Last week's question: What would a transportation system look like if the ground is frictionless?
I have several ideas. There are several transportation systems already in place for traversing a frictionless medium, although not on the ground. Hot air ballons don't rely on ground friction, nor do gliders and blimps. Gladers move by wind, which will work equally well on the ground (land sailing). Blimps and planes, on the other hand, push air away from it for propulsion. Propellers and get engines would therefore to do the same on the ground.
Other ideas I had involve some initial energy. If the distance to be traversed is not too great, then air resistance is negligible. I can imagine nets being spread around an area, and people would just push off to be caught in a net at their destination. Setting up the net initially would probably require a tether, like how astronauts do space walks - which, by the way, is truly a frictionless environment.
On a more science fiction note, it may be possible to do something with eletro-magnets. It will basically be the principle in maglev trains. I can imagine some sort of remote, a magnetic suit, and a magnetized floor. Using the remote will activiate electro-magnets, which will push and pull you in one direction, or alternately slow and stop you.
Considering I just came back from broomball, some of these things sound really exciting to try out.
This week's question: Humans are often fearful of abstract ideas. Job interviews, asking someone out... these things have no immediate physical danger to us. So the question is, do animals have similar kinds of fears, and if so, from what?
Religion and Logic
Unknown, 2009-02-13
This post is actually less blasphemous than my other posts about religion.
Among my many objections against (some, not all) religious people, there is one I really can't stand: their use (or lack thereof) of logic.
Let me introduce the logic concepts first, then return to religion.
P->Q is read "If P, then Q". P and Q can be any statement; for example, if P is "it is raining" and Q is "the sidewalk is wet", then P->Q reads "if it is raining, then the sidewalk is wet". The proper name for this argument is modus ponens.
Elementary so far, right? The rules of logic allows us to define the contrapositive, ~Q->~P. Since if P happens Q must happen too, Q not happening means P did not happen. Using the example above, this would read "If the sidewalk is not wet, then it is not raining". This also has a proper name, modus tollens.
More relevant to the point, logic does not allow us to draw the conclusion that Q->P. This fallacy is called affirming the consequent. This is a fallacy because it assumes P is the only thing which can cause Q. In our example, this would read "If the sidewalk is wet, then it is raining. However, the sidewalk could be wet from rain, but also from car washing, pipe leakage, or other things.
A similar fallacy is denying the antecedent, ~P->~Q. It also stems from the assumption that only P can cause Q. Translated to English in our example, it reads "If it is not raining, then the sidewalk is not wet". Again, the side walk could be wet from other causes.
As a side note, if you do want to argue that given P->Q you know Q->P and ~P->~Q, then you need to use the bi-implication, also known as the if-and-only-if. For example, P could be "it is 5 pm" and Q could be "it is 7 hours until midnight". All of the above arguments would be true, since only in the case of it being 5 pm could it be 7 hours until midnight.
Note that these rules say nothing about the inherent truth of P or Q, or whether it makes sense that P->Q. These rules are only saying that if P->Q is true, then certain arguments are valid. P could be "I am female" and Q could be "there's an apple on the table". Clearly P is false and these two statements have nothing to do with each together. It certainly does not mean that "if there's no apple on the table, then I am not female" (~Q->~P). The original implication, P->Q, is meaningless under this interpretation. Given a sensible P and Q, however, the rules stated above hold.
Now, let's bring this back to religion. A common statement might be that "if you believe in God, then you are a good person". I will ignore whether this implication is valid for the moment. What I want to focus on is how people, after saying that and getting agreement, would go on to say "if you don't believe in God, then you are not a good person." To make this even clearer:
Let's try something else. Here's a recent example:
If you listen to religious rhetoric (or just any persuasive speech in general), you will find these logical fallacies all over the place. It makes me so frustrated when the speakers make them and go on like nothing is wrong.
Among my many objections against (some, not all) religious people, there is one I really can't stand: their use (or lack thereof) of logic.
Let me introduce the logic concepts first, then return to religion.
