Mathematics is the most human of the academic disciplines. Consider one of the most famous laws of physics governing the behavior of light. The reason the natural law that governs illumination is an inverse-square law is that the area at a particular distance from a point in space forms the surface of a sphere. The area of a sphere grows as the square of its radius – so the light spreads out across an area that makes its intensity drop off as the squared distance from the source of the light. The larger sphere has less light at any point on its surface. The key point is this – the star shining in the night does not know what a sphere is, the star illuminates without knowing the laws of illumination. The description of the star’s behavior is a human construct.
Mathematics is called the language of science, which it is, but it is more than that.
Examine the picture of the ways to make brick paths of width two, shown above. The number of possible paths with a given length has a famous pattern. Since you can lengthen a path with one vertical or two horizontal bricks, the paths follow the law that the number of paths of length n is the number of length n-1 (add a vertical brick) plus the number of length n-2 (add two horizontal bricks). This pattern is called the Fibonacci Numbers. We have 1,2,3,5 walks of length 1,2,3,4; the number of walks of length 5 is 3+5=8. The number of walks of length 6 is 5+8=13, and so on. Much as a star is unaware of spheres, bricks know nothing about the Fibonacci numbers – yet a human mind can see that the Fibonacci numbers constrain the arrangement of bricks.
With stars and bricks we have examples of the way that math permits humans to understand more clearly the nature of the universe they live in. In school, far too many students view math as a object of terror. Somehow mathematics has become the Lord Voldemort of subjects – to be feared and avoided if at all possible. There are a number of reasons for this:
- Lack of support and training for teachers in mathematics.
- Failure to teach instructors what the applications of the math are together with failure to ground mathematics in applications.
- Chop-and-change objectives and following fads like Ontario’s current mangling of discovery learning.
- A culture of fear of mathematics in the larger society that is hard to change.
Mathematics grew from art, medicine, and commerce – and it still applies to all of them.
Occupy Math designed the University of Guelph’s business math course. The five faculty from the business college that Occupy Math worked with all said that the primary objective was to get the students to believe that math was needed for business. This means that most of the students that come into the business college firmly believe that math is not needed for business – or that you can just hire math as needed. Does anyone else see a problem when the boss cannot understand the budget underlying the business plan? Yet the secondary education of these incoming business students left them believing that math was not needed.
Over in the sciences, biology-related majors are far and away the most popular. A big piece of this is that they are (incorrectly) perceived as not benefiting from math, statistics, and computer science – disciplines that many students would pay money to avoid. Occupy Math just spent a whole semester with a gifted student – trained in biology but able to navigate the byways of the computational world – trying to replicate a technique for identifying structure critical parts of a protein via co-evolution of critical residues. The project was, in a sense, a disaster; in the end the project became a dissection of the problems with the paper that we set out to replicate.
The mathematics in this alleged scientific publication were buried in an on-line supplement – even though it was the source of the published results. The authors abused mathematics and butchered statistics; they failed to run elementary tests on their technique to see if it was better than random guessing. Scientific papers go through a review process where researchers that are not connected with the research or the author’s home institutions review the work.
For this paper to have been published – and it was – the reviewers had to be completely innumerate.
Would we let illiterates review academic papers in English literature or history? No! It is, however, routine to allow people that cannot reliably do simple arithmetic to review and judge the scientific quality of papers that use statistics, algorithms, and other mathematical tools. This is the price of treating mathematics as the he-who-must-not-be-named of the academic world. It is not hard to find people that are proud of their innumeracy. It is all too common to encounter professors, even in some scientific disciplines, that view math as optional, too hard to understand, and not worth the trouble.
Occupy Math sometimes tries to slip mathematical foundations into his applied computer science papers. Very often the result of this is to be told the material is irrelevant, uninteresting, or – and this causes the most pain – wrong when the person doing the reviewing can understand neither the claims or proof techniques. This cheerful lack of respect for and lack of understanding of mathematics comes from computer scientists and engineers. Occupy Math personally knows computer scientists and engineers who are also skilled mathematicians – but he keeps encountering the other sort too often.
Almost every field of academic enterprise could benefit from a better understanding of mathematical reasoning and mathematical technique. The Renaissance discovery of perspective, medical doctors innumerate terrorizing of their patients, the incredible savings of lives by Florence Nightingale when she did the math – all of these are places where fear of math and proud innumeracy could set the human race back unless sternly opposed and overcome.
Fear of math is literally lethal to individuals and toxic to our survival.
Occupy Math has seen people ridiculed for being able to compute a 15% tip in their heads. This sort of behavior reinforces the idea that its good to be a mathematical ignoramus. We must let go of the fear or continue to pay the price. Math is much harder for those that are taught to fear it. To continue the theme of this post, Voldemort’s power was amplified by people’s fear of him.
The ability to perceive and organize patterns is one that belongs to life. Parrots and dolphins manage it to some degree. Dogs and cats are deeply aware of patterns in the appearance of food. Humans are uniquely skilled at seeing patterns. To cast away this incredible gift and to proclaim with pride that you have no more perception than a brick is a tragedy. It is tantamount to maiming yourself so that you cannot run or lose the ability to sing. Young children take joy in the discovery of patterns, it is a natural part of our being. Embrace your natural abilities and cast aside the blindness of ignorance for the incredible light of pattern and form!
Occupy Math would be very happy to hear from his readers about times when math has proved useful, or has been mocked by the fearful, the ignorant, and the proudly innumerate. Please comment or tweet!
I hope to see you here again,
University of Guelph,
Department of Mathematics and Statistics