Hello, WordPress

May 6, 2010

Well.  It’s been a long time, hasn’t it?  It probably would have been much longer, too, except that as of May 1st, Blogger no longer supports blogs hosted via FTP (which is what this blog used to be).

So, I was finally forced to make the switch to WordPress.  I’ve tried to be careful about preserving the permalinks as they were, so hopefully no broken links will result from the change.  If you find any problems please let me know.  I did notice that some of the HTML markup in the posts and comments got garbled, and I’ll fix those as I have time.  The one change that will be unavoidable is that the links for the RSS feeds will be slightly different–sorry for any inconvenience that might cause.

Of course, just because I’ve gone through the trouble of converting this blog, it doesn’t necessarily mean that I’m going to start posting with any regularity again.  But maybe since I’ve got this shiny new toy to play with, I won’t be able to help myself.

Counter-intuitive science

December 5, 2008

What do you do when you come across a bit of science and engineering that seems totally counter-intuitive? Do you try to construct arguments for why it can’t work and must be a hoax of some kind? Or do you accept that maybe you just don’t (yet) understand the underlying concepts and need to work on improving your knowledge? Maybe you could even try experimentally verifying the concepts yourself, if no special equipment is required? Personally I have always thought that the concept of angular momentum is totally mind-bending, but children verify that this is a real phenomenon every time they spin a top, or ride a bicycle without falling over.

I imagine that your response will depend a lot on the context involved. If you’re sitting in a science class and you generally trust your instructor, you’re probably going to accept whatever you’re told. But in fact, at least for college-level courses, you’re not supposed to just take the instructor’s word for things–that’s why they have labs, so you can excruciatingly recreate classic experiments to verify the concepts for yourself.

On the other hand, if you distrust your source, you’re liable to have the other kind of response. For example, adherents of intelligent design construct all sorts of ad hoc and easily debunked reasons why evolution cannot work as described, and seem to think that mainstream biologists are all either self-deluded or participants in a grand conspiracy. Many of the rest of us might consider the Internet, taken as a whole, to be a not-completely-trustworthy source, and if we see something peculiar on the Web we might be tempted to assume that it’s just a joke or a hoax of some kind.

I mention this as a lead-up to the following hilarious little story that’s current bouncing around some science and tech blogs: A couple of years ago, Jack Goodman posted a YouTube video showing a wind-powered cart he built to demonstrate the concept of “direct downwind faster than the wind” (or DDFTTW for short) travel. It is certainly counter-intuitive at first glance: if you are traveling directly downwind faster than the ambient wind speed, then you are going to be feeling the wind in your face! How could that wind possibly be providing the energy source to make you move forward? And yet (not to give away the story), this is a real effect that does not somehow violate the laws of physics.

Recently, debate over this was reignited when a new video was posted on YouTube to demonstrate the effect beyond any doubt and prove that it is not a hoax:

Perversely, it seems to have only increased the debate about what’s going on. The story was picked up by the tech blog BoingBoing, which took a somewhat skeptical view of things. The pseudonymous poster of the video, spork33, has patiently responded to questions and counter-claims in the comments over there, which seems to have only made the skeptics more vocal in their complaints.

Science blogger Mark C. Chu-Carroll posted a blog entry at Good Math, Bad Math in which he attempted to intellectually eviscerate spork33 and his colleagues:

Via BoingBoing comes a bunch of bozos who believe that they can create a “wind-powered” vehicle that moves faster the wind that powers it. This is, obviously, stupid.

Chu-Carroll goes on to argue that the treadmill demonstration in the video has no relationship to conditions “in the field”, using the same kind of dismissive language. He finishes up with this gem:

Everyone should be able to understand the physics involved here. My third grade daughter can understand this. This isn’t difficult. There’s nothing tricky or subtle about it. If you have a vehicle moving at the same velocity as the wind, the wind cannot possibly exert any force on the vehicle. No force, no acceleration. Period. How can supposedly intelligent, educated people not know this?

Unfortunately for MarkCC, since this phenomenon is completely on the level, he is the one who comes off looking like, well, a bozo.