P->Q is read "If P, then Q". P and Q can be any statement; for example, if P is "it is raining" and Q is "the sidewalk is wet", then P->Q reads "if it is raining, then the sidewalk is wet". The proper name for this argument is modus ponens.
Elementary so far, right? The rules of logic allows us to define the contrapositive, ~Q->~P. Since if P happens Q must happen too, Q not happening means P did not happen. Using the example above, this would read "If the sidewalk is not wet, then it is not raining". This also has a proper name, modus tollens.
More relevant to the point, logic does not allow us to draw the conclusion that Q->P. This fallacy is called affirming the consequent. This is a fallacy because it assumes P is the only thing which can cause Q. In our example, this would read "If the sidewalk is wet, then it is raining. However, the sidewalk could be wet from rain, but also from car washing, pipe leakage, or other things.
A similar fallacy is denying the antecedent, ~P->~Q. It also stems from the assumption that only P can cause Q. Translated to English in our example, it reads "If it is not raining, then the sidewalk is not wet". Again, the side walk could be wet from other causes.
As a side note, if you do want to argue that given P->Q you know Q->P and ~P->~Q, then you need to use the bi-implication, also known as the if-and-only-if. For example, P could be "it is 5 pm" and Q could be "it is 7 hours until midnight". All of the above arguments would be true, since only in the case of it being 5 pm could it be 7 hours until midnight.
Note that these rules say nothing about the inherent truth of P or Q, or whether it makes sense that P->Q. These rules are only saying that if P->Q is true, then certain arguments are valid. P could be "I am female" and Q could be "there's an apple on the table". Clearly P is false and these two statements have nothing to do with each together. It certainly does not mean that "if there's no apple on the table, then I am not female" (~Q->~P). The original implication, P->Q, is meaningless under this interpretation. Given a sensible P and Q, however, the rules stated above hold.
Now, let's bring this back to religion. A common statement might be that "if you believe in God, then you are a good person". I will ignore whether this implication is valid for the moment. What I want to focus on is how people, after saying that and getting agreement, would go on to say "if you don't believe in God, then you are not a good person." To make this even clearer:
- P is "you believe in God"
- Q is "you are a good person"
- "If you believe in God, then you are a good person" (P->Q)
- "If you don't believe in God, then you are not a good person" (~P->~Q) !!!
Let's try something else. Here's a recent example:
- P is "this movement is of God"
- Q is "this movement will last"
- P->Q is "if this movement is of God, then this movement will last" (Acts 5:39)
- "If this movement lasts, then this movement is of God" (Q->P) !!!
If you listen to religious rhetoric (or just any persuasive speech in general), you will find these logical fallacies all over the place. It makes me so frustrated when the speakers make them and go on like nothing is wrong.
Domain Mapping
Unknown, 2009-02-11
In my Sociology of Religion course we recently finished Christian Smith's American Evangelicalism (a/bn). The book is really good; it's one of the few books that, as I read and had questions, eventually answers them. Although sociologists talk about a general secularization of society, what we see in everyday life is that religion is still very much alive. Smith's book looks at why this is, and he forms his subcultural identity theory based on an earlier secularization theory of pluralism. One of Smith's idea is that, looking at religion as a competitive market, the "fittest" religion gets the largest congregation.
This idea, although a little heretical at first, actually has a lot of merit. I highly recommend Smith's book for more details, but one of his points is that a changing religion doesn't equate to a religion giving ground to science; it's merely adapting to what society wants. This would be equivalent to businesses trying to brand differentiate; it's merely a strategy (albeit an unconscious one) to survive.
The idea of mapping one domain to another is old. This is the most obvious in mathematics: Godel's proof of incompleteness rests on mapping the metamathematics language (or any formal system) back to mathematics itself. It goes back further, however, with Descartes. In modern times it seems natural do talk about geometry in terms of x and y, but such a mapping between geometry and algebra was not always obvious to mathematicians. The main idea is that mappings, provided they are correct and you know the limits of any particular map, provide new perspectives on looking at the original domain.
