortgage backed securities. The idea is to take out the bad foundation, and replace it with a sturdier, cash foundation. Paulson is hoping that this will calm investors on Wallstreet, and get things on the road back to normal.

The question that nobody knows the answer to is: will this work? Or is the tower already on its way down?

Riemann Hypothesis Gets Proved Again

Yet another proof of the Riemann Hypothesis (RH) has been proposed by BYU mathematician Xian-Jin Li. Dr. Li posted his proof on the arXiv a few days ago. (Update, 11:05am.)

Why I'm Not Holding My Breath. Although it's tempting to get excited over a proof of RH, here are a few reasons why I'm not holding my breath:

1. Pitkanen's proof of RH (2001). Withdrawn by author due to errors.


2. Castro & Hahecha's proofs of RH (2001, 2002, 2006). Approach has been rejected.


3. Shi's proof of RH (2003). Proof contains errors.


4. de Brange's proof of RH (2004). Remember all the media attention this got? A counterexample was later produced.


5. Chun-Xuan's proof of RH (2005). Proof contains errors.


6. Aizenberg's counterexample to RH (2007). Withdrawn by author due to errors.


7. Madrecki's proofs of RH (2007a, 2007b, and 2007c). Proofs contain errors.


8. Han's proof of RH (2008). Proof contains errors.

These once-hopeful provers of RH are only the tip of the iceberg. But that's not what's really fearful about proposing a proof of RH. Check out the way that Stanford mathematician Brian Conrad layed into this nut job, for being arrogant about a purported proof!

I suppose you can't escape when duty calls. (A note on Conrad's last sentence: he's evidently not a historian of mathematics.) At any rate, the expert verdict on Dr. Li's proof will be out within a year or so. I'm willing to be patient on this one.

What is the Riemann Hypothesis? The Riemann Hypothesis is that the non-trivial roots of the Zeta function on C, given by


all have real component Re(s) = 1/2. In his famous 1859 paper, Riemann wrote that,

Without doubt it would be desirable to have a rigorous proof of this proposition; however I have left this research aside for the time being after some quick unsuccessful attempts, because it appears to be unnecessary for the immediate goal of my study...

You can read more about RH at Mathworld, about failed proofs at Matthew Watkins's homepage, and about the $1 million prize out for its solution at ClayMath.org.

Edit: Update, 11:05am. Field's medalist Terence Tao has pointed out an error in the proof. It is possible that there are more.

Famous Dead Philosophers Speak Again!

Inspired by Shawn's post at Words and Other Things, I compiled a short list of video/audio lectures by famous dead philosophers. If you know of any famous dead philosophers that should be on this list, please tell me!

A. J. Ayer (video interview with Bryan Magee on logical positivism, part 1, 2, 3, and 4) and on Frege and Russell (parts 1, 2, 3, 4 and 5). Sir Freddie Ayer is likely responsible for the popular conception of logical positivism that we all know and love. (1910-1989)

Donald Davidson v. Michael Dummett (discussion at LSE, part 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12). Davidson (1917-2003) brought a very unified view to the philosophy of mind, language, epistemology, metaphysics and more (1917-2003). Dummett is a philosopher of mathematics, logic and language, who retired in 1992 but is still going strong.

Karl Popper (video interview in German). Austrian/British empiricist, friend of the corroborated and foe of the Freudian. Popper is the "physicist's philosopher," famous for popularizing falsifiability. (1902-1994)

W. V. O. Quine (video interview with Bryan Magee interview, part 1, 2, 3, 4, and 5). Quine (1908-2000) was a Harvard logician and philosopher, a well-known critic of logical positivism and supporter of holism.

Bertrand Russell ("Face to Face" video interview, part 1, 2, and 3 -- and winning the nobel prize). Logician, mathematician, logician, philosopher, and of fame that goes well beyond most other 20th century philosophers. (1872-1970)

Wilfred Sellars (audio interview on meaning and language). Thanks to Shawn for this one. Sellars was a pillar of the Pittsburgh school, and one of the primary developers of the study of the history and philosophy of science. (1912-1989)

For more online videos of philosophers, most of whom are not dead, visit a brood a comb.

Update, 1 July 08. Mikolka has compiled a list of Magee's videos, and there are even more philosophers speaking at freevideolectures.com.

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?

When is the Prime Age of Discovery in Physics?

Remember that old adage about young scientists? It goes something like this: most scientists do there best work before they're 25.

I don't know where this folk truism comes from, but I've always wondered if there's any evidence behind it. Here's a little evidence that suggests it might be false, and that the "prime age" for discovery in physics might be around 34.

Haphazardly choosing 20 of my favorite great physicists, I charted each one's date of birth against the date they published a groundbreaking discovery. This indicated how old each physicist was when they made a major breakthrough. Here are the results, organized from youngest to oldest (the physicists inside the dotted lines are the median):


Here are a few interesting features of this chart:

1. There are great physicists on both ends of the list. Those who were above the median age when they made their breakthroughs are at least as respectable as those who were below it. And Richard Feynman, one of the most revered physicists among physicists themselves, was at exactly the median age when he published "Space-Time Approach to Quantum Electrodynamics."


2. Einstein's age on the chart should arguably be 35. In 1905, Einstein was 26. This was his "Miracle Year," when he published three groundbreaking papers, which included "On the Electrodynamics of Moving Bodies" (Special Relativity). But Einstein's greatest work is (arguably) General Relativity, which he completed in 1914 -- when he already 35.


3. Several creators of the "New Quantum Theory" were absurdly young when they made their breakthroughs. For example, Heisenberg was 24 when he wrote his "Quantum Theoretic Re-Interpretation," and Wigner 25 when he wrote "On the Conservation Laws of Quantum Mechanics."


