I wrote up the detailed notes for my latest Extreme Thinking seminar. Check it out:
Self-Reference
Wednesday, April 11, 2007
Tuesday, April 10, 2007
Wednesday, March 21, 2007
Computers Are Fast
What have you done in the last second? Because your computer could have done a billion things.
Do you ever stop to think about how much work a CPU running at 1Ghz is doing? A lifetime isn't enough for a human to consciously do a billion of anything (although the brain's equivalent clock speed is much higher for subconscious tasks like vision processing). The task of calculating Pi to a million digits was beyond the wildest dreams of a millennium of mathematicians. But we can give a computer the task, and it'll come back with the answer in one second!
One nanosecond is too small to ever comprehend, but that is the basic unit of time for a computer's operations. For a computer, one second must be an eternity.
Do you ever stop to think about how much work a CPU running at 1Ghz is doing? A lifetime isn't enough for a human to consciously do a billion of anything (although the brain's equivalent clock speed is much higher for subconscious tasks like vision processing). The task of calculating Pi to a million digits was beyond the wildest dreams of a millennium of mathematicians. But we can give a computer the task, and it'll come back with the answer in one second!
One nanosecond is too small to ever comprehend, but that is the basic unit of time for a computer's operations. For a computer, one second must be an eternity.
Thursday, March 01, 2007
Proving 1+1=2
This is my first philosophy of math post, and I got the ideas from reading Scott Aaronson.
I saw some wiseacre on an internet forum make a reference to this famous page in Russell and Whitehead's Principia Mathematica, and challenging people to prove that 1+1=2. So I thought,
What does it mean to prove that 1+1=2?
Generally when you prove something in formal math, you start by defining axioms, then use logical inference rules to derive the result. If you've learned Geometry, you are probably most familiar with Euclid's axioms for plane geometry.
[Interesting geometry fact: Do you remember learning that when two parallel lines are intersected by a transversal line, pairs of interior angles are congruent? There's no derivation of why that's true -- it's just accepted as an axiom of Euclidean geometry! But it's like the axiomatic black sheep -- much more complicated than Euclid's other four axioms. And it's also what makes the system Euclidean geometry, instead of a different geometry.]
Today, the most common axiom system mathematicians use as a foundation for proofs is called Zermelo-Fraenkel Set Theory. And in ZF set theory, 1+1=2 has a relatively simple proof (although I personally haven't seen it yet)! 1+1 is also easy to prove in a simpler axiom system called Peano Arithmetic.
In the last few centuries, there's been a huge quest by mathematicians to "justify" basic math statements like 1+1=2, in order to "place mathematics on a more secure foundation". That's partly what all this axiom system stuff is about.
Axiom systems are great; in fact, they are an area of concentration for me. But we can make axioms be whatever we want. If you get a kick out of seeing 1+1=3, you can just define a new axiom system where that's the case. You still have to avoid logical contradictions, though, so I hope you weren't too attached to the old semantic meaning of "+" and "=".
So, what is the ultimate secure foundation for 1+1=2? Well, I'm afraid 1+1=2 is part of the foundation itself. Yes, the axioms of set theory prove it, but that's not why anyone is actually inclined to believe that 1+1=2. On the contrary, mathematicians surely listened to their powerful intuition that 1+1=2 when they chose which axioms to accept as part of the "foundation of math".
So where does the 1+1=2 intuition come from? I think you can break it down a little more by seeing 1+1 as the definition of our intuitive notion of two-ness. That intuition, I'm guessing, is a connection we make when the fundamental perceptual notions of repetition or similarity are invoked. Perhaps you are holding a Jolly Rancher, and also a Sweet Tart. They're not identical, but they're both foods, and they're certainly both physical objects with pretty well-defined spatial boundaries. So two is afoot.
I saw some wiseacre on an internet forum make a reference to this famous page in Russell and Whitehead's Principia Mathematica, and challenging people to prove that 1+1=2. So I thought,
What does it mean to prove that 1+1=2?
