Tomorrow morning, I will tutor a Science Olympiad student on astronomy. The topics this year are stellar evolution and exoplants.
It hits a bit close to home, as these were two topics I had spent most of my undergraduate and graduate studies contemplating (when I was actually contemplating astronomy). It should be relatively easy to coach the student on the quantitative aspects; she had already taken an intro astronomy class at Fullerton College, but didn't learn some of the equations required of her.
Though much is taken, much abides.
I had forgotten that there is something attractive about being able, with relatively simple models, to characterize in broad strokes the habitability of a world, the warmth of a star, the importance of just the right amount of greenhouse gases.
Time and Death and God
Perhaps not quite. But death, and rebirth. The precious origins of metal. The cutoffs determining the fate of stars -- just numbers, but each painstakingly determined by the collision of theory and data. Lies, partially. Simplifications -- that's a better way of putting it.
In a minute there is time:
For decisions and revisions which a minute will reverse.
Maybe, maybe, with a bit more math, or even just qualitatively, how to estimate mass limits using the wobble of stars. Maybe direct detection. Maybe gravitational lensing -- GR, which has stormed into the headlines, those waves just a tad late to the 100th anniversary party. And whispers of reflected spectra, and now hushed whispers of an oxygen detection, something that will dwarf even gravitational waves, perhaps not scientifically, but philosophically. Why else look for these other worlds? Why else hunt for a Second Earth?
We shall not cease from exploration
And the end of all our exploring will be
To arrive where we started
And know the place for the first time.
There will be no time, perhaps, to delve into the social history -- the female "computers" that gave us stellar classification, the racism and colonialism and amateurish arrogance that perhaps led to the dismissal of Chandrasekhar, the resignations and scandals. The funding fights. How so many NASA sites ended up in regions of the country that seem, now, to hate the agency so much.
No time for remorse, to miss the learning, even as I know I do not miss the work, or the life, that in spite it all, I am free to not care.
For thine is
I celebrate you friends who stayed, and thrived. It has been a good week for astronomy. It has even been a good week to miss it.
Not alone, of course. I'm not that well-connected or important. But I was one of a few astronomy and physics grad students who were lucky enough to be treated to a delicious dinner (Cornish game hen, if I recall) at the Cornell Hotel School. It was a relatively small setting, and, as I was still reasonably brash, I couldn't resist busting his balls a bit about Pluto. (Tyson, as director of the Hayden Planetarium, had recently and conspicuously demoted Pluto in the Hayden's planetary exhibit.) He responded with good humor, and, I believe, some semi-serious discussion about the reasons for it. (I might discuss this in a separate post, if there's interest, including some speculation as to the timing of the IAU decision -- after New Horizons had been launched.)
During his public talk, after the reception, he did make a great joke about Pluto -- "The real reason it got demoted? It was too small for New York! Ha ha!" He has an infectious laugh.
If memory serves, that same talk, he ventured into what then, and probably now, is controversial territory -- that scientific advances stop when an investigator self-limits, often by invoking God.
But what I remember most of all is running into Tyson and Jim Bell (our grad department chair and one of the lead researchers on the Mars Exploration Rovers mission) at the hotel bar afterwards. They were watching a baseball game.
It was interesting seeing Neil deGrasse Tyson "off". He is a presence, and a performer, and an educator. But like many, he has a stage personality and a normal personality. It wasn't a dramatic difference, but he was less jovial, and probably tired after a long day. I don't know if I was with another student, but we joined them and talked for a bit. He discussed some serious things -- about academia, about his wife and her experiences in it, careers in astronomy, etc. I think I must've confessed my unhappiness at some point.
Anyway, at some point, I think we, the grad students, realized we were intruding on their private time. They weren't, at the moment, lofty role models. They were just a couple guys drinking beer and watching a ball game.
Neil deGrasse Tyson is hated by some astronomers. Leading up to his arrival, a couple emails went around by some lower-ranking staff scientists and researchers (not professors), complaining that he wasn't a real astronomer and that he had done a crappy PhD thesis. At that point, I knew enough about the people on the email list to suspect something less than clear-eyed objective analysis in their judgment.
I encountered similar sentiments in a dinner at UCLA with a couple astronomy professors. I had become a lay person by then, but through a sequences of events, I ended up joining them. There was discussion that he hadn't, in fact, done a stellar job on his thesis, which I think had to do with galaxies -- possibly radio or UV observations. I forgot whether or not I weighed in, but given that I was a guest, and no longer an astronomer, I probably was less brash and more passive this time around.
I haven't seen Cosmos yet. I hope to get around to it. But, unlike many people I know, I never saw it growing up. I hadn't read a single Carl Sagan book before I attended Cornell, and didn't even know he had been a professor at Cornell until I showed up as a grad student. So I don't have a lot of emotional attachment to it.
Interestingly, one did get the impression that Carl Sagan himself was not particularly popular in Cornell's Astronomy department. There was a plaque and a photo. But he wasn't referred to often. No doubt some of the professors had worked in the shadow of his popular image, and that it probably was good for the department to not be anchored to the past. Still, it seemed odd, given the amount of effort made to do outreach, how little it was discussed. At this point, his absence was not deafening, but it was a discernable murmur.
(I once talked with an impressive Cornell grad alum who was active in both science policy and astro research, and one of Sagan's students. He said he had come back only once to the department, for Carl's funeral. I think his words were, "there's nothing left for me here." Perhaps an over-harsh indictment, especially given some of the amazing humans there. But that gives you a sense of the degree of alienation some of Sagan's students felt toward the rest of the department.)
There are people who decide and rank scientific research. It's generally done by peers, and is seen to be a decent system for sorting great ideas from good, and good ideas from terrible ones. It doesn't always work, and the pressures inherent may lead to a host of sins, cardinal and venal. But it's good enough, I suppose, for it to keep going. The process by which Pluto was downgraded was generally accepted within the astronomical community, even if it did arouse controversy within and outside of astronomy.
Yet it always irked me that some scientists -- generally not the best, mind you -- felt that this meant there was a clear measure of defining science in general, value in general, and value of people to science. I couldn't shake the notion that some of these critics of Tyson couldn't handle the idea that the value system they possessed, one ingrained into them since the beginning of their careers, one in which they were completely invested, one which, to varying degrees had rewarded them, might not be universally true. Maybe it takes a level of buy-in in order to make it far enough. But it seemed... myopic, and self-defeating.
How did Tyson's success take away from theirs? How was the popularization of astronomy damaging their work? It didn't make sense, but people do tend to react badly when you question their value system, even obliquely.
I left the faith a while ago, and so I don't have anything to say specifically on astronomy. What I do know is that, looking back, I remember the tired, quiet men at that hotel bar table.
And I realize now that I'm jealous of them -- not because they are successful, respected and reknown, each in his own way. I'm jealous because they can sit down and enjoy a ball game with a friend, and put aside all the other things associated with their jobs and lives. They valued their time, and their friends.
They valued baseball.
Once, one summer, Jim Bell gave me a ride to our Astro baseball team practice. (The team name: The Big Bangers.) I was incredibly depressed at that time, and all I could think of was how grateful I would've been for a dad like Jim to take me to baseball practice. But how could someone say that? So this someone never did, until this moment, though I think he noticed a few tears.
I failed to become a scientist, not because I didn't study enough, or try hard enough. I failed because at some point I separated science from being a person, and failed to build those relationships with other human beings that make a person whole. And part of that is putting aside everything else for time with people.
I'm going to see Cosmos. But I'm going to see it because it gives me a chance to spend time with my mom, and maybe, make up a bit of that lost time.
When I first read this story, I was horrified. But, learning from various other cases, I resolved to wait a full 24 hours before reaching judgment. I thought the story worthy of posting in the interim, but didn't sign any petitions or write any letters. After all, sometimes there is some additional evidence that comes out that, in retrospect, justifies the decisions by law enforcement.
I just read the publication date of the article. It's six days old.
And needless to say, I'm livid.
Some have tried to make this case about race. It may or may not be about that, and I don't think race needs to be a factor at all to feel passionately about this. But I understand if some people view this case through the lens of race.
And it'd be easy -- perhaps easier for me -- to make this about the science culture wars. After all, given the recent noise from Lamar Smith (R-TX), current chair of the House Science Committee, about making political oversight the determining factor for NSF grants, it's clear that one political party (you get two guesses) has adopted a pretty anti-science position, even as it seeks minority opinion to try to make settled issues appear somewhat unsettled. I hope to hell she does get into a good program that gives her the opportunity to get a great science education; she has more native curiosity about science than I did at her age, and if I was good enough to get an NSF fellowship, she probably will be, too. (Who knows? She might even complete her PhD, unlike yours truly.)
