All Righty Now...

Yesterday's post was a possibly on the side of over-reaction.  I still meant what I said and I'm going to be writing a ton of letters to the senate, the house, and there will likely be a note sent to President Obama in the near future.  But it's late and I have to get up early and run tomorrow because right after work I'm leaving to go back to my parents' house for the long weekend!  I'll probably be a bit like this tomorrow morning around 5:

I also want to leave a question that I wonder a lot about: why aren't there more vigilantes?  Whenever I think about it, I am surprised that we don't hear of more vigilantes attempting to take the law into their own hands.  I legitimately wonder about this, but I am also being a little lazy and I'm in the .gif mood so I'll stop writing and get right to the real point of this paragraph:

Justice-Tuna Cassarole

-Lane

Lane Thornton is Burning (Part 1 of 535)

I am luckier than most people.  Most people are sad about how much money they make until pay-day, when they are happy.  I am happy about how much money I make most days until pay-day, when I get incredibly angry about how much taxes I pay.  I have decided that instead of accepting this as inevitable, I will continue to be angry every time I pay taxes and to help remedy the situation, I will write a letter to a congressional representative.  This time, I wrote to Senator Bernie Sanders (I, VT) for two reasons: I am originally from Vermont and I have written to him before.  The text of my letter is below:


"Dear Senator Sanders:

A bit over four years ago, I wrote a letter to your office over concerns that money was being spent on helping Vermont students attend college that wasn't available to me because I dreamed of studying something not offered by any institution in Vermont.  Instead of addressing my concern, I received a form letter pointing me to a website with some scholarship applications on it.

Despite the lack of assistance, I decided to attend Worcester Polytechnic Institute where I studied aerospace engineering and graduated with a GPA of 3.89.  Not only did I study hard, but I also worked a job and ran cross-country and indoor and outdoor track and field.  I interviewed for and was offered a very good job at a large aerospace company that I believe I earned through the years of hard work that I put into my education.

Here I am, writing to your more than four years later because again I feel like I am being failed by my government.  I have more than $50,000 in student debt and I now pay between a quarter and a third of my salary to the government in taxes.  I hear a lot about "the rich" paying "their fair share" but it seems like I'm paying a bit more than my fair share and I'm not sure the solution is to tax other people more, no matter how much money they have.  What upsets me is not how much money I have or don't have, but what percentage of the money I earn by my own hard work the government takes from me.

I have recently moved to Connecticut from Vermont and although you no longer directly represent me, in my heart I am still a Vermonter and I would like to know that someone hears my voice.

Thank you and I look forward to your reply.

Lane Thornton"

I don't expect any action from Senator Sanders, but it is a start.  I also don't expect to reach every senator and representative as they will continue to change and it would take over 20 years to contact each one at the rate of one every two weeks.  It does, however, make me feel like I'm more engaged in the political process.

-Lane

Training, Week of 6/26

Week 6.  Continued the streak to 42 days and there's no end in sight!  I passed my previous streak record of 38 days, though I averaged nearly 10 miles a day when I did that.  This time around, I'm averaging about 6 a day though that number is steadily rising as my mileage does.  This week I covered 60.5 miles in 7:07:20 (7:04/mile average pace).  This week was a good one in terms of a couple training metrics:

• I ran over 60 miles this week.  I feel like this is a threshold where I start to really get some serious benefits from my running.  I don't know where I am in terms of my fitness and ability to run a good time at a particular distance but I feel like by the time July 20th (and my first corporate race) rolls around I'll be in good position to run well.
• I averaged over an hour of running per day.  This is a good milestone regardless of pace or distance covered.
• I had two great workouts: the first was an 8.5 mile steady run at 6:05/mile pace.  It's on a new, hilly route that I created with ~40 turns through nearby neighborhoods.  I really enjoyed it.  I also had a pretty good long run (16.5 miles).  What made this one particularly good is that after 45 minutes, I did four 5-minute pick-ups with 3-minute recoveries in between.  Not only did this help break up the monotony of the long run, but I think this kind of effort will pay dividends later.
• I also bought new shoes using the gift certificate from the 8 Furlongs Road Race.  I was limited to only Nike products and before I got to the store, I was thinking about some a pair of Zoom-XC flats.  They didn't have any, so I ended up with Lunarglide 2's.  I have run in them a couple times and they're all right but I think they'll probably be my shoe for easy runs and I'll stick with my Brooks flats for most runs.

On a note related to the shoe buying process:  I highly recommend the Fleet Feet in Hartford, CT.  I had a really good experience there.  The guy who helped me pick out my shoes was very knowledgeable and even recommended a place to run in the area.  He was also a legitimate competitor and from our conversation it was clear that he had done some serious training.  I will definitely be returning to buy shoes from them in the future.

