In Parts 1, 2, and 3, we treated the Collatz Conjecture like a movie—we watched numbers travel through loops, spirals, and fractals. We were observers of the chaos. But as a physicist, observation isn’t enough. We need classification. Before Mendeleev created the Periodic Table, chemistry was a messy list of elements. Mendeleev realized that elements…
From Mechanics to Metrics In the previous blogs of this series, I have described the app like a theoretical physicist. But a theory is nothing without hard data. We know how the numbers crash, but we haven’t asked: How high do they fly before they fall? And how long do they survive? Today, I am…
The Anatomy of Integers From Dynamics to Structure For the first six installments of this research series, we have been obsessed with the motion of the Collatz Conjecture. We have built instruments to track the chaotic trajectories, measure their dizzying heights, and time their eventual decay. We have studied the dynamics of the problem. But…
The Ghost in the Machine Ever felt like this? You’re in a physics class, copying formulas, and it all seems to make sense. Then you get a homework problem that’s just slightly different, and suddenly you hit a wall. Or maybe you’ve had a wrong idea stuck in your head—like the ghost of a misconception—that…
In my last post, I shared how I used AI to explore the strange “mirror world” of negative integers in the Collatz Conjecture. Today, I want to talk about why I built this visualization app in the first place. The Pen and Paper Struggle Back in 1996, and later during my PhD research, my “computer”…