Isn't there a difference between information and knowledge? Information as I understand it is basically patterns of various sorts. I can see how this can be stored and retrieved infinitely. But knowledge is how we interpret the information. How can you store an interpretation? I mean you can describe an interpretation which in turn produces information, which consists of your description in language. So what you have is a description of the interpretation or knowledge, not the actual knowledge itself. Like you can describe how to drive a car or how to deliver a speech. But the knowledge itself of how to do it is something apart from the description.
This doesn't just apply to practical skills. It applies to "knowledge" in the more abstract sense too. Take for example an historian such as James Joll who writes a book on the origins of the First World War. This historian has a vast knowledge and understanding of the complex causes involved in the historical problem he tackles. What he does is distil this knowledge into various pieces of information and presents it in a way that can be understood as best he can. If the reader gains some knowledge as a result of the description then it may fairly resemble the knowledge that Joll originally possessed in order to write the book, but it will never match that knowledge coextensively or indeed exactly in any of its particulars. This is for a number of reasons: the reader interprets the information in his own way, he compares it with what he already knows, he evaluates it, understands intermittently, variably forgets and misremembers, and so on. His knowledge is his own. In this sense knowledge cannot be stored but only created anew in the mind of each rational being. Information is what is stored and is far more mundane,
Since what is contained in storage is a description of knowledge and not knowledge itself, and since all descriptions are capable of alteration and each fact about the world is capable of multiple descriptions, there is therefore no way of storing all human knowledge. In fact talking about storing all human knowledge (rather than simply bits of information) seems to misunderstand what knowledge is. And it is dangerous! But I won't get into that.