I'm looking to run about 60 miles again this coming week, so we'll see how that goes!  I feel pretty good about my training right now.

-Lane

Engineering Lessons

I've officially been working as an engineer for two-and-a-half weeks now and I have learned a lot.  Not only have I learned things that I need to know for my job, I have also learned things about engineering in general that are good to know:

• There are few things as cool as engineering when it's going well.  On the other hand, there are few things as frustrating as engineering that is not going well.  When I'm working with an analysis program, I live a life time in the seconds it takes between hitting the "go" button and getting either an error message or a confirmation that the program did its job.  Most of the time I get an error message but that makes the elation from success all that much better.
• Engineers are always thinking critically about everything.  When I'm shooting the breeze with my co-workers, I am amazed by the observations that are made and the analysis that goes on.  I am fortunate to work with people who never "turn their brains off".
• For salaried workers, the 40 hour work week doesn't exist.  I haven't worked an 8-hour day since I started.  I would say that I average about 8.5-9 hours a day and there are people who are headed into design reviews or other milestones that are at work much longer than I am.  I don't mind because I'm paid to get a certain job done and so it makes sense that I stay until I do the job.

These are just the beginning but I can't imagine doing any other job and liking it as much as I like engineering!

-Lane

Not Much To Say

I really wanted to write a blog post today, but I don't really have that much to say.  Today was a long day so I'm feeling very uninspired.  The good thing is that tomorrow is another day and I think I'll be busy so I'll definitely have a bit more to talk about.

I feel like I'm being a little lazy with this post, but that's the way it goes.

-Lane

The Five Greatest Covers of All Time!

Since completing the undertaking of choosing the Five Greatest Songs of All Time, I decided to pick out the Five Greatest Covers of All Time.  The original songs were good, but the covers are great.  Here they are:

5.  "Heartless" by The Fray, originally by Kanye West.  I think that The Fray convey the emotion of the song better than Kanye because the vocals don't sound like they've been passed through auto-tune a couple times. Also, the music video is quite a bit cooler.

4.  "Smooth Criminal" by Alien Ant Farm, originally by Michael Jackson.  Alien Ant Farm takes Michael Jackson's song and makes it awesome with heavy guitars playing the main riff while still paying homage to his dance moves from a number of music videos:

3.  "I'll Follow You Into the Dark" by Cadillac Sky, originally by Death Cab for Cutie.  I really like the lyrics and the imagery associated with this song and I think that it translates equally well into the bluegrass style played by Cadillac Sky.  I won't say that the cover is better than the original, but it is as good:

2.  "Land of Confusion" by Disturbed, originally by Genesis.  Although I like the song by Genesis, it was intended to be a criticism of Ronald Reagan and I think that Genesis accidentally created a song much more meaningful than the silly criticism of a single politician.  Disturbed takes this song and runs with it:

1.  "Hurt" by Johnny Cash, originally by Nine Inch Nails.  Johnny Cash essentially says good-bye with this song sung just before his death.  It gets extremely intense at the end and the whole song is a powerful expression of emotion:

So there they are.  The Five Greatest Covers Of All Time.  I really enjoy songs that I like being re-framed, allowing me to see them in a new way.  This also fuels my love of mash-ups which will probably fuel another post likely showcasing The Five Greatest Mash-Ups Of All Time.

-Lane

P.S. Another great cover is Gary Allen's version of Vertical Horizon's Best I Ever Had

Math, The Way it Should Be (Unit 2.2: Triangles)

Here comes another math lesson!  It's all about triangles, probably one of the most important shapes.  However, if you're running a bit behind or are new to the series, you kind find the introductory post here, the start of the first unit is here, and the start of this unit can be found here.  While most of that information is not super necessary to today's lesson, not knowing it will prove problematic later.

Now, about triangles.  On the face, there's not much to say about them.  They have three angles (hence the name) and have three sides.  They are closed shapes and always convex, meaning if you put a rubber band around them it would always touch the sides (and all angles are always less than \(\pi\) radians).  In fact, the angles always add up to \(\pi\) radians (if you're wondering why I haven't mentioned degrees, go here).  This is all well and good, but why are these shapes so important that they get their own lesson?

