Category Archives: Education

Life, the Universe, and Everything

matrix

(Click here for the PDF version of this presentation.)

Math is everywhere, hidden in places where we don’t even expect to see it. For example, take a look at the following image:

Slide2

What do you see?

Most people say “music.” People who have studied the piano might recognize this as a piano score. And a true enthusiast might recognize it as the third movement of Beethoven’s Moonlight Sonata.

What you’ve probably never thought of before, though, is that a musical score is actually a form of graph. It tells the performer what combination of notes to play at a given moment in time. In other words, it shows sound as a function of time.

In the image below, I’ve added labeled axes to draw attention to this:moonlight_sonata_graph

Now consider a photograph. Below is one of the most spectacular images I found when Googling “photograph.” (Thanks to whoever posted it!) I love how it shows the strings of mucus frozen in time.

tiger_photo

Anyway, a photograph itself is also just a type of graph — and not just metaphorically. In fact, even the way images are produced in our brains is just a way of numerically graphing the intensity and frequency of light that falls on different portions of our retinas. In essence, your retina is the x-y plane and the light is the quantity being graphed.

Below is what the photograph looks like when graphed in three dimensions from different angles, with the colors changed to a different color scale:

tiger_photo_graphs_1

Now here is the same graph when viewed from directly above, so that the tiger is easier to make out:
tiger_photo_graphs_2

Here’s another example of a great photo:
frog_photo

And here it is with the same procedure applied to it. This one works a little better than the tiger because it isn’t filled with little white spots that end up looking like noisy spikes in the graph.frog_photo_graphs_1

Below is the graph when viewed from directly above, just as I did for the tiger. Pretty cool, huh?frog_photo_graphs_2

Now consider something that really seems to have nothing to do with math: a piece of literature. Below is the first paragraph from A Tale of Two Cities, by Charles Dickens.
Tale_of_2_cities

It, too, can be considered as a type of graph. It’s a graph that tells the reader what words to speak or think as a function of time:Tale_of_2_cities_graphThere are, of course, many other examples of graphs:

footballstragety

What I’m saying is that anything can be thought of as a kind of graph. Really, though, it’s not just graphs that are so powerful, but numbers themselves. This is because numbers encode information. For example, an entire song can be encoded in a single number. So can a photograph, or even a movie.

What’s particularly fascinating is that physicists now believe that physical reality itself is composed of information. In fact, the universe might even be digital. And since numbers encode information, it is possible that the entire universe could be represented by a single number.

Take a minute to meditate on that.

universe

If that’s true, then there’s only one thing we can conclude…

matrix_drop_math_is_everything

* * * * *

This post is based on a PowerPoint presentation I made for my math students in an attempt to inspire them. Here it is in PDF form:

Math Is Everything (PDF version)

BWYA Graduation Speech – May 2009

GradHat

In the spring of 2009, I had the honor of being asked to give the graduation speech at the Beijing World Youth Academy, where I taught physics from 2007 to 2009. It is (or was at the time) their tradition to ask one of the departing teachers to be the main speaker at the ceremony. They probably asked other people first, but no one else was willing, as we were all busy with our end-of-the-year insanity. And so they turned to me.

With my characteristic modesty, I declare that I did a pretty good job coming up with a simple and inspiring message. Here it is:

BWYA Graduation Speech 2009 – Olen Rambow

Preparing Students for Real Life

schoolHouse

The Houston Chronicle published an article about a new plan to train students, especially in low-income areas, for specific careers. The skills listed in the article are “process technology” (in “chemical, refining, and manufacturing careers”), “electronic engineering,” “network and computer administration,” “logistics and global supply,” and “pharmacy technology.”

Now this is what I’m talking about. If executed well, programs like this could have a significant positive impact on our education system and society in general. This is right in line with some of my proposals in my education essay, namely:

  1. Make the curriculum more practical.
  2. Encourage early specialization.
  3. Reduce the emphasis on “preparation for college.”
  4. Develop trade schools.

The most important thing here is that we give kids something constructive to do. If we give them practical skills and enable them to start working, kids who otherwise might have felt worthless and directionless and turned to gangs and drugs would instead feel like contributing members of society who have some say. That’s the kind of change that will make America a better place to live in.

I hope this program receives the support it needs in order to have a chance at success.

Here’s a link to the article in the Chronicle:

HISD looking to help graduates land jobs

What’s Needed for Effective Education Reform?

After spending four years teaching high school math and physics, I am now entering graduate school to pursue research in applied physics. I wanted to write down my thoughts on teaching and, in particular, on the state of our education system, while the experience was still fresh in my mind. I did so back in June, and I am now ready to post the finished product online. It ended up being a 45-page essay. It’s more for myself than for anyone else, but I think some people will find it interesting. So here it is (as a PDF):

What’s Needed for Effective Education Reform?

In the essay, I make some unconventional proposals, including:

  • doing away with grades entirely
  • doing away with grade levels entirely
  • doing away with the high school diploma entirely
  • encouraging early specialization
  • developing a culture of respect for teachers
  • disciplining students in more effective ways

Enjoy.