4. Not All Creators of (New) QM Were That Young. For example, Schrodinger was 39 when he made a number of important breakthroughs, including "Quantization as a Problem of Proper Values."

Conclusion: Older scientists do great work too! The folk-truism that youth is the age of discovery is not all that accurate -- although it seems approximately true for a generation of quantum theorists.

However, we may still ask: is the age of discovery becoming younger over time? Suppose we restrict our attention to the 19th century and on, and plot the date of birth of each of these physicists against their ages in the year of their major discoveries. Here's what we get:



There does seem to be a trend toward younger and younger discoveries (the spike in the middle is Schrodinger). However, it might also be that the youth of the (new) quantum theorists was unnatural, and that if you added in more recent physicists, you would get an upward trend again.

We'll have to make some less haphazardly assembled charts to find out.

n-Player Chess

Have you ever wanted to play a single chess game with two other people? What about with three or four other people? Is it possible to design a chess game that supports any finite number of players? Here's a precise description of this challenge, followed by my attempt at a solution.

The Challenge: Create an n-player chess board that (i) preserves all the traditional pieces and their degrees of freedom; (ii) is divided into cells with eight directions each (F B L R + diagonal); and (iii) minimally changes the strategy of traditional chess.

First example: here is an interesting 3-player board (link no longer exists). But it doesn't meet the challenge, because it's composed cells with 12 directions each. This means that the pieces also don't move in the traditional ways (For example, the queen can move in 12 directions instead of 8).

Second example: Meignorant found a 3-player board that has 4-sided cells. This board almost preserves the traditional motion of the pieces -- but not quite! In the middle six cells, there are 10 directions, which means that the pieces acquire additional degrees of freedom there.

Another drawback of both of these examples is that it's not obvious how n players can be added, instead of only 3. Here's a board design that makes this trivial.

A Solution. Start with a circle. Divide it into n equal portions. Then divide each portion into an 4x8 grid (4 cells along the radius, 8 along the circumference). For n=3 players, what you'll get is a board that looks like this:
One new board rule: the only way that a piece can pass from one of the n regions to another is by going through the center. In the board drawn above, this means that the three white lines separating the 3 regions are impassible barriers. However, straight lines pass through the central point just as they appear to.

The first two conditions are easily satisfied. All the pieces can keep their original degrees of freedom, because every cell (including each middle cell) has 8 directions (F B L R diagonal). Indeed, each cell even lies in one column and one row, each of length 8 -- just like in traditional chess.

But what about the strategy? The strategy changes about as little as I think is possible. For example, when n=2, the game just reduces to something very similar to traditional chess. (Can you figure out what's different? This difference can actually be avoided, but not without giving the board an unusual topology.)

On the other hand, things definitely start to change in higher-player chess games, although I don't know the extent of this until someone actually plays a game.

Note that from any given player's side of the board, only 1/(n-1) of each of the other players' sides of the board is accessible. (In the image above, 1/(3-1) = 1/2 of the other two regions are accessible from any given region). This might be insignificant when n is small. However, it means that for games with more than 10 players, there are always be regions of the board that you cannot access without first moving to another region.

This feature of many-player games may actually help to limit the chaos, by limiting how many people can attack a single player in a single round. It also makes the following question especially interesting.

A Final Question. For what values of n can a `Knight's Tour' be completed in n-player chess?

A Knight's Tour is possible iff it's possible for a knight to complete a circuit in which it lands on every cell exactly once, and ends up back where it started. Many theorems have been proved about this for different board shapes. It has been proven, for example, that a Knight's Tour is possible on a traditional chess board.

However, solving the problem for n-player chess seems to be quite a bit more complex. But let me leave it as an open question for now.

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.

Does Google's Logo-Artist Like His Father Better Than His Mother?

Too impatient to wait until Sunday, my wife decided to investigate what the Google Logo might be this Mother's Day, on the basis of previous years. She was upset to find that, not only should she expect something boring, but she should expect the father's day logo to be way better!

While Dad can expect to go swimming, fishing, napping, and playing with the kids -- mom can expect a flower or two, or maybe a bad drawing. And she might even get the same flower she got last year!

Want to see for yourself? Compare the history of Google Logos for father's and mother's day, respectively. Dad gets to sip iced tea in the pool, while Mom gets crayon-on-paper? Where's Mom's inner tube?



(2007)

Then there's the previous year, when Dad got to go fishin' with the boy, while Mom got a flower. Ok, flowers can be fun too...




(2006)

...but two years in a row? While Dad scores a nap in the hammock?




(2005)

Even more flowers for mom? This year, Dad even got the kids to do his chores.




(2004)

More flowers for Mom, more relaxing for Dad...




(2003)

and while Dad plays with the kids, Mom gets... more flowers? Come on!




(2002)




(2001)




(2000)

So here's our open question: what's going on, Dennis? Why does Dad get all the fun?

 

Astrophysics with Ice Cube

The article is available here.

That's right. If you thought that identifying galactic cosmic rays was funky, try doing it with IceCube. Wes sai!

Apparently, IceCube has recently been involved in a number of interesting developments. If you thought ''galactic cosmic rays'' was hip, you may also be interested in IceTop: Cosmic Ray Physics with IceCube. Then of course, there's Ice Cube's skillful ability to detect dark-matter. A variety of projects with IceCube are described in Performance, Status and Future, as well as in Ice Cube: The State of the Art. Then there's the much anticipated and the soon-to-be PBS special, New Physics with IceCube, which I personally can hardly wait to see.

Yes, it looks like a pretty exciting research program with Ice Cube is underway. I only hope that these guys aren't having any problems with copyright infringement.