Archive for the ‘mathematics’ category: Page 37

May 16, 2022

Our Reality May Only Be Half of a Pair of Interacting Worlds

Posted by in categories: mathematics, physics

Physicists sometimes come up with bizarre stories that sound like science fiction. Yet some turn out to be true, like how the curvature of space and time described by Einstein was eventually confirmed by astronomical measurements. Others linger on as mere possibilities or mathematical curiosities.

May 13, 2022

Mathematicians Coax Fluid Equations Into Nonphysical Solutions

Posted by in categories: information science, mathematics

The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.

May 11, 2022

Bilayer graphene inspires two-universe cosmological model

Posted by in categories: mathematics, quantum physics

Physicists sometimes come up with crazy stories that sound like science fiction. Some turn out to be true, like how the curvature of space and time described by Einstein was eventually borne out by astronomical measurements. Others linger on as mere possibilities or mathematical curiosities.

In a new paper in Physical Review Research, JQI Fellow Victor Galitski and JQI graduate student Alireza Parhizkar have explored the imaginative possibility that our reality is only one half of a pair of interacting worlds. Their may provide a new perspective for looking at fundamental features of reality—including why our universe expands the way it does and how that relates to the most miniscule lengths allowed in quantum mechanics. These topics are crucial to understanding our universe and are part of one of the great mysteries of modern .

The pair of scientists stumbled upon this new perspective when they were looking into research on sheets of graphene—single atomic layers of carbon in a repeating . They realized that experiments on the electrical properties of stacked sheets of graphene produced results that looked like little universes and that the underlying phenomenon might generalize to other areas of physics. In stacks of graphene, new electrical behaviors arise from interactions between the individual sheets, so maybe unique physics could similarly emerge from interacting layers elsewhere—perhaps in cosmological theories about the entire universe.

May 7, 2022

In Fake Universes, Evidence for String Theory

Posted by in categories: mathematics, quantum physics, space

Circa 2015 o.o!

The publication of Green and Schwarz’s paper “was 30 years ago this month,” the string theorist and popular-science author Brian Greene wrote in Smithsonian Magazine in January, “making the moment ripe for taking stock: Is string theory revealing reality’s deep laws? Or, as some detractors have claimed, is it a mathematical mirage that has sidetracked a generation of physicists?” Greene had no answer, expressing doubt that string theory will “confront data” in his lifetime.

Recently, however, some string theorists have started developing a new tactic that gives them hope of someday answering these questions. Lacking traditional tests, they are seeking validation of string theory by a different route. Using a strange mathematical dictionary that translates between laws of gravity and those of quantum mechanics, the researchers have identified properties called “consistency conditions” that they say any theory combining quantum mechanics and gravity must meet. And in certain highly simplified imaginary worlds, they claim to have found evidence that the only consistent theories of “quantum gravity” involve strings.

Continue reading “In Fake Universes, Evidence for String Theory” »

May 7, 2022

Meet Elliott Tanner, the 13-year-old who just got his college degree in physics

Posted by in categories: mathematics, physics

He is set to start a doctorate next.

13-year-old prodigy Elliott Tanner has graduated from the University of Minnesota with a degree in physics and mathematics.

May 6, 2022

A ‘beyond-quantum’ equivalence principle for superposition and entanglement

Posted by in categories: mathematics, particle physics, quantum physics

The physics of the microrealm involves two famous and bizarre concepts: The first is that prior to observation, it is impossible to know with certainty the outcome of a measurement on a particle; rather the particle exists in a “superposition” encompassing multiple mutually exclusive states. So a particle can be in two or more places at the same time, and you can only calculate the probability of finding it in a certain location when you look. The second involves “entanglement,” the spooky link that can unite two objects, no matter how far they are separated. Both superposition and entanglement are described mathematically by quantum theory. But many physicists believe that the ultimate theory of reality may lie beyond quantum theory. Now, a team of physicists and mathematicians has discovered a new connection between these two weird properties that does not assume that quantum theory is correct. Their study appears in Physical Review Letters.

“We were really excited to find this new connection that goes beyond quantum theory because the connection will be valid even for more exotic theories that are yet to be discovered,” says Ludovico Lami, a member of the physics think-tank, the Foundational Questions Institute, FQXi, and a physicist at the University of Ulm, in Germany. “This is also important because it is independent of the mathematical formalism of quantum theory and uses only notions with an immediate operational interpretation,” he adds. Lami co-authored the study with Guillaume Aubrun of Claude Bernard University Lyon 1, in France, Carlos Palazuelos, of the Complutense University of Madrid, in Spain, and Martin Plávala, of Siegen University, in Germany.

