Thinkers over time have recognized that a person remains the “same person” even though their body undergoes changes over time, even to the extent of losing parts; say, an arm, or a leg. In 1954, it was discovered that "98% of the atoms in the human body are renewed each year". This has led many to conclude that what makes a person a person, must be different and separate from their body. For some, this different thing is a "soul". For others, it is a "mind" or “consciousness”. In general, this is often called mind-body dualism.
Others have concluded that, because nothing exists outside of physical reality, the mind can't be different from the body, but since the body does change over time, there must therefore be some subset of the body (say, the brain) that is identical to the mind. Jews and Muslims believe that there is a bone in the spine, called the "Luz", that doesn't decay, and from which the entire body will be rebuilt during resurrection. Dr. Roderick Chisholm, thinks that, while it probably isn't the Luz bone, it likely is something microscopic within the brain. In "Which Physical Thing Am I?" he writes,
"I am literally identical with some proper part of this macroscopic body, some intact, nonsuccessive part that has been in this larger body all along."[By "nonsuccessive", he means something that is NOT a series of different parts over time. By contrast, an army regiment is successive in that it can exist for hundreds of years even though no individual soldier does.]
Now keep in mind that the Stanford Encyclopedia of Philosophy describes Chisholm as "widely regarded as one of the most creative, productive, and influential American philosophers of the 20th Century", and that Chisholm published the above in 1989 (not 1889), and it is included in anthologies as recently as 2008 (not 1908). It is not just ancient philosophers who get confused over this topic. What are they confusing that programmers know?
Programmers know that software (like the mind) runs on hardware (like the body), but it isn’t synonymous with the hardware. That doesn’t make software mystical or beyond physical reality; it is just at a higher level of abstraction. At that more abstract level, software exists as an information process whose data state at any given point in time is embodied in some set of physical components. But it would be the same software even if running on other equivalent hardware.
In fact, there are several layers of abstraction between your typical program and hardware, what with Java code compiled into virtual machine code, interpreted in a VM written in C code, that compiled to Intel assembly code, that assembled into hexadecimal machine code,… And we haven’t even made the leap to electrons flowing through transistors yet! The point being that software doesn’t care which transistors, even though every i+=1; statement runs in lock step with some transistors somewhere doing something specific to implement them. If that flip-flop didn’t flop then that bit wouldn’t change, and that auto-increment instruction wouldn’t increment, and so on. But, a programmer understands that it isn’t the electrons running through the NAND gate that “makes” a program DO what does, any more than some x=0; statement makes a Square.draw() method DO what it does. They all happen simultaneously at different levels of abstraction.
RAID fights bugs
To Chisholm’s particular point that continuous personhood requires (at least some) continuous body bits, programmers know that the “life span” of any particular set of data, is not tied to any particular physical component. Information is independent of the media used to record, or embody, or carry a copy of, that information. A perfect example is a RAID device containing multiple disk drives. Data in a RAID is kept in multiple physical locations such that any particular location can be destroyed without losing the data. So, an arbitrary set of data (say, a file) can exist unchanged over time, even though the hardware storing it has completely changed. With a “hot swap” RAID, a system using that file would have no idea that a drive died, was removed, replaced with a new drive, and that new drive re-populated with data.
And, just like a mind’s constantly changing data set, that file’s contents on the RAID device can be constantly changing. And those constant data changes are totally independent of the constant drive changes that might be taking place inside the RAID.
The point here is not “the brain is a RAID drive”; the point is that a RAID drive is an existence proof that ongoing software processes do not require “intact, nonsuccessive” hardware. And the larger point is that Mind and Body can both be understood as simultaneous lock-step processes at different levels of abstraction in the same way that C++ method calls are in lock-step with CMOS chip voltage changes.
 Metaphysics, the big questions, 2nd Ed., 2008, chap 35
 Time Magazine, Oct 11, 1954 quoting Dr. Paul C. Aebersold of Oak Ridge