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Category: mathematics – Page 149

I often hear the claim that death is a statistical certainty. This is my mathematical take at why this is not true, assuming the defeat of ageing, and no, being immortal is not required.

If a fully rejuvenated person was hit by a train at full speed, I can promise you they would stand the same pathetically low chances of ever being reassembled into a single, barely functional piece as any non-rejuvenated person of any age. Keeping that in mind, if anyone tried to sell me rejuvenation as ‘immortality’, rest assured I would demand to see the manager right away.

On a different yet unexpectedly related note, if I had a nickel for every time I heard or read something along the lines of ‘death is inevitable because probability’, I could donate so much money to LEAF the IRS would start thinking they’re a bit too well off for a charity.

Oh, and with the rest of the money, I could buy LinkedIn and pay someone to finally give it a user interface you can look at without your eyes bleeding.

Continue reading “Mathematics, rejuvenation, and immortality walk into a bar…” | >

Trying to outrun the expiration of Moore’s Law.

As conventional microchip design reaches its limits, DARPA is pouring money into the specialty chips that might power tomorrow’s autonomous machines.

The coming AI revolution faces a big hurdle: today’s microchips.

Continue reading “Can the US Military Re-Invent the Microchip for the AI Era?” | >

Artificial intelligence can’t understand meaning or emotion just yet, but it can write a pretty good essay on 17th-century maritime trade.

At the 2017 TED Conference this past April, AI expert Noriko Arai gave a talk presenting her Todai Robot, a machine that has been programmed to take the entrance exam to Japan’s most prestigious university, Tokyo University.

While Arai discovered Todai didn’t pass muster to gain acceptance, the robot still beat 80% of the students taking the exam, which consisted of seven sections, including math, English, science, and a 600-word essay writing portion.

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The equations of physics are things that we humans created to understand the Universe, and it can be hard to disentangle them from the Universe’s innate properties. It turns out that one of the weirdest things scientists have come up with, what Albert Einstein derisively called “spooky action at a distance,” is more than just math: It’s a fact of reality.

That concept is also known as entanglement, and it’s what allows particles that have once interacted to share a connection regardless of the separation between them. A team of physicists in the United Kingdom used some dense mathematics to come to their Einstein-angering conclusion, taking an important step towards proving whether quantum mechanics’ weirdness is just the math talking, or whether it speaks to innate physical requirements. Their mathematical proof’s main assumption is that any new physics theory should be backward-compatible with the physics you learned in high school.

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As moviemaking becomes as much a science as an art, the moviemakers need ever-better ways to gauge audience reactions. Did they enjoy it? How much… exactly? At minute 42? A system from Caltech and Disney Research uses a facial expression tracking neural network to learn and predict how members of the audience react, perhaps setting the stage for a new generation of Nielsen ratings.

The research project, just presented at IEEE’s Computer Vision and Pattern Recognition conference in Hawaii, demonstrates a new method by which facial expressions in a theater can be reliably and relatively simply tracked in real time.

It uses what’s called a factorized variational autoencoder — the math of it I am not even going to try to explain, but it’s better than existing methods at capturing the essence of complex things like faces in motion.

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But if there is some kind of unifying computational principle governing our grey matter, what is it? Dr. Tsien has studied this for over a decade, and he believes he’s found the answer in something called the Theory of Connectivity.

“Many people have long speculated that there has to be a basic design principle from which intelligence originates and the brain evolves, like how the double helix of DNA and genetic codes are universal for every organism,” Tsien said. “We present evidence that the brain may operate on an amazingly simple mathematical logic.”

The Theory of Connectivity holds that a simple algorithm, called a power-of-two-based permutation taking the form of n=2i-1 can be used to explain the circuitry of the brain. To unpack the formula, let’s define a few key concepts from the theory of connectivity, specifically the idea of a neuronal clique. A neuronal clique is a group of neurons which “fire together” and cluster into functional connectivity motifs, or FCMs, which the brain uses to recognize specific patterns or ideas. One can liken it to branches on a tree, with the neuronal clique being the smallest unit of connectivity, a mere twig, which when combined with other cliques, link up to form an FCM. The more complex the idea being represented in the brain, the more convoluted the FCM. The n in n=2i-1 specifies the number of neuronal cliques that will fire in response to a given input, i.

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The grand theory of almost everything actually represents a collection of several mathematical models that proved to be timeless interpretations of the laws of physics.

Here is a brief tour of the topics covered in this gargantuan equation.

This version of the Standard Model is written in the Lagrangian form. The Lagrangian is a fancy way of writing an equation to determine the state of a changing system and explain the maximum possible energy the system can maintain.

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(Phys.org)—In the late 1800s when scientists were still trying to figure out what exactly atoms are, one of the leading theories, proposed by Lord Kelvin, was that atoms are knots of swirling vortices in the aether. Although this idea turned out to be completely wrong, it ushered in modern knot theory, which today is used in various areas of science such as fluid dynamics, the structure of DNA, and the concept of chirality.

Now in a new paper published in Physical Review Letters, mathematical physicist Paul Sutcliffe at Durham University in the UK has theoretically shown that nanoparticles called magnetic skyrmions can be tied into various types of knots with different magnetic properties. He explains that, in a sense, these nanoknots represent a “nanoscale resurrection of Kelvin’s dream of knotted fields.”

Skyrmions are the name of a general class of particles that are made by twisting a field. When this field is a magnetic field, the skyrmions are called magnetic skyrmions. Magnetic skyrmions have attracted a lot of attention recently due to their potential applications in spintronics, where electron spins (which are related to the electron’s magnetic properties) are exploited in the design of transistors, storage media, and related devices.

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According to a mind-bending new theory, a black hole could actually be a tunnel between universes, meaning our universe may be nested inside a black hole that is part of a larger universe. The theory explains that the matter doesn’t collapse into a single point, but rather gushes out a “white hole” at the other end of the black one.

The theory was published in the journal Physics Letters B, by Indiana University physicist Nikodem Poplawski. In his article, he presents new mathematical models of the spiraling motion of matter falling into the black hole. His equations suggest that wormholes are probable alternatives to the “space-time singularities” originally predicted by Albert Einstein.

Einstein’s equations for general relativity suggest singularities are created whenever matter in a given region gets too dense as would happen at the center of a black hole. Singularities are infinitely dense and hot, and take up no space. This idea has been supported by indirect evidence but has never been fully accepted into the scientific community.

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