Oooh, thanks Deozaan. I missed this from before. So I'm basically using 30x the processing power NASA had in one room to surf the web and play games. Oddly enough, I'm okay with that.
And now, onto the obligatory pr0n...
That, my friends, is the IBM Selective Sequence Electronic Calculator (SSEC) built in 1948. Operating at a blistering 50 operations per second, it was 140 feet long, had 21,000 relays and 12,000 tubes. Its moon-orbit calculations were used as the basis for the Apollo missions.
While the title is disputed, the SSEC is considered (by some) to be the world's first stored-program computer, in that it used paper tape for both input, output, and as "buffer" memory for intermediate calculations. It even had a small amount of digital RAM. However, IBM avoided using the word "computer" in its sales literature (5600 were sold) in order to give the impression they were trying to replace "human computers", a real job title at the time.
It was programmed using an extremely simple native assembly language, punched onto tape, then read in. For quick calculations like your familiar 4-function calculator the operator could utilize the handy plug-board.
It was a speed demon for its day:
"For each position of the moon, the operations required for calculating and checking results totaled 11,000 additions and subtractions, 9,000 multiplications, and 2,000 table look-ups. Each equation to be solved required the evaluation of about 1,600 terms — altogether an impressive amount of arithmetic which the SSEC could polish off in seven minutes for the benefit of the spectators."
The main control desk was one of its more beautiful features:
Ooh, baby... blink those lights for me. You
know I like it...
(You can read all about the SSEC and its gigantic brethren at the Columbia University Computing History Archive.) 
