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.

# Mathematics

## A visual meditation on infinite patterns in nature

And to think that some want us to believe that there is no underlying pattern or meaning and it all just happened…

## A visual meditation on the numbers that design nature

By Cristóbal Vila NATURE BY NUMBERS from Cristóbal Vila on Vimeo. Hat tip: Philip Cunningham

## A Simple Tutorial on the Hyperreals

Earlier I posted a video on hyperreal numbers. Here is a short tutorial on their usage.

## 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 Read More…

## The war on math targets the equals sign

The plus and minus signs better look out too.

## 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.”

## 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.

## Jonathan Bartlett: Scrutinize evolution claims that depend on curves

Curves often don’t do what people claim.

## 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.”

## 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.

## 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

## 80-year-old problem around irrational numbers solved by new proof

Scientific American: ” At 44 pages of dense, technical mathematics, even leading mathematical minds need time to wrap their heads around the paper. The community, however, seems optimistic. “

## Radical Constructivism, Naturalistic Scientism and Math Education — ideas have consequences

In the thread on Jonathan Bartlett and priorities for Math education, I raised two comments that I think it would be profitable to further reflect on. First, from 33 on how the US National Academy of Sciences tried to classify Mathematics as a “science”: https://services.math.duke.edu/undergraduate/Handbook96_97/node5.html The Nature of Mathematics (These paragraphs are reprinted with permission Read More…

## Rob Sheldon on why statisticians are in a panic

The panic in sociology, psychology, nutrition science, and pharmacology has been growing as >70% papers with “p-values” smaller than 0.05 are discovered to be unrepeatable.