Hello Again, World

Well, here it is, my new website. It only seemed fitting, next to my new job in a new city, my new life after graduate school. I will be updating this space regularly now that I do not have the specter of a dissertation looming over me. Hello again, World.

Spacewalks: A Fifty-Year History

The first-ever spacewalk was performed by cosmonaut Alexei Leonov on March 18, 1965. Since then, humankind has logged over 2,000 hours of extravehicular activity (EVA) beyond Earth’s appreciable atmosphere. Three nations have led spacewalks: Russia, USA, and, most recently, China, following the success of Shenzhou 7 on September 27, 2008.

I developed the following graphic after stumbling upon NASA’s data portal and their dataset on US and Russia’s Extra-vehicular Activity (EVA). The processing and visualization of these data are fully reproducible at github.com/nsgrantham/spacewalks.

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Time Travel with Factorials

Introductory calculus courses often give students the following rules-of-thumb when finding limits of ratios of functions:

  • Exponential \(\exp(x)\) beats a power \(x^{k}\)
  • Power beats a logarithm \(\log(x)\)

For example, this implies \(\lim\limits_{x\to\infty} \frac{\exp(x)}{x^{2} + 7x + 42} = \infty\) or \(\lim\limits_{x\to\infty} \frac{\log(x)}{x^{4}+x-12} = 0\).

However, courses tend not to emphasize just how ridiculous the factorial function is in comparison. Recall that the factorial of a non-negative integer \(n\) is defined such that \[ n! = n\cdot(n-1)\cdots 2\cdot 1, \] where \(0! = 1\) by convention. So, say \(n = 4\). Then \(n! = 4\cdot 3\cdot 2\cdot 1 = 24\).

Factorials are absolute monstrosities for even moderately-sized \(n\). To appreciate just how quickly factorials grow, let’s consider looking back \(n!\) seconds in the past.

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