Happy Square root day, to all of my engineering/math friends! :-)
Granted, it's not as much fun as mole day, but it's more rare (only 9 a century).
Just so you know, Square Root Day isn't the only humorous holiday celebrated in the math world. Pi Day is observed each March 14 (3.14), while Pi Approximation Day falls on July 22 (roughly equal to 22/7). The first Pi Day was observed in 1988 by staff at the San Francisco Exploratorium, who walked around in circles.
Adapted from J. Engr Education, 2008, 97(3), 301 - 302.
Consider this:
It is very important that you learn about traxoline. Traxoline is a new form of zionter. It is montilled in Ceristanna. The Ceristannians gristeriate large amounts of fevon and then bracter it to quasel traxoline. Traxoline may well be one of our must lukized sneziaus in the future because of our zionter lescelidge.
Directions: Answer the following questions in complete sentences. Be sure to use your best handwriting.
1. What is traxoline?
2. Where is traxoline montilled?
3. How is traxoline quaselled?
4. Why is it important to know about traxoline?
- Judith Lanier
Now, anyone who is decently competent in English can answer the questions above without having any idea what the terms mean. But this judgement neglects the important point that a significant amount of grammatical and syntatic knowledge is being tested here. One could not solve these problems without understanding the differences between subjects and objects, how to identify verb tenses and endings, the role and implication of helping verbs etc.
There is a strong analogy between (the above) example and the use of mathematics in science. The mathematics in itself is about grammatical and syntactic relationships, and permits the drawing of complex conclusions about the placeholders (variables) without having any idea what those placeholders stand for.
...We not only expect students in science and engineering to be able to understand mathematics (syntax); we expect them to combine this knowledge with knowledge of what the math is talking about in a tightly integrated way to see the meaning of the symbols. This is different from straight math and can even lead to differences in the way equations are interpreted.
The Differences Between Meanings in Physics and Math: A ShibbolethOne of your colleagues is measuring the temperature of a plate of metal placed above an outlet pipe that emits cool air. The result can be well described in Cartesian coordinates by the equation
T(x,y)=k((x2+y2)
where k is a constant.
If you were asked to give the following function, what would you write?
T(r,q)=?
The above is a problem whose answer tends to distinguish engineers and physicists from mathematicians. An engineer or physicist who works regularly with polar coordinates is likely to give the response T(r,q) = kr2, a result obtained by assuming the variables are related by the familiar polar to Cartesian relation r2 = x2 + y2. A more mathematical colleague is likely to respond, T(r,q) = k(r2 + q2). The function is defined mathematically by saying, “Add the squares of the two variables and multiply by k.”
The engineer will object. “You can’t add r2 and q2! They have different units.” The mathematician might reply, “No problem. I see what you mean. You just have to change the name so that each symbol represents a unique functional dependence. For example, you could write T(x, y) = S(r,q) = kr2.” Unfortunately, your more concrete friend (imagine a chemical engineer at this point) is still unlikely to be satisfied. “You can’t write the temperature equals the entropy! That will confuse everything.”
Many engineers, physicists, and mathematicians are surprised by this story. Each side believes that its way of using equations is the “obvious way” and that surely even a mathematician (or an engineer) would agree. Unfortunately, that is not the case. Each group strongly prefers its own interpretation of how to write an equation.
These two examples dramatically illustrate that in science and engineering, we tend to look at mathematics in a different way from the way mathematicians do. The mental resources that are associated (and even compiled) by the two groups are dramatically different...using math in science requires the blending of distinct local coherences: our understanding of the rules of mathematics and our sense and intuitions of the physical world.
This was shown in the movie 21. I got the answer wrong, and had a vigorous debate with a friend who was watching the show with me. It turned out she had taken a Math class on this in her undergrad. Bugger. She kept repeating - "conditional probability!".
Suppose you're on a game show and you're given the choice of three doors. Behind one door is a car; behind the others, goats. The car and the goats were placed randomly behind the doors before the show. The rules of the game show are as follows: After you have chosen a door, the door remains closed for the time being. The game show host, Monty Hall, who knows what is behind the doors, now has to open one of the two remaining doors, and the door he opens must have a goat behind it. If both remaining doors have goats behind them, he chooses one randomly. After Monty Hall opens a door with a goat, he will ask you to decide whether you want to stay with your first choice or to switch to the last remaining door. Imagine that you chose Door 1 and the host opens Door 3, which has a goat. He then asks you "Do you want to switch to Door Number 2?" Is it to your advantage to change your choice?
Math (Geometry) for (straight) guys. (NSFW)
Like Greg Mankiw, I am also stumped by this question.
Especially so if I am asked by a layperson.
Are you, too? (Referring to my readers who are into engineering, math and physics.)
