Jul 242010
 

I have been reading the celebrated biography of Albert Einstein by Walter Isaacson, and in it, the chapter about Einstein’s beliefs and faith. In particular, the question of free will.

In Einstein’s deterministic universe, according to Isaacson, there is no room for free will. In contrast, physicists who accepted quantum mechanics as a fundamental description of nature could point at quantum uncertainty as proof that non-deterministic systems exist and thus free will is possible.

I boldly disagree with both views.

First, I look out my window at a nearby intersection where there is a set of traffic lights. This set is a deterministic machine. To determine its state, the machine responds to inputs such the reading of an internal clock, the presence of a car in a left turning lane or the pressing of a button by a pedestrian who wishes the cross the street. Now suppose I incorporate into the system a truly random element, such as a relay that closes depending on whether an atomic decay process takes place or not. So now the light set is not deterministic anymore: sometimes it provides a green light allowing a vehicle to turn left, sometimes not, sometimes it responds to a pedestrian pressing the crossing button, sometimes not. So… does this mean that my set of traffic lights suddenly acquired free will? Of course not. A pair of dice does not have free will either.

On the other hand, suppose I build a machine with true artificial intelligence. It has not happened yet but I have no doubt that it is going to happen. Such a machine would acquire information about its environment (i.e., “learn”) while it executes its core program (its “instincts”) to perform its intended function. Often, its decisions would be quite unpredictable, but not because of any quantum randomness. They are unpredictable because even if you knew the machine’s initial state in full detail, you’d need another machine even more complex than this one to model it and accurately predict its behavior. Furthermore, the machine’s decisions will be influenced by many things, possibly involving an attempt to comply with accepted norms of behavior (i.e., “ethics”) if it helps the machine accomplish the goals of its core programming. Does this machine have free will? I’d argue that it does, at least insofar as the term has any meaning.

And that, of course, is the problem. We all think we know what “free will” means, but is that true? Can we actually define a “decision making system with free will”? Perhaps not. Think about an operational definition: given an internal state I and external inputs E, a free will machine will make decision D. Of course the moment you have this operational definition, the machine ceases to have what we usually think of as free will, its behavior being entirely deterministic. And no, a random number generator does not help in this case either. It may change the operational definition to something like, given internal state I and external inputs E, the machine will make decision Di with probability Pi, the sum of all Pi-s being 1. But it cannot be this randomization of decisions that bestows a machine with free will; otherwise, our traffic lights here at the corner could have free will, too.

So perhaps the question about free will fails for the simple reason that free will is an ill-defined and possibly self-contradictory concept. Perhaps it’s just another grammatically correct phrase that has no more actual meaning than, say, “true falsehood” or “a number that is odd and even” or “the fourth side of a triangle”.

 Posted by at 1:36 am
Jul 202010
 

It’s been 41 years since Armstrong’s first “one small step” on the surface of the Moon.

Year after year, I express my hope that it won’t take another, well, 41 years before the next step is taken.

 Posted by at 4:30 pm
Jun 302010
 

Can both climate alarmists and climate deniers be right (or wrong) at the same time? Perhaps so. At least that’s my understanding after reading about a new study that was designed to evaluate the judgment of climate experts.

The way I see it, yes, there is consensus that the planet is warming. Yes, there is consensus that human activity contributes to the warming. Yes, there is consensus that the warming can have disastrous consequences.

However, there is no consensus regarding the magnitude of future warming. There is no consensus regarding the extent to which human activity vs. natural causes are responsible for the warming. And I don’t think a consensus exist that the consequences of the warming are uniformly bad for humanity, or even that the bad consequences outweigh the potentially good ones.

In any case, consensus is irrelevant. Science is not supposed to be a democracy of scientists, but a tyranny of facts.What makes a scientific theory right is not consensus but logical consistency and good agreement with observation.

Scientists are, however, responsible to communicate not only what they know but also what they don’t understand (this is what defines the line between a climate change advocate and a climate change alarmist, I guess.) Conversely, scientists are supposed to be able to express their doubts without questioning or withholding facts (this, perhaps, is what distinguishes a climate change skeptic from a climate change denier.)

Unfortunately when the debate becomes political, such nuances are often lost or ignored. Politics, especially populist politics, abhors uncertainties and prefers to paint everything in black and white. If uncertainties are mentioned at all, they are merely used as “proof” that the other side is wrong, therefore our side must be right, with no room in the middle. You either believe Al Gore’s Inconvenient Truth like the gospel, or you accuse Al Gore of being a fraud artist out to get rich on phony carbon credits.

