You know you're a CS geek when you make computing parts that don't use electricity. How? I've seen plastic brick (a la Lego), wooden dowel (along the lines of Tinkertoy), and I heard of someone using PVC pipe and water.
The most common part I hear constructed are half adders, and for the real obsessive types, whole adders. Whole adders are a complicated chain of half adders that can do addition of up to three numbers, as large as the word size of the processor. Half adders are only made of about five parts, and so can only add two single-digit binary numbers, and at most product a two digit result. Single digit binary numbers can't represent very much by themselves. A whole adder almost certainly exists in your processor, in electric gate format, as part of your central processor's Arithmatic and Logic Unit (ALU).
Why do this? Retro-fun, mostly. There's a wide world of hobbyists who, for fun, practice obsolete skills. There are, assuredly, at least 10 people in my city who practice flint-work, even though flint as a tool material has been obsolete for well over 5 thousand years now. Similarly, analog computers are built from toy parts not for utility, but for bragging rights. And the knowledge that if civilization somehow collapses tomorrow, they can still run VisiCalc. On their own power. Awesome.