The Scintrovert

Edward Lorenz in 1961 wrote down a set of three coupled non-linear differential equations to model the atmosphere. The belief at the time was that once you write down a set of differential equations then provided initial conditions you can always exactly find the parameters of the system at any point in time however long afterwards. Small errors shouldn't deviate you much from the true results. [ The Lorenz system ] But to Lorenz's surprise, small changes in the initial conditions cascaded into huge differences in the outcome of the simulations. Resulting in a butterfly like pattern, which he termed a strange attractor -  Lorenz Butterfly - Bounded and Finite, yet unpredictable. The trajectories neither stabilize nor diverge to infinity, they strangely orbit a finite region without any specific periodicity. The term 'Butterfly Effect' comes from here- small changes leading to huge outcomes. This had huge consequences not just mathematically but physically too. The diffe...

Classical physics states that everything that happened in the past can be exactly know and everything in the future can be exactly predicted, provided you know the position and momentum of every single particle in the universe. Sure that's an absurd demand, a single droplet of water has number of particles of the order 10^23 which is incomprehensibly huge to just think about let alone measure.  A small water droplet has more molecules than the number of grains of sand on earth! But philosophical consequences of determinism in classical physics do not concern with practicality. The fact that once things are set in motion, everything from the time universe was born, stars forming and exploding, dinosaurs going extinct, what you'll eat for breakfast tomorrow or do anything for that matter- can be exactly calculated using Newton's laws of motion. From Big bang to Breakfast, everything can be in-principle predicted exactly in classical physics. [Image by GPT 5.2] A deterministic...