Insights & Essays
From casual daily questions to deep technical dives.
A collection of essays recording unfiltered thoughts and discoveries, spanning across various fields.
Why is Minus x Minus = Plus?
Physical intuition using "velocity and time" vs. rigorous algebraic proof based on the distributive property. The importance of revisiting definitions.
How to Find a Lost Bluetooth Earphone??
Even without signal strength, you can find "where the connection breaks." A geometric search algorithm using boundary points of the "connection limit circle."
Is 0.999... Really 1?
Is an infinite decimal "infinitely close" or "exactly the same"? Proofs via algebraic and intuitive approaches.
Why Doesn't SPICE Converge?
The mathematical meaning hidden in "Timestep too small". Analyzing Newton's method divergence and Predictor failures.
The Formula Containing Every Image
Tupper's Self-Referential Formula Generator. A mathematical library of Babel where your name, history, and future already exist at a specific height $k$.