End of the World, can you dig it!?

May 21st 2011 while the rest of you were probably carrying on with your everyday lives, I was curled up in my bed with my tin alloy mind shield tightly secured to my head awaiting the end of the world. As the my cell phone's clock slowly ticked closer to the dreaded 6:00 pm EST, I thought of all the good things that I had experienced in my 22 years on planet Earth and wondered what the inevitable oblivion would be like. 6:00 pm EST came and went and the Earth continued turning....

Sitting there in the dark slowly removing the pie tin that had protected my brain, I wondered what could have prevented the rapture. Then it occurred to me only the day before Randy Savage, better know as Macho Man passed away in from a heart attack. Macho Man must have been transported to heaven and single-handedly prevented the rapture, and for that I'm eternally grateful.

So take a moment this Memorial Day and remember the men and women who have laid down their lives to protect this great nation, especially the American hero, Macho Man and snap into a Slim Jim.

Lt. Dan*

*product contains alcohol

Artistic rendition of Randy Savage preventing the Rapture

This blog post brought to you by ConAgra Foods, Inc. makers of Slim Jim.

Training, Week of 5/29

This past week was week 2 of the comeback!  I have run 14 days straight and increased my weekly mileage by about 7 miles to 35.3 miles in 4:16:38 (7:17/mile average).  I also started doing a dedicated "long run" which this week a bit over 9 miles.  The temperature has been increasing but so has my tolerance now that I've been running in the heat.

I still don't know what I'm training for.  I feel like running has become a hobby rather than something that makes up the way I define myself, as it has been in the past.  I suppose that the next race I'll run is a down-hill mile in my hometown on July 4th where I am the defending champion (and record holder).  It's not particularly competitive but it is fun and you do get to run in front of the whole town before the parade.  After that... who knows?

-Lane

Apartment Hunting, Round 2

So, while I know Lane already posted about apartment hunting, I figured I would revisit it with my perspective. For starters, I don't start my job until July making it a bit less pressing than Lane's hunt. However, I do get the joy of moving into an entirely different market than Lane. Since I am working in New York City, I was looking for apartments within commuting distance of the city, which adds a whole different market and entirely different pricing.

I actually started my search back in April. I went with friend from school who is also going to be working in the city. We looked at two luxury apartment towers (operated by the same company though) in New Rochelle, NY. While we liked the apartments, and they had a ton of great features (laundry in unit, dish washer, across the street from the train station) they were expensive, charged for parking, and we found that New Rochelle wasn't the nicest of cities (better than Worcester, but still...) Additionally, she really wanted to live in NYC, which I was strongly opposed to (I wanted to be able to keep my car, which would not have been possible if I had to try to park it in NYC and pay NYC income tax), so we determined that we wouldn't room together after all.

Thus began my individual apartment search. I widened my search out to included White Plains, NY; Mamaroneck, NY; and even out on Long Island in Great Neck, NY. I searched around on the Internet using Google, finding agent listings, looking at Craig's List. But, none seemed to turn up anything noteworthy. Finally, a different roommate suggested I check Stamford, CT. He lived there for a while, and knows plenty of people who commute by train to NYC. After ~10 minutes of searching on Craig's List we found two places that seemed interested, both listed by the same real estate agent. So, I sent off an email and set up a time to view apartments.

I went down this past Tuesday and spent three hours having her show me around. We saw a number of different places in different parts of Stamford. Notably, a couple mid level studios and one bedroom apartments which were nice, but not stunning; two higher end 1 bedroom apartments, though one was a ways out and the other felt both cramped and a bit sterile (white lights, white walls, white carpet, etc.). Finally, we viewed a luxury studio near the train station. When I saw it, I was floored. The apartment is only 607 sq. ft. but has huge ceilings and huge windows, so it feels much more roomy. Additionally, it has a dishwasher, laundry in the unit, and is only 1/3 of a mile from the train station. Everything is gorgeous and it should be the perfect size for me. The only problem (and really the problem with most of the places in commuting distance to NYC) was price. They are expensive! But, that goes with the territory.

After returning home, and having a bit of a panic attack about committing to such an expensive place, I placed the call to the leasing office and put the place on hold. So, after all that I should (pending credit check, which should not be a problem) have a place to live lined up for July. A big step toward the real world.

Well, that's it for now, I'll try to keep updates on my life, running, and whatever else comes to mind. Also, I think I will start a series on city living from a small town perspective once I start work, but that is still a ways (though realistically, not as far as it feels) away.

