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About one and a half months ago I got glasses for the first time in my life. I'm trying to record my experience with glasses for all the other people who get them late in life like I did.

I was fine without glasses for the first 24 years or so of my life. My mother is near-sighted and my father is far-sighted, so I figured it all just evened out in the end. My parents had my vision tested a couple of times, but I always had 20/20 vision so no one ever worried.

Things started to change when I was in graduate school. I began to experience a strange "double vision" effect where I could close one eye and see double images out of the other. The double after images always were always offset about 45 degrees and one letter's length away from whatever I was reading. Sometimes I could change the location of the afterimage by blinking my eyes a couple of times.

These after images were worrying at first-- after all, you're not supposed to see double out of one eye at a time. After talking with an eye doctor though, she thought this phenomena could be caused by my chronic eye infection. If I don't wash my eyes every time I shower, I get a white film over my eyes whenever I get dehydrated. If I don't wash my eyes for months, my eyelids can become infected and blinking becomes difficult. I've had this condition since collage, and for the most part I don't have to worry about it. The eye doctor said she thought this "film" was still present, and it was changing the refraction of my eyes. I left the doctor's office satisfied that I would be all right.

The double images got worse and worse as time went on though. They were especially bad when light contrasted with a dark background, like when reading from a projector screen or driving at night. Letters would appear to overlap with each other, making words a chaotic mess of overlapping lines. By the time I was here in Baltimore, my far-vision had degraded so far due to these double-images that I couldn't read street signs while driving. Dani had to read the road signs for me. This naturally made Dani nervous, and I she mandated that I shouldn't drive until I had been to the eye doctor again.

When Dani and I went back to New Orleans for Mardi Gras this February, my mom was gracious enough to set up an appointment with one of her eye-doctor friends. They looked at my eyes and did lots of tests, and found that I had 20/30 vision in one eye and 20/40 vision in the other. They fitted me for a lense and had me try it out, and suddenly all the double images disappeared. I suddenly realized that I was almost as blind as a bat and I couldn't see anything with any detail.

I had glasses made when I got back to Baltimore. The first time I put them on, I experienced the strangest sensations:
- While I could see farther than I could without my glasses, everything looked /wrong/. The ground looked too close to my head and all the ceilings looked low. In order to orient where my body was in space, I had to pretend the pavement was at my knees and I was wading through it as if through a swamp. In the parking garage, I constantly ducked to avoid hitting my head on the ceiling. All cars looked like clown cars.
- I had trouble walking, and I had to take deliberate steps to make sure the ground was actually where I thought it was. Stepping off a sidewalk took me 30 seconds. Dani told me I was taking goose steps, lifting my feet about a foot more than was necessary to walk.
- I got headaches, and I became dizzy often. I also had a compressed feeling at the front of my head. I usually only get this feeling when I'm studying and my brain is just about full.
- Monitors and signs looked really wrong. All computer monitors looked like trapezoids. Whereas I once saw right angles, I suddenly saw 75 degree angles and 105 degree angles. If I turned my head slightly, the monitor would move unnaturally.
- Apparently I would often move my eyes without moving my head. People with glasses don't do this to avoid distortion at the edge of the glasses. This caused all sorts of havoc.

We actually took the glasses back to get them examined and make sure there weren't any problems. I was having so much trouble with my vision that it was affecting my work. Lenscrafters said there was nothing wrong with the glasses and I'd have to get used to them.

And then, all of a sudden, after 1 week things suddenly started to get better. My vision with the glasses didn't improve gradually-- I had sudden jumps in improvements every time I slept. Within 3 weeks my vision with the glasses was almost back to normal and I felt comfortable enough to drive again. Now my vision is just as it used to be when I'm wearing glasses, except that I can see further.

Hypothesis and assertions:
- I think all of my difficulties with glasses came about because I got them so late in life. All my friends with glasses got them when they were children. They've either forgotten how hard it was to get used to glasses, or their brains were more plastic and they were able to adjust more quickly.
- I really felt like my brain was learning a new visual language. I can now see reasonably well enough to get by both with and without my glasses. Computer monitors look the same both with and without my glasses, even though I know the light reaching my eyes is very different. The whole learning process took about a month.
- I think that distorting people's vision with glasses could help them be better artists. When I look at a computer monitor, I see right angles where they don't exist. My brain knows the edges of a monitor are right angles, so it modifies what I see and adds that information. When getting used to new glasses though, my brain wasn't adding all that information. I was seeing the angles as they really were. Other optical illusions also didn't work as well when I was getting used to my glasses.
- I have a neat trick I can do now. By "switching" how I look at a right angle, I can actually make the angle move. By concentrating, I can make the angles on this text box oscillate +/- 10 degrees.
- Things appear really out of focus when I take off my glasses now, but after a few minutes they snap back into focus. From this, I gather that my brain is adding information to compensate for my lack of vision. I still get my double vision out of each eye when I take off my glasses. I think this double vision is an artifact of my eyes trying to focus beyond their limits.
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I went to http://broadband.mpi-sws.mpg.de/transparency/bttest.php today to see if Comcast was blocking BitTorrent. Sure enough, I get the warnings:

Is BitTorrent traffic on a well-known BitTorrent port (6881) throttled?
* 2 out of 2 BitTorrent transfers were interrupted while uploading (seeding) using forged TCP RST packets. It seems like your ISP hinders you from uploading BitTorrent traffic to our test server.
* The BitTorrent download worked. Our tool was successful in downloading data using the BitTorrent protocol.

Is BitTorrent traffic on a non-standard BitTorrent port (10009) throttled?
* 2 out of 2 BitTorrent transfers were interrupted while uploading (seeding) using forged TCP RST packets. It seems like your ISP hinders you from uploading BitTorrent traffic to our test server.
* The BitTorrent download worked. Our tool was successful in downloading data using the BitTorrent protocol.

Is TCP traffic on a well-known BitTorrent port (6881) throttled?
* There's no indication that your ISP rate limits all downloads at port 6881.
* There's no indication that your ISP rate limits all uploads at port 6881.

This is ridiculous. I thought Comcast was getting fined for this?

Here's a Linux firewall rule to get around the issue:
iptables -A INPUT -p tcp --dport 39984 --tcp-flags RST RST -j DROP

Unfortunately, the person on the other end of your connection has to be running the same rule.

Net Neutrality is designed to keep Comcast from being assholes like this. Support it with legislation if you can.
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My latest blog post can be found on my technical blog: Writing new plugins for citeulike.org.
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I spent 2 hours tonight reading the press releases for LiveScribe, a pen that writes on plain paper, but also can record your pen movements and audio in realtime, allowing you to playback meeting notes. I read tech reviews, press documents, a new york times review, and 20 odd support forum posts. Here are my impressions:

First of all, this is not the first time this idea has come around. There are already plenty of "digital ink" pens on the market. You can classify these pens into two major categories: echo-location based and microdot based.

Echo-location based pens require a small piece of hardware placed at the top of your writing surface. As your pen-tip rolls across the page, this hardware senses those vibrations and uses the time difference to calculate where you're writing on the page. These pens can store a digital representation of your writing on any surface, but they require the extra echo-locator to be placed at the top of your surface. Theoretically, if you're writing on a surface with a different speed of sound, these pens will also have problems tracking your position.

Micro-dot based pens use a small camera to track your pen's position as it types. The camera is usually located underneath the pen tip, and it reads microscopic dots printed on special pieces of paper. From what I've been able to read, these pens offer better resolution than echo-location pens, but they require special paper that is usually quite pricey.

The LiveScribe is a microdot pen with some interesting twists: it embeds an LED screen, a processor, a speaker, and a microphone into the pen's body, all under half an inch diameter. The microphone in particular makes it possible to record audio while you are taking notes and revisit those notes later. The processor and the LED screen allow you to use portions of the paper as "applications." For example, all their notebooks come with a printed out "scientific calculator", which allows you to type in numbers with the pen tip and display the answer on the LED screen. Another example application is a photo-printout of a piano keyboard which allows you to play music through the pen's speaker. They've also released an alpha SDK for writing new applications for the pen, based on Eclipse and Java.