[UPDATE: Mark has printed a retraction on his blog and apologized for his intemperate language. Curiously, he says he needed to work through the math to convince himself that the device could actually work. Personally, the "math" is the last thing I'd trust in a situation like this--the various comment threads are full of mathematical calculations by skeptics who claimed that their results show that the device can't work. Their calculations might have even been correct, but the way they formulated their models was wrong, so the results were meaningless. I'd much rather trust my eyes, but evidently Mark and many other skeptics just couldn't bring themselves to believe that the demonstration in the video wasn't using some sleight-of-hand.]

For a proper explanation of the physics involved, you could browse through the lengthy comment threads at BoingBoing or Good Math, Bad Math. It’s a fascinating read if you have the time. Fortunately, Dave Munger has a post at Word Munger where he gives a succinct explanation of what’s going on, and in which he addresses the major questions that have been raised on the other threads. (Dave is perhaps better known for his blogging at Cognitive Daily, and as a founder of ResearchBlogging.org.) Of course, there are still many skeptics who continue to argue in the comments thread on Dave’s post.

Even though DWFTTW travel is totally cool just by itself, the thing I find most intriguing about this whole episode is the mindset of skeptics. I know that I’ve been guilty of this sort of thing too, where I’m totally convinced that such-and-such is a fact, and I discover later that just the opposite is true. What psychological factors cause us to believe what we believe? And what techniques can be used to help change the mind of a skeptic, when it is clear that simply presenting a factual exposition is not going to do the trick? Dave, if you see this, perhaps this question would make a good topic for your Cognitive Daily blog.

The Original of Laura

May 2, 2008

This item is a bit far afield for this blog, but I bring it up because I mentioned the author Vladimir Nabokov a few posts back (scroll down to resolution #3). Nabokov was working on a new novel, to be titled The Original of Laura, at the time of his death in 1977. Nabokov had indicated to his family that he wanted the unfinished novel destroyed if he died before he completed it, and it has sat unpublished ever since.

Now Nabokov’s son Dmitri has decided to go ahead with publication. In an interview on NPR, Dmitri Nabokov talks about the process leading up to the decision. This little bit of trivia caught my ear: when asked how long the novel fragment was, Dmitri said that his father had completed 138 index cards, which would come out to be about 100 pages including some supplemental material. A date for publication has not been set yet, but it should happen fairly soon.

Circular Puzzle

April 26, 2008

Puzzles of various sorts have been popular on the math blogosphere lately, so I thought I’d make my own modest contribution. As puzzles go, there is not very much to this one — no calculations are necessary, you can just look at it and visualize the answer. But the backstory that goes with it is mildly amusing. This appeared as a question on the SAT exam, back many years ago when I was an undergrad.

Imagine a circle of radius 1 unit, sitting on top of a larger circle of radius 3 units, like so: Now suppose that the smaller circle rolls around the perimeter of the larger circle until it returns to its starting position. In the course of doing this, how many rotations about its axis will the smaller circle make?

Before going on, you might want to take a moment to think about what the answer should be… Okay, ready? This particular problem was featured in a story in the news because the answer key used to score the SAT had the wrong value for this question. Let’s just call it x for the time being. A high school student who sat for the exam realized that the correct answer should be y, and the math scores had to be retabulated for everyone who took the SAT that session.

The story appeared in our local paper over the weekend. The following Monday, the professor for my differential equations class, who also happened to be serving as the department chairperson that semester, mentioned that he had received a phone call from a newspaper reporter asking about the question. The professor sketched out the problem for us, and said, “I told him that, of course the answer was x.” Naturally as soon as class was over, several of us students who had read about the problem over the weekend ran up to the professor and explained to him why he was wrong.

For the next week, the problem continued to stir up debate in our math lab. About half the students who looked at it initially believed the answer was x. Most people quickly changed their minds once it was explained to them, but we did have one hold-out who refused to budge. If I remember correctly, he was a Ph.D. candidate in differential geometry, who insisted that since he had advanced training in a geometrical field, we should defer to his judgment on the problem.

(Now, as to what x and y are… You have almost certainly figured out the correct values for those by now. If you are still unsure, though, I’ll put a hint in the comments for you.)

A Short Note on the Halting Problem

April 22, 2008

Over at Shtetl-Optimized, Scott Aaronson recently had an open thread where he invited readers to pose questions for him (this apparently is what Scott considers relaxation after a hard week). There was an interesting exchange in the comments that caught my eye, but since Scott has already closed the comments on that post, I thought I’d write about it here.

