Lifeboat Foundation: Safeguarding Humanity
Toggle light / dark theme

Blog

Category: mathematics – Page 138

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.

Read more | >

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.

Read more | >

“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-se…f-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

Continue reading “The Ouroboros Code: Self-Reference is the Name of the Game” | >

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.

Read more | >

Quantum simulation plays an irreplaceable role in diverse fields, beyond the scope of classical computers. In a recent study, Keren Li and an interdisciplinary research team at the Center for Quantum Computing, Quantum Science and Engineering and the Department of Physics and Astronomy in China, U.S. Germany and Canada. Experimentally simulated spin-network states by simulating quantum spacetime tetrahedra on a four-qubit nuclear magnetic resonance (NMR) quantum simulator. The experimental fidelity was above 95 percent. The research team used the quantum tetrahedra prepared by nuclear magnetic resonance to simulate a two-dimensional (2-D) spinfoam vertex (model) amplitude, and display local dynamics of quantum spacetime. Li et al. measured the geometric properties of the corresponding quantum tetrahedra to simulate their interactions. The experimental work is an initial attempt and a basic module to represent the Feynman diagram vertex in the spinfoam formulation, to study loop quantum gravity (LQG) using quantum information processing. The results are now available on Communication Physics.

Classical computers cannot study large quantum systems despite successful simulations of a variety of physical systems. The systematic constraints of classical computers occurred when the linear growth of quantum system sizes corresponded to the exponential growth of the Hilbert Space, a mathematical foundation of quantum mechanics. Quantum physicists aim to overcome the issue using quantum computers that process information intrinsically or quantum-mechanically to outperform their classical counterparts exponentially. In 1982, Physicist Richard Feynman defined quantum computers as quantum systems that can be controlled to mimic or simulate the behaviour or properties of relatively less accessible quantum systems.

In the present work, Li et al. used nuclear magnetic resonance (NMR) with a high controllable performance on the quantum system to develop simulation methods. The strategy facilitated the presentation of quantum geometries of space and spacetime based on the analogies between nuclear spin states in NMR samples and spin-network states in quantum gravity. Quantum gravity aims to unite the Einstein gravity with quantum mechanics to expand our understanding of gravity to the Planck scale (1.22 × 1019 GeV). At the Planck scale (magnitudes of space, time and energy) Einstein gravity and the continuum of spacetime breakdown can be replaced via quantum spacetime. Research approaches toward understanding quantum spacetimes are presently rooted in spin networks (a graph of lines and nodes to represent the quantum state of space at a certain point in time), which are an important, non-perturbative framework of quantum gravity.

Read more | >

It is the name of the unknown theory of everything which would combine all five Superstring theories and the Supergravity at 11 dimensions together.

The theory requires mathematical tools which have yet to be invented in order to be fully understood. The theory was proposed by Edward Witten.

The following article is somewhat technical in nature, see M-theory simplified for a less technical article.

Read more | >

iOS/Android/Desktop: Default calculator apps suck. They work like a traditional handheld calculator, which only displays one value at a time and can only do basic math. If you want to do anything more than calculate a tip, you’re better off with these free and cheap calculator apps.

These apps help you do typical “real life math” or solve basic textbook math problems.

Read more | >

Cooperation means that one individual pays a cost for another to receive a benefit. Cooperation can be at variance with natural selection: Why should you help a competitor? Yet cooperation is abundant in nature and is an important component of evolutionary innovation. Cooperation can be seen as the master architect of evolution and as the third fundamental principle of evolution beside mutation and selection. I will present mathematical principles of cooperation.

Read more | >

Circa 2012

Hundreds of the world’s brightest minds — engineers from Google and IBM, hedge funds quants, and Defense Department contractors building artificial intelligence — were gathered in rapt attention inside the auditorium of the San Francisco Masonic Temple atop Nob Hill. It was the first day of the seventh annual Singularity Summit, and Julia Galef, the President of the Center for Applied Rationality, was speaking onstage. On the screen behind her, Galef projected a giant image from the film Blade Runner: the replicant Roy, naked, his face stained with blood, cradling a white dove in his arms.

At this point in the movie, Roy is reaching the end of his short, pre-programmed life, “The poignancy of his death scene comes from the contrast between that bitter truth and the fact that he still feels his life has meaning, and for lack of a better word, he has a soul,” said Galef. “To me this is the situation we as humans have found ourselves in over the last century. Turns out we are survival machines created by ancient replicators, DNA, to produce as many copies of them as possible. This is the bitter pill that science has offered us in response to our questions about where we came from and what it all means.”

The Singularity Summit bills itself as the world’s premier event on robotics, artificial intelligence, and other emerging technologies. The attendees, who shelled out $795 for a two-day pass, are people whose careers depend on data, on empirical proof. Peter Norvig, Google’s Director of Research, discussed advances in probabilistic first-order logic. The Nobel prize-winning economist Daniel Kahneman lectured on the finer points of heuristics and biases in human psychology. The Power Point presentations were full of math equations and complex charts. Yet time and again the conversation drifted towards the existential: the larger, unanswerable questions of life.

Continue reading “Rapture of the nerds: will the Singularity turn us into gods or end the human race?” | >