eternal ramblings of an empty mind

Clocks

So I’m in Manhattan for the third time in three weeks. Could have (and probably should have) stayed here over the weekend, but hindsight is 20/20, and the weekend at home wasn’t a total waste of time.

For instance, I finally got Windows 7 installed on my netbook. I did this primarily so I could watch Netflix on a screen slightly larger than 4.8″ (though admittedly much smaller than the 42″ at home). 10.1″ is significantly easier on the eyes, however I’ve noticed that the performance of Silverlight leaves much to be desired. The audio and video have a tendency to get out of sync (the video is slow), and only occasionally will the video “catch up”—though not by a single jump, or a stop to buffer, but by skipping frames: the video appears to go 2–3× faster for a few seconds, then back to normal.

I’ve tried to get a few other things installed on here, but with Sourceforge down at the moment, I can’t get wxPython or py2exe. Besides, without access to the Cessna network, I don’t have the source code I need anyway. The VPN software on the other machine will do the job, and I’ll work with that tomorrow.

So my Kindle reappeared today. It’s quite possible I missed it, despite thinking I had turned the place upside down, but it’s here, undamaged, ready for reading, though I doubt I’ll be doing much of that.

I have the work laptop here. Let me tell you how convoluted something can get. I connect first to a WiFi network, through Citrix Receiver, to a terminal server either in Dallas or Providence, use that computer to start a remote desktop session with my work computer in Wichita. That’s bad enough (had to do that three times today to get various e-mails). If I didn’t happen to have the proper cable, I would have then used that machine to start a WebEx session with the computer in Manhattan, Kansas, a mere two feet from the starting point. Good thing we found a cable, because that would’ve been nuts. And all of that would stem from the fact that I can’t attach USB removable storage to this machine due to “security concerns”. Despite the fact that the higher capacity devices identify themselves as internal storage, and are thus exempt from the restriction. Totally ridiculous.

A couple of quick restaurant reviews—and I’ll note that some bits only apply to the particular location I visited, but:

• La Fiesta: I’ve been here once before, but for whatever reason didn’t order my standard choices at a Mexican place. Started with the queso something-or-other, to go with the chips, then ordered their enchilada sampler. The queso bowl was quite enormous, and would have served at least three quite well. The enchilada sampler contained five enchiladas. Five. Covered with enchilada sauce, piled high with shredded lettuce (covered with it, in fact), topped with shredded cheese and sour cream. I managed to get about half the plate eaten. But it was most delicious.
• Gambino’s Pizza: fairly established franchise, and I was looking for something just a little bit different from Pizza Hut or other “standard” fare, some place I hadn’t been before. Their buffet was priced the same as Pizza Hut, but their selection was severely lacking. Their table had room for 8 pizzas. One was their dessert pizza, one was their cheesy bread, five were sausage pizzas, and one was a “bacon cheeseburger” pizza. Seriously? And there were no more than 6 customers in the shop at any one time while I was there. Try a bit of variety, and put out some pepperoni, which seems to be the undisputed most popular pizza topping in the country.
• Noodles & Company: I had never visited one of these before tonight. Overall, I was quite pleased. The side Caesar salad was small, but to my mind had the right crouton-to-romaine ratio. Besides, my pasta was ready before I finished the small salad anyway. I ordered the Wisconson mac & cheese with Parmesan crusted chicken breast, and it was delicious. Much like last night’s dinner, I was unable to finish, as they served far more than I expected. I did notice that they charged slightly more tax than other restaurants in the area, however: 9.00% instead of the typical 8.55% in the city. Whether this needs to be investigated by someone who cares about their nickel more than I do, or if they got special dispensation by the city government for filling the spot in the new shopping center, I don’t know.

All I Want

This’ll be short. I think. My laptop is, frankly, minuscule, and has a distinct lack of power. If I was running Windows, I could do fancy things like watch Netflix or Hulu on a whopping 10″ screen, but instead I’m relegated to watching it all in TD (tiny definition) on my phone.

For those that are unaware, I’m in Manhattan, Kansas this week troubleshooting an issue on a vendor’s production line which is holding up deliveries. Things aren’t going well there, either.

