Naive Maps of Spectra

Being a math grad student, I figure I should occasionally post some math up here. And since I learned something cool in class today, I thought I'd talk about that.

So, suppose that $E_0$, $E_1$, $F_0$, and $F_1$ are pointed topological spaces (maybe I should say CW complexes throughout?) and we have maps $\sigma_E:\Sigma E_0\rightarrow E_1$ and $\sigma_F:\Sigma F_0\rightarrow F_1$. Let $\sigma_E^{ad}$ denote the adjoint map $E_0\rightarrow \Omega E_1$, and similarly for $\sigma_F^{ad}$. For pointed topological spaces $X$ and $Y$, let $Top_*(X,Y)$ denote the (pointed) space of based maps from $X$ to $Y$.

Using these structure maps (the $\sigma$s and/or their adjoints), we get maps $Top_*(E_0,F_0)\rightarrow Top_*(E_0,\Omega F_1)$ and $Top_*(E_1,F_1)\rightarrow Top_*(\Sigma E_0,F_1)$. Recall that these two targets are naturally isomorphic (=homeomorphic here). So (allowing me some sloppiness (if I were using full LaTeX, I'd put a nice xymatrix here)), we can fit these spaces into a diagram $A\rightarrow B\leftarrow C$. Then, playing with adjoints and things, it isn't too hard to see that the limit (=pullback) of this diagram is the collection of pairs of maps $f_0:E_0\rightarrow F_0$ and $f_1:E_1\rightarrow F_1$ such that $\sigma_F\circ \Sigma f_0=f_1\circ \sigma_E$.

This is the first step in our naive maps of spectra. Recall that a spectrum $E_*$ is a sequence $\{E_i\}_{i=0}^{\infty}$ of spaces together with structure maps $\sigma_i:\Sigma E_i\rightarrow E_{i+1}$. A naive map between two such spectra ($E_*$ and $F_*$) is then a sequence $\{f_i:E_i\rightarrow F_i\}_{i=0}^{\infty}$ of maps of spaces that commute with the structure maps (in the obvious sense (its fun to just say that and let you sort it out :) )). Generalizing from our above work, we can describe this as the limit over a diagram $A_0\rightarrow A_{01}\leftarrow A_1\rightarrow A_{12}\leftarrow A_2\rightarrow\cdots$, where $A_i$ is $Top_*(E_i,F_i)$ and $A_{ij}$ is $Top_*(\Sigma E_i,F_{i+1})\cong Top_*(E_i,\Omega F_{i+1})$.

The reason one calls these maps 'naive' is that there is another notion of maps between spectra that works better for homotopy theory. Adams says the motto is 'cells now, maps later', which we might interpret here has saying that it doesn't really matter if we start defining maps at the 0 part of the spectrum. As long as we eventually have levelwise maps, that should be good enough.

I've always found the definitions of spectra and maps between them to be pretty thorny. While I'm not saying the above helps, necessarily, it was a fun thing to see, playing with limits. I guess the main thing to take away from this is that anytime you describe a space as a subspace of a product space (we've got maps of spectra being a subspace of the product of all levelwise maps), you might try to think about it as a limit construction.

Site Redesign

Redesign might be a strong word. But I messed about with the blogger template for this page, making this slightly more 'my own'. Like anybody else wants it. But anyway, just a few little visual changes, and a picture for the header. It's a start. Let me know what you think.

XO Usage

This isn't to say I've had any XO usage. Sadly, I still don't have mine. For the past week or so I've had a 'Real Soon Now' idea about when I'd get it. Communication with the support people indicated I was in the system, and they were just waiting for laptops so they could ship them out. Silly me, I thought they probably were getting them regularly. Currently though, the delivery message from laptopgiving.org indicates that I (and everybody else waiting) will be waiting until at least the end of February. So my 'Real Soon Now' hope has faded, and has been replaced by 'Surely they meant end of January' feeling. I mean, no new shipment for a month? Sigh. On the wiki, it says that they had some mis-communication about just how many laptops had been ordered with G1G1, and so they didn't end up ordering enough. I guess that's good news, lots of laptops were donated. Except if lots of the people who haven't gotten one generate bad press.

