Lifeboat Foundation: Safeguarding Humanity
Toggle light / dark theme

Blog

Category: mathematics

In my 50s, too old to become a real expert, I have finally fallen in love with algebraic geometry. As the name suggests, this is the study of geometry using algebra. Around 1637, René Descartes laid the groundwork for this subject by taking a plane, mentally drawing a grid on it, as we now do with graph paper, and calling the coordinates x and y. We can write down an equation like x + y = 1, and there will be a curve consisting of points whose coordinates obey this equation. In this example, we get a circle!

It was a revolutionary idea at the time, because it let us systematically convert questions about geometry into questions about equations, which we can solve if we’re good enough at algebra. Some mathematicians spend their whole lives on this majestic subject. But I never really liked it much until recently—now that I’ve connected it to my interest in quantum physics.

If we can figure out how to reduce topology to algebra, it might help us formulate a theory of quantum gravity.

Read more

Under normal electron band theory, Mott insulators ought to conduct electricity, but they do not due to interactions among their electrons. But now, scientists from the RIKEN Cluster for Pioneering Research have shown that pulses of light could be used to turn these materials beyond simple conductors to superconductors—materials that conduct electricity without energy loss. This process would happen through an unconventional type of superconductivity known as “eta pairing.”

Using , the researchers found that this unconventional type of conductivity, which is believed to take under non-equilibrium conditions in strongly correlated such as high-Tc cuprates and iron-pnictides, arises due to a known as eta pairing. This is different from the superconductivity observed in the same strongly correlated materials under equilibrium conditions, and is thought to involve repulsive interactions between certain electrons within the structure. It is also different from traditional superconductivity, where the phenomenon arises due to interactions between electrons and vibrations of the crystal structure, inducing mutual interactions between electrons through vibrations and thus overcoming the repulsion between the electrons.

Thirty years ago, the mathematical physicist Chen-Ning Yang originally proposed the idea of eta-pairing, but because it was a purely mathematical concept, it was understood as a virtual phenomenon that would not take place in the real world. But for the present study, the researchers used non-equilibrium dynamics to analyze the effect of on a Mott insulator, and found that the effect would in fact happen in the real world. “What is interesting,” says first author Tatsuya Kaneko, a postdoctoral researcher at the RIKEN Cluster for Pioneering Research, “is that our calculations showed that this takes place based on the beautiful mathematical structure that Yang and his followers formulated so many years ago.”

Read more

Advances in artificial intelligence have led many to speculate that human beings will soon be replaced by machines in every domain, including that of creativity. Ray Kurzweil, a futurist, predicts that by 2029 we will have produced an AI that can pass for an average educated human being. Nick Bostrom, an Oxford philosopher, is more circumspect. He does not give a date but suggests that philosophers and mathematicians defer work on fundamental questions to “superintelligent” successors, which he defines as having “intellect that greatly exceeds the cognitive performance of humans in virtually all domains of interest.”

Creativity is, and always will be, a human endeavor.

Read more

Shaking a physical system typically heats it up, in the sense that the system continuously absorbs energy. When considering a circular shaking pattern, the amount of energy that is absorbed can potentially depend on the orientation of the circular drive (clockwise/anti-clockwise), a general phenomenon known as circular dichroism.

In 2017, Nathan Goldman (ULB, Brussels), Peter Zoller (IQOQI, Innsbruck) and coworkers predicted that can be quantized in (heating is then constrained by strict integers) forming a “topological state.” According to this , the quantization of energy absorption upon circular driving can be directly related to topology, a fundamental mathematical concept that characterizes these intriguing states of matter.

Writing in Nature Physics, the experimental group of Klaus Sengstock and Christof Weitenberg (Hamburg), in collaboration with the team of Nathan Goldman, reports on the first observation of quantized circular dichroism. Following the theoretical proposal of Goldman, Zoller et al., the experimentalists realized a topological state using an ultracold atomic gas subjected to , and studied its heating properties upon circular shaking of the gas. By finely monitoring the heating rates of their system, for a wide range of driving frequencies, they were able to validate the quantization law predicted by Goldman, Zoller et al. in 2017, in agreement with the underlying topological state realized in the laboratory.

Read more

Researchers have found bees can do basic mathematics, in a discovery that expands our understanding of the relationship between brain size and brain power.

