math and road trips

This summer I'm going to Wyoming for two weeks. There's a math conference at the University of Wyoming in Laramie. I had never heard of such a place (Laramie, not Wyoming), but I thought maybe it would be a nice place since Wyoming has all those national parks and such. It turns out, though, that Laramie is in the middle of nowhere. Now, I know what you're thinking. Wyoming is already in the middle of nowhere. But Laramie is in the middle of nowhere in the middle of nowhere (the latter middle of nowhere being Wyoming). This should not be confused with the middle of the middle of nowhere, since it's actually in the southeast corner of Wyoming. Luckily, Sharayah will be joining me (for the trip, not the conference). We will try to entertain ourselves while I'm not busy math-ing.

We'll be road-tripping it to get there, which should be some mixture of fun and wow-this-is-really-far-what-were-we-thinking. We've actually driven together almost as far a couple times before (just to practice [that was a joke {if you have to say it was a joke, was it still a joke?}]). We'll pass the time by reading to each other or listening to audio books (so if you know any good ones, feel free to suggest them).

We actually could have stayed in the dorms, which would have been a little funny. Sort of like going back to college, except I never had any girls in my room when I was in college. But we weren't too excited about co-ed bathrooms (or the rest of the dorm experience, really), so we managed to find a deal on priceline to stay at a Fairfield for barely more than the dorms.

I asked Sharayah what other details of the trip I should include, and she came over, hi-jacked my keyboard, and added this bit:

Another rather important detail is that since it's going to be such a long time away in the middle of summer (the prime tree growing part of the year), we're going to be bringing Mario and Luigi along with us in the back [on the top?] of the car [for sunlighting and photosynthesizing and such]. I don't really think it's a good idea, but Sharayah is the wisest of them all and she thinks it's a Go. So. To Wyoming they go!

Well, as fun as that would be (and I do regret that we'll miss two weeks of prime summer tree-growth), I wouldn't count on it. As funny as it would be to bring our pet trees on a road trip, I'm not sure they would get enough (any) sunlight in a hotel room for 2 weeks. A missed tree is better than a sad, sunless tree.

Speaking of maths, it's turned out to be quite difficult to prove Brouwer's conjecture on the Laplacian eigenvalues of graphs for k = 3 (that is, that the sum of the largest 3 eigenvalues of the Laplacian matrix of any graph is at most the number of edges of the graph plus 6). I've been proving it for case after case of graphs for weeks, but it seems like it's never-ending. There doesn't seem to be a nice proof that covers many cases at the same time, so I have to keep breaking it down into more and more sub-cases until it can finally be done. That's no problem except the more you break it down, the more cases you have to take care of and the longer it takes. Still, with only two exceptions, I haven't come up to a case for which I couldn't prove the conjecture eventually. For the record, the problem cases are when you take a subgraph of the complete bipartite graph with 3 vertices in one partition and the rest of the vertices in the other, then add either 1 or 2 edges among the vertices in the partition of 3 (if you add no edges or all 3 edges, I can prove it). So, if you could solve that for me, that'd be great. Other than those 2, I've proved it for any graphs with matching numbers 1, 2, or 3, and many of the cases with matching number 4. I only have to consider graphs with matching number at most 5, since a graph with containing 6 independent edges has a subgraph (namely, those 6 edges) whose largest 3 eigenvalues sum to 6, which is the number of edges in that subgraph, and we can show that if a counterexample to Brouwer's conjecture exists, then one exists such that that doesn't happen for any of its subgraphs.

Ok, sorry, had to get that out of my system. I think that's enough for now.

be my escape


spring tidings

It's so easy to miss the little things in life. The moments. The whispers. The unfurlings.

The small things are important.

I find that some of the most smiling-inspiring moments come when I just... stop. Stop hurrying. Stop worrying. Stop drifting.

Did you know you can smell rain? You can. It is a delicious smell. It's both calming and unbelievably exciting. And when the rain comes, don't run inside. Dance. Twirl. Hands outstretched, face upturned. Peace.

Did you know tiny little Asian girls can't help but sing whimsically nonsensical songs to themselves? They cannot help it*. The songs need not be intelligible, witty, coherent, or in tune. Oblivious-to-the-world wiggling/dancing is likely to be going on simultaneously. Joy.

Did you know that in the span of 4 days, this transformation takes place?

I had no idea. New life takes my breath away. Truly the most awe-inspiring things in life are God-made. Fascination.

