u/Ki-Chao

I just made a video diving deep into the math of belief and how we rigorously update our assumptions using conditional probability. It covers why all probabilities are conditional, and the real-world traps we fall into when we get the math wrong.

We cover:

• The Prosecutor’s Fallacy: How juries and lawyers routinely confuse the probability of the evidence given innocence with the probability of innocence given the evidence, leading to catastrophic wrongful convictions.
• Simpson's Paradox: How a developer can have a worse success rate on every individual type of task, yet somehow have a better overall success rate than their coworker. (Spoiler: it's about hidden data volume and confounding variables).
• Bayes' Rule & The Monty Hall Problem: Why switching doors mathematically doubles your win rate from 1/3 to 2/3, and how Bayes' rule proves Monty's choice destroys the 50/50 symmetry.

If you want a visual masterclass on Bayes' Rule, the Law of Total Probability, and the mathematical machinery we use to navigate an uncertain world, I'd love for you to check it out and let me know your thoughts.

Hey Reddit!

I just made a new animated video exploring why the human brain is naturally so terrible at grasping probability and how to correct it.

If you've ever been baffled by the "Birthday Paradox" (where a room of just 23 people gives you a >50% chance of a shared birthday), it comes down to how our brains struggle with scale and overcounting.

In this video, I dive into the math and logic behind uncertainty and break it down. I put a lot of work into the visual storytelling to make these complex mathematical rules easy to digest. Whether you're learning statistics or just want to stop getting fooled by randomness, I think you'll find this helpful.

I'd love to hear your thoughts and am happy to answer any questions about the math in the comments!

I recently put together a video exploring the Secretary Problem and optimal stopping theory.

If you're interviewing n applicants sequentially and must immediately accept or reject them, naive strategies (like picking randomly or picking the first "good" one) give you a terrible probability of finding the absolute maximum.

By splitting the search into an exploration phase and an exploitation phase, you can maximize your odds. If you take the derivative of the discrete sum as n approaches infinity, it converges perfectly to 1/e, or roughly 37%.

If you enjoy visual math, I’d love for you to check it out and let me know your thoughts.

Using Manim, I wanted to tackle the mathematical intuition behind one of the most legendary workarounds in computer science: the Fast Inverse Square Root function used in Quake 3 Arena.

Back in the 90s, calculating normal vectors for 3D lighting was incredibly taxing because division and square roots took up to 40 CPU cycles. To get around this, developers figured out how to estimate the inverse square root using only fast operations.

In the video, I use animations to visually break down:

• How treating IEEE 754 floating-point bits as an integer and bit-shifting them perfectly halves the exponent to approximate a square root.
• The "magic" hexadecimal constant that corrects the mantissa error.
• How applying just one single iteration of Newton's Method bumps the accuracy from 97% up to an astonishing 99.8% without ever using division.

If you enjoy the intersection of calculus and computer science, I think you'll really like this one.

Watch it here:https://www.youtube.com/watch?v=nO-Plj0KcIw

I'd love to hear your thoughts on the visual intuition!

We’ve all probably heard of the Birthday Paradox before: if you put 23 random people in a room, there is a better-than-average chance (over 50%) that two of them share the exact same birthday.

I’ve always found it incredibly difficult to intuitively grasp why this happens, so I made a visualization video to explain the math behind it.

You can watch the full breakdown here: https://www.youtube.com/watch?v=TRPenRtbHSI

I'd love to hear your thoughts on the visualization, or if there are any other math paradoxes you think would be fun to visualize next. Enjoy!