If the Internet goes down, the Amish community will be the only ones going about life as usual

perhaps trading bitcoins using paper wallets?
This would be possible if the miners continue running and part of the population still has an Internet connection. Without internet you need another network. Without a network you can do mining on paper and keep a printed copy of the blockchain, but transaction time would be very slow

Without the Internet, bitcoin buyers and sellers cannot connect to trade with one another and this will dramatically affect bitcoin's price negatively. Even if some people have access to the Internet, the fact that bitcoin usage reverted back to its early days, when not more than a handful of people have access to it, bitcoin will crash in value to that of the early days. But there's some good news: those with Internet connection will be filthy rich from operating an internet cafe just so people can check their facebook and instagram updates. HA!