Axes and ships, though, are just objects. What happens when we apply the "Ship of Thesesus" to a person? There's an interesting way to think about this, using a device common in science fiction. Many science fiction stories feature a "matter transmitter" or "teleporter" a device that can make a thing or person in one place disappear and then cause the same thing or person to reappear, practically instantaneously, elsewhere. Famous examples include the Star Trek "Transporter " and the device used by the unfortunate scientist in The Fly to transmit himself from one place to another. There are several explanations for how such a device might work, some involving unlikely concepts such as moving through a higher dimension or some sort of wormhole in space-time.
The earliest science fiction descriptions of matter transporters imagined them as some sort of scanner which would scan and analyse a thing or person before transmitting a facsimile rather like a telecommunications message. There are some serious difficulties with such an arrangement, but it's a useful way to imagine the "Ship of Theseus" problem applied to people. This type of imaginary matter transmitter would scan something - for our purposes, let's say a person - in exact detail, down to the last electron. Having scanned a an absolutely complete description of that person, it would then transmit that description to another place where, presumably with the aid of a receiver / reassembling unit, the person is recreated. Hey presto, instantaneous teleportation! You walk into the Transport-Me booth in your home town, press a button and reappear in another booth on the other side of the world, in the time that it would take a photo booth to snap your passport photo.
The idea of teleportation by technology in fiction is much older than Star Trek - a quick rummage in Wikipedia came up with an 1877 story about attempted human teleportation based on what was then cutting-edge communications technology:
Edward Page Mitchell's story The Man Without a Body details the efforts of a scientist who discovers a method to disassemble a cat's atoms, transmit them over a telegraph wire, and then reassemble them. When he tries this on himself, the telegraph's battery dies after only the man's head was transmitted.
Now for the "serious difficulties". Let's ignore flat telegraph batteries and Hollywood's problem with a fly in the transmitter causing a hideous human-fly mashup to emerge at the other end and take a brief layman's look at the problems with the engineering, physics and philosophy of the device.
In engineering terms, teleporting a human in this form is almost certainly impossible - the amount of information required to scan and record a complete description of a human body and mind, such that you could recreate an living, breathing, individual person with thoughts, memory and a sense of self at a given moment is so vast as to make such a thing impossible for all practical purposes.
It's worse than that,
Which brings us on to the philosophical problem of identity. Because, even if it wasn't impossible, a matter transmitter working on this principle wouldn't be a form of transport. It would scan and reproduce. The person walking out of the receiver/assembler wouldn't be the person who'd walked into the transmitter, any more than a copy printed by a photocopier is the original document that was scanned. Of course, even if you'd achieved the impossible task of complete fidelity and the document or person copied was absolutely identical to the original scanned in every respect, you'd end up an original and a copy. The original wouldn't have gone anywhere.
To appear to transport people over distances, rather than creating clones of them somewhere else, the scan/transmit matter transporter would have to destroy the originals. If you were to be completely annihilated only for an exact copy of yourself, with all your thoughts, memories and feelings to reappear somewhere else in the blink of an eye, would you take the "trip"? Would that person be you? It's an interesting thought experiment.
As a thought experiment it may seem far fetched but in the real world, in a piecemeal way, we're constantly being destroyed and created. Consider this:
Every cell in the human body is replaced and renewed within a period of seven years, consecutively, for life. This is known as aging; it includes the brain. Not one cell a person is born with is still there when they reach seven, and again at fourteen, then again at twenty-one, etc. The cells are replaced, respectively, and you are a "brand new" person, however, with the same DNA structure and personality you were born with.
Memory cells can be "recycled" as some information is lost over time.
Sleep repairs and reorganizes the brain; as for new brain cell development, research shows that as one educates their mind new cells form as often as the mind is actively engaged.
Like the Ship of Theseus, we're constantly being repaired and replaced plank by plank, until there are no original parts left - the only difference between this process and being destroyed and recreated in an instant is time.
Which brings me to the short film. It's by John Weldon, it's called To Be and it's great. A word of warning - I originally found this on Overcoming Bias, with the comment:
A while back I saw it on YouTube, but couldn’t find it a few months later; it had violated copyright. I actually bought a $15 dvd of it from the National Film Board of Canada. But as Nathan Cook informs us, it is now on YouTube again, here.
So, if this link doesn't work, apologies, it must have been taken down again. If it does, "enjoy it while you can".
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