12/24/07 - 12/30/07 Backlogged Week

12/24
No run. Ran in the rain yesterday and opened up a sore on the back of my achilles tendon.

12/25 - 12/26 No run. Same reason.

12/27
75 minutes on a hotel treadmill. Visiting my sister's family, including new nephew, in North Carolina. Dad's photos

He spelled Bryon's name wrong many times, but later fixed it.

12/28
55 minutes on the roads. Had to waddle it in at the end due to severe gastric distress.

12/29
70 minutes.

12/30
no run. legs sore from being on the roads so much, and being out of shape.

Learned that Google keeps track of your search history. Actually, I thought I might have heard this somewhere, but it didn't sink in. Here are the sites I visit most frequently, all time:
Top sites

1.	en.wikipedia.org
2.	www.amazon.com
3.	www.mcmillanrunning.com
4.	scholar.google.com
5.	www.usatf.org
6.	ideotrope.org
7.	www.youtube.com
8.	www.directathletics.com
9.	running.caltech.edu
10.	www.google.com

Oh, running.caltech.edu, why did you have to go? And why is our current web-running-community foundering, too?

12/17/07 - 12/23/07 sqWeek (30 minutes)

Saturday, 12/22/07 (60 minutes)
Ran at night, on the roads. My legs seemed to hold up fine. Also, it was one less hour that I had to share the house with that killer robot masquerading as a floor-cleaning device.

Friday, 12/21/07 (30 minutes)
I didn't sleep last night because I was trying to get on a more normal schedule, and that was the only way I could think to do it. So I didn't run much.

Thursday, 12/20/07 (no run)
I always have a hard time adjusting my running when I move to a new place. My schedule goes according to some sort of routine, even if the outside observer would disagree. It's very hard to run after dark here, because the my backyard is too uneven and I'm avoiding the roads as much as possible. That means if I haven't started running by 4pm I won't get a full run in.

Wednesday, 12/19/07 (60 minutes)
Ran around the back yard.
I'm trying to figure out why my picture on the header got chopped down. I did not do it - it was all the internets operating of their own accord. Believe me that I would not purposefully crop my own photo down to my crotch.

Tuesday, 12/18/07 (no run)
First: my sister popped one out today. As in, my parents are now my nephew's grandparents. It's name is Bryon Charleston Reed. I had to answer the phone call from North Carolina because my mom was driving. I relayed a quick series of questions from my mom over to whoever I was talking to on the other end, until my mom could be satisfied enough to look back up at the road again. We only sideswiped one traffic cone coming out of the airport parking lot.

Second: My other sister will be coming home on Friday. She now claims to look like this:

I believe her.

Third: I spent the entire day traveling and did not have time to run. While in the airplane I attempted to test my equation for how far you can see around the Earth at a given height when the pilot informed us we were at 37,000 feet. The difficulty was that there was so much atmosphere between me and the horizon 150km away that I could not see a distinct line separating them. I did see a faraway mountain, and estimating rather arbitrarily that it was 5000 higher than the surrounding ground, and holding my thumb up at the end of my arm (to the annoyance of the chick sitting next to me, but it's okay, because she wasn't hot, even though she was trying to be), I figured that 150km was probably about right.

Fourth: My dad hired a robot to clean the floors in the house for him. It lives downstairs, where they're "conveniently" keeping me, as well. If this is my last blog post, let me just say this: BIOTA RULES! YOU CAN TAKE OUR LIVES, BUT YOU CAN NEVER TAKE OUR ABILITY TO OCCASIONALLY BEAT YOU AT CHESS ON A GOOD DAY, BUT NOT CHECKERS, EVER AGAIN!

Monday, 12/17/07 (30 minutes)

I got a call from my Dad this afternoon. My parents don't call me to chat.
"Mark. Where are you?"
"Umm, in my room?"
"Your mother is looking for you at the airport."
"But I'm not at the airport."
"I know. If you were at the airport, she would have found you already."

Very true.

At first I thought they had the date of my flight wrong (I was planning on leaving tomorrow morning), but then I remembered mom is never wrong about anything in a schedule book. I missed my flight and made my mom drive out to the airport, not a quick trip from where we live. Not the most auspicious start to a winter break.

Ran half an hour, because I had to change my afternoon plans to accommodate packing, etc. before tutoring in the evening. I'm heading out to the airport now. There'll be no barefoot running or gym available at home, but no sprinkler heads or chained fences, either.

I'm looking forward to a quiet three weeks.

Further Intellectual Masturbation

J.R. once told me about a friend who wrote a computer program that found the shape of a hanging spring. The shape of a hanging chain is a "catenary" [i.e. y=cosh(x)], a fact I was aware of but didn't know how to prove. The shape of the hanging spring (specifically, a spring with zero rest length but finite mass, and whose density is therefore a delta function) turns out to be a parabola.

The program apparently discovered this by starting with a string of many springs of zero mass and zero rest length connecting point particles with mass. The point particles start off stretching in a straight line between two supports of the same height, horizontally separated by some fixed distance. So it's like the spring hanging from the towers that support a suspension bridge. The difference is there's no bridge, and the spring is stretchy whereas the cables on the bridge basically are not.

The program then calculated the forces from gravity and the springs, took a small step forward in time using F=ma, recalculated the forces, took another step, etc. until the thing came to rest. There must have been a small damping coefficient in the program as well to keep the spring from oscillating forever.

I wanted to solve this problem analytically, but at the time I didn't know how. Later, I saw the solution to the catenary problem in a discussion of the calculus of variations. In this approach, you write a function for the energy of the chain/spring, then use a variational principle to minimize the energy.

However, I today I read about how to treat a similar problem, where you have a massless, nonstretchy chain supporting a massive, flat road (i.e. suspension bridge). Modifying the book's solution a bit, I found that you can solve all three problems (massive chain, massive spring, massless chain with bridge) using only single-variable calculus. Here is how:

Assume the spring has some shape given by the function height = y = f(x), where x is the distance from the middle of the two supports.

Our plan will be to find a differential equation for y using the following assumptions:

• The system is in equilibrium


• The tension in the spring/chain at a point must be along the direction of the tangent to that point.


• The only external force on the spring is gravity, which is in the y-direction.

Not only must the entire spring be in equilibrium, but every differential element ds of the spring must be in equilibrium. So consider the forces acting on an element of the spring ds, as shown below:

The condition of equilibrium in the x-direction requires
T_1x - T_2x = 0
T_1x = T_2x = T₀.

In the y-direction, equilibrium requires
-T_1y + T_2y - F_g = 0

rewriting F_g as p_x(x)*g*dx, where p_x(x) is the mass density per unit distance in the x-direction at the point x (NOT necessarily the same as the mass density of the spring, p_s), this becomes
-T_1y + T_2y = p_x(x)*g*dx

Now we invoke the fact that the tension is along the spring.
T_y/T_x = y'
but we found earlier that T_x = T₀, so
T_y = T₀*y'

so going back to the eqn for equilibrium in the y-direction:
T₀*[y'(x₂) - y'(x₁)] = p_x(x)*g*dx

for sufficiently small segment ds, this becomes
T₀*y''(x)*dx = p_x(x)*g*dx
y''(x) = p_x(x)*(g/T₀)

Now we have the desired differential equation in y. So far, the solution to all three problems is the same. Now they diverge, because the mass density is different in the three cases.

Massless Chain Supporting a Road:

Here, the mass density is just the mass of the road per unit in the x-direction
p_x = p₀
y''(x) = p₀*g/T₀ = C
where C is some constant. Integrating, we get a quadratic - the massless chain supporting a road hangs in the shape of a parabola.
This could potentially be a useful result, because people are interesting in making parabolas, because a parabola is the ideal shape for telescopes, radio antennas, etc.

Massive chain:

The mass density of the chain is constant:
p_s = p₀
From the geometry of the situation, we can get p_x

ds² = dx² + dy²
ds/dx = (1 + y'²)^1/2*dx
p_x*dx = p_s*ds
p_x = (1 + y'(x)²)^1/2*p₀
substituting into the D.E.
y'' = (1 + y'²)^1/2 * C
where I mashed the constant together
make a substitution z=y', z'=y''
dz/dx = (1 + z²)^1/2*C
dz/(1 + z²)^1/2 = C*dx
Look this integral up and you get sinh^-1(z) = C*x
z = sinh(C*x) = y'
y = cosh(c*x), which is the shape of a catenary

Massive Spring

For the massive spring, we have to take a look at Hooke's Law:
T = k*x, where x is the displacement from equilibrium.
Note that if we stretch a string to a length x, its density becomes m/x, where m is the length of the spring.
p_s(x) = 1/T(x)
where T is the tension and I suppressed a constant.
T = (T_x² + T_y²)^1/2
T = [T₀² + (T₀y')²]^1/2
using earlier results for T_x and T_y
T = T₀*(1 + y'²)^1/2
p_s = 1/T = 1/(1 + y'²)^1/2
p_x = (1 + y'²)^1/2*p_s, as in the previous case
p_x = [(1 + y'²)^1/2]/[(1 + y'²)^1/2]
p_x = 1
again suppressing constants.

