ZOOMZOOM
This is fantastic. That’s all you need to know.
(4:00 – 5:15, especially.)
Niiiiiiiiice
That opening is beautiful. I really like this song. It’s my second favorite Passion Pit song.
(Can you guess which is my favorite?)
TWSB: The Problem with Pentagons
Well this is cool. Apparently, a group of mathematicians have recently found a new type of pentagon that can tile the plane—meaning that it can cover the plane leaving no gaps and having no overlaps. It is the 15th type of pentagon known to be able to tile the plane and the first discovered in 30 years.
Apparently searching for tiling pentagons has been a thing for about a century now. Karl Reinhardt, back in 1918, discovered five classes of pentagons that tile the plane. These five were considered all the possible tiling pentagons until 1968, when three more were found. The list continued to grow until about 30 years ago, when it stalled at 14 types of pentagons. Until now!
The discovery was made by Casey Mann, Jennifer McLoud, and David Von Derau. The three, working at the University of Washington Bothell, used a computer to search through a finite set of possibilities.
Why so much interest in tiling pentagons? Well, it turns out that pentagons are the only one of the “-gons” that isn’t completely understood. For example, all triangles and quadrilaterals have been classified as being able to tile the plane, exactly three types of (convex) hexagons tile the plane, and no other –gon is able to tile the plane. But pentagons haven’t been fully classified yet.
So the research must press on! There may end up being more tilings that are discovered, but for now, have a picture of the 15 pentagon shapes known to tile the plane (with the most recent one in the bottom right corner) (picture from article linked above):
Book Review: One Flew Over the Cuckoo’s Nest (Kesey)
BOOK REVIEWWWWWWW~!@!#!@$!#$!\!!!!
(I’m hyper.)
Have I read this before: Yes! High school, I think. 10th grade?
Review: I think I was a little too young to really appreciate this the first time I read it. I like the characters and I like the progression of McMurphy’s antagonism toward Nurse Ratched. I also like how once Chief finally started talking, all the patients basically just took it in stride. It’s a really good book—one of those “classics” that I actually think everyone should.
Favorite part: The fishing trip is pretty great. And it sounds bad to say this, but I also really liked the electroshock therapy part. Not because it was happening, of course, but because I really like the way Kesey shows what the therapy does to Chief’s thought processes while it’s underway. It’s pretty scary.
Rating: 7.5/10
Primin’
HELLOOOOOOO!
So I’ve edited 45 more (single-spaced) pages of Prime since I started working on it about a month ago. That may not sound like much, but it’s 45 more pages than I’ve edited in the past year and a half. (Blame Nate, he’s giving me the motivation to write/edit.)
So.
I seriously doubt I’m going to ever do anything with it (mainly because it will still be crap even after the 30th edit or whatever), but it’s nice to be working on it again. As crappy as Prime is, it’s my baby and I love it.
Are You There, God? It’s Me, Non-Normality
I’m here to talk to you today about nonparametric statistics. What are nonparametric statistics, you ask? Well, they’re a collection of statistical tests/procedures that we can use when data do not satisfy the assumptions that need to be met in order for conventional tests/procedures to be carried out. For example, suppose Test A requires that the data are normally distributed. You gather data of interest and find that they are not normally distributed. Thus, Test A should not be used because its results might be inaccurate or maybe even uninterpretable with these non-normal data. Instead, you must use a test for which normality is not a requirement. If such a test exists—say, maybe it’s Test B—then Test B may be considered a nonparametric test. It can be used in place of Test A if Test A’s assumptions are not met. Cool, huh?
Let’s look at a few examples, because I haven’t pressed any statistics on you guys in a while.
Example 1: Comparing Different Treatments
Scenario: You are a plant scientist. You have a specific type of plant and you want to see to what extent lighting affects this plant’s growth. You have three lighting conditions: sunlight, fluorescent light, and red light. Basically, you want to see if there is a significant difference in the amount of growth for plants grown in these three different conditions.
Parametric test: Analysis of variance (ANOVA) seems appropriate here; you can basically assess the differences in growth by comparing the mean growths for each of the three conditions.
Nonparametric test: For ANOVA to be accurate at all, the data need to be normally distributed. Suppose your data aren’t! What do you do instead? A Kruskal-Wallis Test! A Kruskal-Wallis is basically an ANOVA done on the ranked data rather than on the raw data and allows you to compare the groups without needing to meet the assumption of normality.