But it's not about either of this. This is about childhood, and about America.
It's about whether we, as a country, are so paranoid of our own youth that we can't exercise judgment and come up with proportionate punishment.
Maybe this would've been different if the Boston Marathon bombings hadn't happened. Maybe many are still a bit paranoid about the potential for young people to inflict mass casualties using relatively simple devices. Maybe we've gotten so used to hearing stories of heinous crimes committed by younger, and younger people that it's only natural we've begun criminalizing the young.
Maybe we've become a nation of cowards.
I believe in an America that can't be defeated by one bomb, or a hundred, or a thousand. I believe in an America where our native, sometimes sickeningly naive optimism triumphs over the paranoia and cowardice that are invitations to unchecked power.
Have we become so weak, so pathetic as a country that a little bang on the field is enough to bring down the security apparatus of the state?
If so, we deserve the horrors of the worst paranoid fears realized, for we are no longer a nation worth defending.
You have a 16-year old young person, who happens to be black, happens to be female, happens to be bright, curious, and, by all accounts, a good person. She is now facing two felony charges for something that appears on Youtube, for combining very, very common items.
Did she display a lapse in judgment? Sure. I don't know the details yet about the amount of reactants used, but I suppose she could've seriously injured her eye if the ejected bottle top had hit her in the face. I'm also curious why she didn't get permission from her teacher, and who the mysterious friend is that allegedly told her to do it.
A 16-year old's judgment could be worse. We're complaining about a 16-year old girl who would do a science experiment to impress a friend. There are 16-year old girls who spread their legs to impress someone. Or do drugs. Or break into a house.
Was it uncommon? No.
At my college, we used to blow up things, like, oh, large weather balloons filled with flammable material. Those were stopped before my time. But someone did try to detonate an ice block with thermite once. Yeah, there was some trouble about it, but it was all resolved without a felony charge. And I think there were occasional magnesium fires in the courtyard. All of these were more dangerous than the poof generated by aluminum and toilet bowl cleaner, outdoors, in an uncrowded field.
Was it criminal? I hope not.
It's pretty much impossible to write a good law that covers all possible cases. That's why law is evolving, dynamic, and imperfect. Maybe she did technically break the law (though it's not at all obvious from what I read). But if so, does it make sense to charge her with felony counts?
The whole reason we have a trial by jury, DAs, and judges is that there is, and ought to be, some leeway regarding which cases to bring to trial, which cases merit a guilty verdict, and, even in those cases, some level of judgment regarding sentencing.
I have not seen any of those fine aspects of jurisprudence on display in the last week. What I do see is half-hearted excuses by weak individuals unwilling (with the exception of the school's principal) to stand up and say, this is wrong. We are not doing right by her. We are not doing right by all of the youth we regard, by default, as threats.
I'm disgusted, and will sign petitions, and write letters, and contribute to her legal defense fund. Also, I'll encourage Harvey Mudd College, recently recognized for its success in growing its female student body, to start sending her application materials.
Could something come up in the next few days that will leave egg on my face? Sure. Then I'm sure some people will mock me for running to defend someone not worth defending. Bullshit. I'll choose the promise of youth over the cynicism of the old every day, any day. And if that means I'm wrong occasionally, so be it.
But it looks pretty damn ridiculous right now. Florida has definitely demonstrated some high profile madness in a number of criminal cases in recent years. Here's hoping they get this one right, and let her get back to school soon.
After some discussion with my student (geometry/chemistry) tonight, I think I have an answer to a question that plagued me for a while: why is physics scary?
It's scary because it's the first (and last) exposure to multi-step, multi-tool problem solving in math and science. I had a high school student who found precalculus easy (or at least manageable, even that nasty stuff toward the end) but struggled mightily with physics problem solving. I couldn't figure it out for a while.
At first I thought it was that I found it easier to teach precalculus; the book is set up nicely, and I don't have to worry about abstract concepts (except insofar that I tried to tie it to useful stuff).
Then I thought maybe it had to do with the student having a weak science background. But by her own admission, she had both a weak math and science background.
It wasn't work ethic; this student worked a lot, both in class and outside. (I was dorm RA, so I knew studying was happening even outside of school hours.)
And I couldn't just chalk it up to "being Chinese", and the stereotype that Asian education consists of rote memorization and drills, leading to mathematical fluency but deficient creativity. (I secretly suspect this is an excuse perpetuated by Westerners to ignore the severe gap in educational readiness vis a vis other nations.) "Western" students in the same classes exhibited this pattern, too.
Eventually, it came down to this multi-step, multi-tool problem. Both she and I determined this independently.
***
In the typical high school math class, you solve problems by using a single trick or tool.
In biology, you mostly memorize a bunch of concepts and vocabulary, which are evidently important skills in the first year of med school.
Chemistry presents perhaps the strongest challenge to this thesis. It is possible to generate a multi-step, multi-tool problem in chemistry. There's a reaction, and you have to figure out it's yield and reaction type. First, you might have to do some stoichiometry to balance the equation. Then, you might have to figure out Lewis structures to determine the number and type of bonds, and then calculate the binding dissociation energies. You can then figure out if the equation is endothermic or exothermic. Maybe you adjust the calculation using phase transitions. Then you can determine molar masses, and compare the expected mass to the measured mass, or some other contrived number that allows you to calculate the yield.
So maybe chemistry is the first opportunity. But my experience indicates that plenty of students muddle through chemistry and hit a solid brick wall when they take physics. So there's something different about it.
I think chemistry, in principle, can be taught with emphasis on using multi-step, multi-tool problems to solve chemistry problems. But in practice, it looks like that's not done. I don't have a good explanation why that is; I've never taught a chemistry course. (Those who tutor, teach or study chemistry: your input is definitely welcome.)
***
In general, in the sciences, the problem statements are longer and more involved, making it less practical to have students do a number of problems on a single concept to hammer it in (as it's done in math). As much as we'd like to think otherwise, repetition and drills really do help cement a concept.
Maybe physics would be better if we could better segment subject material, and have more practice problems limited to one topic. This is different than how most textbooks are set up. Most of the better textbooks I've seen have, at the end of the chapter, problems grouped by topic, and prefaced with qualitative questions. It's not like a math book, where the section/chapter problems are divided into clusters in which you are asked to basically do the same thing over and over.
Physics, as a multi-step, multi-tool discipline, requires that all the tools work, and all the steps are clear. Maybe in other classes, even chemistry, a student can half-ass Lewis structures and still get an A. But it's just not possible to half-ass, say, linear momentum and be able to learn the rest. (Chemists: feel free to quibble and argue that the analogy ain't fair; I'll argue that even precious PV=nRT can be botched without irreparable damage to the rest of chemistry learning and the final grade.)
I'm not arguing that physics is better, or necessarily more complicated. But it is different.
Anyway, I think I'm going to revise how I teach physics. I basically need to generate drills, in addition to the problem-solving organizational methods that I'd ask them to use to convey their knowledge in a solution.
Note: this is also a test of MathJax, and my attempt to enable LaTeX in the Blogspot environment. (Easy directions here. My MathJax notes at the end of the post.)
At first glance, air resistance problems seem weird. They don't quite fit with the more familiar forces. It's sort of like friction in that it always acts in the opposite direction of motion. But it is velocity-dependent, which appears to add a layer of complexity that isn't there for other problems.
But it is doable, and within the range of students who have a reasonably solid calculus background.
(Note, however, that if a student is taking calculus for the first time concurrently with calculus-based physics, there might be a problem in which the calculus required to solve certain problems hasn't been taught yet. For best results, take a year of calculus before taking physics C. But, in practice, those taking it concurrently will have to teach themselves a bit of calculus.)
Here I look at a sample air resistance problem. I will use variables instead of specific numbers. I know a lot of students prefer numbers. Tough luck.
I will put commentary in red; what actually should appear in your answer appears in normal, black (or blue) text.
The Problem: A block of mass $m$, initially at rest, starts sliding down a long, frictionless ramp that makes an angle $\theta$ with the ground. (a) Draw a free-body diagram, indicating all forces acting on the block.
(b) Calculate the terminal velocity of the block.
(c) Derive a differential equation describing the motion of the block.
(d) Solve for the velocity of the block as a function of time.
Get it? Got it? Good.
The Solution:
(a) Draw a free-body diagram, indicating all forces acting on the block.
