On 9/21/2011 2:28 AM, Stephen P. King wrote:
The ideal case of a bisimulation is an equivalence between computations. For example, a pair of implemented computations are bisimilar when, given identical inputs, they yield identical outputs. We generalize the idea to the dynamical synchronization and coincidence of propositions within logical algebras.

Here is something that Andrew Soltau wrote that explains the idea well:

"I look in my inbox and here is a message, in my reality. It is from you, but, in my reality, you are an icon of another parallel reality.

Before I click on the message and see the content, in my reality, the content is indeterminate. It is all possible contents with that title. As I look at it, I become one specific version of me, reading a specific version of the message. (So the me that got the message in my inbox, with a specific title and date, but contents unknown, has just fissioned into every possible version.) This makes determinate also which version of you has written the message. But this means solely that I am correlated with a version of Stephen who wrote that message. In my solipsism, this message has come from every possible version of Stephen with whom I have shared a history, and who wrote that exact message, a vast, and possibly infinite, number of Stephens. More accurately, the quantum definition of my specific version of the environment, out of all of the versions which just fissioned into being, defines a specific message. It must have been written by a possible version of Stephen, and all such versions exist 'out there' in their own solipsisms.

I reply, which in my reality means that I formulate a message and commit it to the email system with the address stephe...@charter.net. By doing so I am interacting with the avatar in my reality which I call Stephen Paul King and with whom I have an increasing sense of friendship! None of this does away with the humanistic side of things.

By making this message determinate in my reality, and sending it to stephe...@charter.net, I am making it 'the message from Andrew' for all versions of Stephen who get that version of the message, from that version of Andrew who sent it. But the correlation between the two realities in which this message is sent and received is not a property of the two minds communicating by any medium or interrelationship. In the multiverse of all possibilities, there are bound to be some versions of Stephen who sent the message I got, and who then 'got back' the message I sent. But he is simply dealing with the avatar in his reality. 'Out there' is every possible variation of Andrew, so some of them are bound to get his message, because there is a version of Andrew which gets every possible message. Stephen's message does not 'reach Andrew' in another solipsism. If it did, we would not be in solipsisms. Stephen makes determinate the message he sends in his reality. By doing so, he correlates his reality with all other realities in which an Andrew gets that message from a Stephen. And the you that you know yourself to be is only one of a vast, and possibly infinite, number of Stephens who send that message, all of whom are correlated with the Andrew (actually of course, a vast, and possibly infinite, number of Andrews) who get that message."

Andrew Soltau, not Crag Weinberg, wrote the explanation that I quoted here as it appeared in my last post. My apologies to all for this grievous error!



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