Everyone knows that arithmetic is true: 2 + 2 = 4.
But surprisingly, we don’t know why it’s true.
By stepping outside the box of our usual way of thinking about numbers, my colleagues and I have recently shown that arithmetic has biological roots and is a natural consequence of how perception of the world around us is organised.
For a half century, mathematicians have tried to define the exact circumstances under which a black hole is destined to exist. A new proof shows how a cube can help answer the question.
UC San Diego’s Q-MEEN-C is developing brain-like computers through mimicking neurons and synapses in quantum materials. Recent discoveries in non-local interactions represent a critical step towards more efficient AI hardware that could revolutionize artificial intelligence technology.
We often believe that computers are more efficient than humans. After all, computers can solve complex math equations in an instant and recall names that we might forget. However, human brains can process intricate layers of information rapidly, accurately, and with almost no energy input. Recognizing a face after seeing it only once or distinguishing a mountain from an ocean are examples of such tasks. These seemingly simple human functions require considerable processing and energy from computers, and even then, the results may vary in accuracy.
How close the measured value conforms to the correct value.
In science, the simplest explanations often hold the most truth, a concept known as “Occam’s Razor.” This principle has shaped scientific thought for centuries, but when dealing with abstract ideas, how do we evaluate them?
In a new paper, philosophers from UC Santa Barbara and UC Irvine discuss how to weigh the complexity of scientific theories by comparing their underlying mathematics. They aim to characterize the amount of structure a theory has using symmetry — or the aspects of an object that remain the same when other changes are made.
After much discussion, the authors ultimately doubt that symmetry will provide the framework they need. However, they do uncover why it’s such an excellent guide for understanding structure. Their paper appears in the journal Synthese.
A comprehensive new study provides evidence that various personality traits and cognitive abilities are connected. This means that if someone is good at a certain cognitive task, it can give hints about their personality traits, and vice versa.
For example, being skilled in math could indicate having a more open-minded approach to new ideas, but might also be associated with lower levels of politeness. These connections can help us understand why people are different in how they think and act.
The research has been published in the Proceedings of the National Academy of Sciences.
Though almost every cell in your body contains a copy of each of your genes, only a small fraction of these genes will be expressed, or turned on. These activations are controlled by specialized snippets of DNA called enhancers, which act like skillful on-off switches. This selective activation allows cells to adopt specific functions in the body, determining whether they become—for example—heart cells, muscle cells, or brain cells.
However, these enhancers don’t always turn on the right genes at the right time, contributing to the development of genetic diseases like cancer and diabetes. A team of Johns Hopkins biomedical engineers has developed a machine-learning model that can predict which enhancers play a role in normal development and disease—an innovation that could someday power the development of enhancer-targeted therapies to treat diseases by turning genes on and off at will. The study results appeared in Nature Genetics.
“We’ve known that enhancers control transitions between cell types for a long time, but what is exciting about this work is that mathematical modeling is showing us how they might be controlled,” said study leader Michael Beer, a professor of biomedical engineering and genetic medicine at Johns Hopkins University.
The human brain is the most complex and powerful computer in the world — and, as far as we know, the universe.
Today’s most sophisticated artificial intelligence (AI) algorithms are only just beginning to offer a partial simulation of a very limited number of the brain’s functions. AI is, however, much faster when it comes to certain operations like mathematics and language.
This means it comes as no surprise that a great deal of thought and research has gone into combining the two. The idea is to use AI to better understand the workings of the brain and eventually create more accurate simulations of it. One day, it may also help us to create systems with the complexity and diversity of… More.
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We often believe computers are more efficient than humans. After all, computers can complete a complex math equation in a moment and can also recall the name of that one actor we keep forgetting. However, human brains can process complicated layers of information quickly, accurately, and with almost no energy input: recognizing a face after only seeing it once or instantly knowing the difference between a mountain and the ocean.
These simple human tasks require enormous processing and energy input from computers, and even then, with varying degrees of accuracy.
Creating brain-like computers with minimal energy requirements would revolutionize nearly every aspect of modern life. Quantum Materials for Energy Efficient Neuromorphic Computing (Q-MEEN-C)—a nationwide consortium led by the University of California San Diego—has been at the forefront of this research.
An interdisciplinary team of mathematicians, engineers, physicists, and medical scientists have uncovered an unexpected link between pure mathematics and genetics, that reveals key insights into the structure of neutral mutations and the evolution of organisms.
Number theory, the study of the properties of positive integers, is perhaps the purest form of mathematics. At first sight, it may seem far too abstract to apply to the natural world. In fact, the influential American number theorist Leonard Dickson wrote ‘Thank God that number theory is unsullied by any application.’
And yet, again and again, number theory finds unexpected applications in science and engineering, from leaf angles that (almost) universally follow the Fibonacci sequence, to modern encryption techniques based on factoring prime numbers. Now, researchers have demonstrated an unexpected link between number theory and evolutionary genetics.
There is increasing talk of quantum computers and how they will allow us to solve problems that traditional computers cannot solve. It’s important to note that quantum computers will not replace traditional computers: they are only intended to solve problems other than those that can be solved with classical mainframe computers and supercomputers. And any problem that is impossible to solve with classical computers will also be impossible with quantum computers. And traditional computers will always be more adept than quantum computers at memory-intensive tasks such as sending and receiving e-mail messages, managing documents and spreadsheets, desktop publishing, and so on.
There is nothing “magic” about quantum computers. Still, the mathematics and physics that govern their operation are more complex and reside in quantum physics.
The idea of quantum physics is still surrounded by an aura of great intellectual distance from the vast majority of us. It is a subject associated with the great minds of the 20th century such as Karl Heisenberg, Niels Bohr, Max Planck, Wolfgang Pauli, and Erwin Schrodinger, whose famous hypothetical cat experiment was popularized in an episode of the hit TV show ‘The Big Bang Theory’. As for Schrodinger, his observations of the uncertainty principle, serve as a reminder of the enigmatic nature of quantum mechanics. The uncertainty principle holds that the observer determines the characteristics of an examined particle (charge, spin, position) only at the moment of detection. Schrödinger explained this using the theoretical experiment, known as the paradox of Schrödinger’s cat. The experiment’s worth mentioning, as it describes one of the most important aspects of quantum computing.