So this case is the same as the original problem with the road hanging from a chain, and the hanging spring of zero rest length takes the shape of a parabola.

Additionally, by modifying the function p_x, you could find the differential equation for the shape of the bridge under an arbitrary load, such as combining all three methods to model a suspension bridge supporting a road where the cables have some finite mass and also some Young's modulus, and finite rest length. You could add traffic going across, acceleration of the road when lifting it up to allow a boat to go underneath, etc. Note that a point mass traveling across the bridge hanging from a chain would cause the density function to become a delta function at that point. So y'' is a delta function, y' has a discrete jump, and the result is that a heavy truck driving across such a bridge causes a kink in the cable directly above the truck.

12/10/07 - 12/16/07 Fuck You, Bones!

Who cares if my bones are broken? Fuck that shit. I'm running anyway.

Monday (1:53)
One minute and fifty-three seconds of running, before I was kicked off the North Field. The South Field was also closed, and I didn't have time to go in search of new grass. Still, this represented a significant improve on my recent running mileage.

Tuesday (60 minutes)
Ran in Lacy, where all the moms explained to their little kid why the man was running. I felt great considering I'm out of shape.

Wednesday (EPIC)
Beer Mile 5:56!!!!!

Thursday (65 minutes)
Easy run on the Eichenlaub Grassy Special, which I haven't used much recently. Ran past Garrett on the way back. I realized that Ian runs my route more frequently than I do, and I run Ian's Arroyo Tempo Loop more frequently than he does. Ah, the absurdities of life.

Friday ( 65 minutes)
Repeat of Thurs.

Saturday (60 minutes)
SFTC w/ Kangway, who told me how atrophied I am. Thanks dude.

Sunday (no run)

Math II

Kangway wins Math I. He receives a score of 95%, because he got the answer right, but his answer was really long and included references to things like the "zero product property" and i don't know what he's talking about. the only interesting part is to note that by rewriting 3^2x as (3^x)², we can turn it into a quadratic equation in 3^x. Also, a neater way to express log₃24 is log₃2³3 = 1 + 3log₃2.

Also, Ian gets honorable mention for correctly solving the problem, but he didn't follow the full instructions, and so receives a score of 80%. His method worked, but it wouldn't work for the same problem with some different values plugged in.

Here is my next question:
I was trying to prove that d/dx(a^x) = ln(a)*a^x

lim_h->0 (a^x+h - a^x)/h =
lim_h->0 a^x(a^h - 1)/h

and so now all i have to do is fix the constant
lim_h->0(a^h - 1)/h

which is of the form 0/0, and i want to show that it is equal to ln(a)
normally you would use L'Hospital's rule and take a derivative with respect to h of the numerator and denominator, but that's illegal here since the form of the derivative is exactly what we're trying to prove.

the next thing i thought to do write a^h as (1-(1-a))^h and use the binomial theorem to expand this, ignoring all powers of h greater than 1.
the resulting series is not too complicated, but it is an alternating series whose terms individually diverge, and i don't know how to evaluate the sum.

so my question is: who has another trick to prove that
lim_h->0(a^h - 1)/h = ln(a)?

of course i could look this up in a calculus book/the internet, but that's not as fun. also, i don't understand textbooks because they have no souls.

finally, i'm aware that my task can be accomplished by taking the definition of e to be the number "a" s.t.
lim_h->0(a^h - 1)/h = 1,
but then my problem is to show that this definition of e is equivalent to the common definition
e=lim_n->inf(1 + 1/n)ⁿ

Math

I was tutoring a pre-calculus student today, and she had a homework problem I didn't know how to do. I played it smooth, saying, "Well, if you're not sure how to do it, let's check through the book for an example." So here's the problem. Go:

solve for x by algebra
3^2x + 3^x+1 - 4 = 0

Cells Are Big

I didn't realize before what the scale of a cell is, but I was reading some from a bio textbook today. They say a typical eukaryotic cell would be 10-100 microns, so take 30 microns on a side. Then if a sugar molecule were as big as a person, the cell would be as big as Los Angeles (50km), except that it's 3D, so it's more like a thousand copies of Los Angeles stacked on top each other.
That allows for a hell of a lot of complexity. It gives some appreciation for just how grand the scale of life is. In particular, that of Haile Gebrselassie.

The Round, Pythagorean Earth

My good news today is that the orthopedist agreed to let me go completely free - no cast or even a splint. I have a sling that I should wear most of the time, but in general my orders are to take it easy, be careful with my arm, but move it around a little bit now and then. I'll see him again after a week. I shouldn't regain full range of motion in that time, but I'm already up to 75%. I can't run or exercise yet, but I can type.

Some time ago I wrote in a piece for English class that if you go to the beach and hold a postcard up against the horizon, you can see the curvature of the Earth. I didn't really fact-check this beforehand, though. Now that I think about it some more, I know that not only is it true, but that the ancient Greeks should not have had a very hard time figuring out that the Earth is round, and even could have measured its radius by making simple observations from the shore or from a boat.

The boat's lookout sits in the crow's nest - high above the main deck. This was probably practiced before people knew that the Earth is round. (Although as I Google it now, it turns out that many ancient Greeks did believe the Earth was round, perhaps beginning with Pythagoras, who unfortunately held that belief for retarded reasons. Later Aristotle talked about gravity pulling the Earth into a sphere in and some dude name Eratosthenes actually measured it using the lengths two shadows measured at the same time but at places far away from each other.) Why should the lookout seek a high vantage point? Because he can see farther, of course. This wouldn't be the case with a flat Earth.

On a flat Earth with no atmosphere, you would be able to see all the way to the edge, no matter how high up you are to start. The same is true for the crow's nest. You would have a slightly better vantage point from the crow's nest because objects in the sea far away would subtend a larger angle, but your total distance of visibility would be the same.



On the other hand, on a curved Earth the horizon is in fact further away if you are higher up. The man in the crow's nest can see the mermaid, but the man on the deck cannot.



The first time I sat down to work this out, I calculated the distance to the horizon for a 6-foot tall man standing at the beach, and got something close to an even 5000m. I thought that had to be wrong, since I had seen horizons much further away - when I was climbing mountains.
Only later did I realize that of course you can see further when climbing mountains - you're in a great tall crow's nest.

I originally calculated the distance to the horizon using analytic geometry, but it's an ugly way to do the problem. There's a much cleaner way, as shown here:



So, by the fact that you can see further from a crow's nest, people should have known the Earth is not flat. If you hypothesize a sphere for the Earth's shape, you could measure the radius quite easily by letting a ship sail out to sea, then measuring how far away it is and how high up you have to be to see it. This gives you an estimate of R for every time you measure the distance to the ship. The quality of the estimate will depend on how well you can measure distances out to sea (triangulation from the shore should work well), how accurately you can measure how high you are (probably easy), how spherical the Earth is (spherical enough), whether the ocean is truly flat (over long distances it is), and whether light is refracted on its way from the buoy back to you (variable and hard to control for). But I'd say you should be able to get a pretty good estimate of the radius of the Earth this way, and it can be done with measurements all from one place.


So finally, can you see the curvature of the Earth with your naked eye? Certainly if you go high enough up you can. From far out in space you can see the entire Earth at once. If you want the Earth to curve 1 degree, then you'd need to view about 100km of horizon under your postcard. So the horizon would need to be on the order of 200km away, because if the postcard subtends more than about a 30 degree angle, you can't see both sides of it at once. That means you'd have to be 3000m up. So you probably won't be able to see the curvature of the earth with the naked eye by holding a postcard up at the beach, but you could easily do it from a mountain overlooking the sea.