Unfortunately, the pen has many downsides right now:
- The company is brand new. The pen only started shipping one month ago in June, Investing in a pen now incurs all the early adopter risks. In particular, the company seems to keep delaying their release dates for new features. There was much grumbling about this in the forum, though lately the company has belatedly been coming through on it's promises.
- The micro-dot paper is expensive, and some of the notebooks are low quality. They have been promising since before April 2008 that users would be able to print their own paper "soon." The latest estimate I was able to find for this feature was the end of 2008. If you can't print your own paper, your pen becomes a $200 Bic if the company goes out of business.
- The pen isn't the best pen for writing. I've seen posts requesting gel-tip pen refills, posts about what foamy tubes make the pen easier to hold, and complaints from customers that the pen is too large for them to hold. The pen comes with no cap, so people recommend getting a big sharpie marker cap and stretching it out.
- Right now, the software only runs on Windows, though they promise that a Mac port is coming shortly. Linux kernel hackers have been posting to the forums asking for technical details, but they've been ignored by the support team.

I have to say that I find this pen very attractive. Right now I carry around the following with me at all times--
- wallet
- keys, complete with usb key and leatherman scissors on a keychain
- my phone
- A pad of paper and a pencil, perfect for temporary notes.
- A digital voice recorder ($50)
- Occasionally an ipod

This pen would allow me to get rid of the voice recorder and free up pocket space.

Furthermore, I'm really intrigued by the capability of a "pencast". Most mathematicians learn math from whiteboards and frenzied explanations. In fact, I have learned more by watching a mathematician puzzle something out on a whiteboard than from any mathematical paper. The best math is always done on whiteboards with frenzied explanations, and I think a "pencast" has a much better chance of capturing these explanations than a stately LaTeX document.

Three things are keeping me from purchasing this pen right out:
- Finances are a bit tight with Dani and I right now. We aren't using our savings, but we aren't putting anything away either. Things will get better in a couple of months when both Dani and Kaylie have jobs and can help with the rent. Until that time comes, I can't justify a $200 toy.
- Before I buy this pen, I want to be able to produce my own microdot paper.
- Furthermore, the last thing I really need from a pen like this is the ability to print out pdfs, mark them up, and save my markup digitally. When reading math papers I often do the extra math the authors skip in the margins of the paper. Eventually I loose that markup and have to re-derive it. The whole process infuriates me, but the best way to do math is on a sheet of loose-leaf. Several other people have asked for this feature, so once they allow people to print their own paper I think this feature will shortly follow. 0
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For the last 6 months I have been lusting after a Tablet PC. Every time I close my eyes, I can envision so many uses:
* I would be able to make doodles anywhere and turn them in to pictures.
* When I feel the urge to do a piece of math, I wouldn't have to keep track of whatever scrap of paper I used to jot down my ideas. Instead, I could download my writing to a pdf and save it forever in my archives somewhere.
* I could mark up journal articles directly, instead of printing out the articles, writing notes and math in the margins, and subsequently loosing all those notes when my desk gets too messy.
* I could easily write up math lectures and post the final PDFs to my website.

Unfortunately, I can't justify buying one. From what I've read on the internet, a new tablet PC costs about $1000 (edit, a recent ebay search showed tablet PCs for $400, I might need to reconsider.) In addition, tablet PCs are large, require access to power, and only run Windows with proprietary software.

Recently though, I've been absolutely taken with the idea of getting a LiveScribe pen, or an electronic pen with an embedded microphone. It's designed to help students take notes in class, but it also satisfies everything I would want out of a tablet. Furthermore, it allows you to post youtube-ish videos of your document while it's being created. Look at these pencasts, and imagine the possibilities. This would allow me to write anywhere, mark up anything, and optionally make recordings of myself working though math, just like explaining things on a white board! This would do everything that I wanted out of a tablet for a fraction of the price ($150) and even more flexibility.

At heart I'm a miser, so I can't justify buying something like this without doing a lot of research. I'll post back here when I finish crawling the web and I'll let you know what I think.









My second day of the weekly project continues. http://wiki.rblake.net/bin/view/Rob/CiteULikeExtensionProject .

One of these days I'll have to talk about my plans to become a researcher without going to grad school. Stay tuned.
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Yesterday marked the end of a half-month drama between me and Comcast, my internet provider. As I calculate it, I've stayed home for technicians 5 hours and spent about 9 hours on hold with Comcast, trying to explain the situation. I'll record my tale of woe here, in hopes it might help future generations.

* 2008-06-22 - Internet service goes out during the night at our home. I think nothing of it and go to sleep, assured it will reconnect in the morning.
* 2008-06-23 - Come morning, internet service still isn't repaired. I call Comcast and spend an hour on hold. They agree to send someone out to look at our connection. The problem fixes itself during the day
* 2008-06-24 - A technician looks at our cable line, fiddles with a wire, says there was some water in the cable screw connection. Leaves. Problem redevelops that night.
* 2008-06-25 - I call and ask for another technician. Again, another hour on hold. Problems persist all this time.
* 2008-06-27 - Second technician comes out, says that the voltage on the pole is too low and he can't fix the problem. He needs to call up a line technician. Enraged, I write a script to detail exactly when I do and don't have internet service (attached below)
* 2008-07-01 - I get a message from the line technician saying he came out yesterday and everything looked fine. I should turn my modem back on (it was on the entire time). Another hour on the phone with Comcast. They agree to send another technician, refund me starting at the 24th, and give me a credit of $20. My technician is nice, we talk about his undergrad program. He's taking internet classes at night for a major in Homeland Security.
* 2008-07-03 - Elite technician (number 3) calls at 8 in the morning, asks if my problem fixed itself, then sighs and says he'll be right there. He shows up 90 minutes later. After futzing and making 2-3 calls to his supervisor, he says that the voltage signal is too high, and he'll have to call the line crew for a 1 day rush job. I ask him to get a modem out of his truck just to double check that it's not my modem, and he says the voltages are too high and his supervisor won't let him. Later that evening, I call comcast again to see if the line crew came by, and they say "what line crew?" Turns out he never submitted an order and closed my account as being fixed. Janine the technician hearing my tale of woe and commiserates. We chat while she fills out the forms on her end. It turns out her grandfather was from New Orleans, though he died when she was just a child. She also knows programming, and uses C++. At the end of the call, she thanks me for being nice and not yelling, explaining that I have every right to be irate. She give me her personal extension, vows to get a manager to talk to me, and emails all the support managers in the company putting the heat on her supervisor. I get a manager and he apologizes profusely, says he can get another elite technician out by Sunday.
* 2008-07-06 8AM - Another elite technician comes out (number 4), says that technician 3 was lying outright. He gets a modem out of his truck, verifies that my modem is faulty, and says I should buy a hew one. I buy a new one.
* 2008-07-06 12PM - I plug in the modem and get a connection! Unfortunately, Comcast's servers are blocking my modem because they don't recognize it's serial number. I call up Comcast and ask Robert to push me through Wallgarden, their firewall program. While chatting with Robert, I discover he and Janine are good friends (they go to cookouts together). He has a daughter who just got a new cat that sleeps all a-kilter. 30 minutes in, Robert interrupts our conversation about Disneyworld fireworks to dig into why the Comcast servers aren't pushing me through. Turns out they are doing server maintenence and they have no idea when they will be finished. Robert breaks protocol and says he'll call me back when it's fixed.
* 2006-07-06 2PM - Robert calls back, says his shift is ending and it's not fixed yet. He tells me to call back at 6PM
* 2008-07-06 6PM - Richard the technician takes my call, walks me through the whole disconnection process despite my attempts to explain the full situation. Richard tries to convince me that red lights on my modem should be green, when they can't turn green. I eventually start reading off all the DNS server information and my ping information and he stops treating me like an idiot. He digs further, and finds out that since I tried to register my new modem while the server was down, something got fouled up on my account. He agrees to call me back when the help desk emails him back.
* 2008-07-06 10PM: I call Comcast, explain the situation. The tech on the phone is amazed at my knowledge of their internal systems. He pushes me through Wallgarden with no problems. The internet works perfectly.

