Archive for the ‘mathematics’ category: Page 4

Dec 26, 2023

Inner Experience — Direct Access to Reality: A Complementarist Ontology and Dual Aspect Monism Support a Broader Epistemology

Posted by in categories: ethics, mathematics, neuroscience

Ontology, the ideas we have about the nature of reality, and epistemology, our concepts about how to gain knowledge about the world, are interdependent. Currently, the dominant ontology in science is a materialist model, and associated with it an empiricist epistemology. Historically speaking, there was a more comprehensive notion at the cradle of modern science in the middle ages. Then “experience” meant both inner, or first person, and outer, or third person, experience. With the historical development, experience has come to mean only sense experience of outer reality. This has become associated with the ontology that matter is the most important substance in the universe, everything else-consciousness, mind, values, etc.,-being derived thereof or reducible to it. This ontology is insufficient to explain the phenomena we are living with-consciousness, as a precondition of this idea, or anomalous cognitions. These have a robust empirical grounding, although we do not understand them sufficiently. The phenomenology, though, demands some sort of non-local model of the world and one in which consciousness is not derivative of, but coprimary with matter. I propose such a complementarist dual aspect model of consciousness and brain, or mind and matter. This then also entails a different epistemology. For if consciousness is coprimary with matter, then we can also use a deeper exploration of consciousness as happens in contemplative practice to reach an understanding of the deep structure of the world, for instance in mathematical or theoretical intuition, and perhaps also in other areas such as in ethics. This would entail a kind of contemplative science that would also complement our current experiential mode that is exclusively directed to the outside aspect of our world. Such an epistemology might help us with various issues, such as good theoretical and other intuitions.

Keywords: complementarity; consciousness; contemplative science; dual aspect model; epistemology; introspection; materialism; ontology.

Copyright © 2020 Walach.

Dec 25, 2023

This Machine Learning Research Opens up a Mathematical Perspective on the Transformers

Posted by in categories: information science, mapping, mathematics, particle physics, robotics/AI

The release of Transformers has marked a significant advancement in the field of Artificial Intelligence (AI) and neural network topologies. Understanding the workings of these complex neural network architectures requires an understanding of transformers. What distinguishes transformers from conventional architectures is the concept of self-attention, which describes a transformer model’s capacity to focus on distinct segments of the input sequence during prediction. Self-attention greatly enhances the performance of transformers in real-world applications, including computer vision and Natural Language Processing (NLP).

In a recent study, researchers have provided a mathematical model that can be used to perceive Transformers as particle systems in interaction. The mathematical framework offers a methodical way to analyze Transformers’ internal operations. In an interacting particle system, the behavior of the individual particles influences that of the other parts, resulting in a complex network of interconnected systems.

The study explores the finding that Transformers can be thought of as flow maps on the space of probability measures. In this sense, transformers generate a mean-field interacting particle system in which every particle, called a token, follows the vector field flow defined by the empirical measure of all particles. The continuity equation governs the evolution of the empirical measure, and the long-term behavior of this system, which is typified by particle clustering, becomes an object of study.

Dec 25, 2023

A Close-Up View Reveals the ‘Melting’ Point of an Infinite Graph

Posted by in category: mathematics

A new proof shows what happens tographs before and after a sudden shift called the percolation threshold.

Just as ice melts to water, graphs undergo phase transitions. Two mathematicians showed that they can pinpoint such transitions by examining only local structure.

Dec 25, 2023

OpenAI’s Chaos Linked to Super Powerful New AI It Secretly Built

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

Whether the company’s actually getting closer to achieving this goal remains highly debatable. The company has also historically been highly secretive when it comes to its research, making it even more difficult to read the tea leaves over recent weeks.

But an interesting new twist to the story suggests OpenAI may have been on the verge of a major leap forward, and that it may indeed have been related to the shakeup.

Last week, Reuters and The Information reported that some OpenAI leaders may have gotten spooked by a powerful new AI the company was working on called Q*, pronounced “Q star.” This new system was apparently seen by some as a significant step towards the company’s goal of establishing AGI, and is reportedly capable of solving grade school math problems.

Dec 24, 2023

Why string theory requires extra dimensions

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

String theory found its origins in an attempt to understand the nascent experiments revealing the strong nuclear force. Eventually another theory, one based on particles called quarks and force carriers called gluons, would supplant it, but in the deep mathematical bones of the young string theory physicists would find curious structures, half-glimpsed ghosts, that would point to something more. Something deeper.

String claims that what we call —the point-like entities that wander freely, interact, and bind together to make up the bulk of material existence—are nothing but. Instead, there is but a single kind of fundamental object: the string. These strings, each one existing at the smallest possible limit of existence itself, vibrate. And the way those strings vibrate dictates how they manifest themselves in the larger universe. Like notes on a strummed guitar, a string vibrating with one mode will appear to us as an electron, while another vibrating at a different frequency will appear as a photon, and so on.

String theory is an audacious attempt at a theory of everything. A single mathematical framework that explains the particles that make us who and what we are along with the forces that act as the fundamental messengers among those particles. They are all, every quark in the cosmos and every photon in the field, bits of vibrating strings.