Example 2: Correlation
Correlation, as I’m sure you’re all aware, is a measure of association. Basically, if you’ve got variables X and Y, correlation is a measure of how much X changes in relation to the changes in Y (or vice-versa). A correlation of 1 suggests that there is a perfect increasing relationship; a correlation of -1 suggests that there is a perfect decreasing relationship.
Scenario: You have a bunch of measurements on two variables. Drug measures the amount of a medicine in a patient’s system. Response measures the amount of some disease marker in the same patient. You want to see if there’s a relationship between the amount of medicine in a patient’s system and the amount of the disease marker present in a patient’s system.
Parametric test: the “usual” correlation, the Pearson Product-Moment Correlation, seems appropriate.
Nonparametric test: The key with the “usual” measure of correlation is that it simply measures the degree of linear association between your variables. If you suspect, for whatever reason, that the relationship between Drug and Response is anything but linear, it’s a good idea to use the Spearman Rank Correlation Coefficient, which is sensitive to non-linear monotonic relationships between variables.
Here, I wanna give you an example of this last one, ‘cause it’s cool. Just as a dumb example, let your sample size be obscenely small (n = 10). Here are your data:
drug response 1 1 2 16 3 81 4 256 5 625 6 1296 7 2401 8 4096 9 6561 10 10000
Notice two things: first, if we plot these two variables, their relationship is clearly nonlinear.
Second, you’ll notice that there is a perfect relationship between drug and response, it’s just not linear. Specifically, Response is just the corresponding Drug value raised to the 4th power, meaning that Response is a perfect monotonic function of Drug! We can easily calculate both Pearson’s and Spearman’s correlations here to see what they’ll say:
Pearson correlation: 0.882
Spearman correlation: 1
Spearman’s picks up on the perfect relationship, but Pearson’s does not! Why? Because it’s not a linear relationship! Pretty cool, huh?
THIS IS WHY YOU ALWAYS PLOT YOUR DATA, DAMMIT.
Side note: Pearson feuded with Spearman over his “adaptation” of Pearson’s beloved correlation coefficient and actually brought the issue in front of the Royal Society for consideration. Oh, you statisticians.
Calgary Adventures
So guess who walked 20.5 miles today?
WE DID!
We went down to the southern end of the C-Train because we wanted to see just how far south we could walk in one stretch. Turns out it’s pretty far. This is (approximately) our route. That Dairy Queen was our destination.
YAY! I’ll be doing my “one year in Calgary” walking stats in about a month, so stay tuned!
Also, this. You can buy individual colors/flavors of candy. Do you know how dangerous that is?
ALL APPLE JOLLY RANCHERS ALL THE TIME
NASCAR Racing with Neil Armstrong
Alright, analyze this dream:
So I’m outside this huge NASA building—like where they store the shuttles—and I’m hanging out with some guy who I’m apparently friends with in the dream but who I can’t really see. We’re loitering around outside for a little while and then Neil Armstrong comes out and tells us to go away because he’s going to get into trouble if we get caught.
Other Guy suddenly has a spray can in his hand and we’re both trying to convince Neil to graffiti the outside of the building. He keeps refusing and we keep insisting, to the point where we’re calling him a chicken and a coward for not joining in on our fun.
Finally, when it’s clear he won’t graffiti, Other Guy says, “Okay, fine, if you won’t play with us out here, we’re going to have a drag race!” He points behind him toward a huge NASCAR-like track with a bunch of drag racers on it. In the dream, we know that we’re not going to drag race with the cars but are going to do like an actual NASCAR race with them.
Neil protests this, too, but eventually gives in. He’s afraid of the racecars, though, because he’s never been in one. “This is not like landing on the moon,” he says as we drag him over to the track. “This is complicated.” So Other Guy and I agree to do a test run together in the same car while Neil watches from the sidelines to see how it’s done.
We get in one of the cars and Other Guy’s saying, “See, now let this row of cars pass you first so that it doesn’t look like you’re cheating. The last thing you want is for it to look like you’re cheating. You don’t want to be first.” He was saying this very emphatically and with a lot of emphasis on the words cheating and first. All the while he kept looking back at Neil and gripping the steering wheel really tightly.
Then I woke up.
