Discretization

By mathematical definition, any mapping from a continuous system to a discrete one is going to have information loss. Put more simply, if you’re going to represent something by way of bite-sized chunks, or snapshots, along the way, you’re going to miss whatever happens in between. Unless of course your intervals are infinitely small, which for those of you playing at home, is the definition of a continuous system and the foundation of calculus.

Humanity lives in a discrete world. Things may feel continuous, but that’s only because of it’s own hardware (/wetware) limitations. The human eye can only interpret a theoretical maximum of several hundred frames per second, but that’s enough to lose a fair bit of information in some cases. We’ve only recently constructed tools that allow us to peer between the gaps to realize what we’re missing.

Planck second? So if information is good, and discretization causes gaps, then we should strive for continuity.

Thus far we’ve been describing information loss due to discretization of observation. Consider the opposite – discretization of action. We can start with an example everyone is comfortable with – communication. Prior to the 20th century, the speed in which a message could be delivered was constrained to the speed of the physical object being carried and the lack of obstacles in the carrier’s path. This was advanced a bit by faster mediums of physical transportation, and eventual supplanting by harnessing the ability to organize electromagnetic spectrums culminating in the internet that we know today.