May 31st, 2018
(written by lawrence krubner, however indented passages are often quotes). You can contact lawrence at: email@example.com
If our particles have no identity, how can we?
If the elements are all identical with each other, then it seems like the only measurable identity you could attach to sets of elements is cardinality, right?
Reviving the a notion of “monad” from Leibniz from the 1600s, as a thought experiment:
Imagine beings that exist outside of time and space, in a space that is without dimension. These creatures initially lack cardinality or identity. They are “lazy” in the computing sense, they are Unrealized values. All they have is a desire to better understand themselves, and the ability to ask how many other beings connect to them.
I’ve seen the Greek word “alogos” used for inexpressible ideas, so I’ll use that as the name of this space.
Since they exist outside of time and space, and they lack all dimensions, you can not say these creatures are large or small, nor can you say they are near each other or far away from each other.
Lacking dimensions, one can say that none of them connect, or all of them do. Both statements are true. One can imagine that they are also Realized. Since they are outside of time, it is inaccurate to say that they were Unrealized in the past, and then they were Realized later. Rather, its best to think of time as a special circumstance that sometimes arises when these beings are Realized. But they are both Unrealized and Realized. Both are true.
There are an infinite number of ways these beings can understand their value, when Realized. Imagine an infinite sequence, with an infinite number of cursors, the location and movement of each cursor could be considered its own Realization. Or consider each cursor as every Realization that is possible for every sub-sequence of this overall sequence. Again, don’t confuse Realization with time. Consider time much more specific than Realization.
For every cursor (or, said differently, every instance of Realization) each being will see itself as connected to a different set of beings. This gives rise to its cardinality. There is no reason to think of this cardinality as integers. There is a lack of comparability between the Realizations of each sub-sequence, and thus the overall system should be thought of in terms of a lambda calculus. For Realizations to group into larger groups (sequences of sequences) the beings must understand their cardinality as based on some arbitrary initial value. Basically Church functions:
In such a system, these beings lack of identity in any absolute sense, but if they can consume each other with Church functions, then they can have an identity that is relevant to any number system built with any particular Church function.
There is also no reason to think that these beings can only consume (or Realize, or understand, chose whatever rhetoric you are most comfortable with) one value at a time. They could consume two, which would give them a two coordinates, which could be imagined or describing a two dimensional space, or three describing a three dimensional space, or four, or five, or a billion.
It seems to me that so long as something has unique coordinates, it has a kind of identity. And each being has unique coordinates, under each Realization, relative to each other.
If our dimensions, that we know in this universe, arise from the desire creatures such as this have, then it seems to me all of our particles have a kind of identity. They have a unique place in space and time.
One can imagine a being Realized with several different Church functions at once, with different understandings of cardinality, such that the being is, in a sense, holding several different number lines, some of which must seem very sparse, compared to some of the others.Source