Better Decisions Through Data.
Shown here are Hamming distance error-correcting codes in an illustration resembling a crazy quilt.
In yesterdays’ postĀ we pondered that aliens looking at the Sagan-designed Pioneer Plaque might have a hard time finding Earth due to the various data error. (These were due to the limits of science back in the 1970s.) Some people might regard the errors as a good thing. (Maybe we don’t want aliens to find us. š
But there is some redundancy in the Quasar timing uses. (In part, there had to be, because the timings will slowly change.) Sending a message with extra, redundant information to help the receiver correct errors is known in coding theory as a Forward Error Code. Space aliens trying to decipher the plaque might have to use something more advanced — probably based on Bayesian statistics, the sort of statistics error-detecting and correcting algorithms we’re starting to see in advanced artificial intelligence algorithms that use statistical inference.
A simpler form of these codes is a Hamming code, which uses a Hamming distance. This is the topic of the “crazy quilt” in this photo. A Hamming distance is simply the number of bits that are wrong. The more bits wrong (or different) between two numbers, the greater the Hamming distance.
But they do more than make a cool-looking crazy quilt. Hamming distances are a very important distance metric in artificial intelligence applications, especially self-organizing systems like self-organizing maps. IBM Watson, the computer that played on Jeopardy (and that’ve previously covered), makes extensive use of many distance metrics between potential answers (i.e., questions) to Jeopardy problems and information stored in its databanks. (For example, there is a geographic metric that computes whether an answer is in the correct or expected geography, or who far in might be off. How about time or historical period? How far away is data in its data bank in historical period from the Jeopardy problem being posed?)
Here you see a visual illustration of Hamming distances. The color of each pixel is the Hamming distance between the values of its x and y coordinates. (Clearly, by taking the Hamming distance of something with its mirror image, Hamming distances can also be used to detect symmetry. The illustration shows this, as the pixels where x and y values are similar — along the diagonal for example — have different colorations. The photo was originally cropped to fit in IG’s square, but the diagonal is the special blue pattern running to the top right corner.)
So this is Hamming distance artwork. And you though it was just a crazy quilt.
A version of this article originally appeared as a photo post on our Instagram feed.
[…] Hamming metric (or Hamming Error Correcting Code) quilt got us thinking. Turns out there is a branch of quilting making (or perhaps a branch of mathematics […]