For example, the mapping of religion to economics suggests price discrimination within a church. And with megachurches, we do see that: people can walk in and walk out on Sundays only, or they can join the plethora of prayer groups, social outreach projects, and other activities offered during the week. To each his own; if someone is willing to spend time (more on this in a bit) working for the church and strengthening it, the church will draw them in. They are the consumers at the left end of the demand curve, willing to pay a large sum for religion. For the others who are not as interested, well, they can just come and count towards congregation numbers.
In class we talked about how although in society there are lots of religions to choose from, the background of a person might prevent them from choosing their favorite religion. For example, if someone was raised in a fairly restrictive church, and grew up thinking that way, it is likely that they will stay within that church. They simply do know enough about other religions to make a choice. This makes me think of complex systems, and the general problem in economics of information flow. The general assumption of perfect information is clearly too idealistic; what happens when consumers don't know that on the other side of town you can get the car for much cheaper? Joshua Epstein and Robert Axtell's Growing Articial Societies deals with this a bit. I actually reconstructed their models for a project last quarter, and their conclusion is that while the market does head towards equilibrium price, it takes time. Through in changing preferences and difference in taste between generations, then the economic equilibrium is almost never reached at all. What does this say about religion? Well, there's probably people who would join a church if they required less ("dead weight loss"); people will probably keep changing churches; a single church won't dominate the entire religious market... You get the idea.
The last "map" I will make, although this is not so much a map as a "reminds me of", is to psychology. Smith suggests that with the large number of religious choices in society, people are more likely to find one they like and commit to it. Psychology, however, suggests otherwise. Sheena S. Iyengar and Mark R. Lepper has written papers on how people are more likely to buy jam if given 6 choices instead of 60. This NYTimes article gives a non-technical overview. While this does not invalidate Smith's theory, more research should perhaps be done on choice between religions.
For those who find domain mapping a valuable tool, it might be interesting to you that these metaphors - which are what maps are when you explain them - have been considered by some (in particular, George Lakoff) to be the basis of how we learn. The metaphors also suggest certain attitudes. I used the phrase "spend time" above, seeing time as money. Does that mean I look at time as something I "own", that I should maximize my time, and there's only a finite amount of it?
Lakoff's book Metaphors We Live By (a/bn) will probably give more details on this. I have yet to read the book either; I would gladly read it with you and discuss.
This idea, although a little heretical at first, actually has a lot of merit. I highly recommend Smith's book for more details, but one of his points is that a changing religion doesn't equate to a religion giving ground to science; it's merely adapting to what society wants. This would be equivalent to businesses trying to brand differentiate; it's merely a strategy (albeit an unconscious one) to survive.
The idea of mapping one domain to another is old. This is the most obvious in mathematics: Godel's proof of incompleteness rests on mapping the metamathematics language (or any formal system) back to mathematics itself. It goes back further, however, with Descartes. In modern times it seems natural do talk about geometry in terms of x and y, but such a mapping between geometry and algebra was not always obvious to mathematicians. The main idea is that mappings, provided they are correct and you know the limits of any particular map, provide new perspectives on looking at the original domain.
For example, the mapping of religion to economics suggests price discrimination within a church. And with megachurches, we do see that: people can walk in and walk out on Sundays only, or they can join the plethora of prayer groups, social outreach projects, and other activities offered during the week. To each his own; if someone is willing to spend time (more on this in a bit) working for the church and strengthening it, the church will draw them in. They are the consumers at the left end of the demand curve, willing to pay a large sum for religion. For the others who are not as interested, well, they can just come and count towards congregation numbers.
In class we talked about how although in society there are lots of religions to choose from, the background of a person might prevent them from choosing their favorite religion. For example, if someone was raised in a fairly restrictive church, and grew up thinking that way, it is likely that they will stay within that church. They simply do know enough about other religions to make a choice. This makes me think of complex systems, and the general problem in economics of information flow. The general assumption of perfect information is clearly too idealistic; what happens when consumers don't know that on the other side of town you can get the car for much cheaper? Joshua Epstein and Robert Axtell's Growing Articial Societies deals with this a bit. I actually reconstructed their models for a project last quarter, and their conclusion is that while the market does head towards equilibrium price, it takes time. Through in changing preferences and difference in taste between generations, then the economic equilibrium is almost never reached at all. What does this say about religion? Well, there's probably people who would join a church if they required less ("dead weight loss"); people will probably keep changing churches; a single church won't dominate the entire religious market... You get the idea.
