Examples of 'logicedges'

Logicedges presents aspects of science and logic that are not fully described by that science or logic. They are often very beautiful which many historical developers of science and maths have written about, quoted here.

Here are four examples of such "edges":  

• 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"

 Demonstration

• Incompleteness Consistent theories* contain a statement that cannot be proved within that theory.

 Demonstration 

• Quantum uncertainty Observing very small particles disturbs them in a most fundamental and unpredictable  way**;

• Quantum interpretation 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.