There are different kinds of logical reasoning, which are used in different situation. Mathematics is deductive, natural science is inductive, and the conclusions of Sherlock Holmes are abductive.
WP: Rigour
WP: Logical reasoning
WP: Abductive reasoning
WP: Deductive reasoning
WP: Inductive reasoning
'Deduction' vs. 'Induction' vs. 'Abduction'
The Mertens conjecture was disproved in 1985.
WP: Franz Mertens
WP: Mertens function
WP: Mertens conjecture
Some background regarding the Möbius function and convolutions:
WP: Convolution
WP: Peter Gustav Lejeune Dirichlet
WP: Dirichlet convolution
WP: Hasse diagram
The Möbius function is a nice tool which is useful in number theory:
WP: August Ferdinand Möbius
WP: Möbius function
WP: Möbius inversion formula
What is agile software development? Understanding the meaning of agile is essential, but we find a lot of confusion out there. Allen Holub summarizes several problems arising from a wrong understanding and thus wrong implementation of agile.
Footage from Keynote presentation Software Architect 2014 (London, 14-17 October):
WP: Allen Holub
Manifesto for Agile Software Development
WP: Agile software development
Scrum
WP: Scrum (software development)
WP: Scaled agile framework (SAFe)
Recently in this blog: Introduction to dark matter
This is a follow up video by Angela Collier about several misunderstandings and reactions to her video and the concept of science.
The causal structure and the principle of relativity look to be in conflict when we consider an inertial moving charge in flat space. How can the field of a moving charge be pointing to the charge's actual position rather than an older one? Retarded potentials can help, but also a wavelike information output (as a postulate) is needed for an explanation, where two effects cancel exactly and lead to the observable result, to the principle of relativity and to the effect of length contraction. Is special relativity an epiphenomenon of wave superposition? Is the wavelike description of physics fundamental to relativity and quantum mechanics?
There is an unresolved question in physics regarding the behaviour of an electric charge in a gravitational field. One argument considers gravitation as a force, which leads to the application of the Larmor formula, the other one considers Einsteins point of view and uses the equivalence principle. The answers are quite different. Unfortunately this cannot be resolved by an experiment because the possible expected radiation power in the gravitational field of the earth would be extremly tiny.
Not covered in the video:
First attempts to resolve this question can be traced back to Max Born (1909). A closer look might reveal the occurence of a paradox by the equivalence principle itself.
Even without knowing about weak and strong forces, Einstein had ideas to unify at least gravity and electromagnetism - a theory of everything (TOE). One idea is that matter itself is created by a state of spacetime. His way of thinking was ahead of his time.