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Category: mathematics

In 1884, a schoolmaster and theologian named Edwin Abbott wrote a novella called Flatland, which tells the story of a world populated by sentient two-dimensional shapes. While intended as a satire of rigid Victorian social norms, Flatland has long fascinated mathematicians and physicists and served as the setting for many a thought experiment.

One such thought experiment: How can be controlled in two dimensions?

When a wave of light is confined on a two-dimensional plane by certain materials, it becomes something known as a —a particle that blurs the distinction between light and matter. Polaritons have exciting implications for the future of optical circuits because, unlike electronic integrated circuits, integrated optics is difficult to miniaturize with commonly used materials. Polaritons allow light to be tightly confined to the nanoscale, even potentially to the thickness of a few atoms.

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Too large to be classed as molecules, but too small to be bulk solids, atomic clusters can range in size from a few dozen to several hundred atoms. The structures can be used for a diverse range of applications, which requires a detailed knowledge of their shapes. These are easy to describe using mathematics in some cases; while in others, their morphologies are far more irregular. However, current models typically ignore this level of detail; often defining clusters as simple ball-shaped structures.

In research published in The European Physical Journal B, José M. Cabrera-Trujillo and colleagues at the Autonomous University of San Luis Potosí in Mexico propose a new method of identifying the morphologies of atomic clusters. They have now confirmed that the distinctive geometric shapes of some clusters, as well as the irregularity of amorphous structures, can be fully identified mathematically.

The insights gathered by Cabrera-Trujillo’s team could make it easier for researchers to engineer atomic clusters for specific applications. These could include nanoparticles containing two different metals, which are highly effective in catalysing chemical reactions. Their updated methods provided new ways to determine the structural properties of clusters, the ways in which they convert energy to different forms, and the potential forces between atoms. The technique was also able to distinguish the surrounding environments of atoms in the cores of clusters, and on their surfaces. Ultimately, this allowed the researchers to distinguish between distinctive shapes, including icosahedrons, octahedrons, and simple pancakes. They were also able to identify amorphous shapes, which contain no discernible mathematical order.

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This is amazing, it will save many lives!

A 14-year-old Pennsylvania girl has come up with an innovative way to get rid of blind spots before she can even legally get behind the wheel.

Alaina Gassler, from West Grove, presented her project — called ‘Improving Automobile Safety by Removing Blind Spots’ — during this year’s Society for Science and Public’s Broadcom MASTERS (Math, Applied Science, Technology and Engineering for Rising Stars).

Gassler won the Samueli Foundation Prize for her creativity — and a hefty $25,000 check. More than $100,000 was given out to 30 finalists at the award ceremony.

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A Portland teen won second place in a national technology contest, taking home $2,500 that he can use to attend science camp next summer.

Rishab Jain, 14, is a freshman at Westview High School. His winning project, which he calls the Pancreas Detective, is an artificial intelligence tool that can help diagnose pancreatic cancer through gene sequencing. The algorithm helps doctors focus on the organ during examinations, which is often obscured because it moves around the abdominal area as patients breathe and other bodily functions shift other organs as well.

Last year, the same project netted $25,000 from 3M when he attended Stoller Middle School. He used that money to fund his nonprofit, Samyak Science Society, which promotes science, technology, engineering and math education for other children, Time Magazine reported.

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https://www.youtube.com/watch?v=iNqqOLscOBY

Sean Carroll is a theoretical physicist at Caltech and Santa Fe Institute specializing in quantum mechanics, arrow of time, cosmology, and gravitation. He is the author of several popular books including his latest on quantum mechanics (Something Deeply Hidden) and is a host of a great podcast called Mindscape. This conversation is part of the Artificial Intelligence podcast.

This is the second time Sean has been on the podcast. You can watch the first time here: https://www.youtube.com/watch?v=l-NJrvyRo0c

INFO:
Podcast website:

Artificial Intelligence: AI Podcast


iTunes:
https://apple.co/2lwqZIr
Spotify:
https://spoti.fi/2nEwCF8
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https://lexfridman.com/category/ai/feed/
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EPISODE LINKS:
Something Deeply Hidden: https://amzn.to/2C5h40V
Sean’s twitter: https://twitter.com/seanmcarroll
Sean’s website: https://www.preposterousuniverse.com/
Mindscape podcast: https://www.preposterousuniverse.com/podcast/