A commenter named Abel posed the following question:

Are there any interesting results concerning subsets of Turing Machines for which the Halting Problem can be solved?

For example, it is trivial to see that machines for which you cannot go back to a previously visited state do not halt. But it would be interesting if there were any non-trivial result for a subset in which there are both machines that halt and that doesn’t halt.

A little further down in the comments, Scott replies that a reader has emailed a response:

Matthew P. Johnson writes in to answer Abel’s question, on whether there exists a “nontrivial” but structurally-defined subset of Turing machines for which the halting problem is decidable:
Supposedly, the subset is extremely close to trivial, i.e., almost all of them (!):
“The halting problem for Turing machines is decidable on a set of asymptotic probability one. Specifically, there is a set B of Turing machine programs such that (i) B has asymptotic probability one, so that as the number of states n increases, the proportion of all n-state programs that are in B goes to one; (ii) B is polynomial time decidable; and (iii) the halting problem H intersect B is polynomial time decidable. The proof is sensitive to the particular computational model.”
“The halting problem is decidable on a set of asymptotic probability one”
http://arxiv.org/abs/math/0504351

Since that’s a seemingly remarkable result, I’d like to look at it a little closer, and then offer a different response to Abel’s original question.

The halting problem is decidable on a set of asymptotic probability one is written by Joel David Hamkins and Alexei Miasnikov, both of the City University of New York. The paper appears to be based on a talk by Hamkins at the Fall 2004 CUNY Logic Workshop.

Since they mention that their proof is sensitive to the particular computational model they use (actually, it would be more precise to say result instead of proof), let’s start by taking a look at that. They use a fairly standard, if bare-bones, Turing Machine model. Their TM uses an alphabet consisting of {0,1} and a single tape which extends infinitely to the right.If Q is the set of (non-halting) states of the TM, then the transition function is given by:

δ: Q×{0,1} → (Q ∪ {halt})×{0,1}×{L,R}.

This allows the easy calculation that for a given size n (of number of states), there are (4(n+1))2n distinct TMs.

Now we come to the one little (but critical) feature of their model: if the head is located on the left-most cell, and the TM attempts to move the head to the left, then the computation fails in a non-halting condition. (We can suppose that this TM is implemented in Windows NT, and instead of failing gracefully, we get a “blue screen of death” when the TM attempts an illegal move.) We’re ready to look at their main result.

Define B to be the set of TMs that, on an input tape initialized to all zeros, either halt or fall off the left edge of the tape before repeating a state.

Now, I imagine you can already see where this is going. We can obviously tell if an arbitrary TM is an element of B and if so whether it halts or not, by simply simulating it for n steps. (I wouldn’t call that a structural property of the TM, but in fairness the authors do not describe it that way, either.) The only interesting question is whether B has asymptotic probability one. For this, the authors invoke a result on random walks due to Polya:

In the random walk with equal likelihood of moving left or right on a one-way infinite tape, beginning on the left-most cell, the probability of eventually falling off the left edge is 1.

This can be seen intuitively by imagining the behavior of the TM’s tape head. At each step it can move either left or right. Assuming the TM doesn’t halt first, as n gets larger it becomes increasingly likely that the head will return to the starting point; and each time it does there is a 50% chance it will fall off the left edge on the next step. There is some work involved in making this into a rigorous argument, but basically that’s the entire paper right there. (By the way, for some more interesting background on random walks, see Brian Hayes’ recent post at bit-player.)

I wouldn’t blame you if you find that result less than satisfying.

I think I can offer a somewhat more satisfying answer for Abel. The canonical example of a computing model for which the halting problem is decidable is the linear-bounded automata, or LBA. In an LBA, as well as other space-bounded models, it is possible to tell if a TM is going to loop by simply letting it run long enough to exhaust all possible configurations. It is possible to enforce this syntactically for arbitrary TMs by adopting some conventions for the presence of an outer “control module” that enforces tape boundaries, etc. This same approach also works for syntactically checking for membership in time-bounded classes like P and NP, although of course the halting question is moot for those classes.

This agrees with our intuition about real-life computing. Physical computers are, as a practical matter, space-bounded machines, and they may as well be treated as time-bounded also. For most algorithms we have a pretty good idea of how long they should run, and if a computer program is taking too long to finish we don’t hesitate to pull the plug on it and start examining our code for where we screwed up.

