I wanna be a sponge when I grow up.

I’m madly studying for prelim #2.  I learned that I was not a very good sponge on prelim #1.  The professor included many questions that we did in class that I had not fulling absorbed.  A friend later commented it was not an exam on intelligence, but an exam on “how good of a sponge you were.”  I learned I was not a great sponge.  I was okay, but not truly great.

So, when I grow up, I want to be a good sponge.  I’m practicing my sponge skills now as I study for algebra.  The professor who writes this exam is fairly axiomatic about his topics.  Thus, I’m dutifully studying and trying to understand all the concepts.  But it feels like memorization.  Perhaps that is step one to understanding? Perhaps not?  Regardless, I am here memorizing tactic after tactic and proof after proof, hoping that they will appear on the prelim as I expect them too.   Below I have included an image of the sponge I hope to become.  You can almost see the layers of proofs and theorems hidden in the little holes!

String Theory for the masses? Probably not.

I have recently been reading a book on String Theory. This goes way beyond the scope for this webpage, but I’ve been unemployed and lacking the social interaction required for subject matter. So string theory it is!

I am not a physicist, and that seems to be just fine regardless of this book’s lofty title, “The Elegant Universe: Superstrings, hidden dimensions, and the quest for the ultimate theory” by Brian Greene. The book is theoretically written for the masses. It was a NYTimes best seller after all. But I don’t know how much a non-math, non-physics person can really soak up from a book like this. A friend of mine, a French teacher, is reading another book that Brian Greene has written. She forged through a forth of the book and has since put it down for other, more accessible, books. I was captivated up until a point, probably about 1/4^th of the way through the book. Then I had to force myself to keep reading. I was definitely rewarded with some great topology discussion and some great insights into string theory. But I’m sure it’s not for everyone. But enough of my book review, what about the social part?

This book points out that scientists and mathematicians are now studying aspects of our universe that are very small. They are no longer trying to figure out why an apple falls from a tree. Physicists and mathematicians are trying to determine if various Calabi-Yau shapes are the reason for having three different families of fundamental particles. Some of these particles are smaller than an electron by as much as 10^3 times smaller. In other words, they are looking at something smaller than an atom or an electron or an anything that our generation was taught about in middle school. The learned are trying to determine what the ‘smallest’ piece of our universe is and how that affects everything else.

The only problem is because the things are so small; we don’t have the capability to tangibly test the theories. There is not tangible way to show a non-science person, “Look, here is the visual, do you see what I mean?” The only way to show the details of the theory is to show the mathematical equation. I’ve never seen these equations, but I’m sure they are quite complicated. And so I’m forced to say that there is a line to what the average person can understand in mathematics.

However! I don’t mean to say that you couldn’t understand string theory if you wanted to. I believe that everyone can learn anything they want to. There is no reason that you can’t learn something if you are interested in it. I will concede that if you don’t want to invest a lot of time and effort into understanding string theory, then (at this point in string theory’s journey to becoming an accepted [or rejected] theory you might find yourself in agreement with my French teaching friend. The concepts are intriguing, but the details are elusive.

The most interesting thing I found about this book is how much basic teaching the author does before he can really begin to teach you about string theory.

Falcon’s Flight

Falcon’s are amazing animals in their own right. They fly faster than almost anything in the skies. But when they attack their prey, they don’t fly in a straight line. Wouldn’t they get their faster if they flew straight at their prey? The answer lies in math.

There is a special spiral created by the Golden Ratio, or Phi (pronounced: Fee). What’s that? The Golden Ratio is a ratio created by dividing one Fibonacci number by the next in the series. These Fibonacci numbers consist of a series of numbers where the next unit is created by adding the previous two. So if we started with 1 and 1. Our series would look like: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 … if you divide any two large consecutive units you get the golden ratio. The actual ratio is 1.610833… (it’s irrational so it goes on forever- like pi). This ratio can be used to create a spiral. A very specific spiral found, in one case, in Nautilus shells. You can find lots of information about Phi, the Golden Ratio and Fibonacci’s series by doing a simple internet search. But I want to talk about Falcons.

Falcons’ eyes are located on the side of their heads. The reason that they don’t fly straight at their prey is because they wouldn’t be able to see their prey. A falcon can’t keep their eye on the target unless they tilt their head to the side to see their target with one eye clearly. Sadly, this small head tilt would decrease their streamline nature to such a degree that it isn’t worth it to do that. Instead, they have developed a energy efficient spiral to keep their prey always in eye line. Pretty ingenious!

So falcons make a spiral down to their prey. I encourage you to imagine a Nautilus Shell with is outer point stretched toward the prey and the wider sections of the shell spiraling up into the air. The falcon follows a spiral down to the prey on the exact same path of the imaginary Nautilus shell. The falcon’s flight path of least resistance that allows full view of their prey at all times is the same spiral that creates sea shells! Nature is pretty amazing to be so consistent!