22 Jun 2015

Rubik’s Cube

I decided recently to embrace my dilettantism. I don’t think there have been two consecutive days in my life where I wanted to pursue and learn the same ideas. Now mind you, the complete list of topics is finite and I cycle back eventually.

But recently, when I was reminded of the existence of superfast Rubik’s cube solver people, blindfold solvers, one-handed solvers, and foot solvers, I thought it might finally be time to learn how to solve the cube, and to push down the stack the rest of my crazy research agenda.

A couple weeks later, I can assert that I can solve the cube within a few minutes. And moreover, I am able to do it with some modicum of understanding of what I am doing. My goal was not to memorize recipes, which is the approach that most tutorials assume for some reason. Instead, I wanted to know the most granular small changes that can be made and how to carry them out, and also why they work out. And I achieved that! I am impressed with myself, way more than is warranted. This outcome is of course all due to the existence of the Internet and especially YouTube. Here are my favorite links.

  • all current speed records in one video:
  • one of the better math-flavored tutorials: link
  • same teacher, but now we’re getting somewhere with a discussion of commutators: link
  • dour but breakthrough presentation that clinched my understanding:
09 Jul 2008

On the importance of mentors

I grew up assuming that people make their own way in the world. I thought it was up to me to make every decision, plan every move, open every door, and find my own way in my life and career. Only much later did I learn that I was doing it all wrong. Not only is my way much harder, it’s also completely miserable to be so isolated. Here’s an example. The place where I started making these wrong decisions was in college. I attended my classes, which in some cases were way below my capabilities, and in other cases were way above. Either way, at the end of class, I packed up my things and walked back to my room. I dreamed of being a scientist, just like I had since I was 10 years old. But all I did was go to class, I never spoke with any professors, nor was I ever approached by any. My talents started to appear in my sophomore year, but I was still doing things in this retarded way. Then in my junior year the first consequence of my nihilistic lifestyle happened, and I didn’t even really notice it for what it was until years later. I switched my major from Astronomy to Astrophysics, then I added a concentration (minor) in Math, and then I made Math a second major. This all happened within a couple of months. Even these bureaucratic thrashings didn’t raise any red flags in any administrators or professors. No one cared. So, I shifted my focus to math, threw away the pile of physics grad school applications I had, and requested a bunch of math ones. I went to graduate school for a year at Stony Brook, then transferred back to Columbia for the rest of my Ph.D., because my then-girlfriend, now-wife, was continuing on from Columbia undergrad to grad school.

OK, here’s the denoument to the story. In my second year or so, the reference librarian of the math library was leaving Columbia, and she was well-liked by the department. I had worked for her as an undergraduate, so I was invited to her going away party. At that party, there was a professor who was a fixture in the math department. He was the kind of professor who was very focused on undergraduates and mentoring. I had never had a class with him, and had never met him personally until I was a graduate student. We got to chatting, and it came out that I had attended Columbia as an undergrad as well as a grad student. He was shocked. “How is it that I don’t remember you?” he asked. My answer was “I do a good job of going under the radar.”

This story brings me a whole lot of pain. I know that I somehow failed to do “things” right as an undergrad. All those times I walked straight back to my room to lie on my back, have a cigarette, and listen to music, I suspected that I was doing the wrong thing. I knew I should be doing “more” or seeking more opportunities. But how do you do that? I have never been good at taking that feeling and turning it into non-ridiculous-looking actions. But I also suspect that others also failed me. The professors who taught me recognized my talent, I’m sure. A few years later I heard from a third party that one of them had called me “the best mathematician he has ever met.” WTF? Why weren’t these people looking out for me, then? Couldn’t they see that I had lots of talent but no direction? Professors like the one I was talking to at the going-away party do in fact devote lots of energy to nurturing undergrads. Just not me. So I waver between self-loathing and bitterness.

I am determined to make at least one good thing out of this part of my life story. I will be an excellent mentor, and I will always act when I spot talent. It’s happened plenty at my job, and I have been very vocal about singing the praise of new young employees who are talented. I have been instrumental in having them promoted and being assigned interesting work. I will do what was not done for me. The best would be if I ran across someone like myself, who was incapable of grabbing this kind of attention for him or herself. I will see their talent, and their reticence, and I will help them.

13 Dec 2007

Competitiveness considered harmful?

Over Thanksgiving, I was complaining about people who crowd forward when boarding a plane, even if their row hasn’t been called, so that when it is called, they get on first. And if they can get away with boarding before their row is called, they’ll do that too. Someone close to me retorted, “competition made the human race what it is today.” I haven’t stopped thinking about that remark ever since. Can this person be right? I dearly, dearly hope not. Because all I can think of in reply is, “yes, it did make us what we are — especially the World Wars and the Holocaust.”