[Update: I just got my email from Nick Negroponte. They were serious about the end of February. His email said another 45-60 days. Sigh. Maybe it'll be about the same time I get hit by a falling spy satellite.]

But anyway. I've been thinking I'd use my xo primarily as an ebook reader. I end up reading lots of things online, and lots of pdfs. And it seems like it'd be nice to read this in the xo form factor. So I've been saving a list of things in my google reader and a couple of links to pdfs for some math papers to read when I finally got my laptop. With the extra month to wait... perhaps I should just go ahead and read these things. Or should I stash a huge bunch of things to read, and then have a completely unproductive couple of days (unlike usual) when my laptop gets here?

Any of my loyal readers order and receive their xo already? What are you finding that you use it for the most? What did you expect to use it for?

Successful Stumble

So I was stumbling around the internet today, at the office before classes started, and ran across the following: 'Awesome Way to Get Into Your Car'. And it is that. It seems to be from a commercial, but that doesn't make it less awesome. You should check it out.

Stumbling

Well crap. I've been very careful not to install the stumbleupon firefox extension at home. I have a hard enough time getting things done. But I was looking at something, and noticed the 'Next Blog' button in blogger (I guess... if you are logged in? Update (1/30): you don't have to be logged in). Apparently it takes you to a random recently updated blog. So its a stumble link for pages on blogger. It remains to be seen if it's quite as potent as stumbleupon.

Google Integration

No, google doesn't (as far as I know) have a replacement for 'The Integrator'. Really, this is a followup to my last post about suggestions for them. What I've always felt about the various google services is their disconnection from each other. For no particularly good reason I do think it's getting better, but there's still a ways to go.

The main thing I'd like is a blending of reader and gmail, and this seems like a natural matching. I don't consider myself any sort of email power-user, I just need basic reading/writing capability (which reader has anyway...), so perhaps others really want the two services separate. I did find a greasemonkey script that claimed to put a 'Feeds' thing in gmail, but it didn't work (I think it was designed for the 'Older Version' of gmail, so I suppose I could just use that... but I'm a complainer). And I found that google can (does?) create an atom feed for your inbox. Of course, you need to log in, so the feed reader you want to use has to support the appropriate authentication. I'm still fairly suprised, though, that google reader doesn't handle the feed. I understand that making reader have all purpose authentication is a whole new feature (which I guess will happen someday anyway). But if I'm already logged into my google reader... it's the same login for my email... so what the crap? I'm sure I don't know enough about how all this is set up, so I'm sure it's reasonable that reader doesn't (can't?) get my email feed, but still.

Additionally, I found out something suprising (another suprising thing, that is) about the keyboard shortcuts experimental feature, and its relation to your web history that google keeps for you (if you let it). If you use keyboard shortcuts to open a link, google doesn't seem to notice you clicked on the link - in the sense that it doesn't show up in your web history. I should probably let them know, instead of blabbering about it to you. (Update: I just did)

In other (pointless) news, I updated my webpage yesterday. Now instead of being valid HTML 4.01 Transitional it validates as XHTML 1.0 Strict. It wasn't a big modification, but I still feel like it's a step up. I mean... transitional sounds temporary, and conforming to a strict standard sounds hardcore. So look at me go. I also updated the dr. mario pictures bit. Before I had the dynamic picture set up using multiple images that I pretended to pre-cache by putting them in a div with style display:none. But I read about css sprites, and how putting lots of images into a single image is good because it cuts down on the number of requests to the server. Then you mess about with positioning and clipping to make it look like you use lots of small images. Supposedly (brief trials with firebug seemed to confirm it) you get faster load times with this method. I'm still pretty sure the css and javascript could be improved. Maybe next week.

Oh, and speaking of reader, I thought maybe I'd make a go at using the shared items thing. So I'm currently sharing a couple items. If you're curious, check me out. And did reader update their favicon recently, or is my memory just being shoddy?