~Alex

Math, The Way It Should Be (Unit 1.4: Numbers, Part 4)

If you haven’t seen this series before, you should start here or here.  The last lesson covered rational numbers and how to solve equations involving multiplication and addition.  It also introduced another type of problem, those involving exponents.  Exponents, generally speaking, indicate multiple instances of multiplication.  In other words,

5² = 5·5 = 25

5³ = 5·5·5 = 125

It continues on like this for all integers and rational numbers.  The problem is when you want to go in the other direction.  To do this, you have to use an operation called a root.  The square root of x looks like this:

For equations like the one below, it is easy to find the solution of using a square root.  You just have to keep one thing in mind: a square root generates two answers, a negative and a positive answer.  This is because you are doing the opposite of multiplying two numbers together and the product of two negative numbers is positive.

The answer in this case is either 5 or -5!  If you check this result, you will find that squaring either number results in 25.  There are two problems with the square root, and they come when you encounter two different numbers.

In the first case, you try to take the square root of a number like two.  You can’t choose a rational number that, when multiplied times itself, results in two.  So we need a new kind of number.  These numbers are called irrational.  They cannot be written as the ratio of two integers and none of the previously mentioned numbers are irrational.  The irrational numbers are an ordered set and dense, but that’s the end of their nice properties.  When represented as decimals, they have an infinite number of digits after the decimal point and never repeat.  I try to avoid representing irrational numbers as decimals, instead preferring to solve equations in this way:

Now we can solve equations involving exponents with all positive numbers.  But what happens if we want to take the square root of a negative number?  I already said that the product of two positive or negative numbers is always positive.  So how do you choose a number that, when multiplied by itself, is equal to a negative number?  We introduce a new set of numbers, the imaginary numbers.  I’m not kidding.  That’s what they’re actually called and the most important imaginary number is i.  i is the square root of -1.  This allows us to factor negative numbers into -1 and a positive number.  We then take the square root of the positive number and multiply by i:

Don’t forget that there are still two answers!  When combined with the real numbers (integers, rational and irrational numbers), the imaginary numbers form the complex plane.  A complex number is one that is the sum or difference of a real number and an imaginary number.  Much farther down the line, we’ll see why it’s called the complex plane, but suffice it to say that it’s called that as a result of the complex plane not being an ordered set.  Now we’ve talked about all of the relevant numbers.  We can solve equations involving addition, subtraction, multiplication, division, and exponents for all real and imaginary numbers!

Homework:  as long as you’ve followed this lesson, I’m happy.  For the advanced student, the following exercises can be enlightening:

• Prove the square root of two is irrational (hint, recall the definition of rational and prove by contradiction)
• Prove that the complex plane isn't an ordered set (hint, recall the properties of an ordered set and prove by contradiction)

-Lane

More on the Marriage Front!

Yesterday was a busy day in the realm of planning my wedding.  Brianna and I visited two places we were considering for the reception, both near the town that I grew up in.

One location was in a very beautiful, rustic barn that had been falling apart until it was rebuilt.  It was a large space and the work of the wedding would be left to us. This comes with advantages and disadvantages: we'd be able to do things 100% our way and the space was essentially a blank slate but we'd have to come in the next day and clean up before 10:00am.  We'd also have to set up either the day before or the morning of the wedding.  We would also need to find a caterer.

The other location we visited at a local golf course and country club.  It is located much closer to the local airport and hotels and other things that make it easier on people who might be coming in from far away.  Everything is included in the price, including catering and a bar fee.  It also includes the cake cutting, which is a preposterous fee that most places charge just to cut the wedding cake, a limousine, gardens, and the use of the top deck of the driving range.  Ultimately, this option looked to be the best by far and we decided that we wanted to go with this one.

With both locations, there was one small, teensy-weensy problem: neither place had the date we had chosen (May 19th) available.  The barn was only available in very early May or very late June, which were too early and too late, respectively. The country club was available for the next weekend (May 26th) which will also be memorial day weekend.  Brianna's uncle agreed to officiate at the wedding (how convenient, since he is a priest!)  Changing the date seemed like a good solution, so the wedding is on for May 26th!  That's only a year and a day away!

-Lane

Finally...Another Introduction

Well, I suppose it is about time I get off my duff and introduce myself. I am the second of the two rocket scientists contributing to this blog (Lane is the first if you hadn't gathered). I graduated Worcester Polytechnic Institute with Lane this spring and have been going through many of the same events that he has: moving away from an awesome apartment, looking for a new apartment, getting excited about a new job (except the whole marriage thing-that's probably a ways off for me at this point). Unlike Lane though, I am not continuing my career in Aerospace Engineering, but will instead be heading to a prominent bank in New York City to do business analysis and systems development. Should be an interesting time.

