Explain SMBC — the wiki for Saturday Morning Breakfast Cereal

The Joke

The comic presents a series of "Math Translations" -- plain-English interpretations of popular mathematical phrases that people use to sound impressive. Each panel translates a math buzzword into what it actually means in the context being discussed:

• "Fractals are everywhere!" translates to "Sometimes a little thing looks like a big thing."
• "The golden ratio is everywhere!" translates to "Sometimes one thing is about half as big as another thing."
• "The Fibonacci sequence is everywhere!" translates to the same idea.
• "The harmonic series diverges to infinity" translates to "unless you throw out numbers with a 9 in their denominator."
• "Sometimes things grow exponentially" translates to "Sometimes things grow... what? But how... what the balls?!"

The Humor

The comic skewers the popular tendency to invoke impressive-sounding mathematical concepts in ways that are technically true but trivially obvious when translated into plain language. Fractals' self-similarity just means small things can resemble big things. The golden ratio (approximately 1.618) showing up "everywhere" often just means that some ratio is vaguely in the neighborhood of 1.5-to-1, which is not remarkable. The Fibonacci sequence enthusiasm suffers from the same vague pattern-matching.

The harmonic series panel takes a different angle: the harmonic series (1 + 1/2 + 1/3 + 1/4 + ...) does diverge to infinity, but the Kempner series (which removes all terms containing a 9 in the denominator) converges. This is a genuinely surprising mathematical result, and the "translation" captures mathematicians' delight in counterintuitive findings.

The final panel reverses the pattern. Where most math buzzwords translate to something boring, exponential growth is the one that genuinely deserves its hype -- the translator cannot even finish the sentence because the reality of exponential growth is so staggering.

References

The comic references several mathematical concepts: fractals (self-similar geometric patterns, popularized by Benoit Mandelbrot), the golden ratio (phi, approximately 1.618), the Fibonacci sequence (1, 1, 2, 3, 5, 8, 13...), the harmonic series and its convergent variant the Kempner series, and exponential growth. The observation about the harmonic series with 9s removed converging is attributed to Aubrey Kempner (1914).