Woah. Did they do this right until 2011, or were their systems upgraded?
Apollo 13 whole computer system had less power than the phone in your pocket; yet that was perfectly enough to run the vehicle. Crazy times...
Btw, found my answer after some googling, they were upgraded in the early 90's then again in early 2000's http://www.aviationtoday.com/1999/11/01/the-space-shuttle-mo...
quote "In addition to 11 MDUs in the shuttle, MEDS has four integrated display processors (IDPs) that contain 386DX computers and a 300-megabyte hard disc."
MDU - multiple display unit.
The command module did not have a redundant computer or memory, but the lunar module came with a second computer  of a different type and running different software.
What you remember is probably the Gemini Guidance Computer's tape drive system, which consisted of three identical tape drives that were connected to the computer through a voter circuity.
Re: core rope
Jesus. Now it’s TB/cm...
Very interesting point. A lot of today's "science" works like this, and it is a deeply flawed approach.