Run a Thought Experiment

The cheapest simulation you can do is to run a "thought experiment." Einstein was famous for his thought experiments. When he was only 16 years old, he imagined looking at himself in a handheld mirror. Then he imagined running faster and faster while holding the mirror out in front of him. "What will happen," he wondered, "when I run as fast as the speed of light?" What would he see in the mirror?

Einstein's contemplation of such experiments eventually led him to discover his special theory of relativity.

Another thing Einstein was famous for was his humor. Consider the following thought experiment in which he "explains" how the radio works.

The wireless telegraph is not difficult to understand. The ordinary telegraph is like a very long cat. You pull the tail in New York and it meows in Los Angeles. The wireless is the same, only without the cat.

This is a thought experiment that doesn't explain anything. It's funnier still when you realize that scientists really don't understand how empty space transmits radio waves, especially because Einstein's special theory of relativity eliminated altogether the putative ether—which was supposed to carry the radio waves.

Thought experiments are conducted only in the mind and so are very inexpensive and safe. To be of any real use, your thought experiments must be accurate representations of reality. Einstein could do meaningful thought experiments because he had done so many laboratory experiments as a boy and because he understood physics so well.

But you don't have to be an Albert Einstein to do a thought experiment. In fact, you perform thought experiments all the time, when you plan a trip to the store or a sightseeing vacation across the country. In these everyday cases, you imagine what you need, how long your trip will take, and how much it will cost. For a long and complicated trip, you may find it necessary to use more tangible simulation tools. Tracing your route on a road map is an example of a simulation (albeit, no longer a thought experiment).

Calculating travel time between rest points is not so different from calculating the flight path of a spacecraft traveling from Earth to another planet. Jotting down your itinerary is a recording of your simulation result.

When you plan a trip, you understand that "the map is not the territory," but you imagine for a while that it is. (This Zen-like saying was coined by Eric Temple Bell, author of Men of Mathematics.) If your map is accurately proportioned to the real territory, then your simulation will give you a realistic value for your total trip time and mileage. If that time or distance is too long or the trip is too expensive, you can decide to cancel your trip or modify it to make it work within your budget. This type of thinking is a simulation. Rocket scientists design missions to outer space using much the same kind of thinking.

When I advise my graduate students (who are, in fact, fledgling rocket scientists), I suggest they do a thought experiment in which they imagine how their project will look when it is finished. They may be writing mission design software or developing techniques to solve problems in celestial mechanics, or they may be searching for trajectories to Pluto.

"Imagine what your algorithm will look like to the user," I'll say. "Does it have all the bells and whistles he or she will want? Is what you're doing now going to result in a program that does everything you hope to achieve? If not—change what you're doing."

Realistically imagining how the program or theory or trajectory will look, before you create it, is a great way to judge if your efforts are worthwhile or if you need to change course. That's not just good advice for fledgling rocket scientists—thought experiments are good for everyone.

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