Rabbi Aryeh Kaplan writes in his essay Immortality and the Soul that the Neshomo is effectively the data of our "memories, thought patterns and personality traits" and discusses the idea of transferring it to a computer or a new body. He also explains that Hashem is omniscient, so contains all of this data and never forgets it, thus making our Neshomos immortal.
More recently, physicists have developed theories that information cannot be destroyed. This seems to tie in nicely with what R' Aryeh Kaplan wrote.
With more modern developments of computers, it also makes me wonder about other implications. Presumably all software and all data that ever exists is also "immortal" and contained within Hashem's "omni-cloud". Does this mean that after we die, we can still access this data? R' Aryeh Kaplan writes that Neshomos don't exist in a static state, but continue to be active, because Hashem's memory is active. Does that mean that software can continue to exist in a runnable state as well, and that data is not just accessible as a series of bits, but that eg. images can be "seen", audio can be "heard" and video can be "watched"?
EDIT: Further question - does this open the possibility of humans creating an artificial Neshomo?
I'm not sure what it even means that Neshomos are not static as Hashem transcends time. Does time even apply after death?
I'm curious what other people think about this and whether anyone has come across anything else written on the subject?
Extract from Immortality and the Soul...
Imagine what it would be like to undergo a brain transplant. A man might be suffering from an incurable disease in his body, but still have a healthy brain. The donor, on the other hand, would have suffered irreparable brain damage, but otherwise have a perfectly sound body. The brain is removed from the sick body and placed in the healthy one.
Who is the new man? We have an old brain with all its memories, personality traits and behavior patterns. But it has a brand new body. The old body might have been old and sick, while the new one may be young and full of energy.
Let us ask this man to point to himself. Will he point to his body? Is the real you your body or your brain?
A brain transplant raises enough questions. How about a memory transfer?
The science of cybernetics has discovered many similarities between computers and the human brain. Computer technology allows one to program a memory transfer, taking all the information contained in one computer and transferring it to another. All that passes from one computer to the other is information. What if this were done with the human brain? This may lie in the realm of science fiction, but even if it will never be possible in practice, it is certainly possible in theory.
Let us try to envision such a memory transfer. Assume we have a person with an incurable disease where neither the body nor the brain can be salvaged. We clone a new body for this individual, brain and all. The possibilities of doing this have already been discussed at length in the literature. This new body has a blank new brain, capable of functioning, but without any memories or thought patterns. As a final step, we accomplish a memory transfer, bringing all the information from the sick person into the brain of the new body.
We now have a fascinating situation. If all of a man's memories, thought patterns and personality traits are transferred to a new body and brain, this person literally exists in his new body. But nothing physical has been transferred. No physical part of him has been placed in the new body. All that has been placed in this new body is information that previously existed in the old brain. Yet this information contains the sum total of this person's personality.
But if this is true, then it offers us tremendous new insight into our original question: Who is the real you?
The real you is not your body or brain, but the information contained in your brain -- your memories, personality traits and thought patterns.
What happens then when a person dies?
We know that the body ceases to function. The brain becomes inert and the physical man is dead.
But what happens to the real you -- the human personality? What happens to all this information -- the memories, thought patterns and personality traits? When a book is burned its contents are no longer available. When a computer is smashed, the information within it is also destroyed. Does the same thing happen when a man dies? Is the mind and personality irretrievably lost?
We know that God is omniscient. He knows all and does not forget. God knows every thought and memory that exists within our brains. There is no bit of information that escapes His knowledge. What, then, happens when a man dies? God does not forget, and therefore all of this information continues to exist, at least in God's memory.
We may think of something existing only in memory as being static and effectively dead. But God's memory is not a static thing. The sum total of a human personality may indeed exist in God's memory, but it can still maintain its self-identity and volition, and remain in an active state.
This sum total of the human personality existing in God's memory is what lives on even after a man dies.
EDIT - I missed an important part out earlier: -
[In a Kabbalistic sense, we are here speaking about the lowest level of the soul, the Nefesh Behamis or "animal soul". This most probably can be identified with the information contained in the human brain. However, this interacts with the higher parts of the soul, Nefesh, Ruach and Neshamah.]