Generally when you prove something in formal math, you start by defining axioms, then use logical inference rules to derive the result. If you've learned Geometry, you are probably most familiar with Euclid's axioms for plane geometry.
[Interesting geometry fact: Do you remember learning that when two parallel lines are intersected by a transversal line, pairs of interior angles are congruent? There's no derivation of why that's true -- it's just accepted as an axiom of Euclidean geometry! But it's like the axiomatic black sheep -- much more complicated than Euclid's other four axioms. And it's also what makes the system Euclidean geometry, instead of a different geometry.]
Today, the most common axiom system mathematicians use as a foundation for proofs is called Zermelo-Fraenkel Set Theory. And in ZF set theory, 1+1=2 has a relatively simple proof (although I personally haven't seen it yet)! 1+1 is also easy to prove in a simpler axiom system called Peano Arithmetic.
In the last few centuries, there's been a huge quest by mathematicians to "justify" basic math statements like 1+1=2, in order to "place mathematics on a more secure foundation". That's partly what all this axiom system stuff is about.
Axiom systems are great; in fact, they are an area of concentration for me. But we can make axioms be whatever we want. If you get a kick out of seeing 1+1=3, you can just define a new axiom system where that's the case. You still have to avoid logical contradictions, though, so I hope you weren't too attached to the old semantic meaning of "+" and "=".
So, what is the ultimate secure foundation for 1+1=2? Well, I'm afraid 1+1=2 is part of the foundation itself. Yes, the axioms of set theory prove it, but that's not why anyone is actually inclined to believe that 1+1=2. On the contrary, mathematicians surely listened to their powerful intuition that 1+1=2 when they chose which axioms to accept as part of the "foundation of math".
So where does the 1+1=2 intuition come from? I think you can break it down a little more by seeing 1+1 as the definition of our intuitive notion of two-ness. That intuition, I'm guessing, is a connection we make when the fundamental perceptual notions of repetition or similarity are invoked. Perhaps you are holding a Jolly Rancher, and also a Sweet Tart. They're not identical, but they're both foods, and they're certainly both physical objects with pretty well-defined spatial boundaries. So two is afoot.
Tuesday, February 13, 2007
I Am A Strange Loop
28 years after his classic book Godel, Escher, Bach (aka Introduction to Thinking About Awesomeness), author Douglas Hofstadter is releasing a sequel on March 5: I Am a Strange Loop.
If you've forgotten about the GEB topics over the decades since it came out, here is a quiz to refresh your memory:
If you've forgotten about the GEB topics over the decades since it came out, here is a quiz to refresh your memory:
- True or false: I am a strange loop.
- True or false: For every well-formed statement in formal set theory, there exists a proof that it is either true or false.
- True or false: The axioms of formal set theory do not contain a contradiction.
Will Intern For Money
Hey blog readers,
I am looking for a position in the South San Francisco Bay Area as a Summer programming intern. I am an undergraduate Computer Science and Engineering major, Math minor with experience and drive. Please let me know if you have anything to recommend.
Thanks,
--Liron
I am looking for a position in the South San Francisco Bay Area as a Summer programming intern. I am an undergraduate Computer Science and Engineering major, Math minor with experience and drive. Please let me know if you have anything to recommend.
Thanks,
--Liron
Tuesday, January 09, 2007
Secret Questions
Today I created a password for a website, and it asked me for a secret question in case I forget my password. So I typed in "What is the answer?" And then as the answer, I used a throwaway password because it was displayed on the screen in plaintext, and obviously not going to be encrypted. What an awkward and patronizing experience.
Friday, January 05, 2007
Identifying Yourself to Yourself
I just read a quick thought-provoking everything2.com post called creating a password to convince yourself you have traveled back in time. It got me thinking, if I were to travel back in time, how would I authenticate myself to myself as efficiently as possible? (It has to be quick, or else my present self will proceed to press a red button.)