Anyway, I doubt that I will post as often as Lane will, but I will try to get on occasionally and give life updates.

Thanks for reading, now get back to your homework, I'm sure Lane has another lesson already planned.

~Alex

Math, the Way it Should Be (Unit 1.3: Numbers, Part 3)

Not related to math, but today is my five year anniversary with my fiancée!  I'm so excited to spend the day with her!


As always, the start of the series is here and the start of the unit is here.  When we left off last, we had just talked about all of the integers.  We had learned to solve algebra problems involving addition, subtraction, multiplication, and some instances of division.  But we ran into a problem with division: sometimes we can’t split an integer number of objects into an integer number of groups, each with the same integer number of objects.  In the example last time, we had twelve objects we wanted to put into 5 groups and we couldn't find an integer that worked.

What’s the solution?  Come up with a new set of numbers.  In this case, we use the rational numbers.  The rational numbers are characterized by the ability to be written as the ratio of two integers.  That is, the answer to our 12 objects in 5 groups is 12/5 or x, the number of objects in each group is 12/5:

This is also the solution to the equation:

5x = 12

This set of numbers looks like fractions, but please don’t start hyperventilating until the end of the lesson.  Some things to take note of about the rational numbers:  

• All of the integers are already rational numbers (think of them being divided by one: 5/1 = 5)  
• The rational numbers are an ordered set (5/3 < 5) 
• The rational numbers are the first group of numbers that are said to be “dense”.

Density is a pretty cool property for a group of numbers to have.  In essence, it means between any two rational numbers, there are an infinite number of rational numbers.  Why am I just bringing this awesome property up now?  I haven’t mentioned it yet because the counting numbers and the integers are not dense.  Let’s look at an example.  If we think about two integers, say 3 and 7, we can see exactly how many integers are between them (we can do this because the integers are an ordered set).  We have 4, 5, and 6.  There are a finite (three) number of integers between 3 and 7.  Now let’s look at the rational numbers between 3 and 7.  We still have 4, 5, and 6, but we also have 7/2, 9/2, 11/2, 13/2, 13/3, 14/3, 16/3, 17/3, 19/3, 20/3… and the list goes on forever.

Hold off on the hyperventilation for a bit longer while we delve into decimals.  Decimals are a special way of representing numbers and involve the addition of fractions.  Say for instance, we have the number 3.7.  This number in the ones’ place indicates how many whole objects we have, in this case, three.  The next number after the decimal place indicates how many tenths we have (seven).  So this number is the same as 3 + (7/10).  Now we can change the way the number 3 looks by multiplying by a funny-looking version of the number one.  You would agree that if you put 10 objects evenly into 10 groups, you would have one object in each group, right?  So 10/10 is equal to 1.  Now to multiply two fractions, you multiply their top numbers and multiply their bottom numbers like so:

This is a great result!  We have changed the way the number 3 looks without changing its value!  Now we can add 3 and 0.7.  To add fractions, you make sure their bottom number is the same (in this case, 10) and then add their top numbers:

And all of a sudden, decimals are demystified.  We can see from the above result that because 3.7 can be written as the ratio of two integers, it is a rational number.

I personally prefer fractions and like to avoid decimals because sometimes decimals can only reasonably approximate an actual number.  Take 1/3 for example.  There it is in a simple fraction, for all the world to see.  We can imagine exactly what it is: one-third.  But try writing it as a decimal and you get 0.333333333333… and the threes just keep coming!  You can write it, but only with an infinite number of threes.  This is why I typically don’t deal in decimals.  I also avoid percentages because they are stupid: simply take the decimal and multiply by 100.  So I have good news for you, if fractions, decimals, and percentages give you pain: I won’t be dealing in either of the last two things.  Just remember that to add fractions you make the bottoms the same (by multiplying by 1) and then add the tops and to multiply two fractions you multiply the tops and the bottoms.

Now to solve a problem requiring division:

5x = 12

(5x)/5 = 12/5

1x = 12/5

x = 12/5

Using rational numbers, we can now solve any multiplication or division problem.  The next problem we need to solve looks like this: x² = 5.  That requires two new types of numbers, but after that, we’re done and will be moving on!  One other thing to remember about multiplying and dividing with negative numbers: if you combine two negative numbers or two positive numbers, you get a positive number.  If you combine one of each, you get a negative number.