What an ordeal. For anyone in the Baltimore area, if your Comcast cable breaks, be sure to contact Janine at extension 7124, because she's a good person. I hope none of you ever have to go through this.
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I'm at a bit of a loss on how best to keep up this new writing habit. I realize that good writing skills are important to my future career. How do you learn how to write?

RIght now I don't think I can devote more than 30 minutes a day to writing, so this blog is a good starting point. I can write here for an audience other than myself, and since it's my personal life I have plenty of material to write about. I don't need to edit what I write too closely, and I do think that some writing is better than none at all.

In the future though, I'd really like to learn more about technical writing and editing. I don't know how to practice these fields in 30 minutes a day. Those math articles that I previously wrote in my journal took hours upon hours to compose. After I get bored of writing here, should I work on a new goal of publishing one technical article a week? Is that the best way to proceed?

---

I also need to decide where I should blog. Livejournal is great for keeping up with friends and what's going on in their lives, but it's currently in the hands of a company I don't trust and isn't really suited to writing large articles. I could solve the trust issue by opening my own wordpress site, but I'm not convinced that wordpress is any better for long articles and I'd be leaving all my friends here behind.

What I really would like is a site where I can post an article and work on it in small pieces. When the article is finished, I can release it. The blogging software should also have ways of attaching/managing images, the markup should be simpler than HTML, and preferably I should be able to post equations in latex without too much hassle. The blogging software should also have comment and user management capabilities.

I may not know the best way to go about learning how to write, but I think I've decided what kind of software I'll use. I've decided I'll stick to livejournal for day to day blogging about my life, but I'll be moving technical articles to my wiki. The new TWiki offers a way to keep track of blog comments as well as blog entries. Using my wiki, I can easily modify the blog entries and keep track of pictures associated with my articles. However, I don't think very many people want to run blogs on their wikis, so there are still some bugs in the software. I'll write more when I've written my first technical article and ironed things out.
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No post yesterday, something came up and I lost track of time.

If I remember any part of my wedding until the end of my life, I'll remember the hour immediately before and the exact moment we were married. You see, I refused to see the wedding dress after Dani had it altered. Even though she thought the tradition of the groom not seeing the bride before the wedding was silly, she indulged me and hid the dress for over a month. About an hour before the ceremony started, and long after all our respective relatives had arrived, Dani's mother and sisters whisked her away and told me I had to stay in the bedroom/living room until the ceremony started.

The first 10 minutes or so confined to those two rooms were fine. People came in and out, and through small talk I was able to pretend that it was just like any other slightly surreal day. However, as the time loomed closer, fewer people entered my two rooms (no doubt they were running errands). I started to pace about the room. I didn't have any regrets or unease, but I did have a profound realization of "this is my life, I'm on the edge of a huge life change. I can't believe all this is happening." In order to realize that today is the first day of the rest of your life, you need two things
- A day that abruptly changes the way you view your life
- 10-15 minutes to dwell on that change
Luckily Ben and Melissa came in to save me from those ruminations, with Ben adorned in a fez. Billy, Nathan, Kaylie and Beccah came in shortly after that to talk with me, and I was able to again hide in jokes and bad puns.

I'll also never forget the time standing at the flower arrangements we had substituted for an altar. I was hot, my shirt was starting to stick to my back, and even outdoors everything was quiet. I remember everyone staring at me, and being extremely self conscious of keeping in my gut/standing up straight. And then she came from around the side of the house, and all I could think was that I was that even though she was as nervous as me, she looked absolutely radiant. My next thought was a realization of what this ceremony meant, and that I was the luckiest guy in the world.

Before I go, here are some choice memories from the ceremony
- We didn't know which hand the ring should go on. Apparently your ring finger on your dominant hand is larger than your sub-dominant hand, so we thought my wedding ring didn't fit. I wore my ring on my right pinky during the whole ceremony.
- I messed up my vows because I was too busy looking at Dani to listen to the justice of the peace. I don't think I repeated it verbatim.
- Billy and I sword fought after the wedding
- As is custom after "in game" marriages, Dani and I both rolled a d10. I rolled a 1 and a 2, she rolled a 10.
- My dad tried to give a toast during the wedding, but got choked up half way through and had to sit down
- My sister toasted us, and alluded that we should start having kids.
- I gave a toast at the wedding as well, after my sister. I have no idea what I said.
- I remember sitting with Brock, Amanda, my cousin Ethan, my Mother, and others at the beverage table after the sun went down. We had a good conversation ,and my Dad told the full version of the red chair story.

All in all, I think it was a good wedding. The wedding hasn't changed much for Dani and I, we've been married for years. I see it as a big party where Dani and I got inducted into a very small club of two, complete with our own membership rings. I keep telling her we should get secret decoders inscribed on the back.

Current Mood: sappy

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Again, wedding pictures are here.

I think the best wedding present we received was a joint gift from Dani's grandmother, my mother, and my aunt. Together, they are the ones who planned our wedding. First we were too busy in Illinois, what with my finishing school and Dani working day jobs that exhausted her. Then, we were crazy with planning and executing our move. We only had about a week of semi-rest before we got on a plane for our wedding.

My mother took care of the entire rehearsal dinner, with the help of Dani's grandmother. The choices for restaurants in Mena were kind of limited, but the chinese buffet we ended up in turned out work nicely. There was plenty of food for both the omnivores and the herbivores. Also, the seating arrangements forced everyone to mix and socialize for the first time.

The wedding was mostly planned by Dani's grandmother and my aunt the professional caterer. Dani's grandmother took care of arranging all the food, tents, chairs, reserving the justice of the peace, and so on. My aunt was our wedding planner, and told my grandmother exactly what she should do next. Without them, the wedding would have been us in a courtroom with a trip to the bar afterwards.

Tomorrow, I'll talk about the day of.

Current Mood: sappy

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Ok, so I'm LONG overdue in writing about our wedding.

As many of you know, our wedding was on June 7, 2008. That's 6/7/08, an easy anniversary date to remember. We like to say we'd picked that date for that very reason, but really I wanted a date before I started work at Hopkins on the 16th and Jun 7th was the last viable day.

The wedding was at Dani's grandparents house in Wickes, Arkansas. Their house is nestled beside a little bubbling brook in the midst of the forest and built into a hill. It was originally built by an artist who used stones from the brook that runs nearby in the house's foundation. The scenery and her grandmother's landscaping were absolutely stunning. However, the isolation made things a bit rough on our guests-- there is no cell phone service there, and the house is at least 2-3 hours from any airport and 30 minutes from any hotel. We were worried about people finding the place, but everyone found the place and I didn't hear any complaints.

The wedding was the first time that both sides of the family had met in person. Dani's grandmother and my aunt and mother talked over phone and email, but that was it. Dani's family is also very different from my family-- I only have about 8 extended relatives we talk to on my side of the family, whereas Dani has over 20. My family is all from Ohio going back many generations, whereas Dani's family is all from South Africa with British accents. I still occasionally need translations when I visit her grandparents (apparently, a "zebra" is a crosswalk, and "mooty" is swahili for medicine). I needn't have worried though. Both sides got on splendidly.


My time is up for tonight. Tomorrow I'll talk more about the run up to the wedding. You can find all the pictures here: http://rblake.net/wedding . If you recognize people, we would appreciate the comments and tags.




For those of you who are interested, here's the link to my current WeeklyProject: http://wiki.rblake.net/bin/view/Rob/CiteULikeExtensionProject

Current Mood: sappy

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I've recently made some major life changes:
- I'm quit grad school
- I've gotten married to danithesquirrel
- I've started a new job at Johns Hopkins

Getting married and quitting grad school both deserve their own posts, so I'll save those for later. For now, I'd like to talk about resolutions and life changes. You see, whenever I make a major life career change, for approximately one month all my previous ruts are destroyed. Everything that I do and think seems to be new and exciting, and every behavior is open for re-evaluation. These periods are perfect times to install new behaviors and habits because I know they will stick. For example, the last major habit I installed using this method was GTD, and that has been a skill that has served me well for the last year and a half, at least.

