Once data is collected, its really difficult to figure out how to analyze it. MATLAB can be used to do ODE modeling but what equations to use? Its admirable when someone can put the biological function together with the equations.
I need to decide what type of internet medium to use for teaching. I don’t have a twitter account and I need to look at the web portal for my school in order to see what the best method will be. I know facebook has nice features so I may just use it and link to blog from there.
What is the relationship between fractals and earthquake prediction? How bout fractals and neurological behavior? The last time I tried to explain this to undergrds with no math background higher than algebra and trig I wasn’t very successful. I explained its a way to fit an antenna in a smart phone, by folding it into a specific shape. Then I tried to make a connection to biology by explaining lung structure and cerebellum structure.
Galileo’s contradiction of Aristotle had serious consequences. He was interrogated by the Church authorities and convicted of teaching that the earth went around the sun as a matter of fact and not, as he had promised previously, as a mere mathematical hypothesis. He was placed under permanent house arrest, and forbidden to write about or teach his theories. Immediately after being forced to recant his claim that the earth revolved around the sun, the old man is said to have muttered defiantly “and yet it does move.” The story is dramatic, but there are some omissions in the commonly taught heroic version. There was a rumor that the Simplicio character represented the Pope. Also, some of the ideas Galileo advocated had controversial religious overtones. He believed in the existence of atoms, and atomism was thought by some people to contradict the Church’s doctrine of transubstantiation, which said that in the Catholic mass, the blessing of the bread and wine literally transformed them into the flesh and blood of Christ. His support for a cosmology in which the earth circled the sun was also disreputable because one of its supporters, Giordano Bruno, had also proposed a bizarre synthesis of Christianity with the ancient Egyptian religion. The motion of falling objects is the simplest and most common example of motion with changing velocity. The early pioneers of physics had a correct intuition that the way things drop was a message directly from Nature herself about how the universe worked. Other examples seem less likely to have deep significance. A walking person who speeds up is making a conscious choice. If one stretch of a river flows more rapidly than another, it may be only because the channel is narrower there, which is just an accident of the local geography. But there is something impressively consistent, universal, and inexorable about the way things fall.
Stand up now and simultaneously drop a coin and a bit of paper side by side. The paper takes much longer to hit the ground. That’s why Aristotle wrote that heavy objects fell more rapidly. Europeans believed him for two thousand years.
Now repeat the experiment, but make it into a race between the coin and your shoe. My own shoe is about 50 times heavier than the nickel I had handy, but it looks to me like they hit the ground at exactly the same moment. So much for Aristotle! Galileo, who had a flair for the theatrical, did the experiment by dropping a bullet and a heavy cannonball from a tall tower. Aristotle’s observations had been incomplete, his interpretation a vast oversimplification.
It is inconceivable that Galileo was the first person to observe a discrepancy with Aristotle’s predictions. Galileo was the one who changed the course of history because he was able to assemble the observations into a coherent pattern, and also because he carried out systematic quantitative (numerical) measurements rather than just describing things qualitatively. More systematic descriptions of drag can be seen with a golf ball.
Ok so the monkey hunter demo has excellent explanations of 2 dimensional motion due to gravity. It can be explained without numbers which is good practice for the students so they don’t just substitute numbers into equations. We assume that after the hunter fires his gun at the monkey, the only force acting on the bullet is gravity, its an assumption, but the demo shows that it works so its ok. The monkey lets go right when the gun is fired because he is scared and the hunter is pointing the gun directly at him. The monkey thinks he is being smart by letting go. The monkey drops at a rate of gt and a distance of 1/2gt^2. It doesn’t matter what the velocity is of the bullet , the faster the bullet the higher above the ground the monkey is shot. The horizontal distance covered by the bullet is initial velocity times cosine of the angle to the horizontal times time. The vertical distance covered by the bullet is initial velocity times sine of the angle to the horizontal times time + 1/2gt^2