suspendedreason

Well-known member


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The mathematical theory of bifurcation originated in the seminal work of Henri Poincaré on systems of non-linear differential equations. The term bifurcation was coined by Poincaré to designate the emergence of several solutions from a given solution. Whenever the solution to an equation, or system of equations, changes qualitatively at a fixed value of a parameter, called a critical value, the phenomenon is called a bifurcation. The point in the parameter space where such an event occurs is defined a bifurcation point. From a bifurcation point several stable or unstable solution branches emerge. Successive bifurcations lead to an irregular and unpredictable time evolution of deterministic nonlinear systems, which is designated chaos. The unique character of chaotic dynamics is their sensitivity to initial conditions as described by Poincaré: “It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.”

If prediction becomes impossible, it is evident that a chaotic system can resemble a stochastic system (a system subject to random external forces). However, the source of the irregularity is quite different. For chaos, the irregularity is part of the intrinsic dynamics of the system, rather than unpredictable outside influences. Chaos enables determinism and unpredictability to coexist in the same system.
 

suspendedreason

Well-known member
First thing to point out: binary, .zip files — all branching paths.

In the above tree for 20 Questions, the binary representation is just Y for car, NY for bird, and NN for tree (or in true binary, 1 for car, 01 for bird, 00 for tree)

Zip files work through Huffman Encoding, which counts the total number of characters, then encodes based on frequency. The most common characters get the shortest strings of bits, like 0 or 1 or 01. The least common characters get the longest strings, like 1100110101. This allows the shortest possible representation.
 

suspendedreason

Well-known member
"Uncertainty" is how many possible states there are of the world. A light switch has low uncertainty: it's either on or off. A human being's mood? High uncertainty. Practically speaking, you just need to perform one test to see if a light switch works, or which direction it needs to be flipped — flip it the other direction, see what happens; now you know its orientation (and whether the bulb works).
 

suspendedreason

Well-known member
(I hope someone who actually knows more about information theory, Friston's free energy principle, and the empowerment principle in RL can school me, but I'm gonna put together the pieces I think I understand & see where we get)
 

luka

Well-known member
Staff member
(I hope someone who actually knows more about information theory, Friston's free energy principle, and the empowerment principle in RL can school me, but I'm gonna put together the pieces I think I understand & see where we get)
you might not have noticed but dissensus is violently opposed to facts. we have no interest in learning things. we like to make things up.
 

luka

Well-known member
Staff member
so what i would say is, absorb this information if you must, but then do something interesting with it. make something up. a fun game we can play or something.
 

luka

Well-known member
Staff member
this is what people din't acknoweldge. when youre operating at your most powerful you can think things that later you have no access to
 

luka

Well-known member
Staff member
just like in peak condition you can lift weight that would give you a hernia to look at under normal conditions.
 
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