How to Hack Where's Waldo

Slate has a nice article about how to use an objective method to determine the optimal search pattern for Waldo. There are certain places where Waldo will be more than half the time, so you look there first. I can't wait to try this out on my kids. It also may be a good teaching exercise for a stats class ... or even a psychology, or design class? Are there other methods of analysis we can apply to Waldo's xy coordinates?

Book Review: Chemistry, Quantum Mechanics, and Reductionism by Hans Primas

Well, with a title like that, how can you go wrong? In this book, Hans Primas walks the line between physics-chemistry-mathematics and philosophy. Sections involving advanced mechanics algebra are outside of my field and it's not my field to critique those, but I found this fascinating. Two quotes by Goethe in a physical chemistry text is two more than what I've seen before, and there are other parallels I could make to Owen Barfield's arguments at times. Also, frequently Polanyi comes to mind. This book is as much philosophy as it is physical chemistry. Natural philosophy, of course.

Primas argues that it is not a trivial thing to cross from the quantum physical world to the classical physical world, and that some of the ways we "bridge the gap" mathematically don't work. To do it right, he starts from the ground up with a non-Boolean quantum logic that allows for superposition of states and also for the influence of the environment/measurement on the experiment. The biggest experimental indication that we need to do this seems to be the EPR correlations, which Primas argues shows that experiments are not as separable as we assume. I think I agree but am not enitrely convinced that EPR correlations affect classical outcomes.

Primas argues that we cannot so easily separate the experiment from the experimenter, and that we cannot build a classical physics from quantum mechanics alone. The extra ingredient we need to do so is context or observation on a classical level. Classical properties like chirality and molecular structure constrain the quantum mechanics. The world cannot be added up from quantum mechanics alone with a big enough computer, in other words.

What impressed me was the depth of philosophical thought. Primas is searching for a quantum ontology (if that's the right way to say it), and is not content with the standard "it's just what we measure, let's not think about what it means" Copenhagen interpretation. He digs back to Greek philosophy and makes the connections between his ideas and history as well as experiment and theory. He put his thoughts in the proper context, just like he argues we should do with our experiments.

It's strange to be reading a typed set of lectures from the 80's, but it worked for me, just like reading Polanyi's seminal article on similar topics still works. I found Primas by talking to Robert Bishop (philosophy of science, Wheaton) and reading his article "Whence Chemistry?" published in 2010, so people are still thinking about it, and it's not clear that Primas's objections have been adequately answered in the two decades since publication.

I'd like to list here for reference the six limits Robert mentioned to me that Primas lists, which must be crossed when moving from quantum to classical physics (p. 332ff). These are where the rubber meets the road for Primas's ideas, so they are particularly important:
1.) Shadow edges
2.) The van Hove limit
3.) The Boltzmann-Grad limit
4.) The Brownian-motion limit
5.) The Hartree limit
6.) Molecular structure (e.g., chirality)

I did not expect to get as involved in this book as I did, but it was a fascinating if somewhat vertiginous trip. Still processing and probably will be for quite some time.

PS: One useful tidbit: I did not know, or I knew but then forgot, that the Uncertainty Principle is not only found in Quantum Mechanics, but instead originated in the classical world. It's a consequence of limits on data transmittal, and in fact Heisenberg may have gotten the idea from a classical origin! So one of the prime examples of quantum weirdness actually doesn't require quanta.

PPS: As I was reading this a philosopher of science ran a pair of articles on the NYT philsophy blog about how he's frustrated at people who abuse quantum mechanics to make weird philosophical statements. I agree with him on many points but find his argument ultimately a lot less convincing on what really matters than the arguments of Primas. In fact, Primas argues forcefully against some of the statements made on that blog. Mostly, I'm frustrated with the attitude that if some people do the philosophy wrong, then EVERYONE must be doing the philosophy wrong and we all should just bite the bullet of the Copenhagen interpretation (or worse yet the Everett Many-Worlds interpretation). This is not a subject that can be resolved on a blog. Therefore ... I will shut up now!