It's because a special type of triangle, called the right angle, is super important when it comes to splitting up vectors.  But before we get to that, let's talk about three kinds of triangles.  The first type is acute with all angles less than \(\frac{\pi}{2}\), the second type is obtuse with one angle greater than \(\frac{\pi}{2}\), and the last type is the aforementioned right angle with one angle at exactly \(\frac{\pi}{2}\).  These right triangles have a very special property: the sum of the squares of the two sides containing the right angle is equal to the square of the third side (known as the hypotenuse).  This is known as the Pythagorean Theorem and more formally looks like this:  \(a^2 + b^2 = c^2\)

This is the whole point of the lesson.  I don't know if I have mentioned this before, but geometry isn't my favorite part of mathematics so I'm kind of glossing over it to get to the cool stuff.  But how does this relate to anything that could possibly be cool?  Recall the graph we made in Lesson 1.6 regarding apples and oranges?  If you don't, it looked like this:

This graph shows a fruit vector representing a person who has two apples and three oranges.  The vector is affectionately known as (2,3).  What if we want to know how far away this person is from a person with no fruit at all?  We can't just add the apples and oranges because that adds to five and it's pretty obvious that the shortest path between the two points isn't that long.  But you can see that the apple vector and the orange vector form a right angle with the fruit vector forming the hypotenuse of a right triangle.  We then apply the Pythagorean Theorem:

\(a^2 + b^2 = c^2\)

\(a = 2\)

\(b = 3\)

\(c^2 = 2^2 + 3^2\)

\(c^2 = 4 + 9 = 13\)

\(c = \sqrt{13}\)*

We now know that the length of the fruit vector is equal to \(\sqrt{13}\).  Aren't you glad we learned about irrational numbers?  Other things to know about the Pythagorean Theorem:

• It can be extended to any number of dimensions (even just one!).  All one needs to do to find the length of a vector is to square all of the components and then take the square root.
• It is never described by the term "to Pythagorean" which means "to speculate in the style of Pythagoras".  This is a common misconception among engineering students.
• It only applies when applied correctly.  The square of the two smaller sides equals the square of the third side.  It doesn't work in any other combination.  It also only works for right triangles.
• This is a very important thing to remember when we get to trigonometric functions.  Keep it in mind.
• Any three integers that can be arranged as a, b, and c and satisfy this relationship are known as "Pythagorean Triples".  The most common is 3, 4, and 5.  The one I remember best is known as the "Alexander Triple", named for my high school geometry teacher: 20, 21, 29.

This lesson is running long so here's your homework:

• Revisit the lesson on vectors and number lines with this new information in mind.
• Apply the Pythagorean Theorem in one, two, and three dimensions and convince yourself that it's true. If that doesn't do it for you, think of a proof.  This problem can be approached through geometry, algebra, or calculus.

-Lane

*The astute student will notice the lack of the \(\pm\) sign in this problem.  If you did, good.  If you didn't, that's okay but this is a super important point.  You almost always need to include it.  However, in this case we can reject the negative answer because distances are positive and a negative length is what we call a "non-physical" solution.  Math is a powerful tool but sometimes it tells us things that are impossible.  Learning to know when math is speaking nonsense and not listening is an important skill that requires critical thinking and common sense.

Training, Week of 6/19 and 8 Furlong Race Report

Week 5!  Ran everyday and the streak continues to 35.  I had a slight reduction in mileage due to preparation for a race today (Sunday) and managed to cover 45.1 miles in 5:27:41 (7:16 pace).  There was no dedicated long run, but I did do two moderately long runs.  I didn't really do any quality this week except for the mile race, sticking to mostly easy running.  I plan to return to a Long Run (with capital letters for emphasis) and a Quality Workout (again, for emphasis) this coming week.  I also plan to get in 3-4 easy miles before work a couple times this week to make getting miles in a little easier.

Men's Open Race Time Distribution

As for the race, it was not what I expected.  I ran about what I figured I could (4:37.9) but the competition was a lot stronger than I expected.  From the results, you can see that there is the typical "bell curve" shape to the results, but the peak was very much farther forward than I would have expected.

As far as my own personal experience and performance, I allowed myself to get caught up in the "I can win this and bring home some money" mindset rather than the "I can try my best and have a good time and if I get money, that's awesome" mindset and because of that got pretty nervous before the race.  As usual, when the gun went off, that disappeared and by 150 meters I was in 10th place.  I wasn't concerned, however, because that's the way most open races go.  I wasn't as pro-active in getting to the front as I should have been and lost contact with the leaders.  By the half-mile mark I was in 6th and picked one person off before the three-quarters mark.  Then I started my kick, hoping to catch the guy in fourth, guaranteeing myself the age group "win" (top three overall aren't counted for age-group purposes).  I didn't catch him but ended up with the AG win and a $50 gift certificate anyways.  Physically I don't think I can justifiably be anything but happy with the performance.  Coming back with only five weeks of training and little quality, I ran a decent mile.