The last "map" I will make, although this is not so much a map as a "reminds me of", is to psychology. Smith suggests that with the large number of religious choices in society, people are more likely to find one they like and commit to it. Psychology, however, suggests otherwise. Sheena S. Iyengar and Mark R. Lepper has written papers on how people are more likely to buy jam if given 6 choices instead of 60. This NYTimes article gives a non-technical overview. While this does not invalidate Smith's theory, more research should perhaps be done on choice between religions.
For those who find domain mapping a valuable tool, it might be interesting to you that these metaphors - which are what maps are when you explain them - have been considered by some (in particular, George Lakoff) to be the basis of how we learn. The metaphors also suggest certain attitudes. I used the phrase "spend time" above, seeing time as money. Does that mean I look at time as something I "own", that I should maximize my time, and there's only a finite amount of it?
Lakoff's book Metaphors We Live By (a/bn) will probably give more details on this. I have yet to read the book either; I would gladly read it with you and discuss.
Efficient Transportation
Unknown, 2009-02-09
Last week's question: Are outdoor ice rinks really made with water? Is Zamboni a type of vehicle or a brand name?
- Yes, out door ice rinks are made with water. When I went ice skating last weekend, we talked about mixing some kind of chemical to raise the melting point of water, so it will freeze more easily. I suspect this will make it turn to liquid quicker under pressure though.
- Zamboni is a brand name, with their major competitor being Olympia. The latter is what Millennium Park uses.
Abortion
Unknown, 2009-02-06
I recently had an online discussion about religion, gay marriage, and abortion with a bunch of strangers. It was an exhilarating experience. It occurred to me that while I've written quite a bit about the first two, I have yet to address the latter.
I think my views are logically entailed by several facts/assumptions:
The argument is simple from that point. When we kill cows, chickens, etc. we (in general) use procedures which make sure the animal does not feel pain, or otherwise suffer before it's death. This courtesy towards life should be offered to fetuses as well. And it is also easy to see that only at some point in development the fetus has nerves and therefore can feel pain. And therefore, abortion should be allowed up to that point.
Of course, it might be possible to perform euthanasia on the fetus after that point as well. I suppose I'm fine with this too.
Note that whether abortion is ethical is a different question from whether people should abort. Just because you can jump out of a window and kill yourself doesn't mean you should; in fact, I personally would advice people to keep their babies. But I don't have a moral qualm against those who abort (before said deadline) either.
I would like to share one more thing. In my discussion, someone brought up the idea that abortion is wrong because of legal rights... for the father. If the child is a product of both the father and the mother (so far...), why should the mother have the sole rights to abort? I think this argument has merit, but because of biological and other costs to the mother, I don't think they should have an equal say either. Of course, this is not as simple as taking the weighted average of each other's arguments. But at least it's a viable framework to look at abortion.
I think my views are logically entailed by several facts/assumptions:
- Fetuses, up to a certain point, are not conscious beings
- Humans are animals
- We kill animals - taking certain precautions to avoid inflicting pain
The argument is simple from that point. When we kill cows, chickens, etc. we (in general) use procedures which make sure the animal does not feel pain, or otherwise suffer before it's death. This courtesy towards life should be offered to fetuses as well. And it is also easy to see that only at some point in development the fetus has nerves and therefore can feel pain. And therefore, abortion should be allowed up to that point.
Of course, it might be possible to perform euthanasia on the fetus after that point as well. I suppose I'm fine with this too.
Note that whether abortion is ethical is a different question from whether people should abort. Just because you can jump out of a window and kill yourself doesn't mean you should; in fact, I personally would advice people to keep their babies. But I don't have a moral qualm against those who abort (before said deadline) either.
I would like to share one more thing. In my discussion, someone brought up the idea that abortion is wrong because of legal rights... for the father. If the child is a product of both the father and the mother (so far...), why should the mother have the sole rights to abort? I think this argument has merit, but because of biological and other costs to the mother, I don't think they should have an equal say either. Of course, this is not as simple as taking the weighted average of each other's arguments. But at least it's a viable framework to look at abortion.
