Answering my own question. Today (early 21st century) I can have entire Wikipedia or (probably) a copy of entire Stack Exchange network stored on 1024 GB pendrive that is smaller then my nail. Provided that I strip it off all the "social data" (see below) and keep facts only. Or I can have entire human music collection on my just-a-little-bit-enhanced iPhone.
And both things are so obvious to most of us that we simply don't think about them this way.
It is not a "database" that formulates "big data". It is our (human) "social data" that makes it. Where we where, what we did, what we see, what we bought, what we think, what photos and movie we have. It has nothing to do with things like Wikipedia, Microsoft Encarta or The Great Congress Library.
When we consider Collective knowledge as just another huge database that stores only facts about ten million different species (random number; not a fact) they have ever encountered then I personally think that other answers given here are simply incorrect. It is not only possible, but also very efficient.
I can very easily imagine that after next 200-300 years it will be possible to store entire humankind "database" within single human hair. If we have at least 10k hairs then we can store entire Collective knowledge within each and every drone. Without even a tiny problems.