Posts Tagged ‘AP Calculus’
THE THREE BODY PROBLEM: For Educators
Worthy of a Physics/Calculus Teacher’s Attention particularly high school and particularly for AP or IB Physics students
ALSO instructive for discussions in philosophy and ethics (see bottom paragraph)
High school physics instructors or calculus instructors…this novel would make a great summer reading assignment before your class begins in the Fall. One, the story is entertaining. Two, the story portrays historically some of the greatest physicists to walk planet Earth. Three, The Three Body Problem itself, the actual physics problem, this engages the physicist’s and the mathematician’s mind, Newtonian physics and all that jazz…Not that I understand it all, but I believe these the guys who write on the website: askamathematician.com. The excerpt below is from their website
The Three Body Problem is to exactly solve for the motions of three (or more) bodies interacting through an inverse square force (which includes gravitational and electrical attraction).
The problem with the 3-body problem is that it can’t be done, except in a very small set of frankly goofy scenarios (like identical planets following identical orbits).
The unsolvability of the 3-body problem, rather than being an embarrassing hole in physics, an obvious but unsolved problem, is actually the norm. In physics, the number of not-baby-simple, exactly solvable problems can be counted on the fingers of one hand (that’s missing some fingers), and that includes the 2-body problem.
The dynamics of one body is pretty straight forward, in as much as it travels straight forward.
The dynamics of two bodies, while not trivial, can be reduced by pretending that one body is sitting still, and then restricting all of your attention to the other body. Using that technique, you find (or, at least, Newton found) that the motion of a body under gravity is an ellipse. The same idea can be applied to the quantum mechanics of electrons and protons to find the exact structure of the electron shells in hydrogen (1 proton + 1 electron = 2 bodies). In that case you’re not talking about actual orbits, but the idea is similar.
But, for three bodies, there doesn’t seem to be a fancy trick for finding solutions. As a result, the exact behavior of 3 or more bodies can’t be written down. The exact energy levels and orbital shell shapes in anything other than hydrogen is impossible to find. Even deuterium (hydrogen with one extra neutron)! Can’t be done.
Despite that, we do alright, and happily, reality doesn’t concern itself with doing math, it just kinda “does”. For example, quantum field theory, despite being the most accurate theory that ever there was, never involves exactly solving anything. Once a physicist gets a hold of all the appropriate equations and a big computer, they can start approximating things. With enough computing power and time, these approximations can be made amazingly good. Computer simulation and approximation is a whole science unto itself.
The main actors in THE THREE BODY PROBLEM are almost all physicists and/or mathematicians and they’re nerdy, but not dweebs. Read chapter 5, A Game of Pool if you want a taste of what the novel offers. Then, there is the virtual reality, which unfolds as a puzzle/game and is played often by nanotechnology researcher, Wang Miao. Wang is compelled to understand the mystery introduced in the early chapters of the novel and realizes that the game is key to the revelation he seeks. In the game world, Wang walks through the history of physics with virtual characters like Confucius (our earliest physicists were primarily philosophers…a helpful connection for students to make), Newton and Einstein. Trisolara happens to be grappling with the three body problem. It is a planet in a solar system where there are three suns. The game players, along with the philosophers and physicists throughout history try again and again, in a systematic way, to solve the problem of the planet’s impending destruction. To go through each game level, Wang encounters physicists who have furthered the thinking regarding the problem. It’s like taking a course called The Intro to Physics…all this learning while the reader hurtles toward the big reveal at the end of the novel. Ah…to be entertained while learning…tis a wonderful thing. At the very least, THE THREE BODY PROBLEM ought to raise the curiosity level of your students and give them a glimpse of the relevance of physics and math to their everyday lives.
For the ethicist/philosopher, THE THREE BODY PROBLEM raises interesting issues about elites thinking they know best for all. The Cultural Revolution in China drives the narrative in the early chapters. Many elites are driven out of their positions of authority, killed or exiled by the communist party as it takes power. The author calls this a madness. (Chapter 1’s title is: The Madness Years). However, within the communist party, a new breed of elites rise to the top. Later, toward the final chapters of the novel, a group of environmental activists, along with men and women Liu specifies as elites across the globe, use their power to set in motion what they hope will be Earth’s salvation (knowing that saving the planet may come at the expense of most or all human lives). This small group of people have become judge, jury and executioner for humanity. Moreover, their hope for saving the Earth might not evolve the way they imagine. The stage is set for a discussion about power, elitism, environmental degradation and what might be ways to stem our self-destructive/planet-destroying tendencies.
To read a No-Spoiler review of this novel, click THREE BODY PROBLEM, Book Review
To buy THE THREE BODY PROBLEM, click here.