kaosraven10 (Forest_Horns#7383) wrote: …Most people’s opinion on anything is made by experience not facts and such unless they are taking special effort not to do so, when they talk it’s an opinion… …Some one elses subjective opinion about something that cannot be proven in any way… I wrote: Perception and the empirical context of falsifiability is not necessary to denote a fact. In a logical sense, every entity has an identity and a negation of its identity, so it is possible to mathematically and logically disprove most statements practically. That is not taking into consideration Godel’s Incompleteness Theorem or paradoxes. Read More
When you look in a mirror, and see what you think is a perfect reflection. You might be looking at a universe whose laws are fundamentally different.
How to predict and model the spread of epidemics.
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.
The SIR model is one of the simplest disease models we have to explain the spread of a virus through a population.
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.
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.
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.
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
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.
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
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
Chaos I: Motion and Determinism
The start of Chaos, with one of the foremost ideas of philosopher Heraclitus of Ephesis, who lived in the sixth century B.C. Creatures develop eternally, things have no substance and everything is always on the move: everything becomes everything, everything is everything. The first minutes of the film illustrate this idea with some everyday examples, as well as some mathematical ones.