Arches' arches

Last week's question: what are the fluid dynamics of drafting?

Drafting is the practice of staying behind another moving object to reduce the energy needed to move. This is possible because when air moves past an object, there is a small area behind said object where the air cannot reform as rapidly, creating an area of low pressure. This low pressure is filled by pulling nearby particles, including those of the following object, towards it, hence saving energy on the following object's part.

Despite this somewhat technical explanation, I can't see to find fluid flow diagrams of drafting. Maybe someone would be so kind as to provide one?

This week's question: How are the stone arches in Arches National Park and elsewhere formed?
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I had this conversation more than once with a GSW student this quarter:
Her [working on the problem, looking up to see me smiling]: What? What are you smiling at?
Me: I'm not laughing at you. I smile at everything.
This is becoming truer and truer over time. I don't literally smile all the time, but I see humor in a lot of things. Even if people who smile don't do so well in life, they tend to have more fun... which is the point, right?

My dad has always had this work/play distinction. This is a quote from an actual email he sent me:
Sometimes, I ask myself, am I a bit selfish? Many people start working for charity after retirement - to continue to use their knowledge and experience to help the society grow, and to help the under-privileged people. On the other hand, I think that I have also spent the last 30 years actively involved in the building and managing an excellent railway for the people of Hong Kong. Considering that I work 12 to 14 hours a day, I think I have worked for 45 years already, based on an 8-hour day. I think I have done my part and I do not owe the society anything. Any extra effort must be extra. Should I start playing now, do the things I like to do, reserve the remaining time of my life to myself and spend the time with the people around me? I do not mind doing some volunteer work, but it must not be "work".

The above may seem far-reaching to you. As you know, I always adopt the value of "Work Hard, Play Hard". Work must come first. If I do not work hard in my younger days, I cannot figure out how I can play hard. I may not even have the money for you and your brother to attend an international school and study abroad! Having said all these, I am not asking you to take me as an example. You should always balance working and playing, although still giving "work" the priority. Does that make sense?
We often had semi-philosophical discussions like this, so it wasn't surprising. I wrote back,
About working: you know I've always had a different view. Working should be playing, damn it. Yes you should spent time hiking, running, or something that makes you happy, but why shouldn't working make you happy too? I'm teaching this quarter, and I get paid $400 a quarter. I enjoy teaching, and I enjoy watching people learn. If I didn't, I probably wouldn't have applied for the job in the first place. So yes, "work hard, play hard," but preferably "at the same time."
Besides, the most famous scientists all had a great sense of humor. Einstein:

And Feynman:

who played the bongo drums. He also said to People magazine after getting his Nobel prize, "If I could explain it to the average person, I wouldn't have been worth the Nobel Prize." Nuts.

In fact, Freeman Dyson thought being funny is highly related to these two's fame:
Scientists who become icons must not only be geniuses but also performers, playing to the crowd and enjoying public acclaim. Einstein and Feynman both grumbled about the newspaper and radio reporters who invaded their privacy, but both gave the reporters what the public wanted, sharp and witty remarks that would make good headlines. Hawking in his unique way also enjoys the public adulation that his triumph over physical obstacles has earned for him.
Really the important thing, I think, is making your work fun. I totally agree with Paul Graham, who's essay How to Do What You Love I've referenced ad nauseum. With academia it's easy - I won't go into a field I didn't like anyway.

To drive home the point, here's a TED talk by Stuart Brown on why play is vital.
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Im in ur mekanicle systemz

breakin ur springz.
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Last week's question: Why do things appear smaller when they are further away?

This intriguing problem actually has very little discussion. I found several discussion boards, but the people on there are either really confused or half crazy. The last link is the best explanation, although it was also touched on in the other discussion boards.

But in any case, I figured out the solution before reading the boards. It's nice to have my answers checked though.