Homework:

• Practice adding and multiplying fractions.         
• I should have said this before, but throw away your calculator.  It is a crutch that makes you rely on decimals.     
• Forget about degrees.  The better you do this, the better future lessons will go.  Start now, though, because it will be harder than you think.

-Lane

Training, Week of 5/22

This past week was the first week of training since the end of the track season.  I don't know what I'm training for yet, other than increasing the number of miles I run per week.  I ran 28.8 miles in 3:28:55 (7:16/mile average).  This is probably a little faster than I will be able to maintain as my weekly mileage increases, but I'm not concerned about injury because the runs I've been doing recently are fairly short.

Runs this week have felt a little more difficult than I would have expected.  I think it may be because of the increase in temperature since I last ran and the time off that I took.  My longest run of the week was 6.86 miles which felt about the same as all of the other runs this week, which I take to be a good sign.  I think that I've stopped the atrophy of my fitness but it will be some weeks before my fitness starts increasing again.

-Lane

PR's and Why I Care About Them

In the running world, the acronym 'PR' refers to a Personal Record, or fastest time in a particular event.  They are also known as PB's (Personal Bests) and there are analogous statistics for seasons (SB), countries (NR/NB) and even for the whole world (WR/WB). National and world records/bests have slightly different meanings due to 'official records' not being kept by various governing bodies for certain events, but that doesn't make a whole lot of difference to me.

Why do I care about PR's?  I care about my own PR's because they're one of the ways that I measure my improvement.  Since one of my goals is to run faster in races, if I run a race better than I have ever run before, that's important to me. But if running is an individual sport, why would I care about other peoples' PR's? There are a couple reasons:

• To know if they're credible or not.  When I get running advice from someone, one of the things (but not the only thing) I look at is their PR's.  If that person has PR's that indicate that either he or she has done something right or has experience, they are more credible in my eyes.  If they have PR's that indicate inexperience, they are less credible.
• To know how I compare to them.  If I am considering entering a race, I look at the PR's of the other people I expect to be in the race.  Based on my goals, that may factor into my decision.  For example, if I am targeting a race to try and improve my time in a big way, I will be looking for people whose PR's are about the same as mine or within a reasonable range faster than mine.  
• In order to better get to know them and their goals.  A person's PR's can indicate how much time they spend running, how long they've been running, and which events they've been focusing on.  My mile PR (4:19.70) is much better than my 10k PR (35:08).  This is because I've run dozens of miles and focused my training on that event and only two lifetime 10k's.

So if you're a competitive runner, a weekend warrior, or just considering starting running, know your PR's!  They're important to other runners.  It's important to know your mile, 5k, and marathon PR's (if you have them) because everyone has run at least one mile and can identify with that, the 5k is probably the most commonly raced event right now, and the marathon, for better or worse, is the gold standard for distance running. 

And then when you get married...

I was talking to the mother of one of my high school friends today when she said something that really surprised me: she said "and then when you get married..." Holy crap!  I'm going to get married!  It's one of those things that I know but is strange to hear from somebody else.

I have been dating my fiancée for nearly five years and have been engaged for about a month but it still seems strange to me that I'm getting married.  I think it might be because I've thought of myself as a kid for so long (my whole life, in fact) that it's hard to believe that things that happen only to adults are starting to happen to me.  We've even been considering places to have the reception and have started trying to put together a guest list.

I am super excited for the whole process of planning the wedding!  It's amazing to think that as young as I am, I have found somebody that I want to spend the whole rest of my life with; Brianna is definitely one of the biggest blessings in my life.  In a tangentially related vein, you might be wondering what rocket surgery and knitting have in common?  I don't know, but my fiancée writes a knitting blog!  If you are at all interested in arts and crafts, you should check it out.

No Matter What, The Lawn Still Needs to Be Mowed

A wise man (my high school cross-country coach) once told said: "No matter what happens on Saturday, the lawn still needs to be mowed."  This statement came at the end of a story about the coach on the Sunday after the track and field state championship in two consecutive years.  The first year, the track team had been just barely edged out of first place by a rival team.  Coach was out mowing the lawn the next day.  The following year, the team won the state championship.  Despite his happiness, Coach was still out mowing the lawn the next day.  Upon reflection, he came up with the statement above.

I am become Death,
destroyer of dandelions

Always looking for deeper meaning in the mundane experiences of my life, I thought more about this statement and what it might mean.  I found that in my life, no matter what happened, either good or bad, there were a certain number of things that I had to continue doing.  During college, I had to do homework, work on projects, and take tests.  These were non-negotiable activities, so a couple hours after I proposed to my fiancée, we were both back in the library, hitting the books.  I had finals after my grandfather died and a race the day after my grandmother died.  And now, after graduating from college, I am going to (literally) mow the lawn.