Anyway, my phone’s battery was nearly drained, so I decided I’d get my Kindle and read some of the Mistborn trilogy (just started). However, it’s nowhere to be found. Either the hotel staff swiped it intentionally (seems strange to take that and leave the computer) or it got swept up with bedsheets or something (seems strange to change the sheets and leave the pillows on the floor, though). Whatever the case, I’ve searched the room, and it doesn’t seem to be here. If I can’t find it by the time I check out, and it hasn’t been turned in to the lost and found at the front desk, the hotel is liable (according to a clearly posted sign) for up to $250. But it’s the hassle that’s a bigger issue than the money. If I do have to get it replaced, it’ll be my third Kindle in 4 weeks—not a very impressive track record. Another thing Windows would allow me to do is connect to the network at Cessna, where I could be of use working on a different project. I should have grabbed the Cessna laptop from ICE, at least for the evening, but their evening shift has already gone home. And I’d be rid of these annoying messages about Flash being out of date. Adobe! Citrix! Netflix! Hulu! Get your acts together! I want to be able to use Linux on a netbook! You can’t expect me to install and run Windows inside VirtualBox on an Atom N450 processor with 1GB RAM, do you? In taberna quando sumus Carl Orff and the poetry from Carmina Burana will be at the forefront of my mind for the next few days. I am desperately seeking ways to reduce the activity in my dorsal anterior cingulate cortex (stress response center of the brain), and I’m aware that one method of doing so involves stimulation of the ventromedial prefrontal cortex. My one previous attempt at doing so produced the opposite effect, but I’ve not encountered the same antagonism this time around. The stimulus required for my experiment, however, is unavailable for at least couple of weeks given my anticipated schedule: • Tuesday (last): work, choir rehearsal, bed • Wednesday: work, choir rehearsal, bed • Thursday: work, choir rehearsal, bed • Friday: work, concert #1, greet parents, bed • Saturday: gardening, interior decoration, concert #2, bed • Sunday: see parents off, concert #3, pack • Monday: go to ICE Corporation in Manhattan, Kansas, troubleshoot (fix?) environmental test equipment • Tuesday: ditto • Wednesday: ditto, leave Manhattan for Olathe • Thursday: Thanksgiving dinner with the family (along with requisite traditions, e.g. watching the parade, football games, etc.) • Friday: visit any relatives I didn’t see the day before • Saturday: relax? Not likely. • Sunday: return to Manhattan… • Monday: more work in Manhattan • Tuesday: ditto • Wednesday: back to Wichita? Work on document here? • Thursday: work, work, more work, bed • Friday: work, RPG?, bed • Saturday: Can a guy catch a break? This is the first time I expect to have the slightest bit of free time (and be at home) over the course of the next three weeks. I love my family and all, but there’s nothing like doing nothing in the comfort of your own home. In an ideal world, the “document” I mentioned would be done already, I would be taking three days of vacation next week, spend a day, two at the most, in Manhattan, and clear my plate of the temp control project before the beginning of December. But it ain’t an ideal world. So I’ll retreat into a good book every chance I get between now and the end of the year in an effort to stay sane. Nothing against the authors of the short stories in Pump Six, but it’s nice to have a coherent storyline, thus my purchase of Elantris. See you in three weeks! Blister in the Sun Tomorrow is “The Election”. The media is rife with speculation. I suspect (and hope) that Americans are just as fed up with the campaigning as I am. I’m not saying things were pretty 212 years ago, I just wish that our country could have grown up a little since then. Instead of monarchy and King George, the comparisons are made to socialism and Adolf Hitler. Baseless or not, I really, really don’t want to see Republicans or Democrats in charge of this country. For that matter, the Libertarians, Greens, and Reforms have their share of loose screws. I know that no matter who I cast my vote for tomorrow, Kansas’ six electoral votes will be cast for Mitt Romney. I agree with Obama on some issues, I admit. I listen to NPR. But I am not a Democrat, and I am not a socialist. I have trouble saying I agree with Mitt Romney on anything, because he changed his mind half a dozen times since he spoke, on, well, just about everything, just about anytime. But I agree with certain positions that Republicans have traditionally held, yet I am not a Republican. Going off the beaten (and boring two-party) path, I agree with Gary Johnson on some issues. I don’t see him as quite the loon Ron Paul occasionally seems to be, but on certain issues he would be laughed out of town by a majority, if anyone paid attention to third parties. To be perfectly honest, I know almost nothing about Chuck Baldwin, the other candidate on the ballot. I know more after writing that sentence than I knew about him when he ran in 2008, but as he’s not even a national candidate, and has even endorsed another, the probability of his winning is far, far more remote than even Johnson’s. Nevertheless, I will vote tomorrow, for one of the four candidates. Plucking one tidbit of the above paragraph: “I listen to NPR.” If I mention that to many people, they automatically draw certain conclusions that have no basis in reason. I listen to four shows from National Public Radio on a regular basis: Car Talk, A Prairie Home Companion, This American Life, and Snap Judgement. And frankly, politics rarely enters into it. Car Talk is hilarious, and answers people’s honest questions about cars. Some calls could be fielded by untrained monkeys, but a fairly convincing argument could be made that that’s just what goes on for that “waste of another perfectly good hour”. While Garrison Keillor’s political position is well-known, A Prairie Home Companion has been running for 38 years on good music, radio drama, and small-town charm. A pot-shot at a Republican may be taken now and again, but it’s never nasty. Ira Glass is also known at least as a strong critic of Republicans, but his show, when it touches political issues, feature a refreshing balance, a view that things can be ugly no matter where your ideology takes you—but with the hopeful air that things don’t have to be that way. Glynn Washington is a dynamic host of the storytelling forum, Snap Judgement. While I have no idea what his politics are, it doesn’t matter. Politics never enters into it. The stories are amazing, told by amazing individuals, who can transport you to amazing places. This is not the news, but this is NPR. I get my news from BBC. While they are legally required to be objective in their reporting, an entirely infeasible, but laudable goal, they do at least provide a perspective rarely seen in the US: that America is not the only place on Earth that matters. They see how preposterous campaign season is here, but only report on it once in a while, devoting more bytes to cricket and football matches than to matters of US Politics. The point that I sat down to write about, yes! Whatever my politics are, whatever fuzzy category they fall under, if it even has a label, I have been reluctant to share my point of view with anyone, afraid that, not only I would be alone in my viewpoint, but that others would spend the remainder of their resources in an attempt to convince me of the error of my ways. Thanks to a piece presented by one of those NPR shows, I learned about people who have been disowned by their family because of who they voted for, but also, about the fact that such conversations have strengthened some relationships (more here). It included a plug for what seems to be a very reasonable book, You’re Not as Crazy as I Thought (But You’re Still Wrong), how to have civil discourse about politics without the conversation devolving into a shouting match or the silent treatment. Anyway, while I may still shy away from heated discussions, and am unlikely to bring up issues of political import, so long as the atmosphere remains civil, I am willing to share my opinions. I’ll try not to dodge “the” question next time it’s