What happens is that as objects are further away, the angle it forms in our eyes is smaller. All the light has to pass through a small hole (the pupil for the human eye, some other form of lens for cameras and video recorders) before this gets processed. The larger the angle, the larger than image is. When an object is up close, light from that object forms a very obtuse angle. This translates to a large image. When things are further, however, the angle is smaller. This correspondingly makes the image smaller.

The second part of the question was why this was the case. This is the case because light travels in a straight line. If light curved before entering recording device to make a bigger angle, or otherwise curved after that point and before it hits the retina, then closer objects could appear smaller than large ones. But our vision would also be greatly distorted.

In fact, I wonder if there are animals whose eyes work like this.

This week's question: What are the fluid dynamics of drafting in cycling or driving?
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Trains and Skip Lists

I was on the El to the airport the other day (for my Michigan visit, actually), and I was wondering how the train system could be improved. Someone once suggested that the network should be built like a spider web centered around down town Chicago. There would be trains which take you down town, but also other lines which circle the city. A line like that would certainly make the trip from Evanston to O'Hare a lot shorter, but it's a costly way to make the train system efficient.

Instead, as a nerd computer scientist, I thought about how trains are kind of like linked lists. You start at some node, but to get to another node you have to go through everything that's in between. This is, of course, as opposed to arrays, where you can just jump to the node you need.

And then I realized, people have solved this problem in computer science before. The solution: skip lists. These are not data structures normally taught in courses (although I heard that has changed since I took it... sigh), but the principle it functions on is simple. Going with the train analogy (and only going one way for the moment), instead of having one train stop at every station, you have several trains/tracks. One would stop at every station, another would stop at every other station, then every fourth, eighth, and so on. Getting to your destination would then involve transferring to trains that skip more and more stations, stay on that train until its next stop is past yours, then transfer to slower and slower trains.

Of course, this idea is not new to transportation companies either. Usually it's given the name "express". The only difference is that the express tends only to run during rush hours, and not otherwise. That is understandable - if there aren't that many passengers, profit will be low or even non-existent if there are several trains going around rather than just one.

And yet, the tracks are already there. Between Howard and Fullerton the Red and Purple Lines run on separate tracks. They don't stop at the same stations (except Belmont), but the tracks are there for this to happen.

So here's what I suggest. Instead of doing the whole skip-2, skip-4, skip-8 system, which would require a separate track for each train, just use two tracks. Have the express do a skip-4 or something otherwise in the middle. The express will then travel roughly 4 times faster than the normal train, greatly speeding up travel. At the end of each track, just do a merge to change sides, and the trains are ready to go back.

Unfortunately, in the current economic climate no one will do this. It's probably prohibitively expensive, and will never get enough passengers. And the space to get 4 tracks (2 there and 2 back) is also pricey. But it looks good on paper!

And that is how computer science (tries to) impact real life.
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Car Seating

We have 19 people going on spring break, including myself. I've been thinking about how to organize people in the three vans, and came up with this:

A legend is available, although I did not show the single arrow relations... :D

The problem is that only the people in blue and red are drivers, and the people in red each own one of the vans (and therefore must be in separate cars). The drivers should split evenly between the three cars. I also tried to maintain the male:female ratio in each car.

I assigned points to the relationships (1 to acquaintances, 2 to friends, 4 to boy/girl friends), and derived this:

Clearly the current solution is better than the old one (by a whole 8 points!).

This problem is NP-complete, and while I could write an algorithm to exhaustively search the space of possible allocations,
  1. It's probably tedious, especially with the male:female constraints
  2. I don't feel like it
  3. I think this is a near optimal solution (read: good enough).
It's rather amazing how the human eye can so quickly form a near optimal solution, while a computer has to calculate the points for each configuration separately.

I am open to better solutions.
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Distance Perception

Last week's question: How often does square root day, and other higher order root days, occur?

Because of the way square root day is done (and written in general culture), there are only nine square root days in each century. This boils down to a square root day on average every 11 years.

I read a blog post with more interesting interpretations of dates.

If dates were written 3-3-09, then one person commented that 3 and -3 are both roots of 9. It is unfortunate that the is a dash before the year - because it should more properly be 3i-3i-09.

