Logicedges
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'Edges' or 'limits' of logic, proof and what can be known
Examples of 'logicedges'
• irrational numbers such as √2 cannot be written as a ratio of 2 numbers. The consequence of this leads to a fundamental uncertainty in the behaviour of the physical world shown by the "butterfly effect" in the "three body problem"
• Consistent theories* contain a statement that cannot be proved within that theory.
• Observing very small particles disturbs them in a most fundamental and unpredictable way**;
• Very small particles are best described with a wave which requires the use of the square root of -1**.
*sufficient to be able to describe counting natural numbers.
** from quantum physics currently giving the best scientific description of particles.
Videos
The Barnsley fern animated around the data points out of which it appears to 'grow'.
A zoom into the logistic map
The Lorenz attractor and its match with water flow.
The "Lorenz attractor in the sky"
The Mandelbrot set: selected slides and a zoom with its matching bifurcation tree.
Candle smoke rising
The Schrödinger equation
Flames rolling in a woodburner
The wave equation starting in a simple state and ending in a state similar to the waves on the sea.
Three particles attracted only by, say, gravity generally move in chaotic orbits - known as the three-body problem.
Geometry of a swimming whale (equation chosen empirically)
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