30 Nov 2007

Lord of the Rings soundtrack

I’m listening to The Return of the King: The Complete Recordings at work, and I’m at the point near the (first) end when Frodo and Sam have just destroyed the ring (with Gollum’s unwitting help) and they’re escaping the flowing lava by standing on a rock, feeling a relieved. With all the events of the story to back up the scene, I think it’s truly moving to see these two regular guys, who together destroyed a great and senseless evil power. I actually see it as a very tragic moment, when two of the world’s great forces are being presented to us via the heightened drama of this point in the story: senseless evil/destruction/chaos on the one hand, and the fortitude and perseverance and good of the common person on the other hand. You can ask all sorts of questions at this point, like if the common person is so good, where is all the evil coming from? Why must the most ordinary and good people sustain such injury and sacrifice to ward off the worst effects of the evil?

19 Nov 2007

Masterpiece Theater?

Has Masterpiece Theater always just been some British TV show? Lately they’ve been showing The Amazing Mrs. Prithcard, which felt like an American TV show that happened to be British. Is it a masterpiece? Did they pick it because they felt it was a masterpiece? Maybe they should rename Masterpiece Theater to “Some British TV Show”.

27 Sep 2007

Lord of the Rings, movie versus book

A while back I wanted to read The Lord of the Rings aloud with my wife. We’ve read lots of books together this way, and I’m a huge LOTR fan, so I really wanted to share it. The problem is it’s very long and many people consider lots of it boring. So, I took a clever (if I do say so myself) shortcut! I went through the books and dog-eared ranges of pages where the plot differed from the movies in a way I thought significant or noteworthy. For example, I read the entire chapter “The scouring of the shire” because this was left out of the movie. I highlighted the differences in Denethor’s character as much as I could, as well as Faramir’s. Both were substantially diminished in moral quality in the movies.

I want to go back through what I did, and post it here with annotations, so that others can read the same portions of the books in tandem with the movies to get a much more accurate picture of what the books are all about. The problem is that before I had this great idea, I had already read half of Fellowship, so I’ll have to make some decisions about what parts of that to keep.

09 Aug 2006

The Jasons

I recently heard of a book called The Jasons at the blog of a former colleague, Peter Woit. Since I spent the summer of 2004 doing classified math research for the government, I was very interested to hear of another such group. In a way, the Jasons are a sequel to the very successful Manhattan Project, and there is lots of overlap of personnel. The Jasons came into being in the aftermath of the Soviet launch of Sputnik, in 1960 to be exact.

After buying the book on a recent visit to the Chautauqua Institution, I was fascinated to read that in their very early years, they invented an idea that today is revolutionizing astronomy: adaptive optics. By coincidence, this technique was just starting to move its way to the front of my mind, because I try to keep up with astronomy news, due to my lifelong interest in the subject. I’m thrilled to happen upon it in the quite different context of the Jasons.

25 Jul 2006

The huamn mnid

“Aoccdrnig to a rscheearch at Cmabrigde Uinervtisy, it deosn’t mttaer in waht oredr the ltteers in a wrod are, the olny iprmoetnt tihng is taht the frist and lsat ltteer be at the rghit pclae. The rset can be a toatl mses and you can sitll raed it wouthit porbelm. Tihs is bcuseae the huamn mnid deos not raed ervey lteter by istlef, but the wrod as a wlohe.”

Here’s a link that discusses this phenomenon.

I read about this a while back, but this evening it came back to me. I think I read about it before I became a natural language processing dude, but now that I deal with machines that work with language, it is one of the items I keep in the back of my mind that may be helpful some day.

Language is not data.

12 Mar 2006

Intelligent Design: The Final Word, Part 3

The central question I have been trying to satisfy myself about with these notes is the following: is there a way to formulate Intelligent Design as a scientific theory? (See part 1 and part 2.)

By definition, a scientific theory is a model of a part of the world that makes verifiable and falsifiable predictions about specific observations. To answer this question, I will reformulate the statement of ID. Behe’s formulation looks like this (this is not a quote, I’m summing up his argument):

My summary of Behe’s argument:

Although evolution certainly takes place at a macroscopic level, certain biochemical processes inside our cells cannot be explained by step-by-step evolutionary processes because they involve several interacting parts that are each required for the process to function: they are irreducibly complex and so these must have been designed by an intelligent agent. It is mathematically possible for a random process like evolution to produce one of these systems, but the probability is absurdly low because all parts must mutate to their working form at the same time. The probability that all of our irreducibly complex systems evolved in this way is even more negligibly small.