Thoughts? I wonder if Other Guy was Buzz Aldrin and he was upset about Neil Armstrong being first on the moon instead of him. Maybe he thinks Neil cheated his way down the ladder somehow.
Weird.
McGee and Me! (Blame YouTube)
As many of you know, I went to a Christian elementary school. We had an hour set aside for “religion” study every day, went to church every Friday morning, and had Bible-themed Christmas plays every December and Bible-themed spring plays every April or so.
Every once and awhile, we’d have an event (a BBQ, a “party”, a something-or-other) that required us to be at school during non-regular hours. To entertain us (i.e., to keep us all in the same room), our teacher or principal would opt to play a TV show or movie on our little TV-on-a-roller-cart. Being a Christian school, we never got to watch anything but—you guessed it—Christian-themed shows! The most popular one for us was Veggies Tales, but I was never really into them at the time. The one that I enjoyed (though “enjoyed” is a relative term) was called McGee and Me!
(Source)
It’s basically about this kid, Nick, who has a drawing of his come to life and together the two of them get into all sorts of “you can get out of this by being a good Christian” mishaps. Actually, they were mishaps you could get out of by just being a good person, but they made sure to add “God” and “Jesus” in there because you can’t be a good person without those two guys in your life, right?
Example: the episode “Beauty in the Least” is about Nick’s Romanian pen pal coming to visit unexpectedly during Thanksgiving. Romanian Pen Pal is, according to Nick, super annoying and plan-ruining when he’s not in pen-pal-letter form, so Nick is a jerk to him and the poor dude gets upset (understandably). But through the guidance of God and the “love thy neighbor as thyself” idea, Nick realizes that he’s been a jerk and does his best to make it up to Romanian Pen Pal and his father. So like I said, it’s basically a “be a good person, dammit” show with a Christian bend. I always enjoyed it, though. It was better than Veggie Tales.
Here, have a link to the first part of this episode on YouTube, in case you were a ‘90s Christian kid and you want to nostalgia yourself to death just like I did tonight. That’s the whole reason for this post, haha.
You’re welcome.
This Week’s Science Blog is Cheesy
Always a good topic, huh?
In the Scientific American article linked above, author Steve Mirsky talks about how a decades-old Swiss genetic experiment on flies is related to a more current set of experiments regarding what causes the formation and development of the eyes (or holes) in Emmental (or Swiss) cheese.
In the fly experiment, geneticists managed to get a fly to grow a ton of eyes all over its body by isolating and manipulating a few of the fly’s genes. More recently, 13 researchers at three different Swiss research facilities have figured out the link between the genetic fiddling needed to create the extra fly eyes and the genetic fiddling needed to regulate the size and quantity of holes in Swiss cheese.
The study, published as “Mechanism and Control of the Eye Formation in Cheese,” was published in the International Dairy Journal and contains a discussion on why eye/hole regulation is important.
“The size of the eyes of first-quality cheese should be between the size of a cherry … and a walnut,” says the journal article. However, different cheese-lovers prefer different sizes (and quantities) of eyes. “Italian consumers prefer Emmental cheese with walnut-sized eyes, whereas commercial manufacturers of sliced cheeses ask for cheese with smaller eyes and higher eye numbers.”
In making cheese, bacteria is key. A product of the bacteria is carbon dioxide, which forces the holes to expand to any given size, but until this study, it was unknown what made the holes themselves begin to form in the first place. Turns out, the process is analogous to the process of how a raindrop forms around a particle (a “cloud condensation nuclei”) in the vapor-saturated air. For the cheese, a little particle can act as an eye nucleus, around which the round hole begins to form.
In the study, the researchers chose hay dust as their particles of choice and found, through varying the amount of dust the young Swiss cheese was exposed to, that they could actually control the number and size of the eyes.
So they can basically do cloud seeding, but with cheese. Cheese seeding? Cheeding?
Anyway. Pretty cool!
Book Review: The Caine Mutiny (Wouk)
Alright readers, sit your butts down because today we’re reviewing Herman Wouk’s The Caine Mutiny. Spoilers (maybe?) ahead!
Have I read this before: Many times! This is my favorite book, y’all.