Make Money ($30-$40/hr) tutoring

copying this from email i used to spam Ruddock, and hopefully reaching an audience of Caltech students by the blog being fed into Facebook

Dear Rudds,

I live in purgatory.  By this I mean I have escaped the hell of Caltech,
but not so totally that I am free (or graduated) as yet.  In my current
limbo state between enrolled student a person with degree, I've been
supporting myself financially by tutoring.  I tutor both through the
Caltech tutoring list and a tutoring agency called Supreme Educational
Services.  This email is an advertisement for SES.
http://www.supremetutors.com/laoc/about.php

The company is run by a friendly Caltech grad (and ex-Rudd) name Albert
who started it while he was a grad student at Stanford.  They mostly
work in the bay area but are expanding into LA and especially the
Caltech area.  He's looking for Caltech students to tutor mostly high
school level kids in academic subjects.
Here is a run-down:

Qualifications:

   * have some tutoring experience (I had just a few months.  Being a
     TA would probably work, too)
   * be good at whatever you want to tutor, but don't necessarily need
     a great GPA, or need to major in that subject
   * have to know calculus (also a requirement not to flame)
   * helpful to have a car, but not absolutely necessary (I don't)
   * probably helpful to be an upperclassman
   * US citizen

Good Things About Working There

   * at least $30/hr, i make $40, also you can get travel compensation
   * don't have to deal with the business end of things - just record
     the # hours and dates you work and send in to the company at the
     end of the month.  you get one check.  if you ever have any
     business disagreements with someone, my boss deals with it and you
     don't have to
   * less competition to get clients than on the caltech list
     (sometimes when I talk to someone i met through the CDC list they
     tell me they have 15 other people making them offers)
   * can work very few hours/week (like 2-3) if you are busy or more if
     you are not so busy
   * can preview your students and learn a fair bit about them before
     deciding if you wan to work with them
   * allowed to tutor other students privately on the side, as long as
     you didn't meet them through the agency
   * i got to tutor a guy who is taking basic physics at UCLA and also
     owns an exotic car rental agency, and he drove me around in a
     ferrari for a bit, and then i explained the philosophical
     implications of the symmetry of newton's laws with respect to time
     reversal, and then we played video games (don't tell my boss about
     this)

Bad Things

   * you have the knowledge that the person you are tutoring for is
     paying significantly more money than you are actually receiving.
     therefore, you are working for below your own market rate, but
     then you realize that you are only worth so much BECAUSE you're
     associated with the company.  people would rather pay $70/hr to a
     company to have you tutor their child than $50/hr to you directly,
     and that's depressing, because you realize that an ideological
     picture of the world in which people are rewarded solely in
     accordance to the merit of their work is impossible to realize in
     this harsh world
   * i can't guarantee albert will hire you, or that he won't fire you
     for being sucky, or that if he hires you he'll immediately have
     work available for you, but the more people who interview with him
     the more he'll work on finding clients down here
   * you are a legitimate business professional and will get in serious
     trouble if you tell your student lots of fart jokes and their
     parents overhear and don't like it.  if their parents do like it
     you are golden, so you should always ask parents whether they like
     fart jokes shortly after introducing yourself
   * you may end up teaching someone who, with considerable help, can
     get by well enough to solve the problems on their homework, but
     will never, ever, ever fully understand the concept of a function,
     a limit, a proof by induction, a physical law, or any other sort
     of abstract idea (possibly including multiplication), and
     consequently will miss out on "the pleasure of finding things out"
     for the duration of their existence.  teaching someone who simply
     has no aptitude is depressing because for such a person, learning
     about physics is like going to the symphony on the night they play
     beethoven, watching the conductor's passionate gesticulations,
     reading along with the score on your lap, but sitting and watching
     from a soundproof booth


Anyway, the reason I'm advertising to you is that my boss needs more
tutors in the area to make his expansion viable.  In other words, if no
one else starts working for him, it's not worth his time to try to
organize things in this area just for me.
I think it's a good opportunity because it earns more money than SSEL or
work study and about the same as the being a self-employed private
tutor, and is less effort than being self-employed.  It's something you
can do in your spare time and drop at the end of the year if you feel
like it.  Also, I will get $50  if you say I referred you, and I will
totally use part of it to do something nice for you, especially if you
are physically attractive or an interesting conversationalist (logical
OR, not XOR).

If you want to interview with SES, just email Albert (although you might
want to call him Mr. Lee at first) at atlee@supremetutors.com, and
mention my name.  He will probably set something up with you before the
break and get you some work early in the new year.

If you have any further questions, email me and I will do my best to
answer them, possibly in a direct, succinct, and helpful manner, and
possibly in a snide and degrading one, depending upon both my mood and
my evaluation of your physical attractiveness.

Mark

hiatus

arm broken. bike accident. hospital 6-9pm today, ortho tmrw. type slow. 6weeks recovery.

11/19/07 - 11/25/07 De-Cocooning (225 minutes)

Sunday, November 25 (70 minutes)
North Field Gimp Club run. Solid run, felt great. I was planning on going an hour, but didn't have my watch on me, and probably did 70 minutes. Still nothing really acted up, which is great. Ian claimed to be aiming to inflame everything as much as possible today, so that any and all problems would show up on his MRI tomorrow morning. Seems a reasonable plan.
Gym: crunches, bicycles, bridges, shrugs (for my mildly-injured shoulder), eccentric calf exercise, some back machine, and a few pull ups.
It's been a while since I did much of anything in the gym, because before my back started hurting whenever I did a crunch or arched it in any similar way. If felt good today, except for a bit of tension/soreness down in the lower back. I feel encouraged, both by finally getting in a good run and Ian's upcoming appointment with the "good" physical therapist.

Saturday, November 24 (45 minutes)
More nighttime laps of the North Field. Lower back a little bit sore. I want to start some core exercise soon. Earlier, my back wouldn't hear of it.
Book review: The Trial of Colonel Sweeto (PBF Comics)

Friday, November 23 (40 minutes)
Easy post-nightfall run around the North Field. Got a cell phone from my boss. Email me if you want the number.
While I was running, they locked the gym with my wallet and keys inside. Officially, it had been closed to begin with, but at the time I started my run it was unlocked temporarily due to a basketball game. After I ran I couldn't retrieve my stuff, and no one had the keys to let me in. After some investigation I discovered that the gym is far from impenetrable, and triumphantly slunk out the back door with my bag.

Thursday, November 22 (no run)
Thanksgiving at Parkwood. Pretended to be useful by mashing squashes for Ian's pie. Ate lots of food, met Michelle's family.

Wednesday, November 21 (30 minutes)
Continued the cautious plan. North field was cold, but my feet only went half-numb so I was able to continue the run.

I read the letsrun boards today, and noticed again a phenomenon that seems nearly ubiquitous among runners (and, I'm sure, many other communities), which is that the final championship is something of a letdown.
People spend inordinate amounts of time speculating about who will win, who will move up and who will go down, who will shock us and who will deliver what we expect. It's considered a badge of honor to make good predictions, and the further away they are and the more outlandish, the better.
But the chatter on championships and victors is predominantly about the future (with plenty of talk about the distant past as well). For example, after Ryan Hall won the US Olympic Marathon Trials, there was a fair amount of gushing about how great he looked and how fast and controlled he was. But there was far more talk about what the time was "worth" on a fast course with competition, and whether Hall would go on to medal, and if he would become the greatest American marathoner ever.

We're caught up in the "things to come" rather than the "things that are". When I run an easy hour long run by myself, if I'm thinking about running, it's probably about running months or years from now and wondering how much progress I can make.
This feels wrong. You can miss a great deal of opportunity by spending too much of your time speculating on distant trophies festooning the parade of victories that time will inevitably bring marching your way. I think I do that.
Any weatherman will tell you that only the near future is real. Anything more than a week away is almost unpredictable. So we can all imagine sunny skies and cool, clean air to slice our way through months from now. But when we think about now and what's immediately at our hands, we are forced, despite our wishes, to be realistic.
Maybe, if being realistic becomes a habit, living in reality

Tuesday, November 20 (30 minutes)

I ran an extremely cautious 30 minutes on the north field, and seemed to be the better for it. Ian told me Mike Davies had a bad back spasm and needed six months to recover. Some internet searching confirms that it can indeed take this long to get better.

However, I am putting some faith in the feedback mechanisms of my body to let me know when my back is and isn't better. It seems to be marginally better today than yesterday, which is good enough for me.

I still don't understand what caused (or allowed) this particular injury. I had been lax in my core exercises for months before my back started hurting, so I presume that made some contribution to my susceptibility.

Also, this is not the first time I've had problems with my back. The problem is in my upper and mid back, not lower. I've pulled muscles in that region several times before. Each of those times I could trace the injury to something specific - picking up a chair (which held my sister in it), carrying my luggage through Pasadena, etc. This time, I didn't notice anything that caused the pulled muscle in my back two weeks ago. I first felt it upon waking up in the morning. It was a sharp, localized pain that fired whenever I moved my back much (which is almost all the time). It got better bit by bit over the course of days.

The spasm across my back came about a week after that, occurring suddenly while I was running. I was ten minutes into a run when, in the course of only a few seconds, I had to stop completely. I stretched for a while and tried to jog, but it was clear this was not something I could "walk off".

Erin told me that sometimes muscles simply choose to spasm, especially after an injury. There isn't much I can do about it. Self-massage and ice are practical options, which may help some. Rest seems to be effective, though. It's simply slow. At the moment I feel no rush.

Monday, November 19 (10 minutes)

Midnight Mile. Unfortunately my spasming back would not allow me to compete. I did run the mile with JR in 8:24 (slightly better than half Alex's speed).

I realized how much more interesting this sport is when you're actually competing. I think I didn't notice that while watching cross country races because I don't like them very much.

