My fellow Americans.
As none of you may know, I have, in anticipation of a recall election, decided to run for the highest office in the land – I want to be your next mayor of San Gabriel. While Mr. Hwang reinforces existing negative stereotypes about Asians’ singleminded focus on money and dangerous driving, I promise to give you completely new reasons to regard us with scorn and horror.
Some voices in my head have asked, “Ryan, why would you want to run for mayor?” To answer this, let me tell you a story. A few years ago, I was a lowly graduate student in an obscure school, studying something involving very high things. A guest, Dr. Janna Levin, had a pizza lunch with me and my fellow peons. One particularly interesting question asked was, “If you could be anything except an astronomer, what would you be?” I recall that my answer was “local public official, because it combines the best combination of power and lack of accountability”.
It was then that I realized that in four years, after I grew tired of mooching off my parents, I would embark upon this glorious crusade to ensure an absolute lack of change in how things are done.
This election, we have heard candidates from the left and the right promise change, bemoan the status quo, and spend so much money on television advertisements that I’m actually starting to miss the stupid Geico crying pig commercials.
I am here to reassure you that, as mayor, I won’t change a damn thing. All these candidates who promise change never ask you, the voter, you, the ATM machine, whether you really want change. We (weeeeeeeeeeee!) do not ask ourselves that question enough – though my personal record is 834 times in a day.
If things changed for the better, what would we complain about? Who would be blame for our own failings? Most importantly, who would we feel smarter than? We need our current dysfunctional state of government because it salves our ego, absolves us of personal responsibility, and provides an economic stimulus to the nationally vital late night comedian industry.
And, of course, things could always change for the worse. We could have zombies roaming the streets, the result of an experiment involving so-called “health care”. We could have translucent golems prowling our neighborhoods, scaring our children, the result of so-called “recycling plastic bottles”. We could realize that we are bankrupt, thanks to so-called “transparency” and “standard accounting practices”, rather than live in the only mildly uncomfortable state of suspecting, but not knowing, that we’re all going to have to work until we’re dead.
Remember that it can always get worse. Remember that, and let it infect your dreams. Let it dominate your waking thoughts. For this is what these “change” people offer.
Friends, Bro-mans, and Country Chickeners, lend me your fears!
I promise to reinforce the status quo as vigorously as any 19th century Austrian diplomat. I promise that local government will continue to muck around, displaying no initiative or creativity. I definitely will guarantee no attempts to improve schools – after all, children are the cheap labor of the future, and you can’t have their heads filled with arithmetic, or questions, or, God forbid, ANSWERS. It’s how the Greatest Generation dealt with the Boomers, and it’s how we’ll maintain an 18th century standard of living.
In closing, let me just say that, as mayor, I will be exactly what you expect from local officials – corrupt, incompetent, and crazy. (Shut up.) Who’s talking during my speech? (You are, idiot.) No you’re an idiot.
Anyway, vote for me. Remember – a vote for me isn’t a vote against hope; it’s a vote for fear.
Saturday, October 16, 2010
Sunday, October 10, 2010
The Last Dream
This is actually taken from a dream I had last night. Not "Kublai Khan", but it was vivid enough that I thought I'd try to recreate it.
“David.”
I wanted to tell him that, growing up together, he had always inspired me with his confidence, his athleticism, how effortlessly he had made friends and moved between disparate groups.
I wanted to tell him how much it hurt to see him playing the part of a broken man, and the terror I felt at the thought that it was not an act, an annoying personality quirk that sought recognition through pity, but that it was actually true – that he believed, truly, that he was a worthless has-been, powered only by bitterness and inertia.
So much that could’ve been said. Perhaps some magic combination of words would inspire him to fight, to rise, however slowly, from a tar pit of self-loathing, to save himself, and, because we who lived with him knew he was once the best of us, save all of us.
But all I could say was
“David. My father is dying.”
If he had transformed into a sympathetic, older brother figure of ancient days, I would’ve wept, fallen to my knees, and prayed to God.
If he had grown angry, violent even, and become the noble maelstrom that had dominated the football fields and filled us with such awe and fear with his ferocity, his grace, and his miraculous one-man plays, I would’ve welcomed the hail of abuse and rage, pleaded for mercy, and followed him without question into whatever war he would wage against the wretched world.
But he sat there, unchanged, somewhere between frustration, impotence, and death.
I left him there in his metal folding chair. If I needed him, I knew he would still be on his throne of mediocrity.
I picked up a wind-beaten stick. I breathed the desert air, acrid and heavy. I moved the stick above my head, around, an ancient, unknown ritual, forgotten a hundred generations ago, but invoked now to summon the last of the power of ancient gods to return our champion to us.
In the distance, a muezzin called, singing in a high, plaintive voice. It sounded as if he was telling us that the day had expired, and the sun would never again return.