Here's a list of new behaviors I'm starting at my new job:

Weekly Projects - One of the reasons I went back to grad school is that I felt I wasn't developing intellectually. However, in grad school I discovered that the people who are developing intellectually are doing things. That seems to be the big secret. Therefore, since my new job is very similar to the job that I left, I've resolved to spend 10 hours a week working on a weekly project every week. I've been telling people for years that if they want to be good programmers they should find an open source project and jump in with both feet. This time, I'm actually going to practice what I preach.

For the first couple of months, I'm planning on working on IT projects mostly because I feel those skills atrophied in grad school. This week's project is to add a translator to CiteULike for some journals that I often read. CiteULike is a wonderful service that helps researchers manage their bibliographies and keep track of what they are reading. If you do any sort of research, I highly recommend checking it out-- every person I've recommended it to has loved it.

After the week is up, I'll present a full write up of what I was able to accomplish and my conclusions from the experiment. By setting a fixed 10 hour time limit, I hope to improve my ability to work quickly and decisively on new projects.

Blogging - I realize now that I need to be an effective writer, and I miss having my life catalogued on a blog, so I plan on posting here once a day. I'll talk in another post about how I'm planning on reorganizing my blog.

Health - After looking at my wedding photos, I realize that I need to loose some weight. I've already told Dani that I want to budget how often we eat out, and I have some weekly projects in mind that should help us eat healthier as well. I also have some weekly projects in mind for things that will keep me exercising.

Another resolution I wanted to make is that I'm going to limit myself to 30 min a day journaling, and I'm already 5 min over. I better stop. Talk to you all tomorrow.


One of the things I like best about big life changes is that they give you an opportunity to break out of any ruts and get started

Current Mood: resolute

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Did anyone else in Illinois tonight feel an earthquake at 12:39AM tonight?
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I have too much mental baggage going on in my head right now, so I need to get some of this down in writing. My time in grad school has caused me to do a lot of self-analysis. Here's what I've learned about myself from my time in grad school so far.

- I try to help other people through positive reinforcement, yet I only use negative reinforcement internally.
- I work better in teams than by myself. If I'm with other people, I feel guilty when my work affects them negatively and proud when my work affects them positively. I have no such reservations about letting myself down.
- When isolated at work, I get depressed and off-focus.
- I like being recognized and praised for my work. It's my source of creative energy.
- I like learning new things.
- I like building things and seeing them used by other people.
- If I can pass the NA quals, then I can learn and do anything related to math.
- I like to teach people things.
- I have some problems with rejection
- I don't like working under lots of stress. I can do it, but it just kills my quality of life.
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I got the results at noon. I passed! I messed up one part of the exam horribly, but they passed me anyway because "they knew my research interests, and they were sure I'd know how to derive the weak form of a PDE by rote by the time I left."

Yay! I can't quantify how relieved I am.

Now that I've passed my qual, does this mean that I'm a mathematician now?

Tags: ,
Current Mood: relieved relieved

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I think I need to quit grad school.

Those of you who have talked to me in the last two years can vouch for how unhappy I've been. I've broken down crying more times in the last two years than the rest of my life combined. At times I've felt so bad that my emotions have literally shut down, which from Junior high I know is a path that leads to a very bad place. I've been to counseling for the first time in my life, and they basically said I needed to decide if I wanted to stay, and to stop coming. Lately, I've been having horrible stomach pains and digestive problems. Lately I've had trouble getting out of bed in the morning.

I wonder how much of these recent developments are due to the pre-qual jitters. My qualifying exam is on Feb 13th, and I will probably fail, realistically. I've had trouble doing anything related to the exam in the last month without feeling physically ill, so my studies have suffered. Certainly the qualifying exams are terrifying, but I think they are terrifying for everyone.

Part of this decision might be due to Dani's decision to quit grad school. Ever since she quit, she's been happy and full of energy again. I actually envy her her job making minimum wage.

Even through all this, the only thing that terrifies me more than failing the qual is passing and spending another four years at this school. I have no idea what I want to do for my final research, and just the idea of doing research here sickens me. This realization surprised me this weekend, because the whole reason I came back to grad school is that I liked doing research in Natalia's lab so much. I know I've wanted to be an inventor since the 3rd grade, and I still want to be an inventor. If this school makes me so depressed that I want to quit my lifelong goal, then it's time to leave.

I think a big part of my job satisfaction is that I need to be able to take pride in what I do. Here, they emphasize over and over that classes are not important and TA work is not important, so I can't take pride in my good work there. Only your research is important. Every research idea I've proposed to a faculty member has been shot down as redundant or already done, and no one has proposed an interesting problem to me. The end effect is that I feel like a failure for not developing a research idea that a professor is interested in, and that just drains the hell out of me until my failing becomes a self-fufilling prophecy. I feel isolated and alone here-- there is no one with whom I can share these concerns without repercussions. If I leave, I doubt I'll even be missed or remembered.

I don't regret my time here, I've learned so much. But there is no light at the end of this particular tunnel. Even if I survive four more years, what happens after grad school? Most NA departments are in math departments in other schools, so finding a job at another school will be difficult. Even if I do end up in a math department somewhere, I'll end up teaching theoretical mathematics that I have no drive for anymore. I could go work for a national lab, but if you loose your funding in a national lab for more than one semester, they kick you out. That isn't job stability, and that isn't the life I want. I've had offers to jobs I would definitely enjoy, and ever since Dani quit we're no longer tied to this city.

So, I had a long long talk with my parents this evening. I've set up meetings with academic advisors in order to figure out what's involved in leaving before the Ph.D. I'd like to get a Masters before I go, but I have a feeling that they are going to screw me over.

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OK, I've been studying ODEs (ordinary differential equations) all night, and I've just had a thought.

Say we know apriori that a system of ODEs has a asymptotic steady state solution. This means that the solution is no longer changing, so we have y'=0. If we can write our differential equation in the form y'=f(y), then this means in turn that we only need to examine points where f(y)=0. This can be done with any old root finder, then the candidate "steady-state" solutions can be examined for stability. This we know.

What if, instead, we know apriori that a system of ODEs has a asymptotic periodic solution? In particular, this should be true for the ionic concentrations of heart cells. We can write y(t) = y(t+P), and y'(t)=f(y). How can we solve for all possible periodic solutions? Do people do this sort of thing? I've never seen anyone examine a system this way.

You could rewrite the equations in an integral form and take the Fourier transform of both sides, but what that get you? You still can't compute the Fourier transform because you don't know what y looks like.

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So, danithesquirrel and I are already fighting over the name of our first male child. For about a year, she has been absolutely adamant that our first male child will be named "Simeon Vincent Blake." Simeon is an old family name in my side of the family. The original Simeon Blake was a war veteran who came back to Caldwell Ohio (pop. 400) to become the town sherif. He's famous in the town history for riding through a religious tent revival while drunk, wearing a sheet over his body, and playing the trumpet. This sparked a small riot when the faithful mistook him for one of the four horsemen of the apocalypse.

Anyway, Dani maintains that "Simeon Vincent Blake" is an awesome name (even if it does sound like a villian). I'm against the name because I think that it's too close to "simian," which will lead to "monkey" taunts throughout grade school. We've been fighting over this for a year now, and neither of us will budge.

Therefore, in order to finish this debate once and for all, I'm doing the only rational thing a scientist can do: research. I am on a mission to find as many people with the name Simeon as I can on the internet and ask them for a candid opinion on their name. After I have 20 responses, I'll post the results of the poll.

Here's where you come in, my intrepid googlers. I need to collect more emails. If you are willing to help, could you post the last name and email of a Simeon in the comments? If you do, this is the form I will send them:




Hi Mr. XXXX,

You don't know me, but I'm hoping you can settle an argument between
my fiance and I. She is adamant that our first male child will be
named "Simeon Vincent Blake," but I'm against the name because I
think it's too close to "simian," and will lead to grade school
taunts of "monkey." In an effort to settle the debate, I'm
collecting the opinions of people with the name Simeon.

I was wondering if you could tell me,
1.) Were you taunted for the name Simeon in grade school?
2.) Do you pronounce your name as "Simon?"
3.) Do you abbreviate Simeon? Do people call you Sim?

Thanks for taking the time to answer this. One day I'll post the
results of this poll to ademus05.livejournal.com.




Thank you. As soon as the polls are in, I'll let you know what the results are. Rockethouse members, I've made a wiki page on the subject.