put to me as I have in the past, whatever that question may be. If you catch me, you’re welcome to call me on it. Hmm…I need to read Calvin & Hobbes more often… Four-Fifty-One With the Kindle/Kindle app(s), I have absurd quantities of books at my fingertips. And, since my wiki doesn’t work without regular restarts of the server (I’ll nail down that problem eventually, I’m sure), I’m putting the list here. The ones in italics I already own, and are therefore (mostly) at the top of my list. Those struck through I’ve finished. The precise order is also very much subject to change, but I wanted to get it down so I don’t forget any of these books. This is not to discount anything by Terry Pratchett: I would simply rather have all Discworld books in dead tree form, to make lending their awesomeness to others a much simpler prospect. I have an asterisk by Warbreaker. I “own” it, in that I have downloaded the PDF and sent it to my Kindle. However, the PDF text is tiny. I made a half-hearted attempt to convert the HTML to a Kindle ebook, and realized that, with 58 chapters, formatting would be a bear. So I gave up. I’d rather support an incredible author and get the book that someone else has done the work. But! I have a bunch of books to read first. • Glamour in Glass (Mary Robinette Kowal) • Shades of Milk and Honey (Mary Robinette Kowal) • The Hollow City (Dan Wells) • Pump Six and Other Stories (Paolo Bacigalupi) • Magic for Beginners (Kelly Link) • Old Man’s War (John Scalzi) • Pirate Cinema (Cory Doctorow) • The Secret World Chronicles: Invasion (Mercedes Lackey) • Zoo City (Lauren Beukes) • Signal to Noise (Neil Gaiman & Dave McKean) • Save Yourself, Mammal! (Zach Weiner) • The Most Dangerous Game (Zach Weiner) • Attack of the Bacon Robots (Jerry Holkins & Mike Krahulik) • Epic Legends of the Magic Sword Kings (Jerry Holkins & Mike Krahulik) • xkcd: volume 0 (Randall Munroe) • Warbreaker (Brandon Sanderson)* • Space Eldritch (Howard Tayler &c.) • Gone Girl (Gillian Flynn) • Sharp Objects (Gillian Flynn) • Dark Places (Gillian Flynn) • Elantris (Brandon Sanderson) • Elantris: The Emperor’s Soul (Brandon Sanderson) • Mistborn: The Final Empire (Brandon Sanderson) • Mistborn: The Well of Ascension (Brandon Sanderson) • Mistborn: The Hero of Ages (Brandon Sanderson) • Mistborn: The Alloy of Law (Brandon Sanderson) • Alcatraz Versus the Evil Librarians (Brandon Sanderson) • Alcatraz Versus the Scrivener’s Bones (Brandon Sanderson) • Alcatraz Versus the Knights of Crystallia (Brandon Sanderson) • Alcatraz Versus the Shattered Lens (Brandon Sanderson) • Infinity Blade (Brandon Sanderson) • I Am Not a Serial Killer (Dan Wells) • Mr. Monster (Dan Wells) • I Don’t Want to Kill You (Dan Wells) • Partials (Dan Wells) • Fragments (Dan Wells) • A Night of Blacker Darkness (Dan Wells) • Ringworld (Larry Niven) • The Ringworld Engineers (Larry Niven) • The Ringworld Throne (Larry Niven) • Ringworld’s Children (Larry Niven) • Sundiver (David Brin) • Startide Rising (David Brin) • The Uplift War (David Brin) • Brightness Reef (David Brin) • Infinity’s Shore (David Brin) • Heaven’s Reach (David Brin) • Prelude to Foundation (Isaac Asimov) • Forward the Foundation (Isaac Asimov) • Foundation (Isaac Asimov) • Foundation and Empire (Isaac Asimov) • Second Foundation (Isaac Asimov) • Foundation’s Edge (Isaac Asimov) • Foundation and Earth (Isaac Asimov) • Foundation’s Triumph (David Brin) • I, Robot (Isaac Asimov) • The Rest of the Robots (Isaac Asimov) • The Complete Robot (Isaac Asimov) • Robot Dreams (Isaac Asimov) • Robot Visions (Isaac Asimov) • The Positronic Man (Isaac Asimov) • The Caves of Steel (Isaac Asimov) • The Naked Sun (Isaac Asimov) • The Robots of Dawn (Isaac Asimov) • Robots and Empire (Isaac Asimov) • Caliban (Roger MacBride Allen) • Inferno (Roger MacBride Allen) • Utopia (Roger MacBride Allen) • The Stars, Like Dust (Isaac Asimov) • The Currents of Space (Isaac Asimov) • Pebble in the Sky (Isaac Asimov) • Existence (David Brin) • Redshirts: A Novel with Three Codas (John Scalzi) • Player Piano (Kurt Vonnegut) • The Sirens of Titan (Kurt Vonnegut) • Mother Night (Kurt Vonnegut) • Cat’s Cradle (Kurt Vonnegut) • God Bless You, Mr. Rosewater, or Pearls Before Swine (Kurt Vonnegut) • Slapstick, or Lonesome No More! (Kurt Vonnegut) • Jailbird (Kurt Vonnegut) • Deadeye Dick (Kurt Vonnegut) • Galápagos: A Novel (Kurt Vonnegut) • Bluebeard, the Autobiography of Rabo Karabekian (1916-1988) (Kurt Vonnegut) • Hocus Pocus (Kurt Vonnegut) • Timequake (Kurt Vonnegut) • VALIS (Philip K. Dick) • The Divine Invasion (Philip K. Dick) • The Transmigration of Timothy Archer (Philip K. Dick) • Solar Lottery (Philip K. Dick) • The Cosmic Puppets (Philip K. Dick) • The World Jones Made (Philip K. Dick) • Eye In The Sky (Philip K. Dick) • The Man Who Japed (Philip K. Dick) • Time Out of Joint (Philip K. Dick) • Confessions of a Crap Artist (Philip K. Dick) • The Man in the High Castle (Philip K. Dick) • We Can Build You (Philip K. Dick) • Martian Time Slip (Philip K. Dick) • Dr. Bloodmoney (Philip K. Dick) • The Simulacra (Philip K. Dick) • The Three Stigmata of Palmer Eldritch (Philip K. Dick) • The Zap Gun (Philip K. Dick) • Now Wait For Last Year (Philip K. Dick) • Counter-Clock World (Philip K. Dick) • Ubik (Philip K. Dick) • Galactic Pot-Healer (Philip K. Dick) • A Maze of Death (Philip K. Dick) • Our Friends from Frolix 8 (Philip K. Dick) • Flow My Tears, the Policeman Said (Philip K. Dick) • Radio Free Albemuth (Philip K. Dick) • The Divine Invasion (Philip K. Dick) • Catch-22 (Joseph Heller) • The Catcher in the Rye (J.D. Salinger) • Harry Potter and the Philosopher’s Stone (J.K. Rowling) • Harry Potter and the Chamber of Secrets (J.K. Rowling) • Harry Potter and the Prisoner of Azkaban (J.K. Rowling) • Harry Potter and the Goblet of Fire (J.K. Rowling) • Harry Potter and the Order of the Phoenix (J.K. Rowling) • Harry Potter and the Half-Blood Prince (J.K. Rowling) • Harry Potter and the Deathly Hallows (J.K. Rowling) • Tears in Rain (Rosa Montero) • Consider Phlebas (Iain M. Banks) • The Player of Games (Iain M. Banks) • Use of Weapons (Iain M. Banks) • Excession (Iain M. Banks) • Inversions (Iain M. Banks) • Look to Windward (Iain M. Banks) • Matter (Iain M. Banks) • Surface Detail (Iain M. Banks) • The Hydrogen Sonata (Iain M. Banks) I know there are books missing, but my website is now totally MIA. Good Times The BBC has done it again. Sherlock is the best modern day Sherlock Holmes story, Benedict Cumberbatch the best Holmes since Jeremy Brett. Affectations, mannerisms, they’re “spot on.” I would very much suspect that the greatest consulting detective of all time would do much the same as this one, given today’s technology. I’ve only seen “A Study In Pink” and “The Blind Banker” so far, and while they’ve done the sensational stories first, I hope they delve deeper into development of the characters as the series progresses. It’s been too long since I’ve read the books, but I recognized so much of these episodes, and they remind me of “A Study In Scarlet” (obviously), “The Sign of the Four”, and “The Five Orange Pips” along with a hint of “The Adventure of the Dancing Men”. Had her name been Mary Morstan…but perhaps she’ll show up later. The discrete Fourier transform. Simple enough, sure: $\mathcal{F}_n=\sum_{k=0}^{N-1}{f_ke^{-2\pi ink/N}}$ I have no problems with this. Or the conversion to a matrix formula: $\mathcal{F}_n=\begin{bmatrix}f_0 & f_1 & \cdots & f_{N-1}\end{bmatrix}\begin{bmatrix}W^{(0)(0)} & W^{(1)(0)} & \cdots & W^{(N-1)(0)} \\ W^{(0)(1)} & W^{(1)(1)} & \cdots & W^{(N-1)(1)} \\ \vdots & \vdots & \ddots & \vdots \\ W^{(0)(0)} & W^{(1)(N-1)} & \cdots & W^{(N-1)(N-1)}\end{bmatrix}$ where $W=e^{-2\pi in/N}$ (so $W^N=1$, these are roots of unity or de Moivre numbers). Eventually I found the Danielson-Lanczos lemma, which gives $\mathcal{F}_n=\sum_{k=0}^{N-1}{f_ke^{-2\pi ink/N}}$ $=\sum_{k=0}^{N/2-1}{e^{-2\pi ikn/(N/2)}f_{2k}}+W^n\sum{k=0}^{N/2-1}{e^{-2\pi ikn/(N/2)}f_{2k+1}}$ $=\mathcal{F}_n^e+W^n\mathcal{F}_n^o$ This is all fine and good. Then it comes to working the FFT, using the Danielson-Lanczos lemma and the Cooley-Tukey algorithm, I’m suddenly stumped. Not the mechanics, but the programming bit. I know I’ve done this successfully before, certainly in college and at least once since then—I had a Python script that used