Review: Dude. Dude. I love this book. I love Captain Queeg. I’m pretty sure he’s my favorite literary character, apart from maaaaaaaaybe Jay Gatsby. I like the other characters in this book too, especially Maryk. While the plot may take a bit to start up (i.e., the first several chapters are a bit slow), I think the rather gradual introduction of the characters and the situation and Willie himself really help to amplify Queeg’s apparent craziness up to during the eventual mutiny. It also helped to show, once the trial for Maryk was underway, how the men who were against Queeg very quickly felt the ridiculousness of their claims of Queeg’s insanity were once they were all out of danger. The timing and tenseness of the book were really well done, in other words.
AND QUEEG. QUEEG IS GREAT.
Favorite part: The whole thing. But specifically:
- Willie not knowing any of the terminology/slang when he first got on the Caine.
“‘Sir, it was my fault,’ spoke up the boatswain’s mate. He began an alibi which sounded to Willie like this: ‘The port bandersnatch got fouled in the starboard rath when we tried to galumph the cutting cable so as not to trip the snozzle again. I had to unshackle the doppleganger and bend on two snarks instead so we could launch in a hurry.’” - Queeg obsessing about all the wrong things at all the wrong times.
- The way the crew, once they were sick of Queeg, decided to basically make it look like they were responding to his requests/demands when in reality they were being ignored everywhere the captain wasn’t.
“The crew with its vast cunning had already charted most of the habits and pathways of the captain. He was moving now in a curious little circle of compliance that followed him like a spotlight, extending to the range of his eyes and ears; beyond that, the Caine remained the old Caine.” - THE STRAWBERRIES
- The speech/rant Greenwald gives Keefer and Maryk near the end. It gives the lawyer (Greenwald) a lot of depth in very few pages. I like it.
Rating: 10/10
I AM ROOMBA HERE ME ROAR
I’m to the point with my walking where any walk shorter than 8 or 9 miles feels like absolutely nothing and, if that’s all the distance I go in a day, it feels like I’m slacking off and not walking enough.
Which is a pretty stupid thing to think, since before we moved to the new place I was walking about 7 miles a day (four times a week at least) going to/from campus. Now I’m going 10+ about four days a week, plus at least 5 or so the remaining 3 days of the week. So I’m obviously not walking less, but it really feels like I am. It’s like this:
- 15+ miles: Good walk!
- 12 – 15 miles: Decent walk!
- 9 – 12: Yeah, sure, okay.
- 8 – 9: At least you moved a little. Sort of.
- < 7: GO DIE IN A CORNER YOU LAZY CRAP
I’m sure my mind will return to realistically looking at mileage once next semester starts up and I’m actually busy (especially with thesis stuff), but right now, this is how it is.
At least I’m putting good mileage on these shoes!
COMPY
I got a new computer. BEHOLD!
His official name is BIG COMPY THE REDUX 2015 EDITION XXL MEGA BIG AWESOME-TRON, but I just call him Big Compy for short.
This is actually the first time I’ve ever bought a desktop computer for myself. Old Big Compy was my mom’s from like 2008 or so; it somehow survived about 8 moves around the continent before crapping out on me, forcing me to get the new guy.
But this is also the second computer I’ve bought this year, which is a little stressful (recall I had to replace my laptop back in February).
Actually, this whole year has been about most of my stuff finally breaking/falling apart/becoming unusable. Hopefully my iPod will make it to the end!
WOO!
Hiking Time!
Monday is a holiday up here in Alberta, so yesterday Nate and I drove down to his parents’ place in Crowsnest Pass and today went with them to Waterton Lakes National Park for some hiking! It was hot, but fun. 11-ish miles. Have some pics!
Yay. This is nice.
This is the guy who does the United State of Pop mashups at the end of the year. His summer ones are more hit-and-miss than the end of the year ones, but this one’s pretty good.
MOON THE WALK
WALK THE MOON is now one of my favorite bands, I think.
I discovered them—as I’m sure most people did—through their awesome song Shut Up and Dance. However, they’ve got other songs that, in my opinion, are just as good and maybe even better. Here, have some!
Work This Body (I love this song, holy crap)
Oops
*hangs head in shame over the long period between blog updates*
*attempts to justify lack of updates with flimsy excuses*
*half-heartedly promises to update more frequently*
*offers Ridin’ Ritz Man as recompense for being a crappy blogger*
*disappears into the night*
Zyzzyva
Tonight I was bored so I Photoshopped the hell out of some of my art. Got some cool results.
Here’s “Chameleon” crystallized.
