256GB Paper Storage Claims Simply Don't Add Up
A story first posted on ArabNews.com has been making the rounds on the Internet, involving an Indian student who has allegedly found a method of storing compressed digital information on a regular sheet of paper. Sainul Abideen claims that his technique, dubbed Rainbow Technology, can store between 90 and 450 GB on a single sheet of paper. The system allegedly works by encoding data into small geometrical shapes (circles, squares, and triangles) in various colors, then printing them out on a piece of paper. A scanner is used to read the data back in to the computer. Abideen claims that his storage method is more environmentally friendly due to the biodegradable nature of paper, and envisions magazine publishers printing tear-out sheets of paper containing demos and programs, replacing the traditional plastic-wrapped CD or DVD. Storing digital information on paper dates back to the earliest days of computing. When I was a little kid, my dad used to bring home punched cards from his job programming a mainframe computer at Vancouver General Hospital. The cards had 80 columns—an artifact that remains with us today as the default width for console-mode applications—and could only store a maximum of 120 bytes (about one-eighth of a kilobyte) per card.
However, despite technological advances in scanning and printing technology since those days, Abideen's claims quite simply do not hold water. A little bit of math is in order here. Starting with a scanner with a maximum resolution of 1,200 dots per inch, this leads to a maximum of 1,440,000 dots per square inch, or just over 134 million dots on a sheet of standard 8.5" by 11" paper (excluding margins). Getting a scanner to accurately pick up the color of a single dot on a page is a difficult affair (it would take near-perfect color calibration, for example, and be prone to errors from ambient light and imperfections in the paper) but let's be generous and say that the scanner can accurately pick out 256 shades of color for each dot. That's a single byte per dot, making the final calculation easy: a maximum theoretical storage of 134MB, which would likely go down to under 100MB after error correction.
It's a decent amount of storage, but several orders of magnitude smaller than the 450GB claimed by Abideen. The claim that "circles, triangles, and squares" can achieve these extra orders of magnitude can be easily challenged. There is a word for using mathematical algorithms to increase the storage space of digital information: it's called compression. No amount of circles and triangles could be better than existing compression algorithms: if it was, those formulas would already be in use! Compression could easily increase the 100MB theoretical paper storage by a factor of two or three, but so could simply compressing the files you wished to store into a .zip archive before converting them to a color printout. Ultimately, storage is about bits, and the smaller the bits are physically, the more storage can be packed into a given space. The magnetic bits on hard drive platters and the tiny pits in optical media are orders of magnitude smaller than the smallest dot that can be recognized by any optical scanner, and this is the simple reason why they store orders of magnitude more information. Even if a much higher-density printer were used (such as an expensive laser printer or offset printing process) the limiting factor is still the scanner required to get the information back into the computer. In the end, a picture may be worth a thousand words, but it cannot be worth half a thousand megabytes.
. He'd first have to invent a new printer that prints at 9600x9600 to actually pack enough dots onto a sheet of plain paper