I might start listing off passwords I use, but those could be hacked. I think a good approach would be to list the stuff I concern myself with and worry about. So I was imagining myself rapidly describing my innermost thoughts to myself, and I think I stumbled on a good exercise. Describing my innermost thoughts quickly and matter-of-factly in the second person gave me a bit of perspective.
I might start listing off passwords I use, but those could be hacked. I think a good approach would be to list the stuff I concern myself with and worry about. So I was imagining myself rapidly describing my innermost thoughts to myself, and I think I stumbled on a good exercise. Describing my innermost thoughts quickly and matter-of-factly in the second person gave me a bit of perspective.
Monday, January 01, 2007
All I've Got Against Moderate Religion
The religion that we see today comes in fundamentalist and moderate varieties. I consider the two to be wrong and meaningless, respectively, but that's a subject for another post.
As an atheist, what truly moves me to action is fundamentalism, which I believe is actively destroying society (e.g. preventing stem cell research because of idiotic absolutist classification of a clump of cells as a human in good standing). But the bone I have to pick with moderate religion is much smaller.
Moderate religion is usually pretty fine in practice, because our moral intuitions and enlightened time period generally override a rational interpretation of what's really written in the bible. However, I would still prefer that the moderates give it up already, and here are all the reasons I can think of why moderate religion is bad.
As an atheist, what truly moves me to action is fundamentalism, which I believe is actively destroying society (e.g. preventing stem cell research because of idiotic absolutist classification of a clump of cells as a human in good standing). But the bone I have to pick with moderate religion is much smaller.
Moderate religion is usually pretty fine in practice, because our moral intuitions and enlightened time period generally override a rational interpretation of what's really written in the bible. However, I would still prefer that the moderates give it up already, and here are all the reasons I can think of why moderate religion is bad.
- The prevalence of moderate religion masks the true egregiousness of fundamentalist religion. For example, a moderate Christian doesn't think that Genesis is literally true, but when incredibly radical "Intelligent Design" comes along, which robs modern science of so much integrity that it might as well be asserting the full literal truth of the Genesis story, the average moderate is tempted to give it equal time in the classroom. Richard Dawkins expands on this in The God Delusion.
- Moderate religion seems like an inconsistent worldview that straddles the boundary between proven rationality and comforting superstition. Scientists traditionally use the humble line of having nothing to say about philosophy. But the truth is that science had a lot to say about the subject. For example, every philosophy about the meaning of life that was written before Darwin must be completely re-examined -- the knowledge of our natural origin changes everything.
Likewise, modern biology tells us that our cells, organelles, DNA and proteins are made of the same passive atoms as any other matter in the universe. It seems that the modern, enlightened, scientific worldview is a completely materialistic one. There don't seem to be any gaps for supernatural intervention, even in what was once the most promising place -- our brains.
In light of the changes that science has had on our worldview, moderate religion seems to be nothing but a historical relic. Imagine that a baby were born into a completely secular, modern society, schooled in modern science, but largely ignorant of religion. Can you imagine a priest who finds him at age 20 and tries to convince him that there is a God? Even such a fixture of moderate religion as solitary prayer would seem absurd and outlandish to this rational character. In the world today, I believe moderate religion is using its moderation as an excuse to avoid some major burdens of proof. - My last argument is a very interesting one I read in a recent post by renowned philosopher Daniel Dennett, recovering from surgery after his heart almost exploded, entitled Thank Goodness! (highly recommended).
I am not joking when I say that I have had to forgive my friends who said that they were praying for me. I have resisted the temptation to respond "Thanks, I appreciate it, but did you also sacrifice a goat?" I feel about this the same way I would feel if one of them said "I just paid a voodoo doctor to cast a spell for your health." What a gullible waste of money that could have been spent on more important projects! Don't expect me to be grateful, or even indifferent. I do appreciate the affection and generosity of spirit that motivated you, but wish you had found a more reasonable way of expressing it.
