Why did René Descartes invent scientific notation?

Answer 1

I'm not sure that Descartes invented scientific notation. No offense: Descartes was a brilliant and important figure, but this is hardly the achievement to remember him for.

Descartes did introduce the modern notation for exponentiation (7x3 for example) in his Geometrie, published in 1637. I think we make a bigger deal of this notational innovation than it really is: the concept of exponentiation was alive and well already, and other mathematicians used notation remarkably close to this (Hume would have written 7xiii for example).

The idea that very large or very small numbers need special notation certainly did not begin or end with Descartes. We are constantly finding new ways to write inconveniently scaled numbers: $3B rather than $3 x 109 or $3,000,000,000 or 4GB rather than 4,294,967,296 bytes. If you've ever heard someone say something like "the mass of the sun in kilograms is 2 followed by 30 zeros," that person has had the same basic idea.

As to your question "why" we have scientific notation (or any of these other ways to deal with inconveniently scaled numbers), I think there are two reasons:

1. It helps us deal with the scale of these numbers better. What I mean by this is that 2,000,000,000,000,000,000,000,000,000,000 Kg is really hard to read or say, while 2.0 x 1030Kg is more manageable. When we do computation with these numbers (for example, dividing a kilogram of water by the mass of a single water molecule to get the number of molecules), scientific notation is especially convenient.

2. It reminds us that only the first few digits actually mean anything. That figure up there for 4GB is a good illustration: we don't usually care about the *exact* number of bytes, we just care whether the memory in our computer 1GB, 2GB, or 4GB. In physical measurements typically used in science or engineering, we simply can't measure precisely enough that the *exact* number matters. That's why 2 x 1030Kg means something different than 2.0 x 1030Kg (the difference tells me something about how good the measurement is).