Lucien Brulé

In 1905, Russian Mathematician Andrey Andreyevich Markov asked a heretic question for the time: if randomness is allowed to remember something, do averages still behave or does probability theory fall apart? His answer was a very specific kind of memory. The next step only depends on the present, P(Xₙ₊₁=j | Xₙ=i, Xₙ₋₁, …) = Pᵢⱼ, and yet the law-of-large-numbers stability survives. The bead jitters forever, but long-run occupation settles. Time-averaged state frequencies converge to a fixed profile π satisfying π = πP. Fast-forward to 1931, another Russian Andrey Nikolaevich Kolmogorov, takes the same Markov mechanism and turns it into dynamics. Instead of only asking where does the chain spend its time?, you watch the whole distribution move in real time through the Kolmogorov forward (master) equation dp/dt = pQ, where Q is the generator of the continuous-time chain. That’s exactly what the render is showing as the same mechanism wearing two different lenses. The fog is p(t) spreading through the labyrinth, the flux layer is the net current pushed through corridors and the portal, and the particles are just sample paths driven by the same generator. One Markov engine...either you look at the evolving law, or you watch trajectories and let ergodic averages do the estimating. That’s also why Markov’s "memory without collapse" became a workhorse. MCMC engineers a chain whose stationary distribution is the target, then uses time-averages to estimate things you can’t integrate directly (posteriors, partition functions, constrained geometries). The same skeleton appears in hidden Markov models for time series, in biophysics as channels switching between states, and in control/RL through Markov decision processes. #ProbabilityTheory #MarkovChains #ContinuousTimeMarkovChains #KolmogorovForwardEquation #StochasticProcesses #Kolmogorov #Markov #MCMC

“oboe is trash just give my man ripgrep.” Then I crashed ChatGPT, reverse engineered the SIGTRAP, and filed it loud. github.com/LucienBrule/cr…

Alan Watts: Prickly people vs Goo people.

Starting book number 660, of the ones I count. Current progress suggests I’m on target for 1000 books by age 30. Turning 28 next week, what a time to be alive. Phone time down to sub hour daily. Consistently getting into flow, shipping often. Lux Æterna

this is us, guys

StyleGAN, but as a feature in games. grab a mushroom, drink a juggernog, do some jet… bam, intense ai visuals. like playing on low res with DLSS maxed, but better.

Mr robot remake but Elliot has a remote job and the show never leaves his apartment

👀

🤷🏽‍♂️ I DO like cats!

time to ship b2b saas

reddit twitter and instagram are hosed moved to doomscrolling github only social media I know of that still maintains chronological sort

raspberry pi rp 2040 has an a dual core arm m0 with a 133mhz clock. it’s $0.80 on digikey in 1980 the motorolla 68k (macintosh etc) had a single core clocked at 10mhz. on release msrp was $487 adjusted for inflation that’s $1477 today wild

hear me out

devops do be like that sometimes