The limits of knowledge

An illustration of M4, the sponge after four iterations of the construction process

We will never know everything but you already know that, right? Georg Cantor proved this to be so with infinities within infinites using his Canter Sets to make it happen. The Menger Sponge, seen above, is a 3D representation of the set seen below. 

Zoom in Cantor set. Each point in the set is represented here by a vertical line.

The Set ... Using the idea of self-similar transformations

Cantor's set pointing to infinities residing in infinities within finite space shows, indirectly, the inherent limits of knowledge.

Why this exercise in contemplating this fascinating issue? Well, the limits of knowledge remains forever universal simply because we cannot ascertain the complete totality of a given event let alone properly describing the initial condition of said event in question as stated by chaos theory. 

An animation of a double-rod pendulum at an intermediate energy showing chaotic behavior. Starting the pendulum from a slightly different initial condition would result in a vastly different trajectory. The double-rod pendulum is one of the simplest dynamical systems with chaotic solutions.

For deterministic systems, even if one could not know exactly what would happen in practice (because of inexact or otherwise incomplete knowledge of earlier states), well-formed probabilistic estimates of the most likely outcomes might still be possible. Thus, even if we cannot know whether a particular flipped coin will end up heads or tails, we know that its end state will surely be either heads or tails and even what the likely distribution of heads and tails will be over any repeated set of tosses.

Implicit in that probabilistic analysis, however, is an assumption that all the possible outcomes can be stated in advance. Without foreknowledge of this sample space, one lacks the basis for compiling the appropriate statistics. Systems for which the sample space cannot be prestated seem to preclude the formation of meaningful probability statements.

As described in the main text, we believe that economic systems fall into this category. One cannot anticipate all possible future innovations by simply listing all possible combinations of prior ones: it is impossible to know what features of those earlier goods might be useful in the future because new goods and services can invent completely novel uses of old ones (and sometimes eliminate old ones).

Full knowledge of the movements of a  two body system works but not for three.

In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation.[1] The three-body problem is a special case of the n-body problem. Unlike two-body problems, no general closed-form solution exists,[1] as the resulting dynamical system is chaotic for most initial conditions, and numerical methods are generally required.

End result, the limits of knowledge remains forever absolute so ... as per the Tao, assume nothing. :)