“David.”
I wanted to tell him that, growing up together, he had always inspired me with his confidence, his athleticism, how effortlessly he had made friends and moved between disparate groups.
I wanted to tell him how much it hurt to see him playing the part of a broken man, and the terror I felt at the thought that it was not an act, an annoying personality quirk that sought recognition through pity, but that it was actually true – that he believed, truly, that he was a worthless has-been, powered only by bitterness and inertia.
So much that could’ve been said. Perhaps some magic combination of words would inspire him to fight, to rise, however slowly, from a tar pit of self-loathing, to save himself, and, because we who lived with him knew he was once the best of us, save all of us.
But all I could say was
“David. My father is dying.”
If he had transformed into a sympathetic, older brother figure of ancient days, I would’ve wept, fallen to my knees, and prayed to God.
If he had grown angry, violent even, and become the noble maelstrom that had dominated the football fields and filled us with such awe and fear with his ferocity, his grace, and his miraculous one-man plays, I would’ve welcomed the hail of abuse and rage, pleaded for mercy, and followed him without question into whatever war he would wage against the wretched world.
But he sat there, unchanged, somewhere between frustration, impotence, and death.
I left him there in his metal folding chair. If I needed him, I knew he would still be on his throne of mediocrity.
I picked up a wind-beaten stick. I breathed the desert air, acrid and heavy. I moved the stick above my head, around, an ancient, unknown ritual, forgotten a hundred generations ago, but invoked now to summon the last of the power of ancient gods to return our champion to us.
In the distance, a muezzin called, singing in a high, plaintive voice. It sounded as if he was telling us that the day had expired, and the sun would never again return.
Saturday, October 9, 2010
Sample question from a student, and my reply
Looking for feedback on whether I'm providing good help to my students via email. A sample (in fact, to this point, the only) email exchange for precalc.
How are you today? I am a student in your pre-calculus class.I have some questions on my homework.Could you please give me some help?
1.How to find out real zeros from all possible rational zeros of a function?(I have read the samples in the texrbook ,but I can't understand.Please give me a specific sample like page 160 :11)I know how to find all possible rational zeros ,but real zeros ,I can't.
2.Page 160:In exrcise 25-28 ,I have no idea to sketch the graph of f so that some of the possible zeros in part (a) can be disregarded)
Thank you for your help!Have a nice weekend.
My reply:
Hope you're enjoying your weekend so far!
1.How to find out real zeros from all possible rational zeros of a function?(I have read the samples in the texrbook ,but I can't understand.Please give me a specific sample like page 160 :11)I know how to find all possible rational zeros ,but real zeros ,I can't.
So the first thing to do is to use the rational zero test.
Remember that the rational zero test can be used on functions of the form
f(x) = an*x^n + a(n-1)*x^(n-1)+... + a1*x + a0.
where an is the coefficient of the term of order n (x^n).
We find the rational zeroes by taking the factors of the a0 term (the constant, which is -6) divided by the coefficient on the highest order term. In this case, the function is of order 3. The coefficient for x^3, a3, is 1.
If a0 is -6, the factors of a0 are {-6, -3, -2, -1, +1, +2, +3, +6}.
and the factors of a3 are {-1, 1}.
So, dividing the factors of a0 by the factors of a3 give us the possible rational zeroes:
a0/a3 = {-6, -3, -2, -1, 1, 2, 3, 6}.
I picked one root to try, +1. I substitute x = 1 into the function.
f(1) = (1)^3 - 6(1)^2 + 11(1) -6
= 0.
I got lucky! So I know that x = 1 is a rational root of f(x).
Now, there are two things I can do at this point.
1. Keep trying the other rational roots.
If you do this, you try the other possible rational roots (factors of a0 / factors of a3) and see if any of them are a zero.
2. Divide by x-1 to get a quadratic equation, which I will solve either by guessing or by using the quadratic formula.
Remember that if x = 1 is a root of f(x), (x - 1) is a factor of f(x), and we can divide f(x) by the factor to find the other roots.
This is the approach I used, because I didn't want to waste time in case there are no other rational roots. If x = 1 is the only rational root, then the quadratic formula will give us the real (or complex) roots, guranteed!
So, using long division,
(x^3 - 6x^2 + 11x - 6)/(x-1) = x^2 - 5x + 6
Now, I can guess the factors - it looks like x = 2 and x = 3 will work. Sure enough,
x^2 - 5x + 6 = (x - 2)*(x - 3)
which means the real roots of f(x) are x = {1, 2, 3}.
But it's a good idea to solve it using the quadratic formula, in case we can't factor it easily.
The quadratic formula can be used for any equation of the form
ax^2 + bx + c = 0
where a, b, and c are real numbers.