A more momentuous day, a commenter suggested, is 2/2/2008, which could be called "cube root day", because 2*2*2 = 2^3 = 8. But no one ever takes apart the year like that.

My personal favorite is rather than celebrate square root day, we should celebrate exponent day. This occurs whenever the month taken to the power of the date gives the year. While this is a more general holiday, it doesn't occur very frequently either, because the exponential quickly goes above 100. Dates raised to the month power works slightly better.

The list of month^date=year is below:
  • 01/01/01
  • 02/01/02
  • 03/01/03
  • 02/02/04
  • 04/01/04
  • 05/01/05
  • 06/01/06
  • 07/01/07
  • 02/03/08
  • 08/01/08
  • 03/02/09
  • 03/03/09 [EDIT: clearly I do not know how to do math]
  • 09/01/09
  • 10/01/10
  • 11/01/11
  • 12/01/12
  • 02/04/16
  • 04/02/16
  • 05/02/25
  • 03/03/27
  • 02/05/32
  • 06/02/36
  • 07/02/49
  • 02/06/64
  • 04/03/64
  • 08/02/64
  • 03/04/81
  • 09/02/81
This week's question: Why do things appear smaller when they are further away? In what world is this not true?

Re: Deserve Victory

A while back I wrote about this motto I have, "Deserve Victory". I recently read another one of Terry Goodkind's Sword of Truth series (Faith of the Fallen - "available" here), although it was out of order of the series. It did make me think of broader meanings for the phrase though, and I would like to share that in this post. They roughly separate into the stages of committing to an act, acting, and reflecting after the act.
  1. "Your life is yours alone. Rise up and live it."
As I said before, "deserve victory" doesn't mean "I deserve victory". It means "work to deserve victory" - that victory does not come flying into your arms. Victory can be taken as whatever is desired: happiness, fame, fortune, a good job, etc. Especially for happiness, if you are not happy now, sitting on your ass and waiting will not change that fact. Act to change the circumstance, and find that happiness. You are responsible for your victory, and it's time to make yourself deserve it.

Another way to look at it is as a challenge: you think you deserve victory, so prove it. Show the world why you deserve it, and then you'll get it.
  1. Do not accept defeat.
It seems obvious, but if you are to be victorious, you must not give up in the face of opposition. Refuse domination. Refuse defeat. This goes well with the "prove it" version of the first point. If you give up at the slightest hiccup in your plan, then how can you say you deserve victory?

I heard a recent lecture (The Last Lecture, by Randy Pausch - I highly encourage you to watch it, despite its length) where the speaker describes obstacles as the way to separate you from other people. Obstacles, or "brick walls", are "there fore a reason: they let us prove how badly we want things." If you want something badly enough - if you truly deserve something - then a brick wall won't stop you.
  1. Do not regret.
Two things can happen after you've done everything you can:
  • You fail - You did your best. You can - and should - try again, but either way be glad that you have tried. You miss 100% of the shots you never take.
  • You succeed - What can I say. You deserved it.
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Prizes in Education

The New York Times recently had an article about how rewards influence student behavior. It basically revolves around the debate of whether extrinsic rewards can diminish intrinsic rewards. The fear is that, if students are used to getting prizes for doing well in tests, then their only purpose in doing well is to get those prizes. When the prizes are no longer given out (as in real life), then students don't work as hard. Another problem that was presented is that even if students are getting prizes, students getting a small prize might feel that he was punished, comparatively, and therefore have less motivation to try as hard.

Before I take a side in this debate, I want to say that prizes can sometimes be extremely helpful. Peter Diamandis, the founder and chairman of the X Prize Foundation, gave a talk about prizes as motivation at the Long Now Foundation, from which I've quoted before. A summary is also available. His basic thesis is that having a substantial prize encourages competition, and the aim of getting that prize motivates the economy as a whole to spend more than that amount. The result of that extra spending is a growth spurt in that industry. This was done with commercial flight, and more recently as a result of Diamandis' work, space tourism.

