Lifeboat Foundation

In 1931, a 25-year-old Kurt Gödel published a paper in mathematical logic titled “On Formally Undecidable Propositions of Principia Mathematica and Related Systems.” This paper contained the proofs of two remarkable “incompleteness theorems,” which state:

For any consistent axiomatic formal system that can express facts about basic arithmetic.

1. there are true statements that are unprovable within the system 2. the system’s consistency cannot be proven within the system.

Was given test for Singapore students and failed.

The publication compared ChatGPT with students who have taken the PSLE in the past three years using questions from the latest collection of past year papers that are available in bookstores.

ChatGPT received a mere 16 out of 100 points for three math papers, 21 points for the science papers, and 11 out of 20 for the English papers.

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Cancer is not a uniform disease. Rather, cancer is a disease of phenotypic plasticity, meaning tumor cells can change from one form or function to another. This includes reverting to less mature states and losing their normal function, which can result in treatment resistance, or changing their cell type altogether, which facilitates metastasis.

In addition to direct changes in your DNA in cancer, a key driver of cancer progression is where and when your DNA is activated. If your DNA contains the “words” that spell out individual genes, then epigenetics is the “grammar” of your genome, telling those genes whether they should be turned on or off in a given tissue. Even though all tissues in the body have almost exactly the same DNA sequence, they can all carry out different functions because of chemical and structural modifications that change which genes are activated and how. This “epigenome” can be influenced by environmental exposures such as diet, adding a dimension to how researchers understand drivers of health beyond the DNA code inherited from your parents.

I’m a cancer researcher, and my laboratory at Johns Hopkins University studies how the differences among normal tissues are controlled by an epigenetic code, and how this code is disrupted in cancer. In our recently published review, colleague Andre Levchenko at Yale University and I describe a new approach to understanding cancer plasticity by combining epigenetics with mathematics. Specifically, we propose how the concept of stochasticity can shed light on why cancers metastasize and become resistant to treatments.

In the second episode of this 12-part podcast series, Tales of the Synapse, neuroscientist Anil Seth describes his research into consciousness, which he describes as “insurance against falling into a single, disciplinary hole.”

Alongside neuroscientists, Seth’s research group at the University of Sussex in Brighton, UK, also includes string theorists, mathematicians and psychologists. The team also collaborates with academics in the arts and humanities.

His 2021 book Being You: A New Science of Consciousness. begins by challenging the idea that consciousness is beyond the reach of science, and concludes with a look at consciousness in non-human animals, before asking if artificial intelligence will one day become both sentient and conscious.

Humans and animals detect different stimuli such as light, sound, and odor through nerve cells, which then transmit the information to the brain. Nerve cells must be able to adjust to the wide range of stimuli they receive, which can range from very weak to very strong. To do this, they may become more or less sensitive to stimuli (sensitization and habituation), or they may become more sensitive to weaker stimuli and less sensitive to stronger stimuli for better overall responsiveness (gain control). However, the exact way this happens is not yet understood.

To better understand the process of gain control, a research team led by Professor Kimura at Nagoya City University in Japan studied the roundworm C. elegans. They found that, when the worm first smells an unpleasant odor, its nerve cells exhibit a large, quickly increasing, and continuous response to both weak and strong stimuli. However, after exposure to the odor, the response is smaller and slower to weak stimuli but remains large to strong stimuli, similar to the response to the first exposure to the odor. Because the experience of odor exposure causes more efficient movement of worms away from the odor, the nerve cells have changed their response to better adapt to the stimulus using gain control.

Then the researchers used mathematical modeling to understand this process. Mathematical modeling is a powerful tool that can be used to better understand complex biological processes. They found that the “response to first smell” consists of fast and slow components, while the “response after exposure” only consists of the slow component, meaning that the odor experience inhibits the fast component to achieve gain control. They further found that both responses could be described by a simple differential equation and that the slow and fast components correspond to the leaky integration of a first and second derivative term of the odor concentration that the worm senses, respectively. The results of this study showed that the prior odor experience only appears to inhibit the mechanism required for the fast component.

An unusual form of cesium atom is helping a University of Queensland-led research team unmask unknown particles that make up the universe.

Dr. Jacinda Ginges, from UQ’s School of Mathematics and Physics, said the unusual atom—made up of an ordinary cesium atom and an elementary particle called a muon—may prove essential in better understanding the universe’s fundamental building blocks.

“Our universe is still such a mystery to us,” Dr. Ginges said.

Now, THIS is useful AI — controlling Nuclear Fusion reactions.

#AI #Deepmind #GTC23
In this Video I discuss Recent AI Breakthroughs in Science — in Physics, Astrophysics… and Math!

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When two black holes collide into each other to form a new bigger black hole, they violently roil spacetime around them, sending ripples, called gravitational waves, outward in all directions. Previous studies of black hole collisions modeled the behavior of the gravitational waves using what is known as linear math, which means that the gravitational waves rippling outward did not influence, or interact, with each other. Now, a new analysis has modeled the same collisions in more detail and revealed so-called nonlinear effects.

“Nonlinear effects are what happens when waves on the beach crest and crash,” says Keefe Mitman, a Caltech graduate student who works with Saul Teukolsky (Ph. D. ‘74), the Robinson Professor of Theoretical Astrophysics at Caltech with a joint appointment at Cornell University.

“The waves interact and influence each other rather than ride along by themselves. With something as violent as a black hole merger, we expected these effects but had not seen them in our models until now. New methods for extracting the waveforms from our simulations have made it possible to see the nonlinearities.”

David Hilbert was a great leader and spokesperson for the discipline of mathematics in the early 20th Century. But he was an extremely important and respected mathematician in his own right.

Like so many great German mathematicians before him, Hilbert was another product of the University of Göttingen, at that time the mathematical centre of the world, and he spent most of his working life there. His formative years, though, were spent at the University of Königsberg, where he developed an intense and fruitful scientific exchange with fellow mathematicians Hermann Minkowski and Adolf Hurwitz.

Sociable, democratic and well-loved both as a student and as a teacher, and often seen as bucking the trend of the formal and elitist system of German mathematics, Hilbert’s mathematical genius nevertheless spoke for itself. He has many mathematical terms named after him, including Hilbert space (an infinite dimensional Euclidean space), Hilbert curves, the Hilbert classification and the Hilbert inequality, as well as several theorems, and he gradually established himself as the most famous mathematician of his time.