this, first to compute DFTs, then to multiply numbers. Obviously unnecessary with Python supporting arbitrary precision arithmetic built in, but the purpose was (and is) to bolster my own understanding of one of the principles behind APM. So, University at Buffalo to the rescue. Found some C++ code that gave me what I needed. So here’s (hopefully) a more-or-less plain English version of the method (with an example): Given a vector (we’ll start small, a size of 8) $f=\begin{bmatrix}7 & 3 & 9 & 1 & 3 & 7 & 3 & 5\end{bmatrix}$. If the number of elements in the vector is even, split the odd and even parts of the vector into separate vectors (so I cheated and chose a nice number. But the method doesn’t help if the above isn’t true). We’ll call those $f_o$ and $f_e$, respectively: $f_o=\begin{bmatrix}3 & 1 & 7 & 5\end{bmatrix}$ $f_e=\begin{bmatrix}7 & 9 & 3 & 3\end{bmatrix}$ These are still divisible by two, so repeat: $f_{oo}=\begin{bmatrix}1 & 5\end{bmatrix}$ $f_{oe}=\begin{bmatrix}3 & 7\end{bmatrix}$ $f_{eo}=\begin{bmatrix}9 & 3\end{bmatrix}$ $f_{ee}=\begin{bmatrix}7 & 3\end{bmatrix}$ Still even! $f_{ooo}=\begin{bmatrix}5\end{bmatrix}$ $f_{ooe}=\begin{bmatrix}1\end{bmatrix}$ $f_{oeo}=\begin{bmatrix}7\end{bmatrix}$ $f_{oee}=\begin{bmatrix}3\end{bmatrix}$ $f_{eoo}=\begin{bmatrix}3\end{bmatrix}$ $f_{eoe}=\begin{bmatrix}9\end{bmatrix}$ $f_{eeo}=\begin{bmatrix}3\end{bmatrix}$ $f_{eee}=\begin{bmatrix}7\end{bmatrix}$ Now the size of these vectors is odd, so the only choice is to do a regular discrete transform. But this turns out to be nice and simple. Using superscripts to denote which of the above vectors I’m refering to, since $\mathcal{F}^{ooo}=\sum_{k=0}^{N-1}{f_ke^{-2\pi ink/N}}$ we can plug in each of the above into this formula: $\mathcal{F}^{ooo}=\sum_{k=0}^{0}{f_0e^{-2\pi i\times 0 \times k/1}}$ which nicely reduces to $\mathcal{F}^{ooo}=f_0$ But this is only the discrete transform of the one-element vector—these need to be recombined to get the DFT of the entire thing. So if you reduce the vectors to size 1, the DFT of that is trivial. Then we need to combine them. So let’s start that combination one level higher, with the two-element vectors. $f_{oo}=\begin{bmatrix}1 & 5\end{bmatrix}$ From the Danielson-Lanczos lemma, $\mathcal{F}_n^{oo}=\mathcal{F}_{n\mod(N/2)}^{ooe}+W^n\mathcal{F}_{n\mod(N/2)}^{ooo}$ Therefore, $\mathcal{F}_0^{oo}=\mathcal{F}_0^{ooe}+W^0\mathcal{F}_0^{ooo}$ $\mathcal{F}_1^{oo}=\mathcal{F}_0^{ooe}+W^1\mathcal{F}_0^{ooo}$ In this case, $W=e^{-2\pi i/2}=e^{-\pi i}=-1$, so $\mathcal{F}^{oo}=\begin{bmatrix}1+5 & 1-5\end{bmatrix}=\begin{bmatrix}6 & -4\end{bmatrix}$ So for a two-element vector, $\mathcal{F}=\begin{bmatrix}\mathcal{F}^{e}+\mathcal{F}^{o} & \mathcal{F}^{e}-\mathcal{F}^{o}\end{bmatrix}$ “Solving” the others in a similar manner, we get $\mathcal{F}^{oo}=\begin{bmatrix}6 & -4\end{bmatrix}$ $\mathcal{F}^{oe}=\begin{bmatrix}10 & -4\end{bmatrix}$ $\mathcal{F}^{eo}=\begin{bmatrix}12 & 6\end{bmatrix}$ $\mathcal{F}^{ee}=\begin{bmatrix}10 & 4\end{bmatrix}$ Of course, each step gets a bit more difficult. Thanks to the DLL, we know $\mathcal{F}_n^{o}=\mathcal{F}_{n\mod(N/2)}^{oe}+W^n\mathcal{F}_{n\mod(N/2)}^{oo}$ so let’s take it one step at a time. First, $W=e^{-2\pi i/4}=-i$ So $\mathcal{F}_0^{o}=\mathcal{F}_0^{oe}+W^0\mathcal{F}_0^{oo}$ $=10+6=16$ $\mathcal{F}_1^{o}=\mathcal{F}_1^{oe}+W^1\mathcal{F}_1^{oo}$ $=-4+-i\times -4=-4+4i$ $\mathcal{F}_2^{o}=\mathcal{F}_0^{oe}+W^2\mathcal{F}_0^{oo}$ $=10+-1\times 6=4$ $\mathcal{F}_3^{o}=\mathcal{F}_1^{oe}+W^3\mathcal{F}_1^{oo}$ $=-4+i\times -4=-4-4i$ Therefore, $\mathcal{F}^{o}=\begin{bmatrix}16 & -4+4i & 4 & -4-4i\end{bmatrix}$ Do the same thing to find $\mathcal{F}^{e}$: $\mathcal{F}^{e}=\begin{bmatrix}22 & 4-6i & -2 & 4+6i\end{bmatrix}$ Putting it all together, $W=e^{-2\pi i/8}={{1}\over{\sqrt{2}}}(1-i)$ $\mathcal{F}_n=\mathcal{F}_{n\mod(N/4)}^{e}+W^n\mathcal{F}_{n\mod(N/4)}^{o}$ $\mathcal{F}_0=\mathcal{F}_0^e+W^0\mathcal{F}_0^o$ $=22+1\times 16=38$ $\mathcal{F}_1=\mathcal{F}_1^e+W^1\mathcal{F}_1^o$ $=(-4+4i)+{{1}\over{\sqrt{2}}}(1-i)(4-6i)=(-4-\sqrt{2})+(4-5\sqrt{2})i$ $\mathcal{F}_2=\mathcal{F}_2^e+W^2\mathcal{F}_2^o$ $=-2+-i\times4=-2-4i$ $\mathcal{F}_3=\mathcal{F}_3^e+W^3\mathcal{F}_3^o$ $=(-4-4i)+{{1}\over{\sqrt{2}}}(-1-i)(4+6i)=(-4+\sqrt{2})+(-4-5\sqrt{2})i$ $\mathcal{F}_4=\mathcal{F}_0^e+W^4\mathcal{F}_0^o$ $=22+-1\times 16=6$ $\mathcal{F}_5=\mathcal{F}_1^e+W^5\mathcal{F}_1^o$ $=(-4+4i)+{{1}\over{\sqrt{2}}}(-1+i)(4-6i)=(-4+\sqrt{2})+(4+5\sqrt{2})i$ $\mathcal{F}_6=\mathcal{F}_2^e+W^6\mathcal{F}_2^o$ $=-2+i\times4=-2+4i$ $\mathcal{F}_7=\mathcal{F}_3^e+W^7\mathcal{F}_3^o$ $=(-4-4i)+{{1}\over{\sqrt{2}}}(1+i)(4+6i)=(-4-\sqrt{2})+(-4+5\sqrt{2})i$ Thus $\mathcal{F}=\begin{bmatrix}38 & (-4-\sqrt{2})+(4-5\sqrt{2})i & -2-4i & (-4+\sqrt{2})+(-4-5\sqrt{2})i & 6 & (-4+\sqrt{2})+(4+5\sqrt{2})i & -2+4i & (-4-\sqrt{2})+(-4+5\sqrt{2})i\end{bmatrix}$ Seems like a lot of work, I know. But here’s the thing: normally, using the straight definition, you’d be doing 64 multiplications, 64 sums, and 64 exponentiations ($O(N^2$). We did 24 of each ($O(N\log_2{N})$. And that’s without using a trick: if all $f_k$ are real, $\mathcal{F}_{N-n}=\overline{\mathcal{F}_{n}}$ Yes, it’s still a lot of work, but as the vectors get longer, these savings adds up fast: Vector Size Naive Operations FFT operations 1 1 0 2 4 2 4 16 8 8 64 24 16 256 64 32 1024 160 And once you put it in a computer program (like the following listing), massive data sets become easy to analyze. Contact The Mandelbrot set. Computer visualizations are often beautiful. The deceptively simple equation that produces these gorgeous images, $z_{n+1}=z_n^2+c$, winds up taxing standard calculations rather quickly. A double-precision float has a precision of just 4.44089209850062616169452667236328125e-16. That may sound like a small number, but it isn’t nearly small enough. Utilizing the GMP Bignum Library, it’s dead simple to get resolutions of approx. 1e-53. And this is as deep as Fractint ever went, so far as I could tell, and also appears to be the limitation of most free Mandelbrot programs. Obviously, this frustrates me. I’d like to be able to keep going, and going, and going… But in creating a dynamic, browseable Mandelbrot visualization, concern number one is raw speed. And the only way I know how to present an image is pixel-by-pixel, whether it’s by generating a bitmap or plotting on an SDL canvas. Neither of these are particularly fast. As a matter of fact, they’re both slower than molasses in midwinter (for a computer program, anyway). Is there a quicker way? Because I’d love to know what that method is… Wednesday, I spent$263.90. $20.71 of that was tax (I am aware that the number doesn’t come out to 7.3%: gasoline has a state tax rate of 43.4¢/gallon, or 13.5% at today’s price). Anyway,$138.42 of that was for the ability to post this. My Terayon TJ715x cable modem was dead. The company, as it turns out, hasn’t existed for more than 5 years. Anyway, this new modem is DOCSIS 3.0 (finally). How much this affects my speed I’m not entirely sure, because although my theoretical (downstream) limit is apparently 304Mbps, I pay for 22Mbps, and get 20 according to Speedtest.net. And if I base my analysis on theory, DOCSIS 3.0 should therefore have no effect unless I bump my service to the “Ultimate” package. I find it suspicious that, when I test my speed using the tools on my ISP’s website, the results it gives are slightly better than what they claim I should be getting, yet somehow significantly different than the aforementioned “independent” website. I also wonder if such testing websites/servers are “whitelisted” by the ISP somehow, so traffic to those IP addresses is not filtered, logged, or throttled, to give the impression of better speed. All in all, I wonder if my DOCSIS 3.0 modem is more gadgetry for the sake of the latest and greatest rather than practicality. There’s another downside: my Cisco/Linksys/DD-WRT router is currently useless, as the cable modem is also a router. But because it’s Netgear, and so new or so specialized that even they don’t have the product listed on their website, I can’t install DD-WRT. So I can’t (as far as I know) change the router administrator username, and the associated password is restricted to a paltry 15 characters (with a default of “password”—I changed that one in a hurry).