Also, what do the readers think of the name Simeon?

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This person build a wooden adding machine using gravity and marbles. Your computer does the same thing as this computer, but uses groups of electrons instead of marbles and the AC outlet instead of gravity.*




* Note: This is an extreme simplification.

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Alright, inspired by a conversation with my dear sister castlerock, I've decided to publish something a little different today. I'm going to be talking about infinity, and the different types of infinity that occur in higher mathematics.

Most people deal with infinity every day:
  • "I will love you forever"
  • "When you die, you are dead forever."
  • "You go to heaven forever."

We also play games as children:
  • "I'm better than you times infinity, plus 1!"


In one way, the concept of "infinity" is easy to understand. I believe the brain has a special internal language for the words "this pattern holds," also known as "and so on", "yadda yadda yadda," "forever". Forever encompasses the idea of closure. It means that if you understand a finite number of things, you can extrapolate and deal with real world problems. Mentally, we perform this powerful reduction all the time. Without it, we wouldn't be able to cope. In this way, infinity in comforting.

However, if you look at infinity from a size standpoint, infinity is dizzyingly terrifying. Most people don't have a proper concept of what "large" means, but mathematicians know better:
  • The universe is 13.7 billion years old, or 4.3*10^-17 seconds. Current quantum theory has trouble measuring time below Planck's time constant, or 1.855×^-43 s. If we treat the idea of time as a discrete number of Planck's constants, then the age of the universe is 8*10^60 of these constants. Infinity is bigger than this.
  • The number of atoms in the universe is estimated to be around 10^80.
  • The biggest number ever seriously used in mathematics is Graham's number. The number is an upper bound for some mathematical property. The number is so huge that it cannot be written with scientific notation (the exponent would have more digits than atoms in the universe). Still, infinity is bigger than this number.
  • The Ackermann function is a strange non primitive recursive function:

    This function generates huge finite numbers. For example, A(5,2) is so large that it cannot be describing it with common math notation would take more letters than there are atoms in the universe (this includes 9^9^9^9^9^9... etc.). Still, infinity is bigger than this number.


In fact, infinity is more than just a really huge number. Infinity breaks our notion of numbers altogether.
  • Say we have a set of all integers, and we split that up into a sets of all even integers and all odd integers. Obviously, any integer is going to be even or odd, and no integer can be both. Therefore, the set of all even integers is smaller than the set of all integers, right? Wrong. The size of the set of even integers is the same size as integers.
  • A line goes to infinity in two directions, but a ray only goes to infinity in one direction. Still, lines are the same size as rays, even though if you divide a line in half, you get two rays.


The reason our intuition breaks is that infinity isn't a number. x/2 is less than x if x is finite, but infinity/2 is an abuse of notation, and technically gives you infinity again. The same goes for infinity+1, or infinity+infinity. All our intuition about the "measure" of things is broken by infinity, so we need a new idea of what it means to measure something infinite.

Richard Dedekind and George Cantor came up with a clever solution to compare sets with infinite size. If you have two sets A and B, and you can construct a mapping (a->b) so that every b is covered, then size(A) >= size(B). For finite sets this can be seen by the following diagram. As you can see, there is no mapping from B to A that covers all of A.



This idea is useful because it allows us to compare the size of sets without having to say what size(A) is. Also this definition corresponds to infinite sets as well: For example, positive integers = even integers because we can construct the mappings (n -> 2n) and (2n -> n). Therefore, A <= B and B >= A, so A=B.

So what infinite sets are equal to each other? The following sets all have the same size:
  • N, the set of positive integers
  • The set of all integers
  • All subsets of integers
  • The 2d natural number plane, (N, N)
  • Q, the set of all numbers that can be written as n/m where n and m are integers.


However, you can prove that the set of real numbers between 0 and 1 (which includes things like sqrt(2)-1) is BIGGER than the set of all positive integers. Wikipedia does a good job of explaining the proof, I'll write it out in detail if people are interested.

Higher mathematics has two different words for types of infinity. Countable infinity means the size of the set is equal to the size of positive integers, and uncountable infinity means that it's not. We distinguish between these two cases because working with countably infinite things is nice and working with uncountably infinite things is messy.

In numerical analysis, this is really important for solving equations. Let's say that we're trying to find a unique function from 0 to 1 to real numbers with a special property. There are an uncountably infinite number of these functions. If we write a computer program to test all these functions and let it run forever, that computer program can only do a countably infinite number of function tests. We can prove this by numbering the tests that the computer does them. Therefore, no computer can test all possible functions, even if it runs forever.

Does this mean that trying to solve a differential equation on a computer is hopeless? The answer is yes and no. We cannot solve a differential equation exactly, but by allowing some error, we can transform the uncountably infinite space into some thing that is countably infinite or even finite. This is the heart of all numerical analysis.

(
Side note, if you want to win the "I'm better times infinity plus 1" game, here are a couple of guidelines:
* ack(n,n) > n^n for large n
* n^n > n! for large n
* n! > x^n, x finite, for large n

When someone tells you they are better than you by "infinity plus 1", use some of these huge functions to blow them away.
)

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I have vowed never to buy an apply product again, no matter what cool technologies they come up with. The reason: this money pit called the Macbook Pro. The initial computer was about $2000. Within the first year of my purchase, I have had
- 1 screen die, leading to the replacement of the whole computer.
- 1 battery death which lead to the replacement of the battery
- 1 fan die, leading to sending in the whole thing again for repairs.

Due to all the problems in my first year, I decided to purchase the extended Apple Care for $350 so my computer would be protected for another 3 years. Since then, I have had
- My power adapter die, leading to the replacement of the power adapter.
- Recently, my battery is dying, loosing it's full charge in about 1.5 hours.

I called Apple today to see if I could get my failing 10 month old battery replaced since I have the fancy Apple Care. However, Apple says they won't replace the battery because I've charged it over 200 times. Apparently they only build the batteries to survive for 300 charges. If I want a new battery, I need to buy one for $130.

In other words, the ownership cost for this laptop is about $150 per year. In order to use this computer for another 3 years, I'll have to spend about $400-$500 over the computer's lifetime. This is in addition to the $350 I had to spend because some bit of the hardware dies every 4 months or so.

If you are thinking about buying an Apple product, beware. The hardware sucks.

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Last time, I covered the differential equation for Newton's Law of Cooling. The example I used was modeling the temperature of a cup of coffee sitting on your desk. The temperature of the coffee is described by



where C(t) is the temperature of the coffee at a given point in time (starting at 90 degrees F), S is the temperature of it's surroundings (70 degrees F), and p is some constant given by experimental measurement (1/20).

By itself, this equation isn't all that useful. We'd really like to find an equation for C(t) that only has constants and t. When we find an explicit formula for C(t) that only involves constants and time, we say that this formula "solves" or "satisfies" the differential equation. Note that solving a differential equation is not like solving an algebra equation. You can't just simplify and get C(t) to one side because that pesky C'(t) gets in the way.

For now, I'll skip the solution process and just give you the answer. Those of you in the audience who know calculus can verify that this C(t) solves the differential equation by plugging it in and verifying that it solves the equation.



Here, C(0) means the starting temperature of the coffee, 90 degrees in our last example. You can verify this equation in your head: when t=0, the exponential part equals 1, and we get C(0)=C(0). When t is really really huge, the exponential part goes to 0, and we get C(t)=S, or in other words the coffee has cooled.

The graph of this function is shown here.



Now that we have an explicit formula for C(t), we can find the temperature of the coffee at any moment in time. Lets assume that you like your coffee at 80 degrees F. This graph tells you that you'll have to wait about 14 minutes in order for the coffee to get that cool.




I just used a differential equation to describe how a cup of coffee cools over time. I showed you how we find all the parameters in the equation. I pulled a solution to the equation out of thin air, and showed you how we can use that solution to find exactly how long we should let our coffee cool. At this point, you should have some questions. I'll try to cover the concept of differential equation modeling from a few different viewpoints.

Practical Viewpoint - Why do we need all this complicated math to model how a cup of coffee cools? Can't we just stick our pinky finger in the coffee and be done with it?