Notes for part (a):
1. You should always draw a picture of the whole system, even if you aren't explicitly required to do so by the problem statement. A picture helps you figure out what's happening. A picture also serves as a convenient place to store bits of information - constants, variables, etc. Finally, failing anything else, it's tangible evidence that you tried, and may earn you some pity points. 2. Always define and label your coordinate system. Notice that, in this case, you want one that is tilted such that the x-axis is parallel to the surface of the plane. Hopefully, by this point of the course, you understand why -- motion will be one-dimensional in this coordinate system, and two-dimensional otherwise. Choose this one, and don't forget to label the coordinate system! 3. Drawing the free body diagram separate from the overall diagram makes it easier to draw without getting your diagram cluttered. But, if you
prefer, you can draw this directly on the original image. I don't recommend you place the coordinate system directly on the block, even though the center will be the origin. (Again, it will clutter the image.)Your teacher might prefer that you do so; make sure you check.
If you do, it will look like this. Note that you can distinguish the x- and y-axis from the force vectors by making sure the lengths of the arrows are different, such that the arrowheads don't overlap.
4. Forces should always be drawn
from the point where the force acts on the block. For normal and drag forces,
this means the center of a surface. For weight, this is the center of the
block. Yes, this matters; some past test solutions indicated taking off a half-point if this isn't done correctly. That may not sound like a lot, but keep in mind that a free response problem might be worth a total of about six points.
5. It's a good idea to define the forces if you abbreviate them in a diagram. Note that I used common
abbreviations for weight (W) and normal force (N). Air resistance doesn't really have a standard abbreviation, so I use a “f” and subscript “air” to make
it clear I’m talking about air resistance. It doesn't have to be lower-case; I personally
like to use the lower-case "f" for
frictional forces and upper-case "F" for other forces.
You don't have to label the forces as vectors. You can get away with writing this:
normal force : $N = mg\cos \theta$
air resistance: $f_{air} = -bv$
weight: $W = mg$ (These aren't intended to be bold; the LaTeX just makes it appear so.)
Just make sure you're consistent. Don't label it a vector on one side but not on another. Also, I follow the convention of using boldface to indicate a vector in a typed document. You can't really do bold when you're writing, so you would indicate a vector by drawing an arrow. Ex: $\overrightarrow{W}$. At this point, you know this, but for now I want these notes to err on the side of too much detail.
6. On the diagram, I drew some shaded, slanted lines on the plane surface. These lines are a standard way
of noting that the contact surfaces are “frictionless”. Not at all mandatory, but potentially useful.
(b) Calculate the terminal velocity of the block.
No motion or net force in y-direction, so all forces, velocities, and accelerations will be in the x-direction.
Terminal velocity $\rightarrow$ net force in x-direction is zero.
Notes for part (b): 1. Explicitly state that there is no motion in the y-direction. This allows you to ditch the $x$ and $y$ subscripts when talking about motion. It should be kind of obvious that the block isn't moving through the plane or taking off, but it doesn't hurt to mention it. 2. You should explicitly state that terminal velocity happens when the net force in the x-direction is zero, or, alternatively, when the net acceleration is zero. Note that the expression $F_{net} = 0$ is basically $F=ma$ in the special case of $a=0$. Just about every problem invokes Newton's Second Law in one form or another, so keep it in mind.
3. I explicitly defined $v_T$ as terminal velocity. It may seem nitpicky, and it probably is. But this basically makes it clear that you are solving for a specific velocity, and that this expression isn't for the general velocity of this object. In other words, you are emphasizing the fact, to the grader and yourself, that this is a constant, and not a general expression of the velocity of the object.
4. If you don't already, box your answers. It makes the job easier on the grader, which is good for everyone. (c) Derive a differential equation describing the motion of the block.
$F_{net} = ma=m\frac{dv}{dt}$ $mg\sin \theta -bv = m\frac{dv}{dt}$ $\enclose{box}{\frac{dv}{dt}=g\sin \theta -\frac{b}{m}v}$
Notes for part (c): 1. It helps to explicitly make it clear that you are replacing $a$ with $\frac{dv}{dt}$, as demonstrated in the first line. You must do this to make this an ordinary differential equation -- an answer in terms of both $v$ and $a$ probably won't get full credit. Besides, you'll need to convert everything to one variable anyway for part (d), and writing it in terms of $a$ would involve expressing $v$ as an integral -- something not allowed in a differential equation.
2. You don't have to solve everything in terms of $\frac{dv}{dt}$. But it will help later. (You are thinking ahead, right?) (d) Solve for the velocity of the block as a function of time.
Quick note: See note 1 for this section if you don't know why I want to take the time derivative of both sides.
$\frac{d}{dt}\left[\frac{dv}{dt}\right]=\frac{d}{dt}\left[g\sin \theta -\frac{b}{m}\right]v$ $\frac{d^2v}{dt^2}=-\frac{b}{m}\frac{dv}{dt}$
Substitute $a = \frac{dv}{dt}$ and $\frac{da}{dt} = \frac{d^2v}{dt^2}$ $\frac{da}{dt}=-\frac{b}{m}a$
Quick note: Skip the steps listed in blue if you're confident you can integrate this successfully without showing all the steps.
$\frac{da}{a}=-\frac{b}{m}dt$ $\int \frac{da}{a}=\int-\frac{b}{m}dt$ Separate variables and integrate both sides. $\ln a = -\frac{b}{m}t + C$ $e^{\ln a} =e^{-\frac{b}{m}t + C}$ $a = Ce^{-\frac{b}{m}t}$See note 2.
Initial condition from part (b): $a(0) = g\sin \theta -\frac{b}{m}(0)$ See note 3 if confused. $a(0) = g\sin \theta $ $Ce^{-\frac{b}{m}(0)}=g\sin \theta$ $C=g\sin \theta$See note 4 if confused.
$a = g\sin \theta\ e^{-\frac{b}{m}t}$ Substitute $\frac{dv}{dt}= a$. $\frac{dv}{dt} = g\sin \theta\ e^{-\frac{b}{m}t}$ $\int dv = g\sin \theta\ e^{-\frac{b}{m}t}dt$ Separate variables and integrate both sides. $\int dv =\int g\sin \theta\ e^{-\frac{b}{m}t}dt$ $v = -\frac{mg}{b}\sin \theta\ e^{-\frac{b}{m}t}+C$See note 2. Initial condition: block starts at rest, so $v(0) = 0$. See note 3 if confused. $0= -\frac{mg}{b}\sin \theta\ e^{-\frac{b}{m}(0)}+C$ $0= -\frac{mg}{b}\sin \theta+C$ See note 4 if confused. $C = \frac{mg}{b}\sin \theta$ $v = -\frac{mg}{b}\sin \theta\ e^{-\frac{b}{m}t}+\frac{mg}{b}\sin \theta$ $\enclose{box}{v = \frac{mg}{b}\sin \theta\left(1-e^{-\frac{b}{m}t}\right)}$
Notes for part (d):
1. Why did I take the time derivative at the beginning? It's because, unless you've had a dedicated differential equations class and know how to solve a first-order ordinary differential equation with an additive constant, you probably need to go through these steps to make sure you end up with the correct constant coefficient. At time of writing, I'm not sure when (or if) this is covered in AP calculus AB or BC. But for those students taking AP calculus and physics C concurrently, it's possible they will have had no experience with solving these kinds of problems. (Some of my students have confirmed this.) Therefore, I'd recommend this more detailed derivation.
2. It pays to be careful. Note that the constant of integration for $a(t)$ involves a multiplicative constant, while the constant of integration for $v(t)$ is an additive constant. If you don't understand why it's a multiplicative constant for $a(t)$, go back and look at the derivation, and review the section in your calculus book that covers derivatives and integrals involving the natural logarithm and exponential functions.
3. Note that the initial conditions. At $t=0$, the initial velocity is zero, or $v(0)=0$. The initial acceleration is not zero, however. Because the initial velocity is zero, we can substitute into the expression for $v$ from part (b). 4. $e^{(0)} = 1$ 5. Note that, as $t\rightarrow \infty$,$v \rightarrow \frac{mg}{b}\sin\theta$, which is precisely what you calculated as the terminal velocity in part (b). More generally, substituting in limiting cases like $t=0$ and $t=\infty$ are really good ways of checking that you didn't screw up.
***** Summary:
I know, I know -- the problem looks too long. The calculation for (d) is a bit longer than most of the derivations you will have to do on the free response. But it's a good problem. And if you take out all my red commentary, you'll find that the actual solution should fit within the space allotted.
Everything in red text will get more or less automatic as you practice questions. Assuming I consolidate this and other materials into an e-book at some point, a lot of the text will be consolidated into earlier chapters, with possible hyperlinks to the relevant section if someone is confused.
Do let me know if you've found this useful, or if you would make any changes. If you have a preferred way to simplify the long-ish derivation in (c), I'd love to hear it. If you think it's overkill to be picky about various aspects of notation or explanations in solutions, I'd also like to hear it.