While quantum theory has proven to be supremely successful since its development a century ago, physicists have struggled to unify it with gravity to create one overarching “theory of everything.” This suggests that quantum theory may not be the final word on describing reality, inspiring physicists to hunt for a more fundamental framework. But any such ultimate theory must still incorporate superposition, entanglement, and the probabilistic nature of reality, since these features have been confirmed time and again in lab tests. The interpretation of these experiments does not depend on quantum theory being correct, notes Lami.

May 4, 2022

Neurocompositional computing: From the Central Paradox of Cognition to a new generation of AI systems

Posted by in categories: mathematics, robotics/AI

What explains the dramatic progress from 20th-century to 21st-century AI, and how can the remaining limitations of current AI be overcome? The widely accepted narrative attributes this progress to massive increases in the quantity of computational and data resources available to support statistical learning in deep artificial neural networks. We show that an additional crucial factor is the development of a new type of computation. Neurocompositional computing adopts two principles that must be simultaneously respected to enable human-level cognition: the principles of Compositionality and Continuity. These have seemed irreconcilable until the recent mathematical discovery that compositionality can be realized not only through discrete methods of symbolic computing, but also through novel forms of continuous neural computing.

May 4, 2022

Computers could revise past conclusions with AI

Posted by in categories: economics, mathematics, robotics/AI

To better automate reasoning, machines should ideally be able to systematically revise the view they have obtained about the world. Timotheus Kampik’s dissertation work presents mathematical reasoning approaches that strike a balance between retaining consistency with previously drawn conclusions and rejecting them in face of overwhelming new evidence.

When reasoning and when making decisions, humans are continuously revising what their view of the world is, by rejecting what they have previously considered true or desirable, and replacing it with an updated and ideally more useful perspective. Enabling machines to do so in a similar manner, but with logical precision, is a long-running line of artificial intelligence research.

In his dissertation, Timotheus advances this line of research by devising reasoning approaches that balance retaining previously drawn conclusions for the sake of ensuring consistency and revising them to accommodate new compelling evidence. To this end, he applies well-known from to formal argumentation, an approach to logic-based automated reasoning.

May 1, 2022

The basics of decentralized finance

Posted by in categories: blockchains, computing, cryptocurrencies, finance, information science, mathematics

Decentralized finance is built on blockchain technology, an immutable system that organizes data into blocks that are chained together and stored in hundreds of thousands of nodes or computers belonging to other members of the network.

These nodes communicate with one another (peer-to-peer), exchanging information to ensure that they’re all up-to-date and validating transactions, usually through proof-of-work or proof-of-stake. The first term is used when a member of the network is required to solve an arbitrary mathematical puzzle to add a block to the blockchain, while proof-of-stake is when users set aside some cryptocurrency as collateral, giving them a chance to be selected at random as a validator.

To encourage people to help keep the system running, those who are selected to be validators are given cryptocurrency as a reward for verifying transactions. This process is popularly known as mining and has not only helped remove central entities like banks from the equation, but it also has allowed DeFi to open more opportunities. In traditional finance, are only offered to large organizations, for members of the network to make a profit. And by using network validators, DeFi has also been able to cut down the costs that intermediaries charge so that management fees don’t eat away a significant part of investors’ returns.

Apr 26, 2022

The Human Calculator

Posted by in categories: education, mathematics

Thomas Fuller, an African sold into slavery in 1,724 at age 14, was sometimes known as the “Virginia Calculator” for his extraordinary ability to solve complex mathematical problems in his head. He was asked how many seconds there were in a year, he briefly answered 31,536,000 seconds.

He was asked again how many seconds a man who is 70 years old, 17 days and 12 hours lived, he answered in a minute and a half 2,210,500,800. One of the men was doing the problems on paper and informed Fuller that he was wrong because the answer was much smaller. Fuller hastily responded, “Nah, you forgot about leap years. When leap years were added to the account, the sums matched up.”

Fuller was one of the first cases recorded in the literature of the wise man syndrome, when in 1,789, Benjamin Rush, the father of American psychiatry, described his incredible ability to calculate, without having an education and training in mathematics, his ability was used as proof that enslaved African Americans were equal to whites in intelligence, fueling some pro-abolitionist discussions.

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