11/12/07 - 11/18/07 Still Messed Up

Here what happened this wee:
Monday and Tuesday I was sick. Wednesday I was sick, but ran some, and got some sort of spasm in my back ten minutes into the run. I had to stop. Thursday it still hurt. Friday it hurt, but I ran a little. Saturday, it still hurts now, and I'm still sick.

11/5/07 - 11/11/07 Another Lost Week

Sunday - continue being sick. feel like running would be counter-productive. got a burger with kiesz for lunch and it was scrumptious.

I don't really remember how much I ran this week. 45 minutes yesterday, because I got a cramp. 45 the day before, because my knees hurt. 70 the day before that. 30 today because I'm sick and my head hurts. I would really like to train but the world seems to be conspiring against me.

10/29/07 - 11/4/07 Dammit (80 minutes)

Sunday, 11/4/07 (60 minutes)
Finally felt good enough to run. Did an hour, starting from the house. Only option was to run mostly on roads, but I kept the pace easy and felt good. I was basking in the cool damp air and simply enjoying the fact that I could get out and go for a run.
book reviews:
The Stuff of Thought, Steven Pinker (9/10)
Dilemmas of an Upright Man (5/10)

Wed-Sat
Pulled back muscle still hurting. Friday I took three Aleve, the first time I've taken medication of any sort in years. As of now (Saturday morning) it seems marginally improved.

Tuesday, 10/30/07 (20 minutes)
I pulled a back muscle, although I have no idea how. I tried to run but it hurt too much.

Monday, 10/29/07 (no run)
Schedule got messed up and didn't run.

10/22/07-10/28/07 Only You Could Have Prevented Those Forest Fires

Sunday, October 28, 2007 (no run)
I forget why not.

Saturday, October 27, 2007 (tempo)
Was warming up with the team when Reed and Beck came by on a tempo, so I joined them. Led Reed the wrong way.

Friday, October 26, 2007 (no run)
Too smoky.

Thursday, October 25, 2007
I finally got myself to update by thinking of how disappointed poor Kangway will be if I don't, and I don't want him to stay up all night worrying.
I ran 30 minutes today because the air was as thick with ash as is your mother's squaw cheese.
Here is my good deed for the day:
letsrun homework thread time!
I seem to spend more time doing other people's homework than my own recently.

Wednesday, October 24, 2007
60 minutes. Really smoky out. If those stupid panda bears escape from San Diego you can be damn sure they ain't gonna make it too far.

Tuesday, October 23, 2007
60 minutes. Smoky. Fortunately I'm immune to lack of oxygen and felt fine.

Monday, October 22, 2007
95 minutes. Long run on the track. It was hot out. There were these high schoolers there and I beat them, even though they were running intervals. Yeah, I'm that badass. Fourteen year old girls got nothing on me. And fortunately, child molestation cops got nothing on me, too.

10/15/07 - 10/21/07 OneWeekAllAtOnce (320 minutes)

Sunday - 60 minutes
Saturday - 60 minutes
Friday - 60 minutes
Thursday - no run
Wednesday - no run
Tuesday - 45 minutes
Monday - 95 minutes, strides

10/8/07 - 10/14/07 The Trots (360 minutes, 1 steady state, 1 pace run)

Sunday, 10/14/07 (no run)
Here is a quick thought for you:
I frequently see the calculation made of how much weight you can lose by drinking cold liquid. For example - you drink 4 liters of water at 0C, which your body must warm to 25C. For water 4liters = 4 kg, so it takes 100 Calories to heat up that water. Do it for a month and you lose one pound. Do it for thirteen years and technically you will disappear.
But for those who don't want to wait 13 years to literally drown their weight sorrows, here's a better idea:
Drink hot water instead. Cold water won't get much colder than 0C, but hot water can go up to 100C, which means it has to be cooled down much more than cold water has to be heated. Technically, your body doesn't have to do any work to cool the water down - it can just sit there and let the water cool itself. But I bet your body actually spends quite a lot of energy cooling itself down if you drink a liter of boiling hot water. Hey, there's only one way to find out (and no, it isn't rational scientific analysis) it's anecdotal evidence! So try it today!

Saturday, 10/13/07 (80 minutes)
Ran around mostly naked during SCIAC multi-duals. Tough conditions for racing. Guys/girls ran decently, but I think Riverside was a better performance for most. Story was Chris Gurney passing Keith Blumenfeld and Galen Smith in the last few meters to give CMS the victory. Pomona doesn't look to be in the running. For conferences Ramon should return and then it will be no contest.

Friday, 10/12/07 (75 minutes)
North field track club. Good run.

Thursday, 10/11/07 (pace run)
Ran with the team in Lacy, 5-4-3-2-1. Got attacked by a maniac later identified at Pat McGrail.

Wednesday, 10/10/07 (steady state)
16 laps at lacy in 45:12 = 5:39/2 laps. The pace was highly erratic, with the slowest mile #2 at 5:57, and the fastest #5 at 5:20. There were a bunch of high school girls in the park, and I ran much faster whenever our paths converged. They were running intervals compared to my straight 45 minutes, but I'm still not getting past by anything with pigtails, and that's that.

Tuesday, 10/9/07 (no run)
Did not run. Since I had a flat yesterday, I walked everywhere I would normally have biked, and put close to 25 miles in on my feet. So I took the day off.

Monday, 10/8/07 (95 minutes)
North Field Track Club run. Stretched it out five minutes longer than last week, but made no attempt to pick up the pace at the end of the run. Connective tissues didn't feel up to the challenge.

10/1/07 - 10/7/07 Emit at aloof gels gets Teg's leg fool at a time.(420 minutes, 1 steady state, 1 interval session, 1 fartlek)

Sunday, 10/7/07 (60 minutes, strides)

Book review: Avoid Boring People , James Watson. 5/10
(now links to Ideotrope instead of Amazon. Couldn't buy a grape with the Amazon money.)
Also should appear in The California Tech.

North field run, completes a good week of running.

On the crapper, I picked up Parade magazine, and flipped to Marilyn vos Savant's column. I read this column because I am severely annoyed by vos Savant's profession, which is essentially "Professional Smart Person." My goal is to find her mistakes and thereby simultaneously achieve forms of deflation of my target and self-exaltation. This is illogical, since Marilyn herself has no idea. See, the reason you point and laugh when someone trips going down the stairs is that it makes him feel bad. It's not the pointing and laughing that makes you feel better about yourself. It's the pain eating away the other person's soul that makes you feel better about yourself. And I'm frustratingly incapable of fomenting soul-consuming pain in Marilyn vos Savant.

In her most recent column, vos Savant replied to an astute reader who wondered why he could stick his hand in a 450 degree oven for several seconds with no ill effect, but sticking his hand in 212 degree boiling water for the same duration, would be severely scalded. "Okay," I thought, "good question. Has to do with the density of the medium, which affects the rate of molecular interactions, which transfer thermal energy..." But no. vos Savant simply replied that air and water have drastically different coefficients of heat transfer, and that this also explains why potatoes cook faster through boiling than through baking.

This is borderline idiocy. To measure this heat transfer coefficient cited would involve exactly the same sort of interactions vos Savant was supposedly trying to explain. Her answer had as much physical content as, "it is that way because it is that way." (Well, maybe not that little. It did have the content "your hand interacts with hot air and water in a way similar to how a potato interacts with them.") But despite the vacuity of her response, I can imagine millions of Americans reading this exchange and giving a long, knowing, "ooooooooh," as if God had just beamed enlightenment down on them from heaven.

This sort of thing makes me angry. And I have a little theory, that I use sometimes when I'm angry, and generally it makes me lose my anger. The theory is that when I'm angry at something, it's because I'm projecting a fault that I see in myself on to someone else. To explain: I see faults in people all the time. (Okay, that sentence didn't come out quite the way I was hoping, but after the discussion of public mockery as a spiritual practice I better not pull any punches now.) But they don't anger or annoy me. Someone drives erratically, and I think, "Whoa, bad driver. I'll keep my distance." Not, "Fuck you." Someone uses bad grammar on an internet message board and I think, "this is difficult to understand." Not, "Learn some damn English, dimwit."

But if you slow me down because you're poorly organized, or can't do something you promised because you slacked off on your work, it has a much better chance of making me mad. I think the difference is that, whether or not I'm a good driver or grammarian, I have no insecurities in my abilities in those areas. I'm at least decent at them, and I don't care much if I make a mistake. Organization and procrastination are two problem areas for me. I think that I'm only mad when I see these faults in others because I'm frustrated by my own struggles with the same problems.

This is a strange reaction. On the surface, you'd think I'd be more sympathetic towards people with the same weaknesses I have, and intolerant of people who can't do the things that I do easily. But observation suggests this not to be the case. It could be a reflection of my personality. Maybe when I generate anger, it's generally directed at myself, and only gets channeled out to others when I use them as effigies of me. Whatever the reason, when I stop and think about this, my anger, or impatience (which feels to me like simply a less-intense version of the same emotion) fades.