***** MathJax note: It appears that MathJax scales the font size of mathematical expressions dynamically according to the size of adjoining text. It presently looks too small. Workarounds that involve scaling commands in the html are evidently not recommended, at least according to some of the posts I saw online. For Blogger, it is sufficient to highlight the LaTeX code and set the font size to "Large", though that plays a bit of havoc with line spacing.
Also, it took me a while to realize that I had to edit the html to activate an additional package, "enclose.js", to box my answers. This actually took a lot more time to figure out than actually installing the base package. There are a lot of optional packages that are only activated if you edit the html to call them on the MathJax server. More details on the optional packages here: http://docs.mathjax.org/en/latest/tex.html
This is the story of how I got interested in astronomy and managed to will myself somewhat far down the professional path.
There were three primary influences: a man, books, and television.
The man:
I think I was about six when I met Uncle Kimo, a cousin-in-law-in-law. (My aunt married a man who had a sister who married Uncle Kimo.) At the time, Uncle Kimo worked at JPL as an instrumentation engineer. I really liked "Uncle Kimo". He seemed to know a lot of things! We spent time drawing maps of continents and he would tell me about space. Over the years, he sent me some of those nice high-gloss photos from Voyager and other space missions. Some of my personal favorites were a radio reconstruction of Venus' surface, Jupiter's volcanic moon Io, black and white images of Uranus' satellites, and that stunning deep blue shot of Neptune and the Great Dark Spot, accented by some bright white storms (the largest called "Scooter", if memory serves).
I think I loved Uncle Kimo not just because of the cool space stuff. He was maybe the first male family member I really felt comfortable around. My dad was crazy and unstable; my uncles either scared me because of their anger or were just not that interesting/good with kids. I loved my grandpa, but he was intimidating (especially to everyone older than me), and the language barrier made us not quite as close as we might have been.
Also worth emphasizing: Uncle Kimo was the first adult who really tried to teach me about the world around me, and do it in a way that didn't assume I was just a dumb kid.
I only saw Uncle Kimo a few times growing up, but I'd still place him as a tremendous influence on my life in general, and my interest in astronomy in particular.
Books:
I spent a lot of time alone growing up. My parents divorced when I was three. My mother worked, and so my grandparents played a large role in raising me. They were kind and loving, but didn't speak much English, so I ended up turning to books. My mom says I initially hated to read, and would slam my little hand down on any book she tried to open and read to me. Maybe I was creeped out by Shel Silverstein's artwork in Where the Sidewalk Ends. But, eventually, I did start reading on my own.
I read it probably a couple hundred times. I loved the artist's depictions (all images of the planets were hand-drawn).
I still remember it mentioning NGC 5128 (depicted on the cover, right side), thinking "That's a weird name for a galaxy. Why wasn't it called something like the Milky Way? Or Snickers?" (It's a radio source, and got special mention, though I thought it made weird sounds because the artist's depiction made it look like it was surrounded by hair.)
I also went through a weird phase as a kid in which questions in a book would freak me out. They scared me! Because of that, I'd have to skip over the last part of the Mars section? "Was there ever water on Mars? Could there have been life?" It was that and an earthquake preparedness pamphlet that creeped me out with those "?", which I must have mentally read in some sort of spooky voice. (Did anyone else have this, or was this a leading indicator for profound mental unsoundness? -- again, with scary questions!)
I loved that book so much.
More books. Remember Scholastic catalogs? Or Arrow? Or the other one? Classroom teachers would give us these catalogs filled with books that we could buy at (what I thought were) reasonable prices. Now, I didn't know how money worked, even though I loved Scrooge McDuck in Ducktales and tried to swim in a pile of dimes in my grandparent's living room. (Maybe another flag that this boy ain't right.) I remember that in first grade everyone wrote a letter to President George H. W. Bush. I wrote that the process of making change (money, not policy) seemed unfair -- why does someone get to keep more of the money? My teacher helped me write it, but I'm a bit annoyed she didn't try to sit down and explain it to me at the time. I got a photo back, but I don't think the letter had an answer.
Also, in retrospect, this was one place where economic differences started to show. A lot of my classmates probably couldn't afford any books. I always got to pick a few, as well as get a subscription to Highlights! magazine.
Goofus generally gets what he wants, even if he is an asshole. Gallant is a spineless appeaser and a fake, pretentious prick. Guess who I grew up to be?
This was not my favorite book. I don't know why -- I carried it around everywhere. It just seemed not as exciting, or less accessible because of more data. There were tables of numbers, I think, and maybe fewer dramatic, page-filling images.
I got a more important book that had both dramatic pictures and tons of numbers (though not derivations) around first or second grade. My Sunday School teacher gave me his old college astronomy textbook, a paperback that cost $34.75 at the Aschula's student store. (I still remember the sticker on the cover.) The book was Essentials of the Dynamic Universe: An Introduction to Astronomy, Second Edition by Theodore P. Snow. Sadly, I can't track down the cover image, but it must have been a saturated image of a star, or an AGN, or something like that, with some rainbow accents suggesting spectra.
I think I read that book cover to cover several times. This was the source of nearly all of my knowledge of introductory astronomy. Memory being what it is, those early memories were retained much more easily than ones in college, making it sometimes challenging to rewrite my knowledge of certain important constants. (The distance light traveled in a second was, in my mind, 186,282 miles, and not 299,792 kilometers. Mercury orbited the Sun at a distance of 38 million miles -- and unfortunately all my distance scales inside the Solar System remain imperial.)
Same church: our rather conservative junior minister occasionally called on me, possibly for comedic effect, to quote some astronomical fact -- closest star, distance to the Sun, etc. -- that had some tie-in to his sermon.
Years later, after being accepted at CU Boulder's astronomy grad program, I happened to meet with Theodore P. Snow. (I think he went by Ted at the time.) Usually, meetings were about prospective research, but I spent the entire time as a fanboy gushing about how incredibly important his textbook was to my life. I have no idea whether it was flattering or scary for him, but I was thrilled to put a name to a face. (It also helped that he seemed nice -- read: Not A Professor Asshole.)
This book and interactions with that pastor explain why I never, ever thought of a conflict between science and religion until I started paying attention to politics/went to college. I still think it's misguided/overrated.
Books were a good substitute for technology. I was lucky enough to get a small telescope for Christmas, but quite frankly, it was a piece of crap Celestron. I probably should have read the manual more carefully, but none of us really took the time to figure out how to use the RA and DEC wheels, or how to use coordinates to find things in the sky. Oh, and perhaps most importantly, I couldn't see jack shit because I was too close to Los Angeles. Saturn's rings and the Galilean satellites were nice to see, but a bit anticlimactic after spending years staring at NASA images.
Television
As a kid, I watched a ton of TV, unsupervised. I remember being confused as to why "Orchie Bunkur" was so angry all the time. (This is a reference to All in the Family.) I even wrote a letter to that effect, to no one in particular. (I liked writing letters as a kid.) This letter was proudly placed in my grandpa's scrapbook without further comment, a testament to both his love and the complete absence of analytic evaluation of child behavior in my family.
I watched a lot of Star Trek: TNG. Remember that it ran from 1987-1994. From the age of four to eleven, I saw brand-new TNG episodes. I saw the very first airing of "The Best of Both Worlds". Eat your hearts out, young nerds.
I would record a lot of these episodes and re-watch them endlessly (VHS, in case the young people are curious). I didn't have particularly good taste -- I recorded as much as I could, and ended up with a skewed impression of the overall series, with Data being held up by Samuel Clemens with a .45 revolver playing a more important role than, say, "The Inner Light" or "Darmok". More fortunately, I also recorded and watched "Chain of Command", though maybe even scrubbed and tidied torture scenes weren't the best thing for a young child to process.
I also watched Babylon 5 and Star Trek: Deep Space Nine. Again, I had no taste -- I thought Babylon 5 was an incredibly well-acted show and ST: DS9 weak by comparison (I would reverse those judgments years later.)
But in addition to sci-fi, I watched some sci-fact. NOVA specials were great, and what I know of cosmology comes from them.
The most personally important program, however, was a National Geographic documentary titled Asteroids: Deadly Impact. It primarily focused on Gene Shoemaker and his study of asteroid and comet impacts. Of course, no one man or team can claim sole ownership of such a broad field, but it made for great watching.
Again, I recorded this, and watched in at least 50 times. I returned to it a few times in high school, especially when I had an abysmally poor physics teacher, to sort of remind me why I thought astronomy was worth studying.
Epilogue:
These influences were critical. I enjoyed reading books. I had a person who cared about me, and encouraged my interest. Even my religious authority figures fed this interest in astronomy.
I didn't really know what astronomers do until later, and in retrospect, I probably should have looked into it a bit more before embarking on a professional path.