Dennett's point is that while a little prayer by a religious moderate is not a big deal, it is as inappropriate to the situation as sacrificing an animal -- a completely unjustified waste of time. Furthermore, praying in the hope of actually being helpful can seem, to an intelligent sufferer, like a mockery of the things that truly are helpful and valuable (such as the practice of medicine with scientific rigor).
AIM Profile Dump 2
Note: All of this content is plagiarized. If you want to find the sources, just search for the strings in quotes :)
Some professors asked a monk to lecture to them on spiritual matters. The monk ascended a podium, struck it once with his stick, and descended. The academics were dumb-founded. The monk asked them, "Do you understand what I have told you?"
One professor said, "I do not understand."
The monk said, "Then I have concluded my lecture."
Another professor said, "We will not pay you for this lecture."
Two sages were standing on a bridge over a stream.
One said to the other, "I wish I were a fish. They are so happy."
The other replied, "How do you know whether fish are happy or not? You're not a fish."
The first said, "But you're not me, so how do you know whether or not I know how fish feel?"
The other thought for a moment and replied, "Because I was a fish in my previous life."
The first scowled at him. He said, "then you wouldn't mind if I threw you off this bridge, would you?"
At that moment, the first sage attained enlightenment.
He told the other sage what had happened.
"Yeah, I attained enlightenment too," the other sage said. He was lying.
There are two kinds of people in the world: those that can count.
"The truth is, I removed all my evidence of creating this world so that the smarter guys wouldn't believe in me. And what were the consequences? My Heaven only welcomes smart people. Those people will believe in me when they meet me in person! That's what I gave them the brains for, see? The last thing I need is a bunch of loony fanatics wandering around up there, getting their nose hairs all over the furniture."
--God
"I know when you are sleeping, I know when you're awake. I know if you've been bad or good... crap, there I go, confusing myself with Santa Claus again! Seriously, though, I do know." --God
Redundancy is the unnecessary use of either needless, tautological, pleonastic or superfluous text, by which one repeats, in duplication, the same, identical, aforesaid things over and over again, beyond what would be needed or required to explain, or make comprehensible, the intended or signified meaning of that which one wishes to convey. Customarily, it is usually common in redundancy to repeat, sometimes with different phrasing or words, the same idea or reasoning, thus restating one's thoughts, sometimes paraphrasing oneself and effectively saying the same thing twice, or double.
John J. Johnson Jr. II, the current and present president of the Society for Redundancy Society, has proposed that "Redundancy is an art, capable of being captured only by the minds of those with minds capable of capturing the art of redundancy."
All-Time Favorite Russian Reversals
In Firefox, you keep tabs on your browser. In Soviet Russia, browser keeps tabs on you!
Also: In Soviet Russia, fox fires you!
In Soviet Russia, ride pimps you!
In Soviet Russia, time kills you!
In Soviet Russia, day seizes you!
In Soviet Russia, remote controls you!
In Soviet Russia, Waldo finds you!
In Soviet Russia, joke overuses you!
If all the village idiots, in all the villages in the world, left their villages to form their own village, of village idiots, in that village, of village idiots, you would be the village idiot.
How many members of a (given demographic group) does it take to change a lightbulb?
N+1 (where N is a positive whole number) -- one to hold the lightbulb, and N to behave in a fashion generally associated with a negative stereotype of that group.
Some professors asked a monk to lecture to them on spiritual matters. The monk ascended a podium, struck it once with his stick, and descended. The academics were dumb-founded. The monk asked them, "Do you understand what I have told you?"
One professor said, "I do not understand."
The monk said, "Then I have concluded my lecture."
Another professor said, "We will not pay you for this lecture."
Two sages were standing on a bridge over a stream.
One said to the other, "I wish I were a fish. They are so happy."
The other replied, "How do you know whether fish are happy or not? You're not a fish."
The first said, "But you're not me, so how do you know whether or not I know how fish feel?"
The other thought for a moment and replied, "Because I was a fish in my previous life."
The first scowled at him. He said, "then you wouldn't mind if I threw you off this bridge, would you?"