Mentally and emotionally (perhaps spiritually?) I am a little mixed up.  I feel like I should be disappointed or upset or vowing to re-dedicate myself to training harder because I *only* ran 4:38.  I am a bit disappointed that I didn't win money, but despite not running a particularly fast time and making a tactical mistake I feel kind of numb.  I'm not mad, but I don't really have the "I don't care" mentality.  Maybe I'll be able to un-mix my feelings and figure out what it all means.

Lessons learned:

• I still have some decent speed.  4:37.9 is a good time for 8:00am running around a stadium in the parking lot.  This will be good for the 5k's and 10k's that I'm planning on doing.
• Racing on the roads in CT is not the same as racing on the roads in VT.  The big dogs are just a little bit bigger and I can't just show up and win anymore.  The rewards are bigger but so is the competition.
• I need to focus on personal improvement and letting the placing happen.  I tend to forget that in addition to personal fitness, the place one gets in a race also has to do in large part with who else decides to show up.  I think if I get into some longer races, I'll be able to be a little bit farther back and enjoy races more.

-Lane

Edit: Race coverage (in youtube form) here:

New Bed and Some Big Changes Around Here...

First and most exciting, my new bed was delivered this morning!  I'm very excited because up until just now, I've been sleeping on this:

It's an air mattress with slightly too big everything!

It hasn't been too bad but I know the sleep quality hasn't been what many would term "awesome".  Fortunately, that's all in the past!  My new bed looks a little like this:

New bed!

In fact, my new bed looks exactly like that.  I'm very excited to sleep in a bed that doesn't require an air pump.  It came just in time, so I can have a good night's sleep before the big race tomorrow!  As far as that goes, I'm a little nervous but I know that I'll do just fine and hopefully walk away with a couple extra bucks.  I just hope that if I get a check, I'll be able to cash it instead of framing it and putting it up on my wall.

As you may have noticed, there have been some cosmetic and structural changes to the blog recently.  I have been trying to find a suitable picture-font-color combination for this blog to replace the ridiculous map theme that existed here previously.  The Don Quixote picture is a favorite of mine for a couple reasons, so I'd like to keep it as the background but a black and white picture presents challenges when choosing a color for the text.  I like the Don Quixote picture because I have always seen the friendship between Alex and me as something like that of Don Quixote and Sancho in the first part of the story and since this is our shared blog, I thought it a fitting background.  Also, there has been a structural change to make editing and creation of mathematics a little better, as mentioned here.  The major problem with this is it makes the use of the dollar sign nearly impossible but I think that I can survive that.

Finally, I finished my first full week of work, got bills, and got paid and then paid my bills!  What a good feeling to get something, get the bill, and be able to pay it.  On the other hand, I saw how much Uncle Sam was taking out of my paycheck and that was a little less inspiring, but I suppose I'll think about that while I'm driving on the roads and enjoying the freedom made possible by our armed forces.  On the other hand, I'll probably think about it when I see satellite dishes on every unit in a government subsidized housing complex.  In any case, this was a good week and it's not even over yet!

-Lane

Math, The Way it Should Be (Unit 2.1: Introduction to Angles)

I've had a hard time figuring out quite how to approach this subject.  It's not my favorite but it sets up a lot of important things that are coming in the future.  All right... here come angles.

So we know how to measure lots of things.  Lengths come in inches, miles, angstroms, meters; time comes in seconds, hours, decades; but in what units do we measure angles?  There are a few options: degrees (the most common), gradians, and radians are a few examples.  If you did your homework from Lesson 1.3, degrees will be news to you.  If you didn't, that's okay.  Units are always arbitrary and the majority of units for angles are also kind of dumb.  So forget about everything but radians.

Why radians?  They're a little trickier at the beginning, but once you get up to speed radians make everything easier.  Let's start with a circle.  How many radians are there in a circle? That's simple! There are this many: \(2\pi\)*.  I usually forget (temporarily) about the \(\pi\) and think about radians in terms of half circles.

Why that many?  That's a trickier question.  It has to do with the interior angle of a portion of a circle being the ratio of the radius to the arc length.  If you understood that last sentence, it all makes sense given that the circumference of a circle of a given radius is \(2r\pi\).  If not, here's an example.  Say you have one quarter of a circle and you want to know what the interior angle is.  The arc (that's the curvy part) length is \(\frac{\pi}{2}\) (one quarter of the full circle or \(2\pi\frac{1}{4}\ = \frac{\pi}{2}\)). and the radius is 1 (for my own convenience).  We then take the ratio, or \(\frac{\pi}{2*1}\) and that is our angle.  It's pretty nice that for a circle with \(r = 1\) the interior angle is the same as the arc length.

Once you have this concept down, the rest is easy.  Digest the concept of radians and always remember that for a circle with \(r = 1\) the angle in radians is equal to the arc length and you will be golden, provided you can figure out the arc length.  Just figure out what fraction of the full circle it is and multiply that fraction by \(2\pi\).