 Posted by at 4:46 pm
Jun 232010
 

Ouch! That was quite the rumble. Enough to freak out all the cats. This is the third significant earthquake I experienced here in Ottawa; it may not have been the strongest as measured by instruments, but it certainly felt the most, hmmm, “hostile” sounds like the right word.

 Posted by at 7:49 pm
Jun 142010
 

Hayabusa, or at least the part of it that was meant to survive atmospheric re-entry, has returned. Hayabusa, also known as MUSES-C, is a Japanese spacecraft, the first ever asteroid sample return mission. Unfortunately it is not yet clear if it has actually managed to collect any samples. Even so, it’s been one impressive mission.

 Posted by at 7:33 pm
May 282010
 

This Homer Simpson is one smart fellow. While he was trying to compete with Edison as an inventor, he accidentally managed to discover the mass of the Higgs boson, disprove Fermat’s theorem, discover that we live in a closed universe, and he was doing a bit of topology, too.

His Higgs mass estimate is a tad off, though. Whether or not the Higgs exists, the jury is still out, but its mass is definitely not around 775 GeV.

 Posted by at 4:36 am
May 262010
 

This is going to remain a memorable picture for some time to come:

It’s not every May, after all, that we measure 35.8 degrees Centigrade in what is supposedly the world’s second coldest capital city.

 Posted by at 8:01 pm
May 242010
 

Sitting on the surface of Mars, a space probe that was not designed to survive the Martian polar winter did not survive the Martian polar winter. Not exactly a surprise.

The surprising bit is that another space probe orbiting Mars, designed to operate for two years but still working fine after four, has been able to snap high resolution pictures of Phoenix, which tell us what likely happened: the weight of carbon dioxide snow and ice broke Phoenix’s solar panels.

It is amazing that we have this kind of infrastructure around Mars.

 Posted by at 8:05 pm
May 152010
 

It seems that the German news magazine Spiegel  managed to do the impossible: provide an impartial, balanced assessment of the story behind Climategate.

And by “balanced”, I don’t mean balanced in the American journalist’s sense, giving equal weight to both sides, no matter how ludicrous one side happens to be compared to the other, but balanced in the sense of not taking sides, not assuming guilt, and assessing the faults of all the participants regardless of which side they represent.

What I am reading is very discouraging. Climate science should really be called climate politics, with a little bit of science thrown in just to provide fodder for arguments. Meanwhile, both proponents and opponents of climate change sometimes fail to get even the basic physics right; as a minor example, recently I felt compelled to write a short paper about the proper use of the virial theorem in a planetary atmosphere, after reading way too much uninformed discussion by supposed experts online.

Of course way too much is at stake. Trillions of dollars, for starters, and quite possibly the future of our planet. Could it be that this compelled some good people to embellish the truth a little? If that is the case, they did a huge disservice to the very cause that they champion. By compromising the one currency science really has, its objectivity, they increased the likelihood that the public won’t listen to them just when it matters most, should it prove to be the case that real sacrifices are necessary to keep the planet habitable.

That is not to say that taking climate scientists to court is the right answer. If that’s the cure, it’s worse than the disease. Worse yet, it will only ensure more entrenched positions and more secrecy, justifying the hostility towards “deniers”. That is not the way to do science. Informed skepticism should be welcome, but skepticism should be about questioning methods and deductions, not the honesty and integrity of researchers. Will climate science ever be like this? I sure hope so, otherwise we’re all in very deep trouble.

 Posted by at 4:41 am
May 142010
 

I was watching the noontime local CTV news today. At around 12:39 (!), in three consecutive reports, the number 39 popped up. First, a report about a youth who is charged with vandalizing 39 tombstones. This report mentioned the number 39 several times, which is probably why I noticed that in the next report, one about the recent terrorism-related arrests in the US, footage shown in the background included the front door of a house bearing the number 39. At this time, I began paying attention. The next report was about Ottawa tourism advertisements in American newspapers; it didn’t seem likely that the number 39 would pop up there until the official being interviewed answered a question about funding and mentioned their 39 member hotels. That’s when I told my wife that this is getting a tad creepy.

The other day, I was watching a Stargate Universe episode in which one of the protagonists was reliving a part of his life while his brain was connected to an alien computer, and a particular number kept popping up as a clue. That number was 46, the number of chromosomes in a human cell. So that’s what makes 46 special. But what about 39?

