by James Bailey |
AncientEgypt

Mathematics began with map, the “earth measure” of the ancient Egyptians who had to restake the land along the Nile after its annual flood. The land itself had its full richness of particularities: a little higher in one corner, needing a bit more fertilizer in another, and perhaps in the same family for four generations. The Egyptians, however, lacked the disk drives to store all this data richness and the computers to process it, so inexorably a “place” became a “polygon”, shorn of all its ecological specificity.

Number Science (“Beauty Bare”)

The Greeks continued to strip all the particularities out of earth measure until Euclid was able to, as Edna Vincent Millay famously wrote, “look on beauty bare.” This form of unclothed beauty, however, existed mostly in the unchanging dome of the heavens, not down here on earth. So it was that Thales, the legendary founder of science, focused up instead of down and fell into a well. As his companion Thratta noted, “In his zeal for things in the sky he does not see what is at his feet.” And so it was that Galileo recognized his sheer inability to apply the mathematics of his day to the particularities of life on earth:

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If only the flying of birds didn’t give me as much trouble as .... all the other experiments put together! .... These, I say, stagger my imagination... If you drop a dead bird and a live one from the top of a tower, the dead one will do the same as a stone... But as to the live bird.... what is to prevent it from sending itself by the beatings of its wings to whatever point on the compass it pleases?

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There is no need for a disk drive to store the data involved in the law of acceleration that Galileo did discover. The back of an envelope is more than enough. Nor is there any need to map it, because, in the words of the 20th century mathematician Eugene Wigner, Galileo’s formula is “... true not only in Pisa, and in Galileo’s time, it is true everywhere on the earth, was always true, and will always be true.” And, until recently, prodigiously fruitful. The entire Machine Age is testimony to the value of Renaissance quantification and so-called “universal law.” Three hundred years after Newton saw (“and all was light”) we still focus our children on mathematical problems that have so little data they can be solved “by hand.”

Data Science (Beauty Fully Clothed)

We, however, are no longer constrained to the backs of envelopes in the same way Thales, Galileo, and Newton were. We have the disk drives to keep track of all the pesky wells and birds and hydrocarbons that were beyond their mathematical reach. Indeed our disk drives and public internet sites are already brimming with billions of earth pixels from satellite data, with billions of records of societal transactions, and with more than a hundred billion base pairs of genomic knowledge. And we have the computer power to map where previous generations could only numerate.

The Role of Mathematics, and Mapematics, In the 21st Century Curriculum

As emphasized by Rene Descartes, mathematics education offers a double benefit. Not only will it teach some skills, but it will simultaneously train students in how to think. Indeed, it was the latter that he felt most important:

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It was not the case that this part of our method was invented for the purpose of dealing with mathematical problems, but rather that mathematics should be studied almost solely for the purpose of training us in this method.

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The Latin classroom once held a similar double role: unlocking the door to society’s most treasured knowledge (the classics) whilst imbuing valuable habits of thought. Then society moved away from reliance on the ancient authors to focus on other knowledge not expressed in Latin. For a while, we said, “Study the language anyway. It is good for you.” That no longer works.

Now society is making an equally big shift, from the number sciences of astronomy and physics to the data science knowledge created by ecology and biology. The old equations of algebra and calculus are overwhelmed by the terabytes of data involved. And the habits of thought they instill are not the right ones. A single example: algebra teaches children to solve problems by breaking them down into pieces—by the process of “factoring”—then treating these pieces in isolation, ignoring the others. In ecology, focusing on one aspect at at time, while ignoring the others, is a recipe for a very hot planet. Is it any wonder that math malaise is spreading through our schools?

Amidst the hue and cry about declining scores in algebra and calculus, educators should celebrate the fact that a whole new generation of data science maths have come into routine use among ecologists and biologists. These maths are different. They require electronic computers; they cannot be carried out “by hand.” They map changing realities rather than numerating static ones. Yes they have still-unfamiliar names like “neural networks,” “cellular automata,” and “genetic algorithms,” but they are the future of data-rich mathematics education.

A Focus On the What, Not Just the How, Of the Mathematics Curriculum

We are not going to reinvigorate mathematics education simply by rearranging the desk chairs on the algebra floor. And mathematics is too important to overall education to go the way of Latin. Instead of just looking for new ways to teach the old maths better, we as a society need to be focused on equipping classroom teachers to broaden the syllabus and to teach the exciting new maths of the 21st century along with those of the 19th.

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