Two Book Ethics
Unknown, 2009-02-04
This has been sitting in my draft box for a while.
I read Flowers for Algernon (FoA) not too long ago, and then read Ender's Shadow (ES) two weeks or so ago, and realized that both authors are playing off the same theme: that of giving up long life for extreme intelligence. There were some side effects too - a decreased ability to understand social motivations, isolation, etc. I'm not sure if this is what the authors see happening in real life, of it's just coincidence that both of them used the same events.
I am really more interested in whether I, given the choice, would choose extreme intelligence over life. Charlie in FoA didn't really know what he was getting into, whereas Bean in ES had no choice at all. For Charlie the outcome was unavoidable; by the end of the book he had already fallen back to his previous state. Bean, on the other hand, went on a relativistic journey so others can discover a cure.
If I had the choice, it wouldn't take long for me to decide at all: I would go through the surgery. I'm not sure what it is that compels me to do so. Part of it certainly has to do with the fame - not of the surgery as with Charlie - but of discovering something in the short time that you are brilliant. The career peak of many mathematicians and scientists are in their 20s, after which they simply don't have the mental agility to do anything great. Is such a surgery not simply being shortly brilliant at will, then dying off?
The other compelling factor is anticipating how much you will learn and know. Here I am reminded of Charles Babbage, who said that he "would gladly give up [his] life if [he] could have lived three days five hundred years hence." This is a deal that I would make, too. Being in a religion class now makes me think of transcendence, a plateau of intellectual nirvana at the end of the surgery. But think also how mankind would advance! If I'm not the only person willing to do this - and I'm pretty sure I'm not - then science would grow in leaps, led by consecutive short generations of super-geniuses. Even without a cure to the aging side effect, there would not be the start and stop of current scientific progress.
I see why this is attractive now: it's a very transhumanist idea. Valuing intelligence above many things and not caring if we are displaced by others, the leadership of super-geniuses doesn't bother me at all.
My only regret would probably be, after being brilliant for a short period, the uselessness I would feel afterwards. Like Charlie I would probably contemplate suicide, and unlike him I won't be bound by observation. By then death doesn't bother me either.
"For God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods..."
I read Flowers for Algernon (FoA) not too long ago, and then read Ender's Shadow (ES) two weeks or so ago, and realized that both authors are playing off the same theme: that of giving up long life for extreme intelligence. There were some side effects too - a decreased ability to understand social motivations, isolation, etc. I'm not sure if this is what the authors see happening in real life, of it's just coincidence that both of them used the same events.
I am really more interested in whether I, given the choice, would choose extreme intelligence over life. Charlie in FoA didn't really know what he was getting into, whereas Bean in ES had no choice at all. For Charlie the outcome was unavoidable; by the end of the book he had already fallen back to his previous state. Bean, on the other hand, went on a relativistic journey so others can discover a cure.
If I had the choice, it wouldn't take long for me to decide at all: I would go through the surgery. I'm not sure what it is that compels me to do so. Part of it certainly has to do with the fame - not of the surgery as with Charlie - but of discovering something in the short time that you are brilliant. The career peak of many mathematicians and scientists are in their 20s, after which they simply don't have the mental agility to do anything great. Is such a surgery not simply being shortly brilliant at will, then dying off?
The other compelling factor is anticipating how much you will learn and know. Here I am reminded of Charles Babbage, who said that he "would gladly give up [his] life if [he] could have lived three days five hundred years hence." This is a deal that I would make, too. Being in a religion class now makes me think of transcendence, a plateau of intellectual nirvana at the end of the surgery. But think also how mankind would advance! If I'm not the only person willing to do this - and I'm pretty sure I'm not - then science would grow in leaps, led by consecutive short generations of super-geniuses. Even without a cure to the aging side effect, there would not be the start and stop of current scientific progress.
I see why this is attractive now: it's a very transhumanist idea. Valuing intelligence above many things and not caring if we are displaced by others, the leadership of super-geniuses doesn't bother me at all.