The solutions are found using this formula
roots = (- b +/- sqrt(b^2 - 4ac)/(2a)
where sqrt("something") equals the square root of "something".
For
x^2 - 5x + 6
a = 1, b = -5, and c = 6.
Using the formula,
roots = (- (-5) +/- sqrt((-5)^2 - 4*1*6))/(2*1)
= (5 +/- sqrt(25-24))/2
= (5 +/- 1)/2
= {2, 3}.
So we see that the solutions are x = 2 and x = 3.
In summary, for a polynomial function, you do the following steps:
1. Use the rational root test to find possible roots.
2. Try the roots and see if any of them work.
3. For every root that works, divide the function by its factor. For example, if the rational root is x = 4, you divide the function by the factor (x - 4).
4. After dividing, see if the function is of order 2 (looks like ax^2 + bx +c). If so, you can use the quadratic formula. This is how you get real roots that are irrational, and also complex roots.
2.Page 160:In exrcise 25-28 ,I have no idea to sketch the graph of f so that some of the possible zeros in part (a) can be disregarded)
The easiest way to graph it is to use your calculator. But if you don't have that, then the easiest way to graph is to find out what f(x) equals for a number of x values.
For example, on problem 25, f(x) = x^3 + x^2 - 4x - 4
Using the rational zero test, the possible rational roots are
x = {-4, -2, -1, 1, 2, 4}.
So I need to graph it at least over the domain of x:[-4, 4] (everywhere from x = -4 to x = 4).
I would write two columns like this
x f(x)
-4
-3
-2
-1
0
1
2
3
4
And calculate what f(x) is for each x.
x f(x)
-4 -36
-3 -10
-2 0
-1 0
0 -4
1 -6
2 0
3 20
4 60
If you draw the points and connect them, they look something like the picture I've attached in this email.
Note that from this picture, it's easy to eliminate -4, 1, and 4 as possible roots, but -2, 1, and 2 look like rational roots of f(x).
This is an easy example, but sometimes you'll get a function that is more complicated. That's why it's a good idea to graph it, especially in cases where you have a lot of possible rational roots to test.
Good luck! And thanks for asking good questions!
How are you today? I am a student in your pre-calculus class.I have some questions on my homework.Could you please give me some help?
1.How to find out real zeros from all possible rational zeros of a function?(I have read the samples in the texrbook ,but I can't understand.Please give me a specific sample like page 160 :11)I know how to find all possible rational zeros ,but real zeros ,I can't.
2.Page 160:In exrcise 25-28 ,I have no idea to sketch the graph of f so that some of the possible zeros in part (a) can be disregarded)
Thank you for your help!Have a nice weekend.
My reply:
Hope you're enjoying your weekend so far!
1.How to find out real zeros from all possible rational zeros of a function?(I have read the samples in the texrbook ,but I can't understand.Please give me a specific sample like page 160 :11)I know how to find all possible rational zeros ,but real zeros ,I can't.
So the first thing to do is to use the rational zero test.
Remember that the rational zero test can be used on functions of the form
f(x) = an*x^n + a(n-1)*x^(n-1)+... + a1*x + a0.
where an is the coefficient of the term of order n (x^n).
We find the rational zeroes by taking the factors of the a0 term (the constant, which is -6) divided by the coefficient on the highest order term. In this case, the function is of order 3. The coefficient for x^3, a3, is 1.
If a0 is -6, the factors of a0 are {-6, -3, -2, -1, +1, +2, +3, +6}.
and the factors of a3 are {-1, 1}.
So, dividing the factors of a0 by the factors of a3 give us the possible rational zeroes:
a0/a3 = {-6, -3, -2, -1, 1, 2, 3, 6}.
I picked one root to try, +1. I substitute x = 1 into the function.
f(1) = (1)^3 - 6(1)^2 + 11(1) -6
= 0.
I got lucky! So I know that x = 1 is a rational root of f(x).
Now, there are two things I can do at this point.
1. Keep trying the other rational roots.
If you do this, you try the other possible rational roots (factors of a0 / factors of a3) and see if any of them are a zero.
2. Divide by x-1 to get a quadratic equation, which I will solve either by guessing or by using the quadratic formula.
Remember that if x = 1 is a root of f(x), (x - 1) is a factor of f(x), and we can divide f(x) by the factor to find the other roots.
This is the approach I used, because I didn't want to waste time in case there are no other rational roots. If x = 1 is the only rational root, then the quadratic formula will give us the real (or complex) roots, guranteed!
So, using long division,
(x^3 - 6x^2 + 11x - 6)/(x-1) = x^2 - 5x + 6
Now, I can guess the factors - it looks like x = 2 and x = 3 will work. Sure enough,
x^2 - 5x + 6 = (x - 2)*(x - 3)
which means the real roots of f(x) are x = {1, 2, 3}.
