the rise of the machine world 2, with teaching

Each year, I realize that little bit more how much I love teaching. I realize how much I enjoy taking a small piece of the mathematical universe, digesting it and showing my students all of the strange and wonderful flowers I have found growing along the sides of our path. I am reminded of how much I enjoy the engagement with students, inculcating in them in the joy of mathematical exploration.

What does this have to do with the machine world? Through one lens, it can be viewed as a manifestation of an old story of Issac Asimov, The Feeling of Power. These days, a retelling might result in a cautionary tale a la Skynet and the Terminator, or Colossus, of outsourcing aspects of how we understand the world, and gifting the machine world with dominance. When it was written, though, while it was a cautionary tale, it was a hopeful tale, with humanity slowly, painfully, discovering its gifts.

And what does all of this have to do with my teaching? One of the readings I give my students is The Feeling of Power, because I like to be reminded each year and I think it’s a story worth everyone reading. We make us of our colleagues in the machine world, to undertake calculations beyond for reasons of practicality our ability to do ourselves. But I make use of the machine world with the understanding that we might get out answers to our questions, but we still need to provide for ourselves the reasons why those answers are actual correct answers to our questions.

Mathematics has for some time been an experimental science, wherein we can use the machine world to conduct our experiments, under our direction. We take the outputs from these calculators experiments and we can then formulate conjectures about the behaviour in situations far beyond our ability to calculate, and we then try to construct the arguments that allow us to pierce the veil of the logistically practical and make statements in truth about the infinite.

And this is what I work to share. The deep intellectual joy we can find in our quest, in our exploration of the infinitude of possibility. The harnessing of the power of the machine world to assist us in our quest. The use of language to provide short cuts along the path of understanding, and the exploration of the subtleties of that use of language.

And now, I go to write the next lecture, the next episode for my students, taking them a bit further along the path.

~ by Jim Anderson on 26 April 2020.

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