But in some ways I was more successful than I should have been. How many of us dreamed of being a paleontologist as a kid? Or a marine biologist? At some point, most of us revise those dreams -- ideally because we discover other interests, but often because the impracticality of our dreams are beat out of us by parents, teachers, or others.
When I was about four, I said I wanted to be a pediatrician, probably because my pediatrician, Dr. Nakashima, was a hilarious and awesome guy who claimed to be a ninja turtle, and maintained that despite my challenges. But my mom's asshole friend said that that wasn't a good idea, and I never, ever considered being a medical doctor, even though, in retrospect, I probably would have been a good one.
I was lucky, in some sense. I was lucky to have enough resources and opportunities to follow my dreams without reality intruding. Sure, it was unfocused and overly idealistic. Sure, I hit points when the contradiction between what I felt were my skills and interests diverged from what I appeared to be doing. And yes, it ended pretty badly, and I'm still recovering from poor choices I made.
But I got away with it for a hell of a long time, partly because I was good enough at math and science to do it, but partly because I had just wanted it so badly and didn't know "better" not to irrationally pursue what should have been a more deliberate, cautious, and considered course of action.
Maybe I shouldn't think that I failed spectacularly. Maybe I should instead be grateful that I got away with it for so long.
I swear, I thought this was an article from The Onion. But it's from Buzzfeed. And it's an accurate quote.
Reality has been out-Onioning The Onion for a while, to the point where I think they'll go out of business in the next few years. How can you mock the world when it consistently steals your punchlines?
I read the article, and still had a piece of doubt. Surely, this must be an elaborate hoax. What leader could be credibly anti-smart, especially a leader who was a credible Presidential candidate for a major party?
Then I saw the video.
I admit, I laughed. A lot. I laughed more than I had laughed at all of the stand-up comedy I had listened to today - and I listened to some absolute gems.
But then I thought a bit, partly triggered by some of the quasi-defenders on the thread. Some people, including some who strongly dislike Santorum, are on the thread are questioning whether the title is misleading. Do they have a point?
In a word, no.
In _____ words,
*breathes in*
Ok. First, it's a direct quote.
Second, it's pretty clear from the context that "smart" is supposed to have negative connotations. At the bare minimum, he is associating it with academics or expertise, and this is clearly evident within the context of the wider speech.
So "smart" is being used as an insult.
Oddly, my experience has indicated that you can call a person a lot of things and not have them be bothered, as long as you don't attack their intelligence. Once you question that, the reply you can expect is the communicative equivalent of a honey badger released in your pants, and said badger having been told that delicious termites exist somewhere within your entrails.
I could leave it at that. But I can't. Because at this point my laughter at the sheer ridiculousness of having been "Rick Roll'd" has given way to consuming rage that he, and a huge number of people in this country - and around the world - are serious. He's not a somnambulant stand-up comedian genius - he's fucking serious.
And another thing: put aside the blindingly breathtaking bullturd of trying to make "smart" a dirty word. When did "elite" stop being a compliment and start being derogatory? When did it get conflated with "elitist", which has a distinct meaning? In the world of policy, business, academics, and science, I HOPE the people leading an area of research, or for that matter, the country, are elite. I HOPE they are better than average. I HOPE they're smarter than I am. I HOPE people who enjoy large amounts of power, beauty, success, and responsibility are endowed with above-average capabilities.
I hope that, in part, because we've got some damn meritocratic values that are pretty fucking cemented into the foundation of our ideal of America.
I know we like to call them idiots and numbnuts, etc., and politics can be pretty stupid. It's fun, and mocking politicians is truly the only global sport. It's way more entertaining than watching dirty foreigners spend 90+ minutes chasing a sphere of white hexagons or black pentagons - or black hexagons and white pentagons... I care so little I didn't bother researching which it was - only to finish in a goddamn tie. As a good American, I don't do ambiguity - moral or athletic - well.
But there is a naive part of me - perhaps the part that still believes in Santa Claus, the Easter Bunny, and Justice For All - that believes elite (but not elitist) leadership is a desirable thing. Hell, there's a part of me that believes it operates at some level - hopefully higher than my pessimistic weltanschauung would have me believe.
Otherwise, the nation is truly fubar.
When, when, did the passion for individual sovereignty override any sense that some people have better knowledge over some things than other people? When did we start believing that movie stars have special insight into vaccinations, or psychotherapy, or anything that isn't fucking movies? Why, with such bitter irony, does a political slant against concepts of wealth transfer and affirmative action embrace the democratization of truth, debasing expertise into mere opinion?
It's not just an American thing, as Dara O'Briain, an Irish comic, points out. (He, by the way, studied physics and mathematics in college before going into comedy.)
The sad truth is, no, my opinions are not better than expertise. I think I know a lot about things, and certain things a great deal. But I'm not an expert in health policy, or fashion, or abstract expressionist art. I'm not even a goddamn expert in astronomy - I've only got a masters degree in it. I quit my PhD program in part because I had a vague sense of how fucking much I needed to know about a specific area, and how goddamn hard I'd have to work to get there, in order to be anywhere near a credible expert. And I didn't care enough, even about planets around other stars (which is pretty damn awesome, even by the lofty standards of astronomy), to do it.
I know more than other people, a lot of people, most people, about a lot of astronomy. But there are people who know more than me. And in order for society in general, and science in particular, to, you know, progress beyond rudimentary levels, I have to TRUST people that have more knowledge than I do. I have to. I can't research every goddamn thing; hell, memory is such that a good chunk of the things that I think I know, and think are well-founded, are probably partial or complete bullshit.
Yes, experts sometimes lie, or cheat, or fuck up. There's a measure of skepticism we have to learn. But at some point, I have to trust - or I become, in the most literal sense, some sort of paranoid schizophrenic.
I have to decide whether fluoridation is a massive conspiracy with untold health effects that aren't covered by my knowledge of chemistry, or if it really is something that is the product of (known) health and economic benefits outweighing against (known) health and economic costs.
Maybe I could speculate on the extent to which the cult of individualism is a coping response to a host of unresolved existential crises modern individuals face, or the possibility that it's a reaction/protest to cultural and religious sources of guilt and shame.
But I'm not an expert. I'm not elite. I'm not smart.
That doesn't preclude me from an incoherent opinion - the standards of fact-checking and refereeing are pretty low for blogs in general, and this one in particular.
But this is too long already. And I got some stupid, pointless-ass shit to do... like watch Youtube comedy clips. Better that than contemplating the intellectual suicide of our great nation.
Like Stephen K. Amos, I, too, am trying to find the funny side of life.
PS: If you actually clicked on "Rick Roll'd", congratulations. You've just Rick Rolled yourself, and you have no one to blame except you.
Nowhere is it more clear that the expert is dead than in political discourse over climate change in America.
More evidence won't help the case of global warming/climate change environmentalists. More evidence would only help if there was a consensus on the legitimacy of the evidence, as well as a better sense of the baseline levels of crackpots in the scientific process. (The latter is necessary to judge roughly whether the current levels of dissent about anthropogenic global warming are actually indicative of a real "debate" or "open question".)
Scientists can't defend the models and implications of climate change if scientists themselves, and perhaps the scientific process in general, is regarded as illegitimate. Consequently, I am pessimistic about the prospects of "education" or "more, better evidence" changing the politics of climate change. More research, of course, will help refine models and provide, hopefully, better predictive power for mitigation efforts.
In case what I've said is completely beyond comprehension of those reading this for whom science in general, and scientists in particular, take that they are legitimate as a given, let me use what I believe to be an accessible example.
Many (but not all) scientists are somewhere between agnostic and atheist. For them, Biblical literalism is seen as ridiculous because the Holy Bible itself lacks legitimacy, either as absolute historical truth, or a legal/moral authority. Quoting scripture to justify an interpretation of God's will won't convince an atheist for pretty obvious reasons - the entire line of argument is seen as starting from a bad foundation.
Now, there will be people who argue that this is an unfair comparison. Science, they might say, is based on observable, testable results, while religion in general, and fundamentalist Christianity in particular, is not.
That's not the point.
The point is that it is often a waste of time to argue with someone using what you perceive as gold but the other person perceives as crap. All it does is reinforce your own prejudices and piss everyone the hell off.
I think that the grumbling I hear/read from economic conservatives, moderates, and intellectuals about the ridiculousness of present-day politics comes from the decline of the legitimacy of experts. Americans, historically, have distrusted central authority. But during certain periods (the Cold War being a particularly good example), experts in general, and scientists in particular, were held in particularly high esteem. They were seen as highly trusted, dependable, and patriotic.
So what happened?
I'm speculating that it could be traced to three reasons.