The Physiology of Religious Experience

March 13, 2008

I posted a couple of months ago about TEDTechnology, Entertainment, Design, and the wonderful presentations that can be viewed on their website. Great new material is continually being posted there, and a case in point is a recent talk by brain researcher Jill Bolte Taylor. From the description:

Neuroanatomist Jill Bolte Taylor had an opportunity few brain scientists would wish for: One morning, she realized she was having a massive stroke. As it happened — as she felt her brain functions slip away one by one, speech, movement, understanding — she studied and remembered every moment. This is a powerful story about how our brains define us and connect us to the world and to one another.

The language that Dr. Taylor uses to relate her experience is very much like what one might expect to hear from someone describing a mystical or religious experience, and it would be hard not to draw connections between the two. This is simply a fascinating talk. (It also deserves mention for Dr. Taylor’s use of a certain visual aid.)

To view this talk at the TED website, go here. You can learn more about Dr. Taylor at her website, and she also has a book about her experience available from Lulu. (Hat tip to Mo at Neurophilosophy.)

New Year’s To-Do List

January 16, 2008

Well, it’s once again the time of year when I review the state of my life, and resolve to do something about all the shortcomings that inevitably present themselves. Unfortunately, although I have no trouble coming up with worthwhile resolutions, I’ve never had much success in keeping them, to paraphrase Jerry Seinfeld. Therefore I don’t think I’m going to waste time with making any resolutions in the traditional sense. Resolve is such a weighty word. I’m going to try taking a less serious approach here. I see that Jane has given herself a to-don’t list, but I’m a little skeptical of this approach. The standard truism applicable here is that it is better to prescribe the desired behavior than to proscribe the unwanted behavior, and I have to agree with this advice. However, I do like the idea of a to-do list — it’s much more matter-of-fact than a resolution. A to-do item is like doing the laundry or paying the bills; it’s something you do every day. Most importantly, it’s something you know that you can do. So, here is my to-do list for 2008.

Where to start? According to Dave Munger at Cognitive Daily, having too many resolutions reduces your chances of success, so I’m going to limit myself to five items. His list of most-commonly made resolutions looks depressingly predictable, but as I am not one to break with tradition, I will start out with a health-related to-do.

One

I’m currently about 20 pounds over my “ideal” weight. I figure that if I set my goal at the modest target of losing about one pound per week, and allowing for a little bit of back-sliding, I should reach my ideal weight by mid-year. I debated about whether to include this item in this post (since, after all, who out there cares about how much I weigh?), but it gives me an opportunity to demonstrate the neat little chart API from Google. This API lets you generate graphs on-the-fly just by specifying a URL with the necessary parameters. So for example, here’s a line graph I can use to chart my weight progress:

Weight Graph

I’ll have to post an updated graph every month or so, so that you can shame me into staying on target. (Hat tip to Brian Hayes at bit-player for this.)

If you need an extra incentive to get going on your own health to-do, this news item about a recent health study might help. Researchers in England found that middle-aged men and women who followed four good-health practices (don’t smoke, consume alcohol in moderation, get some exercise, and eat lots of fruits and vegetables) were 4 times more likely to have survived through the duration of the study than those who followed none. Participants who only followed 1, 2, or 3 of the practices still showed (correspondingly smaller) benefits. Not surprising, but I think that one of the points of the study is that a few simple, relatively easily implemented practices can make a big difference in your health. You can read the whole article at PLoS Medicine.

Two

Also high on Dave Munger’s list of typical resolutions is getting organized. If you’ve ever seen the HGTV show Mission: Organization, you have an idea of what my personal space looks like. I can’t think of an aspect of my life that couldn’t benefit from some organization, but just to keep things simple I’m going to focus on one item: my filing cabinet. I need to redo my filing system, and I’m going to set a target date of March 1st, which will force me to get my tax records together in plenty of time for tax season. I don’t have any fancy links to help with setting up the physical files themselves (although I do like the looks of these MAGNIfiles). However, once the files are set up the tricky part is keeping them in order. I’ve been told that the adage to keep in mind is “handle each piece of paper only once”, and if you Google that expression you’ll get hundreds of relevant links. This one (somewhat randomly chosen) seems pretty sensible. Of course, since most of this is just common-sense stuff, the trick is not knowing what to do, but actually doing it.

