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.
The Round, Pythagorean Earth
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
11/19/07 - 11/25/07 De-Cocooning (225 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)
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.