Dec 24, 2023

Holograms Might Save Physics

Posted by in categories: holograms, mathematics, mobile phones, quantum physics, satellites

Even though the guts of General Relativity are obtusely mathematical, and for decades was relegated to math departments rather than proper physics, you get to experience the technological gift of relativity every time you navigate to your favorite restaurant. GPS, the global positioning system, consists of a network of orbiting satellites constantly beaming out precise timing data. Your phone compares those signals to figure out where you are on the Earth. But there is a difference in spacetime between the surface of the Earth and the orbit of the satellites. Without taking general relativity into account, your navigation would simply be incorrect, and you’d be late for dinner.

As revolutions go, general relativity is a big one. And as unifications go, it’s a warning. To make this union happen Einstein had to radically, permanently alter not just our conceptions of gravity as a force acting through space and time, but our conceptions of space and time itself. It took no less than a complete overhaul of our entire philosophical understanding of the relation between space and time to bridge the gap.

Continue reading “Holograms Might Save Physics” »

Dec 23, 2023

AI consciousness: scientists say we urgently need answers

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

Could artificial intelligence (AI) systems become conscious? A trio of consciousness scientists says that, at the moment, no one knows — and they are expressing concern about the lack of inquiry into the question.

In comments to the United Nations, three leaders of the Association for Mathematical Consciousness Science (AMCS) call for more funding to support research on consciousness and AI. They say that scientific investigations of the boundaries between conscious and unconscious systems are urgently needed, and they cite ethical, legal and safety issues that make it crucial to understand AI consciousness. For example, if AI develops consciousness, should people be allowed to simply switch it off after use?

Such concerns have been mostly absent from recent discussions about AI safety, such as the high-profile AI Safety Summit in the United Kingdom, says AMCS board member Jonathan Mason, a mathematician based in Oxford, UK and one of the authors of the comments. Nor did US President Joe Biden’s executive order seeking responsible development of AI technology address issues raised by conscious AI systems, Mason notes.

Dec 22, 2023

Researchers from Indiana University Unveil ‘Brainoware’: A Cutting-Edge Artificial Intelligence Technology Inspired by Brain Organoids and Silicon Chips

Posted by in categories: biotech/medical, information science, mathematics, robotics/AI

The fusion of biological principles with technological innovation has resulted in significant advancements in artificial intelligence (AI) through the development of Brainoware. Developed by researchers at Indiana University, Bloomington, this innovative system leverages clusters of lab-raised brain cells to achieve elementary speech recognition and solve mathematical problems.

The crux of this technological leap lies in the cultivation of specialized stem cells that mature into neurons—the fundamental units of the brain. While a typical human brain comprises a staggering 86 billion neurons interconnected extensively, the team managed to engineer a minute organoid, merely a nanometer wide. This tiny but powerful structure was connected to a circuit board through an array of electrodes, allowing machine-learning algorithms to decode responses from the brain tissue.

Termed Brainoware, this amalgamation of biological neurons and computational circuits exhibited remarkable capabilities after a brief training period. It was discerned between eight subjects based on their diverse pronunciation of vowels with an accuracy rate of 78%. Impressively, Brainoware outperformed artificial networks in predicting the Henon map, a complex mathematical construct within chaotic dynamics.

Dec 21, 2023

A new mathematical language for biological networks

Posted by in categories: biological, evolution, genetics, health, mathematics

A team of researchers around Berlin mathematics professor Michael Joswig is presenting a novel concept for the mathematical modeling of genetic interactions in biological systems. Collaborating with biologists from ETH Zurich and Carnegy Science (U.S.), the team has successfully identified master regulators within the context of an entire genetic network.

The research results provide a coherent theoretical framework for analyzing biological networks and have been published in the Proceedings of the National Academy of Sciences.

It is a longstanding goal of biologists to determine the key genes and species that have a decisive impact on evolution, ecology, and health. Researchers have now succeeded in identifying certain genes as master regulators in biological networks. These key regulators exert greater control within the system and steer essential cellular processes. Previous studies have mainly focused on pairwise interactions within the system, which can be strongly affected by genetic background or biological context.

Dec 19, 2023

Hybrid Biocomputer Fuses Human Brain Tissue With Computer Chips

Posted by in categories: biotech/medical, cyborgs, information science, mathematics, robotics/AI

Scientists have fused human brain tissue to a computer chip, creating a mini cyborg in a petri dish that can perform math equations and recognize speech.

Dubbed Brainoware, the system consists of brain cells artificially grown from human stem cells, which have been fostered to develop into a brain-like tissue. This mini-brain organoid is then hooked up to traditional hardware where it acts as a physical reservoir that can capture and remember the information it receives from the computer inputs.

The researchers wanted to explore the idea of exploiting the efficiency of the human brain’s architecture to supercharge computational hardware. The rise of artificial intelligence (AI) has massively increased the demand for computing power, but it’s somewhat limited by the energy efficiency and performance of the standard silicon chips.

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