@RealPrincessJas@yvzyayla1071@latestincosmos I think it’s a simple and beautiful design. A wave with no beginning and no end. And with every distinction we process and every new question we generate we become closer to the source.
What Happens When Randomness Learns to Flow?
Markov (1906) showed that randomness can remember the present and still obey long-run stability. The bead jitters, the path looks unpredictable, but the occupation pattern settles into a stationary glow.
Kolmogorov (1931) takes that same Markov idea and turns it into motion. Instead of asking where the chain spends its time, we watch the whole distribution move in real time.
dp/dt = p Q
Here, p(t) is the probability fog spreading through the labyrinth, Q is the transition-rate generator, and the bright flux layer shows the net current being pushed through corridors and the portal.
Jᵢⱼ(t) = pᵢ(t)Qᵢⱼ - pⱼ(t)Qⱼᵢ
The particles are sample paths of the same generator. The fog is the evolving law. The flow is probability itself moving through state space.
This idea now appears everywhere:
Queueing Systems, Population Dynamics, Chemical Reaction Networks, Ion-Channel Models, Reliability Theory, Epidemics, Finance, And Modern Stochastic Simulation.
Its One Markov Mechanism With Two Lenses... Microscopic Paths And Macroscopic Evolution.
#ProbabilityTheory #RussianMathematics #Kolmogorov #MarkovChains #StochasticProcesses #Mathematics #AppliedMath #StatisticalPhysics #MathAnimation
Been in the receiving end. Know more than I say. But at this point it’s so far down the road it’s become less hurtful and more fascinating. Still have my screenshots but I want no part of the yucky anymore even though technically I could blow some shit up. Going to grab my lawn chair and bevvy and just watch.
Honestly requires strength. And I’m sure she has used all her strength to get through this. But Corri I completely agree…now it’s time for KR to show the honest impact of years of stolen life and safety by being caught in a corrupt system. She actually speaks for so many people. I hope she finds her voice. ✨
We built an interactive 3D module to teach kids about what temperature does to water.
- You adjust the temperature in real time
- You see the impact on the state of water and what's changing at a molecular level
- You can unlock two secret states in there if you pass a quick quizz
This is the first of a giant series. We're turning the open source @withmarbleapp curriculum into a full bank of these interactive lessons. One for each topic kids learn in primary school.
If you are a parent or primary school teacher, let us know in comments which module you want to see next.
Link to play with the water lab below 👇