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.

Suggestions for Google

So, in previous posts I have indicated ways to set up the keyboard shorcuts experimental search feature in google. I predicted that signing in to google, and then clicking the 'join' button on an experiment would translate to other computers. That is, my hope was that when I logged in at the office, my google searches would use keyboard shortcuts. Well, I played with it today and that is not the case! When playing with it, it felt more like clicking the 'join' button just set a cookie. I didn't experiment with this hypothesis too much, digging into my cookies or turning them off or anything, but that's not the point. The point is, some of my google preferences don't transfer to other computers when I log in. Which is annoying. So suggestion (1) is for them to fix this.

I also think the top menu choices (upper left), the links to other google services, should be customizable. That is, I should be able to pick (in order) a handful (≤7?) of the services I want linked to up there, and then that's what I'll see when I log in. And they can put the 'More' dropdown menu there, with the remaining ones. This is suggestion (2).

The final (real) suggestion is along the lines of suggestion (2). I get annoyed with the fact that switching between services opens up new tabs (presumably new windows that firefox interprets as tabs for me). If I wanted something to open in a new tab, I'd middle click on it. Clicking on these service links at the top should open, by default, in the same window. Make it so (or make it customizable), that's suggestion (3).

So, what do you all think? You like these suggestions? Have some of your own? Know who to talk to in order to make them happen? Know how to set it up already, without google making changes on their end? I guess one could probably mess about with making a greasemonkey script.

Suggestion (4) is directed to a larger audience, not just google. Somebody should sponsor me. Give me money to live for, say, a year (I'm not asking for more than my grad school salary), with the idea that I spend the time learning whatever I feel like. No pressure to do research, no pressure to produce anything useful for others. Just learn a lot, on my own schedule. If you felt like it, you could start setting aside money to do this now, and then we can work something out when I finish with grad school. Let me know.

LaTeX in Blogger

I'd really like to see native LaTeX support in blogger here. I'm sure the folks that keep this thing going could implement it.

Searching around a bit today, I found another thing I thought I'd try, until native support works out. So lets see.
$a^2+b^2=c^2$ and $e^{\pi i}+1=0$

Well holy crap, check that out. I found this from this blog post, but its a javascript file from a Dr. Woodall. I guess that means I have a javascript file to study :)

If you want to try it yourself (in blogger) you have to customize your template file. You do this by clicking the 'Template' tab and then 'Edit HTML'. There, put the following:

<script type="text/javascript"
src="http://www.maths.nottingham.ac.uk/personal/drw/LaTeXMathML.js">
</script>

after the <head> tag (line 7 for me). Then the .js file seems to take things between \$\$s (which you have to type in using a backslash) and converts the LaTeX to MathML, for display in browsers. Perhaps I'll dig through it a bit and see if that's actually true. If I understand (even if I don't), some browsers don't support mathml? Firefox works, which is all I need.

Free Stuff

There are currently a plethora of commercials for medical products, many of which offer free trials. I never have trusted these sorts of products. One of the commercials has somebody saying 'if its free, it must be good', and I always scoff. However, it occurred to me recently that I have basically the opposite view with software. Most (all?) of the software I use at home is from the Free/Open Source community. I'm always encouraging people to use such software (firefox, linux in particular).

So why the difference? Am I just a huge hypocrite? Do I not really believe, deep down, in the FOSS movement?