Homework:

• Continue forgetting about degrees.
• Start slipping your new radian knowledge into everyday conversation.
• Look for triangles, because that's where we're headed next.

-Lane

*If you notice, the math is a bit fancier.  That's because in addition to the changing background picture, I have also added the ability to type math in using LaTeX commands.  I'm new to this format so it will take me a little longer to write posts but the material lends itself to shorter posts so we can move through this a little more quickly anyways.

Some of the best things in life...

Behold!  The Toilet Fountain

... are on the internet.  Not really, but it seemed like a clever way to go about starting this blog off.  Some of the good things are...

...  funny pictures from the internet.  I used to be in the habit of saving internet pictures that I thought were pretty cool.  I don't do it as much because of the vast number of pictures I've seen and really liked and there's a finite amount of space on my computer.  The toilet fountain is one of my favorites:

... are blogs that I enjoy reading like Learning to Do, Riding the Wind, Of Knitting and Things, and Dances with Fat.  Learning to Do is written by a friend of mine and hits a bunch of my interests including running, engineering, and his life and thoughts in general.  Riding the Wind is a also about running, only a much longer and somewhat slower scale than I'm used to.  Of Knitting and Things is written by my fiancée and that explains my readership despite not knowing a darned thing about knitting, which is the main topic.  Dances with Fat is a strange one for me, though.  I don't know how I originally stumbled on it, but I started reading it and have continued.  I'm not even sure that I agree with the author most of the time.  It is about "Body Positivity" or the fact that no matter what size a person is, they should love their body and should be treated with respect because either way, we all make choices about our bodies which we are entitled to make (which I agree with).  I don't always agree with some of the other points and the science that she uses, but I continue reading.

... endless access to information.  The internet is one of the greatest information sharing inventions in the history of the world, perhaps after only the spoken and written word.  It allows people all over the world to share ideas and information at ridiculous speeds.  If I have a question about something I can always go to wikipedia or an endless number of specialized databases on any number of topics.  It's pretty neat.

The internet also has a darker side.  It allows the spread of negative information and ideas as well as gives an illusion of anonymity which, while it makes the internet safer, gives some the opportunity to act hurtful and ignorant towards others.  It's also not very good at conveying tone or intent, two really important things in information exchanges between two or more people.  So as not to leave this post on a sour note, see picture below.  No need to thank me.  You're welcome.

-Lane

Training, Week of 6/12

Week 4!  I ran every day, extending my running streak to 28 days.  I don't know how long I will keep this up, but it's fun for now.  I covered 53.3 miles in 6:15:33 (7:03/mile average).  I got lost again on my long run.  I intended to run to the top of a local mountain but missed several possible turns and ended up giving up and doing an out and back.  I ended up with 15.4 miles so I can't complain.

I also threw in a steady run on Thursday which was intended to be about 8 miles in around 52 minutes but I ended up running quite a bit too fast for the first 6.5 miles and stopped and jogged the remainder.  I was still happy with the effort.

I also registered for a one-mile road race this coming Sunday morning.  I discussed that briefly here.  It's pretty exciting, but I'll probably keep my weekly mileage about the same as this past week while keeping the race in mind.

Interactions with the locals were a bit more positive this week.  There were a number of honks (which I interpreted as friendly) and one gentleman (probably under the influence) hanging out the passenger-side window of a truck attempted to sing me an excerpt from Iron Maiden's "Run to the Hills".

-Lane

Math, the Way it Should Be (Unit 1.6: Summary and a bit of Philosophy)

The last lesson in each unit will go quickly over what was covered in the lessons of the unit and then give some insight into what’s going on in my head with regards to mathematics.  In the Lesson 1.1, we covered addition, subtraction, the signs indicating less than and greater than, and the counting numbers.  In Lesson 1.2 we added zero and the negative numbers to form the integers as well as covering multiplication and some instances of division.  In Lesson 1.3, we learned about the rational numbers, allowing us to carry out division with all integers as well as reviewing addition and multiplication of fractions.  In Lesson 1.4, exponents and roots were introduced, leading to the definition of irrational and complex numbers.  Finally, in Lesson 1.5, the number line and Cartesian plane were introduced as well as some basic vectors and vector operations.  More will come on these topics later.

