While statistically it is possible (or, in an infinite universe, certain) that another person will come into being in another place and/or time whose physical form and reactions to specific stimuli would be exactly the same as mine, in what sense would this identical personality be me if he had no memory of my experiences? Without continuity of memory, or at least connectivity of memory, there cannot be continuity of consciousness.
Dave
Well, you're obviously aware of the difference between possibility and probability, but lest someone take it too seriously, let me illustrate why we don't even have to worry about the continuity part.
I'm too lazy to calculate it all again, but, lucky me, in an infinite universe someone will have already written it. And it so happens it was me, in this thread:
http://www.internationalskeptics.com/forums/showthread.php?t=147003
A human brain has 100 billion neurons. On the average each has 7000 inputs. (The ones in the cortex more, of course, the others less.) It's estimated that a 3 year old has 10^15 such synapses, though the number decreases as you grow up.
Now the "strength" or sensitivity of a synapse is pretty much how your brain learns, and that's really an analogue number. But let's pretend it's an on-off affair, i.e., binary. I.e., we'll only model here which synapses broke off so far.
We'll also ignore that new connections grow in that self-reconfiguring FPGA.
(We'll _massively_ underestimate the information needed to reproduce that C(t) this way, but I kinda like the idea of an afterlife all of a sudden.)
So the information needed for even just that carricature of a model is basically 2 to the power 1,000,000,000,000,000. Read that carefully. It's not just a million billions, it's two to the power a million billions! Well, 2^10 is approximately 10^3, so that's approximately 10^300,000,000,000,000. Yes, you write a one and then 300,000,000,000,000 zeroes behind it.
Even assuming that some particles assembled themselves in the equivalence of a brain (already improbable), it would be one chance in 2^1,000,000,000,000,000 that it's configured like yours.
And again: that's just which synapses are completely off. If we go into more details it only gets more ludicrious.
So on the whole I wouldn't set my hopes too high there of it happening by chance. Yes, in infinite time it would, but in a universe that has a FINITE time before which it's unable to support life or any kind of using energy to control chaos, when I put my pragmatic engineer cap on, I wouldn't bet on it happening.
And in an infinite universe, surely someone has already calculated what those probabilities mean. Oh, look, it's me again on page 2 of that thread. What are the ODDS, man?
Let's do even more maths, to put those numbers into perspective.
IIRC the number of electrons in the observable universe is anywhere between 10^79 (for an average one atom of hydrogen per cubic metre) and 10^130 (how many spheres the size of an electron you can pack in it).
Let's say that each electron once a second would form a different configuration equivalent to a different brain. (Absurd, because one single electron isn't enough for a a brain, but let's be unbelievably generous with our upper limit.) Basically it's the "monkeys on keyboards" scenario with as many monkeys as electrons you could fit in the observable universe.
A year is 31 556 926 seconds, and let's give the universe a good 300 billion years for that experiment. That works out to about 10 billion billion seconds, or basically 10^19 seconds.
So if every single electron in the universe formed the equivalent a different brain configuration every single second, the universe would only have time to "try" a maximum of 10^149 different combinations. While your brain is one in 10^300,000,000,000,000 different combinations as shown earlier.
So I _really_ wouldn't set my hopes high of such a clone of your synapse configuration happening randomly.
So basically not only the odds are beyond negligible that another brain with the same memories happens before the universe pretty much dies, it's beyond negligible that even some cluster of particles will ever have the same up/down spin combinations as your brain's synapses are on or off.
We don't even have to worry about continuity basically. Because the moment where we have to worry whether it's continuity or coincidence will just never happen.