24 Dec 2009

Yet Another 2009 Retrospective

2009 was an interesting year for me to say the least.

I was laid off from my software engineering job in January, when I thought I was safe from it. I should have known better, of course. As I've said to many people many times, though, it turned out to be good for me. I was already trying to figure out how I would balance work with school, so that event clinched the decision for me. In February, Suresh asked me if I wanted to work with him in a formal capacity, and it was done. I became a grad student.

There's a question that I've been asking myself recently, however. If I had this to do over again (that is, leave a career in software to go to grad school), would I do it? I don't know.

On one hand, I'm doing something that I feel is right. I believe that I should have done this some time ago, and had I made the right decisions, I would have been steered there. It's too easy to see the past with a present-day bias, so I'm not going to get into that too much. It's also a topic for a different post. Nevertheless, I felt like I was drowning daily and I should have been trying to do research for the last ten years. Unfortunately it took nine before I figured that out. And when I finally did, I hit the ground running, with a lot of help from Suresh. We had a paper at FWCG '09 and we submitted a larger version to SoCG '10, and we've got more ideas about where to go from here. It's been a blur of a year and my last career seems so far over the horizon.

But it's also been a hard year. It's been difficult to adjust to the drop in income, not because of the amount on the paycheck -- that part wasn't too hard to adjust to -- it's just too easy to forget where we are financially and slip back to old habits, like overspending. Our ability to buffer against costly events has been stripped down considerably.

Then there's the change in work style. I spend a lot of time alone thinking about things, especially because I work on something that no one else works on. Sometimes it's liberating but it also means that I've spent a bit too much time alone in my head. The daily ins-and-outs are a lot different too, but those are small things that I'm just getting accustomed to.

I think the thing that weighs most in my mind at times is the fact that I'm ten years behind anyone else doing this. Don't get me wrong -- it's not the "vitality" thing. In fact, I have some advantages like experience and outlook that make up for that. At first I thought that my age might make a difference in my work but I've come to realize that it doesn't. What's difficult is my personal time horizon. I don't have a house. I don't have savings to speak of. By the time I graduate, I'll have ten fewer years to put these things in order than anyone else in my class. But the thing that's killing me most? I just realized at Thanksgiving that I was at that moment just about the age my dad was when I was conceived. And I'm his last kid. I have all of grad school in front of me, and if I want to finish in a reasonable time, I can't start having kids yet.

Would I do this anyway? Probably. I can't do software development anymore, or at least regular software development. But I would recommend to anyone starting grad school late to really think hard about it before you make the final decision.

Have a happy holiday season, and be safe. Here's to 2010.

14 Sep 2009

How to write multi-part definitions in LaTeX

This post explains how to typeset multi-part definitions in LaTeX.

The absolute value function is a simple example of a two-part definition.

absolute value definition

While the "cases" environment takes care of much of this, something I found useful in this post was how to typeset an empty delimiter. It's also good tutorial on how to do this kind of stuff in general.

14 Sep 2009

Cardinality of infinite sets, part 1: four nonstandard proofs of countability

Media_httpdivisbyzerofileswordpresscom200909cwtree1png_vhoxxmnmhhejfbb

Pretty cool set of cardinality proofs. I really like proof III; it's an elegant way to show, for example, that the algebraic numbers (roots of polynomials [Edit: with rational coefficients]) are countable.

Edit: Hmm... I'm not sure I like the way that the Posterous share widget does links. The image above links to the original article, by the way.

10 Sep 2009

0.999... Revisited

After I wrote my post on 0.999... I got a couple comments about this proof:

Let X = 0.999999...
10X = 9.99999...
10X - X = 9.99999... - 0.99999...
9X = 9
X = 1
(from Parasaran's comment)

First, I want to thank everyone for commenting; it was a fun discussion and it gave me even more to think about.

Mark Reid asked what was unsatisfactory about th 9x explanation to my friend. I didn't bring up that explanation to him at the time, but I took the opportunity to ask him about it last night. That is, if he heard it and what he thought of it.  His reply was that "it uses mathematical flim-flam to prove other mathematical flim-flam." His words, not mine. :-) But I happen to agree with him.