It's a shame to let life get cluttered by stress, frustrations, or fears. There is so much goodness to drink in and enjoy. Whenever I let a case of the stomach jumblies [yes, that is a word] start to jumbly up the rest of me, I try to think of the small things. Those things that bring peace, joy, and just utter fascination. Focus on the goodness in the small things and He who is forever good will take care of the big stuff.

With all that said, it's SPRING. Thus, our quarterly blog renovation! Like? Did you have any idea that all those little things in the center of this kind of flower [vague terminology because I sadly have zero knowledge about flower anatomy] had such a distinct pentagon shape?! That little discovery thrilled me for a full 5 minutes. I'm telling you, the little things seriously make my day.

Jason and I have been trying to go to Longwood Gardens each weekend so we can see the transformation of all the buddings into flowerlings [like the one on our background right now!]. So far, I haven't tired of visiting because it really feels like a new place each time we go. They have benches everywhere, so you can even just bring some books and read in super peaceful surroundings. One thing that I really like is that there isn't really a big bunching of benches in one area. Each bench is nicely separated from other benches so you're never sitting there awkwardly avoiding glances with other bench-sitters. Many of the benches are set off in semi-secluded places that allow for more nature immersion and less people annoyance. Ideal.

Spring is here. Smile.

And God saw everything that He had made, and, behold, it was very good!

*Based on my study of at least 3 random Asian girls under the age of 4.

This pretty much sums up "little things" and "spring." You're welcome.


oh! the free moneys!

Yep, that's right, folks. Free moneys.

I like most things free, and so Free Money ranks right up there under Free Four-legged Furriness and just barely edging out Free Lettuce Wraps. Oh! the non-free things you can do with free money! Special date nights, spur-of-the-moment book purchases, kitchen avoidance [i.e. dinner out], or even just that neato condiment gun that you know you can't possibly justify in your household budget [Sadly, no, I have not yet used my free moneys for such a glorious purchase... yet. Just kidding. Kinda. No, really. Seriously. I think. Hey, don't judge my desires for whimsical awesomeness! No worries, I generally refrain.] Since the money is free, it completely frees me from feeling guilty about using it in a semi-irresponsible fashion [definition of irresponsible:  If the answer to "Can we justify this in our month's budget?" is "Duh, of course not."]. Free money = awesome.

Just this year alone, not even 3.5 months so far, I've earned over $100 in Amazon gift cards and $75 straight to my Paypal account from one particular Magic Well of Free Money. I know that may not sound like much, but it's $175 I wouldn't have had otherwise, so I'm pleased. At this pretty dependable rate, by the time Christmas rolls around [the time of year when we inevitably discover that our budgeted gift money is sadly not enough to buy Super Awesome Gifts for all the fine peoples in the world], I should have accumulated a small pile of Hooray Money, even taking into account the guilt-free Heres and Theres [as outlined above] that may pop up along the way.

So with all of these rambly sentences out of the way, I suppose I should get to the important part of this whole post:  How does one find the tiny pot of legitimate currency at the end of the gigantic rainbow known as the interwebs? Answer:  Swagbucks. [And yes, that is a shameless (almost) referral link.]

I'm not generally one to do the whole referral thing for, really, anything, but this one time I shall make an exception simply because... well, Swagbucks has actually been worth it for me*. And if someone by chance happens upon this post and happens to like what they read and happens to also want Free Moneys, then by golly why not sign up under my name and reward my strange writings with $10?

Ok. So Swagbucks. In a nutshell, they reward various activities that you do on the web like searching, watching ads, signing up for free offers, or shopping online with points that you can cash in for gift cards [Amazon, Wal-Mart, Paypal, etc.]. They also give away points for playing games, finding Swagbuck codes, meeting daily point goals, and a bunch of other random things. The beauty of it is that most of the "earning" that I do just requires idle activity [oxymoron?], things that don't necessarily require being in your browser's focus or your constant attention.

Why I love Swagbucks so much is that it works in perfectly with my job as a transcriptionist. I sit at my computer all day typing horrendously structured sentences from ESL doctors [i.e. "The patient's both eyes is diagnosed as cataracts subsequently to caregiver." (Say hwhaat?)], and all I have to do to earn a little extra cash on the side is keep another browser open with SBTV playing in the background or search a few of my medical terms using Swagbucks' search engine. Easy peas [yes, peas].