One final link on filing, just to keep this post from being too un-mathy: Jeff Erickson had a neat post a couple of years ago on the time-complexity of various filing strategies. It turns out that the system I’ve been using isn’t so bad after all!

Three

Next up, I want to try to improve my productivity. To keep this concrete, I’m going to set as my goal to write for 2 hours a day. I’m using “write” very loosely here, to mean pretty much any form of output in which I’m creating something instead of just passively reading or viewing. Now, this kind of goal is notoriously hard to keep, and I’m deliberately choosing it in order to try out some motivational techniques. On his blog, Jim Gibbon describes the Seinfeld method, which consists of getting a big, full-year wall calendar and making a large mark on each day you meet your goal. The aim is to try to keep the resulting string of marks from being broken. I love the simplicity of this technique, and I can use it to track my progress on my other goals as well. Jim Gibbon also describes a technique called contingency management, in which you give yourself a reward each time you complete your daily goal (or a punishment when you fail). I suspect that I would be too tempted to cheat using this method, but I’ll give it a try as well.

One general problem I’ve had with writing is that ideas invariably occur to me at the most inopportune times, and I end up forgetting them before I have a chance to write them down. I can’t be bothered with carrying a journal around with me all the time, and I tried using a voice recorder but was too self-conscious to make good use of it. But I recently read that Vladimir Nabokov did his writing using index cards, and this seems like such a great solution that I can’t wait to give it a try.

Four

One of the things I plan on doing with that writing time is to produce some actual mathematical content for this blog instead of the typical link-fests (like this entry). But to present the math properly, I think I need to bite the bullet and convert this blog to WordPress. After all, if it’s good enough for Terry Tao’s What’s New, Scott Aaronson’s Shtetl-Optimized, Tyler DiPietro’s PowerUp, and Foxy’s FoxMaths! (among others), then it ought to be good enough for me.

Now, just setting up a new blog takes almost no time at all. But it’s been ages since I’ve updated anything else on this site, so I think I need to give the whole place an overhaul. Since I’ve committed myself to getting my files in order first, I think I’ll set a leisurely goal of May 1st for my new web digs.

Five

So if all goes according to plan, by mid-year I’ll be fit, organized, and churning out math posts on my remodeled blog. That leaves the second half of the year open for something perhaps a little more ambitious.

Bill Gasarch recently posted his predictions for 2008, and I couldn’t help noticing a hint of a contradiction between his 2nd and 3rd items:

  1. There will be a big breakthrough in theory. Very hard to predict what it will be- note that this years big breakthrough, faster algorithm for integer multiplication, would have been hard to predict.
  2. P vs NP, P vs BPP, will not be solved.

Now, to me that seems almost like a dare. So, this gives me the perfect project for the second half of this year: write a proof that P≠NP.

To help guide me with my proof-writing, Scott Aaronson recently posted a list of Ten Signs a Claimed Mathematical Breakthrough is Wrong. If I take care to avoid the pitfalls on this list, I’ll be sure to get everyone to read my results. Actually, the one item that I think I would deliberately indulge in is this:

8. The paper wastes lots of space on standard material. If you’d really proved P≠NP, then you wouldn’t start your paper by laboriously defining 3SAT, in a manner suggesting your readers might not have heard of it.

Since a proof of something like P≠NP would be of interest to a wider audience than your typical math result, I would try to make it as self-contained as possible.

So to recap, here’s my to-do list for 2008:

  1. Lose 20 pounds.
  2. Organize my files.
  3. Commit to writing for 2 hours a day.
  4. Update this web site and switch to WordPress.
  5. Write a proof that P≠NP.

As I mentioned near the beginning of this post, since these are to-do items and not resolutions, I can be confident that I can matter-of-factly complete each task. We’ll check back in December and see how I did!

What have you changed your mind about?

January 6, 2008

A couple of months ago I wrote about Edge Foundation’s What is your formula? question. Well, the results of the Edge annual question for 2008 are now online. The question posed to Edge’s contributing scientists and thinkers this time around was, What have you changed your mind about? Why? (You’ll need to scroll down past a bunch of blurbs on that page before you come to the list of responses.)