I'm not the only one who wants to bring Marilyn down. A google of her name yields, as the fourth hit, a page dedicated to documenting her every published fault, complete with big, bold, proclamations of Marilyn's error, accentuated with liberal use of superlative language, overdocumentation (a favorite tactic of detractors, vitriolists, and conspiracy theorists), and exclamation points. After a few minutes of browsing this page (and I'm sure there are more like it), things came into new perspective.

Give the woman a break. She's not a writing a scholarly research column. She's an entertainer, writing for a cheaply-produced throw-away entertainment magazine. Yes, there are mistakes, and yes, Marilyn vos Savant is an easy person to hate, given her presumptuously-implied advertisement of being the world's smartest person. But anyone else would make mistakes, and advertisement is just the way our society works. So yeah, Marilyn's column is sometimes crap. When I consciously realized that Marilyn's crap irks me because I'm afraid I also misunderstand and overlook important aspects of the things I'm trying to explain, I gently put the magazine back down on the floor, rather than tearing it into strips to wipe up with.

Saturday, 10/6/07 (steady state)
8xarroyo tempo. First 1.5 laps with Matt, after that he went up ahead and I was by myself for the next ten miles. Final watch time was 1:12:52, but that's incorrect because I had to take a shortcut or two to avoid the cops.

What does the police department do with their horses anyway? As far as I could tell, they were just sitting idly on the trail chatting the entire morning, getting in my way. Don't you guys have some protecting and serving to do? Tell me one way in which a horse benefits the police. Do you canter down bad guys on the horse? Can you see foul play from a hundred yards away atop the high perch of your saddle? Maybe, if your horses were racehorses, I could understand keeping them. Racehorses are badass. But your horses trot slower than a normal person walks. To the gallows. Those horses were the rejects from McDonald's.

Friday, 10/5/07 (30 minutes)
Backflipping through hoops; standing on one hand, on top of ladder, on top of a board, rolling back and forth on a coffee can; and lying on my stomach, pulling my feet up in the air behind me all the way over my body and laying them flat on the ground next to my chin, are some examples of the things I did not do today. However, I did watch other people do these things, and it gave me a somewhat-humbler outlook on the athletic ability I'm displaying by touching my toes.

I saw the Shangri-La Chinese Acrobats in Beckman, and their feats were simply astounding. These performers combine balance, strength, power, agility, flexibility, and pretty much any other athletic measure you can think of, with the exception of cardiovascular endurance. Which made me realize - I completely ignore almost every athletic measure you can think of, with the exception of cardiovascular endurance.

I used to love sprinting. And baseball. And swimming. My attentions flipped through rock climbing, weight lifting, karate (extremely briefly), and a host of impromptu exploration. But over time, these have evaporated. This doesn't bug me at all. To say I appreciated the show would be an understatement; to say I was awed by it would not be much of a stretch of the truth. But I felt no desire to emulate them, as I previously would have (and did after seeing the Peking Acrobats ten years ago).

I would say I've come to terms with being a one-dimensional athlete, as is necessary for a distance runner, but "coming to terms" with something implies sacrificing for it. By this point, the fact I can't take up rock climbing or karate doesn't feel like a sacrifice any more. It simply feels natural.

I have no intellectual analog. Although I'm aware that eventually, I'll have to choose an intellectual discipline to pursue if I want to master it, and others will suffer neglect because of it, I don't yet feel capable of excluding the possibility of becoming a writer to study physics, or to exclude becoming a physicist to become a teacher, etc. I can't imagine devoting the bulk of my intellectual effort to one (or two) things. But maybe time and maturity will eventually change that, as they once did athletics.

Thursday, 10/4/07 (fartlek)
4 on, 2 off * 5 with Kiesz. I had some reservations about working out in consecutive days, but I simply banished them to Castle of Good Intentions where I send all my reasonable autoadvisory ruminations.
It took one repeat for my legs to come alive, but after that I felt good.

Wednesday, 10/3/07 (intervals)

I spent the last hour watching Youtube videos of great distance races, indexed here. Some showed tremendous courage, like Dave Wottle's come-from-way-way behind victory in the 1972 Olympic 800m. Others were feats of unfathomable greatness, like Alberto Juantorena's frontrunning victory in the same event 4 years later, in which he set a new world record and trounced a field of 800m specialists. But the treasure was this video: a geniune, slow-motion, Hicham El Guerrouj nipple slip.

Yesterday I realized that aside from some strides/reps, I haven't done anything at 5k pace or faster in a long time. I don't need too much of it, since I'm training for 13.1, but the rule of thumb I hear is go 10% on either side of your race pace (or variations of that rule) for your workouts. So I did 3x1600, going 4:54, 4:50, 4:45. I didn't feel wonderful, but I got through it fine and wasn't toasted afterwards, so I figure it's good solid work.


Tuesday, 10/2/07 (60 minutes)
My nonsense sentence title for this week's entries both references the fourth-place finisher at this year's world championships and is read identically forwards and backwards.

While I'm on the topic of foolishness, I'll describe another math trick I used today. My student was doing a problem that required her to compute 23.4^2. I shocked her by announcing the answer immediately. There are two parts to this trick. The first part is to do the beginning of the problem really fast, so that you know the required computation is 23.4^2 long before your student does, and you have some time to work on it. The second part is the trick part, which I got from a book.
This particular problem could be done directly without too much difficulty, that is
23.4*23.4 = (20+3+.4)*(20+3+.4) = 400 + 60 + 8 + 60 + 9 + 1.2 + 8 + 1.2 + .16, which if you keep a running tally as you go along, possibly condensing some steps by doing 23.4*20 all at once, you will find is 547.56

But take note of this:
suppose we want to calculate the square of a number, a
a^2 = ?

algebra says
(a+x)(a-x) = a^2 -x^2
a^2 = (a+x)(a-x)+x^2

which originally looks harder. but let a = 23.4 and x = 3.4, and you have
23.4^2 = 20*26.8 + 3.4^2
26.8 is easily doubled by taking 52+1.6 = 53.6, so 20*26.8 = 536
for 3.4^2 (which you should do first, so you don't forget the 536 in the mean time) can be done by the same trick:
3.4^2 = 3*3.8+.4^2 = 3*(4-.2)+.16 = 12-.6+.16 = 11.56
Adding these
23.4^2 = 536 + 11.56 = 547.56

So we worked through this, and through a few easier examples, and now, even if she doesn't completely understand 1-D kinematics, my student can find the square of a number better than her teacher can. Also, she thinks I'm pretty much on par with God. Which has me worried, because I've used my most-handy arithmetic tricks up already, and we're only a few weeks into the school year.

Of course I have more (various approximation methods, for example), but they'll be less applicable as we go along. My favorite foray in this vein of playing around is the article "Logarithms!" by David Mermin.
I'm not a master of using his techniques yet (why would I be when I have a calculator, or better yet, the Google toolbar, right in front of me), but reading that paper, I love the obvious joy he gets out of just playing around with numbers to see what he can find.

Note: article on JSTOR. Caltech IP or other access needed to read it.

Monday, October 1, 2007 (90 minutes)

My plan was to do a progression run, with the last thirty minutes getting eventually down to a tempo-like pace. But either because it was hot, because I haven't done it in a while, or because my focus was lacking, I didn't hold much faster a pace over the final half hour than over the rest of the run. My mind would wander, and then a minute or two later I'd realize I let the pace slip again. I think next time I'll only consciously try to pick it up over the last 15 minutes, then gradually extend that as I do more progression runs.

I've been neglecting my core work again, which I really shouldn't. I used to think I had a pretty strong core. Then I saw this video:


I also made a unintentionally long post on Katherine's topic on the jock blog, a portion of which I'll copy here in hope of getting a response on what I am most interested in.

i couldn't tell you the cellular or molecular origins of either type of stress. what i keep hearing is that muscle soreness is due to "microtears", but from what i understand this is not certain. as far as being generally tired, i'm equally stumped. pH and blood lactate levels return to normal just hours after working out, as do body temperature and heart rate. i'd imagine blood sugar, and cellular sugar and ATP levels also are normal not long after a hard workout. heck, on average a stem cell can divide once per day, so if you can make a whole new cell in that time frame you'd think a cell could clear out metabolic waste in that time easily. i'm left to hypothesize something hormonal is taking place after hard workouts. if that's true, it could explain why some performance-enhancing drugs work by reducing recovery time between workouts, because drugs could presumably either act like hormones or regulate hormones related to that lethargic feeling the day after a hard effort.

9/24/07 - 9/30/07 not actually STANFORD (380 minutes, 8000m time trial)

Sunday, 9/30/07 (60 minutes)
Ran as the sun set. My anterior tibialis were sore after the time trial, so I took both yesterday and today easy.