At that moment, the first sage attained enlightenment.
He told the other sage what had happened.
"Yeah, I attained enlightenment too," the other sage said. He was lying.
There are two kinds of people in the world: those that can count.
"The truth is, I removed all my evidence of creating this world so that the smarter guys wouldn't believe in me. And what were the consequences? My Heaven only welcomes smart people. Those people will believe in me when they meet me in person! That's what I gave them the brains for, see? The last thing I need is a bunch of loony fanatics wandering around up there, getting their nose hairs all over the furniture."
--God
"I know when you are sleeping, I know when you're awake. I know if you've been bad or good... crap, there I go, confusing myself with Santa Claus again! Seriously, though, I do know." --God
Redundancy is the unnecessary use of either needless, tautological, pleonastic or superfluous text, by which one repeats, in duplication, the same, identical, aforesaid things over and over again, beyond what would be needed or required to explain, or make comprehensible, the intended or signified meaning of that which one wishes to convey. Customarily, it is usually common in redundancy to repeat, sometimes with different phrasing or words, the same idea or reasoning, thus restating one's thoughts, sometimes paraphrasing oneself and effectively saying the same thing twice, or double.
John J. Johnson Jr. II, the current and present president of the Society for Redundancy Society, has proposed that "Redundancy is an art, capable of being captured only by the minds of those with minds capable of capturing the art of redundancy."
All-Time Favorite Russian Reversals
In Firefox, you keep tabs on your browser. In Soviet Russia, browser keeps tabs on you!
Also: In Soviet Russia, fox fires you!
In Soviet Russia, ride pimps you!
In Soviet Russia, time kills you!
In Soviet Russia, day seizes you!
In Soviet Russia, remote controls you!
In Soviet Russia, Waldo finds you!
In Soviet Russia, joke overuses you!
If all the village idiots, in all the villages in the world, left their villages to form their own village, of village idiots, in that village, of village idiots, you would be the village idiot.
How many members of a (given demographic group) does it take to change a lightbulb?
N+1 (where N is a positive whole number) -- one to hold the lightbulb, and N to behave in a fashion generally associated with a negative stereotype of that group.
Sunday, November 12, 2006
Smart Voting Website
Last Tuesday, I voted in the midterm elections. I did it by filling out an absentee ballot in front of a computer at the library. I thought many of my votes were well informed, but frankly, my votes for the less prominent positions were not very well informed at all (I briefly consulted a few web pages), and for some votes I didn't feel informed enough to make any decision at all. This state of affairs is just unacceptable for this country in this age.
Today I got an idea from this post by Scott Adams. Scott says he doesn't vote because he doesn't know enough to make an informed decision. In the future, he thinks there will be a website where people can go to get informed to a sufficient degree, and when that time comes, he looks forward to voting.
I would like to develop a website with a very specific goal. For each election ballot item, there should be a single dynamic page that gives people the info they need to make a decision. It should allow people to quickly pinpoint the differences between the candidates that are relevant to their values. I don't know what that will look like yet, and I will appreciate any ideas other people suggest.
The site should be informative, smart, and unbiased the same way that Wikipedia is -- by fairly presenting input from lots of users. Maybe each voter can enter what their values are, and then the page will be modified to point out differences in stances that similar voters thought were important. One idea for ballot proposition issues is to have polls whose results are weighted by voters' scores on a short knowledge test (basic facts about the propositions).
By the way, I made my first web application last year -- a proof of concept for a new type of social networking site. A demo of RelationCraft is currently online. But I hope my politics site, or a future idea, will be a more practical candidate for wide release.
Today I got an idea from this post by Scott Adams. Scott says he doesn't vote because he doesn't know enough to make an informed decision. In the future, he thinks there will be a website where people can go to get informed to a sufficient degree, and when that time comes, he looks forward to voting.
