Why maths?
I suppose I could go on about the austere beauty of mathematical truths — and there’s actually something in that. The world of mathematics has a comforting stability and solidity. It’s 'a less fretful cosmos,' according to Bertrand Russell. When the turmoil of life is getting you down — or keeping you up at night — it’s a relief to noodle away on a little maths problem, tucked away in the back of your head. And it’s such a pleasure when you finally solve it.
But mathematics is not just problems and solutions, or theorems and proofs. It’s also a human endeavor, a social activity carried on by a community of people with distinctive histories, traditions, habits of thought, rituals, stories, jokes. I find it a fascinating culture, and part of what I’m up to is trying to give the rest of the world a peek into the lives and minds of mathematicians.
Why this book?
Some stories are worth telling more than once. And sometimes it takes more than one telling to get a story right.
Over the years, I’ve written lots of essays on mathematical and computational themes, published in Scientific American, The Sciences, and American Scientist. In putting together Foolproof, I collected a dozen of these essays that I thought deserved a second chance to find an audience. It’s a second chance for me, too: an opportunity to update, revise, improve.
The aim of the book is not to teach mathematics. I’m not going to help you brush up your calculus. But neither is it a book of recreational mathematics, focused on puzzles and clever problems (although there is a chapter on sudoku). I think of it more as a travel book, where I visit various mathematical territories, sample the cuisine, and try to learn a few words of the language by chatting with the locals.
Incidentally, the magazine versions of all the essays are still available on the web (though without the updates, revisions, and improvements). I provide links to PDF files on the book’s website. The site also has a couple of live-action playthings based on illustrations from the book.
What's next?
I’m working on a book-length project called Tinkering with the Universe, about mathematics and computation as tools for exploring the world we live in. If you want to understand how rivers carve their meandering channels, how birds in flocks coordinate their flight, or how rumors spread through a population, a computer model can be highly illuminating. Computer models of the earth’s climate have assumed special importance in recent years; based on what those models tell us, we’re asking seven billion people to change their behavior.
I have written about many such models and simulations, but having only words and pictures to explain them leaves me frustrated. I want to give my readers a chance to play with the models themselves, twiddling all the knobs and watching what happens. In the past few years, it’s become possible to offer that experience on the web: The program for a simulation can be embedded in a web page, so that the reader can experiment with it. Yet even that marvel of modern technology still falls short of the ideal. It turns out that the big learning opportunity in computer modeling comes not from running the finished model but from building it in the first place. You have to get your hands dirty mucking about with the source code. That’s what I’m aiming for in Tinkering with the Universe. A web page will offer both a running model and a live view of the source code; when the reader modifies the program, the model changes accordingly. The first chapters should go live next year.
I also have a side project — a work of fiction. I’m not ready to reveal much beyond the working title: Fork Me on GitHub: A Novel for Nerds. This too I expect to serialize on the web starting next year.
What's exciting you at the moment?
I’m intrigued by the current enthusiasm for artificial intelligence, machine learning, and neural networks. I’m old enough to remember two previous waves of AI optimism. In the 1960s and early 70s the grand goal was 'general AI' — building a mind something like a human one. In the 1980s attention shifted to more specialized 'expert systems,' which would master a single domain, such as medical diagnosis. Both of those undertakings were thought to require a deep understanding of how reasoning works, as well as extensive knowledge about the world at large. That’s where they faltered. The new AI takes a much shallower approach, applying statistical methods to masses of unstructured data. I never would have expected it to work, but the results are impressive, at least in areas such as image recognition and language translation. I’m amazed. I’m also unsure how it will all end.
Apart from what excites me, I also have to mention what scares me. I cherish my opportunities to withdraw into Bertrand Russell’s less fretful cosmos, but I can’t help noticing that the world outside my cozy nook seems to be falling to pieces. We should all remember the story of Archimedes, who was too engrossed in his geometry to look up at a Roman soldier who disturbed his studies, and then slayed him.
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