The first piece of philosophy regarding the education of mathematics that I will share regards the treatment of “word problems”.  In my opinion, word problems are demonized by students everywhere because the way they are taught (or at least, taught to me) requires a step of memorization.  For example, when I was taking my second algebra class in high school, we covered “solution problems” (problems where two or more liquids were combined in a mixture) in great depth (no pun intended).  The teacher I had was a great teacher, but we were taught that every time we encountered a solution problem, we would solve it using the same steps every time.  While this worked for the exact type of problems we faced in class, I feel like this isn’t the best way to solve problems.  Since I learned to approach problems like an engineer, I have started building equations from the problems.  For a new problem, I either create new equations based on what I know about the problem or use a couple, very basic equations (relatively speaking) that I then tailor to the problem.  I use the second approach for complex engineering problems, but the first approach is appropriate for almost all problems faced by high school and underclassmen in college.

I will likely not cover any word problems until later, when I plan on dedicating an entire unit to learning how to do every kind of word problem possible.  Like many things, however, it will require lots of practice to master and experience is something you can’t get on the internet.

-Lane

The Past Week at Work and the Week Ahead

Today was my first Friday as a "real person".  For three days in a row, I got up, shaved, put on nice clothing, and drove to work.  There were other real people there and I learned a lot.  I found out about my future responsibilities and met my co-workers.  I'm super excited about it all!  My new job is pretty much what I've wanted to do for a long time and my co-workers are really nice and accommodating of all my questions.  I've mostly been trying to absorb as much background information as possible and will hopefully begin analysis next week.  I've been working towards it for so long, I can't believe that real-world engineering is so close!

Running-wise, I just signed up for a road mile on Sunday.  This race is going to be special for a couple reasons.  The first is that it's my first post-collegiate race and it's a mile, probably my specialty.  It's rare that they're offered on the roads so I'm looking forwards to taking the challenge on.  It's also going to be neat because it's the first race that I'll have entered with cash prizes for finish placement.  The top three places take home cash and there are still age-group prizes, so as long as I don't blow it, I'm pretty much guaranteed to take home a prize which is exciting.  Races with cash prizes are few and far between and until recently, it was against NCAA policy for me to accept them, so this is going to be an exciting opportunity.

Everything is just so exciting right now!  I know that the novelty will eventually wear off, but hopefully I will have matured into a really strong appreciation of what I am doing, both as a runner and as an engineer.

-Lane

First Day At Work!

Today was my first day at my new job!  I got up at 5:30 to go for an easy run before work and was out the door and in the car by 7:25 at work by 7:50.  Did orientation-type things for a couple hours, learned some brief history about the company, and then headed out for my new office.  Got my new cubicle, met my co-workers, and found out what I'll be working on... etc.  Everything is so cool but it's weird and not yet quite comfortable to be a "real person".  I felt strange walking out of work at the end of the day without "checking out" with anyone like I've had to at every other job I've had.

Still, I think that I'm really going to love working at this job and can't wait to get up and do the same thing all over again tomorrow!

-Lane

The Five Greatest Songs Of All Time!

I have taken it upon myself to choose the five greatest songs of all time (since the 80's).  After years of intense musical immersion, I have chosen these five:

5. "Mr. Roboto", by Styx (1983).  Originally on their Kilroy was Here album, this song tells the story of Kilroy, the last rock star in a society which has banned rock music.  I don't know how good the story is, but the urge to do the robot is good enough for me.

4. "The Downeaster 'Alexa'", by Billy Joel (1989).  This song tells the story of a fisherman struggling to make ends meet.

3. "The Night", by Disturbed (2009).  Although the tone of the song is very dark (no pun intended), this song pretty much contains everything that I like about this genre, including an extremely masterful guitar solo.

2. "Melody of You", by Sixpence None The Richer (2002).  Just a fantastic song about a calling to become a musician.

1. "The Safety Dance", by Men without Hats (1982).  After hearing it once, it becomes clear why this song is the greatest song of all time since the 1980's.  The video completes the total package.

I noticed after compiling this list that there isn't a whole lot from the 90's.  While unfortunate, my memories of the 90's involve a lot of boy bands and Brittany Spears and neither really inspired me.  There were a few bright spots, such as "If I Had 1000000 Dollars" by the Barenaked Ladies, but as they're from Canada and this song came out in 1993, it would be more appropriately titled, "If I Had 782167 Dollars" (exchange rate from June 7th, 1993) which isn't nearly as catchy.

-Lane

Solving Partial Differential Equations with Excel

To begin with, this post is not a part of the "Math, the Way it Should Be" series. Although it is a post filled with mathy-goodness, the mathematics involved here are far and away more complex than what I've presented so far in that series.  If you're inclined to think things are nerdy, you'll probably think this is pretty nerdy. That being said, let's begin with a short introduction and then I'll tell you what I did.

