Mind Reading

So I sat down today and read 'Kluge: The Haphazard Construction of the Human Mind' by Gary Marcus [amazon]. It was overall enjoyable, but I think 'On Intelligence' by Jeff Hawkins [amazon] will still stick with me more. If you've got the time, both are worth reading, but I'd start with Hawkins' book.

My favorite part of Kludge, and a decent proportion of the text, was the numerous references to studies that had been performed, testing varying aspects of the mind and human behaviour. Examples:

• Groups were given scrambled sets of words that, properly unscrambled, formed sentences. Those groups with words "designed to elicit the concept of the elderly" tended to leave the study walking slower than other groups. (p. 25)
  
• An apparently isolated indigenous group (in the mountains of central Asia, in the 1930s) was presented with the following: "In a certain town in Siberia all bears are white. Your neighbor went to that town and he saw a bear. What color was the bear?" To this, individuals responded that they wouldn't know, and the neighbor should be asked directly. (p. 63)
  

One quote I liked from the book was (p. 149)

To be human is to fight a lifelong uphill battle for self-control. Why? Because evolution left us clever enough to set reasonable goals but without the willpower to see them through.

I also learned a new strange sentence in this book: "People people left left" (p. 117). That is, 'a group of people, who were left by a group of people, left'. It reminds me of this one.

Another thing I'll take away from this book is a new method of remembering lists. I've grown to distrust memory, as it seems like one of the more fallible parts of the (at least my) brain. Anyway, the technique: if you've got a list of things to remember, associate each with a room in a building that you know well. Then to remember the list, just 'walk through the building'.

While I'm at it, I'll share a memory technique of my own, which I got from my reading of 'On Intelligence' (I don't know if it was mentioned there explicitly or not, I'd have to re-read it to find out). Frequently, as I'm trying to fall asleep, I'll remember something I need/want to do. If it's not important enough to deal with immediately, what I'll do is take something nearby my bed (a book, or shirt or something), and place it somewhere that I'll be surprised to see it in the morning (toss it across the room, maybe, or, in the case of the shirt, fold it up neatly). The idea being that when I wake up, I'll notice something out of place, and it will trigger the associated memory from the night before of the thing I have to do. It's worked out well enough for me so far.

Lockhart's Lament

I just finished reading "Lockhart's Lament" [pdf] which seems to have been posted as part of a monthly column at the MAA (if the page had an rss feed...). It was a great article about mathematics education, or lack thereof. I very much encourage you to read it. There is also, I just noticed, a followup, but I've not read that yet.

I hope I can do something, in my own classes, to address the issue brought up by the paper. Hopefully I remember to re-read this paper several times while preparing classes, and let if affect my course. I think I may also encourage my students to read it, especially if I can get my course to strike them as 'not a typical math course' (or even just certain class periods). Perhaps they'll be more on-board with atypical exercises if they have some idea where I'm coming from. Of course, his essay was geared toward K-12 classes, and I am (and hope to continue) teaching college classes, but still.

I also found the article inspiring on the 'math is awesome' level, which I've been lacking a bit as of late. Not making progress on research is frustrating, but math really is awesome. Reading 'A Mathematical Journey' by Schumer has also been helpful. I was thinking last night that this book is probably one I can return to throughout my life, and always (re?)discover wonderful things.

Exciting Times

While I may sometimes forget it, and get lost in day to day trivia, this seems to me an exciting time to be alive. Of course, I wonder if that is something people always think. Throughout much of recent history, has there generally been some segment of (basically average?) people who thought they were living in exciting times?

So why now? Well, the primary reason I think now is exciting is because of the technical advances. I love computers and playing with them and seeing what they can do, and dreaming about what they will soon do (and what mine, in particular, will do. Lots of the things I want already exist). I eagerly anticipate more (at least slightly more) ubiquitous (wearable) computing. I'm looking forward to having a pair of glasses in which I can see a 'computer screen', and be able to easily interact with while I walk around.

At a slightly more reserved (less fun) level, I just finished reading 'Geekonomics' (which I encourage you to read), and I enjoyed it. It presents interesting historical case studies, and I also learned a little about economics and our legal system. The subtitle is 'The Real Cost of Insecure Software', and the book provides convincing evidence that change is eminent in the software engineering field. The code we depend on is largely dangerous, with all of its security holes, and something needs to happen soon to address this issue (says the book). The net result will be higher quality software all around (again, says the book), and I like the sounds of that. So that, too, is exciting.

This summer CERN gets ready to make black holes in France and Switzerland, and that's exciting. I've seen claims (today's reminder came from a link off digg) about them creating things with temperature comparable to that of the Sun. So perhaps all of this future tech I anticipate... the world won't be around for. But that, too, is somehow exciting - being around for the end of the world, that's gotta be worth something.

And in just over 20 years (depending on who you ask), 'The Singularity' will... well... we don't know. That's the point.

Exciting times indeed.

Fandom and ARGs

I like to consider myself a fan of several things. The two I want to mention now are: (1) The Matrix, (2) Nine Inch Nails. Part of the reason I've been thinking about these things is that I relatively recently read 'Convergence Culture' by Henry Jenkins, which I encourage you to check out.