Another $53.64 of my hard-earned money went to an over-the-air TV antenna. I pick up a whopping 16 channels, and I hope that the$20 premium I spent on the “better” antenna was worth it, if I ditch cable as I intend. The other obstacle to doing so, even though I now have an Internet-connected Blu-Ray player, is the lack of certain channels and shows. The entire Discovery network is unavailable through that device. No A&E networks. No documentaries to discover by chance, like the backstory to the upcoming movie Argo that was on the Military channel earlier this evening. How much, then, does Hulu Plus actually give me over Netflix Streaming? Since Discovery Networks will only let me watch their shows on my computer until they are released on DVD, A&E apparently won’t even let me watch them there unless/until the DVD release. Hulu Plus gives me the option of watching some TV shows the day after they air. Is it worth $7.99 a month? Will Netflix be worth$7.99 a month to me? I’m still undecided on both those issues. I have 5 more days of Hulu Plus for free, and 28 more days of Netflix Streaming for free. But if I dump cable, \$85.98 of that bill goes away each month, and it’s then unlikely that I’ll miss the happenstance documentaries that make The Science Channel and The History Channel so unbelievably addicting, because the temptation won’t be there.

I do find it somewhat interesting the omissions from Hulu Plus, iTunes, and Netflix: Castle Season 1 (Hulu Plus), Top Gear Series 1 (Netflix), and Top Gear Series 5 (iTunes). All rather good, and available on one or more of the other services. But iTunes would require hooking up a computer to the television, which means VGA or HDMI, rather than the more convenient DVI.

