Lifeboat Foundation

David Smith, a retired print technician from the north of England, was pursuing his hobby of looking for interesting shapes when he stumbled onto one unlike any other in November.

When Smith shared his shape with the world in March, excited fans printed it onto T-shirts, sewed it into quilts, crafted cookie cutters or used it to replace the hexagons on a soccer ball —some even made plans for tattoos.

The 13-sided polygon, which 64-year-old Smith called “the hat”, is the first single shape ever found that can completely cover an infinitely large flat surface without ever repeating the same pattern.

Basic, or “elementary,” cellular automata like The Game of Life appeal to researchers working in mathematics and computer science theory, but they can have practical applications too. Some of the elementary cellular automata can be used for random number generation, physics simulations, and cryptography. Others are computationally as powerful as conventional computing architectures—at least in principle. In a sense, these task-oriented cellular automata are akin to an ant colony in which the simple actions of individual ants combine to perform larger collective actions, such as digging tunnels, or collecting food and taking it back to the nest. More “advanced” cellular automata, which have more complicated rules (although still based on neighboring cells), can be used for practical computing tasks such as identifying objects in an image.

Marandi explains: “While we are fascinated by the type of complex behaviors that we can simulate with a relatively simple photonic hardware, we are really excited about the potential of more advanced photonic cellular automata for practical computing applications.”

Marandi says cellular automata are well suited to photonic computing for a couple of reasons. Since information processing is happening at an extremely local level (remember in cellular automata, cells interact only with their immediate neighbors), they eliminate the need for much of the hardware that makes photonic computing difficult: the various gates, switches, and devices that are otherwise required for moving and storing light-based information. And the high-bandwidth nature of photonic computing means cellular automata can run incredibly fast. In traditional computing, cellular automata might be designed in a computer language, which is built upon another layer of “machine” language below that, which itself sits atop the binary zeroes and ones that make up digital information.

Researchers have discovered a new 14-sided shape called the Spectre that can be used to tile a surface without ever creating a repeating pattern, ending a decades’ long mathematical hunt.

General relativity, part of the wide-ranging physical theory of relativity formed by the German-born physicist Albert Einstein. It was conceived by Einstein in 1915. It explains gravity based on the way space can ‘curve’, or, to put it more accurately, it associates the force of gravity with the changing geometry of space-time. (Einstein’s gravity)

The mathematical equations of Einstein’s general theory of relativity, tested time and time again, are currently the most accurate way to predict gravitational interactions, replacing those developed by Isaac Newton several centuries prior.

Continue reading “If light has no mass, why is it affected by gravity? General Relativity Theory” »

Joscha Bach is a cognitive scientist focusing on cognitive architectures, consciousness, models of mental representation, emotion, motivation and sociality.

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Continue reading “Joscha Bach: Time, Simulation Hypothesis, & Existence” »

In a new landmark study, University of Minnesota research shows surprising links between human cognition and personality—pillars of human individuality that shape who we are and how we interact with the world. Personality influences our actions, emotions and thoughts, defining whether we are extroverted, polite, persistent, curious or anxious.

On the other hand, cognitive ability is the umbrella that reflects our capability for navigating complexity, such as articulating language, grasping intricate mathematics and drawing logical conclusions. Despite the prevailing belief that certain connections exist—for instance, introverted individuals are often perceived as more intelligent—scientists lacked a comprehensive understanding of these intricate connections.

The research, published in the Proceedings of the National Academy of Sciences, synthesizes data from over 1,300 studies from the past century, representing more than 2 million participants from 50 countries and integrating data from academic journals, test manuals, military databases, previously unpublished datasets and even proprietary databases of private companies.

Perfect recall, computational wizardry and rapier wit: That’s the brain we all want, but how does one design such a brain? The real thing is comprised of ~80 billion neurons that coordinate with one another through tens of thousands of connections in the form of synapses. The human brain has no centralized processor, the way a standard laptop does.

Instead, many calculations are run in parallel, and outcomes are compared. While the operating principles of the human brain are not fully understood, existing mathematical algorithms can be used to rework deep learning principles into systems more like a human brain would. This brain-inspired computing paradigm—spiking neural networks (SNN)—provides a computing architecture well-aligned with the potential advantages of systems using both optical and electronic components.

In SNNs, information is processed in the form of spikes or action potentials, which are the electrical impulses that occur in real neurons when they fire. One of their key features is that they use asynchronous processing, meaning that spikes are processed as they occur in time, rather than being processed in a batch like in traditional neural networks. This allows SNNs to react quickly to changes in their inputs, and to perform certain types of computations more efficiently than traditional neural networks.

Paraconsistent logic challenges this standard view. A logical consequence relation is said to be paraconsistent if it is not explosive. Thus, if a consequence relation is paraconsistent, then even in circumstances where the available information is inconsistent, the consequence relation does not explode into triviality. Thus, paraconsistent logic accommodates inconsistency in a controlled way that treats inconsistent information as potentially informative.

The prefix ‘para’ in English has two meanings: ‘quasi’ (or ‘similar to, modelled on’) or ‘beyond’. When the term ‘paraconsistent’ was coined by Miró Quesada at the Third Latin America Conference on Mathematical Logic in 1976, he seems to have had the first meaning in mind. Many paraconsistent logicians, however, have taken it to mean the second, which provided different reasons for the development of paraconsistent logic as we will see below.

Paraconsistent logic is defined negatively: any logic is paraconsistent as long as it is not explosive. This means there is no single set of open problems or programs in paraconsistent logic. As such, this entry is not a complete survey of paraconsistent logic. The aim is to describe some philosophically salient features of a diverse field.

Now there’s a mathematical model that could maximize the effectiveness of exercise.