Lifeboat Foundation

Research unveils a mathematical model for ice nucleation, showing how surface angles affect water’s freezing point, with applications in snowmaking and cloud seeding.

From abstract-looking cloud formations to roars of snow machines on ski slopes, the transformation of liquid water into solid ice touches many facets of life. Water’s freezing point is generally accepted to be 32 degrees Fahrenheit. But that is due to ice nucleation — impurities in everyday water raise its freezing point to this temperature. Now, researchers unveil a theoretical model that shows how specific structural details on surfaces can influence water’s freezing point.

Continue reading “Freezing Point Phenomena: Unlocking the Strange Secrets of Ice Nucleation” »

“They remove some of the magic,” said Dimitris Papailiopoulos, a machine learning researcher at the University of Wisconsin, Madison. “That’s a good thing.”

Training Transformers

Large language models are built around mathematical structures called artificial neural networks. The many “neurons” inside these networks perform simple mathematical operations on long strings of numbers representing individual words, transmuting each word that passes through the network into another. The details of this mathematical alchemy depend on another set of numbers called the network’s parameters, which quantify the strength of the connections between neurons.

Scientists trained an AI system to think before speaking with a technique called QuietSTaR. The inner monologue improved common sense reasoning and doubled math performance.

Fermat’s last theorem puzzled mathematicians for centuries until it was finally proven in 1993. Now, researchers want to create a version of the proof that can be formally checked by a computer for any errors in logic.

By Alex Wilkins

This paper introduces a novel theoretical framework for understanding consciousness, proposing a paradigm shift from traditional biological-centric views to a broader, universal perspective grounded in thermodynamics and systems theory. We posit that consciousness is not an exclusive attribute of biological entities but a fundamental feature of all systems exhibiting a particular form of intelligence. This intelligence is defined as the capacity of a system to efficiently utilize energy to reduce internal entropy, thereby fostering increased order and complexity. Supported by a robust mathematical model, the theory suggests that subjective experience, or what is often referred to as qualia, emerges from the intricate interplay of energy, entropy, and information within a system. This redefinition of consciousness and intelligence challenges existing paradigms and extends the potential for understanding and developing Artificial General Intelligence (AGI). The implications of this theory are vast, bridging gaps between cognitive science, artificial intelligence, philosophy, and physics, and providing a new lens through which to view the nature of consciousness itself.

Consciousness, traditionally viewed through the lens of biology and neurology, has long been a subject shrouded in mystery and debate. Philosophers, scientists, and thinkers have pondered over what consciousness is, how it arises, and why it appears to be a unique trait of certain biological organisms. The “hard problem” of consciousness, a term coined by philosopher David Chalmers, encapsulates the difficulty in explaining why and how physical processes in the brain give rise to subjective experiences.

Current research in cognitive science, neuroscience, and artificial intelligence offers various theories of consciousness, ranging from neural correlates of consciousness (NCCs) to quantum theories. However, these theories often face limitations in fully explaining the emergence and universality of consciousness.

Until recently, researchers were unsure of the minimum thickness of a transparent substance required to take in a given quantity of light.

Konstantin N. Rozanov of the Institute for Theoretical and Applied Electrodynamics in Russia discovered more than two decades ago the amount of light that a gadget might absorb at various wavelengths if one side of it was coated in metal. This metal establishes a barrier where light is absorbed or bounced back, simplifying the mathematical solution.

Duke researchers find limits of energy absorption in transparent materials.

Researchers at Duke University in the US have determined the theoretical limits of how much electromagnetic energy a transparent material can absorb. This can help researchers optimize device designs in the future, but it has also ended a 20-year wait for a mathematical solution to the problem.

Everybody involved has long known that some math problems are too hard to solve (at least without unlimited time), but a proposed solution could be rather easily verified. Suppose someone claims to have the answer to such a very hard problem. Their proof is much too long to check line by line. Can you verify the answer merely by asking that person (the “prover”) some questions? Sometimes, yes. But for very complicated proofs, probably not. If there are two provers, though, both in possession of the proof, asking each of them some questions might allow you to verify that the proof is correct (at least with very high probability). There’s a catch, though — the provers must be kept separate, so they can’t communicate and therefore collude on how to answer your questions. (This approach is called MIP, for multiprover interactive proof.)

Verifying a proof without actually seeing it is not that strange a concept. Many examples exist for how a prover can convince you that they know the answer to a problem without actually telling you the answer. A standard method for coding secret messages, for example, relies on using a very large number (perhaps hundreds of digits long) to encode the message. It can be decoded only by someone who knows the prime factors that, when multiplied together, produce the very large number. It’s impossible to figure out those prime numbers (within the lifetime of the universe) even with an army of supercomputers. So if someone can decode your message, they’ve proved to you that they know the primes, without needing to tell you what they are.

Neural networks have been powering breakthroughs in artificial intelligence, including the large language models that are now being used in a wide range of applications, from finance, to human resources to health care. But these networks remain a black box whose inner workings engineers and scientists struggle to understand.