Or perhaps all this was just a clever form of subliminal advertising for a Web site called The 39 Clues, which happens to be the first hit on Google when one searches for “39”?

 Posted by at 5:19 pm
May 062010
 

Here’s an idea that only Dr. Strangelove, Edward Teller, or the Communist Party of the Soviet Union could come up with: nuke that oil leak at the bottom of the Gulf of Mexico. Apparently, it has been done before, and only one out of five attempts was unsuccessful. So how about that, folks? What’s a bit of radioactivity when you have an 80% success rate?

 Posted by at 7:54 pm
May 032010
 

OK, I don’t usually play the geek game and look for nits to pick in television science programs. But…

Today’s gem comes courtesy of the Canadian History Channel and their Aftermath series, the first episode of which I just watched over the Internet. The show had many eyebrow-raising moments (and I don’t mean the implausible concept itself, about the Earth’s rotation slowing down to zero in a mere five years; I could get over that if the science had been right otherwise). This particular gem of a sentence, complete with fancy animation, especially caught my attention:

“The rotation of the Earth creates constant patterns of east-moving winds in the Northern hemisphere, and west-moving winds in the Southern. This is called the Coriolis effect.”

Oh really. I wonder if pilots flying in the Southern hemisphere know this.

 Posted by at 12:31 am
Apr 302010
 

When I started this here blog site, my intent was to write a lot about physics. I ended up writing a lot less about physics than I wanted to, in part because a lot of the physics I’m thinking about is “work-in-progress” which would not be appropriate to write about until, well, until it is appropriate to write about it!

But, there are a few exceptions. Lately, I’ve been thinking a lot about scalar-tensor gravity. Indeed, as I am waiting for the completion of a virus scan (could my recent computer troubles have been caused by a virus? I now took out my computer’s hard drive, put it in an external enclosure, and I am scanning it using a “known good” computer) I am thinking about it now.

Einstein’s gravity theory (tensor gravity) can be written up using the Lagrangian formalism. This is the infamous Einstein-Hilbert Lagrangian, which takes the form L = [(−1/16πG)(R + 2Λ) + LM]√−g, where G is the gravitational constant, R is the so-called curvature scalar, Λ is the cosmological constant, g is the determinant of the metric, and LM is the Lagrangian representing matter.

In one of the simplest modifications of Einstein’s gravity, Jordan-Brans-Dicke theory, the gravitational constant G is promoted from constant to field: it becomes variable, and a “kinetic term” is added to the Lagrangian representing the kinetic energy carried by this scalar field.

In this theory, gravity is still determined by the geometry of space-time. However, in addition to matter, there is this scalar field (which carries mass-energy and is thus a further source of gravity in addition to matter.) Then, this scalar field also determines the strength of coupling between matter and space-time (i.e., the extent to which a unit mass of matter bends space-time.)

Now it so happens that it is possible to transform away this variable gravitational constant and make it truly constant by a mathematical transformation called a conformal transformation. Basically, it amounts to reparameterizing space-time in such a way that the value of the gravitational constant becomes the same everywhere. (This transformation is described as switching from the Jordan frame to the Einstein frame.) However, this transformation is not without cost. As we transform away the coupling between the geometry of space-time and the scalar field, we end up introducing a variable coupling between the matter Lagrangian LM and the scalar field. The physics is now different! The geometry of space-time is now determined by a fixed coupling constant as in Einstein’s theory, but the trajectory of matter is no longer determined by geometry alone: there is an extra force, a so-called scalar force, acting on matter.

At first sight, this might seem weird. A simple mathematical transformation should not change the physics, or should it? Well… it does yet it doesn’t. If you fire a cannonball in Jordan-Brans-Dicke theory and calculate its trajectory, it will trace the same trajectory regardless which frame, the Jordan or the Einstein frame, you use to calculate it. It’s the interpretation of this trajectory that differs between the two frames. In the Jordan frame, the cannonball is said to follow a geodesic trajectory, but that geodesic, i.e., the curvature of spacetime, is affected by a varying gravitational constant. In the Einstein frame, the cannonball’s trajectory is not a geodesic anymore; the geodesic trajectory is determined by a fixed gravitational constant, but on top of that, an extra force deflects the cannonball.