Building on their finding that honeybees can understand the concept of zero, Australian and French researchers set out to test whether bees could perform arithmetic operations like addition and subtraction.

Solving requires a sophisticated level of cognition, involving the complex mental management of numbers, long-term rules and short term working memory.

Read more

If the forecast calls for rain, you’ll probably pack an umbrella. If it calls for cold, you may bring your mittens. That same kind of preparation happens in buildings, where sophisticated heating and cooling systems adjust themselves based on the predicted weather.

But when the forecast is imperfect—as it often is—buildings can end up wasting , just as we may find ourselves wet, cold or burdened with extra layers we don’t need.

A new approach developed by Fengqi You, professor in engineering at Cornell University, predicts the accuracy of the forecast using a machine learning model trained with years’ worth of data on forecasts and actual weather conditions. You combined that predictor with a that considers characteristics including the size and shape of rooms, the construction materials, the location of sensors and the position of windows.

Read more

Human health depends on age and evolutionary history. Firstly, adaptation is age-specific, with Hamilton’s forces of natural selection leading to much greater adaptation at earlier ages than later ages. This of course is how evolutionary biologists explain the existence of aging in the first place. Secondly, when environmental conditions change, it takes surprisingly few generations for populations to adapt to such new conditions, at least at early ages when natural selection is intense. Thirdly, at later ages, when the forces of natural selection are weak, natural selection will often fail to produce adaptation to a selective environment that is not evolutionarily ancient. All three of these themes will be illustrated using both explicit mathematical theory and findings from experimental evolution. At the end of the presentation, we will apply these general scientific insights to the case of human evolutionary history, human aging, and optimal human diets.

Read more

Mention artificial intelligence (AI) or artificial neural networks, and images of computers may come to mind. AI-based pattern recognition has a wide variety of real-world uses, such as medical diagnostics, navigation systems, voice-based authentication, image classification, handwriting recognition, speech programs, and text-based processing. However, artificial intelligence is not limited to digital technology and is merging with the realm of biology—synthetic biology and genomics, to be more precise. Pioneering researchers led by Dr. Lulu Qian at the California Institute of Technology (Caltech) have created synthetic biochemical circuits that are able to perform information processing at the molecular level–an artificial neural network consisting of DNA instead of computer hardware and software.

Artificial intelligence is in the early stages of a renaissance period—a rebirth that is largely due to advances in deep learning techniques with artificial neural networks that have contributed to improvements in pattern recognition. Specifically, the resurgence is largely due to a mathematical tool that calculates derivatives called backpropagation (backward propagation)—it enables artificial neural networks to adjust hidden layers of neurons when there are outlier outcomes for more precise results.

Artificial neural networks (ANN) are a type of machine learning method with concepts borrowed from neuroscience. The structure and function of the nervous system and brain were inspiration for artificial neural networks. Instead of biological neurons, ANNs have artificial nodes. Instead of synapses, ANNs have connections that are able to transmit signals between nodes. Like neurons, the nodes of ANNs are able to receive and process data, as well as activate other nodes connected to it.

Read more

Brief mention of AI implications…

As a mathematical concept, the idea of zero is relatively new in human society—and indisputably revolutionary. It’s allowed humans to develop algebra, calculus and Cartesian coordinates ; questions about its properties continue to incite mathematical debate today. So it may sound unlikely that bees — complex and community-based insects to be sure, but insects nonetheless — seem to have mastered their own numerical concept of nothingness.

Despite their sesame-seed-sized brains, honey bees have proven themselves the prodigies of the insect world. Researcher has found that they can count up to about four, distinguish abstract patterns, and communicate locations with other bees. Now, Australian scientists have found what may be their most impressive cognitive ability yet: “zero processing,” or the ability to conceptualize nothingness as a numerical value that can be compared with more tangible quantities like one and two.

While seemingly intuitive, the ability to understand zero is actually quite rare across species—and unheard of in invertebrates. In a press release, the authors of a paper published June 8 in the journal Science called species with this ability an “elite club” that consists of species we generally consider quite intelligent, including primates, dolphins and parrots. Even humans haven’t always been in that club: The concept of zero first appeared in India around 458 A.D, and didn’t enter the West until 1200, when Italian mathematician Fibonacci brought it and a host of other Arabic numerals over with him.

Read more