Bicycle of Theseus

I described the Ship of Theseus problem in a blog post not too long ago, and this made me start thinking of how this would apply to the bicycle. Clearly, a bicycle is comprised of many parts. Each surface of every part can be carefully tuned for light weight, durability, aerodynamic qualities, and so on. If I walk into a shop today and buy a new road bike, then change the wheels and brakes, is it still the same bike? This is a simple thought experiment, but its result helps me keep track of my bicycles.

My solution is to choose one immutable part of the bicycle to encompass the whole thing, and that's the bottom bracket shell of the frame. I find that this definition nicely handles the edge cases:

• intuitively, a frame defines the bicycle's fit, handling, and performance characteristics, so it makes sense to define the atomicity of "bicycle" by a frame, or at least part of its frame.
• it is relatively simple, and sometimes necessary, to change the fork, wheels, and other components on the bicycle.
  
• the bottom bracket shell is the point about which the cyclist applies almost all motive power to the bicycle frame.
• it is possible to repair or replace a dented or broken frame section, or paint the frame, while leaving the bottom bracket shell intact.
• replacement of an entire frame, due to upgrade or repair, constitutes a new bicycle.
  
• the bottom bracket area traditionally contains the bicycle's serial number.
  

When I talk about clearing space in the bicycle room, I say that the goal is to reduce the "bottom bracket count". When I describe the mileage on a bicycle, I'm really describing the distance that the bottom bracket has traveled (though I do include indoor "miles").