Instead of feeling brought down by the responsibilities of day-to-day life,  they ground me and keep me moving forward in my life.  I can't afford to wallow in my sorrows or rest on my laurels because life will pass me by.  So in a couple hours, the lawn in the picture above will be empty of dandelions and I will have moved a little bit further from the excitement of graduation and a little bit closer to the next big event in my life, whatever that may be.

Dear Vermont: What the Heck?

Today I drove to my parent's home from my apartment.  The majority of the trip was very uneventful.  However, when I entered my home state, I was greeted by a very poorly thought-out set of construction zones.  First, there were a series of signs stating that either the right lane or the left lane were ending.  Once, however, there was no lane closure.  This was annoying, but because of light traffic, there was very little inconvenience.

I-89 in Vermont

The next stretch was characterized by signs indicating construction with no obvious signs of construction.  No cones, machines, or people working.  As before: annoying, but not inconvenient.  Finally another sign indicating a lane closure.  However, in this case, both lanes were closed!  Where did I drive, you may ask?  I drove on the shoulder, my car straddling the rumble strip, kept carefully between the cones on the road and the guard rail.  There was no work happening on the road, and the pavement was merely scarified.  There was no obvious reason not to drive on it.

Once I had successfully navigated through this area, I was greeted by a long stretch of scarified pavement across both lanes.  There were no signs indicating that the area was a construction zone and no obvious signs of construction going on (other than a missing top layer of pavement).  Very frustrating.  I-89 has always been lousy (thank you, Howard Dean), but this was the worst I've ever seen it.

Math, The Way It Should Be (Unit 1.2: Numbers, Part 2)

This the second part of the first unit on numbers.  If you want to start at the beginning of the unit, go here.  If you want to start at the very beginning, go here. This lesson doesn't contain any new symbols but does have a lot of vocab.

Recall that we started with the counting numbers (1, 2, 3, ...).  These are your very basic numbers, the first we encounter in our education, and this re-education is no different.  Next, we include the number 0 (which represents nothing) to the set.  This is a fairly big step that took human civilization thousands of years.  It is important because it is the "additive identity", in that zero added to any number results in that number.  After that, we include negative numbers, which are less than zero.  They mirror the counting numbers and are referred to as their opposites.  For example, the opposite of 4 is -4.  The interesting thing about two opposite numbers is that their sum is always zero.  This leads to the realization that subtraction is really just the addition of a number and the opposite of another number:

4 - 4 = 4 + (-4) = 0

The set that includes the counting numbers, their opposites, and zero is called "the integers".  You may convince yourself that the integers are an ordered set. Now everyone is happy.  We can effectively solve algebra problems that involve addition and subtraction.  For example:

x + 4 = 5

x + 4 + (-4) = 5 + (-4)

x + 0 = 1

x = 1

Ta dah!  An algebra problem is solved.  Don't be frightened by the unknown variable.  It is easy to find once you know how.  To eliminate the number that accompanies the variable, you add it's opposite.  Since the sum of a number and its opposite is zero and zero is the additive identity, you are left with only the unknown variable.  Of course, you must do the same thing on the other side, since you can't change one side and not the other and still have them be equal.

Side note: any variable can be used instead of x.  One of my math teachers was especially fond of "dead dog" and "house".  This flexibility will be useful later.

Now for multiplication and division.  I feel like these operations are poorly understood and difficult to explain. Multiplication can best be thought of in terms of rectangles.  Imagine a square with side length equal to 1.  The  following expression:

3 x 4

Can best be thought of as a rectangle containing 3 of these squares on a side and 4 on the other, like this:

Count the number of squares.  You'll find there are 12, a result that you should have expected.  This can be alternately be represented in the following ways:

3(4) = 12

3·4 = 12

3 x 4 = 12

3*4 = 12

Only the first two are commonly used, so forget about using the third one.  The fourth is used in computer applications because the asterisk is on the keyboard. Don't hand-write that one.  An important property to point out is that 1 is the multiplicative identity, that is, that one multiplied by any number results in that number.

Imagine now that you have 12 boxes in the above configuration.  If you want them put in three groups.  You would find that evenly split up, there are four in each group.  This is represented in the following ways:

12 ÷ 3 = 4

12/3 = 4

The twelve may also be put directly over the 3 in the second case (this is the most commonly seen).  Don't write the first one.  It makes you look like an amateur. One is also unique in division: divide any number by one and you will have the number you started with.  Also, never divide by zero.  Mathematicians don't agree on what happens when you do this, but it's always bad.