I want to say up front that I am not going to attack the probability part of this argument in order to argue whether it is scientific. It is perfectly reasonable to say that something we observe has a very low probability of arising from some process, and to remove evidence from the applicability of that process in so doing. If you can demonstrate what that probability is. In a further essay I will look at this issue more closely, but only when I want to discuss the correctness of ID, not whether it is a scientific theory in the first place, which is our current aim.

I’m going to reformulate the statement above summarizing Behe a couple times to draw out out what I’m looking for. I expect that an ID enthusiast will object to my reformulations at some point because the conclusion will follow immediately from the final reformulation, but I wonder where the objections will arise exactly.

Reformulation 1:

Certain subcellular processes are irreducibly complex. Irreducible complexity implies design by an intelligent agent, because to arise randomly by a mutation has nearly zero probability. Therefore subcellular processes were designed by an intelligent agent.

I will now add to the discussion that I fully grant that all of Behe’s examples are in fact irreducibly complex, which simply means that the systems involve several interacting parts without any one of which the system fails to function. It’s a simple to define concept, and surely his examples are all in fact irreducibly complex. Granted. Now, also losing the bit about probability, we can reformulate:

Reformulation 2:

Evolution cannot explain irreducible complexity.

This is entirely equivalent to Behe’s statement of ID, once you remove the question about whether the systems are irreducibly complex, and replacing the caveat about probability with the blank statement “cannot explain.” If you agree with the complexity part, then all ID says is that evolution cannot explain this complexity.

The problem with ID is that this not the statement of a scientific theory. It is the contradiction of one, namely of evolution. It only makes one prediction, that evolution will not be able to explain irreducible complexity. The only way to study this idea is to study the evolution of molecular systems and try to explain how the irreducible complexity of some particular system came to be. See, ID doesn’t substitute anything for evolution, it merely fills the gap it creates with the Designer. It cannot make any new predictions, and it doesn’t try.

Here is an analogous scenario. The 6 o’clock news reports that there are crop circles on a farm outside town. A scientist on TV expresses his theory that it is the work of teenagers playing a prank. Another scientist puts forward the theory that the crop circles cannot be explained as the work of humans, they must be the work of extraterrestrials. Furthermore, the second scientist argues that his theory is just as scientific as the first theory, because they both purport to explain a particular phenomenon. The problem with the second theory is that its central claim is that the first claim is wrong, and in so doing it creates a gap, which it then fills with extraterrestrials. But the gap is not a theory, just the contradiction of one. The way to proceed to investigate crop circles, then, is to pursue the first theory and try to find a natural explanation. That’s the same course of action we’d take if there was no second theory. And of course crop circles were eventually found to be easily made by teenagers using planks of wood with rope handles to press down the crops in just a few hours overnight.

It’s the same with ID. The way to pursue this issue is to investigate natural ways that these irreducibly complex systems may have come about. That’s the same approach we’d take if there was no ID theory. ID theory adds nothing and makes no claims other than to contradict an existing line of inquiry.

The funny thing is that ID is falsifiable. Finding a viable evolutionary path for the cilium or any of the systems Behe is interested in will falsify ID, and Behe himself points this out. That’s an important point, because when I started this line of thinking I assumed I’d be determining that ID isn’t falsifiable. What I’ve learned instead is that ID isn’t predictive. No theory whose statement can be summarized as “that other theory over there won’t work in this case” is predictive. It doesn’t make any claims of its own that can be tested, and so the only way to investigate it is to investigate the original theory, making the contradictory theory actually meaningless.

What does this tell us about teaching ID in science classes? My short answer is that since it is not a scientific theory, it should not be taught. It certainly should not be required, and probably its absence should be required. But why? Because science is about skepticism, model-building and model-testing. It’s never about authority, never about personal preferences. It makes no contact with our political or spiritual structures. It is completely confined, completely focused on material predictions that can be tested and falsified. Theories that limit the domain of science, the way ID claims science will never apply to certain biological systems, may or may not be correct. But science does not place such limitiations on itself, for to do so is impossible within the framework of science. Scientists will be the first to admit that they have a poor understanding of how evolution applies to sub-cellular systems. Science demands such concessions — science is the requirement to make such concessions. And that state of affairs may continue to hold for a million years for all I know. It does not change the central point, that science is a process for adding to the accuracy of our models, not for defining boundaries.