I hope not. I think the difference is that the medical products are given away in hopes that people will spend lots of money later. And it is my impression that most people are fairly gullible about lots of the medical (and dietary) crap these days, and I feel like the companies are preying on, and encouraging, this. Alternatively, 'free' (as in speech) software comes from a community that wishes to make great software, and happen to believe that the software should be available to use and modify and redistribute without restriction. Damn hippies. :)

Online Stars

For no particular reason, with no particular goal in mind, I've been thinking a little about star ratings (perhaps by writing something down here, I can free up those mental cycles for something I should actually be thinking about, like my research). Like in Netflix, you're supposed to rate a movie 1-5 stars. But I expect everybody has a different idea what those stars mean. For example, I've given very few movies 1 (though I do use 'not interested' for some movies I haven't seen). I interpret 2 as 'I wish I hadn't bothered sitting through that' (which I've hardly used), while 4 is 'I'd happily watch that again' and 5 is along the lines of 'I actively enjoyed that movie' or 'I'd consider owning that'. I left out 3, which is kinda my default if I don't really care. My point, though, is probably other people use different interpretations, maybe handing out more 5s or 1s, or fewer 3s. How do you interpret the netflix stars?

What's important, then, from a recommendation viewpoint, is not the actual rating, but the relative rating. If I give a movie a 3, that doesn't really mean anything by itself. It only means something in the context of all the other movies I've rated higher and lower. Movie ratings (and other such ratings) don't really form a poset; there is no absolute grading, only a relative grading. I'm sure if you are competing for the netflix prize, this isn't a new (or even worth-pointing-out) observation.

In my daily online experience, stars also come up in google reader (and occasionally in the web history or gmail). There they act only as a flag, a binary 'starred' versus 'unstarred'. And it's handy (especially with the 's' keyboard shortcut). What I'd like to see, especially in combination with the keyboard shortcuts experimental search option in google, is a 's' shortcut to star search results from google. Even without keyboard shortcuts on, just put the little star next to items so I could click to star/unstar them. This then gets saved in the web history bookmarks, just like if I'd gone in manually after the search and starred an item that I had clicked on. This is a lot easier than copying links into my google notebook, for example. I suppose I could check out the google notebook browser extension again, but I'm kinda not hugely keen on using browser extensions much. I'm not sure why.

Also, with the keyboard shortcuts experimental search feature in google, the 'O' shortcut opens the link in a new tab. But in my firefox, it doesn't open in the background (like it would if I middle-clicked). Is this the case for other people, or do I have something set up poorly? How do I change it?

While I'm at it, in an earlier post I mentioned how to easily use the keyboard shortcuts feature in google. I was just looking around today, and if you have a google account, there's an even easier way. At the experimental search labs page, just click 'Join this experiment'. I think I'm going to like this. At my office, I didn't configure my google keyword shortcut in firefox, so I don't have the keyboard shortcuts. But now, after I log in to google (which I'd do to check mail anyway), I'm expecting that I'll have those shortcuts. Hurray!

Fireballs

I've been pretty delighted with my geekologie rss subscription. The author is hilarious, and the topics generally aren't far from interesting. Enter 'Magic Fireballs Are So Freaking Awesome', which was from metacafe. I wish I were, well, whatever it takes, enough to try these things out. Because they really are (at least, seem to be, in the video) freaking awesome.

Trig Tips

I thought maybe it was about time I post something actually useful here. It occurred to me that the method I use to memorize my trig tables is something that my students never seem to have seen, so maybe others haven't either. I don't claim it's brilliant, but I was pleased to notice it.

The first thing you have to remember is the angles that you are supposed to remember: 0, π/6, π/4, π/3, π/2 (in that order). Now, lets start with the values for sin. Going from least to greatest (in the angles), the values for sin are (√0)/2, (√1)/2, (√2)/2, (√3)/2, and (√4)/2. Writing them this way, it is easy to see the pattern. They're all (√n)/2, where the n goes from 0 to 4. Of course, sin(0), sin(π/6), and sin(π/2) simplify to 0, 1/2, and 1, respectively. To get the values for cos, reverse the process. The way I do it is to go backwards in the angles (π/2 to 0), but use the same ordering for the values.

Origami Projects

The last week before the start of a semester is always a good time to mess about. While I've spent some time reading about buildings and apartments and chambers (Tits Systems and Coxeter Systems and such), I also did some origami. I've done the 5 interlocking tetrahedra before, but it wasn't very nice (I used pieces of paper that were too long). This one's a bit better, with color and all (trying to use up my color paper). Plus this gives me a chance to see how blogger does pictures. Gotta have some excuse to play with stuff, right? If you're looking to make your own, I used the plans from Thomas Hull's 'Project Origami' book, but they are also in the book I got that started my hobby: 'The Origami Handbook' by Rick Beech. In fact, Dr. Hull has the plans online.