Which brings me to my next point: I need to run two network cables (and therefore network jacks) to my front room, right where the entertainment center currently sits, one for the Blu-Ray player and one for a computer to be added at some unspecified future date. My low-voltage wiring in this house is…rather strange, because I did it myself, I had little time to think about where the furniture was going to end up, and subsequently a few outlets for low voltage are rather out of place. And one standard voltage dual outlet is on the wrong wall in one room, causing some cable confusion. My last order to Monoprice should have included the keystone plate and jacks, but I was too shortsighted to add that to my shopping cart. Then again, I don’t even have the CAT-6 cable, so it wouldn’t have done much good unless I bought that as well.

For some reason this seems rather more rambly than usual, and yet I’m sticking to a single topic longer than usual. Odd…

Games Without Frontiers

Enough about that. A zillion things I want to say…

So I’ve been thinking about getting a dog. I am aware of the vast implications, and consequences, of doing so, but there are great benefits as well. The first and foremost in my mind is the psychological benefit to myself: a companion, someone who I can talk to, play with, spend a lazy day on the couch, run around outside, etc. There’s the benefit of the requirement of walks (or runs) around the neighborhood—exercise for both of us, which results in a healthier me, and possibly/probably a requirement that I get up earlier in the day to take him/her out. Another beneficial side effect is the fact that I’d have to keep the house with a…better balance of chaos and order. The entropic function working in my house needs some modification. The downsides are the vet bills, the food, the invisible fence (I am, and probably forever will be, very much against the visible kind), and deciding exactly what to do with the dog while I’m at work, or out with friends, or in any situation I can’t bring him/her along. All I know for sure is, if I do get a dog, it’ll be through adoption.

I have begun listening to StarTalk, hosted by celebrity astrophysicist Neil deGrasse Tyson. He interviewed Bill Maher roughly a year ago (from clues I pick up in the broadcast) and the question of the supposed incompatibility of science and religion (specifically Christianity) came up, as such a thing inevitably must when discussing, well, anything, with Bill Maher. I bring all this up because I want to discuss his, and others, vehement atheism. He acknowledges that there are scientists, from 40% in the general community (according to a survey) and 7% in the National Academy of Sciences (or something like that) who pray to a personal god, yet, regardless of their status, renown, or contributions, dismisses them as somehow substandard intellectuals. He, and a few others, seem to want to force a war between science and religion, and longs for a world devoid of any notion of gods, except perhaps in an anthropological or historical context, some “passing fancy” the human race once had.

I was raised in a Christian home. I was taught, at home, at the Christian schools I attended, and at church, that Earth, the solar system, the galaxy, the universe, was 6,000 years old (created 22 October 4004 BC according to James Ussher, or 5773 years ago last week according to Jewish reckoning). I maintained that belief through most of my academic career, then came the “evil”, “liberal”, “secular” university where I came to the realization that science doesn’t work like that. It doesn’t take much to reconcile the age of the universe as 13.7e9 years old, halfway through it’s existence to the best of our knowledge, with Christianity, with Genesis 1. I wonder if these atheists recognize their own zealotry, the hypocrisy almost inherent in their devotion to a belief in the lack of a higher power. I pick on Maher because he’s the latest to remind me of it. Christopher Hitchens, Richard Dawkins, and Bertrand Russell are probably the most prominent advocates of irreligion.

I could go on and discuss things like Christian atheism (yes, it’s a thing), but I’ll leave with one more thought: I see devout atheism as illogical as they perceive any theism. Agnosticism is as far as I see logic taking a person. It takes a leap of faith to make the move to atheism.