For complicated differential equations, we have three options for finding a solution.  In some cases, the solution may be found analytically but under some circumstances this may involve infinite series to match boundary and/or initial values.  The second option is to look up a solution that someone else may have come up with.  This approach has limitations as well as not every problem has already been solved by someone else.  This leads us to our third option, a numerical solution.  The limitations here are that there is always error (analytical solutions are usually exact), serious computing power can be required (I like to use MATLAB), and the last problem is that the user really has to know what he or she is doing in order to avoid unphysical or unrealistic solutions.  If you can get past these, however, you are on your way to a powerful tool.  Using the following steps, I used Microsoft Excel 2007 to solve the following problem (Laplace's Equation with mixed boundary conditions):

Note: y ranges between 0 and 5 and x ranges between 0 and 10

The first step is to set up Excel: The first step is to allow Excel to iterate on cells with circular references.  This is done by first clicking on the round Microsoft Office button in the upper left-hand corner and selecting "Excel Options".  Click on the "Formulas" tab.  You will see this:

Click the box enabling reiteration.  Set the maximum iterations to 32767 (this is the maximum number) and reduce the maximum change to the desired level of accuracy.  I like 0.0000001 for this application.

The next step is to prepare your domain.  This is done in the workbook itself.  I will be using 0.5 unit change in both x and y, so the boundary conditions are fairly easy to set up:

Now comes the mathy-goodness.  The next step is to discretize the equation.  This is where the math comes in and is a little bit more complicated than I can do a good job explaining.  The required background information can be found on Wikipedia.  Suffice it to say that from this, we find that the value at each point inside our domain is approximately equal to the average of the points in each cardinal direction.  Put mathematically, we have:

Note: i index indicates position on x-axis, j index indicates position on y-axis

This can now be entered into the domain.  Start in the upper left corner.  The proper entry (in this case) should be "=0.25*(E2+E4+D3+F3)".  Then take the black box in the lower corner of the selected cell and drag this equation across the domain.  Then do this again with the whole row, only drag downwards to cover the entire domain.  Watch as Excel iterates through and solves the equation over the domain!

The final step is to make it a little easier to see what's happening.  I started by adding color using the conditional formatting color scale option:

This is pretty cool and gives a pretty good idea of what's going on.  Another option is using the 3-dimensional graph:

If you've been following this, you're probably thinking this is pretty good.  I am always surprised by the things you can get Excel to do if you want.  If you haven't been following this but have still made it to the bottom of the post, I'm glad you stuck with it to the end but I apologize for an ending that's probably pretty disappointing.  The posts after this one deserve some less intellectual content and I intend to deliver.

-Lane

Training, Week of 6/5

Week 3!  I ran every day this week for 45.4 miles in 5:20:22 (7:04/mile average).  This increases my weekly mileage by about 10 miles over last week and extends my run-every-day streak to 21 days.  I had originally planned on about 42 miles this week but a combination of slightly longer than originally intended runs and getting lost on two runs, extending their lengths, brought the mileage up more than anticipated.  The temperature also decreased slightly this week which was a factor in the reduction in pace.  I also think that I'm adapting to the hills around here, helping to bring the pace down.

This week's long run (11.28 miles) was a good example of getting lost.  Compare the following pictures to get an idea of what getting lost in Meriden is like:

Where I wanted to run...

Where I ended up running...

As you can see, not only did I end up adding about a mile to the run, from the elevation profile, I also added a gigantic hill.  Meriden is a very hilly town and I expect that all the uphill running will help me get a lot stronger.

I also had my first notable negative runner-driver interaction.  A woman in a beat-up red sedan drove up to the stop sign just after I arrived.  I looked in through her windshield and believing that we had made eye-contact, started to cross.  As I was right in front of the car, she started to move, so to alert her to my presence, I said "Whoa whoa whoa".  Then the following exchange happened:

Driver: "I didn't see you!"
Me: "Then you should do a better job of looking"
Driver: "You should be on the other side"

After this, I was a bit too far along to continue the conversation without stopping.  Who was at fault here?  Objectively, I should have done a better job making sure she knew where I was before crossing the road.  I also probably shouldn't have have replied to her.  On the other hand, it's my firm belief that drivers should be looking where they're going, not over their shoulders.  If she had been doing this (as she should have been) then she would have seen me and there would have been no problem.  Finally, in response to her final comment, I was running on the sidewalk on the left side of the road.  Pretty much 100% perfect on my part.

In any case, I'm happy about my progress towards getting back into shape.  In addition to the 4th of July Down-hill Mile Title Defense, I am also looking to do the Ocean Beach 11.6 Mile Road Race in the fall.

-Lane

Math, The Way it Should Be (Unit 1.5: Number Lines, Planes, and Vectors)

It’s been a bit of time since the last math post.  Hopefully you’ve used the time to review the previous lessons and done all your homework.

