Deck16

(Pictured: Prototype metre bar, once used to define how long a metre was.)

The Hard Drive with Unlimited Capacity

Suppose I were to claim that I could hold an infinite amount of information with a metre-long bar and a finely pointed needle?

Consider your hard drive now, or any hard drive or other binary storage medium. It is full of 0s and 1s, correct? These make a large number, say 010010110101. Dream up as long a number you like — terabytes, petabytes, think big!

How do I store that number with my modest equipment? Simple. I take your very long number, put a 0 and a decimal point in front of it, and point the needle that many metres along the bar’s length. (Heck, I’ll never need to move the needle more than 12 cm down the bar!)

To reverse simply measure (accurately, of course) the distance between the needle and the closest end, remove the leading zero and decimal point, and you’ve got your data back.

There you have it — a storage mechanism of infinite capacity.

Of course, it isn’t practical, and I’m sure you know why — accuracy! What instrument could measure a length so precisely? What needle could have such a fine point? What horrible data corruption would happen if you took a measurement while the needle vibrated due to the breeze of a passing butterfly? And then there’s the trouble of working at around the Planck length scale…

This little bit of food-for-thought was inspired by The Computational Beauty of Nature, a book I’m reading.