Yes, we could, and using a differential equation to model the cooling of a cup of coffee is probably overkill. I just wanted to pick an example that was common to most people. I wanted you thinking of me the next time you are in Starbucks.

However, the same equation that works for coffee works for any heating situation. Let's take an example that is closer to home. During hurricane Katrina in New Orleans, lots of people lost power to their homes for a long time. If the power goes out for more than a day or so, you need to worry about the contents of your freezer. If the power goes out long enough, you need to find a way to cook the meat and other perishables you have so they don't spoil. However, you don't want to open the fridge too often to check the temperature, because every time you open the door you let out the cold air. How long do you have until you need to cook all your meat?

The normal temperature for the contents of your freezer is about 0 degrees. In a New Orleans summer, the temperature of your outside surroundings is about 90 degrees. Meat begins to spoil above 37 degrees. As soon as the power goes out, your fridge's temperature is governed by Newton's Law of Cooling.

By opening your fridge one hour after the power goes out, you can get an estimate of p. The exact value of p will depend on the insulation of your freezer and how much meat you have stored in there. After you've measured p, you can use the solution to Newton's Law of Cooling to estimate up to the hour when you'll have to start eating the meat inside your freezer.

Physics viewpoint - You said before that Newton's Law of Cooling made a whole bunch of simplifications. Can we change our differential equation to account for those things?

Yes. You can add extra terms to the differential equations so that it can account for the following things:
1.) The fact that the top of the coffee looses heat faster than the side and bottom of the coffee.
2.) The fact that the air around the coffee is warmer than the rest of the room
3.) The fact that the temperature in the coffee itself is non-uniform
4.) The fact that the temperature differences in the coffee causes the hot parts to rise, creating movement within the liquid.
5.) Etc.

You can do all these things, but as a result the equation gets harder and harder to solve. With (1), you no longer have a single variable for the coffee, so you need to take the coffee's 3D shape into account. With (2), the variable S becomes a function in time, S(t), and you need more differential equations that describe how S(t) is related to it's derivative. With (3) and (4), you need differential equations that describe how fluids move due to temperature differences. Note that even if we took (1-4) into account, we still would only have about 10 differential equations we would need to solve simultaneously. This is the great thing about differential equations-- a few simple equations can model even the most complex physical systems.

Math viewpoint - How do we solve an arbitrary differential equation?

This is what makes differential equations so interesting. Most of the time, we CAN'T solve a differential equation. Mathematicians have been working on this for 300 years, but even after all this time, we don't have a way to solve an arbitrary differential equation. Take the following two equations, but instance:



The top equation can be solved by y=e^(-t), but the bottom equation is much trickier. We know that a solution exists, but we also know that this mystery solution cannot be described by any finite number of math symbols!

We only know how to exactly solve a few easy equations like Newton's Law of Cooling, and we know how to find the solution to some special cases. For most of the interesting physics equations though, we can't find a solution to the differential equation even though we can prove that a solution exists. Solving these equations gets so complicated that some researchers spend their whole life trying to come up with approximations to the solutions to one differential equation.

What I do



Now that we have all this background, I can finally describe what I do. These differential equations are too hard to solve exactly, but often we can find approximate answers that are close enough for practical use. I work on designing computer calculators that solve approximations to these differential equations.

I want to post here more often, so over the next couple of weeks I'll be spending one post per day on one differential equation. For now, I don't want this journal to get too mathy-- instead, I want to try and develop an intuition as to what kinds of things you can model with differential equations. After I've convinced you that solving differential equations is important, I'll show you how we can cheat and find a "good enough" answer to a differential equation even if we can't solve it exactly. I'll show you what goes into making these advanced calculators.

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I covered calculus in such detail before because I wanted to move on to the cool stuff-- differential equations. A differential equation is an equation between a function and it's derivatives. These equations occur all the time in physics-- in fact, most Newtonian physical laws can be written as differential equations. This is why I kept on re-iterating that calculus is the language of physics.

For example, assume that you have a cup of hot coffee that is sitting on your desk. The temperature of the coffee over time can be determined by Newton's Law of Cooling. The following website has an excellent explanation of Newton's Law of Cooling: "The rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e. the temperature of its surroundings). " This statement makes a whole bunch of simplifications. It assumes that the heat coming from the coffee won't affect the heat of the surroundings. Anyone who has used a cup of coffee to warm their hands in the winter knows that this is false. Also, it assumes that the top of the coffee is the same temperature as the rest of the coffee, even though everyone knows you can cool down the surface of the coffee by blowing across its top. Still, even with all the simplifications, Newton's Law of Cooling is a pretty good description of how a hot cup of coffee cools over time.

When Newton says "rate of change of the temperature," he means the instantaneous rate of change of the temperature. At a single moment in time, let C(t) be the temperature of the Coffee at time t, and let S be the temperature of the Surroundings. We can express this equation as



"Proportional to" means that one is a multiple of the other, so we can make this an exact equation by introducing a Proportion p:



I need to explain two things in this equation: the negative sign and the constant p. The p constant here is a positive number determined by the exact physical situation we are modeling. If our coffee is in a thermos, then it will stay hot longer. We can model this by making p smaller, so that the rate of temperature change is smaller. Likewise, if we have less coffee or if our coffee is in a paper cup, then p is going to be a large number. In reality, we can estimate p by measuring the temperature of the coffee after 1 minute of cooling. Lets say our coffee is 90 degrees F, and the surroundings are 70 degrees F. If the coffee cools to 89 degrees in 1 minute, we say that C'(t) is approximately 1 degree per minute, and C-S is 20 degrees. Therefore, we can solve for p:



The negative sign in the differential equation is just an artifact of the math. The negative sign says that "If the coffee is hotter than the surroundings, then the temperature of the coffee should decrease." For our hot coffee example, if our coffee is at 90 degrees F and our surroundings are at 70 degrees F, then the temperature of our coffee should be decreasing. Without the negative sign, for p=1/20 we would have that the rate of our temperature change would be p(C-S)=(90-70)/20=1, a positive number. This would imply that the temperature would be increasing, which is the opposite of what we are describing! The negative sign fixes this problem.

Next time, I'll give you the solution to this differential equation and talk a bit about why differential equations are so hard to solve.

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Brock, I'd like to thank you for the links and sending attention my way.

Again, if you're confused by any of this, please respond in the comments. I'll edit the post to make things even clearer. I'd like to keep these posts as a reference that I can refer people to later.

Today, we're going to talk about the other half of calculus: finding the area under a curve. You occasionally need this in engineering. Let's say you are an aircraft engineer, and you've figured out an equation g(x) that describes the perfect cross section for an airplane wing.

airplane wingCollapse )

Assume for the moment that the wing doesn't taper, and that the wing is 10 meters long. The total volume of metal you need to build the wing equals (base area of cross section)*(length of the wing). Therefore, you want to know what is the area of the cross section under the curve so you can tell your boss how much metal he needs to buy. How do you find the area under this curve?

In calculus, this process is called "integration." Much like computing derivatives, the idea behind integration is simple: To measure the area under any curve, divide it up into a whole bunch of tall and thin rectangles, then add up the area of those rectangles.

Estimate the areaCollapse )

As your rectangles get thinner and thinner, you get a better and better estimate until you get exactly the right answer. Also, notice that the left side of each rectangle touches the function. This is just a convention. I could have chosen the right side, the midpoint, or pretty much any point. As the rectangles get thinner, you get closer to the correct answer regardless of your choice.

Like the derivative operation eventually produces a new function that describes the slope, you can use math to define a function that computes the area under a curve. Given any function g(x), you can write a math equation for these thin rectangles, factor out the small "h" (where h is the width of the rectangle), and get another function G(x) so that the area between "a" and "b" is G(b)-G(a). As an engineer, this helps you because you can now you have a simple expression that gives you the exact area under the curve. Unlike the derivatives, I'm not going to show you this because it's a bit mathy and doesn't give you any intuition. The important thing to remember is that like a derivative, integration is a process you apply to a function g(x) that produces another function G(x), and G(x) allows you to measure the area under a curve.

