Memex, created by Vannevar Bush, was proposed in 1945, and made public in his article, As We May Think. As quoted from Vannevar Bush's Memex, it was "part computer, part microfiche, part database, and included an information retrieval system bearing an uncanny resemblance to today's hyperlinks." Memex is in a way, like a direct influence to the Internet today. Ted Nelson was greatly influenced by Vannevar Bush --- in fact, Ted Nelson coined the word "hypertext."

What it Was

This machine had the ability to create what Bush called "'trails,' enlarged intimate supplements to memory, and to combine those trails with personal notes to form a separate and distinct record (from Vannevar Bush's As We May Think sub-article of Vannevar Bush's Memex)."

Purpose

(Note I'm citing this from Layer 9: Protocol) Vannevar Bush put forward a new plan to extend memories called Memex, in 1945. It was a system to review information in a microfilm on a half-transparent screen. he planned to compress information and access it quickly.

Relation to Serial Experiments Lain

The next scene after the above describing Memex shows Lain receiving an envelope package from JJ at Club Cyberia. She opens it and empties the item into her hand. It is a microchip. The music in the background silences as she focuses her attention on the microchip. Does that explain something right there?