What I'd really like to do next is an origami trefoil knot, using the Phizz units, along the lines of the torus. Now, I'm not very bright, and have never done an origami model without the plans sitting in front of me. So I asked my friend google to tell me about possible models. The only thing I've found so far is this paper (.doc, ewww), which does have plans for the trefoil. In fact, I really enjoyed the paper, and learned some things from it (the counting bits at the end). But the plans seem to lack the 3-fold symmetry I expect is possible. Perhaps I just don't know enough (any) of the geometry involved, but I figure there should be a fundamental domain that is a third of the model. Or perhaps the three things go together, but each one is 120 degrees rotated (along the meridian) to get the appropriate twisting. So, if you know of such a model, and can send me a link, it'd be much appreciated. If you know a reason such a model can't exist, please do tell me about it. Otherwise, one of these days, I may start folding some more units. That sounds productive.

Actually, now that I think about future origami plans, hot on the heals of this five tetraheda model, there's another large project I've been wanting to do. The five tetrahedra made from penultimate units. I've sat down to do it before, but you have to cut paper to specific sizes. And not something like '1.5in x 4in', but 'a 4x3 rectangle whose width is 2.58 inches'. Right. Perhaps I'm missing something (besides a functional brain).

OLPC Delivery?

It was just Sunday I got an email from OLPC customer service saying 'you should receive your laptop no later than January 15, 2008'. Now when I signed up (Dec. 30), I figured it'd be a while before I saw my laptop. And that's fine - I don't need one. The program isn't designed for me, it's for poorer nations. But when I got that email, it did get my hopes up. Its not like Sunday was that long ago, that predicting something for Tuesday was a long shot. If you haven't figured out yet, I didn't get my laptop today. I shouldn't be aggravated. I just hope they're a bit more on the ball with the deliveries that matter.

NiN and Saul Williams

I ran across, today, some recent interviews with Trent Reznor and Saul Williams, concerning the distribution of Saul's 'The Inevitable Rise and Liberation of Niggy Tardust' album, produced by Trent. Saul sounds pretty jovial about it all and optimistic about the future of this album. Trent, on the other hand, is a bit more disappointed. I guess he'd hoped, reasonably so, that more than 1 in 5 people would pay for the album.

I've been a Nine Inch Nails fan for quite a while now. So when I read the news about the work with Saul Williams on Niggy Tardust, I decided to give the album a try. I assumed it would be fairly different from what I generally listen to, but that's ok. And hopefully my participation would help the next NiN album come out in a similar manner? So I did the free download (that's what it's for, right? trying things out?), and have listened to the album many times since. I'd been planning on going back and buying the $5 version online, and these recent interviews were the push I apparently needed. I would have happily paid more. Perhaps, in the future, let the user specify how much to pay? Maybe set a minimum if you want, that's fine. I know I could go and order it again, and just not download it, but I don't really have any motivation to.

So, if you are looking for something new to listen to, I do encourage you to check out the album. Though it is no longer free, $5 is still a great price for a whole new cd worth of music. It sounded, from the interviews, like a cd is forthcoming, as well as a larger marketing campaign.

Busy OLPC Week

No, sadly, not busy in the sense of me playing with my XO. I'm still waiting. But I know I'm not alone, so its ok.

There were three big news items recently:

1. Mary Lou Jepsen has left to branch out into her own for-profit company, Pixel Qi. From what I've ready, she was the main figure in many of the awesome technical features of the XO.
2. The split with Intel, after only a few short months together.
3. Microsoft working on getting XP to work on the XO.

