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| Are we losing the skills we need to solve new math problems? |
To make my point more clear, let me point you to this article by David Akeman. In "Insane Problems of Math and Physics" he talks about time travel. Time travel is a fun topic. Who wouldn't want to go back in time and tell their younger self to correct a mistake they made. There have been a few movies that addressed this idea: "Time Cop" and "The Butterfly Effect" come to mind. And when you get into a time travel story eventually you run into a paradox. The classic paradox is the one where you change the past without wiping yourself from existence. "The Butterfly Effect" played up this theme brilliantly. The poor kid had to keep going farther and farther back in time to correct the mistakes he was making when he tried to fix mistakes in the past.
The mathematics of time travel are so complicated that we don't have any way to theorize how to do it. Yes, physicists have proposed some ideas but we're a far cry from building a time machine. How long would it take to do the calculations for a single journey?
The last "Avengers" movie took the team on a time travel journey through the quantum universe. They had to steal infinity stones from historical moments, use them, and then take the stones back to their respective moments in time. This is a time travel trick that you'll find in a few science fiction stories. You're not really changing the past as long as everything you do takes place outside of known history. That's a principle based on Schrodinger's Cat, which is a metaphor for the undetermined state of a quantum particle. The particle's state is only known when it is observed. Schrodinger compared that principle to the idea of putting a cat in a box. The cat's state (alive or dead) is thus indeterminable. Only Schrodinger's Cat has always been inside the box. The moment you open the box is the first time the cat exists in a single state -- it could be dead or alive but only from that moment on.
Time travel should not work that way. If you are already in the past then when you travel back to the past you should not be able to interfere with yourself because your state has been determined. If part of what determined your state was the fact that you existed in two places at once then you should be able to travel into the past. But how does the universe decide when that can happen?
We're going to need a lot of math to figure out what is possible. And we may never be able to do that. Not because the math or physics won't allow us. But because we're becoming too dependent upon simple technology. Students prefer to use calculators and computers to do hard math problems for them. And if we let the machines solve the math problems then who will program the machines to solve new problems?
Maybe that's why our scientists are making math mistakes. Two recent examples involve misplacing a galaxy by millions of light-years and calculating the wrong amount of vitamin D intake. It's only going to harm some astronomers' careers when we miscalculate how far away a distant galaxy is. But miscalculating nutritional requirements affects everyone. Mistakes happen and even the smartest people make mistakes. These news stories are not signs of the impending mathematical apocalypse. And yet they underscore just how challenging math has become.
Even the most common of mathematic problems may be rendered incorrectly. When such mistakes are repeated and recorded in the literature they become indelibly fixed. We may one day want to use a time machine to go back and tell someone to fix all these errors.
But then, what if someone has already tried in the future and learned that didn't produce the desired results? Indeed, if time travel has already been used in the future that means the future has already been determined and we're trapped in a world filled with mathematical errors. The only way out of that is to assume that you can change the past and therefore your present and the future. And if that is so then how much more complicated will the mathematics of time travel become? Even the experts may not know the answer to that question.