One more topic of discussion for me today, brought about by an e-mail exchange. This exchange prompted some, let’s call it soul-searching. I find my opinions and viewpoints diverging significantly from those in my primary social circles. You can claim I was influenced by that secular university (possibly one of the most conservative state universities around), or by the liberal media (careful of those commies at the BBC!), or whatever environmental influences you wish to blame it on, but I think I might have arrived at these same conclusions if left to my own devices. It probably just would have taken me longer. But the philosophical and sociological point I’m bringing up is the exchange of ideas with those closest to me. While I enjoy debate (do not confuse debate with conflict—that I abhor), I shy away from it. Some of my viewpoints may shock my family or close friends. Some may agree with me, but are themselves too timid to speak up. But if I don’t say anything, why should I expect anyone else to do so? Granted, many of the debates on which I hold an opinion, however strongly, seem so heated by the time I might interject that I decide it a far wiser choice to remain silent, lest I draw the ire of all participants. No discussion of import (or, just as often, insignificance) seems to be about rational challenging of one another’s opinions. Whether the subject is comic books or theology or science or gaming, even if I’m called as an “expert witness” (this is not the expert you’re looking for), I prefer to distance myself. That’s not debate, that’s one-upmanship, “I’m right, you’re wrong”, “Go away or I shall replace you with a very small shell script” noise, and it’s ugly. But that is the nature of the beast. I heard Denver described as a “‘Pale Blue Dot‘ in the middle of a red state”. Well, I’m a paler purple dot in the middle of a very, very red state. Neither Republican nor Democrat, with views that I won’t specify here that would gain criticism from the Republicans surrounding me, yet I’d be shunned from the Democratic party for other views. I’ll likely be “throwing my vote away” again this year—but think of it: if people would “throw [their] vote away” on a third party candidate, one might actually get elected! The two-party mindset is so deeply ingrained in our culture, another disturbing thing to think about. But I’ve wandered far off topic. I need rational discussion. I need a sounding board. Finding willing partners for such discourse is proving imminently difficult.

And with that, I sign off. CM10 with (working) Google Wallet, here I come (I hope).

Words

“Political Correctness” is all about going too far, I know. But this is just ridiculous. From the folks at Language Log, the potentially offensive phrases mentioned in the original article (“hold down the fort”, “rule of thumb”, “going Dutch”, “handicap”) are not offensive at all. “Hold [down] the fort”, cited as being offensive to Native Americans, was apparently used by Sherman speaking of defending a fort against the French, not the Native Americans. It’s also used regarding defense against cattle rustlers, train robbers, horse thieves, and others, but no mention of “savage Indians” anywhere. “Rule of thumb” has nothing to do with wife beating. Twice in the 19th century such a principle was acknowledged, but the judges ruling on the case gave no citation for it (and summarily ruled against the abusers anyway). And this was certainly not the origin of the phrase. “Going Dutch” doesn’t imply that the people of the Netherlands are cheap, but possibly refers to a Dutch-style door, or Dutch culture (where it is often appropriate to pay separately). “Handicap”, however, has nothing to do with begging, rather a game of chance, gambling.

Here’s an interesting tidbit, though: when it comes to the use of the words “chord” and “cord”, everyone is wrong!

More interesting artifacts of a bygone age: what is the icon you click on in most applications to save a file? A floppy disk. Who uses those anymore? What do you click to send or receive e-mail? An envelope, again, rarely used. What do you look for on your smartphone when looking to call someone? An “antique” handset. Oh, and “Wi-Fi” was a brand name, and has nothing to do with “hi-fi” (high fidelity/wireless fidelity—there’s no indication of quality in IEEE 802.11)

Now, some tips on grammar, Microsoft Word, and Windows-based input in general. Hyphenation. It’s a trickier thing than you may realize. Most people use the “-” key on their keyboard, not realizing its implications. It was and is called the “hyphen-minus”, carrying the dual meaning throughout the days of the 7-bit US-ASCII character set, and even the 8-bit ISO-8859-1 character set (not to be confused with ISO/IEC 8859-1:1998 or Windows codepage 1252). That’s all well and good, but Unicode has been around since 1988, and supported by the world’s dominant operating systems (Windows) since Windows 95 (remember “unicows.dll”?). Because of this, we have better methods for character separation. Many will say they can’t spot the difference between -, ‐, −, —, –, and ‑, or the sometimes invisible ­ (yes, there is something in there). I can, and do, notice the difference most of the time, though the one between ‐, ­, and ‑ is impossible to spot unless it occurs at an obvious location.

Proper usage, in my estimation (I am only an amateur grammarian):

First, terminology: the hyphen-minus, U+002D (I’ll cover character entry in a bit). The hyphen, U+2010. The minus sign, U+2212. The em-dash, U+2014. The en-dash, U+2013. The figure dash, U+2012. The soft hyphen, U+00AD.

Basic character entry: for small numbers (less than 256) and in Windows, characters can be entered by holding the “Alt” key and entering the number “0” followed by the character number being entered. For instance, what I list above as U+002D is Unicode (hexadecimal) code point 2D, which translates to the decimal number 45. Thus this can be entered by holding “Alt” while entering the digits “045” sequentially on the number pad (not the row of numbers above the normal keyboard letters), then releasing “Alt”. Likewise, U+00AD can be entered with Alt+0173 (this latter notation is fairly standard for discussing entry of these characters). The leading zero is important. If left out, you may wind up with an unexpected character, but there’s a time and place for these as well (they’re codepage-specific; perhaps I’ll cover that some other time).

Some additional warnings: Microsoft Word will often change the font on you when entering specific characters. I’ve seen it switch from the default Cambria (version 2007) to Cambria Math or MS Mincho, depending on the character. Sometimes this is required, but that is often not the case, as Cambria and Calibri (the fonts that ship with Office 2007) handle most of the code points used in western typography. Some applications will hijack the last entry method explained, and ignore what it’s supposed to mean.

Back to usage:

Use a hyphen or hyphen-minus to join words to form a compound (where that compound is not in common usage), or to eliminate ambiguity, say between recreation and re-creation, or between a man-eating shark and a man (who is) eating shark. When adding a prefix to a proper noun, insert a hyphen (un-American). There are other rules, but these are the most common. When to use which is discussed below.

Use a soft hyphen when a word (especially a long word) can be broken at a specific point within, but for one reason or another, line breaks at word boundaries in the surrounding text would be awkward.

