After spending 12 years working as a blogger, designer, entrepreneur and social media guy, I decided to go back to school last year. I stepped back into class last fall and am studying computer and environmental sciences. The biggest adjustment has been teaching my brain to do higher-level math after more than a decade of not touching algebra, trigonometry and geometry (to say nothing of calculus). It's required a lot of study time, but it's slowly seeping back in.
One of the things that attracts me to computer science and math in general is how cool numbers and their manipulation can be. It blows my mind to think about how nearly everything that happens can be described, in one way or another, with numbers and math. Some of the concepts like using binomials to describe the motion of objects in flight and using trigonometric identities to find the height of trees can be understood by anyone with a few good years of high school math, but I find other concepts still far beyond my comprehension. The fun stuff falls somewhere in between — the ideas that can be explained well enough to get a taste of comprehension while leaving the meat of the concept as something to be gained after further study. There are few things that feel as good as the first time you grasp a seemingly impossible problem.
Graham's number is one such concept. The number, named after its discoverer Ronald Graham, is the upper bound to a solution of a certain mathematical theory and holds the record for being the largest known number to ever be used in a serious mathematical proof. It's almost impossible to truly understand just how big Graham's number is; it's so big that the entire observed universe is not big enough to hold a representation of it, even one that's able to print digits the size of atoms. The Wikipedia entry for the number is not easy to understand, but a few minutes spent watching this video and reading this post over at Reddit helps clear things up a bit.
One of the cool things about Graham's numbers is that, while the starting digits are unknown and even as big as it is, mathematicians have been able to calculate the last 10 digits- 2464195387.
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