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Deriving a Non-Recursive Fibonacci Function Using Linear Algebra

2008 Aug 20, 10:51

In my Intro to Algorithms course in college the Fibonacci sequence was used as the example algorithm to which various types of algorithm creation methods were applied. As the course went on we made better and better performing algorithms to find the nth Fibonacci number. In another course we were told about a matrix that when multiplied successively produced Fibonacci numbers. In my linear algebra courses I realized I could diagonalize the matrix to find a non-recursive Fibonacci function. To my surprise this worked and I found a function.
The Nth Fibonacci value is (1 + sqrt(5))^N - (1 - sqrt(5))^N all over sqrt(5) * 2^N
Looking online I found that of course this same function was already well known. Mostly I was irritated that after all the algorithms we created for faster and faster Fibonacci functions we were never told about a constant time function like this.

I recently found my paper depicting this and thought it would be a good thing to use to try out MathML, a markup language for displaying math. I went to the MathML implementations page and installed a plugin for IE to display MathML and then began writing up my paper in MathML. I wrote the MathML by hand and must say that's not how its intended to be created. The language is very verbose and it took me a long time to get the page of equations transcribed.

MathML has presentation elements and content elements that can be used separately or together. I stuck to content elements and while it looked great in IE with my extension when I tried it in FireFox which has builtin MathML support it didn't render. As it turns out FireFox doesn't support MathML content elements. I had already finished creating this page by hand and wasn't about to switch to content elements. Also, in order to get IE to render a MathML document, the document needs directives at the top for specific IE extensions which is a pain. Thankfully, the W3C has a MathML cross platform stylesheet. You just include this XSL at the top of your XHTML page and it turns content elements into appropriate presentation elements, and inserts all the known IE extension goo required for you. So now my page can look lovely and all the ickiness to get it to render is contained in the W3C's XSL.

PermalinkCommentstechnical mathml fibonacci math

[whatwg] Web Applications 1.0 Draft

2008 Aug 20, 9:48Apple will or will not license the canvas tag? 'Apple Computer, Inc. ("Apple") believes it has intellectual property rights ("IP Rights") relative to WHATWG's Web Applications 1.0 Working Draft, dated March 24, 2005, Section 10.1, entitled "Graphics: The bitmap canvas". At this time, Apple reserves all rights in its IP Rights and makes no representations as to Apple's willingness or unwillingness to license these IP Rights. However, in the event that the Web Applications 1.0 Working Draft, dated March 24, 2005, becomes part of a formalized draft standard at W3C or IETF, for example, Apple is prepared to address the disclosure/licensing rules of such organizations.'PermalinkCommentsapple patent html ip html5 canvas whatwg browser browser-war

Braid Recommendation

2008 Aug 14, 9:38

Braid screen shot. By gamerscoreblogI recently finished Braid, the Xbox Live game, and a comparison with Portal is helpful. From a screen shot Braid looks like a normal 2D platformer, but that's like looking at a screen shot of Portal and saying its a first person shooter. While the scaffolding of the game-play may sort of fall into that category, the games are actually about exploring the character's ability and solving puzzles. In Portal the ability is bending space and in Braid its bending time. However, whereas in Portal there is one space bending mechanism, the portal gun, Braid's protagonist explores several different time bending techniques including, most prominently, reversing time, but also time dilation, multiple time-lines, and other odd things.

Similar to the difference in game-play, while Portal has a strict simplicity to its visual style, Braid is much more ornate, like you're playing in an oil painting. Without seeing video of the game, or playing the demo (which is available for free on Xbox Live) its difficult to convey, but it is quite lovely and the animation adds quite a bit. Both games too are rather short leaving you just a bit hungry for more and have an interesting plot and an ending that I'd hate to spoil although Braid replaces Portal's humor with melancholy. If you enjoyed Portal and Twelve Monkeys then I'd recommend Braid.