How, then, will the introduction of prizes as rewards for students work? Diamandis stressed that prizes need to be "at the intersection of audacity and achievability". In principal, it seems that prizes will have the same effects on students as on market competitors. Students will work harder to get the prize, thus increasing the output of the classroom (the "market") at a much lower cost. And I think this is the case.

The problem is that, unlike industry where once the technology develops everyone benefits in the long term, in the classroom both the students and the environment change, and only benefit in the short term. The team that won the Ansari X Prize will continue to have funding for their work, because now they have caught the attention of the media, the government, and various other groups. For a student who gets the highest score in a test though, there is no similar future motivation. Once the test is over, the motivation is lost, and the student goes back to the level he was pushing himself before.

Then there's the problem of the overjustification effect: when people are given external rewards for doing something, this reduces their internal motivation to do that. For example, let's say for participation in a reading program, one student is given some money as a reward. Another reads the same books outside of the program, and gets no reward. Who do you think enjoys the reading more? Probably the latter child - the first one comes to believe that he is reading for the money and not for enjoyment.

Why doesn't this happen with the X Prize? Because the teams chose to enter that competition. If I told a group of engineers that they have to build an orbit capable aircraft, they probably won't be too happy, even if they are astronautical engineers. The very purpose of the X Prize is to lure people who may not otherwise be interested in a problem. This is a very intuitive effect, and yet in schools this is often ignored. Everyone in the class is competing for the prize, regardless of whether you want to or not.

So how to best use prizes? First, they should only be used when the motivation is not high enough. If a student likes to read, there's no reason to reward him - his enjoyment from reading is enough to keep him at it, and rewarding him risks making him lost interest. Second, when prizes are offered, they should be voluntary. Sure, there may be students who are not motivated and won't join the competition, but if they are not impressed by the reward they're not going to try hard even if they were in the competition. The prize is to help motivate those on the border, who, given just the right nudge, might become intrinsically motivated.

There is one final facet I want to address. The prizes should be for tangible and useful results. More specifically, prizes should not be used for tests. With the debate on going about whether the SATs and GREs measure real education or test taking skills, it would be a great mistake to reward someone for being an excellent test taker. Tests are only proxies to measure the amount of learning. The prizes should instead be awarded based on how much extra effort someone put in. A presentation about what you learned in class is good, but the presentation which shows the student read more outside class, did some of his own experiements, is the one worthy of the prize.

Square Root Day

Last week's question: Why is comparative advantage defined between people and countries, but not between units such as counties, states, or continents?

The question is actually slightly deceptive. I asked it to get at another point, because simple answer is easy: there are more people looking at production of countries and people than the production of counties or continents.

I also noticed that last week's post was incorrectly titled; I was originally thinking about production possibility frontiers, but then sliped into comparative advantage and forgot to change the post name.

By to the topic at hand, I am troubled by the idea of comparative advantage. There seems to be a problem of scale which needs to be addressed. Let's say, for example, that Iowa and Wisconsin both produce cheese and corn. Even if one state is better at doing both, the theory of comparative advantage says they should specialize and trade instead, because that will increase the total yield of corn and cheese combined.

But now, let's switch to a country level view. US and China may both produce corn and cheese, and again the theory says they should specialize and trade to maximize output, regardless of how much they can produce.

So what happened to the state level loss? If the US specializes in corn, in Wisconsin in particular there will be a lost of opportunity cost. Similarly, if the US specializes in cheese, Iowa will incur an opportunity cost. That is, all else being equal, the total production would be higher if the level of production was measured at a smaller unit. If Iowa could trade with a province in China for cheese, and that province can produce cheese cheaper than Wisconsin can (assuming similar quality), then the specialization makes sense.

The smaller the unit, the higher the total production. This argument leads to a human level comparative advantage. You might be an excellent painter and sculpture, but if your painting is better, you should paint rather than sculpt, and buy other people's sculptures. Logically, then, comparative advantage argues that everyone only do what they do cheapest comparative to other people. In addition, direct people to people trading generates the largest total production.

