During one of those late night dorm chats somebody asked me what the source of the "magic" is inside of a computer. How can a machine think? I responded by saying that at it's heart, computation is a completely mechanical process and that a computer could be made out just about anything without any fancy electronics or other magical artifacts. Afterwards, I couldn't help but think about how exactly one would go about building a computer out of common household materials and my binding agent of choice - a glue gun.
The plan I finally settled on was a turing machine whose bits are lego squares positioned on a sort of train track. There is a car which can drive back and forth along the track. In order to detect which side the current block is on it lowers two popsicle sticks and a switch is closed on the side without a block. It is also equipped with a solenoid that it uses to move the blocks. The timing is determined by a big wheel that slowly turns and hits various switches along the way. You can program the machine by hooking up the solenoid and wheels to the switches that are governed by the position of the lego block. The entire thing is made out of popsicle sticks, plastic bottles, rubber bands and CarboPlast which is a cheap plastic cardboard. It has the respectable speed of about 1 operation per minute.
Here is a video of it in action.
The current model sadly has only one state which slightly limits the number of algorithms it can implement. However, in theory, all that it would take to add a state would be to simply build a replica S of the machine TM described above and put it on a track with only one block which would encode a state. We could then connect the switches determined by the position of the block in machine S to the solenoid and wheels in TM. By adding enough states the machine could eventually go universal but I leave this as an exercise to the reader.