What if you want to put your 12 boxes in five groups?  There is no integer that can result from putting 12 objects evenly in 5 groups.  We will need a new kind of numbers to solve the following equation:

That is the subject of another lesson.  I hope by now that you see that I am presenting new groups of numbers as the solution to new kinds of problems. Counting numbers are required to count.  Integers are required to do addition, subtraction, multiplication, and some division.  But not all division can be done this way.  The next lesson on numbers will cover these numbers.

One last thing to take note of: adding and multiplication can be done in any order (for now).  Subtraction and division are best done in the order they're written in.

1 + 2 = 2 + 1

2 - 1 ≠ 1 - 2

Homework: 

• Learn your "times tables".  No joke.  They're important and will come in handy later.  
• Forget that you ever saw this: ÷
• Never, ever again say "times it by" in reference to multiplication.  To say something like "to do multiplication, one simply takes the first number and times it by the second" is wrong.  Not only is it incorrect, but it's against the morals and ethics of society.  Most importantly, it makes my blood boil.

-Lane

College Graduation and The Comeback Begins

Two big things happened in the past couple days: I graduated from Worcester Polytechnic Institute with a bachelors degree in aerospace engineering and I took the first steps in my post-collegiate running career.

Graduation was awesome.  I spent the whole weekend surrounded by friends and family and received a diploma symbolizing all of the hard work I've put into my education.  For me, it represents not only the work I put in the past four years, but also the work that went into the previous 13 years of schooling to put me in the position I found myself in freshman year.

The ceremony itself was nice but nothing out of the ordinary for a graduation.  Speeches were given and the diplomas were handed out.  Everything went smoothly and I can't wait to see the pictures.  I was somewhat apprehensive as there had been some controversy regarding the speaker, Rex Tillerson.  Mr. Tillerson is an accomplished businessman (he's the CEO of ExxonMobile) and the President of the Boy Scouts of America and delivered a speech that was good, if somewhat clichéd.  A small but very vocal minority was upset that the CEO of a giant oil company was being brought in to speak and initially intended to disrupt the ceremony.  After negotiation with the administration, a compromise was reached: the students would be allowed to walk out before the keynote speech and then return after and receive their diplomas in a way that would not distract from the pomp and circumstance.  As it turns out, I couldn't even tell that anyone left (even though I looked) and only eight students left.

The rest of the weekend was spent hanging around the apartment with my family, friends, and their families as well as eating at some of Worcester's best restaurants.  Over the weekend, we ate at 111 Chophouse and Bocado.  They were both delicious and I ate to extreme fullness both times.  The best part of the weekend, though, was seeing family I don't get to see nearly enough.

Today, the great comeback began!  After the end of my scholastic running career, I took about three weeks off from running.  I found that without running, I feel somewhat hyper-active and require several hours less sleep to feel rested.  My guess is that this is an adjustable thing that wouldn't last if I continued not running.  In any case, I ran 3 miles with my roommate, Alex in 22:36 which is a very easy effort for me. I have thought a lot about the next step over the past couple weeks and I think that in the next couple months I'll be focusing on trying to put some solid, non-specific training in and building a strong base.  This will require more steady and tempo runs and less interval work than I am used to, though I will be trying to incorporate regular strides into my running.

-Lane

Math, The Way It Should Be (Unit 1.1: Numbers, Part 1)

This is the first lesson of the first real unit in the "Math, The Way It Should Be" series.  If you missed why this is happening, you should look here.  This post is going to cover some basics about numbers and the way we write them and some of the things that we do with them.  Again, don't skip this section, even if you think you have a pretty good handle on numbers (even though you probably do).

Each lesson will begin with an explanation of the symbols that you will need to know to get the lesson off the ground.  The symbols that we are going to need right now are as follows:

Now I know that you've seen these before and I'm not trying to be a wise-ass.  They are very important and I'm including them here for completeness and I want everyone to be on the same page as I am.  They are, in order: equal to, less than, greater than, less than or equal to, and greater than or equal to.  The first symbol means that the objects on both sides have same value (value to be discussed later).  The second symbol means that the object on the left has a smaller value than the object on the right.  The third symbol means that the object on the left has a greater value than the object on the left.  The fourth and fifth symbols indicate the same thing as the second and third, except that they also admit the possibility that the two objects have the same value.

Now that we know what the symbols are, let's talk about some numbers.  Numbers are essentially symbols that have certain values that we all agree on.  The first type of numbers are the first ones that you learn: 1, 2, 3, 4, etc.  They are called the counting numbers and refer to a set (or group) of numbers that one uses to count things.  If you have one duck and then get another and count your ducks, you have 2 ducks.