The Drake Equation: Easy to Calculate but Hard to Solve

The Drake equation was put together to estimate the probability of (detectable) extraterrestrial life. That is, the number of planets who might be able to talk to us. As equations go, the math's not hard. All you need to do is multiply seven probabilities together:

N = R* * fp *ne * fl * fi * fc * L

Straight outta Wikipedia:

N = the number of civilizations in our galaxy with which communication might be possible (i.e. which are on our current past light cone);

and

R^* = the average rate of star formation per year in our galaxy

f_p = the fraction of those stars that have planets

n_e = the average number of planets that can potentially support life per star that has planets

f_ℓ = the fraction of the above that actually go on to develop life at some point

f_i = the fraction of the above that actually go on to develop intelligent life

f_c = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

L = the length of time for which such civilizations release detectable signals into space

The trouble is that the farther you go to the right, the murkier the numbers become. Two months ago I posted on how we got surprising news that the first variable, star formation (R*), may be lower than expected. (for the universe at least). On top of that, we just got a better fix on the number of stars per planet (the second and third terms in a sense). Each star in our galaxy probably has 1 or 2 planets on average.  That means there are over 100 billion planets in the Milky Way. That's ... a lot.

But the story doesn't end there. Notice that term three includes the phrase "that can potentially support life." Our best guess is that this requires liquid water and temperatures between 0 and 100C. Our system does this but the other systems don't look like our system:

"... according to Johnson ... our solar system is extremely rare. 'It's just a weirdo,' he says."

Of course, these other systems are around cooler stars, and so the liquid-water zone will be closer to the planet, and we know at least some planets are in the right zone. So there's hope yet for alien life, but it's worth noting that we live in a weird solar system (on galactic terms). How necessary is the weirdness? Is it possible that being too close to a cooler star could doom the prospects of life for some reason, even if liquid water persists? (I'm thinking radiation damage may be greater closer in?)

At any rate, we're closer to getting more parameters fixed but I'm not sure how much closer to solving the Drake equation we actually are. The bootom line is that our solar system appears exceptional -- but is it unique? Still don't know.

The Thinking Brain's Music

This is what a brain sounds like. With a little help from math and science, that is. In a recent issue of PLoS ONE, researchers used math to turn brain waves into music. The result sounds to me a bit like some of the music James Horner put into the most recent Spider-Man movie when Gwen was hiding from the lizard in the tower -- in other words, it actually almost sounds like music! (That was one of my favorite moments of the movie, by the way.) For those of us who can't read that music above in our heads ... um, for all of us ... the music itself is can be heard from where it's embedded on the left side of this Wired article.

The upshot of all this is that if brain waves can be turned into sound waves this easily, perhaps there's something to the idea that music is fundamental to consciousness. Your neurons are all singing together in concert as the waves of chemotransmitters and sodium/potassium fluxes rock to and fro inside your head.

Or, in fewer words, life is music.

Considering that tomorrow is the Christmas concert that my whole family* has been preparing for, for months now, it gives me hope that all those hours of prep for an hour or so of sounds might be worthwhile and real.


* Baby Ben and Brendan have been helping out by keeping us in shape running after them so that our stamina is up for the concert. Sam and Aidan will be in it!

An 11-Set Venn Diagram

You're probably used to 2- or 3-set Venn Diagrams:

Apparently mathematic explorers have been searching for how high they can go. It took a long time to get the number of sets up to 7. And now they've found an 11-set diagram, which is just beautiful in its slight asymmetry:

Hopefully this news can inspire new apprentice math explorers to search out these virtual lands and find new species like this flower diagram. It's like Alice in Wonderland, but it's real ...

No Team is an Island ... Except the 2010 Mariners

At least on this graph the Mariners are similar to Houston, but if you break it down by league, the Mariners are, as the author of part one of this series put it, "an island." It can only get better!

In Memory of Herb Haugo: Math is Not Linear

Since my father-in-law (who recently passed on) was a math teacher, I thought of him when I saw this great presentation. I don't think he'd agree with everything in it, but it would definitely interest him, and it makes good use of the Prezi presentation platform for zooming in and out.

Book Review: Logicomix

Not sure where to file this one. It's a biography of Bertrand Russell, focusing on his work in logic and mathematics, ending up in World War II, written by Greeks with a bit of ancient Greek tragedy thrown in for good measure. Although Russell is the main figure it's really about the other characters as well: Cantor, Wittgenstein, and Godel. Godel's Incompleteness theorem is presented right (far as I know, since it goes along with what I read in Godel, Escher, Bach long ago!), but there's just so much logical depth one can achieve with a comic book! It really is about the characters, and I enjoyed going with the flow. Although I wonder how much of the story is colored by what the authors want to say rather than what is really there. For instance, did the computer really win WWII for us? I think it was a factor but a lot more factors were more important. Radar, for instance (was the computer necessary for radar, in the sense that without Turing there would be no radar?). The book puts forward democracy as a solution against evil and skates on by the fact that Germany in the early 20th century was pretty democratic! As a thought-provoking way to learn some math history and to start a line of thinking this is an excellent book. What it doesn't do is resolve the issues it brings up -- but I wouldn't expect that anyway!