1. The gulf between promises and reality
Remember when we were supposed to have floating cars by the 1970s? Or travel to Europa in phallic spacecraft by 2001? These didn't happen. And while we do have things that, upon further contemplation, may be even more amazing (and useful) , it still remains that the nature of both funding and human behavior causes advocates of long-term projects, however necessary, to often overpromise and underdeliver. If one manages expectations appropriately, it is possible that one will lose funding to those that are willing to promise the Moon (sometimes literally). Consensus projects like National Science Foundation Decadal Surveys are supposed to counteract this possibility, but this process is not immune to abuse, or more probably, managerial incompetence.
2. The abuse of public trust and scientific research by a few bad apples
Many scientists were, and remain, exemplary models not only of professionalism, but also of citizenship. The bad apples are rare - but they do damage far out of proportion of their numbers. Every scandal, every instance of academic fraud, or even the suggestion of fraud, damages the public trust in the scientific process, and those engaged in research.
During the Cold War, science had it pretty good, physicists in particular. Masters of the atomic bomb, they had unparalleled access to policymaking and funding priorities. Some departed company from real science and became engaged in influence peddling. There are probably many examples of this, but the example talked about in my field was Edward Teller. In addition to leading the development of the thermonuclear bomb (the H-bomb), he ruined Oppenheimer by leveling McCarthyist charges against him, advocated creation of harbors using nuclear weapons, and promoted the Strategic Defense Initiative (a missile shield), a program that, then as well as more recently, has been a huge drain on resources and promising very little in terms of practical ICBM defense.
3. Lack of contact between professional researchers and the public
By its nature, scientific research is challenging and demanding. It takes a very specific type of person, with very specific priorities, to be successful in research science as it is currently constructed. Research is also conducted by a relatively small percentage of people. It is also true that these people don't always fit into mainstream patterns. For example, a former professor once told me that 94% of AAAS members are atheists. Even if he was off by a factor of two, that would still indicate a divergence in cultural values from mainstream America.
Interestingly enough, there are parallels to the cultural effects of having a professional military in which service is limited to about 1% of the US population, and generally more prevalent in the South than in other parts of the country. The experiences are widely divergent, obviously. But the fact remains - when you have a small minority of the population engaged in specialized work, or with very distinct experiences, integration with and understanding by the rest of society is often lacking.
One great counterexample I have for this: the liberal churches I have attended in my life. In both the church I grew up in, Montebello Plymouth United Church of Christ, and the church I attended in graduate school, St. Paul's United Methodist Church, there was a sizable scientific population, and also a majority of non-scientists. We got along well. It may have helped that the churches were liberal, and that, whatever doctrinal differences individuals may have had, generally we adhered to that key principle of Jesus:"Don't be an asshole."
4. Neo-Ludditism
Americans love technology; NSF surveys indicate that we are one of the most techno-friendly cultures of the OECD. But I don't think we love science. Especially recently, I think we see technology and science in terms of a divergence between opportunities afforded the technical elite and the rest of us. When the narrative shifts away from "working on the arsenal of freedom" to "20-year old college dropout Internet millionaire", look out!
There might be other cultural effects here - anti-nerd tendencies, jealousy/anger toward academically successful kids, etc. They all feed into this odd combination of a love of gadgetry but a distaste for science, especially if science is somehow tied to the obsolescence of your job.
5. The dilution of the definition of "expert".
"Expert" used to mean something pretty specific. It meant that someone was well-respected by his or her peers, had made critical contributions to the field, etc. Now that news has become more entertainment-based, anyone can be an expert, a "talking head". This has debased the value of the title "expert". There's a lot I could write about this, especially in its relationship to the proliferation of "think tanks" that are, functionally, lobbying and advocacy groups. But time grows short, and this post is long enough already. But don't confuse brevity with unimportance - this is a critical aspect of the modern American story of expertise. I just don't know if it is a symptom or a cause (likely both).
Next post: The expert is dead! Long live the expert?
I am happy to report that I did not witness - or at least was not aware - of any fraud during my time at Cornell. It might be harder to get away with in astronomy and the natural sciences, as opposed to the behavioral sciences discussed in the articles, simply because there are fewer excuses for nonrepeatability of results. Mice could behave differently, but photons generally don't.
That said, it's an opportunity to share my personal experiences with cheating. Rather, it's a single experience, but it's bothered me enough to admit it.
I never cheated on any homework or test in K-12. In fact, I even turned in a poor guy who was cheating on an 8th grade science test. I did it discreetly, and I have hope that the teacher was gentle, but I still feel guilty about it. I should've approached him directly. But I didn't, maybe because I had a rigid view of right and wrong, and maybe because I was particularly hierarchical in my value system.
Thanks to a belief in both Harvey Mudd's Honor Code and my own (somewhat unrealistic) belief in my own abilities, I never cheated in college. There were a few reported incidents of cheating by peers in college, but they were largely regarded as one-offs. I'm sure it happened, but, charitably, I'd like to think it happened less frequently than at other colleges.
At Cornell, I remember the stress, panic, and depression starting to set in toward the end of the first semester. My grades were reasonably good, but my research was not, and the doubts I had about pursuing astronomy were beginning to be confirmed. It was perhaps a product of my decreasing confidence that I cheated for the first and last time on an academic test. I don't recall which class it was, but I recall using outside materials and seeking outside help.
I felt terrible about it, terrible for a long time. It may or may not have made a difference in my final grade, but as the difference was perhaps between a B+ and a B, it didn't matter by grad school standards.
It did, however, profoundly impact my view of myself as an honest scientist.
Much later, I did hear about other tales at Cornell of academic dishonesty. They included the absurd - a former professor, well before my time, was caught double-billing his travel expenses to NSF. They also included the depressing - an employee admitted to working half-time for the last few years on a program, but then proceeded to hold the project hostage. Such are the perils of smaller research projects - one person really can be irreplaceable.
I was never, ever pressured to deliver results by others; in that, I think I was far more fortunate than most people in grad school. (It helped I had my own money - the NSF fellowship.) However, I can understand and sympathize with the self-imposed pressures of individuals - some of whom, let's admit frankly, are the product of a selection effect that discourages those who are well-rounded or have developed a healthy self-esteem across multiple areas - who would be so obsessed with academic approval that we would compromise our values to keep the supply flowing. This in no way applies to my former colleagues - most of whom, I confess, I was jealous of because they did seem pretty well-adjusted.
All this to say that self-imposed pressures can lead good people to cheat. And, like so many sins, once it is committed, it becomes easier to continue along that path.
I never cheated in school again - honestly, it wouldn't have helped. But I can imagine that those who find a way for it to work, those who have a combination of bad fortune to have an onerous PI, or uncooperative project, coupled with disinterest in making the project work, or perhaps a desperate need to be a "success", would feel that cheating was a way out.
It also brings up the issue of redemption - in science, there is none for cheating. What about in the rest of life? Do we really believe in the possibility of transformation stories - to use a biblical reference, the conversion of Saul to Paul - or do we really ascribe to a view that reform is impossible?
I think our words and our actions reveal two different answers. For a Christian nation, we do believe in the death penalty, life without parole, incarceration over rehabilitation, and marking individuals who are released with their own version of Jean Veljean's yellow convict papers. We hold people's past misdeeds against them, and forget their good actions. We're bad at weighing things in a balanced fashion. There may be evolutionary reasons for this, but I'd hope that we depend upon more than evolutionary selection to base our moral philosophy.
Have you cheated? Academically? Personally? Did you feel remorse? Did you get away with it?
I’ve just been hired by Excelsior school, a private boarding school in Pasadena, CA that serves about 60-70 predominately international students from East Asia and Russia. I will be teaching six subjects: pre-calculus, calculus, physics, chemistry, Algebra 2, and SAT math. I will be teaching five days a week, about six hours a day. Pay is $24/hr. Health benefits typically aren’t offered until one has worked there for a year, though I’ve got a verbal promise that I will be given them after one semester.
I don’t have a teaching credential. But, as the interviewer mentioned, he tends to view those credentials as secondary to skills involving classroom management, subject area knowledge, and organizational skills. He said, three times, over the job offer call that he has great confidence that I’ll be able to do the job. It might be something that is said to every new hire, but it made me feel better.
I expect this will be a pretty grueling job. I’m expected to take over from the current teacher within the course of about three days. At least they have textbooks and, I’ve been promised, clear guidelines from the principal about what are the objectives for each class over the course of a year.
I’m not completely sure what I’ve gotten myself into. But at least I’ll have a reason to be in Pasadena after school hours, and will tutor AP courses at another nearby location.
I’ll save celebration for when I’ve survived a few weeks. In the meantime, I will be soliciting everyone I know who is/was a physics/math/chem teacher for advice, materials, websites, and general psychological preparation. (Help me get the “Charge of the Light Brigade” out of my head whenever I think about this job.)