I would like to develop a website with a very specific goal. For each election ballot item, there should be a single dynamic page that gives people the info they need to make a decision. It should allow people to quickly pinpoint the differences between the candidates that are relevant to their values. I don't know what that will look like yet, and I will appreciate any ideas other people suggest.
The site should be informative, smart, and unbiased the same way that Wikipedia is -- by fairly presenting input from lots of users. Maybe each voter can enter what their values are, and then the page will be modified to point out differences in stances that similar voters thought were important. One idea for ballot proposition issues is to have polls whose results are weighted by voters' scores on a short knowledge test (basic facts about the propositions).
By the way, I made my first web application last year -- a proof of concept for a new type of social networking site. A demo of RelationCraft is currently online. But I hope my politics site, or a future idea, will be a more practical candidate for wide release.
Saturday, November 04, 2006
AIM Profile Dump
I didn't want to make this blog into a link blog, but I come across a lot of interesting stuff on the web, and I usually just post it to my AIM profile. So my AIM profile is becoming a link blog with no archive. Here is today's AIM profile dump.
Grey's Anatomy is a great show. It had to be said.
"Don't inter-fucking-rupt!"
Expletive infixation
"By making misogynistic, racist statements in the friendliest way and asking people to high-five over them, [Borat] gets folks to say things they wouldn't if they knew the film was going to be shown in their own country." --Borat Makes Funny Joke On Idiot Americans
"They all laughed when I said I wanted to be a comedian. They're not laughing now." --Bob Monkhouse
Great pickup lines from Weird Al:
You must have fallen from heaven -- that would explain how you messed up your face.
Girl, you'd look like the Venus de Milo if I just cut off your arms.
HOST: I'm curious, have you ever Googled anybody? Do you use Google?
BUSH: Occasionally. One of the things I've used on the Google is to pull up maps.
Bush Says He Uses The Google
"If you came from the future, wouldn't you do exactly what Bill Gates did???"
"The criterion by which we cherry-pick morals from the bible is available to all of us -- religious or not." --Richard Dawkins
Hey baby,
If I were an endoplasmic reticulum, how would you want me?
Smooth... or ROUGH??
"I wish I were your problem set, because then I'd be really hard and you'd be doing me on the desk."
While arresting a speeding driver, a police man asked this question: "Do you know how fast you were going?!"
The driver replied, "No, because I knew exactly where I was."
Any fool can criticize, condemn and complain -- and most fools do. --Benjamin Franklin
Grey's Anatomy is a great show. It had to be said.
"Don't inter-fucking-rupt!"
Expletive infixation
"By making misogynistic, racist statements in the friendliest way and asking people to high-five over them, [Borat] gets folks to say things they wouldn't if they knew the film was going to be shown in their own country." --Borat Makes Funny Joke On Idiot Americans
"They all laughed when I said I wanted to be a comedian. They're not laughing now." --Bob Monkhouse
Great pickup lines from Weird Al:
You must have fallen from heaven -- that would explain how you messed up your face.
Girl, you'd look like the Venus de Milo if I just cut off your arms.
HOST: I'm curious, have you ever Googled anybody? Do you use Google?
BUSH: Occasionally. One of the things I've used on the Google is to pull up maps.
Bush Says He Uses The Google
"If you came from the future, wouldn't you do exactly what Bill Gates did???"
"The criterion by which we cherry-pick morals from the bible is available to all of us -- religious or not." --Richard Dawkins
Hey baby,
If I were an endoplasmic reticulum, how would you want me?
Smooth... or ROUGH??
"I wish I were your problem set, because then I'd be really hard and you'd be doing me on the desk."
While arresting a speeding driver, a police man asked this question: "Do you know how fast you were going?!"
The driver replied, "No, because I knew exactly where I was."