Use a hard-hyphen or non-breaking hyphen when a hyphen is necessary, but the possibility of a break across lines is undesirable. In business, at least mine, this is often an issue with part numbers. When called out in a report, occasionally the part number will break at a hyphen-minus, and I admonish report authors to use the non-breaking version to avoid the break.

Use a minus sign when discussing subtraction. On a related topic, use the multiplication sign (U+00D7), interpunct/middle dot (U+00B7), or dot operator (U+22C5) when discussing multiplication, rather than the asterisk (U+002A) or letters “X” (U+0058) or “x” (U+0078).

Use a figure dash when using a dash as a separator between groups of numbers, yet not when indicating a range or subtraction. For instance, the US Phone number, 555‒1212. This would also be an appropriate substitute for my company’s part numbers (as they are all digits).

Use an en-dash when discussing ranges of values, whatever they may be (numbers, dates, times, page numbers, etc.). Examples: “Jimmy Carter was President from January 1977–January 1981.” “Product designed for ages 3–5.” “For your assignment, read pages 16–38.” “The program lasts from 7:30 pm–10:00 pm.” It should not be used as a contraction in ranges of SI units, in place of “to” or “and” in constructions such as “between 17 V and 28 V”, so as to avoid any possibility of confusion with subtraction. Another use of this is to denote a relationship between objects or names. “The Supreme Court voted 5–4…” “The Shays–Meehan bill…” “Kansas City Royals 4–2 victory…” Again, there are more rules, but these are the common ones.

Use an en-dash when inserting a parenthetical statement, as an alternative to those parentheses. Also, when quoting someone, where the last word is cut off for some reason (reminiscence, interruption). See many of my entries in this blog for uses of the em-dash in the former sense of the word. And enjoy this quote from Star Wars: A New Hope for an example of the second: “I sense something; a presence I’ve not felt since—”.

Hope that clears things up!

So in 1952 a PhD student at MIT named David Huffman chose to write a term paper instead of taking a final exam for his information theory class, taught by Robert Fano. With this term paper, “A Method for the Construction of Minimum-Redundancy Codes”, he bested his professor’s collaborative work with the discoverer of information theory at constructing optimal binary encoding. I heard this story when I took my information theory class, though I don’t think we were ever tasked with even an implementation of Huffman coding. So, out of boredom, I put together something in Python that does the job. Its usefulness is severely limited, as it expects a string input and produces a string output (plus the generated tree as a nested…well, list, basically). However, it does produce an optimal binary encoding for the input text, and can compress “The Raven” to 57.09% of its original size: 3603 bytes compared to 6311 in the original. In addition to that, the storage of the tree would be required, which in its Python format is 1074 characters. Anyway, the longer the text, the better ratio I’m likely to get, and the smaller the relative overhead would be of storing the Huffman tree. But this is just step one of a larger goal: I wish to be able to provide a clear guide to what audio compression algorithms make the most sense, and are objectively the “best” for a particular application. A comparison between the big contenders in the lossy market: MP3, AAC, and Windows Media in the non-free corner, and Ogg and Opus in the free corner. Along the way I suspect I’ll create image encoders and decoders and implementations of one or more compression algorithm (like DEFLATE), but I’m aware that, in the end, the choices of what bits of sound to chop away are what is going to matter. This is a research project on my part, and, while I don’t expect to win any awards, hopefully what I turn up will help someone, somewhere, in their understanding of the algorithms involved and how best to digitally store their music libraries.

Speaking of which, I’ve given in and installed iTunes on this computer. I refuse to give it control over my library, and my desktop player of choice will remain WinAMP, unless/until I write my own player.

To continue my rambling, there was a new version of Catalyst that for some reason my computer wasn’t picking up in its daily checks for updates (a little excessive for checking, but it didn’t even notice?) So either the 2D driver 8.01.01.1253 or some other part of the driver package 8.982-120727a-145524C-ATI seems to have solved the blue screen issue. Yay for dual monitors! Now I need a decent mount for them…

On to games. Wizards has finally recognized that by ceasing the printing of its most popular table-top RPG rulebooks it was cheating itself out of (I’m sure quite a bit of) cash. So I was pleasantly surprised to find three core books for D&D 3.5 on the shelf at Prairie Dog today when I picked up my comics. I have purchased World of Warcraft: Mists of Pandaria, which comes out on the 25th. With the massive changes they made in version 5.0.4 (and have already patched to 5.0.5), I’m still re-learning how to play a warlock. But I’ll be a Panda monk just like a zillion other people come the 25th. And Batman: Arkham City Game of the Year edition finally came out on Steam. Just shy of a full year after initial release. And honestly? I’m no longer excited about it. After the newness of being a Panda monk wears off, I’ll probably play it, but at this point I’m not bothered. Perhaps I’ll pick it up during one of Steam’s famous awesome sales.

Perhaps it’s the apathy of the week catching up to my stomach, but right now food bores me. I’m hungry, it’s past 9pm and I haven’t eaten dinner, but I look in the fridge and, despite there being plenty of sandwich making materials, I don’t want a sandwich. Besides, I’m out of bread. And milk. But when I think about going out, I’ve had this problem all week of not really wanting to eat anywhere. So I make my usual rounds: Pizza Hut, McAlister’s, Schlotzsky’s, tomorrow’s lunch with the guys will probably be Genghis or the Mexican Irish place (Carlos O’Kelly’s), and before the week is up I’m sure I’ll see the inside of Freddy’s and or Mr. Goodcents. All with zero enthusiasm. Cooking for one sucks (plus I hate the dishes that are concomitant with that duty). Eating out 7+ meals a week is extremely hard on the wallet. Perhaps it’s the 30 years of a sandwich every day that’s got me down, but it hasn’t bothered me until now, and it doesn’t feel like the blame belongs there. And the cooking for two option has a broken foot because I had to get a replacement credit card, and eHarmony won’t let me go in on a month-to-month plan, the only way I can re-up my subscription is by paying for 3, 6, or 12 months now, where, 3 months has a rate higher than the month-to-month does (how stupid is that). Not that I was talking to anyone. Maybe I’ll meet someone at The Color Run, or at “Sleepwalk with Me“. Unlikely, but possible.

Well, I need to stick something in this pie-hole, so I’ll call this entry quite long enough and begin another one tomorrow (which might be posted in a day, or a week, or a month).