I had a brutal interview today for a tutoring job. Writing it up as a lesson to myself and others about under-preparation and overconfidence going into an interview with a test component.
It started nicely enough –resume questions from the president, who is an econ major, and some jovial joking with a Caltech engineering major who had worked at JPL. I bedazzled with my complicated one-sentence statement of my previous research and my more understandable explanation of what “non-redundant aperture masking with adaptive optics” really meant. I displayed a comfort level with the subjects I’d be expected to tutor (biology, chemistry, physics, calculus, pre-calculus) and even tied in my behavioral econ knowledge to indicate how I can relate to individuals from different disciplines and career aspirations.
I was anticipating a diagnostic test, which I had prepared for by taking a sample Physics B AP test. I did reasonably well, missing a couple questions concerning induction and the lensmaker equation (apparently I forgot the sign convention for the focal length, where it is positive if the lens is convex and negative if it is concave).
Just as I’m about to be asked some qualitative physics questions from a high school physics textbook, another tutor arrives. He is apparently a Caltech senior physics major, currently applying to grad schools. His engineering colleague, seeing the physicist arrive, decides to have him ask me some questions.
Continuing the theme of "ultra-heavy Sunday", I'm considering a grim possible future outcome of the energy crisis. This, I admit, is inspired by the Discovery Channel special on global energy consumption: Powering the Future. This is going to be a lazy, "for-fun" analysis - don't expect numbers or a lot of research.
Imagine a world where energy costs have become a high, and possibly primary, cost of input. Imagine further that the economic and environmental stresses have led to shooting wars over remaining energy resources in the Middle East, the Arctic Ocean, the East China Sea, and the Niger delta. The conflict has also made deployment of a number of large-scale solar power arrays (photovoltaic or concentrated solar) and wind farms prohibitive, as their geographic and technical requirements mean they are particularly vulnerable to attack.
"Character may be manifested in the great moments, but it is made in the small ones." - Phillips Brooks
I’ve been thinking about the words of Phillips Brooks for some time. It’s amazing how an Episcopalian minister from 19th century Massachusetts can still touch lost seekers.
There is nothing I have found from science that compares. Science can provide drama, mystery, and grandeur, but it, and its practitioners, neither acknowledge nor touch the soul.
I love my former colleagues, more than they will ever know. That is why it breaks my heart when I consider the cynicism, the hate, and the fundamental fear that stems from the denigration of faith in general, and Christianity in particular, that I witnessed. And that is why I found comfort on Sundays at church.
The following comments were in response to an Economist article, "Science behind closed doors", concerning climate change science. This is perhaps the first time I've publicly communicated my thoughts on the ongoing discussions of global warming and climate change. I would appreciate your input.
Vitriol surrounding climate change appears to conflate a few separate topics that have to be discussed in turn:
(1) The science of the greenhouse effect
(2) How much of it is caused by human activities (anthropogenic, in IPCC-speak)
(3) The effect of increased CO2 on temperatures, crop yields, disease, etc. on a regional basis
(4) Scientists’ roles as analysts/messengers/advocates
(5) How much governments, industry, and individuals should do to prevent it
I had the opportunity to interview Dale a couple times at the Kendall retirement community in preparation for a 50th anniversary Sputnik panel discussion. He is, today, at 95 years young, a bright and wonderful conversationalist. I began to understand WHY there are jokes about Kendal having a better physics department than Cornell - there are a lot of brilliant people there.
I think the book focuses on his tenure as Cornell President and controversies centered around the Vietnam protests. But I'm actually more interested in his earlier years. From what I gathered, Corson was a figure in the Presidential Science Advisory Council and was party to the remarkable post-Sputnik efforts in science education. He was also a key figure in creating Cornell's Science and Technology Studies department.
If you're interested in science policy or the history of science in postwar America get a chance, try to get a chance to speak with him. His legacy continues to be written - as are all of ours - by simple words and stories that, unknown to the speaker, sticks with the listener for a long time.
I've had a head cold all week. It's terrible, and entering into the achy, can't-drive-so-I'll-nap-and-drink-coffee-at-Starbucks-in-Virginia-because-I-needed-to-get-out-of-the-house-but-underestimated-my-fatigue phase. I should at least be no longer contagious by the time Mom stops by on Sunday, giving me a chance to acquire whatever contagions she picked up flying through O'Hare.
One good thing came of this trip. (It wasn't the Mexican food in Leesburg - what the hell was I thinking?) I listened to parts of both hours of Science Friday, hosted by Ira Flatow. Ann, it's taken me four years to actually getting around to sampling the program. And I can safely say that your enthusiasm for the show wasn't just your characteristic enthusiasm for life in general. It's an excellent program that discusses substantive issues in an easy-to-understand way.
I recently wrote three long-ish letters (not e-mails) to three old men at my church in Southern California. All of them are suffering from health problems of varying degrees. If you are so inclined, I'm sure that Jack, Kenji, and Jim would appreciate your prayers. This post is a product of the fond memories and thinking those notes catalyzed.
Sometimes I wish I could say that I'm a Christian because I felt that the Bible was the revealed word of God, or because, after a careful study of all religions and philosophies of life, that I found that this religion most closely aligned to my understanding of morality and justice. In all honesty, I was a Christian because I was born into a family that attended a Christian church - specifically, a United Church of Christ congregation.
I love Robert Ballard. I grew up with his books on the Titanic, the Bismarck, and the Isis. I must have read the first two about 80 times each.
I also have a friend working for Bob Ballard in Rhode Island on underwater archaeology.
So I was unpleasantly surprised when I saw him trash talk NASA on the Colbert Report on Feb 10, 2009.
Admittedly, he makes a lot of good points. Because of maritime law, which guarantees countries owning habitable land exclusive economic zones (EEZs) 200 miles offshore, there is a lot of real estate that the US knows precious little about.
But why make NASA your whipping boy? And why attribute it to quasi-religious needs to become closer to God than historical/economic reasons stemming from the Cold War and the importance of satellite systems to the modern economy?
On a side note, in a conversation I had with a member of the National Academy of Sciences staff, he said that astronomers are the whiniest constituency of scientists fighting for NSF budgets. Maybe Ballard knows something I don't.
Today I had a long conversation with a friend from Harvey Mudd. He, like many of my friends, is excited that Barack Obama won the presidency on Tuesday. And he, like many, is dismayed that the voters in California decided to pass Proposition 8: “Eliminates Rights of Same-Sex Couples to Marry.” In our conversation, I realized that the issues surrounding whether or not same-sex couples should have the right to marry is tied to an aspect of religious belief in a way that reminds me of another area of social conflict – the fight over evolution. I thought it was time for me to share my experiences and thoughts on this other battle, and then see if I can apply the lessons inferred to this present conflict.
On April 15, former presidential candidate Mike Huckabee spoke at Cornell. I was struck by how likable he was. He was charismatic and well-spoken. I thought he made a wonderful and correct point talking about how his experiences as a minister were distinctly valuable, and very different from his fellow candidates. As a pastor, he said, he saw every form of human frailty, and spoke with men and women from all walks of life. I have been, and remain, in favor of the separation of church and state. But considering that the legal profession (as I imperfectly understand it) is focused on specificity, precedent, and argument, I believe there is something to be learned from the shepherd-leader who knows how to listen, to make those around him or her feel heard and cared for, even if there is no final resolution of the difference of opinion.
I found one brief portion of the talk particularly enlightening. Throughout his talk, he poked fun at himself and the controversy he generated—Eisenhower, Sherman, and other impressive American leaders have been very effective at the art of disarming self-deprecating humor while maintaining decisive leadership and command. When the topic of evolution came up, he relieved the potential tension with a joke. He pointed out that “he didn’t know…. He wasn’t there.”
It struck me a bit odd, and it took a few days for me to realize why that brief, rather mild joke was so important. It goes to a point Phil Muirhead at Cornell Astronomy once pointed out – that there was a world of difference between scientists, whose work depends upon trusting the results of other experiments that they did not personally conduct, and individuals for whom the threshold of truth is personal experience.
This is odd because Governor Huckabee does trust the custodianship of another set of events for which he has no personal experience—namely, the crucifixion and resurrection of Jesus Christ.
I point this out not to highlight inconsistency, but to underline a key point that is missed during the talking past one another that secular scientists and religious community members seem to have, or conservative Christians and homosexuals, or Democrats and Republicans.
There is a deep disagreement on the sources of truth, legitimacy, and authority between the great cultural divides in our society.
A good scientist will study and question the custodianship and legitimacy of the set of experimental and theoretical work that has led to modern evolutionary biology. And a good Christian will examine the ecclesiastical and temporal histories that shaped, and were shaped by, Christianity. And ideally, both are willing to study outside their areas of competence, and discover and construct a more complicated, subtle and meaningful identity for themselves than existed before.