OUTLINE:
0:00 — Introduction
1:23 — Capacity of human mind to understand physics.
10:49 — Perception vs reality
12:29 — Conservation of momentum
17:20 — Difference between math and physics.
20:10 — Why is our world so compressable.
22:53 — What would Newton think of quantum mechanics.
25:44 — What is quantum mechanics?
27:54 — What is an atom?
30:34 — What is the wave function?
32:30 — What is quantum entanglement?
35:19 — What is Hilbert space?
37:32 — What is entropy?
39:31 — Infinity
42:43 — Many-worlds interpretation of quantum mechanics.
1:01:13 — Quantum gravity and the emergence of spacetime.
1:08:34 — Our branch of reality in many-worlds interpretation.
1:10:40 — Time travel
1:12:54 — Arrow of time
1:16:18 — What is fundamental in physics.
1:16:58 — Quantum computers
1:17:42 — Experimental validation of many-worlds and emergent spacetime.
1:19:53 — Quantum mechanics and the human mind.
1:21:51 — Mindscape podcast

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Mathematicians have uncovered a big new piece of evidence for one of the most famous unproven ideas in mathematics, known as the twin prime conjecture. But the route they took to finding that evidence probably won’t help prove the twin prime conjecture itself.

The twin prime conjecture is all about how and when prime numbers — numbers that are divisible only by themselves and 1 — appear on the number line. “Twin primes” are primes that are two steps apart from each other on that line: 3 and 5, 5 and 7, 29 and 31, 137 and 139, and so on. The twin prime conjecture states that there are infinitely many twin primes, and that you’ll keep encountering them no matter how far down the number line you go. It also states that there are infinitely many prime pairs with every other possible gap between them (prime pairs that are four steps apart, eight steps apart, 200,000 steps apart, etc.). Mathematicians are pretty sure this is true. It sure seems like it’s true. And if it weren’t true, it would mean that prime numbers aren’t as random as everyone thought, which would mess up lots of ideas about how numbers work in general. But no one’s ever been able to prove it.

Related: Mathematicians Edge Closer to Solving a ‘Million Dollar’ Math Problem.

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The three-body problem, one of the most notoriously complex calculations in physics, may have met its match in artificial intelligence: a new neural network promises to find solutions up to 100 million times faster than existing techniques.

First formulated by Sir Isaac Newton, the three-body problem involves calculating the movement of three gravitationally interacting bodies – such as the Earth, the Moon, and the Sun, for example – given their initial positions and velocities.

It might sound simple at first, but the ensuing chaotic movement has stumped mathematicians and physicists for hundreds of years, to the extent that all but the most dedicated humans have tried to avoid thinking about it as much as possible.

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“If you are not convinced by the idea of reductive materialists that consciousness magically emerges from complexity in material structures or processes or if you are not satisfied with the viewpoint of idealists that matter is a mere thought form, then the present hypothesis may be something for you,” writes Dr. Antonin Tuynman when presenting his new book The Ouroboros Code. https://www.ecstadelic.net/top-stories/the-ouroboros-code-self-reference-is-the-name-of-the-game #OuroborosCode

In “The Ouroboros Code” I will address the cybernetic dynamics of consciousness. Starting from the premise that Consciousness is the Ontological Primitive, I will propose mechanisms which may explain how a digital mathematical and material existence can be generated. Digging into Category Theory, Computational Simulacra and Quantum Computing, I will explore the mechanics of self-sustaining self-referential feedback loops as the Modus Operandi of Consciousness.

Let’s dive in the vortex of kaleidoscopic reflections, the wormhole of a dazzling “mise-en abyme” of recursiveness and the roller-coaster of the quantum non-locality. Explore the map which is the territory simultaneously by drawing your map of maps. Discover the non-dual bridge closing the gap between Science and Spirituality.

-Antonin Tuynman, PhD

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The universe is kind of an impossible object. It has an inside but no outside; it’s a one-sided coin. This Möbius architecture presents a unique challenge for cosmologists, who find themselves in the awkward position of being stuck inside the very system they’re trying to comprehend.

It’s a situation that Lee Smolin has been thinking about for most of his career. A physicist at the Perimeter Institute for Theoretical Physics in Waterloo, Canada, Smolin works at the knotty intersection of quantum mechanics, relativity and cosmology. Don’t let his soft voice and quiet demeanor fool you — he’s known as a rebellious thinker and has always followed his own path. In the 1960s Smolin dropped out of high school, played in a rock band called Ideoplastos, and published an underground newspaper. Wanting to build geodesic domes like R. Buckminster Fuller, Smolin taught himself advanced mathematics — the same kind of math, it turned out, that you need to play with Einstein’s equations of general relativity. The moment he realized this was the moment he became a physicist. He studied at Harvard University and took a position at the Institute for Advanced Study in Princeton, New Jersey, eventually becoming a founding faculty member at the Perimeter Institute.

“Perimeter,” in fact, is the perfect word to describe Smolin’s place near the boundary of mainstream physics. When most physicists dived headfirst into string theory, Smolin played a key role in working out the competing theory of loop quantum gravity. When most physicists said that the laws of physics are immutable, he said they evolve according to a kind of cosmic Darwinism. When most physicists said that time is an illusion, Smolin insisted that it’s real.

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