Negative exponentsNow we’re on a roll — what does a negative exponent mean? Negative seconds means going back in time! If going forward grows by a scaling factor, going backwards should shrink by it.The sente
Put down the calculator and pitchfork, I don’t speak heresy. The birthday paradox is strange, counter-intuitive, andcompletely true. It’s only a “paradox” because our brains can’t handle the compounding power of exponents. We expect probabilities to be linear and only consider the scenari...
We rotated our rate and pushed ourselves into the negative numbers. And a negative growth rate means we're shrinking -- we should expect i^i to make things smaller. And it does: Tada! (Search "i^i" on Google to use its calculator) Take a breather: You can intuitively figure out how...
Once your account hits negative (say you're at$50), then your boss gives a legit$50/week raise. Again, your income might be negative, but eventually the raises will overpower it. This constant pull towards the center keeps the cycle going: when you rise up, the "pull" conspires to pu...
Tada! (Search "i^i" on Google to use its calculator) Take a breather: You can intuitively figure out how imaginary bases and imaginary exponents should behave. Whoa. And as a bonus, you figured out ln(i) -- to makeexbecome i, make e rotateπ2radians. ...