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Mathematics

The remarkable connection between mathematics and physics

According to Mullings, the reason for the association between mathematics and physics is not that the mathematics is causative but rather that mathematics studies the logical structure of possibility and constraint. As a result, if the mathematics successfully captures the possibilities and constraints in the real world, it will provide a tool for further analysis of potential possibilities. Read More ›

Faith: Even mathematics depends on some unprovable assumptions

Pachón: The result was shattering. Gödel showed the limitations of any formal axiomatic system in modeling basic arithmetic. He showed that no axiomatic system could be complete and consistent at the same time. Read More ›

The Hyperreal Number System

The hyperreal number system is a way of treating infinities and infinitesimals in a rigorous way that is consistent with the way that we treat ordinary numbers. I recently posted a short video introducing the concept in a simple way. I thought some of you might be interested. I find the hyperreals interesting for a number of reasons. First of all, I think that infinities and infinitesimals are somewhat of the equivalent of Intelligent Design for mathematics. Infinitesimals were essentially banned from mathematics in the 1800s because it was said that they were inconsistent and non-rigorous (this is why calculus switched from infinitesimals to limits). This move was largely philosophically motivated, with Hilbert and others trying to naturalize mathematics. However, Read More ›

Researchers: Big data shows math laws that underlie life’s unity

From the release: “The work, led by Ian Hatton at ICTA-UAB in Barcelona, shows how metabolism, abundance, growth and mortality all follow strikingly consistent relationships with body size from the tiniest bacteria to the blue whale.” Read More ›

The war on math continues

Some of us remember back to when only the arts disciplines were being ruined. But yes, math can be ruined too. That will make it hard to talk to people about a lot of science stuff, including science controversies. But hey, they'll still have astrology. Read More ›

Researchers: The Golden Ratio is found in human skulls but not other animal skulls

Researchers: "The other mammals we surveyed actually have unique ratios that approach the Golden Ratio with increased species sophistication," says Rafael Tamargo, M.D., professor of neurosurgery at the Johns Hopkins University School of Medicine. "We believe that this finding may have important anthropological and evolutionary implications." Read More ›

Cells’ feedback circuitry is all in the math

At Quanta: “What math and engineering and biology have in common, at least modern engineering, is enormous hidden complexity,” Doyle said. Take, for example, a cellphone. It seems simple to operate, but underneath, many layers of control circuits are built atop one another. Read More ›

Fields medalist says math really exists

So okay, if math really exists, it undermines a great deal of the nonsense barked about consciousness as an evolved illusion. That is, if consciousness enables us to apprehend what really exists, there is good reason for believing that consciousness itself exists Read More ›