When you learn about new groups of numbers, it's nice to think about what properties the group has.  One nice thing about this group is that it's an "ordered set" meaning that if you take two of the objects, you can say one of three things:

1. The first object is greater than the second object (4 > 2)
2. The first object is less than the second object (4 < 6)
3. The first object has the same value as the second object (4 = 4)

This is an extremely useful property because it allows us to count, which is the whole point of these numbers.  From this set comes two very useful things to do with numbers: addition, subtraction.

Addition is the combination of two or more objects to create a collection of objects.  We use the + sign to indicate this type of combination.  Returning to the duck example, you had one duck and got another duck and ended up with two ducks.  This is written as 1 + 1 = 2.  Subtraction is the removal of one object from a collection of objects.  We use the - sign to indicate this process.  This symbol comes up again in a very interesting way later.  You eat one of your ducks and now you have one*.  This is written as 2 - 1 = 1.

As this is the first lesson and I hope that everyone has a pretty good handle on this material, if you're happy with the pace, there is no homework.  If you feel that I am insulting your intelligence, I encourage you to leave a rigorous, mathematical proof that 1 + 1 is always equal to 2 in the comments.

-Lane

*No ducks were harmed in the making of this post.

Bill Rodgers and Good-byes

Today, there are two things on my mind:  A conversation I had yesterday with Bill Rodgers about running and running shoes, and saying good-bye.

First: Yesterday, my fiancée, my friend, and I went to Boston to a high school classmate.  It's also convenient to go to the Bill Rodgers Running Center when I'm in Boston because they sell racing flats which are hard to come by.  Lo and behold, Bill Rodgers* himself was tending the store and I tried on the shoes that I had had in mind and ended up buying them.  I commented to him that flats were very hard to find and he sighed and said that flats don't sell very well because people aren't as interested in becoming very competitive in racing.  He mentioned that more people run, but fewer and fewer people are getting to the point where they need flats.

It brought me back to the last time that I had gone looking for flats at a different running store.  I had called ahead to ask if they had flats, which they assured me they did.  When I arrived, I was taken back to a wall of spikes (for racing on the track or on a cross-country course).  After attempting to communicate exactly what I wanted, I was shown waffles ("spike-less spikes") and minimalist shoes.  I told them that they didn't have what I was looking for and started to leave and the owner came over and asked me what I was looking for and took me back to the minimalist shoes.  I finally managed to get out, but I was disappointed that people who sell running shoes for a living no longer know what shoes go with what races.

In any case, talking to Bill Rodgers about the fall of competitive, "club level" road racing in the United States was disappointing.  I think that it's cool that running is so democratic, that I can interact normally with one of the most decorated American runners in history, but it's sad that he has to witness the decline of the US from world power in running to a mere mid-packer.

Today, I said goodbye to my co-workers at my work-study job.  I have worked there since freshman year and have seen a lot of changes happen.  People came and went, but they all cared for me and took an interest in how I was doing.  It was a little embarrassing (in a good way) when they told my family how helpful I've been, but I'm happy that that's the way I was embarrassed.  I learned so much from working there and met a great number of very important people that I won't ever forget.  I owe them so much, but the funny thing is that they got ME gifts!  I am going to wish for two things: that my future co-workers are as good to me as they were and that I can be as good to other people as people have been good to me.  Saying good-bye is hard!

-Lane

*Bill Rodgers is basically the Tom Brady of American distance running.  Hero of Boston and all that.

Apartment Hunting

I've been looking for a new apartment.  I really like the one that I have right now: the room is great, the roommates are great, and the location is pretty good (read: walking distance from campus).  Unfortunately, it's not near my new job and my roommates are moving away anyways.  So I started looking for a new place to live.

The first step was determining what I was looking for in a new apartment.  I decided that I wanted my apartment to be reasonably close to my new workplace, relatively cheap, and also near where my fiancée will be living.  This narrowed the options down considerably.  The next step was to search the internet, which resulted in a number of different places.  I narrowed those down and decided on three to visit.

Yesterday, I set out for the apartments.  The first place I visited was my anticipated first choice.  It's a town-house style apartment in a very large complex for a reasonable price.  I was very excited though it wasn't initially what I had imagined.  I next stopped by a large tower of apartments, but that turned out to be a home for the elderly, so that was less desirable.  Finally, I drove to the next town down the interstate and visited an apartment complex there... and things got interesting:

The landlord met me in the lobby and took me to the available apartment.  It was "cozy" (read: small) and although cheaper than the other apartment I looked at, was not quite as nice.  Also, the landlord kept telling me things that I immediately recognized as bologna.  He changed the price, he said that he had a waiting list to get in but had "moved me to the top".  He also didn't do any sort of credit check or anything, which struck me as a bit strange.  In any case, I opted to go with the first option.