Here's the surprising part: Derivatives and integration 'undo' each other. In other words, (area of f'(x) from a to b) = f(b)-f(a). Do you remember that we showed yesterday that if f(x)=x^2, then f'(x)=2x? If you wanted to find the area under the graph of f'(x)=2x from 0 to 1, all you need to compute is f(1)-f(0) = 1-0 = 1. This matches our geometric formula: (area of a triangle)=0.5*(base)*(height)=0.5*(1)*(2)=1. The amazing thing is that this works for any function and it's derivative.

If you understood all that, you should be experiencing utter disbelief. We said that derivative meant "slope of" and that integration meant "area under the curve". How can these two operations 'undo' each other? Why are they even related? What's going on? You don't find out the reason why until your junior or senior year of college as a Math major. Most people never find out. This brings us to our third take home point: Derivatives and integration undo each other because they are Magic.

There you go, that is everything that you learn in a year of calculus. The rest of the time is spent doing endless drills and problems, which you forget in 5 years anyway. If you've gotten this far, you have as good a conceptual understanding of calculus as anyone who has taken 1 year of study in the subject. The ideas behind calculus are simple.

Here's a summary of everything you need to know about calculus to understand the rest of my posts.



  • Calculus is the language of physics.
  • The "slope of a graph at a point" is called the derivative at that point.
  • If you zoom into any function, it becomes a straight line with a measurable slope.
  • Whenever you are at a maximum or minimum, the slope of the graph is zero.
  • To find the area under a curve, we say you "integrate" that curve
  • To measure the area under any curve, add up the area of tall thin rectangles.
  • Derivatives and integration undo each other because they are Magic.

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In my last post, I talked about how I want to do research on how to build better calculators. However, I was being a bit misleading. Your basic hand-held calculator can solve all the math problems that most people encounter in their daily lives, so that problem has already been well solved. When I say I want to build better calculators, I mean that I want to build computers that solve harder math problems.

Here's where I come to a dilemma. My research usually tries to solve problems written in the language of calculus, and just the word "calculus" scares most people. Calculus seems to have this mystique of difficulty. For 85% of the population, calculus means "hard math that you never had because you chose a non-calc path in high school." For the other 14.9% of the population, calculus means "The highest (and hardest) math I know." My high school physics teacher never took calculus. Whenever he talked about it, his voice was filled with equal parts fear and awe, as if calculus were some black art that could rip the physical planes asunder if used improperly.

I want to dispel this myth. Today, I'll try to explain the notation of calculus and how it helps us. Then, I'll explain half of the results of calculus in 5 minutes. The target for this posts is the absolute lay person-- an amateur. I sometimes expect simple geometry, simple high school algebra, and that's about it. So if you don't understand these posts, please let me know in the comments.


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This, in a nutshell, is the first 3 months of calculus. You spend all your time calculating "slopes", or "derivatives" of many different functions. You learn some tricks that allow you to quickly calculate the "slope" of arbitrary functions. Then, you drill solving 100 maximization problems until you can do it in your sleep. The reason that you had to learn all those complicated simplification procedures in Algebra II was because calculating the "slope" can sometimes involve some tricky simplifications. From a conceptual standpoint though, you can sum up the first three months of calculus with the following ideas:


  • The "slope of a graph at a point" is called the derivative at that point.
  • If you zoom into any function, it becomes a straight line.
  • Once you zoom in, you can just measure slope at that point.
  • Whenever you are at a maximum or minimum, the slope of the graph is zero.
  • Calculus is the language of physics. If there is a Heaven where you can learn the mysteries and wonders of the universe, then you can be sure that everyone in Heaven knows calculus.


Next post, I'll talk about the other half of calculus: integration. I'll show you why the "slope of" aka derivative operation is magically related to the area under a curve.

(Edit, fixed the statistics as per this this graph from the NSF.)

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When I used to work for Natalia Trayanova, I used a program to track how I spent my time each day. I started doing this because I was placed into a mostly unsupervised position and I wanted to make sure that I was working 8 hours a day. The results of this analysis were extremely fascinating. I found that on bad days I would spend up to 2 hours a day goofing off on the internet, and it often took me over 1 hour every day to answer emails. I also spent a good hour or two a day just talking with people in the lab, helping them with technical support, etc. By tracking how long I spent on various tasks, I had a way to measure how much effort I was putting into an otherwise nebulous job. On a good day, I could do 4-5 hours actual work in 8 hours, so if I did 5 hours work then I allowed myself to go home early. I was able to work shorter days with less stress, just by keeping track of how long I spent goofing off each day. I firmly believe in the old adage: "That which is measured, improves."

To track how I spent my time, I used a linux program called karm (now renamed ktimetracker). Unfortunately, this program doesn't work very well in Mac, nor does it work well when I have to work on 3 different machines during the day. Because tracking my time became so inconvenient, I stopped the practice when I came to grad school.

Those days are no more, though. A week ago, I found an online program called SlimTimer that allows me to track how I spend my time online. It's an AJAX application (like gmail) so it works across multiple computers and any operating system. The system is great: you create a list of tasks, click a link, and a window opens up beside all your tabs. From there, you can start and stop tasks like stopwatches. Furthermore, you can add comments and tags to certain recorded periods of time. The system also can generate complicated reports of how you spend your time, and it has an API so you can download the data you've accumulated and manipulate it as you see fit. Just this week, I've discovered that I'm only really working an average of 3 hours a day, once you account for classes and such.

Signing up is free. I highly recommend documenting how you spend your time for at least one week. You'll be utterly surprised at where all your time goes.

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Here's an article about Jerry Seinfeld's system to make himself write every day. To quote the article:

[Jerry Seinfeld] then revealed a unique calendar system he was using pressure himself to write.

Here's how it worked.

He told me to get a big wall calendar that has a whole year on one page and hang it on a prominent wall. The next step was to get a big red magic marker.

He said for each day that I do my task of writing, I get to put a big red X over that day. "After a few days you'll have a chain. Just keep at it and the chain will grow longer every day. You'll like seeing that chain, especially when you get a few weeks under your belt. Your only job next is to not break the chain."



I read this a month ago and I loved the idea. Who here hasn't kept with an old tradition just because we've been doing it forever? For the geeks in the audience, who of you have regretted restarting a computer because it had been so long between restarts? We sees these sorts of behaviors as time investments, and we sometimes go to inordinate lengths to preserve our percieved investment. Why not use this flaw in human behavior to your advantage?

Of course, I'm too lazy to buy a calendar, and I'm never in one place very long. I am in front of a computer all day though, so I've come up with a way of painlessly implementing the Seinfeldian system using web applications.

ademus05&apos;s Personal Score Badge

This link comes courtesy of http://www.joesgoals.com . It allows you track your daily progress on your habits. It automatically keeps track of your longest chain in any habit. Furthermore, it gives you a little banner like this that you can post onto whatever page you visit most often so you see it every day. As you can see, I slipped a bit during last weekend. My next goal is to spend a week at +1 or above.

Signing up is free, and the service is dead simple to use. I highly recommend it.

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I'm keeping up with this blog in an attempt to improve my technical writing.

Whenever I visit relatives or meet new non-science people, I'm often asked that dreadful question: "So what are you studying?" My answer depends on lots of things: the levity of the conversation, my energy, the earnestness of the asker, etc. If someone is obviously just being polite, I answer "Math stuff" or something sufficiently scary like "Scientific computation," or "Numerical analysis," or "Parallel scalability for algebraic multigrid methods applied to symmetric positive definite systems that arise from computational biological problems," just to keep the conversation moving along. Occasionally though, the asker is truly wants to know about my research interests. In these cases, I'm often at a loss as what to say. How can I describe a differential equation solver to someone who doesn't have calculus?

This post is my attempt at a 2 minute answer to that question for the absolute lay person. I want to describe what I do and why my field exists.

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I study how to solve math problems with computers. In other words, I study how to make better math calculators.

Picture of a calculatorCollapse )
My field covers how to represent numbers on computers, and how to quickly perform addition, subtraction, multiplication and division in hardware.
My field covers how to calculate things like logarithms, exponentials, and square roots using only addition, subtraction, multiplication and division.
If we abstract the notion of a calculator, my field covers things that can do algebra for you and simplify expressions.
Abstracting further, my field develops calculators that can solve more than one equation, solving systems of equations, no matter how big.
Abstracting further, my field produces calculators that can solve differential equations, which includes most equations produced by physics. The solutions produced by these calculators describe how the world works. When ever you see a weather forecast, you're seeing the output of these types of these advanced calculators.

