Saturday, July 19, 2008
Now, I have seen most of Michael Moore's films and I know that many times he exaggerates reality with the purpose of making the US look bad so I naturally don't believe him immediately. On top of this, I have never been in any other country for enough time to need medical care and therefore I lack data to make up my mind on the topic of health care. Stop by and leave your country's health care story!!!!
Among my friends, the biggest debate was that we could visualize situations in which we think a different thing will happen. I should admit though that I agree with the video.
By the way, I was told that the Professor in charge of PQW has asked these questions to many Assistant, Associate and Full Professors, including Nobel Laureates and supposedly they don't all get them right. So, don't feel bad about getting it wrong either.
Tuesday, July 15, 2008
My claim is that Physics is independent of Mathematics. Yes, yes... I know when you take physics in school it's always mathematics or at the very least full of mathematics, but that is understandable because Mathematics is just another language and it turns out to be one which everyone is suppose to know plus it allow us to calculate numeric answers for Physics problems. I know all of these, but I still think that Physics exists whether or not I can put them in an equation, or whether or not you can put numbers to it.
Let's just think of a child. S/he knows that to reach the top of the kitchen counter he needs to jump higher than he needs to reach the top of the couch (where he might not even need to jump), and therefore the initial upward velocity needs to be large enough. He goes through all this process and eventually gets it right. Now, I think the kid learned Physics by trial and error, however some people think the child unconsciously solved a complicated (or not so complicated) mathematical model. Some of the advocates of a mathematical world believe that we are born with the mathematical abstraction, some others believe that we subconsciously learn it as we go. Also, some people are not amazed by the fact that relatively simple (by simple I mean something that at least 1 person in this world can do) mathematical models can "describe" the universe. Why should they be? After all, Physics is Mathematics, or so they claim.
Here is the list of (some) points I have heard in favor of Physics being independent of Math:
1) If Mathematics is just another language, I should be able to say the same things in English, or Spanish or Chinese or whatever. Mathematics is then not special at all and there is no reason the world should be mathematical.
2) It's hard to believe that a kid or an animal have a subconscious mathematical machinery that solves some kind of equation for every single world situation. It would be easier to just learn by experience where left or right, up or down are.
3) Before Newton, people could also tell things fell to the ground. They just didn't make much of it.
4) This is similar to 3 - Physical phenomena exist whether or not we have a mathematical theory for it.
Now, for Math is basically just the negation of every point above mentioned:
1) Mathematics is NOT just another language, it is THE language.
2) Whether or not you believe it, we all have the mathematical machine inside our heads.
3) We don't know new Physics until we can explain them with a mathematical model.
There are probably more, and better points to consider. However, usually these points are defended with examples which makes it hard to convince anyone. Like I said at the beginning, I don't think this battle will ever end but if you have a good argument for either one (or maybe a different option) please share it.
Saturday, July 5, 2008
The main idea of the article is that people think gas savings go linear with MPG when "upgrading" their vehicles, for example, going from a 10 MPG to 15 MPG would be considered a worse option than going from 40 to 45 MPG. Or, even going from a 20 MPG to a 30 MPG being worse than going from a 20 MPG to a 40 MPG. It turns out it's not so easy, because gas consumption is not linear with MPG,
If one also considers that high MPG vehicles can cost significantly more these days, it might be wise to reconsider how to shop for a car.
From this graph, which I reproduced it from the paper and added the two linear regimes, it easy to see that somewhere around the 30 MPG the gas consumption difference slows significantly for a given change in MPG. This calculation was done for total travel of 10,000 miles a year which I think seems a pretty good average.