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What if? [Q&A]

Vinay

I had previously mentioned a technique called order-of-magnitude estimation that scientists of all stripes find extraordinarily useful, and Atul of Canara College asked me what that meant.

One of the most important characteristics of doing science is that scientists look to work on problems that can be solved. There is no point in wasting years and years of effort on pie-in-the-sky problems that no one knows what to do next to get closer to solving it. But how can you know whether something can be solved or not before it has been solved?

What one does is to set up a simplified version of the full problem, and work out the arithmetic for an approximate case. For example, to be able to launch satellites into orbit, you have to know the mass of the Earth. But you don’t need to know it accurate to the gram to figure out what kind of launch mechanism you will need. You only need to use numbers within a factor of a few of the right values to get a very good idea of what the problem looks like. The process of working that out is the order-of-magnitude estimate. It helps you define the boundaries of the problem and take the first step towards a solution. Of course, having an order-of-magnitude estimate is not a guarantee that the problem will be solved, but without one, it definitely cannot be solved.

Randall Munroe (of XKCD fame) is writing up a weekly column with brilliant examples of order-of-magnitude estimates. It is called What If?, and has so far dealt with questions like like what happens if you threw a ball at relativistic speeds, what if you put together a mole of moles, can you move the entire human population off the planet, and so on. Highly recommended reading!