how does the internet work and will it continue to operate work during
a power outage?

Hi, dko-ga:

The Internet is much more than just the "World Wide Web".  It's a
patchwork of networks which share information through standarized
protocols (like TCP/IP) that allow various kinds of peer-to-peer
communication.  A good overview is here:

[How Internet Infrastructure Works by Jeff Tyson]
http://computer.howstuffworks.com/internet-infrastructure.htm

A local power outtage that takes down your computer is unlikely to
have any effect on a Web server that hosts content which you were
browsing remotely (HTTP).  However other kinds of Internet
interactions such as file transfers (FTP) may have adverse
consequences due to a power outtage at one end of the communication.

The standards for such protocols attempt to limit consequences of
service interruptions.  A file transfer, for example, is probably
broken into small pieces (which may wind up being routed over the
Internet in a variety of ways), but sufficient information is provided
in the "packets" for them to be reassembled at the destination into a
copy of the original file or else detect that the transfer has failed.

regards, mathtalk-ga

Good.  Thanks very much

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till-ga