Saturday, 9/29/07 (am jogging at Riverside, pm 30 min with Ian)
I arrived at the gym almost ten minutes before anyone else, in the kind of morning where every sound only magnifies the quiet. I lay down on the island at the parking structure's entrance, and tried to make the moon float past the clouds. It's a perceptual trick. The motion of the moon across the sky is very slow by human standards, about 360 degrees per 24 hours, or 15 arcseconds per second. The is about the same speed as the tip of the minute hand of a clock 10cm in radius, viewed from a distance of about arm's length. That is, maybe, detectable. But the problem is that unlike the minute hand of a clock, the moon has nothing stationary behind it. Its motion relative to the stars and planets is much slower, and so you'll never see the motion of the moon by watching it with the naked eye on Earth. But when the clouds float by overhead, it can appear for a moment as though the moon is sailing through them, slicing its way past and illuminating in pale tones only its closest companions, for a few brief moments, until they move on, and are forgotten, replaced by new clouds, just coming into view. The moon consumes all of one ten-thousandth the night sky, as I estimated by holding my thumb up out in front of my face. But that one ten-thousandth can assume the attention of a man, or even of an entire race, when the moment is right.

Things quickly become different when there are people around. Though the night is equally dark and the moonshine equally brilliant, the splendor evaporates in the soft murmur of human voices standing not far away. So I went from forgetting about 99.99% of the sky to forgetting about all of it, which is a bigger shift than it mathematically appears. The guys performed shockingly well at Riverside. Matt, Sachith, Ben, Nathan, and Garrett all had big PR performances. With Cupcake finally asserting his desire to compete on the SCIAC stage again, the men's team now has three competitive runners up front, and a couple more who can run well against the some of the scoring runners from Cal Lu, La Verne, and Whittier. The SCIAC is still fairly-clearly divided between the teams that are trying to win year to year (this year, I'll pick Oxy, PP, CMS, Redlands in that order) and the teams that are racing against each other in the bottom half. But in that bottom half the competitive level has been rising for a few years now, at all the schools. I'm glad to see it, and only wish I had one more chance at racing for an all-conference spot.

After placing last in 2006, the men may move up a couple of spots this year, the last for Matt and David, who came in three years ago as the program's shining hopes. The women also had a good day. Katherine is unlikely to admit to being satisfied with a race performance, ever, but her blog entry is about as close to that as I expect to see. Justine continues to improve, and our 1-4 spread was only 36 seconds (although the 5th runner was another 40 seconds back of that). The only SCIAC competition available was from Redlands and Pomona-Pitzer, last year's 1st and 3rd place teams, but the women are ready for multi-duals, and could easily surprise some of the teams who beat them last year.

Also, I spent a lot of time playing this game with Matt where you throw a piece of fruit up in the air, then try to hit it with a second piece of fruit before it comes back down. It was pretty hard, but in the end I started playing with rocks, and then I won twice in a row. Finally, there was no Gerry Lindgren this year, since Hawaii didn't come and also he was fired for being insane, but I did get to take mile splits standing next to Steve Scott.

Friday, 9/28/07 (8000m time trial)
Missed the plane to Stanford due to general stupidity. Time trialed on the track instead. 8000m in 25:41.
5:11, 5:09, 5:07, 5:08, 5:06
Halves of 12:56, 12:45. 5000m in 16:06
Felt pretty okay. My right leg got tired before my left one, probably from going in circles. Other than that I was fine. No sprint, felt like a 90% effort.

Thursday, 9/27/07 (70 minutes, strides)
Doing this run has become sort of a default when I don't know what else to do. It's like trying to put everything on hold for a day. Long enough to be a legitimate training run, easy enough not to take anything out of you for a hard effort the next day.

Later, I was presented with a test of my manhood - an unopened glass jar of pasta sauce with a tight lid. I took several unsuccessful tries at opening it, redoubling my efforts only when Soyoung suggested maybe she should go find someone else to do it for her. I wiped the sweat off my palms and immediately heard air sucking in under the newly-liberated jar.
This reminded me that it's grip strength, not "twisting ability" that limits your ability to torque the lid - hence the usefulness of a thin, flat sheet of rubber designed for the purpose as an aid in opening the jars.

Suppose the jar will be opened when you apply a torque T Nm to the lid. Then the tangential force to be applied to either side of the lid is T/r N where r is the lid radius. If you plan on doing this by gripping with your hand, you'll need to have enough friction to prevent slipping, so mu*G > T/r, where mu=coefficient of friction between your hand and the lid, and G is the radial force applied to the lid, limited by your grip strength.

Making an experiment just now, I found that I am unable to do a "hands pullup", where I pull myself up a few centimeters by curling my hands into a ball using grip strength and keeping the angle of my forearms constant. I conclude my single-hand grip strength is less than my body weight of 700N. With a generous mu of .5, I can apply no more than about 200N (45 pounds) of tangential force to a jar lid. However, in my adult life I have not encountered any jars which I have been unable to open. I conclude that most American jars are not tightened with a force greater than 200N, but probably many are tightened with greater than 100N force, because I've frequently been asked to open jars by my mom, who I roughly judge to be no less than half as strong as I am.

Wednesday, 9/26/07 (70 minutes, strides)
My right achilles was sore during the run last night, but fine today. I think this may be because two days ago I was particularly aggressive in my rehab exercise, while yesterday I intentionally took off. So I think the exercises are helpful in the long run, but they day after they actually weaken me a bit.

In the past, I've gotten injured, started rehab exercises, shown no improvement, stopped rehab exercises, gotten better, resumed training, and eventually re-injured myself. My thinking in this process has been "these exercises aren't making me better. I should stop them." Then when I do stop them, I miraculously heal. But I've been adopting the thinking of a guy who learns about lifting weights to get stronger. So he goes to the gym and lifts weights. The next day he's sore and weak. So he stops doesn't lift. The day after that he feels great. So he assumes lifting makes him weak and rest makes him strong. Idiotic, perhaps, but it's what I'm frequently guilty of doing. There's also the rationalization: "I don't have time for such-and-such today, and besides I'm not hurting right now anyway." No matter how many aphorisms about ounces of prevention I hear, it never seems to sink in. But at least I've achieved temporary reprieve from injury, and am probably racing for the first time in a while this weekend.

We had a big snafu with the Juice team and being denied entry into the Stanford Invite. I think the race director is just mad all the good teams are running at Bill Dellinger instead.

Tuesday, 9/25/07 (90 minutes)
Good run with the NFTC (North Field Track Club), whose activities consist of Ian and I putting in some laps. Here is a fun math problem that I read from a book. It's not exceedingly difficult, but once you understand what to do there is room for some cleverness in the execution:

Three men (Adam, Alan, and Ryan) and their wives (Kara, Sara, and Shayne) were comparing their previous week of training. They noticed that each runner wound up for the week running the same number of total runs as they averaged miles per run (so if they ran five times, they also averaged five miles per run). Each husband ran 63 more miles than his wife. Alan did 23 more runs than Shayne, and Ryan did 11 more runs than Kara. Who is married to who?

I like this problem because for me, the moment I read the last line, my reaction was simply surprise. Who is married to who? That didn't seem to be where they were leading me (although on rereading it's the obvious thing to ask), but the fact that you can glean it from the information given is what makes the problem cute. (I considered calling it "elegant", but I think that word is better reserved for more meaningful uses).

Toy math has been helpful for me lately. I have one regular tutoring customer now. I like this kid - she's polite, smart, and most importantly, eager to learn. We were working today on the concept of acceleration. While this may seem straightforward enough, since people can intuit acceleration directly because we physically feel it, I was really hoping that she could get how the relationship between position and velocity is the same as the relationship between velocity and acceleration.

I don't think I'm a very good tutor, yet. I try hard at what I'm doing. But have you ever tried to teach someone to whistle? It's not possible. You can tell them each of the things they need to do, with their lips and tongue and how to breathe, but they will just sit there blowing air around and getting progressively more frustrated. The only way someone learns to whistle is by going and actually trying the thing for themselves, playing around and experimenting until they get it. At first they'll get it one moment, and forget it the next, and have no control over it. But once they have the basics of how to make some noise, the rest comes far more easily. The whistler will only get there, though, when they find they really want to, or else they'll never put in the effort required.

Teaching a math or physics concept is just the same. I cannot possibly teach you the concept of a derivative. I can explain it, ask you leading questions about it, give you examples of it. But the understanding, you must do for yourself. My job as a tutor, then, isn't to teach the concepts. It's to make you want to learn them. And here's where math came in.

Both my student and I were exhausted from banging our heads against the wall trying to communicate on this particular subject. I was giving example problems, trying to lead her on in small conceptual steps. And at one point, a problem required, as part of its solution, the computation 31-17. She dutifully wrote it out on the page (this is my favorite student, the one who doesn't automatically reach for the calculator for every computation).
31
-17

31
-17

2¹1
-17
___
14

Which is fine. It's right. It's effective. But it's not fun. So I saw an opportunity here, to help us both out, by taking a break and having some fun with math.