But it's a good idea to solve it using the quadratic formula, in case we can't factor it easily.
The quadratic formula can be used for any equation of the form
ax^2 + bx + c = 0
where a, b, and c are real numbers.
The solutions are found using this formula
roots = (- b +/- sqrt(b^2 - 4ac)/(2a)
where sqrt("something") equals the square root of "something".
For
x^2 - 5x + 6
a = 1, b = -5, and c = 6.
Using the formula,
roots = (- (-5) +/- sqrt((-5)^2 - 4*1*6))/(2*1)
= (5 +/- sqrt(25-24))/2
= (5 +/- 1)/2
= {2, 3}.
So we see that the solutions are x = 2 and x = 3.
In summary, for a polynomial function, you do the following steps:
1. Use the rational root test to find possible roots.
2. Try the roots and see if any of them work.
3. For every root that works, divide the function by its factor. For example, if the rational root is x = 4, you divide the function by the factor (x - 4).
4. After dividing, see if the function is of order 2 (looks like ax^2 + bx +c). If so, you can use the quadratic formula. This is how you get real roots that are irrational, and also complex roots.
2.Page 160:In exrcise 25-28 ,I have no idea to sketch the graph of f so that some of the possible zeros in part (a) can be disregarded)
The easiest way to graph it is to use your calculator. But if you don't have that, then the easiest way to graph is to find out what f(x) equals for a number of x values.
For example, on problem 25, f(x) = x^3 + x^2 - 4x - 4
Using the rational zero test, the possible rational roots are
x = {-4, -2, -1, 1, 2, 4}.
So I need to graph it at least over the domain of x:[-4, 4] (everywhere from x = -4 to x = 4).
I would write two columns like this
x f(x)
-4
-3
-2
-1
0
1
2
3
4
And calculate what f(x) is for each x.
x f(x)
-4 -36
-3 -10
-2 0
-1 0
0 -4
1 -6
2 0
3 20
4 60
If you draw the points and connect them, they look something like the picture I've attached in this email.
Note that from this picture, it's easy to eliminate -4, 1, and 4 as possible roots, but -2, 1, and 2 look like rational roots of f(x).
This is an easy example, but sometimes you'll get a function that is more complicated. That's why it's a good idea to graph it, especially in cases where you have a lot of possible rational roots to test.
Good luck! And thanks for asking good questions!
Saturday, October 2, 2010
I got a job
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 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.)
Learning some humility from a technical interview
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.
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.
Friday, October 1, 2010
Hale's invitation
If you find yourself wandering and lost,
stop by
my corningware oubliette.
Bring me a touch
and I will share with you the loveliness,
the loneliness
of eternal sky
stop by
my corningware oubliette.
Bring me a touch
and I will share with you the loveliness,
the loneliness
of eternal sky
My favorite astropolitik story
Louis XI (1423-1483), the great Spider King of France, had a weakness for astrology. He kept a court astrologer whom he admired, until one day the man predicted that a lady of the court would die within eight days. When the prophecy came true, Louis was terrified, thinking that either the man had murdered the woman to prove his accuracy or that he was so versed in his science that his powers threatened Louis himself. In either case he had to be killed.
One evening Louis summoned the astrologer to his room, high in the castle. Before the man had arrived, the king told his servants that when he gave the signal they were to pick the astrologer up, carry him to the window, and hurl him to the ground, hundreds of feet below.
The astrologer soon arrived, but before giving the signal, Louis decided to ask him one last question: “You claim to understand astrology and to know the fate of others, so tell me what your fate will be and how long you have to live.”
“I shall die just three days before Your Majesty,” the astrologer replied. The king’s signal was never given. The man’s life was spared. The Spider King not only protected his astrologer for as long as he was alive, he lavished him with gifts and had him tended by the finest court doctors.
The astrologer survived Louis by several years, disproving his power of prophecy but proving his mastery of power.
-Robert Greene, The 48 Laws of Power
One evening Louis summoned the astrologer to his room, high in the castle. Before the man had arrived, the king told his servants that when he gave the signal they were to pick the astrologer up, carry him to the window, and hurl him to the ground, hundreds of feet below.
The astrologer soon arrived, but before giving the signal, Louis decided to ask him one last question: “You claim to understand astrology and to know the fate of others, so tell me what your fate will be and how long you have to live.”
“I shall die just three days before Your Majesty,” the astrologer replied. The king’s signal was never given. The man’s life was spared. The Spider King not only protected his astrologer for as long as he was alive, he lavished him with gifts and had him tended by the finest court doctors.
The astrologer survived Louis by several years, disproving his power of prophecy but proving his mastery of power.
-Robert Greene, The 48 Laws of Power
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