“Fractured Fresnel” with color halftone.
“Persistent Petals” with all sorts of things.
“Data” extruded twice (this is my favorite).
“Eyes of the Sphere” extruded once.
WOO!
Petition for General Mills to make a cereal called “Bernoulli-O’s”
Happy birthday, Johann Bernoulli!
Johnann is one of the eight math whizzes of the Bernoullis, a Swiss family that somehow kept birthing amazing mathematicians into the world over a few generations.
This particular Bernoulli spent a lot of his time studying (and teaching!) infinitesimal calculus way back when calculus was at its very beginnings. He tutored both L’Hopital and Euler in math and was specifically thanked in the very first calculus textbook (written by L’Hopital). He also worked with his brother Jakob on a lot of problems, though there was a good deal of friction and the two often fought.
Johann is extra badass, though, because he was a good friend of LEIBNIZ and a student of his calculus. He was also one of the few who took Leibniz’ side and defended him when the whole Newton-Leibniz calculus controversy began. He actually took several problems and showed that they could be solved using Leibniz’ methods, but not Newton’s. A pretty cool guy, if you ask me.
I DON’T HAVE A TITLE ALSKFAJLFKASDJG5SGA
I love living in Calgary, yo.
I mean, I loved Vancouver, but that was different. I loved the city. It was my escape from everything else (mostly school and the fact that I had zero friends and the fact that I was so, so sad there). Here, I not only love the city but I love school and I (sort of) have friends and I have Nate and I have happiness!
It’s big enough population-wise that there’s the feeling of anonymity, but it’s big enough area-wise that there are good chunks of the city that don’t feel “big city” at all, which is nice for walking.
I also feel a weird connection with Calgary. It’s probably because the 1988 Olympics were held here just a few days after I was born. Which is a weird reason to feel connected to a city, but what are you gonna do.
Finally, everything that’s happened up here so far has made this the most accurate fortune cookie fortune I’ve ever received:
Inside Out!
Nate and I went to see Inside Out today. It was very enjoyable! When I first saw the previews back in May (when we went to see Age of Ultron), I didn’t think it would be a movie that was up to Pixar’s usual standards, but the reviews are right: it’s a very good movie. I really like what they did with the geography of Riley’s brain and how it all fit together at various points in the story.
Also, the Bing-Bong part (you know what I’m talking about if you’ve seen the movie) was really freaking sad.
But yeah, it’s definitely worth seeing in my opinion. While I still haven’t seen some of Pixar’s films (Up and WALL-E are the big ones), of the ones I’ve seen, Inside Out ranks pretty high up there. Not Toy Story high, but high.
[insert nonsensical keyboard mash here]
It’s time for the not-quite-semi-yearly “Claudia feels materialistic” blog post!
(Note: I don’t actually need any of this, I just like to look at pretty things.)
Ready? GO!
iPhone 5s. I’m on the fence about getting a smart phone (not any time soon; when I can afford it, that is). I want one because they’re cool and useful, but I don’t want one because Claudia + constant access to the internet = disaster AND because I would probably damage it somehow within a month or so of getting it. Even so, I’m keeping my eye on the iPhone 5s as an option. I want the iPhone 4 because I love the shape, but no one sells them anymore and the software probably doesn’t even update anymore, either (that’s happening with my 2012 iPod, at least). So if I DO get a smart phone, the iPhone 5s is where it’s at.
The new iPod Touch. I don’t need one (and hopefully won’t for a long while), but I’ve had my current iPod since February 2012. Probabilistically, with all the walking I do (I use it as a pedometer and keep it in my back pocket), it’s going to get broken one of these days. Which would be sad. But if/when that happens, I’d like to get one of the new models. Probably in silver (since I’d just be covering it in a case, anyway). Of course, if I get an iPhone before that, I’d probably just use that as my pedometer, though I’d be really paranoid about breaking it.
I guess the one thing on this list I kind of need is a new desktop computer. Mine died like a month ago—which is okay, considering it survived like 7 moves around the continent and is old enough to still have Vista on it—but I need a new one. Preferably one that can run Fallout 4 once it comes out.
Rainbow socks! My old ones got holey a long time ago and I need replacements.
These two books on the history of statistics.
The end!
BloggiBlog
Okay, so I know we’re still like 9 months away from it, but I’m already excited about my “10 years of blogging” thing next May. That’s a decade of blogging, dudes. That’s a long time.