"That's right," I said, "but let's see if you can do it in your head. What's fifty eight minus twenty three?". No problem. You can easily see in your mind that you subtract the ones digits (three from eight) and the tens digits (two from five) separately, and then put them back together to get 35. She got it. "Good, try 91-31." I gave her a couple more, then asked, "What's 56-39?" Stumped. Once you try to "carry digits" as elementary school teachers would have it, it gets inordinately more difficult. So I told her I would teach her a short trick. I wrote this out (she is used to algebra, but not calculus):
56 - 39 = x
40 - 1 = 39
39 = (40 - 1)
substitute in
56 - (40 - 1) = x
56 - 40 + 1 = x
(56 - 40) + 1 = x
16 + 1 = x
17 = x
"But that's so complicated. It has so many steps. I can't do all that in my head!" she protested. I told her to have more faith in herself, and did a few more problems with her. Soon, she found that I was right - she could do the problems quickly in her head. 64-15 becomes 64-20+5 = 49. She can subtract any two two-digit numbers now just as fast as I can. So after this break, we went back to work, and in just five minutes she was answering questions about acceleration perfectly accurately, despite our having worked fruitlessly on it for a long time before before the math excursion.

My guess would be this sort of break worked because:
1) It gave her confidence - she was soon doing something she didn't know she ever could, and doing it easily.
2) It was fun. If you used to scrub the toilet with a toothbrush, and suddenly someone gave you a brush for Christmas, you'd probably go scrub the toilet with it right away. It's still a chore, but it's the comparison with what the thing used to be that makes it so suddenly enjoyable.
3) It was a break. Maybe we could have talked about tennis for five minutes and done just as well.

These things together had the effect that when we went back to the textbook, she was excited about learning, and keenly receptive for more. Hopefully, with many more such tidbits thrown into tutoring sessions throughout the year, my students will see that there is more to math and physics than formulas and methods to follow. I want my students to intuit answers before finding solutions. I do not want them to know anything by heart. I want them to know it by gut.

All this has little to do with running, except that the fundamental principle is the same. The ultimate motivation must come from within. No one can run your repeats for you any more than they can put the principle of least action into your head. You must do it for yourself.

Monday, 9/24/07 (no run)
Off. Soyoung finally came back from Korea! I decided to make food for her, but my muffins tasted as bland as cardboard. Actually worse. Think, "as bland as a bleached, desiccated cardboard cutout of Bob Dole," and you're getting close. Also made Hungarian Goulash, and completely forgot to make noodles. I suck at cooking, and probably always will due to anosmia. Of all the senses to lose though, smell is not that bad. At least this way I can stand my own company.

Book review: Marty Liquori's Guide for the Elite Runner (3 stars)
Another book review: The Left Hand of Darkness by Ursula K. LeGuin (4 stars)

If you click the above links then by something from Amazon, I will personally get a 4% kickback. I hereby vow to devote all funds gained in this manner to the greater good of the Caltech cross country and track teams, probably in the form of fruits, or if profits exceed expectations, new copies of Running Times for the training room.

9/17/07 - 9/23/07 "Nice hip abductors. Do you work out?" (400 minutes, 1 tempo, 1 rep workout)

Sunday, 9/23/07 (5 mile tempo)
In answer to Matt's list of fruits, here is a list of my favorite fruits, in order of favoritism. Someday I hope to make a similar list, but instead of fruits, it will feature my children.

1. mango


2. watermelon


3. cantaloupe


4. strawberry


5. clementine


6. pineapple


7. banana


8. kiwi


9. blueberry


10. raspberry


11. kumquat


12. apple


13. honeydew


14. grape


15. pear


16. peach


17. orange

Here are a few fruits I have either not eaten recently, or not eaten at all, and need to try sometime:

1. pomegranate


2. cranberry


3. fig


4. apricot


5. guava


6. passion fruit

Here are some fruits that I don't especially like. I don't dislike them, but I won't go out of my way to get them. Eating one of these fruits is like riding the monorail at Disney World. Nothing wrong with it, but you know there are more exciting options available.

1. papaya


2. plum


3. anything dried (raisin, prune, etc. exception: banana)


4. date


5. cherry


6. lemon


7. lime


8. grapefruit


9. ugly fruit


10. Orange Walk oranges


11. something I bought at the farmer's market, possibly a nectarine, but I'm not sure

This is a very small sample of the culinary fruits available on Earth. Wikipedia has a much longer list.

Now that the important business is taken care of, I ran a 10-lap tempo at Lacy, taking a route back through the picnic tables to get closer to 800m/loop. I ran 2-lap splits of:
5:36, 5:34, 5:26, 5:28, 5:20 = 27:24 for the entire run.
This is the same run I did on 8/14/07, about a month ago, just after getting back from Stanford. But today I ran it more than a minute faster at the same or less effort. So I'm very pleased with how it went. I'm also pleased with the way I ran, telling myself to stay cool and relaxed, checking the watch only once per two laps and keeping myself under control and totally focused. It was fantastic. I feel pretty good going into Stanford six days from now.

They say the course is fast (short) but for now I'll just put the goal at setting a new PR, and if I get anything on top of that, it'll be a great bonus.

Saturday, 9/22/07 (90 minutes, strides)
The pattering of rain urged my too-willing body back to sleep this morning. I justified my torpor with baseless suppositions about the poor navigability of the arroyo trail and the futility of attempting a steady state there. Later, Sachith told me it hadn't been bad at all, but I remember many times trying to run in the arroyo during or after rain, and thinking a tempo would be nearly impossible. I think he was probably lying to me. Brown people do that a lot, you know.

I ran alone later in the day, making 90 minutes for the first time in recent memory - a sign that my injuries are recessing in step with my withdrawal from the roads. These two salient features of my recent training - my health and my aloneness (I don't say loneliness.), have been warring in my mind recently.

I would like to run with the team regularly. I enjoy running alone, but I enjoy good companionship even more. This isn't the full reason, though. Running with the team gives me some delusion of higher purpose. I get to think that, having been through four years of a Caltech education, and having improved my running consistently throughout that time, I've become a sage guide for the younger runners. I get to feel like I'm passing on my knowledge where it will do some good. And most importantly, I get something that implies. Because in order to pass on knowledge, you have to know something to begin with. So running with the team, in addition to its companionship and altruistic "do good for others" aspects, also contains an element an ego-boosting element. Not just because at the moment I'm in better shape for cross country than the team is, but because I'm up higher, on a different literal level, than the rest of the runners. There's nothing like having people below you to prove how petty the interior workings of your mind are.

On the other hand, I feel drawn to running alone, as well. Alone, I'm truly in charge. I take issue with some of Scott's training, and for years I've been modifying it the way I want - sometimes to good effect and sometimes to bad. It's hardly a reflection of my opinion of Scott. It's just my personality. I crave sovereignty. I want to be both in charge and responsible, self-motivated, self-coached, self-dependent. For me there's a beauty in aloneness. It's the beauty of simplicity. Whether running, reading, studying, writing, playing, or working, doing it alone forces me to a higher level of introspection of self-knowledge, which I love. There's no need to pretend to be interested, or pretend to laugh, when I'm alone. There's simply myself, and my thoughts. If I have demons, I'm alone with them, too. And I don't mind that at all.

I believe that at this stage in my life, my primary responsibility must be to myself - to understanding myself as fully and deeply as possible. How can I devote myself to others, help them and work with them and derive joy from life together, if I do not first know and appreciate my own being? How can I coach someone to a level I've never explored before myself? How can I become a guide before I've even found one way through?

Friday, 9/21/07 (70 minutes, strides)
Laps on the infield and some strides. Pretty straightforward run. I was having all sorts of gastric trouble because of eating sugar for the first time in maybe two weeks last night. Somehow it lingered all day. It was really bad. I was trying to tutor this girl in math, explaining what "domain" and "range" of a function mean, and I kept having to pause in my explanations and drill questions to squich my face up really tight and try to hold a fart in, because her mom was right in the next room, and there's no way that Asian woman would keep inviting me back in her home if I just keep dropping methane bombs in her daughter's face.

Thursday, 9/20/07 (25 minutes)
I was going to run more, but pyschologically it just wasn't there today. I was feeling stressed out about school, distracted, and I just kept getting the feeling that there was something better for me to be doing than running just then. So I stopped. Later I read Purcell, and suddenly understood a lot of stuff all at once. It was amazingly cathartic, and all because I stopped running. Maybe I'll write more about that later.

Wednesday, 9/19/07 (45 minutes)
Recovery day. North field laps.

Tuesday, 9/18/07 (reps)
20 wu, 6 strides, 2x300 (49, 47), 4x200 (31, 30, 29, 29), jog, 2 strides, 2 accelerations, 2 strides, short cd.