I'm not authoritatively familiar with any of these aspects. There must be some remorse in losing Mary Lou Jepsen, but it sounds like she plans on keeping on doing good things, and helping out OLPC in the process. So that's ok. As far as the split with Intel goes, we're supposed to believe competition is good. It seems to me that Intel can generate some pretty stiff competition, and I wouldn't be surprised if it lead to some new distribution models for OLPC. Especially as this seems to be the main issue soo far. Finally, Microsoft's plans... well, I'm not a fan. But then, I can't imagine wanting to run XP on this thing, so with any luck they'll be investing this time and energy and not end up with much to show for it. Time will tell. I do find it humorous that the XO comes with a 1GB drive, and that's enough room for the OS and space to work, but that Microsoft is apparently working very hard to get their stuff down to 2GB (to fit on an external flash drive).

Travel Mugs

I'm discontent with all of the travel mugs I've run across. The problem of a good travel mug design has been somewhere in the back of my mind for a while, so I've been looking at mugs (their lids, specifically) when I find them. And they all annoy me.

My ideal travel mug is simple (most of them basically have this) but moreover simple to really clean. Ideally this means my hand fits in it comfortably (since I mostly end up doing my dishes by hand), though this sacrifices the ability to fit in car cup holders. More importantly, 'cleanable' means, for starters, no screw on lid - I never feel like the threading gets really clean. In fact, no interior corners at all - mugs (dishes in general) should be smooth. The worst part about all travel mugs I've seen is the lid though. They all involve some sort of moving bit with an inside (or underneath or between) that liquids can get to, but you can't (short of disassembly). That's terrible.

So, what does my lid look like then? How does it work? Well, I'm honestly not sure how to create my ideal lid, reasonably, but I'm sure it is possible. Here's what I'm envisioning: near the top of the (circular) mug, there will be an interior rim (remembering no corners) on which a circular lid will sit. I've kinda got a man-hole cover in mind here. The lid should be a solid disk. What makes the lid useful is a single button (maybe two? or one of them is a slider?) on the top. After setting the lid down on the rim of the mug, you can press the button and the diameter of the lid increases (this is the part I'm not sure how to engineer - see below). Now the lid fits tightly against the mug (in an ideal setup, this forms a perfect container, you could turn the mug upside down and not have any issues). So how do you drink out of it? Well, press the other button on top, and some part of the disk shrinks back, making a place for liquid to come out (looking at the lid from the top, it'd look like a circle except for a point on the edge where somebody pushed in with their finger, I recon). Of course, travel mugs have that extra little hole opposite the bit you drink from, so that air can get into the mug and you don't have to worry about vacuums. No problem. Just, when you press that second button, have a little indentation show up opposite the drinking indentation (all one mechanism, doing the same functionality on both sides, just much smaller on one side).

I have some vague thoughts on how to implement such a lid. Part of me wonders about having the interior of the lid have an air bladder. Then pushing on the button on top forces the disk to increase diameter. I'm not sure how you then have a separate button to open/close the drinking hole - perhaps the interior has two air bladders, or the lid is made out of two materials or so? I also worry about the air bladder popping, or leaking, so it's not my first choice. Another idea that comes to mind is along the lines of the steamer tray I have. Its a little tray that you stick in whatever pot you are using, and its got a bunch of metal wedges that fit together, and can lie flat to fit in larger pots, or stand up straighter for smaller pots. Now, for my lid, flip that tray over, and wrap it in some sort of rubber. Pushing down expands the diameter. Using a spring mechanism like in clicky pens, pushing down again unclicks it and decreases the diameter. I figure this has potential, because you could pick one of the wedges and (somehow) make it so that you could decrease just the size of that wedge, without affecting anybody else. That gives you your hole to drink from.

Anyway, if anybody ever reads this and knows how to make this dream a reality (or knows that somebody else already has, and can point me in the right direction), I'd be delighted to hear about it. I'm also happy to try to clarify any of my descriptions above. Maybe I'll get truly ambitious and post some picture(s) here. If this thing doesn't already exist, I want somebody to use some sort of open source manufacturing or whatever to get it in production. That is, the design and plans are online, and people can view them to make their own or change the design to make improvements and fit their needs. If it doesn't exist, and this is my idea, I'm allowed to ask for such a thing (the open manufacturing bit), right?

