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All of the computer-related museums and exhibits I'm aware of seem to only cover the history of computing machinery, but nothing on topics of computer science.

You are involved in the creation of a new Museum of Computing, chartered to educate, entertain, and inspire the general public in a wide variety of computing/computer science/communication/mathematics topics. Though history and celebrity can be part of the exhibits, this is not a history museum. Instead, visitors learn about timeless concepts that enable computing, from the hardware layer on up. Budget is not specified but ideas should be durable and practical for high volumes of visitors in permanent installations, with minimal staffing/disposable materials similar to the world's best science centers.

What exhibits would you include?

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up vote 6 down vote accepted

Scott Aaronson addresses this particular question on his blog Shtetl-Optimized when considering the timeline of Computer Science. The relevant posts in chronological order:

Timeline of Computer Science

Top 150 computer science events to be decided once and for all

CS timeline voting: the results are in!

Most of the events in his list would make good exhibits, although it might be difficult to figure out how to present some of them physically.

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That's a great list! I'm particular interested in ideas for presenting these ideas physically and meaningfully. –  uosɐſ May 2 '11 at 11:57
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I'd put in an exhibit showing how electronic relays, as a more visible alternative to transistors, can be assembled to form computing machines. A progression of complexity, starting with a single relay, then a chain of relays to demonstrate propagation, then a single NAND gate, then a 1-bit Full Adder (18 NAND gates for this should still be manageable, visually), maybe even an interactive 4-bit Full Adder.

From there, a feature on clocked circuits, latches, memories.

All components could be exaggerated in size, slowed intentionally, or highlighted with light-guides for clarity.

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