My goal here was to get a bit of training for the paces I haven't hit at all this summer except for strides here and there. Training is a pyramid - most of your time is spent at the slow paces at bottom, and a tiny bit is spent up top. But the whole pyramid is still there all year. Reason being that only a very small amount of work tends to be sufficient to maintain old fitness, while much more is needed to improve, and none at all yields atrophy. So this time of year a huge effort goes into slower paces from distance runs to tempos, but a little still goes into these faster guys. I wanted to run the 300's at date mile pace and the 400's at goal mile pace, but I probably got a little ahead of myself on both counts.

Monday, 9/17/07 (80 minutes, strides)
I started a letsrun thread bemoaning my injury woes. But I managed to get 80 minutes in without falling apart, which is the best I've done recently.

9/10/07 - 9/16/07 Bite My Asphalt (355 minutes, 1 fartlek)

Sunday, 9/16/07 (no run)
Took completely off. My big toe was hurting. There's always something new.

Saturday, 9/15/07 (40 minutes)
I love small cross country races like the open race at Aztec, where guys like Matt and Anton can place place in the single digits, rather than two or three. The winner ran 27:28, which is an excellent time for such a difficult course, but it won't win many collegiate races. The result was that a guy who is his team's leader, but used to being a middle-of-the-packer at large invites, was suddenly in the lead. When his teammates and friends cheered for him, their surprise was exceeded by their excitement, and both wrapped themselves around the race and its runners, pointing the way ahead and pushing the leader on to greater efforts. And when, after giving his teammates the thrill of watching him lead for four miles, an unattached runner came up alongside him to challenge for the win, he made the day into a perfect race for himself and his team by holding off the challenger and sprinting in for the win.
I couldn't help but be happy for the runner. Winning a race was, to judge by the reactions of his supporters, a triumph not only for him but vicariously for his entire squad. It was a rare charge of excitement a team like that rarely gets, and so savors all the more. If I could help bring something like that to Caltech, I'd consider my time and effort well-spent.

Friday, 9/14/07 (AM: 45 minutes, strides PM: 15 minutes, strides)
I decided it would be a good idea to sneak in a quick core workout before we left for the day. As a result, my back was horribly sore the entire drive down to San Diego, and slowly improved over the course of the weekend, so that on the drive back it was only mildly uncomfortable. This is encouraging, in that my body apparently still enjoys the regenerative powers of youth, but simultaneously discouraging, in that my brain still harbors the foolhardy decision-making processes of youth.

Thursday, 9/13/07 (fartlek)
4on, 2off x 6 at Garfield park. Felt good, controlled and strong. I like this sort of work, although I can probably put a little more into the rest periods for a stronger aerobic workout.

Also, I received this email from the Carlsbad woman. I'm now officially an elite distance runner!

To: Mark Eichenlaub
From: Lynn Flanagan

Mark, thanks for your interest in running the Carlsbad Half Marathon in
January.  Our cut off for elite athlete men in the Half Marathon is 1:10.
It sounds like you will be very close to that so I will give you the comp
entry you are requesting.  Please download an entry firm, fill it out and
fax to my attention at 760-692-2901.  See you in January.

Lynn Flanagan
Carlsbad Marathon

Wednesday, 9/12/07 (60 minutes)
To: lflanagan@inmotionevents.com
Dear Mr./Mrs. Flanagan,

I'm writing to request an elite athlete entry to the Carlsbad Half Marathon this winter, because in my opinion Carlsbad is the premier half-marathon on the West Coast. I wrote several weeks ago with this request, but have not received a response.
I have run the race the last two years, and my finishing times and places were:

2006: 1:15:50, 21st overall, 4th 18-24 age group
2007: 1:13:01, 13th overall, 2nd 18-24 age group

My most recent race was April 30, 2007 when I ran a personal-best 15:28.21 for a 5000m track race (http://web.whittier.edu/athletics/spring_sports/trackandfield/2007/07SCIACresults.htm).

I anticipate that I will be fit enough to run a half-marathon in under 1:11:00 this winter. I am requesting an elite athlete entry because I believe my performance is comparable to that of other invited athletes (last year I finished ahead of 6 of the invited men), and I am eager to test myself against this higher caliber competition. I have enjoyed the fun atmosphere, beautiful course, and fine organization of the Carlsbad Half Marathon in the past, and so my hope is to be able to continue competing there in the future.

There are several options available for winter half marathons, and I'm trying to decide which race to register for, and so I would very much appreciate a response, either in the positive or negative.

Thank you,
Mark Eichenlaub


Tuesday, 9/11/07 (45 minutes)
Here is a fairly long and complicated story, which begins on Tuesday, and is intended to explain why I was late to practice on Wednesday morning:

After biking to practice on Tuesday morning, I went directly to Target because I needed supplies for my new room, having moved in with Matt's help on Sunday. I bought, among sundry domestic items, two bookshelves to stock my absolutely gratuitous supply of books, bloated throughout the last four years by a compulsive acquisitive habit that is neither productive nor financially sound.

My next step was to transport these bookcases back to my room, 1.3 miles away. I briefly considered the Herculean feat of hoisting the shelves onto my back, but thankfully for my nonexistent chiropractor, who I wish to remain in his purely hypothetical state, I chose to use a Target shopping cart instead. I didn't know the carts are equipped with an automatic wheel-locking device which prevents them from rolling (or, being rolled) out of the Target parking lot.

So, after struggling with the cart for about three minutes, and stopping to eat a recently-purchased Clif Bar (I hadn't had breakfast. And by the way - don't go shopping when you're extremely hungry. Candy and other junk food begins to look far too tempting at that time. The ideal time to go shopping is right after you eat an entire plate of brownies, and feel so guilty about it you'll take home nothing but tofu, carrots, and omega-3-fatty-acid-enriched flaxseed bran fiber powder to eat for the next week.), a friendly old guy told me what the heck had happened, and helped me transfer my stuff into a working cart still inside the parking lot.

I went back to the store, managed to flag down the "cart guy" (identifiable by his orange vest and shoulders permanently stooped to the height necessary to rest his forearms on a shopping cart's plastic push bar) and ask him to allow me to take the cart back. Amazingly, he agreed to do this, and even personally escorted me all the way out to the sidewalk.

It was hot. The cart wouldn't go straight. The weight was all in the front, making it impossible to get over the smallest cracks and bumps in the sidewalk. The sidewalk sloped, pushing the cart out into the street. The wheels stuck. My hands were sweating and slipping on the plastic bar. I had half an hour of walking, pushing, and grunting ahead of me. My left arm was horribly sore from having to torque the cart in one direction all the time. And as if all that wasn't bad enough, everybody in Asia is getting killed by earthquakes and panda bears and shit.

But at last, I finally got the stuff back to my apartment. When I got back to north Garfield, where I live, I saw there was a farmer's market set up directly outside my house - so things were finally going my way. I stashed my stuff up by my room, took the cart back outside and left it on the grass while I walked through the stalls at the market. I was buying all sorts of fruits and vegetables, many of which I couldn't even identify. "Cuanto cuesta?" I said (everyone was speaking Spanish.) "Buck fifty a pound, man," the guy replied. At least he was charging me the same price as everyone else, I think. I probably spent fifteen minutes wandering through the market, and when I was done, I saw that my impromptu plan had worked perfectly - while I stocked up on fresh fruits and veggies, someone had come along and stolen the cart.

Now, I didn't purposefully lose the cart. I didn't give it to anyone. I didn't fail to return it, either. How could I after it had been stolen? All I did was leave it out in front of my house for a few minutes. Not my fault someone came along and took it. And this relieved me of the responsibility of pushing the damn thing a mile and half back to Target. So I spent the rest of the day eating slightly-mealy, unidentified fruits and assembling bookshelves.

The next morning, I got up as usual at 6:20, went to the bathroom, checked email, etc. and at 6:40 went to go to practice. I went out by the garage only to discover that my bike was gone. After just a moment of wondering who could have stolen it, I remembered - it was still locked up outside Target because I walked back with the cart instead of riding back. Perhaps I should have attempted to put the bike in the cart, but I wasn't thinking that far ahead to begin with. So instead of biking in to campus in the morning I had to walk to Target first, unlock the bike, and only then roll the rest of the way in. So that's why I was 15 minutes late to practice this morning, just in case you were wondering.

Monday, 9/10/06 (60 minutes AM, 20 minutes + drills PM)
It's been a while since I did drills and plyos with Susan. On mildly-injured legs I had to sit a few out, but in general I think these could be helpful if I do them regularly enough. They force my legs through an increased range of motion, encouraging dynamic flexibility, which is sorely lacking from a training schedule which, to be honest, is primarily consisted of slow-moderate paced running.

I think they were fairly rough on me, since the next day I could only manage 45 minutes before the achilles started to feel mildly insulted by the load I was placing on it, but with practice and gradual adaptation these could be a valuable training tool.