so this is going to be pretty geeky and “in to physics” but my roommate and i were talking today about a theory for the new season of LOST involving Lorenz Attractors. these are sets of differential equations that describe systems that seem to be chaotic and in disarray or even random, however they are centered around “equilibria” and are fully and completely described by mathematical equations – in other words predetermined (im looking at you, john locke). i guess a good way to describe this is very complicated, non-linear math system that follows patterns, but not any sort of pattern we can easily discern ourselves.

lorenz attractors

an interesting thing about these differential equation systems is that they can support different equilibria based on different boundary or initial conditions. for example think of a spring with a hanging weight. if you pull the weight down an inch or two, it will wobble back and forth for a while and eventually go back to the resting state. now on the other hand if you pull the weight down and inch and every few bounches give that weight a little push, in theory the spring would bobble back and forth through equilibrium forever. now if you take that system again and instead of just giving it a little poke, you give it a big poke… now the system will gain energy every time and eventually the spring would be violently swinging until the spring snapped or exploded or something crazy like that.

Belousov–Zhabotinsky reaction

imagine the “LOST” parallels. we have a system in a very smooth equilibrium – the island, pre-nuke. now imagine we add a ton of energy – the nuke. it seems we now have two parallel systems going towards very different equilibrium states – maybe even perpendicular equilibria. furthermore, with all the flashing/LOST sounds that act as transitions between the seemingly different worlds (the plane landing in LA vs. the island as we remember it) it seems as though we are actually jumping randomly between the two worlds as opposed to simultaneous but different worlds. These chaotic but determined systems exist in several real-life applications – notably the hopf bifurcation (a system describing how our neurons work), certain chemical reactions, atmosphere and weather, and finally lasers

check out this website to see an illustration of what im talking about

Lorenz Attractors in 3D

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