As always, the start of the series is here and the start of the unit is here.  This lesson doesn’t have very much new notation, either.  I think that later units will have more new notation.  This lesson is about looking at numbers in a more visual way and sets up the entirety of the next unit.

One artifact you’ve probably seen before is the number line.  It represents the continuum of numbers and looks something like this:

Here, you can see the integers between -5 and 5 and the arrow heads indicate that the numbers continue in either direction.  The line may be marked at any interval.  For example, if I had wanted, I could have put only even numbers on the line and the number line would have been equally legitimate.  This can be a very useful way of thinking about numbers and the things we do with them.  Addition can be thought of as movement to the right along the line, while subtraction is movement to the left.  To explain multiplication in a similar way, I need to introduce something called a vector.

A vector is commonly described as a magnitude and a direction.  In other words, it is an arrow with a known length and we know which way it points.  On the number line, the vector starts from zero and points to the number which corresponds to its length.  A vector representing the number two looks like this:

To multiply by two, we simply double the length of the arrow:

We get the expected result, which is four.  I feel like this is a much better way of imagining multiplication, rather than the rows/columns method presented earlier.  Division can be described in a similar way: instead of doubling the length of the arrow to multiply by two, you halve the length of the arrow to divide by two.

Once upon a time, a mathematician named Descartes put two number lines together like this (we call it a Cartesian Plane):

These two lines can represent anything, especially things that can’t be compared, like apples and oranges.  One line would represent apples, and the other oranges, and any combination of apples and oranges could be represented by a place on this “plane”.  The number lines are now called axes.  For example, if you have two apples and three oranges:

A vector could be drawn to this location (from the point representing a person having no apples and no oranges).  In either case, the point where you are with your fruit and the vector pointing to you are represented by (2,3).

This vector can be broken into two vectors, one for each axis:

The two red vectors are your apple vector (2,0) and your orange vector (0,3) and they add to your fruit vector (2,3).  BAM! You just learned vector addition.  When adding two vectors, you simply add their components.  If I have one orange and three apples (3,1) and give them to you (2,3), you will move to (5,4).  Vector subtraction is similar.  If you eat two apples and two oranges, you go down two on the orange axis and to the left two on the apple axis to (3,2).  Keep this in mind.

Homework:

• Review your times tables.  I'm not kidding, they really are that important.
• Draw a Cartesian plane and label the axes.  Label the vertical axis something made-up, like unicorns and the horizontal axis something real, like fire trucks.  Imagine yourself somewhere on this plane with at least one unicorn.  This is also important, as you will see later.

-Lane

Moving Out, Moving In

No internet at home means no serious blog posts for a while.  Fortunately, that has passed and I should hopefully be posting regularly again.  Why haven't I had internet?  In case I didn't mention it, I moved out of my apartment in Worcester to be closer to my new job!  The process looked something like this:

Morning of May 30th

Around noon, May 30th

Afternoon, May 30th

Morning, May 31st

Just before I left on May 31st

All moved in to the new apartment!  Thanks to my sister (pictured here) for helping!

What a crazy time!  Getting everything moved out of an apartment and into an new one in two days!  Since I moved in, I've been discovering all of the things that I'm missing.  Silverware has been a bit of an issue.  I'm lucky that Brianna gave me chopsticks for our anniversary!  I've been very busy trying to get my apartment ready to be lived in for the next year.  I will have to repeat the process again next year (to move in with Brianna) but after that I will hopefully be able to stay in one place for a while.

Unfortunately, my start date at work, which was set to be this Monday has been pushed back to Wednesday because there was a mix-up with my drug test results and I have to retake them.  As if I wasn't already nervous enough about starting at my new job, things needed to get more complicated.  Regardless, I'm still really excited about starting!

Vacation...

Having finished moving out of Worcester on Tuesday I am now really on vacation until I start work in July. Thus, I really don't have anything that I have to do. I was going to write a real post, but I'm on vacation and will just leave this picture to sum up my day:

~Alex

Shopping for the Internet on the Internet

I moved into my new apartment yesterday.  Everything is great and there will be a much longer post later for reasons that will soon be clear.  However, I am currently sitting at the local public library, using their internet (not to mention enjoying their air conditioning!).  I have air conditioning at home but no internet yet.  I've been researching internet companies in the area and this is how I feel:

The Experience of Shopping for Internet on Public Internet

It's not that I don't appreciate the ability to walk into a building I've never been to, hunker down, and utilize the greatest information sharing system without being molested by bills, but I think one of the other users put it best when she suggested that I "pray to the internet connectivity gods because the connection speed is frigging slow".  Also, there are parts of the internet service provider's website that don't work, specifically the "order now" button which takes me to a page filled with indecipherable html.

In any case, once I have my own internet I will write something more positive about my moving experience.