Identity seems to be a function of position and time. That is, all 'things' with the same s(t) function possess the same identity. While a given rock is sitting there, no other rocks can take that spot. The rock is that rock, and none of the other rocks around are the same rock because they are not 'there' 'now'.

Or another example to try to blur the lines. 


  Class Thing

    Property X as Double

    Property Y as Double

  End Class



  Public Sub Main()

    dim obj1 as Thing

    dim obj2 as Thing



    set obj1 = New Thing

    with obj1

      .x = cdbl(1)

      .y = cdbl(1)

    end with



    set obj2 = New Thing

    with obj2

      .x = Cdbl(1)

      .y = Cdbl(1)

    end with



    msgbox "at this point, the two objects are indistinguishable."

  End Sub
However, if you look at a low enough level, obj1 is a pattern of electricity in one area of physical memory and obj2 is the same pattern but in a different area of physical memory. obj1 and obj2 each have their own identity because they physically occupy separate points in space-time.

Even though 2 things may present the same pattern, because of their different s(t) curves, they have the potential to deviate from one another, that is, to evolve along their own separate histories.

Of course, the pattern is the really important part when it comes to personal identity. If the rock gets buried deep into the crust of the earth and is transformed into quartz, it's probably not going to be considered the same rock afterwards. However, human beings rearrange and regenerate the matter making up their self continuously, and yet we consider beowulft2 to be the same, in some way that everyone easily understands, but cannot easily explicate, as beowulft1. It's not so much the matter that is traveling along "beowulf's" s(t) curve that matters as it is the particular pattern of that changing matter - information.

I become fatter or thinner and my skin changes tone along with the color and pattern of my hair. Not only that, but my thoughts and opinions and fundamental assumptions about reality change over time, but in some sense I'm still me - everyone agrees about that. So, even though this pattern and the matter it's made of changes over time, there's some core to the pattern that persists (or does it? is persistent identity a necessary illusion that the pattern must maintain about itself?). If this "core" is real, what is it? It's not genetics exactly because identical twins share the same genome. It has to be the accumulated experiences from traveling a unique s(t) function. Twins have separate histories and perspectives and therefore must have separate identities - or maybe saying they have separate histories and perspectives is the same thing as saying they have separate identities.

Does this hold up under scrutiny, though? I don't think so, particularly at the level influenced by quantum mechanics. The Heisenberg Uncertainty Principle holds that conjugate variables can only be known to inverse levels of accuracy. As position is more accurately measured momentum or velocity measurements are less accurate. Wave-Particle duality. The wave function for two particles can overlap for certain probabilities. As a consequence it becomes impossible to know (on a small enough scale) whether two particles share the same s(t) curve. Actually, it becomes unclear whether there's such a thing as an s(t) curve. The Pauli exclusion probably has something to say about identity as well, but I don't really understand the Pauli exclusion principle beyond some vague recollections about electrons; s, p, d, and f "shells"; and quantum number tables. Besides, I'm not made up of bosons.