## Archive for the ‘mathematics’ category: Page 2

O.o!

A mind-expanding and funny trip to the edge of mathematics

How big is the universe? How many numbers are there? And is infinity + 1 is the same as 1 + infinity? Such questions occur to young children and our greatest minds. And they are all the same question: What is infinity? In Beyond Infinity, Eugenia Cheng takes us on a staggering journey from elemental math to its loftiest abstractions. Along the way, she considers how to use a chessboard to plan a worldwide dinner party, how to make a chicken-sandwich sandwich, and how to create infinite cookies from a finite ball of dough. Beyond Infinity shows how one little symbol holds the biggest idea of all.

#survival #coronavirus
In light of recent events its a good opportunity to go over the basics of pandemic preparedness.

*Correction* I need to make a correction to information provided within this video. The case-fatality rate of the Spanish influenza is often quoted by virologists as 2.5 % when in reality the math on this doesn’t add up as the population of the planet at the time doesn’t align with this statistic. This stat is misinterpreted to mean the overall case-fatality rate was (greater than) 2.5%. It is presumed a safer mortality estimate was between 7.5%-15% at the pandemics peak wave. The correct statistic is the 2.5%-5% of the WORLDS population perished as a result of this. It should be noted that there were several waves to this pandemic hence the 2.5 (greater than) statistic. The first wave was relatively tame, the second wave was devastating, the third wave was less severe. https://www.cdc.gov/flu/pandemic-resources/1918-commemoration/three-waves.htm

The YangDAO was created specifically to allow the Yang Gang community to coordinate and fund projects that we decide are in our shared interest, whether that’s a Federal Meme Reserve 🏛, Freedom Dividend pilots 💰, or that new MATH blockbuster movie 🎬.

Complex cognitive dissonance disorder guaranteed. 😬.

Garrett Lisi, the so called “Surf Bum with a Theory of Everything (or T.O.E.)”, is a PhD theoretical physicist who has refused to be captured by the theoretical physics community. By making shrewd investments, he has avoided holding meaningful employment for his entire adult life. Instead, he lives in Maui and travels the world chasing the perfect wave.

A team of researchers, two with the French Atomic Energy Commission (AEC) and a third with the Soleil synchrotron, have found evidence of a phase change for hydrogen at a pressure of 425 gigapascals. In their paper published in the journal Nature, Paul Loubeyre, Florent Occelli and Paul Dumas describe testing hydrogen at such a high pressure and what they learned from it.

Researchers long ago theorized that if gas were exposed to enough pressure, it would transition into a metal. But the theories were not able to derive how much pressure is required. Doubts about the theories began to arise when scientists developed tools capable of exerting the high pressures that were believed necessary to squeeze hydrogen into a metal. Theorists simply moved the number higher.

In the past several years, however, theorists have come to a consensus—their math showed that hydrogen should transition at approximately 425 gigapascals—but a way to generate that much pressure did not exist. Then, last year, a team at the AEC improved on the diamond anvil cell, which for years has been used to create intense pressure in experiments. In a diamond anvil cell, two opposing diamonds are used to compress a sample between highly polished tips—the pressure generated is typically measured using a reference material. With the new design, called a toroidal diamond anvil cell, the tip was made into a donut shape with a grooved dome. When in use, the dome deforms but does not break at high pressures. With the new design, the researchers were able to exert pressures up to 600 GPa. That still left the problem of how to test a sample of hydrogen as it was being squeezed.

There’s nothing quite like a maddening math problem, mind-bending optical illusion, or twisty logic puzzle to halt all productivity in the Popular Mechanics office. We’re curious people by nature, but we also collectively share a stubborn insistence that we’re right, dammit, and so we tend to throw work by the wayside whenever we come upon a problem with several seemingly possible solutions.

This triangle brain teaser isn’t new—shoutout to Popsugar for unearthing it a couple years ago—but based on some shady Internet magic, the tweet below reappeared in my feed today and kick-started a new debate on our staff-wide Slack channel, a place traditionally reserved for workshopping ideas, but instead mostly used for yelling about other stuff that we occasionally turn into content.

Not everything is knowable. In a world where it seems like artificial intelligence and machine learning can figure out just about anything, that might seem like heresy – but it’s true.

At least, that’s the case according to a new international study by a team of mathematicians and AI researchers, who discovered that despite the seemingly boundless potential of machine learning, even the cleverest algorithms are nonetheless bound by the constraints of mathematics.

“The advantages of mathematics, however, sometimes come with a cost… in a nutshell… not everything is provable,” the researchers, led by first author and computer scientist Shai Ben-David from the University of Waterloo, write in their paper.

Computational biology is the combined application of math, statistics and computer science to solve biology-based problems. Examples of biology problems are: genetics, evolution, cell biology, biochemistry. [1].

Isaac Newton and other premodern physicists saw space and time as separate, absolute entities — the rigid backdrops against which we move. On the surface, this made the mathematics behind Newton’s 1687 laws of motion look simple. He defined the relationship between force, mass and acceleration, for example, as $latex \vec{F} = m \vec{a}$.

In contrast, when Albert Einstein revealed that space and time are not absolute but relative, the math seemed to get harder. Force, in relativistic terms, is defined by the equation $latex \vec {F} =\gamma (\vec {v})^{3}m_{0}\,\vec {a} _{\parallel }+\gamma (\vec {v})m_{0}\,\vec {a} _{\perp }$.

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