I was in the process of preparing an overly long explanation of why one explanation is more satisfactory than the other, but I realized that ultimately, the 9x proof feels to me like one of those tricks such as "36/26 = 3/2 because you cancel the 6's", except that it works (there are tricks like this that *do* work, but for the wrong reason; I just can't recall any). That is, it feels like a trick. That happens to work. Universally. For all the right reasons.

Ultimately, the same system of numbers is being used for both my explanation and the 9x explanation, so really it's just a matter of taste. The 9x explanation just tastes bad to me, even though it's true and well-founded.

7 Sep 2009

0.999999999...

A really good friend of mine is going back to school and taking the math he needs. He was skeptical about the fact that 0.999999999... is the same as 1, and asked me to help him understand why this is. I tried a few explanations (trying to leave out the numerical analysis that's fresh in my brain; I'm in a graduate real analysis course this semester), and we finally settled on one that he found satisfactory:

If we have two numbers a < b, they have a nonzero difference b - a. This means that there is a point between them (just use the average): a < (a+b)/2 < b. But 0.999... is clearly not greater than 1 and is obviously greater than any intervening number (replacing the number's digits with 9 will always yield a greater number, as will padding 9's out to infinity if there are a finite number of digits), so there can't be a number between 0.999... and 1, so 0.999... = 1.

1 Sep 2009

Too Much Twitter

Email, news feeds, Facebook, Twitter. In that order, those are the
things that I check. Email is an important part of what I do, so that
can't go unchecked; RSS feeds are how I check up on the blogs, news,
and comics I follow, and it's a better way to do it than Twitter.
Facebook is how I keep up with my friends and family, so that's up
there with RSS feeds.

 Which leaves Twitter. It was fun while it lasted, but I just can't
seem to use it the way that I want. The people that tweet in my field
don't seem to tweet as much as the other people that I want to follow,
so they get buried under the others. Setting up groups or filters and
managing them is a pain with Twitter, even with desktop clients
(compared with Facebook, which makes it ridiculously easy; more to the
point, the groups follow you around because you set them up on FB's
servers).

 When you follow more than 100 people, you absolutely need a way to
manage them all, because the signal-to-noise ratio just gets too high.
 There's no really great way to sift through the updates for the ones
that you care about. There's search, but then you get search results
from *everyone* following twitter. Facebook lets you narrow that to
just your friends. Then there's the fact that Twitter is a gigantic
timesink. I got into this mode where I felt compelled to look at
*every* tweet from everyone I followed. I just couldn't do it. I
stopped looking at all of the updates, and just looked at a few.
Which means there's no point to following the others. Now I just look
at replies and direct messages.

 So I'm probably going to unfollow a bunch of people, and just drop in
every once in a while. It was fun for a bit, but now it's just too
much. Time to move on.

19 Aug 2009

The Little Hater

This is a pretty good video about defeating yourself in producing
creative material.

 

 Plus I like listening to Jay Smooth.

18 Aug 2009

Yellowstone Trip Day 1 (Boring Post but Has Photos)

I've got a few things lined up to blog about, but I figure that I
should post about the Yellowstone trip because we went almost two
weeks ago, so the topic is getting stale.

 My wife Aimee has been begging me to go to Yellowstone for some time.
Aimee had a week off between ending her old job and starting her new
one, and I work from home, so we'd probably drive each other nuts were
we to stay home together. We've been trying to save some money, so we
stayed at the KOA in West Yellowstone. For those who don't know, a
KOA is camping-lite. You can pitch a tent, park an RV, or get a little
cabin with just a bed. But there are amenities and food on the
grounds. And wi-fi.

 Aimee is a city girl, so while I don't mind a tent, she'd have a
pretty hard time, so we went with the cabin (or "kabin" as they're
called there; I know). It was pretty cheap for Yellowstone and
reserving the week of. Plus, we got free smores! This is the first
time that Aimee has ever had a real smore, so that was kind of fun to
watch her assemble it. I prefer to go with the ignite & extinguish
method.

