Posts

2017-08-22: A rebuttal on the beauty in applying math

2017-04-22: Free googles book library

2016-11-02: In search of Theodore von Karman

2016-09-25: Amath Timeline

2016-02-24: Math errors and risk reporting

2016-02-20: Apple VS FBI

2016-02-19: More Zika may be better than less

2016-02-17: Dependent Non-Commuting Random Variable Systems

2016-01-14: Life at the multifurcation

2015-09-28: AI ain't that smart

2015-06-24: MathEpi citation tree

2015-03-31: Too much STEM is bad

2015-03-24: Dawn of the CRISPR age

2015-02-12: A Comment on How Biased Dispersal can Preclude Competitive Exclusion

2015-02-09: Hamilton's selfish-herd paradox

2015-02-08: Risks and values of microparasite research

2014-11-10: Vaccine mandates and bioethics

2014-10-18: Ebola, travel, president

2014-10-17: Ebola comments

2014-10-12: Ebola numbers

2014-09-23: More stochastic than?

2014-08-17: Feynman's missing method for third-orders?

2014-07-31: CIA spies even on congress

2014-07-16: Rehm on vaccines

2014-06-21: Kurtosis, 4th order diffusion, and wave speed

2014-06-20: Random dispersal speeds invasions

2014-05-06: Preservation of information asymetry in Academia

2014-04-16: Dual numbers are really just calculus infinitessimals

2014-04-14: More on fairer markets

2014-03-18: It's a mad mad mad mad prisoner's dilemma

2014-03-05: Integration techniques: Fourier--Laplace Commutation

2014-02-25: Fiber-bundles for root-polishing in two dimensions

2014-02-17: Is life a simulation or a dream?

2014-01-30: PSU should be infosocialist

2014-01-12: The dark house of math

2014-01-11: Inconsistencies hinder pylab adoption

2013-12-24: Cuvier and the birth of extinction

2013-12-17: Risk Resonance

2013-12-15: The cult of the Levy flight

2013-12-09: 2013 Flu Shots at PSU

2013-12-02: Amazon sucker-punches 60 minutes

2013-11-26: Zombies are REAL, Dr. Tyson!

2013-11-22: Crying wolf over synthetic biology?

2013-11-21: Tilting Drake's Equation

2013-11-18: Why $1^\infty != 1$

2013-11-15: Adobe leaks of PSU data + NSA success accounting

2013-11-14: 60 Minutes misreport on Benghazi

2013-11-11: Making fairer trading markets

2013-11-10: L'Hopital's Rule for Multidimensional Systems

2013-11-09: Using infinitessimals in vector calculus

2013-11-08: Functional Calculus

2013-11-03: Elementary mathematical theory of the health poverty trap

2013-11-02: Proof of the area of a circle using elementary methods

A rebuttal on the beauty in applying math

On August 18th, 2017, the PBS NewsHour had a short piece Math is amazing and we have to start treating it that way by Dr. Eugenia Cheng. Dr. Cheng's actionable proposal was the introduction of specialized math teachers into K-5 education. This is a worth-while idea, allong the lines of having specialized music teachers. I know I profitted from having good math teachers in 3rd and 5th grade (Mrs. Nichols, Mr. Gregory). Alas, the idea does not free us up from the financial constraints that have forced us to cut music teachers from our schools, and if we have to cut math instruction in the same way some day, we're worse off than we're starting.

For me, the essay is wrong. There are a number of factual issues that may mislead the general reader (see below). But primarily, I strongly disagree with Dr. Cheng's perspective that "The usefulness of math is a burden". I believe the usefulness of mathematics is what makes it fun and worth-while.

While we each may find beauty in abstractions like the paintings of Jackson Pollack and the jazz scatting of Ella Fitzgerald, abstraction is not our only source beauty. Our world itself is beautiful, complex, and full of mysteries from the flight of butterflies, down to the functioning of the atom and out to the shape of galaxies of stars millions of lightyears across. But much of this beauty is difficult for us to comprehend and express. Rachel Carson needed 3 books to complete her expression of our ocean's beauty in the 1950's and 60's, and since then we've learned so much that more volumes could be easily be added. But some of this beauty cannot even be expressed at length -- common language is just not expressive enough for us to explain how waves roll accross the ocean without moving the water itself, or how the rotation of the earth creates the spinning of a hurricane.

Mathematics enriches our language in ways that let us comprehend and express more of this beauty. We've created mathematical equations that describe the flow of fluids and the pull of gravity, and let us express the interconnection of the spinning of a hurricane to the rotation of the earth, and how the motion of a little-league baseball player's home run mirrors the motion of the moons of Jupiter. Mathematics can open our eyes to the pieces of the world we could not see otherwise, like how the glimmer's of an emerald arrise from the arrangement of the electron's in its atoms. It is an essential element of the discoveries of science because it can say so many things that we'd never needed words for before. And in saying these things, math broadens our understanding and empowers us to do and build and engineer what we'd not yet even imagined.

In 1764, Charles Mason and Jeremiah Dixon were trudging through the wilds of colonial America to map out what we now call the "Mason-Dixon line" now forming the state boundaries between Pennsylviania, Maryland, and Delaware. The land was so wild and rugged, and the distances were so great, that despite several attempts, nobody had yet been able to reliably establish these boundaries. Part of the difficulty was that over these long distances, the familiar rules of Euclidean geometry no longer worked. The earth, after all, is a ball and not a flat plane. But thanks to their careful procedures and smart application of mathematics, Mason and Dixon succeeded where others had failed. Part of their success was due to the use of beautiful little formula called the "Spherical Law of Sines", which allowed them to calculate distances from angle surveying in much the same way that it would have been done in Euclidean geometry. This formula traces back to the works of men in the Medieval middle east and ancient Rome, who developed their formulas to help themselves make sense of the stars in the night sky.

Another classic example was the work of Joseph Fourier describing how heat moved through an iron bar when one end was stuck in a furnace and the other end was stuck in a bucket of water. This was an important problem for things ranging from the construction of wine cellars to the firing of cannons. Fourier found a way to solve this problem but also many other practical problems for the motion of heat and waves. But his contemporaries railed against his work, complaining that it was not sufficiently abstract and rigorous. Yet today, Fourier's analysis is a fundamental part of things like the MP3 music file format that made distribution of music across the internet possible.

History is full of beautiful stories like these where applying mathematics smartly changed the world, a little or a lot. I find beauty and joy in the math of these applications just as much as I do stories like those of Fermat's last theorem. I think some of our students will as well, and may be inspired to go on to become the engineers, scientists, and mathematicians of the next generation when we embrace the beauty of practical things.

Factual issues

Briefly, some "factual" issues with Dr. Cheng's essay are the following...