Here are a few things I plan on doing for the big anniversary:
- Yearly stats: which years had the most words, which years had the highest/lowest GFI scores, all that stuff.
- Category stats: which categories had the most posts, which had the least, which had the most words, which had the least, etc.
- Title stuff! I want to see how many titles I’ve repeated (and how many times) and do a list of my favorites.
- Tag stuff! When I first started using the tags I was super serious about it, but that’s quickly devolved into “can I fit a stupid joke or two in the tags of this post?”
- Graphs. THERE WILL BE GRAPHS.
And probably a bunch of other things I’ve forgotten to include here. Sorry, I started this post and then got distracted reading about Johann Bernoulli, then came back and forgot what else I was going to add to this list.
Claudia: Master Blogger.
Well…
Things to do in Calgary:
- See the Calgary Tower
- Watch a Flames game
- Go to Cross Iron Mills Mall
- Seek shelter from tornadoes
Yeah.
Apparently parts of the city were under tornado warnings this afternoon. Check out some of these pictures.
Menacing, huh? Aaaaaaaaaaaand then it was gone.
Oh, Canada.
(Sources for pics: 1, 2, 3, and 4)
Why I Walk
As you all know, walking is kind of my thing. Which is funny if you think about it, because I used to think of walking as a boring waste of time. Why not just take a car? What kind of weirdo would go walking for fun in their spare time? Why do people waste their lives doing something so dull??
Obviously my opinion has changed. And since I’ve been doing this “walking for fun” thing since late 2010, I figured it’s about time I actually explained why I do it and why it’s enjoyable for me.
The whole reason I started walking in the first place was for stress relief. In August 2010 I was just starting my second year of grad school at UBC and I was already obscenely stressed out about it. It got to the point where, one weekend, I was so anxious that I felt like I just needed to get out of my apartment. So I put my shoes on, grabbed my keys, and just went for a very brief walk. I didn’t have any sort of pedometer with me on that walk, so I can only guess that the walk was likely no longer than a mile tops, but it almost instantly calmed me down and made me forget all my school-related nonsense for the half hour or so I was out there.
Knowing that I’d likely want to go do this again, I dug out a basic pedometer I’d gotten from somewhere and just put it next to my shoes. On my next walk, which was within the same week as the first, I started tracking my steps.
Well, because I’m me, the “walking for relaxation” very quickly became the “walking so I can beat my previous step count,” which was surprisingly just as relaxing as simply walking for walking’s sake. So I kept at it. By that point I’d bought an iPod Nano ‘cause my old one finally died, and it had a built-in pedometer feature that I started using instead of the clip-onto-your-waistband pedometer. Once I bought my iPod Touch, I downloaded the pedometer app I still use today and was able to keep even better track of my walking stats.
Over the next horrible, horrible 8 months of grad school, walking was really the only thing that kept me from jumping off a bridge. Unlike nowadays, when I’ll gladly walk 7+ miles on any given day, I pretty much resigned my walking to Saturdays while I was in Vancouver (though that was mainly due to the fact that it rained about 5 out of the 7 weekdays in that freaking city). But my Saturday walks took me all around Vancouver and were the only things that would get my mind off of my impending thesis and all the other hellish nonsense that second grad school year brought me.
And I’ve been walking ever since. While I’ve never been nearly as stressed as I was in that last year of grad school, walking has consistently been the thing that’s calmed me down and given me time to just think. I always feel like my mind clears up and just works better when I’m out walking and for hours after. It allows me to explore cities (and Moscow) and to get a better grasp on directions/knowing where I am—which is super helpful, because I have the fantastic ability to get lost even with a map in my hands.
And the stats. I freely admit that I would not walk as often as I do now if I didn’t have a way to keep track of my steps/mileage/calories burned/walking time. I really, really like keeping track of things like that. It’s a nice feeling to me to be out on a 4 hour walk, for example, knowing that every step and every second is being counted and recorded and can be referenced and explored later. I just love that. Plus I can do analyses on all the old walks, which is the BEST FREAKING PART OF IT ALL.
So yeah. What began as a desperate attempt at regulating the stress of grad school has evolved into something that is very much a part of me now. I walk because it’s just what I do, and I can’t see myself wanting to cut down on it or stop any time soon.
So yay!
Eigenblogger 