Lifeboat Foundation: Safeguarding Humanity
Toggle light / dark theme

Blog

Category: mathematics – Page 21

This is a series of videos that I decided to make on Georg Cantor’s groundbreaking works published in 1,895 and 1,897 titled Contributions to the Founding of the Theory of Transfinite Numbers.

This work could probably be counted among the most influential and significant works in mathematical history — Cantor’s transfinite numbers changed the face of mathematics completely (although, not to everyone’s pleasure). The impact of Cantor’s work can’t be underestimated.

In this series of videos I will go through the definitions of aggregate, cardinal numbers, simply ordered aggregates, ordinal types and ordinal numbers amongst others. I will also go through some of the properties of these objects including arithmetical operations of cardinal numbers and ordinal types and culminating in the arithmetic of the ordinal numbers of the second number class.

Read more | >

A simple concept of decay and fission of “magnetic quivers” helps to clarify complex quantum physics and mathematical structures.

Researchers employed magnetic quivers to delve into the fundamentals of quantum physics, specifically through the lens of supersymmetric quantum field theories. They have provided a novel interpretation of the Higgs mechanism, illustrating how particles gain mass and the potential decay and fission within QFTs.

Pioneering Quantum Physics Study

Read more | >

The American theoretical physicist, Brian Greene explains various hypotheses about the causation of the big bang. Brian Greene is an excellent science communicator and he makes complex cosmological concepts more easy to understand.

The Big Bang explains the evolution of the universe from a starting density and temperature that is currently well beyond humanity’s capability to replicate. Thus the most extreme conditions and earliest times of the universe are speculative and any explanation for what caused the big bang should be taken with a grain of salt. Nevertheless that shouldn’t stop us to ask questions like what was there before the big bang.

Brian Greene mentions the possibility that time itself may have originated with the birth of the cosmos about 13.8 billion years ago.

To understand how the Universe came to be, scientists combine mathematical models with observations and develop workable theories which explain the evolution of the cosmos. The Big Bang theory, which is built upon the equations of classical general relativity, indicates a singularity at the origin of cosmic time.

Continue reading “Brian Greene — What Was There Before The Big Bang?” | >

Actually, nothing is wrong with it if you are a computer science major. It’s just that it has no place in the philosophy department.

From the point of anyone wanting to work in natural language, symbolic logic has all of the vices of mathematics and none of its virtues. That is, it is obscure to the point of incomprehensibility (given the weak neurons of this English major at any rate), and it leads to no useful outcome in the domain of human affairs. This would not be so bad were it not for all those philosophy major curricula that ask freshmen to take a course in it as their “introduction” to philosophy. For anyone looking to explore the meaning of life, this is a complete turnoff.

What were the philosophy mavens thinking?

Read more | >

As opposed to black holes, white holes are thought to eject matter and light while never absorbing any. Detecting these as yet hypothetical objects could not only provide evidence of quantum gravity but also explain the origin of dark matter.

No one today questions the existence of black holes, objects from which nothing, not even light, can escape. But after they were first predicted in 1915 by Einstein’s general theory of relativity, it took many decades and multiple observations to show that they actually existed. And when it comes to white holes, history may well repeat itself. Such objects, which are also predicted by general relativity, can only eject matter and light, and as such are the exact opposite of black holes, which can only absorb them. So, just as it is impossible to escape from a black hole, it is equally impossible to enter a white one, occasionally and perhaps more aptly dubbed a “white fountain”. For many, these exotic bodies are mere mathematical curiosities.

Read more | >

A single universal equation can closely approximate the frequency of wingbeats and fin strokes made by birds, insects, bats and whales, despite their different body sizes and wing shapes, Jens Højgaard Jensen and colleagues from Roskilde University in Denmark report in a new study published in PLOS ONE on June 5.

The ability to fly has evolved independently in many different animal groups. To minimize the energy required to fly, biologists expect that the that animals flap their wings should be determined by the natural resonance frequency of the wing. However, finding a universal mathematical description of flapping flight has proved difficult.

Researchers used dimensional analysis to calculate an equation that describes the frequency of wingbeats of flying birds, insects and bats, and the fin strokes of diving animals, including penguins and whales.

Read more | >

ICTP lectures “Topology and dynamics of higher-order networks”

- Network topology: 1 https://youtube.com/watch?v=mbmsv9RS3Pc&t=7562s.

- Network topology:2 https://youtube.com/watch?v=F6m5lPfk5Mc&t=3808s.

-Network geometry.

Continue reading “CMSP series of lectures on “Topology and dynamics of higher-order networks”: lecture 3” | >