PermalinkCommentsbraid game videogame portal nontechnical

WERBLOG - Blog Archive - Response from Michael Powell on McCain's tech plan

2008 Aug 14, 5:04"Former FCC Chairman Michael Powell sent me this response to my criticism of John McCain's technology policies." Michael Powell helped draft McCains technology policy and is responding to Kevin Werbach who helped draft Obama's technology policy.PermalinkCommentsmccain technology policy politics michael-powell kevin-werbach

Early Creative Commons history, my version (Lessig Blog)

2008 Aug 14, 2:23Lawrence Lessig's video presentation on history of Creative Commons.PermalinkCommentslawrence-lessig lessig video legal law cc history copyright

Paris Hilton Responds to McCain Ad from Paris Hilton, Adam "Ghost Panther" McKay, and Chris Henchy

2008 Aug 6, 1:43"Paris Hilton Responds to McCain Ad An ad for The Paris Hilton Presidential Campaign. Paid for by Funny Or Die". Found this just after I saw the McCain Ad mocked on the Daily Show.PermalinkCommentsparis-hilton humor politics video mccain

New office, new cubes

2008 Aug 5, 6:32

Second Window OfficeNew Patent CubesMy previous window office was ripped from me when our team moved buildings but now I've got another. The photo is poor because I didn't get the lighting correct and it depicts the office before I've moved all my crap into it. I have a lovely view of our parking lot and freeway which Jane spun as an 'urban view'. At any rate I'm not complaining: I like knowing what its like outside and that there is an outside. The day after I found out about my office, I also got two new patent cubes. I didn't have any pictures last time so I took some now and blacked out their text for fear of laywers.

PermalinkCommentsmicrosoft patent cube office nontechnical

Dark Knight and Mariners Baseball

2008 Aug 4, 8:39

The weekend before last I saw Dark Knight with some friends from work and then we all ate at Z'Tejas after. Like everyone has said and as the name implies Dark Knight is... dark. Dark Knight was a little over the top at times as compared to Batman Begins but I really enjoyed it. Two times during the movie I thought it had ended but I was wrong. The Joker is both frightening (Cringe inducing line "Wanna know how I got these scars?") and humorous ("Where is Harvey Dent? ... You know where Harvey is? You know who he is?", as well as the pencil magic trick). I can certainly recommend it to anyone who enjoyed Batman Begins. The previews included Burn After Reading a new Coen Brother's comedy that I look forward to, and Quantum of Solace which hopefully does the same thing Dark Knight has, keep up the new direction on the refreshed franchise.

Safeco Field Suite photoThis past weekend Sarah and I went to a Mariners baseball game. I think this is the first MLB baseball game I've seen in person. Sarah's company gave out tickets for the game and the use of a suite. Its a room half way up the stadium with comfortable chairs, a mini-fridge built-in to the marble counter-topped center table, and a big flat screen television with the game on it. I suppose that's in case you don't want to turn to the right and sit at the window, or walk out onto the balcony which features three rows of comfy chairs overlooking the field. Anyway there was free food and drinks and I met some of the people Sarah works with.

PermalinkCommentsbaseball batman nontechnical

Reporters sans frontieres - Beijing Games 2008

2008 Jul 30, 10:45"Reporters Without Borders therefore offers the following practical advice to foreign journalists to help them cover the human rights situation in China." Install Tor, use PGP and other interesting things.PermalinkCommentscensorship china internet privacy olympics journalism

New Scientist Short Sharp Science Blog: What do your belongings say about you?

2008 Jul 22, 6:15Determine one's personality based on their home. Feels like pop science, fortune cookie results still fun though: "Sam Gosling, psychologist ... analysed photos from a handful of New Scientist readers to see what he could deduce about their personalitiesPermalinkCommentsscience psychology article personality

Kirkland Uncorked Weekend

2008 Jul 21, 10:36

Kirkland Uncorked posterSaturday we went to Kirkland Uncorked, a wine tasting festival near our home. We took the bus and after finding the correct one (they really should have different numbers for buses that are on the same route but traveling in different directions) made it to the festival. Unfortunately I don't remember any of the names of the wines just which ones I enjoyed by order. Recalling that I enjoyed the first one I had and the second to last one, doesn't really help me find them again. There were local artists who had setup booths and Sarah got a lovely necklace. After that we ate at Cactus which, because it was such a lovely day, had all its windows and doors open.