So I went back and filled out an application.  The woman I had been interacting with offered to run my credit immediately and I didn't have anything pressing to attend to, so I waited.  I didn't anticipate having anything, but it turns out I have credit that is pretty darn good.  I was accepted and brought the deposit today.  So I officially have a place to live!  That is one of the last things that required my attention before my job starts in June.  Now I have to figure out how to get health insurance between graduation and the start of my employer-sponsored insurance and get myself a drug test...

...and one other thing: graduate from college!

-Lane

The End of An Era

I am graduating from college in less than a week now, which brings with it a lot of very exciting things: a degree, a new job, moving to a new town, etc.  It also means the end of my scholastic running career.  It is a little bittersweet: on the one hand, I started running in the context of a school team and it has grown to be a pretty big part of who I am.  On the other hand, I think that after 8+ years, I am ready to take a slightly more relaxed approach to running.

As a member of a team, I always felt that I should run every race as hard as I could, regardless of the way I was feeling.  This led to both more successes and blow-ups than I otherwise would have experienced.  My last race in a school uniform was a 5k in a championship meet (after I also ran the 1500m) where I was tired but started out with the leaders to give myself the best chance to score.  I ended up fading towards the back and finishing in the low-17 minute range, but I was proud of the way that I ran.


I have had a lot of success through the years, from state championships and school records (and a state record!) in high school to fast times in college.  I will probably have very limited opportunity to run either track and field or cross country again, so any future races I do will likely be done on the roads.

I don't yet know what my plans for running in the future are but I have decided that I won't run until I can't stand not to.  I expect that My first run back will be on May 30th, but I'm not holding myself to that.  In any case, I definitely want my nagging aches and pains to go away.  For now, it's time to hang up the spikes, take a long rest, and then start something brand new!

-Lane

Math, The Way It Should Be (Unit 0: The Beginning)

I have encountered many people who are not good at math. There are a number of reasons for this, many of them perfectly legitimate. Perhaps learning more math never seemed useful, perhaps a teacher wasn't able to explain fractions very well and things went downhill from there. My intention at this point is to start at the very beginning (waaaaay at the beginning) because I firmly believe that a lack of foundation is the root of many people's trouble with mathematics.

Why am I doing this? Reason number 1: math is part of the way I look at the world. At a sufficiently high level, the math becomes a beautiful expression of the way the world works. If the universe were an Italian opera, mathematics is Italian. You can enjoy it without the language, but there is something rewarding to me about getting as much of the full story as possible. Reason number 2: math is surprising useful. All it takes is a little creativity in application and all of a sudden you're making things a lot easier!

Right now, I estimate that there are going to be 12 units, each with multiple parts (this introductory post doesn't count as a unit). This is not intended to replace education, but if you've stopped where you left off, hopefully I can give you a little more understanding. Don't skip topics, they're very important because I'm going to go in the order that makes the most sense after looking back on my own mathematics education. That leads me to my next point: this series of posts is dedicated to the people who made me the mathematician I am today: Mrs. Peck, Mrs. Wells, Ms. Graves, Mr. Atherton, Mr. Alexander, Mr. McGowan, Mr. Anthony, Professor Volkov, Professor Humi, Professor Mosco, and Professor Mitrea.

One last thing: there will be homework, but it won't be collected for credit. This week's assignment: brush up on your times tables. If this is the only thing you get out of this series, it will have been completely worth it.

-Lane

The First Post (Again)

Okay... Now for try two. This is a blog about what's going on in my life and the lives of my roommates (if they ever get off their duffs and write posts of their own). Two of us are bona fide rocket scientists and we have varied interests and I'm sure a lot of different things to write about. As a preview, I suspect that there will probably be posts about home brewing beer, mathematics, running, and planning a wedding, and those will be just from me. One of my friends has a blog and he has been doing "series" of posts about one topic, roughly one post a week and I really like that, so I'll probably give it a try.

I like to think that I'm going through a pretty exciting time in my life right now. I'm about to graduate from college and I recently got engaged to my girlfriend. I'm headed to a pretty sweet job as an entry-level engineer in company that designs and builds jet engines. I am looking forward to sharing all kinds of new experiences.

-Lane