alt Hacker NewsI see it that prediction is a form of compression.
Say you have a computer file composed of two parts, the first represents the setup of an experiment, and the second is the data produced by the experiment.
If you have a good theory relating to this type of experiment, then you can predict much of the second part of the file. So you only need to store the first part and possibly some corrections to the least significant bits of some of the parts of the second part of the file.
Thus with good prediction, you can compress this type of file.
Another example is encrypted data. Statistically, encrypted data is indistinguishable from random. Truly random data is impossible to compress losslessly.
But if you had a predictor so smart that it could crack the encryption key, it could start predicting the rest of the encrypted stream, and therefore compress it.