Sunday was quieter. A few household chores and plenty of GTA4. I almost got the One Man Army achievement but I found that after four minutes with six stars I eventually dropped back down to three stars without realizing it.

PermalinkCommentswine weekend nontechnical

Finished First Three Zelda Games

2008 Jul 17, 4:45
Screen shot from Legend of ZeldaScreen shot from Zelda II: The Adventures of LinkScreen shot from Legend of Zelda: A Link to the Past

I want to once again profess my love for the Wii's Virtual Console. Sarah and I recently finished playing through the first three Zelda games. Although I'd played a bit of the first two I never had a Nintendo as a kid and so unlike Sarah this was my first time completely playing through Zelda I & II. What people say about Zelda II is true... its all so true. And on the flip side I have fond memories of beating the third Zelda game which Sarah hadn't played.

In hilarious Zelda related news, a friend from work's husband posted the following blog post concerning their son named Link.

PermalinkCommentszelda link video-games nontechnical wii

Gametrailers.com - Xbox 360 - E3 2008: Exclusive Dashboard Walkthrough HD

2008 Jul 16, 8:05"Not just an update, but an entire overhaul is planned for the Xbox 360 Dashboard, and we get an in-depth look at the new features."PermalinkCommentsgame video xbox xbox-360 videogame

FORA.tv - Neal Stephenson: Science Fiction as a Literary Gen

2008 Jul 14, 4:37"Neal Stephenson delivered a talk entitled The Fork: Science Fiction versus Mundane Culture at Gresham College." Talk is sort of pop analysis of geeky entertainment. Lots of annecdotal evidence but interesting ideas anyway.PermalinkCommentsgeek history neal-stephenson scifi fiction literature culture video

Unbreakable Fighting Umbrella Splits Watermelons, Defends Presidents | Gadget Lab from Wired.com

2008 Jul 14, 2:15"The entourage of the Philippine president, Gloria Macapagal-Arroyo, has an unusual secret weapon. Her security team defends the head of the government with umbrellas. Not ordinary umbrellas, but unbreakable fighting umbrellas."PermalinkCommentshumor video weapon security umbrella

DoxPara Research

2008 Jul 14, 10:32Dan Kaminsky's blog.PermalinkCommentsdan-kaminsky blog security dns ip networking browser windows unix microsoft hack

YouTube - Resonantie

2008 Jul 12, 12:33Rice on a speaker makes interesting patterns based on the tone played. Like the cornstarch subwoofer video earlier.PermalinkCommentsrice video youtube sound science via:swannman

Crispin Porter + Bogusky

2008 Jul 11, 1:39The ad agency that Microsoft has a new deal with has done all of the interesting or weird ad campaigns I can think of: crazy BK commercials, f'd up Sprite commercials, the KNOW HIV dancing people... Of course their site is Flash.PermalinkCommentsad advertising business

Advertising: Microsoft Hires Too-Cool Ad Agency In Brilliant/ Dumb (?) Move

2008 Jul 11, 1:35Furious George comments: "Extensive focus group testing shows that having Seth Rogen present as a relatable everyman enhances positive feelings about the possibility of having sex with Megan Fox, and hence, using Windows."PermalinkCommentsad advertising microsoft

YouTube - Dancing Liquid

2008 Jul 11, 1:12Non-Newtonian liquid on a subwoofer displays creepy results. I need to try this sometime. This links to lots of other similar experiments.PermalinkCommentsvideo physics science youtube via:boingboing
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