There's a learning curve to it all, obviously. When I first started, I made about 20 points a day. Nowadays, I generally make at least 120. [Each point is about 1 cent.] Many people who use Swagbucks would still consider 120 a bad day, as they can often get well above that depending, but I'm happy with it at the moment. Just as a warning, it may start off a bit slow until you find out the most efficient point-earning method for yourself.

I could get super detailed about how to get the most money for the least amount of effort, but I will spare you. If you want more details, feel free to ask away. Instead, here's a brief bullet-pointed (!) list outlining a couple of helpful tips:

  • Use a dummy email address, maybe one that you use for junk mail or, better yet, even one designated solely for Swagbucks. 
  • There are often points to earn by allowing Facebook apps for various companies/products and so a dummy Facebook account is advisable. The name on the account doesn't matter as long as you use the same email address you used for your Swagbucks account [another reason to use a junk email as mentioned above].
  • Speaking of Facebook, the Swagbucks' Facebook page is pretty helpful for knowing when codes are out, what special offers or surveys are crediting, or just when people are getting wins by searching [which is a good indication that you could potentially get a nice search win].
  • Try not to get caught up in making as many points as you can because, let's be realistic, it is just a few cents here and a few cents there [here a cent, there a cent, everywhere a cent cent!]. Some people let that one video that didn't give them their 2 cents ruin their entire mood/day/life. Not worth it, folks. You'll eventually learn what guarantees points, what will hopefully get points, and what to avoid due to it being a poor use of time and/or good mood.
  • It's definitely worth getting the daily point goals each day [consecutively is best!] as there are 1-week, 2-week, 3-week, and monthly completion goals that, at the most, guarantees an extra $5 each month. 

Anywho, this is long enough. I get carried away typing. My apologies. 

Go get some.

*My meager earnings may or may not show how low my standards are for something being "worth it." :/ To each his own! 

He's doing the free money dance. Elephants do it best.


here is a post.

Well. I guess I owe you, the reader, aka future me, an apology. It has been too long since I blogged. I am without excuse.

You may recall that I play soccer on a rather unlucky (and also not very good?) soccer team. As a whole we've been getting better but in the leagues we've been playing in we've usually been outmatched. This winter in the indoor league we seemed close to several teams. We went into halftime winning as often as not. Somehow, though, we always ended up losing. That's the unlucky part. Anyway we just started a new season in another indoor league, and I think it's more on par with us. We won our first game 7-0. We didn't play an amazing game, but we played pretty solidly most of the time. It's weird, the team we beat was probably as good as 3 or 4 teams who we've lost to before. Like I said, we're often winning at halftime. For whatever reason, in this game we never fell apart. We never even lapsed long enough for them to score (though much of that is due to our beastly goalie, who is typically the best goalie in whatever league we happen to be playing in. which makes it that much worse for the rest of us when we lose). Anyway, it felt good to finally follow through with a win after a whole season of almost winning almost every game. Hopefully we can be competitive against more of the teams in that league.

Spring is here and we're starting to play tennis again. And by that I mean we played yesterday and today. Shawn played with us yesterday. None of us are any good (though if I recall, Shawn was pretty good back in the day), but it's still pretty fun for some reason. If Sharayah mentions tennis in her next post she will tell you she's better than us, but we're still being lenient with her on the rules, so don't let her fool you. We're big and strong and aren't getting creamed by a beginner little girl. Anyway, hopefully we'll find the time to get plenty of good tennising in for the next few months while it's warm. Then next summer we'll probably hit the pro circuit.

Maths have been pretty tough lately. I'm still working in spectral graph theory, though I've been spending most of my time on a new problem lately. I could try to describe it, but it would just be more gibberish than what I already said. Anyway it's been painstakingly slow, trying to chip away at case after case trying to prove this big theorem. The worst is when you know something is true, you're completely sure, but you can't prove it. Ugh. I'll just keep plugging along.

Our little trees are starting to bud again. We moved them to bigger pots just in time. These new ones are pretty big and should last a few years. Now that they're in the giant pots, they look tiny again, like when we got them last year.

Sharayah has decided to do a silly experiment. I guess she was curious about whether this lotion we have would actually do anything, so she's going to put lotion only on her left leg each day for a week or two and see if she can tell the difference at the end. I don't know how long it should be so that it's a valid test. I'm not actually sure lotion does anything. I guess we'll find out and let you know.