Posted in mathematics, robotics/AI
“We got a thousand times improvement [in training performance per chip] over the last 10 years, and a lot of it has been due to number representation,” Bill Dally, chief scientist and senior vice president of research at Nvidia said at the recent IEEE Symposium on Computer Arithmetic.
Gates will provide grants to prepare teachers better for teaching math and to curriculum companies and nonprofits to develop higher-quality teaching materials. The foundation will also support research into math education and make grants to help high-school math courses prepare students for college and the workplace.
A big problem with math as it is taught today is that students learn in isolation and can feel crushed when they get the wrong answer to a problem, says Shalinee Sharma, co-founder of Zearn, an educational nonprofit and Gates grantee who, with Hughes, spoke with reporters this week. Zearn uses computer-based lessons that incorporate a lot of visuals to keep students interested and provides feedback on progress to help teachers tailor lessons for individual students. A new approach in which students work in teams to solve problems, she said, can turn all students into “math kids.”
“When all kids are ‘math kids,’ making mistakes will be OK,” she said. “It won’t be embarrassing. In fact, making mistakes will be considered normal and an essential part of math learning.”
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Welcome everybody to our first episode of Science News without the gobbledygook. Today we’ll talk about this year’s Nobel Prize in Physics, trouble with the new data from the Webb telescope, what’s next after NASA’s collision with an asteroid, new studies about the environmental impact of Bitcoin and exposure to smoke from wildfires, a test run of a new electric airplane, and dogs that can smell mathematics.
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00:00 Intro.
00:35 Nobel Prize in Physics 2022
01:21 Trouble with data from Webb?
04:05 What’s next after NASA’s asteroid crash test?
06:48 New Study about the Environmental Impact of Bitcoin Mining.
08:38 Test of New Electric Aircraft.
09:42 New Study about Air Pollution from Wildfires.
10:44 Dogs Can Smell Maths.
12:19 Sponsor Message.
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Posted in mathematics
Recent explorations of unique geometric worlds reveal perplexing patterns, including the Fibonacci sequence and the golden ratio.
In an effort to clarify how deductive reasoning is accomplished, an fMRI study was performed to observe the neural substrates of logical reasoning and mathematical calculation. Participants viewed a problem statement and three premises, and then either a conclusion or a mathematical formula. They had to indicate whether the conclusion followed from the premises, or to solve the mathematical formula. Language areas of the brain (Broca’s and Wernicke’s area) responded as the premises and the conclusion were read, but solution of the problems was then carried out by non-language areas. Regions in right prefrontal cortex and inferior parietal lobe were more active for reasoning than for calculation, whereas regions in left prefrontal cortex and superior parietal lobe were more active for calculation than for reasoning. In reasoning, only those problems calling for a search for counterexamples to conclusions recruited right frontal pole. These results have important implications for understanding how higher cognition, including deduction, is implemented in the brain. Different sorts of thinking recruit separate neural substrates, and logical reasoning goes beyond linguistic regions of the brain.
Matrix multiplication is at the heart of many machine learning breakthroughs, and it just got faster—twice. Last week, DeepMind announced it discovered a more efficient way to perform matrix multiplication, conquering a 50-year-old record. This week, two Austrian researchers at Johannes Kepler University Linz claim they have bested that new record by one step.
In 1969, a German mathematician named Volker Strassen discovered the previous-best algorithm for multiplying 4×4 matrices, which reduces the number of steps necessary to perform a matrix calculation. For example, multiplying two 4×4 matrices together using a traditional schoolroom method would take 64 multiplications, while Strassen’s algorithm can perform the same feat in 49 multiplications.
How many bottles does he have to sell to buy out Twitter? You do the math.
The world’s richest person Elon Musk launched a new perfume, and about 24 hours later, he had orders worth two million dollars. With no prior exposure in the business, the perfume has sold on Musk’s reputation alone, and rightly so; the Tesla CEO now changed his Twitter description to Perfume Salesman.
Last Sunday, Musk unveiled the Burnt Hair perfume to his Twitter followers and how it would be a product from his tunneling venture, The Boring Company.
JDLasica/Wikimedia Commons.
Musk’s quirky products.
An interdisciplinary team of researchers has developed a blueprint for creating algorithms that more effectively incorporate ethical guidelines into artificial intelligence (AI) decision-making programs. The project was focused specifically on technologies in which humans interact with AI programs, such as virtual assistants or “carebots” used in healthcare settings.
“Technologies like carebots are supposed to help ensure the safety and comfort of hospital patients, older adults and other people who require health monitoring or physical assistance,” says Veljko Dubljević, corresponding author of a paper on the work and an associate professor in the Science, Technology & Society program at North Carolina State University. “In practical terms, this means these technologies will be placed in situations where they need to make ethical judgments.”
“For example, let’s say that a carebot is in a setting where two people require medical assistance. One patient is unconscious but requires urgent care, while the second patient is in less urgent need but demands that the carebot treat him first. How does the carebot decide which patient is assisted first? Should the carebot even treat a patient who is unconscious and therefore unable to consent to receiving the treatment?”
AlphaTensor opens the door to a world where AI designs programs that outperform anything humans engineer—including AI itself.
It was a big year. Researchers found a way to idealize deep neural networks using kernel machines—an important step toward opening these black boxes. There were major developments toward an answer about the nature of infinity. And a mathematician finally managed to model quantum gravity. Read the articles in full at Quanta Magazine: https://www.quantamagazine.org/the-year-in-math-and-computer-science-20211223/
Quanta Magazine is an editorially independent publication supported by the Simons Foundation.
