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Archive for the ‘mathematics’ category: Page 4

Oct 8, 2024

AI challenge seeks questions to test human-level intelligence

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

Two of San Francisco’s leading players in artificial intelligence have challenged the public to come up with questions capable of testing the capabilities of large language models (LLMs) like Google Gemini and OpenAI’s o1. Scale AI, which specializes in preparing the vast tracts of data on which the LLMs are trained, teamed up with the Center for AI Safety (CAIS) to launch the initiative, Humanity’s Last Exam.

Featuring prizes of US$5,000 (£3,800) for those who come up with the top 50 questions selected for the test, Scale and CAIS say the goal is to test how close we are to achieving “expert-level AI systems” using the “largest, broadest coalition of experts in history.”

Why do this? The leading LLMs are already acing many established tests in intelligence, mathematics and law, but it’s hard to be sure how meaningful this is. In many cases, they may have pre-learned the answers due to the gargantuan quantities of data on which they are trained, including a significant percentage of everything on the internet.

Oct 6, 2024

Sabine Hossenfelder, physicist: ‘If you trust the mathematics, we are immortal’

Posted by in categories: life extension, mathematics

The German scientist argues that information cannot be destroyed and, in principle, it is possible that a higher being, one day, in some way, could reassemble it and bring it back to life.

Oct 5, 2024

Hosting the Universe in a Quantum Computer: Scientists Simulate Cosmological Particle Creation

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

The foundation of this simulation, as described by the team, is a well-known cosmological model that describes the universe as expanding uniformly over time. The researchers modeled how a quantum field, initially in a vacuum state (meaning no particles are present), responds to this expansion. As spacetime stretches, the field’s oscillations mix in a process that can create particles where none previously existed. This phenomenon is captured by a transformation that relates the field’s behavior before and after the universe expands, showing how vibrations at different momenta become entangled, leading to particle creation.

To understand how many particles are generated, the researchers used a mathematical tool called the Bogoliubov transformation. This approach describes how the field’s vacuum state evolves into a state where particles can be detected. As the expansion rate increases, more particles are produced, aligning with predictions from quantum field theory. By running this simulation on IBM quantum computers, the team was able to estimate the number of particles created and observe how the quantum field behaves during the universe’s expansion, offering a new way to explore complex cosmological phenomena.

According to the team, the most notable result of the study was the ability to estimate the number of particles created as a function of the expansion rate of the universe. By running their quantum circuit on both simulators and IBM’s 127-qubit Eagle quantum processor, the researchers demonstrated that they could successfully simulate particle creation in a cosmological context. While the results were noisy—particularly for low expansion rates—the error mitigation techniques used helped bring the outcomes closer to theoretical predictions.

Oct 4, 2024

Why Is Anything Conscious?

Posted by in categories: biological, mathematics, neuroscience

We tackle the hard problem of consciousness taking the naturally-selected, self-organising, embodied organism as our starting point. We provide a mathematical formalism describing how biological systems self-organise to hierarchically interpret unlabelled sensory information according to valence and specific needs. Such interpretations imply behavioural policies which can only be differentiated from each other by the qualitative aspect of information processing. Selection pressures favour systems that can intervene in the world to achieve homeostatic and reproductive goals. Quality is a property arising in such systems to link cause to affect to motivate real world interventions. This produces a range of qualitative classifiers (interoceptive and exteroceptive) that motivate specific actions and determine priorities and preferences.

Oct 3, 2024

The Complex Structure of Quantum Mechanics

Posted by in categories: mathematics, quantum physics

I have been thinking for a while about the mathematics used to formulate our physical theories, especially the similarities and differences among different mathematical formulations. This was a focus of my 2021 book, Physics, Structure, and Reality, where I discussed these things in the context of classical and spacetime physics.

Recently this has led me toward thinking about mathematical formulations of quantum mechanics, where an interesting question arises concerning the use of complex numbers. (I recently secured a grant from the National Science Foundation for a project investigating this.)

It is frequently said by physicists that complex numbers are essential to formulating quantum mechanics, and that this is different from the situation in classical physics, where complex numbers appear as a useful but ultimately dispensable calculational tool. It is not often said why, or in what way, complex numbers are supposed to be essential to quantum mechanics as opposed to classical physics.

Oct 2, 2024

Monumental Proof Settles Geometric Langlands Conjecture

Posted by in category: mathematics

This is amazing face_with_colon_three


In work that has been 30 years in the making, mathematicians have proved a major part of a profound mathematical vision called the Langlands program.

Oct 2, 2024

Denis Noble — Why The Last 80 Years of Biology was Wrong

Posted by in categories: biotech/medical, genetics, life extension, mathematics, robotics/AI

We’re joined by Dr. Denis Noble, Professor Emeritus of Cardiovascular Physiology at the University of Oxford, and the father of ‘systems biology’. He is known for his groundbreaking creation of the first mathematical model of the heart’s electrical activity in the 1960s which radically transformed our understanding of the heart.

Dr. Noble’s contributions have revolutionized our understanding of cardiac function and the broader field of biology. His work continues to challenge long-standing biological concepts, including gene-centric views like Neo-Darwinism.

Continue reading “Denis Noble — Why The Last 80 Years of Biology was Wrong” »

Oct 1, 2024

Looking back at President Jimmy Carter’s science policy

Posted by in categories: chemistry, education, energy, mathematics, physics, policy, science

As President, Jimmy Carter established several science-related initiatives and policies.


Carter also sought to promote scientific research and development in a number of areas. He increased funding for basic science research in fields such as physics and chemistry, and established the National Commission on Excellence in Education to promote improvements in science and math education in American schools.

Continue reading “Looking back at President Jimmy Carter’s science policy” »

Sep 29, 2024

Mitochondrial DNA Evolution: New Study Reveals How Selfish mtDNA Evolve and Thrive

Posted by in categories: biotech/medical, evolution, mathematics

Vanderbilt University researchers, led by alumnus Bryan Gitschlag, have uncovered groundbreaking insights into the evolution of mitochondrial DNA (mtDNA). In their paper in Nature Communications titled “Multiple distinct evolutionary mechanisms govern the dynamics of selfish mitochondrial genomes in Caenorhabditis elegans,” the team reveals how selfish mtDNA, which can reduce the fitness of its host, manages to persist within cells through aggressive competition or by avoiding traditional selection pressures. The study combines mathematical models and experiments to explain the coexistence of selfish and cooperative mtDNA within the cell, offering new insights into the complex evolutionary dynamics of these essential cellular components.

Gitschlag, an alumnus of Vanderbilt University, conducted the research while in the lab of Maulik Patel, assistant professor of biological sciences. He is now a postdoctoral researcher at Cold Spring Harbor Laboratory in David McCandlish’s lab. Gitschlag collaborated closely with fellow Patel Lab members, including James Held, a recent PhD graduate, and Claudia Pereira, a former staff member of the lab.

Sep 27, 2024

Mathematicians Surprised By Hidden Fibonacci Numbers

Posted by in categories: information science, mathematics, physics

What I believe is that symmetry follows everything even mathematics but what explains it is the Fibonacci equation because it seems to show the grand design of everything much like physics has I believe the final parameter of the quantified parameter of infinity.


Recent explorations of unique geometric worlds reveal perplexing patterns, including the Fibonacci sequence and the golden ratio.

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