It’s a challenging question to answer, and I was expecting some intriguing responses. There are some interesting answers, to be sure, but not as many as I initially expected. In retrospect, I guess that’s not too surprising. (Ha! Look, I changed my mind about that!) Since a change of thinking is required, it kind of implies that the holder’s original point of view was wrong. So, if someone has an important idea, but it is their original point of view on a subject, then it just isn’t going to show up in this year’s mix. In fact, in browsing through the responses I frequently found myself thinking, “Of course you changed your mind–your original ideas were clearly wrong!” And there were also a couple of entries were I’m pretty sure the authors changed their minds in the wrong direction.

When I try to answer this question for myself, I have a hard time coming up with a clear-cut example. Of course, there are lots of little mundane day-to-day opinions that change, like what kind of toppings I like on my hot dogs. But for the “big ideas”, it’s more a matter of gradual refinement over time as I learn more about a subject, than a complete change in direction. (I am of course limiting myself to my opinions as a mature adult. If my opinions during my teen years were included, I’m sure my parents could produce many examples where I’ve since done a complete about-face, but thankfully I have pretty much total amnesia about that time of my life.)

Here are just a few selections that struck me as I read through them…

Susan Blackmore talks about how she stopped believing in paranormal phenomenon. I’ve never been a real believer in this kind of stuff, but I did spend a lot of time researching it in college because it’s the kind of thing that would be so cool if only it were true. I quickly realized, however, that nearly all the research published in parapsychology journals was just plain crap. It made me wonder how any self-respecting scientist could continue to work in the field.

I had to re-read Daniel Hillis’s entry more than once to convince myself that I understood him correctly. He talks about how, as a child, he was told that hot water froze faster than cold water and he refused to believe it because it defied common sense. He challenges the reader to try the experiment for themselves in order to convince themselves otherwise. I’m pretty sure that he’s just trying to taunt us into adopting an experimentalist mindset, but I’ll be damned if I’m not going to have to try this for myself now.

Many respondents talked about changes in religious belief. Conflicts between fundamentalist religious beliefs and science have been in the news a lot lately (for example, in the context of the primary election debates), but moderate religious beliefs are generally portrayed as compatible with modern science. Clay Shirky has come to disagree with this perspective and argues that even moderate beliefs are not reconcilable with science, and we are entering a long period of societal restructuring on this issue.

Finally, there were a number of mathematically oriented entries. These tended to deal with philosophical shifts, such as Keith Devlin’s move away from platonism and toward socially or evolutionarily constructed mathematics. But Bart Kosko had a very specific change of mind: he argues that the median should be the preferred measure of central tendency, instead of the mean.

Some inspirational videos to close out the year

December 31, 2007

2007 has been a depressing year, and I don’t think that it’s just me. I’ve pretty much given up on watching TV news or reading newspapers. Doing so just adds to the malaise. And because of the writers’ strike, the one remaining palatable news source has been unavailable. (Now if I could only wean myself from the Web, I might start feeling better…but that’s a topic for another post.) So to close out the year, here are a couple of items that have managed to cheer me up and inspire me, in the form of Internet videos.

First up is TED. TED is an acronym for Technology, Entertainment, Design, and at its core it is an annual conference where the movers and shakers of the intellectual world gather to make short (15-20 minute) presentations on what is challenging and inspiring them. The best of these presentations have been made available as streaming video on the TED website. There is a truly eclectic assortment of topics, so there’s bound to be something of interest for everyone. The TED staff maintains a blog where you can find out about the latest talks to go online. A while back they posted a list of all the talks that are available, which makes a handy reference point even though it’s a couple of months out of date now.

Here’s a quick sampling of some TED talks: Neuroscientist V.S. Ramachandran describes how we can learn about how the brain works by looking at how it fails to work normally in patients with neurological disorders. Ramachandran is a great lecturer and I was blown away by this talk. Biology student Eva Vertes talks about her ideas for finding a cure for cancer. Watch this not so much for the specific ideas presented but just to be reminded of the promise of youth. (Hat tips to Mo and Bora, respectively, for these two talks.) A couple of my own picks: Computer scientist and entrepreneur Jeff Hawkins talks about modeling the human brain on a computer. This talk is basically an executive summary of his book, On Intelligence. In the time constraints of the talk, Hawkins comes across as less than convincing, although in his book he develops a much stronger case for his ideas. Finally, for the math-ed crowd, be sure to check out “mathemagician” Arthur Benjamin, who puts on an amazing display of rapid-fire mental arithmetic. It’s interesting to look at the comments for that presentation–some of the viewers seemed to think that Benjamin must have had a secret radio receiver in his ear with an accomplice sending him the answers! Michael Shermer joins in the comments to point out that he and Benjamin co-authored a book on how he performs his mental feats.

