Lifeboat Foundation

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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 $latex \vec {F} =\gamma (\vec {v})^{3}m_{0}\,\vec {a} _{\parallel }+\gamma (\vec {v})m_{0}\,\vec {a} _{\perp }$.

Continue reading “How (Relatively) Simple Symmetries Underlie Our Expanding Universe” »

The information-processing capabilities of the brain are often reported to reside in the trillions of connections that wire its neurons together. But over the past few decades, mounting research has quietly shifted some of the attention to individual neurons, which seem to shoulder much more computational responsibility than once seemed imaginable.

The latest in a long line of evidence comes from scientists’ discovery of a new type of electrical signal in the upper layers of the human cortex. Laboratory and modeling studies have already shown that tiny compartments in the dendritic arms of cortical neurons can each perform complicated operations in mathematical logic. But now it seems that individual dendritic compartments can also perform a particular computation — “exclusive OR” — that mathematical theorists had previously categorized as unsolvable by single-neuron systems.

“I believe that we’re just scratching the surface of what these neurons are really doing,” said Albert Gidon, a postdoctoral fellow at Humboldt University of Berlin and the first author of the paper that presented these findings in Science earlier this month.

Continue reading “Hidden Computational Power Found in the Arms of Neurons” »

In the quantum realm, under some circumstances and with the right interference patterns, light can pass through opaque media.

This feature of light is more than a mathematical trick; optical quantum memory, optical storage and other systems that depend on interactions of just a few photons at a time rely on the process, called electromagnetically induced transparency, also known as EIT.

Because of its usefulness in existing and emerging quantum and optical technologies, researchers are interested in the ability to manipulate EIT without the introduction of an outside influence, such as additional photons that could perturb the already delicate system. Now, researchers at the McKelvey School of Engineering at Washington University in St. Louis have devised a fully contained optical resonator system that can be used to turn transparency on and off, allowing for a measure of control that has implications across a wide variety of applications.

https://youtube.com/watch?v=J8Eh7RqggsU

Recent AI lecture by Stanford University.

What do web search, speech recognition, face recognition, machine translation, autonomous driving, and automatic scheduling have in common? These are all complex real-world problems, and the goal of artificial intelligence (AI) is to tackle these with rigorous mathematical tools.

Continue reading “CS221: Artificial Intelligence: Principles and Techniques | Stanford University” »

By Donna Lu

A trippy maths program that visualises the inside of strange 3D spaces could help us figure out the shape of the universe.

Henry Segerman at Oklahoma State University and his colleagues have been working to interactively map the inside of mathematical spaces known as 3-manifolds using a program called SnapPy.