Wikia Search

So I guess in the last few days wikia has opened up an alpha version of their search page. I've been a wikipedia fan (both as a place to find information, and more philosophically), so I've been waiting to see what this (hyped) search would deliver. Reactions were mixed, from 'complete letdown' to 'more intrigued'. And, reading this article, I feel like I agree with the spirit of the wikia project, its openness and transparency (on a side note I tried to spread the good word on open source today. I was teaching LaTeX, and said that something being open source was like having the .tex file, instead of just the .pdf. Hopefully that helped).

That being said, I gave wikia a try. Now, I don't personally care about the social network aspect of it. And apparently to view the profiles that pop up when you do a search you are supposed to be registered, so whatever (maybe I'll hide that div with Ad-Block Plus). They do have a pretty decent interface, and I kinda like the dynamic fetching of the 'next 10 results' sort of thing. What I'm most excited about by this project is the idea of star rating search results (also a nicety of the interface for this feature), and having those ratings affect future results.

Now I clearly don't know much about all the bits currently relate, or how they will relate in the future. But I think it would be cool to see this star system used powerfully to determine customized search results. If it remembers my star ratings (after I register) for search terms, and compares that with other people's stars for the same(/similar) searches, then it can pair them up to help pick nice choices for later searches. That is, I search for A, and wikia notices that among other people who have searched for A I agree with person P on lots of other searches (not A). Then wikia looks at P's stars for the search on A, and boosts those results in my search.

Anyway, that all sounds complicated to set up, so maybe I'll let other people worry about it.

I suppose, since it is a search engine, I should talk about its current results for example searches. My initial (few searches) reaction is that these results are noticeably different (somehow) from the ones I might expect from google. But I think that's a good thing. Getting more, varied, results is a positive. My initial searches were math things, since that's what I generally search for anyway ('category theory').

Finally, I do wonder about 'gaming' the system. Apparently, Jimmy Wales thinks it won't be a problem. But with the indexing algorithm out in the open, it seems like people would be able to figure out ways, and do so more easily than in hidden systems (google's algorithm). Then again, this sounds vaguely along the lines of 'security through obscurity', which I don't buy in general.

Whatever, I'm happy to wait and see how it all plays out.

Pointlessness

So over the break, at our big family get-together, relatives asked me what I did, and also my sister. "I teach calculus, and am supposed to be doing research" - that's me. "I'm working on things associated with progeria" - that's her (of course, in her conversation she didn't link to wikipedia). All paraphrased, clearly.

I just found it amusing that my sister was doing things that will have an actual, significant, impact on other people's lives. She could, for all I know, be saving lives. Me? I'm making students miserable talking to them about things they don't mostly care about, and then grading them on it. And my research? Like lots of mathematics, the things I'm looking at are completely non-applicable to the real world.

Which reminds me - why do I get paid again? I don't remember the last math paper I read, for my own work, with real-world applications. How many mathematicians removed am I from the real world? How many theorems away - that is, what is the theorem 'nearest' the things I am looking at that is still applicable to some real-world setting? Even just the nearest general theory? I guess knot theory is the closest, though I've heard rumors that category theory has computer science applications. I've not seen anything serious, but I can't say I've spent a whole lot of time looking. But anyway, I don't anticipate any of my work to be close to any of this, and I don't expect any of the ideas to trickle down somewhere useful, even for decades upon decades (and with the coming singularity, or weather issues, how many decades do we have left?). Oh, so I guess I must get paid for teaching (and the research somehow makes me a better teacher?). But these kids are bright enough, they could be reading it from the book. Even if they don't think they could. And anyway, I'll be quite suprised if more than 1 or 2 use anything I teach outside of other classes.

Anyway, off to bed. Gotta get up and teach in the morning :)

Netflix News!