Any fool can criticize, condemn and complain -- and most fools do. --Benjamin Franklin
Sunday, October 29, 2006
Me and Richard Dawkins
In the background signing books is renowned scientist Richard Dawkins (I'm in the center foreground). I think Richard Dawkins constitutes the perfect specimen of an intellectual, because he:
- is brilliant
- is a gentleman
- has a great sense of humor
- has a really crisp British accent
Saturday, October 28, 2006
Sunday, October 15, 2006
Base
My computer in my dorm is my base. Whenever I'm in my room without having decided exactly what to do next, I get in my computer and see what's up -- email, AIM, Facebook, reddit.com, my Google RSS feed aggregator, and my bittorrent downloads. Even though I'm on the computer more than average, I know most of the people I know have this "base" relationship with their computers.
What I'm wondering is, did people had an analogous base state in their homes before computers became ubiquitous? I guess in the last century it was in front of the TV. Before that, in front of the radio? In the easy chair with a newspaper? At the desk with a pen and paper?
I guess without an incredibly entertaining way to idle, people kind of had to move from one task to another. The "base" thing may be an unprecedented transformation of the American lifestyle.
What I'm wondering is, did people had an analogous base state in their homes before computers became ubiquitous? I guess in the last century it was in front of the TV. Before that, in front of the radio? In the easy chair with a newspaper? At the desk with a pen and paper?
I guess without an incredibly entertaining way to idle, people kind of had to move from one task to another. The "base" thing may be an unprecedented transformation of the American lifestyle.
Thursday, September 14, 2006
Queerer Than We Suppose
Here is a video of a brilliant talk by Richard Dawkins entitled "Queerer Than We Suppose: The Strangeness of Science". Very good stuff.
Human Pheromones
I remember my introductory biology textbook said that the existence of human pheromones was still basically a mystery. Now researchers at Penn State claim that fathers emit pheremones that hold off their daughters' sexual maturity!
Read the article - it's pretty fascinating.
Read the article - it's pretty fascinating.
Friday, September 08, 2006
Atheism and Morality Revisited
I wrote some quick thoughts on this once, but here's a post that really nails it.
Thursday, August 31, 2006
Piano
I've been playing piano for two years. I don't take lessons, I just practice harder and harder pieces, and I'm reading some of the theory as well. I practice regularly and quite a lot. I've consistently put in four hours a week, so by now I've had over 400 hours of practice.
The main thoughts I have about playing piano are:
Incidentally, I am moving out of my apartment tomorrow, moving out of the bay area on Sept 10, and going back to UCI on Sept 20.
The main thoughts I have about playing piano are:
- It's fun to play good music. I don't know why I can't get the same enjoyment from a good recording that I can from playing it. It seems a little irrational.
- It's really fun, and I have no trouble practicing consistently. I don't exercise nearly as regularly as I'd want to, or even read music theory that much, but I practice plenty. It's cool to have a random skill that's constantly developing like that.
- A lot of the best music I've heard is still too hard for me. Here are some targets I am shooting for in the next few years:
- Gershwin - Rhapsody in Blue (an advanced piano adaption)
- Beethoven - Eroica Symphony, 1st movement (piano adaption by Liszt)
- Chopin - Scherzo in Bb Minor
- Chopin - Impromptu Fantasie
- Bach - Well Tempered Clavier Book 2, Prelude #6
Incidentally, I am moving out of my apartment tomorrow, moving out of the bay area on Sept 10, and going back to UCI on Sept 20.
Thursday, August 24, 2006
Bush is a Moron
During the 2004 election season, there was this idea that President Bush isn't as dumb as his words, actions and policies. It seemed plausible that Bush's image as an imbecile might be a misleading one.
Today I saw two pieces of evidence that helped me to finally make up my mind:
What a Moronic Presidential Press Conference! (Slate)
Your President, the Visionary Genius (Huffington Post)
I am forced to believe that the man is clearly too stupid to be the president. He is simply unqualified and incompetent. It really is that simple.
Today I saw two pieces of evidence that helped me to finally make up my mind:
What a Moronic Presidential Press Conference! (Slate)
Your President, the Visionary Genius (Huffington Post)
I am forced to believe that the man is clearly too stupid to be the president. He is simply unqualified and incompetent. It really is that simple.
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