Ok, so I know The Matrix isn't really news. But when the first came out in 1999, I saw it many times in theatres, and have watched it many more times since. Same goes for all the other releases (well, I guess I missed the animatrix in theatres). Anyway, they're all good stuff, both as plain old entertainment as well as thought provoking works (I wish I had an ample vocabulary). What I'm trying to say is that I mostly think I'm a bigger fan than most. However, I never read the associated comic books, nor played the video games. So am I just fooling myself? Or was the scope of the project, its many facets, too large for even a supposedly loyal fan? Of course, that's a stupid thing to wonder. The people in charge were artists, using a new form (a combination of forms) to display their work. Who am I to wish they hadn't done as much? I sincerely hope that many people out there engrossed themselves more fully in the world of the matrix than I did. I hope the artist's full work was appreciated. Perhaps I'm just more a fan of being stubborn and lazy than I am of the movies (well, the whole artwork). I could have, after all, played the video games (and now that I know about them, I'd like to check out the comics) and read more of the things online... etc. etc. etc. When I think about it, I wonder what, if the matrix couldn't, would get me to play a video game to more fully engross myself in a story, or piece or art. I haven't really come up with anything, though I have been wondering about this game spore for a while. I mostly only like little video games, dr. mario, for example.

Onto item 2. I've mentioned several times my draw to nine inch nails. I own most of their 'halo's, including many of the singles. However, when their Alternate Reality Game (ARG) came out for year zero, I didn't do much about it. I remember spending a day or two looking at what was around, about messages on t-shirts and messages in Morse code in songs. I visited many of the links, reading supposed files about 'The Presence', and 'Opal'... And then I lost interest. I couldn't tell how I was supposed to participate. I don't have any real skills at all, so I don't expect I could have helped find hidden messages or anything. Plus, I'm kinda lazy (I just started reading a book 'How to be Idle', by a Hodgkinson, so perhaps you'll hear more about this in the near future), and not particularly creative (though I'm realizing that I like to create - through origami, programming, even this blog nobody reads (over-inflated self worth strikes again)). So, again, what happened? Am I not a fan enough to keep up with and immerse myself in these things? Or did this one particular game end earlier than expected? I looked at things again recently, and something said it was supposed to be an 18 month time frame for the game. So is there more to come in the next couple of months? We've got til... September/October I think. Perhaps this ghosts release is part of it all. I hope so, but my initial impression is that it is just Trent wanting to make some music (which I am, of course, happy to listen to). I'd be happy to be wrong, perhaps there are messages floating around in all of these new tracks. I should go look...

So anyway, what's the deal? Am I just too damn lazy to be allowed to consider myself a fan? Too old school and set in my ways to play with these relatively new avenues of entertainment? I mean, I don't care at all for text messages (or phones in general), and don't quite see the point of 'micro-blogging' or 'lifestreaming' sorts of sites. So am I not really keeping pace with technology these days, despite what I'd like to think? It is my impression that these ARG things are a relatively new form of media (again, see 'Convergence Culture'). In that case, perhaps whatever recipe for them hasn't quite been worked out yet? Maybe they won't even pan out as a trend? I mean, my understanding of them goes like this: a group of people sit down and try to create a puzzle for, essentially, everybody to solve. Of course, not everybody will hear about it, or care, or participate. But my point is that the intended audience is much larger than the group creating the puzzle. So... that group better be _quite_ impressive at puzzle-making in order to be able to entertain a significantly larger audience. I'm not saying it can't be done. But maybe, assuming it is a newish sort of venture, the puzzle creators could still use some more practice? Of course, I recognize that as a hugely arrogant thing to say, and must refer you back to the Matrix paragraph, about the creators being artists, who should be encouraged to make what they want.

News from wired today about a possible new ARG starting with some relation to McDonald's and the coming summer Olympics. Perhaps this'll be a big turning point for the medium? I mean, everybody has heard of both McDonald's and the Olympics, while a drastically fewer number have heard of Mr. Reznor.

Quick Book

In the past few days I read 'The Most Beautiful Mathematical Formulas', by L. Salem, F. Testard, and C. Salem. Which isn't to say it took a while to read. Probably about an hour in all. But it was a perfectly enjoyable hour. The formulas are fun and mostly simple. Each formula (~49ish) occupies a chapter, which generally corresponded to two pages: 1 of text, and 1 full-page drawing.

The one thing that stood out the most, for me, was a quick deduction of the double-angle identities for sin and cos, using complex numbers. You look at e^2θi in two ways. First, it is e^i*(2θ), which is cos(2θ)+i sin(2θ) (Euler's formula), and secondly it is (e^iθ)². Expanding this (again, Euler's formula on the inside, then square it out) and then equating real and imaginary parts for the two versions gives you the double-angle identities. Not bad.

Putting in Time

Well, I spent most of the afternoon trying to learn things. Might as well have just watched movies though.

Suppose I let R_{k-1}^{k} be the poset of vector subspaces of real k-space whose dimensions are bigger than 0, and no more than k-1 (that is, a point in this poset is a vector space E that is a subspace of real k-space, and 0<dim E<k), ordered by inclusion. This is then a topological category (that is, a category internal in Top), with object space the disjoint union of so many Grassmannians and morphism space the disjoint union of flag manifolds (flags of length 2, I guess you'd say). I've been trying to sort out the realization of this category, because it comes up in a homotopy limit I'd like to calculate. The nerve is a simplicial set whose non-degenerate simplices are flag manifolds (the length gives the dimension of the simplex), and so the largest dimension in which there are non-degenerate simplices is k-1 (those chains E_1<E_2<...<E_{k-1} where dim E_i = i). Anybody have a reference for somebody else's work on this topic? Because I'm not getting anywhere, and it feels like the sort of thing people would have been interested in already. [Update: Found it]

Also finished reading E. T. Bell's "Men of Mathematics" today. I don't remember getting a whole lot out of it, but I guess that'll happen. So now I gotta figure out what to read next. Kinda feel like I should read "Women in Mathematics", which I feel like I've seen in the library. Also just heard about an author Pynchon, sounded like he might be fun.

Guess I should go prepare something to teach LaTeX to high schoolers.