Fourier Transforms and Nephew Mishaps
Imagine everything is made up of small ripples (it actually is!). From the sound of music (great movie!) to the silence of the lambs (scary movie!). These elemental waves are not limited to sound, far from it. They affect every dimension known and beyond.
Joseph Fourier[i]
introduced a new way of describing the behaviors of our wonderful universe.
Usually, people would use time as a
reference to describe a phenomena. For example, in the case of a goof off
session with one’s young nephew, if 
is a theoretical function that outputs
activity name for given time 
then its Fourier equivalent would be 
where the function would tell us how much time
of a certain activity 
I’ve done with my nephew during our goof off
session.
Example:
Which can be broken down to even smaller
activities which make up the ones above:
So if we graph our whole “Goof Off Session” we’d have:
And it’s Fourier Transform counterpart:
More granular with elemental activities:
So an event like ‘Hide Seek’ is made up
of various activities such as running, laughing, about-to-cry and being-surprised.
Realistically, activity A is a metaphor
for frequency – ξ.
Instead of base activities like Running and Laughing that make up more complex
ones like ‘Hide and Seek’ and ‘Playing Catch’, according to Fourier, the world
is made up of waveforms or sinusoids which are identified by frequency 
where 
is
cycles and 
stands for time. These make up more complex
waves, analogous to ‘Hide and Seek’ and ‘Playing Catch’.
Mapping Activities
to Frequencies ξ
Running
à
50 Hz
Laughing
à
20 Hz
About
To Cry à
10 Hz
Being
Surprised à
9 Hz
For all the nephews out there with uncles
in love with knowledge and the magic of the world, I am truly sorry!
PS: If my nephew is reading this in a
close future, you were not used as a guinea pig! I fell and goofed off way more
than you, if anything I was! J