Mathematics

The Big Bang Theory sitcom’s Sheldon Cooper insists that in no universe would he dance with Penny. That mighrt be true, says Marks but there still isn’t an infinite number of universes: But, some claim, there is an infinite number of universes in the multiverse. That is ludicrous because there are no infinities in the physical world. Even if there were, Cantor’s theory of the infinite shows that, if there were an infinite number of contingencies, not all contingency combinations could be accounted for by an infinite number of universes. Therefore, even if there is an infinite number of universes with an infinite number of contingencies, then—among an infinite number of Sheldons—it’s possible that none of the Sheldons dance. Robert Read More ›

Also, earlier:, a friend writes to say, this follows up Cristobal Vila’s 5-million-views classic from 2010, Nature By the Numbers: Sleep tight.

Here is a simple SIR model — Susceptible- Infected- Removed: Here, “removed” can be by recovery or death. Obviously parameters are not exact so the next level would explore randomised changes in possible values and time varying models; noting particular clusters that give dramatic outcomes. The S(t) line is an inverted cumulative case curve — if people don’t flee. So C(t) = 1 – S(t) is cumulative cases, a logistic curve. C(t) will at first look exponential until resistance and running out of susceptible population leads to saturation. A supplementary equation could partition recovery vs death, and we can work back from observed patterns with infection and deaths. Further analysis could stratify the population as susceptibility varies with factors such Read More ›

Involving quantum mechanics: In an enormously complicated 165-page paper, computer scientist Zhengfeng Ji and colleagues present a result that penetrates to the heart of deep questions about math, computing and their connection to reality. It’s about a procedure for verifying the solutions to very complex mathematical propositions, even some that are believed to be impossible to solve. In essence, the new finding boils down to demonstrating a vast gulf between infinite and almost infinite, with huge implications for certain high-profile math problems. Seeing into that gulf, it turns out, requires the mysterious power of quantum physics. Tom Siegfried, “How a quantum technique highlights math’s mysterious link to physics” at ScienceNews It’s not entirely clear why a link between physics and Read More ›