The second item for your consideration is the Last Lecture by Carnegie-Mellon computer scientist Randy Pausch. Pausch is suffering from incurable pancreatic cancer, and in his recorded farewell lecture at CMU, he recapped his career and his perspective on life so that his now-young children would one day be able to know a little more about him. This talk has become something of an Internet sensation after being reported about on network news and in other media. The “last lecture” is also going to be developed into a book, with the assistance of Wall Street Journal writer Jeff Zaslow. (Hat tip to my mom for this one–as I mentioned, I don’t follow the main-stream media much any more.)

Pausch described his lecture as being for his children, and I think he’s absolutely right about that. The lecture will be extremely meaningful for his kids as well as for other family and friends. But for outsiders, I’m not sure I understand the appeal. I mean, Randy Pausch is an extremely positive person, and there is no doubt that his attitude played an important part in helping him achieve his goals in life. But this is a lesson that pretty much everyone already understands. The problem is that for someone who feels beaten down by life, telling him or her to be more positive simply isn’t going to help. It’s just not inspirational to someone who’s not already on the program.

So why am I including this video here? Well, one of the accomplishments that Pausch mentions in his lecture is a programming language named Alice. Pausch’s research areas included human-computer interfaces (HCI) and virtual reality, and he was also interested in attracting kids, especially girls, to computer science. These combined interests gave birth to Alice, which is a programming platform designed to be easy to learn, and which uses story-telling as its central paradigm, instead of a more abstract treatment of algorithms. This is supposed to work as a hook to draw girls into programming, and it seems to have been very successful at Carnegie-Mellon. My daughter has taken an interest in learning Alice, and I’ll be keeping an eye on how things progress. You can find a demo video of Alice on this page. I would recommend skipping the promo video at the top of that page, and scrolling down to the demo at the bottom.

**********************************

So that’s it for another year. I hope that you survived 2007, and here’s looking forward to a better year in 2008.

String Theory

December 29, 2007

Physicists in the lab have produced hard data for string theory! Well, for a theory about strings. Actually, knot theory might be technically a more accurate label. Okay, the truth is that the only reason I’m writing this post at all is so I could make a pun about string theory in the title.

This research evidently made the news when it was published a couple of months ago, but I missed it until Keith Devlin mentioned it in passing last week on NPR. Physicists Doug Smith and Dorian Raymer at the University of California at San Diego have developed a mathematical model for how loose string in a box becomes tangled when the box is jostled. Their paper, Spontaneous knotting of an agitated string, was published this past October in the Proceedings of the National Academy of Sciences (PNAS). (The full article can be accessed without a subscription here.) There have been numerous write-ups about it in science and math publications; a couple of particularly nice articles were in Science News Online and in The Mathematical Tourist column in MAA Online.

The experimental apparatus consisted of clear acrylic boxes of various sizes which were rotated by a computer-controlled motor. Strings of various lengths and stiffnesses were placed in the boxes, and after being spun, the strings were analyzed to see what knots had formed. This was done in large part by taking digital photos of the ending configuration of the strings and using a computer analysis to compute the Jones polynomials of the knots. The PNAS website contains Quicktime movies of the apparatus in action, which are definitely worth a look.

As for any practical advice from the study, the bottom line seems to be that you should pack your loose cords tightly to prevent them from moving around. I don’t think that’s going to be of much help when I put away the Christmas lights next week. Each year they inevitably come out of the box a tangled mess, in spite of being packed more snuggly than sardines. Perhaps Smith and Raymer can do a follow-up study using Christmas lights instead of string, that are shaken side-to-side instead of being spun. (My Christmas lights, despite being tangled, are usually not knotted at all in a strict mathematical sense, and I don’t think that Smith and Raymer examined this type of phenomenon in their study.)

 
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