What does it mean that, “My computer can do what your computer can do?”  My computer can play Crysis, and yours probably can’t, but is that really a meaningful distinction?  My computer has a bunch of ports and things on it—USB, HDMI, etc.—and there’s probably a bit of overlap between my computer and yours there.  But my computer could be missing most, if not all of its ports, and it could definitely still be said to compute.

You might have a Mac, and I have a PC, but again, that seems like a superficial difference—while there may be certain programs that only run on PCs and not Macs, it’s not like a similar sort of program couldn’t be written for a Mac that did the same thing.

We could play this little reductionist game all day—winding down past the processor of the computer, comparing flip-flops and NAND gates, past transistors, down to the electrons themselves—those tireless carriers of the binary alphabet of our information age.

But what’s the difference between electrons carrying out computations versus me carrying out a computation?  After all, given enough time, I (or perhaps, Suzie) could manually reproduce anything either my or your computer is capable of computing.  We’d just have to follow the correct rules (and possess a sufficient amount of paper…and pencil lead).