“Is the task impossible or does it only seem that way? The beauty is: Nobody knows.”
Someone talking about solving the Traveling Salesman Problem in polynomial time? No, though I wouldn’t blame you for thinking that. This is from a new book of wire walker extraordinaire Philippe Petit, “Cheating the Impossible: Ideas and recipes from a rebellious high-wire artist“. It is a short TED book, available as an Amazon single. Here is the related TED talk, though I found the book better than the talk (and does not take much longer to read).
Philippe Petit is most famous for his wire walk between the twin towers in 1974. I saw him twice while I lived in New York, once at the opening of Man on Wire, and once doing his juggling show in Washington Square Park. Admittedly, I am a bit of a fan, and have read a couple of his previous books—even going through one in French on pickpocketing—and tried my own hand at walking the line (though the greatest danger here was for the chickens).
Each chapter of Cheating the Impossible begins with a suggestion for musical accompaniment and ends with a suggestion for further reading. Here is Django Reinhardt’s Jeepers Creepers to put you in the mood for this post.
The book is at times self indulgent, but has a contagious energy and undeniable passion. The main focus is on problem solving, and I was surprised how much was equally relevant for the creative process in science. He discusses both technical problems like those involved in rigging wires (what knot to use here?) and artistic problems, like how to create a character for his street juggling show (the mute Lippo, now with over 45 years of developement).
There are some familiar problem solving strategies, like breaking a problem down into smaller, more manageable, parts: ”As long as I keep collecting those miniscule atoms of a problem, one at a time, as long as I make progress, as long as I am not stopping to look up at what’s still an enormous mass of insoluble matter hovering over me, I will overcome!” I like this emphasis on the psychological aspect of attacking a huge open problem, that by absorbing our focus in smaller problems we forget the enormity of the larger task—in building a scale model of the twin towers to plan rigging strategies
we no longer see the behemoths outside.
Back to the impossible. For a wire walker, the impossible is a wire impossibly high, conditions impossibly treacherous, security impossible
to breach. For a computational complexity theorist the impossible is a proof that something can’t be done, a lower bound. The holy grail
of impossible is showing that NP-hard problems cannot be solved efficiently. And here there is some difference with wire walking. We are not out to cheat the impossible. There is no cheating in mathematics: an idea is ultimately judged by its correctness. It could be that P=NP. We must be prepared to fall on either side of the line, wherever truth lies. In wire walking falling off the line is failure, and what is worse, it does not prove impossibility, just that you could not do it.
As complexity theorists we do not want to cheat the impossible, but to reveal it. Which, at this point, seems pretty impossible.
Now, I leave you to read “Cheating the Impossible” by Philippe Petit.