Then again, Babbage's Analytical Engine was the epitome of mechanical calculation (had it been realized).
It may be someday. Have you heard of http://plan28.org/. Some guys are trying to raise enough money to build it. I've pledged $20 US.
Also there is a great series of podcasts on how computers work. The guy literally starts with what a voltage divider is and how it works, then what a transistor is and how it works, and how you can use them in different combinations to create and/nand/or/nor gates. He move on to flip-flops and eventually how to store a bit of information. Following his explanation you could almost build it yourself on a breadboard. (I know it's not all 100% accurate but he's trying to give a general overview.)
Really amazing series. No replacement for school but a good listen if you're interested.
The podcasts you can download here... GRC | Security Now! Episode Archive
Here are the ones you should look for...
How a Computer Works series:
Let's Design a Computer (part 1)
#233
Machine Language
#235
Indirection: The Power of Pointers
#237
Stacks, Registers & Recursion
#239
Hardware Interrupts
#241
The “Multi”-verse
#247
Operating Systems
#250
RISCy Business
#252
What We'll Do for Speed
#254
One other one that's good is when he was a kid he created what he calls a "Portable Dog Killer" which really was just an ultrasonic gun to teach a neighborhood dog a lesson. That one is episode #248.
Sorry for the long post.