 After the first night we went into town and had breakfast, which took
way too long. We got into the park, and saw the Paint Pot area first.
The parking lot was insanely crowded so I was even more annoyed at the
restaurant delay. We snagged a good spot, though, and we looked at
the stuff there, which is pretty par-for-the-course at Yellowstone:

 

 We moved on to the Old Faithful area after that, and walked around a
ton before finding the geyser. We had some time before the next
eruption, so we had some lunch. I had bison meatloaf, which was a lot
like beef meatloaf. We were seeing a lot of bikers, so we started to
wonder if the Sturgis rally was going on (it turns out that it let out
earlier that week). If I had any illusions about Sturgis being gritty
before that point, they were shattered in Yellowstone. Every biker we
saw was either old or wealthy; lots of vets, and lots of rich
Europeans.

 Old Faithful is cool the first time you see it, but if it's a return
trip, it's just not as exciting (we both saw it as kids). So we went
and looked at the other geysers and pools around Old Faithful:

 

 We moved on to West Thumb, which is the West bay of Lake Yellowstone.
It's a geyser area too, and some of the geysers are underwater; we
didn't get to see them erupt, though.

 

 We were planning to go up to Lake Village to stick our feet in the
water (or try), but a storm rolled in and we just stopped for snacks.
We had planned just to return home the next day, but there was more we
wanted to see, so we decided to see it the next day and return home
through Jackson after. More about that later.

13 Aug 2009

Posterous May Become My New Personal Blog

It turns out that it's ridiculously easy to set up Posterous.  There
are also not a whole lot of things to worry about, and they make it
simple (formatting is out, but that's not a big worry).  One of the
cool things is how it figures out how to "do the right thing" with
links and images that you put in the email (you post by emailing;
another thing that makes it super-easy).

 Well, not quite. You can attach a bunch of images to your email, and
Posterous will make a little album for you. But you can't interleave
attachments with text. You can also insert links such as Flickr photo
links, and Posterous will display the image inline with your text, but
it won't group image links into an album. Oh well.

 One of the things that I thought was cool at first was the ability to
link your Flickr account to your Posterous account, so that if you
posted images to your Posterous account, it would add them to Flickr.
It didn't seem to post all of the images correctly, and my Gmail
account has a 25 MB limit on attachments (maybe that's universal?), so
I don't think that this is a good way to update Flickr, especially if
you have several-megapixel photos like I do that you want to post to
your Flickr account. That's ok, though, because you can always put a
Flickr photo link into your post and Posterous will take care of
making it appear as an image (it does the same for YouTube links and
such too).

 You can also link your account to Facebook and Twitter, so that it
posts a link to the Posterous page that it creates. This is pretty
handy (but not unusual). The nice thing is that you can configure it
all from the Posterous side, and they give you a bunch of services
that you can link to.

 I think this will be great. I've been meaning to post more about my
personal life (for people who care), and this makes it easy. To be
honest, not having any formatting ability is kind of nice. I get
caught up in the formatting sometimes and I don't just write; plus I
can just drop media links straight in without any hassle. That makes
it kind of liberating.

10 Aug 2009

Yellowstone in Infrared

It happens that I have a digital camera modified for infrared
photography. A good friend of mine introduced me to IR photography.
Most digital cameras have a filter that sits on top of the sensor that
removes almost all of the infrared light that passes through the lens.
This is necessary because almost all camera sensors are sensitive to
near infrared light. If you remove this filter then obviously the
sensor will detect these photons, so if you place a filter on the
sensor or the end of the lens that blocks visible radiation and admits
infrared radiation, then you can take IR false-color photos. I have a
camera with a fixed lens, so I use an IR filter on the lens, which
lets me change filters to take visible shots as well.

 This is also the first time in over a year that I've brought out the
camera. I'm not a particularly good photographer, but I can set up a
basic shot. These photos aren't much different than my other work in
IR photography, but mostly I use IR to appreciate elements of the
landscape that I like. Vegetation is fairly "bright" in IR and the sky
is usually fairly dark (which also makes water dark), so you can
achieve some pretty dramatic effects.

 If you want to see what can *really* be done with IR photography,
check out Ethan Killian's IR Flickr page:

 http://www.flickr.com/photos/ethankillian/collections/72157600259382556/

 As it so happens, his F828 is mine now, and that's what I used to take
these shots. These are IR shots of the Grand Canyon of the
Yellowstone and Yellowstone River.

 

(download)

John Moeller's Space

Comp Sci PhD student, ex-software engineer, and curmudgeon. Currently attempting to construct geometric primitives for points in non-Euclidean spaces.

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