Fine Structure

I whipped together a quick plugin over the past couple days to autoconvert LaTeX formatted text to images in MovableType. LaTeX is a popular formatting tool for people that talk math on the web. More info about LaTeX in general here. Documentation and the download for the plugin is here: LaTeX for MovableType

I picked up Arjendu's Confused on a higher level blog the other day from Chad and made a little comment on a post about refereeing for expensive journals. I'm still a little conflicted about the fact that high-profile journals seem to effectively do the same job as record companies; controlling their clients' work because it's in their own "best interest" whereas they'd get a lot more eyeballs on their work if it wasn't behind such an absurd paywall. That's not to say I don't recognize the positives behind having a random^[1] selection of qualified people commenting on the merits of any particular paper - there's no way a small number of people could understand or even read all the contents of everything submitted to the most popular journals. Similarly, the referee and journal system should make it possible to have a completely unknown author break out with a really excellent paper since we're evaluating based on merit alone. Unfortunately I don't think this is the case for reasons I'm not completely clear about right now.

I'm still trying to come up with specifications for a system that's effective where the current one fails. And this includes my first complaint^[2] as well: referees are volunteering their time for free and journals still see fit to charge absurd amounts for subscriptions.

^[1] I'm actually unsure if the process is random, I'm just assuming that it would be to weed out any referee stacking in favor of a particular author with influence.
^[2] Posted as a comment on Arjendu's blog here

Inevitably, any culture that develops new technology will have their fair share of armchair luddites who point the finger and shout "There's your monster!" at whatever invention is busy making our lives easier at that particular moment. Case in point: this article which has a university professor claiming that Google makes his students dumber. My intent isn't to debunk this particular article - anyone who seeks out a blog containing science content should have some sense of why this is wrong - but to comment on the reasons for the effect itself (that is: students taking the easy way out), which I don't doubt.

Nothing I've seen suggests that a certain subset of students will NOT take the easy way out given the opportunity. This applies equally as well to a time when Google did not exist in popular form. Of course Google is quite popular with the youngins these days and is, quite frankly, a useful tool for researching almost anything you want to know about. Unfortunately, the professor in question places the blame for the laziness of some of his students squarely on Google itself:

"Professor Brabazon does not blame schools for students' cut-and-paste attitude to study. Nor is she critical of students individually."

The suggestion that your first search result is not always your best is fair but to claim that the only culpable party is Google is pure ludditry! Students (and I speak from experience here) are not taught to develop their own interests in subjects. They are taught to write papers and do practice problems. It's a problem I see over and over again and as I become slightly closer with some particular academic institution I'm sure I'll have more to say on it.

But do you know what the first number generated by two sums of two distinct numbers to the fourth? That would be 635318657. Or the first number by the sum of three distinct numbers cubed? 1009. Or to the fourth in that case? 6578.

To make it short, these taxicab numbers get to be fairly large numbers very quickly. Just for kicks I wrote up a little perl script that calculates a range of different sum-of-multiple-distinct-exponent numbers. You can configure it however you like but it's set by default for checking the familiar sums of two numbers cubed from 1 to 12 (this'll give the popular 1729).

Pick it up here. It's just some quick perl using the helpful Math::Combinatorics for generating the numbers to check. I'm open to suggestions if you think you can build a better mousetrap though. Leave a comment or email me.

I'm curious to do some graphing of these numbers and see what kind of variation they produce and if you can predict some certain subset of them. This is originally why I made the script to produce a range of numbers rather than limiting it to this or that number. Perhaps I'll figure that out later.