Who would study calculators for a living? I like math, but I want to do something with it that will have tangible effects on the world. Most math is just theory, but scientific computation works on solving math problems that people just can't do by hand. If you can write your question as a math problem, then my field can help you. My field is the backbone of most modern engineering, and my research can simultaneously affect fields as disparate as sociology and quantum physics.

That is my field of study in a nutshell. I study calculators.

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Bonus: did you know that the following code will compute a square root of C?

start with x=1
repeat until x isn't changing
set x = (x*x+C)/(2x)
end repeat

Viola! x = the square root of C.

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(Part of my motivation for starting up this journal again was to improve my writing skills. I'm not the best writer, I'm not the worst, but I very well might be the slowest. My clock reads 1:30 in the morning as I type this, and I intend to post whatever I have at 2:00. If this post seems dis-jointed, you've been warned.)

So far, my posts on the current state of academia have been very negative. I took this approach because I wanted to dispel the myth that academia is a haven for idealistic do-gooders that think of nothing but performing research and working to expand human knowledge. Instead, academia is a broken medieval artifact -- a guild formed to control and regulate the creation of new scientific knowledge. Those who decide to venture up the academic food chain should be warned: the path requires needless sacrifice, and the end goal may not be what you expect.

That said, ironically academia is filled with semi-idealistic do-gooders that think of nothing but performing research and working to expand human knowledge. Most people who become scientists do it because they really love science. If you don't love research enough to devote your life to it, there is no way you'll be able to put up with the sadistic requirements needed to become a tenured professor. I've been to countless scientific meetings with my parents and I've met plenty of scientists. Those I've met are all kind, thoughtful, and rational people. They are a rare breed of individual that will change their long held beliefs on any topic as long as you present a strong enough argument.

Academia is insane, but science is alive and well. My advice is this: If you really love research, just get involved. Read papers, design experiments, and pitch ideas to people. Grad students go into academia because they love learning and discovering new things. If you want to do research, just start doing research, and don't let the academic machinery get in your way.

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I've been putting off this post for days, because I really wanted to find a link to a story someone once told me. Since I can't find a reference, I'll have to assume this is an urban legend:

"Once, someone developed a test of simple but counterintuitive physics questions, and posed the test to both liberal arts Harvard professors and to 3rd grade children. The professors and the children scored about the same, but the children often admitted that they weren't sure of the answer. The professors' confidence never wavered."

A fine story, and we can all chuckle about egotistic professors that think they know everything. However, sometimes the results aren't so amusing. Here's a link describing a economic study where researchers showed that experts can easily talk people into acting against their best interests, even if the conflict of interest between the expert and the lay-person is disclosed beforehand. Link Even more worrying is the book Freakonomics that started this whole post series. In the book, Stephen Levitt shows that experts rarely act with your best interests in mind. In an economic study, he showed that real estate brokers leave their own houses on the market longer and sell them for more money than the houses the sell for others. A similar analysis was done for doctors.

I assert that the same phenomena happens in academia. I believe that professors trump up what they know, hide what they don't, and push pet projects that aren't in the public's best interest. Furthermore, I believe that this process isn't malicious, but an unfortunate side effect of a reward system based on impact and number of published papers.

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Let's talk for a moment about the economics of science in academia. When a grant gets funded, the school takes about 40% off the top in "overhead." This money is supposed to be used to keep the building maintained, keep the offices clean and well lit, but in reality any money left over is kept by the department as a slush fund. Therefore, professors who bring in money not only cost the university less, they are actually helping to fund the department. Funded professors have much more say about how money gets spent, because after all, it's kind of their money. This is why the professors who bring in the most funding usually have best lab space and the best equipment. Furthermore, professors with funding don't have to teach as many classes because they are paying their own salary. This increases their research productivity, and gives them more time to get more grants.

Grant acceptance rates are low, usually (much?) lower than 25%, and last for 2-6 years. Therefore, each professor applies for as many grants as they can. Each grant requires about 20-30 pages of text. Usually professors have 2-3 grants active at a time so they have a steady source of income between funded projects (remember that their student's and postdoc's salaries depend on this funding.)

One of the deciding factors in grant awards is how "influential" you are in your field. Influence is measured by number of academic papers published, and how many times those papers are cited. Grants also expect you to publish papers regularly, or they cut your funding. Therefore, getting published is often is very important. The better the journal, the more often your work will be seen and cited, but there is also more competition. Also, the better the journal, the more your paper is scrutinized for problems in the research. This is yet another reason that better journals are cited more often. It's yet another vicious cycle.

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For the most part, this competition between researchers is healthy for science. By pitting the experts against each other, grant agencies can measure the quality of research without being experts themselves. It keeps scientist's goals honest and their budgets reasonable. However, it does have some nasty side effects. Here are the rules of scientific publishing as I see them:

1.) Do NOT lie. Even the suggestion of making up data is enough to get you instantly fired. Furthermore, no one will hire you in science ever again, nor will they hire your students or post-docs. Professors that are known to be your friends may have a hard time getting grants in the future. The penalties are so extreme that you are basically forced to give up your profession and throw away 8 years of school. Every annecode my parents have told me about falsified research generally ends in attempted suicide.
2.) Show no weakness. Your competitors are going to be reviewing your papers and grants. Therefore, you should NEVER show any weakness in any published result. If you do show a weakness in your idea or approach, you should always follow it up with a way to fix it, no matter how impractical. You are also encouraged to manufacture false weaknesses in your science, such as "we could have increased our data resolution by 5% if we had 3 times the money." Showing weakness is the quickest way to get your grant and your publications tossed out.
3.) Be as minimally helpful as possible. After all, you've done the research so you have an advantage over other researchers trying to break into the field. By giving away all your secrets, you are loosing your competitive advantage. Now, grants wont get accepted and papers wont get published if your methods are incomplete, but you shouldn't tell everyone everything. If you work with computers, you definitely shouldn't give them the code needed to reproduce the experiment.

This writing mindset turns professors into hype machines for their own research. A good scientist is able to advertise his or her results. After years of this mindset, you start to believe your own hype and your ego inflates. You start mis-advising granting agencies, placing too high a value on your own field.

The best example of this in my mind is string theory. From an academic perspective, string theory is great. It lets you publish papers with very little funding. Also, the theory has many problems, so any attempt to fix its problems produces even more papers. I think that after years of easy publications in string theory, scientists actually started to believe their own hype. When that happened, string theory started to receive more and more funding, so even more people went into the field, which increased the hype, which led to a feedback loop. Only now are nay-sayers getting heard, now that the field has become saturated with grad students.

Tomorrow I'll post on how to find interesting research topics, and how science gets done despite all the obstacles.

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For those of you who couldn't tell, one of my new-semester resolutions is to write something thoughtful and meaningful in this blog every day. I've slacked off too much tonight, so I'll delay my next substantiative post until tomorrow.

For those of you who don't know, I had a rough first year of graduate school. My first semester, I took an RA with a professor whose research I found intriguing. Had I been a good fit for the lab, this RA my first semester would have given me a huge head start on my research. Unfortunately, I just couldn't do the programming that I was being asked to do. Towards the end of the semester, I came home crying once a week due to stress. It was then that I decided I would rather drop out of school than continue in my current situation.

First, I made some major lifestyle changes. I started using GTD to keep myself organized, and employed a whole host of other tricks to reduce stress nd improve productivity. When that didn't help nearly enough, I told that advisor that I had to leave his lab.

My second semester, I was in limbo. I wanted to change areas, but my RA had separated me from the people with whom I wanted to work. After feeling lost for a semester, I started to "court" Luke Olson, who does fascinating work in algebraic multi-grid methods.

I'm happy to report that today I had a meeting with Luke. I think he wants to take me on as his student! Finally! My grad school career has some direction!

After I finish this series on grad school, I'll start a series explaining Algebraic Multi-Grid for lay people.
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