A modern day poet once said:
“My hump, my hump, my hump, my hump, my hump, my hump; My hump, my hump my lovely little lumps. Check it out” – My Humps, The Black Eyed Peas
Fergie was clearly alluding to the Gaussian Function pictured above, a lovely little lump. Although, I’m not sure she truly appreciates the significance of the equation and how it permeates our culture. I couldn’t have chosen a more appropriate equation to start off my “Equation of the Month” post series. Great equations small and large will be discussed and how their applications shape our lives!
You can’t really talk trash about the Gaussian because it’s so damn useful. Here are just a handful of its supporters.
- Statisticians love it for probability distributions and related purposes.
- Graphic Designers dig it for blurring your images (ie, gaussian blur in Photoshop).
- Professors use it to bell curve the hell out of your marks.
- Accountants like it because it’s the logarithm of stock price indices, exchange rates and possibly other financial variables.
- Chemists appreciate it for helping to compute electron orbitals.
- Mathematicians use it in studying hermite polynomials, which in turn gets put to good use my Physicists. Not to mention it’s a great time to integrate and use as an error function.
- Physicists love it for beam purposes and photon counting in optics. But personally I like it because it describes the wave function of ground state of the harmonic oscillator. Yes!
- Psychologists like it because supposedly it describes the results of IQ tests and makes them wonder if intelligence is normally distributed across the population aswell.
- Even Paddington Bear Likes It
So think twice next time you listen to Fergie!
Note: The Equation listed above is 1-dimensional case with constants a,b, and c, and does not correspond to the 2-dimensional graphical depiction.