A landmark proof in computer science has also solved an important problem called the Connes embedding conjecture. Mathematicians are working to understand it.
The laws of physics imply that the passage of time is an illusion. To avoid this conclusion, we might have to rethink the reality of infinitely precise numbers.
Mathematicians from the California Institute of Technology have solved an old problem related to a mathematical process called a random walk.
The team, which also worked with a colleague from Israel’s Ben-Gurion University, solved the problem in a rush after having a realization one evening. Lead author Omer Tamuz studies both economics and mathematics, using probability theory and ergodic theory as the link—a progressive and blended approach that this year’s Abel Prize-winning mathematicians helped to trailblaze.
The Royal Society is to create a network of disease modelling groups amid academic concern about the nation’s reliance on a single group of epidemiologists at Imperial College London whose predictions have dominated government policy, including the current lockdown.
It is to bring in modelling experts from fields as diverse as banking, astrophysics and the Met Office to build new mathematical representations of how the coronavirus epidemic is likely to spread across the UK — and how the lockdown can be ended.
The first public signs of academic tensions over Imperial’s domination of the debate came when Sunetra Gupta, professor of theoretical epidemiology at Oxford University, published a paper suggesting that some of Imperial’s key assumptions could be wrong.
Governments across the world are relying on mathematical projections to help guide decisions in this pandemic. Computer simulations account for only a fraction of the data analyses that modelling teams have performed in the crisis, Ferguson notes, but they are an increasingly important part of policymaking. But, as he and other modellers warn, much information about how SARS-CoV-2 spreads is still unknown and must be estimated or assumed — and that limits the precision of forecasts. An earlier version of the Imperial model, for instance, estimated that SARS-CoV-2 would be about as severe as influenza in necessitating the hospitalization of those infected. That turned out to be incorrect.
How epidemiologists rushed to model the coronavirus pandemic.
Using the same technology that allows high-frequency signals to travel on regular phone lines, researchers tested sending extremely high-frequency, 200 GHz signals through a pair of copper wires. The result is a link that can move data at rates of terabits per second, significantly faster than currently available channels.
While the technology to disentangle multiple, parallel signals moving through a channel already exists, thanks to signal processing methods developed by John Cioffi, the inventor of digital subscriber lines, or DSL, questions remained related to the effectiveness of implementing these ideas at higher frequencies.
To test the transmission of data at higher frequencies, authors of a paper published this week in Applied Physics Letters used experimental measurements and mathematical modeling to characterize the input and output signals in a waveguide.
Our body’s ability to detect disease, foreign material, and the location of food sources and toxins is all determined by a cocktail of chemicals that surround our cells, as well as our cells’ ability to ‘read’ these chemicals. Cells are highly sensitive. In fact, our immune system can be triggered by the presence of just one foreign molecule or ion. Yet researchers don’t know how cells achieve this level of sensitivity.
Now, scientists at the Biological Physics Theory Unit at Okinawa Institute of Science and Technology Graduate University (OIST) and collaborators at City University of New York have created a simple model that is providing some answers. They have used this model to determine which techniques a cell might employ to increase its sensitivity in different circumstances, shedding light on how the biochemical networks in our bodies operate.
“This model takes a complex biological system and abstracts it into a simple, understandable mathematical framework,” said Dr. Vudtiwat Ngampruetikorn, former postdoctoral researcher at OIST and the first author of the research paper, which was published in Nature Communications. “We can use it to tease apart how cells might choose to spend their energy budget, depending on the world around them and other cells they might be talking to.”
What is interaction, and when does it occur? Intuition suggests that the necessary condition for the interaction of independently created particles is their direct touch or contact through physical force carriers. In quantum mechanics, the result of the interaction is entanglement—the appearance of non-classical correlations in the system. It seems that quantum theory allows entanglement of independent particles without any contact. The fundamental identity of particles of the same kind is responsible for this phenomenon.
Quantum mechanics is currently the best and most accurate theory used by physicists to describe the world around us. Its characteristic feature, however, is the abstract mathematical language of quantum mechanics, notoriously leading to serious interpretational problems. The view of reality proposed by this theory is still a subject of scientific dispute that, over time, is only becoming hotter and more interesting. New research motivation and intriguing questions are brought forth by a fresh perspective resulting from the standpoint of quantum information and the enormous progress of experimental techniques. These allow verification of the conclusions drawn from subtle thought experiments directly related to the problem of interpretation. Moreover, researchers are now making enormous progress in the field of quantum communication and quantum computer technology, which significantly draws on non-classical resources offered by quantum mechanics.
Pawel Blasiak from the Institute of Nuclear Physics of the Polish Academy of Sciences in Krakow and Marcin Markiewicz from the University of Gdansk focus on analyzing widely accepted paradigms and theoretical concepts regarding the basics and interpretation of quantum mechanics. The researchers are trying to determine to what extent the intuitions used to describe quantum mechanical processes are justified in a realistic view of the world. For this purpose, they try to clarify specific theoretical ideas, often functioning in the form of vague intuitions, using the language of mathematics. This approach often results in the appearance of inspiring paradoxes. Of course, the more basic the concept to which a given paradox relates, the better, because it opens up new doors to deeper understanding a given problem.
I have not been a supporter of an extended public quarantine or shut down, if any. There are a number of reasons why (governments steal liberty during such times; national debt increases and is used to the point of total socialism; inequality becomes permanent; etc), but in this letter below to everyone I want to talk specifically about why a quarantine is ultimately harming the life extension and #transhumanism movements. Don’t ever forget, we are in a race to save the lives of “everyone” right now with the plague of aging, not just those who might get #coronavirus.
Dear Fellow Humans.
If you believe in the life extension movement of trying to live indefinitely through science and technology, then you likely should not support the worldwide quarantine (at least don’t support it over 14 days in the West where we don’t have the ability to do it as efficiently as Asia). It’s horrible that so many lives will be lost by COVID-19, but in a worse-case scenario it’s likely 100 million people will die globally (mostly older people who have only a few years left to live due to their underlying medical conditions of aging — and who have likely been kept alive due to science and 21st Century medicine anyway). But the damage we could cause (and almost certainly are causing) with the quarantine and shut down to the US and global economy may cost the life extension movement and its scientific research possibly three to five years of progress — because the funding, projects, and jobs around the anti-aging industry will disappear for a notable time. The math shows that if we achieve indefinite lifespans for the human race by the year 2035 vs 2040, approximately 250 million lives will be spared and could then go on indefinitely. The aging math (or life hours) for any transhumanist shows that if we care about human life and longevity — about how long people alive today live — then we should not quarantine the world right now, but get the economy going again as a first priority so that we may fund the future of anti-aging science for the species. Some of us call this reasoning the Transhumanist Wager. For the sake of everyone alive today, it must be acknowledged that there is a dramatically larger percent gain (many thousands of percent) of overall life years for our species by not quarantining and shutting down the world. This is all a horrible scenario, and one I am terribly sad to share with you, but that doesn’t mean we should cower from facts. We owe our species the most courageous decision for its long-term longevity of all its living citizens.
Two retired professors are sharing the mathematics version of the Nobel Prize for their lifelong contributions to the changing nature of math in the computing age. Both Hillel Furstenberg and Gregory Margulis spent decades applying ideas from probability theory to different kinds of discrete mathematics in order to shake loose new ways to solve seemingly intractable problems. The Abel Prize, awarded since just 2003, honors career mathematical accomplishments with a prize of about $700,000.
Wait—there’s not a Nobel Prize for mathematics? It’s true, and although you may have heard a lascivious story to explain why, no one really knows for sure.