I guess my question (privately, not the question of the week) is, why are we analyzing economics through countries? It would make more sense to analyze by industry - all the corn growers vs. all the cheese makers and how much they trade.

I know, I know, people care more about countries than industries. But it makes more sense to do it.

This week's question: 2009-03-03 was called "square root day" by many, presumably because 3*3 = 9. How often does square root day occur? What about higher order roots?
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My Ideal Love

  • has long hair. I really like long hair.
  • would be highly disappointed if I cheat on her. She might be angry too, but it's important she is disappointed.
  • believes in something simultaneously more and less than marriage.
  • cannot help but kill the cat. Multiple times.
  • discusses and is knowledgeable on a wide range of subjects
  • know that talking doesn't mean communication, and communication doesn't mean talking.
  • wears a short skirt and a loooong jacket
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Academic Typecasting

We often hear stories about actors who don't want to be typecasted. Although this is a term that's also thrown around in computer science, what actors usually mean is that they are seen too often in characters with similar personalities, and are therefore unable to get other kinds of roles. Jim Carrey, I think, is a great example; he tends to appear in slapstick-like comedies, although he is also capable of dramatic acting (Eternal Sunshine of the Spotless Mind; I love that movie).

So I was thinking about grad school the other day, and how I will spent a chunk of my life solving one small problem. As an aspiring renaissance man, I am a little apprehensive of the idea, but I understand that it's a necessary path to being an expert on anything. What I do want to avoid though is being typecast as someone who only does computer science.

The thing is, once I get a PhD (5 years from now) and become a professor (who knows how long), I still want to have discussions about things far from computer science. One good thing about doing AI is that the field is inherently inter-disciplinary. At the very least you have to know some psychology, and then maybe some math. There will be senimars on education, so that's good, and it's always easy to branch into philosophy. But that's about it. The people I interact with daily, then, will be defined by these fields - just as I will be. What if I want to talk about social issues? Or perhaps explore the graphic design of some house? Global warming? While I'm sure other people will have some interest in things like this, I don't see any heavily promoted open forum to talk about whatever you want, with whoever's interested.

I can read (although I haven't done any leisure reading for the past month; I'm just too busy), but that's a very passive way of learning. I want to discuss ideas with people, to express my own and expect rebuttals and disagreements.

I'm not changing my mind about grad school; it's just a concern I have about my general well-being.

I guess my point is: please keep commenting on my blog.

Production-Possibility Frontiers

Last week's question: How does a low gravity environment affect a women's menstruation?


I realized the day after that, through the comments of female friends, that I don't know a thing about this question. I know nothing about low gravity environments, and I know nothing about women's periods.

So instead of giving an answer, I direct you to the comments of that post. There's also a MetaFilter thread devoted to this topic.

This week's question: why does comparative advantage typically refer to people or countries, but not counties, states, or continents?

PS. I've been a little worried lately by the fact that I ask questions and write posts which have nothing to do with computer science. While it shows my wide ranging interests, I'm also afraid that I'm not learning much in computer science. This reminds me of a Budhist lesson:

There is a scholar had an extensive background in Buddhist Studies and was an expert on the Nirvana Sutra. He came to study with a master and after making the customary bows, asked her to teach him Zen. Then, he began to talk about his extensive doctrinal background and rambled on and on about the many sutras he had studied.

The master listened patiently and then began to make tea. When it was ready, she poured the tea into the scholar's cup until it began to overflow and run all over the floor. The scholar saw what was happening and shouted, "Stop, stop! The cup is full; you can't get anymore in."

The master stopped pouring and said: "You are like this cup; you are full of ideas about Buddha's Way. You come and ask for teaching, but your cup is full; I can't put anything in. Before I can teach you, you'll have to empty your cup."
I am worried that I am too comfortable with computer science that I can't ask questions anymore.
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