• Government archives. (Ask a historian)
• Financial records. (There were banks then also)
• Library of Alexandria

They all can be considered as big data. They were physical archives and there were actual people doing transactions. Calculations were done on paper. We are generating and recording data for a very long time.

• Computational power
• Storage capacity ("You will never have to delete an email again")
• Algorithms

Digitalization allowed us to have the superpowers of replication, scalability and portability at minimal marginal costs.

You can burn down the Library of Alexandria but now you can rarely completely destroy a digital record.

Sometimes, the mere attempt provokes more replication (see Streisand Effect).

• Replication (copy-paste, back-up, cost of a TB)
• Scalability (digital banking, telecoms, email)
• Portability (size of a 2TB HD, cloud)

• Algorithms are automatons that help us do tasks.
• They are perfect for well defined, rule based and repetitive works.
• They are getting better at unstructured tasks (e.g. Deep Learning). But they require a lot of data (hence the importance of Big Data).
• They will never get worse. Their capacity to more progress is restrained by availability of electricity, computational power and data.
• They are used at everywhere that flow of information is important. Navigation, news, games, surveillance, finance, shopping, love, art, warfare…
• Eventually robotics. IoT. ASI?

You may read

• Unreasonable Effectiveness of Data
• How a Math Genius Hacked OKCupid to Find True Love
• Google's AI won the game Go by defying millennia of basic human instinct
• My battle to prove I write better than an AI robot called "Emma"
• Google's Artificial Brain Is Pumping Out Trippy—And Pricey—Art