Gigahertz, nanoseconds, Grace Hopper, and a plastic coat hanger

Personal computer manufacturers proudly quote clock speeds for the microprocessors they use in units of gigahertz (GHz). A Hertz is one cycle per second, and we can visualize that by the tick of a pendulum clock. Then we just roll our eyes in disbelief when someone tells us that a gigahertz is a billion (1,000,000,000) Hertz. Another way of thinking about that speed is to say instead there is only a nanosecond between ticks. How can we visualize that tiny time interval?

In a blog post yesterday Nick Morgan reminded us of how it was done brilliantly by Grace Hopper, the computer pioneer. In her lectures she used to describe a nanosecond by how far an electrical signal could travel down an insulated wire, at almost the speed of light in a vacuum. That distance is 11.3 inches. There is a video from a 1982 Sixty Minutes TV interview with her handing out lengths of thin hookup wire. Dr. Morgan say he still has one of those simple, inexpensive props from almost three decades ago. Right now you could go to a Radio Shack store and buy a fifty-foot roll of 30AWG wire for less than $5.

Your audience couldn’t clearly see that small diameter wire when you held it up on stage. They could easily see a larger diameter object, like a piece cut from a plastic coat hanger. (You also could get a piece of wire the size of the jumper cables you carry on your car or truck).  

How much has changing technology reduced the time between ticks? The first computer I remember seeing up close was the Bendix G-21 at Carnegie Tech back in 1962. It went 6000 nanoseconds between ticks. The first computer I owned was an Apple II Plus, with 1000 nanoseconds between ticks. I’m writing this post on an Apple iMac with only 0.33 nanoseconds between ticks (a 3.06 GHz clock speed). In that time interval a signal travels just 3.73 inches, or slightly more than the 3-1/2" width of a business card.