With Wings As Eagles: Tech/Computer/Electronics Entries

Data Sizes As Lengths

2013 April 10 07:51

Draft number two of this post.

How big is data? Human minds often have trouble encompassing more than a few orders of magnitude at a time. When the amount of somethings goes from thousands to millions to billions, it's difficult to really keep the whole picture in your grasp. This is particularly true of the sizes of quantities of data, which vary by many orders of magnitude even within a single computing device.

I sat down one time a few years ago and tried to come up with an analogy for the difference between the largest and smallest useful units of data to the largest and smallest animals on the earth. Unfortunately, animals don't have nearly enough range of sizes to accomplish this. More recently, I realized I could use length as a proxy for data size and give a fairly good idea of how big things are.

The bottom of the scale is 8 kilobytes, or 8000 bytes. This picked for both historical and practical reasons. ENIAC, the first electronic digital computer, only had registers but didn't have anything like a "memory". However, its immediate successor did; the EDVAC had a memory of about 8k in the 1950s (it was a room-sized computer). The Apollo Guidance Computer (super-miniaturized computer built in the mid-1960s about the size of a small suitcase) had an erasable memory of 2000 15-bit words or about 4k. The level-1 cache of a single integer core of an AMD Interlagos processor is 16k. So across the 3, which covers, 50 years of computing hardware, 8k is a reasonable starting point for the smallest amount of data storage worth bothering with. In our length analogy, we'll make 8k equal to 1 inch, 2.5 cm, or about the width of a person's thumb at the first knuckle.

A high-density 3.5-inch floppy disk is 1.44 MB. The analagous length is 180 inches, or about the length of a mid-sized sedan.

A digital photo is usually 2 to 3 MB; the analogous length is about that of a bus or a truck.

A CD is 650 MB. The analogous length is about 81,000 inches, 6700 feet, or a mile and a quarter.

A DVD is 4.7 GB, analagous length is 588,000 inches, or 9.3 miles. It's about the length of Manhattan island; you can drive that in 10 minutes on a highway.

As of this writing, the middle size option of both the middle iPad Mini and iPhone is 32GB; this is also a fairly common size of SD card. The analagous length is 4 million inches, or 63 miles; about an hour's drive.

A reasonable hard drive in a new laptop is 250 GB. The analogous length is 31 million inches which is about 500 miles. That's the distance between Boston and Washington DC, or between London and Edinburgh; about what you can drive in a car in a very long day.

Around the biggest single hard drive that you can buy in a retail store today (as of early 2013) is 4 Terabytes. The analagous length is 500 million inches or 7900 miles, or about 1/3 of the circumference of the earth.

So the ratio of the sizes of the smallest useful amount of data and the largest reasonable single chunk of data is the same as the difference between the width of someone's thumb and 1/3 of the way around the earth. There you have it.