In the spirit of April Fools’ Day, I’d like to tell a story of trickery and deceit. This is a story of how I was fooled, or rather, how I will be fooled.
Every equinox, residents of Chicago line the sidewalks to witness Chicagohenge, when the sun rises and sets perfectly along the east-west streets. For the amateur astronomy enthusiast, it’s a captivating sight. I’ve watched Chicagohenge a few times now, and I’m always amazed. The perfect alignment of the sun and the city creates a beautifully cinematic moment, like the sun is a paid actor and we’re operating the camera.
During the most recent equinox, a few hours before sunset, I noticed the sun wasn’t directly aligned with the buildings but just slightly south of west. The misalignment made me pause. Before this, I had noticed the sun generally stays in the southern half of the sky during the day, but I had never thought about when the sun would transition from south to not south. Living north of the Tropics, I assumed the sun would always appear south of me, and I couldn’t imagine why it wouldn’t. I watched Chicagohenge that day, but I was unable to enjoy it. My senses and my intuition were at odds.
In moments like this, when my senses and intuition conflicted, I turned to the only reliable source of answers: math. I opened my notebook and started drawing spheres and planes and lines, trying to decipher the truth. After a few pages of scribbled calculations, I was thoroughly convinced that on the equinox, the sun rises perfectly east and sets perfectly west. (It’s worth noting that this result holds true anywhere on Earth, which means it’s true for you too, dear reader.) While I didn’t trust my senses or my intuition, I placed unwavering trust in math and formal logic.
And therein lies the problem. I use math to check my senses and my intuition, but I have no system to disprove math when math fails. I trust formal logic entirely, but blind faith is a dangerous game, no matter how rational. Even the philosophy of mathematics cautions against finding complete truth in a fixed set of axioms. Gödel’s incompleteness theorems highlight the existence of mathematical statements that can never be proven true or false, so finding absolute truth in mathematics is impossible.
Any source of “absolute” truth has its risks. While I’ve decided to place considerable trust in mathematics, any system of truth can deceive you. Your senses fall victim to illusions, and your intuition won’t always be right. No finite number of observations will ever be complete, and no gut feeling can guarantee correctness. Even when you’re doing something as simple as watching the sun rise over your city, you might be fooled, and that’s alright. The truth was never guaranteed anyway.
$$(4 \cdot 1)! = 24$$