The Mathematical Structure of Integrated Information Theory

Integrated Information Theory is one of the leading models of consciousness. It aims to describe both the quality and quantity of the conscious experience of a physical system, such as the brain, in a particular state. In this contribution, we propound the mathematical structure of the theory, separating the essentials from auxiliary formal tools.

What Is Organic Chemistry?: Crash Course Organic Chemistry #1

Organic chemistry is pretty much everywhere! In this episode of Crash Course Organic Chemistry, we’re talking about the amazing diversity among organic molecules. We’ll learn about the origins of organic chemistry, how to write Lewis structures, condensed structures, and skeletal formulas, and what gross organic compound the Romans used to dye their fabrics pretty colors.

Oxford Mathematician explains SIR Travelling Wave disease model for COVID-19 (Coronavirus)

The SIR model is one of the simplest ways to understand the spread of a disease such as COVID-19 (Coronavirus) through a population. Allowing the movement of populations makes the model slightly more realistic and results in ‘Travelling Wave’ solutions.

Oxford Mathematician explains SIR disease model for COVID-19 (Coronavirus)

The SIR model is one of the simplest disease models we have to explain the spread of a virus through a population.

How Do Quantum States Manifest In The Classical World?

Quantum mechanics tells us that the atom’s wavefunction can be in a superposition of states – simultaneously decayed or not decayed. So is the cat’s wavefunction also in a superposition of both dead and alive.

Chaos IX: Chaotic or not?

There are many kinds of dynamics. Some are complicated, others are not. To try and understand this better, we can take a vector field that depends on just one parameter, and let this parameter change slowly. This shows that the dynamics, under influence of this parameter, is sometimes simple and then, without warning, becomes very complicated. We see bifurcations happening.

Chaos IX: Chaotic or not?

Chaos VIII: Statistics

The dependence on initial conditions for the future of a system can look discouraging. However, there is a positive and constructive approach. In fact, this Lorenz’ real message, but it is not that well known by the general public.

Chaos VIII: Statistics

Chaos VII: Strange Attractors

In 1963, Edward Lorenz (1917-2008), studied convection in the Earth’s atmosphere. As the Navier-Stokes equations that describe fluid dynamics are very difficult to solve, he simplified them drastically. The model he obtained probably has little to do with what really happens in the atmosphere. Read More

Chaos VI: Chaos and the horseshoe

First, an old idea by Henri Poincaré (1854-1912): when studying a vector field in space, we can sometimes find a small disc that the trajectories hit repeatedly. Studying the points on the disc where the trajectories pass through is often a lot simpler than studying the vector field as a whole. We go from dynamics in continuous time to dynamics in discrete time.

Chaos VI: Chaos and the horseshoe

Chaos IV : Oscillations

We need two numbers to describe a swinging pendulum: one is its position, the angle versus a vertical line, and the other is its speed, the sign of which indicating that it moves to the right or to the left. Read More

Chaos II: Vector fields

At the end of the 17th century, Gottfried Wilhelm Leibniz (1646-1716) and Isaac Newton (1643-1727), independently one from the other, invented a brilliant mathematical tool: infinitesimal calculus or differential and integral calculus. Read More

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