Moving On: Fourier Series

Well, its about that time to start thinking about putting this blog to rest.  I do this for a couple of reasons:

1.  It takes a ton of time to research each topic.
2.  It takes a ton of time to figure out how to "translate" each topic is a way normal humans can understand.
3.  My appointment as a visiting professor is now up and I'm returning back to the world of engineering.
4.  There are a ton of science bloggers out there who have more free time on their hands than I do.

With that being said, I plan to hone my focus more.  I've decided to concentrate in the future on the best way I tend to learn...visually.  As we all know, psychiatrists tend to lump everyone into 4 types of learners:  Visual, Auditory, Read/Write and Tactile.  For some reason, science academia chose to focus on auditory and read/write learners with lectures, note taking and textbooks.  This is one of the reasons academia fails so spectacularly in science education: a large majority of people are visual/tactile learners.  I have insisted many times that EVERYONE can fully understand science and math, the problem is that it is presented in the wrong format which has, unfortunately, been institutionalized by academia.  If there is any group that innovates slower than molassas, its an academic faculty.
I've been toying with the idea of "Visual Math" leading up to "Visual Science" as a future blog endeavor.  Mostly because these types of learners are traditionally underserved, and also because that is the type of learner I am myself.

I will leave you with an clear example:  Fourier Series.


Here is the way a well known and respected engineer attemps to explain a fourier series in a well known engineering manual:

"Any periodic waveform can be written as the sum of an infinite number of sinusoidal terms, known as harmonic terms.  Such a sum of terms is known as a Fourier Series, and the process of finding the terms is Fourier Analysis.  Since most series converge rapidly, it is possible to obtain a good approximation to the original wave-form with a limited number of sinusoidal terms."

-Lindeburg, "Mechancial Engineering Reference Manual"

To a read/write or even auditory learner, this may work fine.  For the majority of us however, this explanation probability leaves your eyes watering, ears bleeding or wanting to through the text out your window.

Now let us contrast Lindeburg's written explanation with the following visual explanation:




Now I bet that makes MUCH more sense to most people.  If you now go back and read Lindeburg's explanation, it will also make more sense.  For most people, the why's of the science need to be illustrated visually before one can move into the details.  A fundamental failing of science education that I hope to address with a new blog.