Big news today about Netflix teaming up with LG to make a set-top box that will play their 'Watch Now' library. Nobody has a whole lot of information on this for now, but have some links: [1], [2], [3].

I've been a Netflix fan for about 3.5 years now (my grad school career, as it were, including a pointless year of about 370 movies (not all from Netflix)) and recommend it to any friends or family that talk about movies. I have at times been up to the 5-at-a-time option, but have since slacked off a bit, down to 1-at-a-time. I still aim to watch and return movies the day I get them. When they started their 'Watch Now' thing I was optimistic, but this was quickly shot down when I realized it only worked under Windows. As a Linux-only user (at home), I was disappointed, but not particularly suprised.

This optimism is cautiously renewed with this news for their set-top box(es). As usual, January will be a fun month for tech people, with the CES and Macworld shows (and I feel like I'm forgetting at least one more). I guess LG is expected to do something about this box at CES. But we can't forget Apple TV (actually, given how many people I know that have ever talked about it = 0, maybe we can), which may also get new news soon. [Competely off topic, but Google also apparently has 2 booth at CES. Go Android!]

Now, as a fan and movie watcher, I can actually give my own opinions related to this news. I'm glad to see it happen, and I hope it is a success (in some sense, see final paragraph). It sounds like this LG box is the first of hopefully several different hardware options, so I expect at some point one might come along that fits me. Now if LG decides to include this Netflix thing in their $800 box (as mentioned at engadget), count me out. I've already got a dvd player, and am avoiding the HD/Blu-Ray argument - hoping for the next format to come along quickly (I seem to recall reading an article along the lines of this being the last hardware format war, but haven't yet found a link). So all I'm looking for in a Netflix box would be something that'll hook up easily to both my tv and router, and will play the 'Watch Now' titles. The above articles mention that the movies you want to watch will have to be selected from a computer. I'm not entirely sure what that setup entails, but I wonder why its necessary - why the box can't handle that itself.

In brief, here's what I'd be after in a Netflix set-top box:

• Easy to install. Plug in the wires, set up accounts, and go. It should, probably, permit multiple accounts, like if roommates have seperate netflix plans, but I don't see this as a big issue. If it does have multiple accounts, they should clearly be password protected, and whenever you pick a movie (or maybe whenever you turn the thing on?) you are presented with an easy way to choose which account to use.
• Cheap. I don't care if the box doesn't have any optical drive (leaving one out and getting a nice, smaller, form-factor is appealing. I'm thinking cable-modem size/shape). I don't care if it only has enough internal storage to do whatever buffering it needs. Simple means cheap, and simple fits my bill.
• Linux based. This is the big one for me, and the one I worry about. The form factor doesn't matter too much, and I expect little trouble making the box easy to use (everything is these days). But if the box is some Windows-based box, I'm out, no question. I'd rather wait, and just do mail rentals. Even if I could do unlimited watch nows without changing my monthly plan (I mean, I should be doing work anyway).

This last point is where I think the problem will be. If I can't 'Watch Now' with my current Linux distro (Ubuntu-Gutsy Gibbon, if you were curious), then I don't expect the LG box to be Linux based. The next question is: If I could use Watch Now on my computer, would I also spring for a set-top box? Then the cost is the issue. I guess its academic though.

PSTricks

I got "The Latex Graphics Companion" from the library the other day. While I don't generally use much in the way of graphics (besides xymatrix for commutative diagrams), I thought it'd be fun to look through. I'm sure its full of thousands of gems, but the one I want to keep a record of is text following a curve. This is from page 109:

\usepackage{pstcol,pst-text}
\begin{pspicture}(-4,-3.2)(3,0.2)
\psset{linecolor=lightgray}
\pstextpath
{\pscurve(-4,-2)(-2,0)(0,-3)(2,-1)(3,-2)}
{\color{blue}
If you want to type
$3 \int^x_y = \sum^{n=1}_{33}$
and let it follow along a
curving line \ldots}
\end{pspicture}

Someday I'll sit down and get more awesomeness out of the book. But for now, I should return it and let somebody else enjoy it.