Introduction Picture two doctors updating the same patient record at the same time - one in São Paulo, the other in London. Both are offline. When connectivity returns, whose changes prevail? This is not a hypothetical. It is the everyday reality of distributed systems: multiple nodes, no shared clock, no guaranteed network. The conventional answer has long been locking - one node waits while an
It started at midnight I had 24 hours, a free Replit subscription, and an idea: what if I could build something like Miro — but actually understand every line of code in it? The core problem I had to solve first Multiplayer sync sounds simple until you actually build it. The hard part isn't sending a canvas update — it's figuring out what to send. canvas.on('object:modified', (e) => { socket.emi
Introduction Some code works. Some code lasts. The difference rarely comes down to typing speed, syntax mastery, or how many nights you're willing to push through. It comes down to how you think about a problem before you write a single line. Big-O notation is a mathematical framework that describes how an algorithm performs as its input grows. In plain terms, it answers one question:
If you use ChatGPT, Claude, Grok, Copilot, or Gemini daily, it feels like you're talking to a person. It remembers what you said three messages ago. It references the project details you shared yesterday. It feels like the model has a persistent brain that is learning about you. But it’s a lie. From an architectural standpoint, an LLM is the most "forgetful" piece of software you will ever use. Ev
Most symbolic systems rely on multiple primitives. Addition, multiplication, exponentials, logarithms — each plays a different role in structuring expressions. But what happens if you force everything through a single operator? This idea becomes concrete with the EML operator: eml(x, y) = exp(x) − ln(y) In theory, this operator can express all elementary functions. But theory doesn’t tell us what
I write a lot of READMEs. I ship faster than I document. I work with AI agents that write code in seconds and READMEs in minutes, and somewhere between the first commit and the third refactor, the README I wrote on Tuesday stops matching the code I wrote on Friday. The install command says npm start. The package.json defines start:prod. Anyone copying that command would have failed instantly. I'd