Sensitive dependence on initial conditions (SDIC) means that nonlinear chaotic systems whose initial states can be located only within a small neighborhood ε of state space will have future states that can be located only within a much larger patch δ.
A system where the outputs don't change in simple proportion to the inputs; small changes don't necessarily produce small effects.
Patch (δ)(as used in mathematics)
A larger region or area in the space of possible outcomes—the Greek letter delta (δ) represents how much larger this patch is compared to the starting zone.
State space(as used in mathematics and physics)
An imaginary space that describes all the possible conditions a system can be in; each point in this space represents one possible situation.
initial conditions(Stipulated by convention to ground the causal framework)
Starting states of affairs that are stipulated to be caused, serving as the base case in a causal account of true propositions
sensitive dependence on initial conditions (SDIC)(Mathematical chaos theory; contrasted with empirically measured uncertainty growth in physical systems)
A property of dynamical systems whereby exponential growth in the separation between neighboring trajectories is derived under assumptions of infinitesimal initial uncertainties and infinite time
Premise (A) makes clear that SD is the operative definition for characterizing chaotic behavior in this argument, invoking exponential growth characterized by the largest global Lyapunov exponent. Premise (B) expresses the precision limit for the state of minimum uncertainty for momentum and position pairs in an \(N\)-dimensional quantum system (note, the exponent is \(2N\) in the case of uncorrelated electrons).[8] The conclusion of the argument in the form given here is actually stronger than