My only regret would probably be, after being brilliant for a short period, the uselessness I would feel afterwards. Like Charlie I would probably contemplate suicide, and unlike him I won't be bound by observation. By then death doesn't bother me either.
"For God doth know that in the day ye eat thereof, then your eyes shall be opened, and ye shall be as gods..."
Zamboni!!
Unknown, 2009-02-02
Last week's question: How can you estimate the speed of a passing plane? Certain assumptions are allowed. In the first case, let the distances sound and light traveled be the same. In the diagram and equations below, the variables are
To get v_plane, first we find d through the law of sines:
Then we equate the travel times of light, sound, and the plane. Assume the plane has moved a negligible amount between the reflection of light to your sighting of the plane. This gives:
That was pretty easy, wasn't it? This formula seems roughly correct; if the sound and sight of the plane forms a 30 degree angle, the planeis traveling at 176 m/s. Online sources say a B747 actually travelsat around 240 m/s, which would be about 41 degrees.
Now for the bonus part: what if the distance traveled by light and sound were not equal? Then we have the situation below:
I don't actually have a neat equation for this one, but I managed to set up four (hopefully) independent equations, which will allow us to solve this system. The four equations are below.
The simple ones first. By the sum of angles in a triangle:
By the law of sines:
That gives us four equations in the four variables d_light, d_sound, theta_l, and theta_s. As I said, these should be independent; if someone solves this (or fails), please let me know.
After these four are solved for, we use the same time equivalence equation:
And we're done.
Note that in both cases, if you are also given the angle the plane and the horizon phi, you can also calculate the height of the plane:
Faye tagged me for a photo thing, and after questioning her definitions, I have this:
This was taken while I was at CTY. We were walking back to Stanford from dinner, and passed by the Facebook headquarters. From left to right, we have Sam, Lizzy, Hina, Erin, and me; Erica's behind the camera. We're all TAs for different courses. You can see more of this set on Picasa, and the tagged version on Facebook.
To compensate for the tough question, this week's will be merely fact finding, both related to ice rinks:
- xl - the distance traveled by the plane since it produced the sound you're hearing. l is the length of the plane, which you can look up by the model. x is how many plane lengths there are between the source of sound and the source of light.
- theta - the angle between the paths of light and sound.
- d - the distance traveled by light and sound. d_light = d_sound
- theta_s, theta_l - the angle opposite the paths of sound and of light, respectively.
- v_? - the velocity of various entities. The speed of sound and light are given.
That was pretty easy, wasn't it? This formula seems roughly correct; if the sound and sight of the plane forms a 30 degree angle, the planeis traveling at 176 m/s. Online sources say a B747 actually travelsat around 240 m/s, which would be about 41 degrees.
Now for the bonus part: what if the distance traveled by light and sound were not equal? Then we have the situation below:
I don't actually have a neat equation for this one, but I managed to set up four (hopefully) independent equations, which will allow us to solve this system. The four equations are below.
The simple ones first. By the sum of angles in a triangle:
By the same relation, and the trigonometric tangent relationship:
By the law of sines:
Finally, this mess is created by using Heron's formula and the trigonometric sine relationship:
That gives us four equations in the four variables d_light, d_sound, theta_l, and theta_s. As I said, these should be independent; if someone solves this (or fails), please let me know.
After these four are solved for, we use the same time equivalence equation:
And we're done.
Note that in both cases, if you are also given the angle the plane and the horizon phi, you can also calculate the height of the plane:
Faye tagged me for a photo thing, and after questioning her definitions, I have this:
This was taken while I was at CTY. We were walking back to Stanford from dinner, and passed by the Facebook headquarters. From left to right, we have Sam, Lizzy, Hina, Erin, and me; Erica's behind the camera. We're all TAs for different courses. You can see more of this set on Picasa, and the tagged version on Facebook.
To compensate for the tough question, this week's will be merely fact finding, both related to ice rinks:
- Are outdoor ice rinks actually made from pure water?
- Is Zamboni a brand, or the name of the actual machine?
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