One particular kind of scalar-tensor theory can be written in a form in which there is no variable gravitational constant and no coupling between the scalar field and matter either. This is the so-called “minimally coupled” scalar-tensor theory, in which the scalar field influences matter only indirectly: the scalar field has mass-energy, which gravitates, and this contributes to the overall gravitational field. Things can get tricky here: a scalar-tensor theory may be written in a form that does not look like a minimally coupled theory at all, yet it may be possible to transform it into one by an appropriate conformal transformation. However, this is not always the case: for instance, Jordan-Brans-Dicke theory cannot be transformed into a minimally coupled scalar-tensor theory this way, the two classes of theories are manifestly different.

When things get really interesting is when additional fields are present in a more complex theory, such as scalar-tensor-vector gravity. In that case, a conformal transformation can have surprising consequences on the coupling between these additional fields and the scalar field.

 Posted by at 2:58 am
Apr 152010
 

Just like after 9/11, the airspace of an entire region is closed today, grounding thousands of flights in the UK and Northern Europe.

Unlike on 9/11, this time around the closure is not the result of the panicked, knee-jerk reaction of clueless politicians and officials. It is the result of a volcanic eruption in Iceland:

The plume, clearly visible in this Eumetsat image, is a grave threat to aviation. 28 years ago, volcanic ash almost brought down a British Airways 747 full of passengers, and since then, numerous airliners have been damaged as they flew through similar plumes. Grounding all flights in the affected areas seems like a dramatic, but justified response to a very real threat.

Now the question is this: how long? According to news reports, the eruption shows no signs of abating. Will they keep flights grounded for days, even weeks if necessary?

 Posted by at 1:52 pm
Apr 112010
 

Apollo 13, NASA’s “most successful failure”, was launched forty years ago today. One thing I didn’t know about the timing of the accident is the fact that the tank rupture occurred on the fifth stirring of the oxygen tank, which normally would have taken place 120 hours into the mission, when the lunar module was already on the Moon’s surface. Without the lunar module to serve as a lifeboat, the fate of the spacecraft would have been sealed. However, an unrelated sensor problem caused them to stir the tank more frequently, causing the accident to occur earlier.

Had the crew of Apollo 13 died in space, it has long been assumed that their spacecraft would have served as a frozen tomb for their bodies, orbiting the Sun. But now, some argue that the orbit of Apollo 13 was such that it would have returned to the Earth and burned up in the atmosphere just a few weeks later. I am not sure how you can really tell, with uncontrolled gas leaks, a tumbling spacecraft, and no precision radio-metric navigation data.

 Posted by at 9:54 pm
Apr 032010
 

I’m back from a week-long trip to Hungary, visiting my Mom, relatives, and friends. Apart from the fact that the second half of my trip was made unnecessarily unpleasant by some cold bug I picked up on the flight from here to there, it was fun. But, it’s good to be home, even though, it seems, I came home in the middle of a heat wave. Yesterday, the heat almost killed me when I was looking for my car at Montreal airport (cars have the nasty habit of moving about when you leave them in large, public lots) while hauling my 60-pound suitcase. Today, it’s going to be even warmer. (No, we’re told, it’s not global warming… it’s the same El Niño weather that brought an unusually cold spring to parts of Europe.) I better check to see if our A/C still works after its winter hibernation.

 Posted by at 3:35 pm
Mar 222010
 

Imagine solving one of the most profound outstanding problems in mathematics. Imagine living in poverty, in a cockroach-infested apartment in St. Petersburg, Russia. Imagine being awarded one of the world’s most prestigious prizes in science, the Millennium Prize of the Clay Mathematics Institute, which, incidentally, also comes with a cool $1,000,000.

And imagine turning it down. Which is precisely what reclusive Russian mathematician Grigory Perelman apparently did.

I don’t know what to think. Was it a matter of principle for him? Perhaps. But then, he could have indicated in advance that he wouldn’t accept the award, just as he refused to accept the Fields Medal a few years earlier. Why did he keep the world in suspense? Was it posturing? Or is he, hmmm, how can I put this politely, one fry short of a happy meal, to use a favorite phrase of mine from the television series Stargate SG-1?

 Posted by at 10:13 pm
Mar 162010
 

An interesting anniversary today: 25 years ago, on March 15, 1985, the first ever .com domain name was registered, symbolics.com. The company, in addition to building their own brand of “Lisp Machine” computers, also happened to be selling the commercial version of the MACSYMA computer algebra software. The same software that, in the form of its open-source version, Maxima, continues to evolve thanks to a devoted team of developers… of which I happen to be one.

Alas, Symbolics is no longer, at least not the original company. A privately held company by the same name which obtained much of Symbolics’ assets still sells licenses of the old MACSYMA code.

 Posted by at 3:18 am