Yet it is the nature of power to react against the threat posed by other sources of truth and legitimacy. Though human beings are complex, our limited resources often cause us to focus on specific salient aspects of ourselves. At any given moment I may be a man, an Asian, a scientist, a job seeker, a Christian, a Democrat, a writer, a son, an American citizen, and a trader. But rarely do I retain awareness of all those aspects. Even if I did, I might underweight or overweight the contributions of any one in my actions and reactions to a given situation.
Wisdom comes from knowledge and experience. Both depend upon two factors:
(1) our ability to analyze and arrive at greater truth
(2) our ability to recognize the limitations of both the processes we use and the scope of our conclusions.
By (2), I mean that we need to depend upon multiple processes for understanding our world and the truth, in both a physical and a moral sense.
As an astronomer, I used multiple wavelengths of light to infer greater knowledge about stars and planets. Were I to limit myself to the one band where I have personal experience (visible), I would be unable to detect brown dwarfs around nearby stars, unable to detect ice on the Moon, unable to track star formation in distant galaxies. Indeed, the different academic disciplines provide different lenses and different toolboxes by which we can analyze and process texts, external events and personal experiences. (This is why I support a broad liberal arts background combined with a rigorous scientific education.)
And as a Christian, I have studied not only the Bible and prominent Christian theologians, but also other major religions, the complicated relationship between temporal and ecclesiastical authority in the Roman Empire and Medieval Europe, and how the evolution and decline of mainline American denominational churches has affected poverty work.
And I have tremendously enjoyed the opportunities afforded by my limited travels, my education, and inscrutable fate to have wonderful conversations with men and women of all walks of life, of varying degrees of power, wealth, charisma, culture, faith, and political persuasion.
Our success—in all senses of the word—in this life is facilitated by a willingness to learn as much as possible from any and all sources, combined—critically so—with a temperament, character, and system of values that change less in response to direct pressure from others than our own desire to change in response to new information and insight.
I don’t know precisely why Proposition 8 appears to be on track to pass. Perhaps those who voted for it are homophobic. Perhaps they value their heterosexual marriages. Perhaps they were concerned about how it would affect what their children were introduced to in schools. Perhaps they believed that their pastors would be forced to perform marriages between gays and lesbians or face legal sanction. Perhaps their faith proscribes homosexuality. Perhaps they were concerned about the already substantial federal deficit, and the implications should homosexual couples receive the same financial benefits that heterosexual spouses enjoy. Perhaps it was a reaction to the focus on sex that often is found in discussion and expressions of homosexual identity.
At the core of the religious opposition to same-sex marriage is a presumption that Christian truth includes a component that explicitly regards same-sex marriage, or same-sex relationships as sinful and proscribed, and that this truth passes through trustworthy custodians cognizant both of the complexities of modern life, the variegated and complicated identity of being gay, and the application of Christian principles and lessons to both of these.
This belief and its implications are at loggerheads with other aspects of our collective identities to restrict or remove rights through means of constitutional amendment.
I do not know for certain whether the state of California, or any other state, has enacted constitutional amendments that restrict or remove the rights of any individual or group. As far as I know, the United States Constitution has only one: the 18th amendment on the prohibition of alcohol, which was enacted in 1917 and repealed by the 21st Amendment in 1933. (I do not count the 22nd Amendment, which limits a president to two elected terms.) All other amendments seek to extend or confirm the rights of its citizens, or to clarify procedural issues.
Let's take a step back. One could easily argue that Caracalla’s extension of Roman citizenship to all free men within the Empire in 212 C.E. was prompted more by necessity as progressivism. The same can be said for the Magna Carta, signed by King John I of England in 1215, which placed limits on the power of the sovereign, or the 1688 Bill of Rights, which created in England a constitutional monarchy. But it is undeniable that all represented steps toward the modern liberal democracy that we enjoy today, which we would regard as superior to the times when none, or one, or the few, were free.
We can look to our own, more recent history, to the liberty, and the enfranchisement, of African-Americans and women, of the removal of restrictions on property ownership by Asian immigrants, and the Miranda Rights. The trend and trajectory of the progress of human civilization is toward greater, not lesser, individual freedom, limited by the harm principle, guided by a state that is, ideally, strong enough to enforce the law, free enough to provide the greatest possible individual and collective liberty, and wise enough not to attempt to legislate tolerance or morality.
It has been a slow path, an undulating, halting journey toward universal liberty, one that perhaps can only poorly described as progress. I have cherry-picked history, glossed over humanity’s recidivist tendencies toward conquest and oppression, the temptation to construct conflict and corrupt the blessing of distinct identities to divide and rule. Who among us is here who cannot look back into our ancestral past, and find a lineage unscathed by our own Trail of Tears?
Proposition 8 is bad on a number of counts. It sets a precedent for constitutional amendment that is low, that will encourage others to codify their vision of how the world should operate in what should be a very difficult document to modify.
It creates the ground for retroactive implementation of the amendment to nullify existing marriages to same-sex couples, further damaging both the letter and the spirit of the legislative process.
Yet perhaps most destructive is the corrosiveness that the bitter electoral battle has created between the different camps.
I note that the Constitution, the Holy Bible, and the Origin of Species are all, in it of themselves, pieces of paper. They contain information and knowledge. Yet they are absolutely worthless in it of themselves. They retain power and influence only insofar as individual humans are able to read and interpret these documents, apply them to their own lives, and attempt, with varying levels of care and wisdom, to shape the course of human progress by the knowledge and wisdom so created by our collective thoughts and actions. We ultimately must judge the success and merits of Christianity, of science, and of America by its living legacy, by those who represent and promote each.
By this metric, I believe this proposition damages this living legacy of extending rights and the Christian values of love and inclusiveness.
Our future depends upon our ability to recognize the merits of our ideas and values, new and old, resolving conflicts where they exist, as best we can, and occasionally subordinating the desire for consistency in one realm with adherence to a broader one. I do not yet know if this means that I must choose between Leviticus or On Liberty—thus far, I feel I have navigated, however imperfectly, the margins of identity of Christianity, science, and American citizen. What I do know is that the greatest burden, and the greatest virtue, is to be honest with the demands of each.
And the demands of what I feel Christianity to be truly about – faith in a benevolent higher power, hope in the potential for humanity to improve itself, and love for the “other” – and what I feel America is about, and what I feel the pursuit of knowledge is about, all indicate that it is damaging to use the authority of the state to eliminate the rights of a minority simply because the majority wishes it so.
Christ’s message of love and inclusiveness, especially for individuals at the margins of society, is at odds with the metaphorical interpretation of the tale of Sodom and Gomorrah. Yet I cannot conclude that the existence of the latter invalidates the former—just as we recognize the precedence of federal law over state statutes, I recognize the supremacy of the spirit of Christianity can, and in this case does, trump the letter of Christian law as interpreted from Genesis 19. (In fact, I tend to agree with the Jewish interpretation that hostility to the “stranger”, and not homosexual relations, is the real sin that is proscribed in the story.)
Each of us is ultimately responsible for the choice of belief and action. We are the heirs of the historical legacy that enables us to live as we do today. But we are not the final heirs. With our limitations, but also our greatest possible ability, we must look to the lessons of the past and the realities of the present. And we must live, lead, and govern with an eye to the world we wish to leave to those who come after us, those who are yet innocent of the conflict and hatred that poison and destroy all it consumes.
As a man who had no father at home, a father who lacked the mental stability to be a father or a husband, I have this to say about the issue of same-sex adoption.
I am far more fortunate than the number of children who enter the sex industry, or are abused by their parents, or have lost their parents to war, famine, or disease. I have seen the triumph of individuals who grew up without support at home, but always in spite of, not because of, their absence of parental leadership and love. I have also worked with, lived with, and laughed with many gay men and women whom I think will be excellent parents.
I have met gay men who were more of a father to me than my biological father. And I will never forget their contribution to my life, to my character, to my conviction that we are far, far more than the simple atomistic identities we frequently apply to others, and ourselves.
If you are worried about what your children will learn, or what it means to have a gay parent living next door, I would encourage you to examine your fears, examine the availability of good parents in society, and consider whether those children deserve the chance to have a parent, of any sex, of any orientation, who cares and loves them. And I would encourage you to focus not just on educating your children in the particulars of right and wrong as you see it, but to give them the character and temperament to live and lead a world of the many, and not the few.
I believe this is how we best serve our God, our nation, our profession, and our future.
I welcome disagreement, and would love to have a dialogue with anyone who agrees, disagrees, or is curious how I came to this conclusion. I will promise to not have the goal of convincing anyone, but rather to listen and learn, as I hope those who read this also learn, if not about themselves, about me and what I believe.
