Hi Dummy Boy
You ask many questions (good). The first one is probably the more complex to answer, as it needs a bit of quantum mechanics, which is not needed for the UDA, but can be used to illustrate some of the, probably startling or disturbing (for some), consequences of Digital Mechanism (computationalism, comp, etc.). The second one is not so easy too, and probably needs a big part of ... the UDA.
My problem is that I have no idea of what you know about quantum mechanics. So we can work by approximation: I answer, and you ask further in case you are not satisfied.
To be sure, we don't need any answer to those two first question to proceed in the UDA, and so, if I answer them, it is more for the fun, and to ease your impatience. We might at some point create a "quantum mechanics thread" to dig deeper on that issue.
I see also you have edited four times the first post, I hope you will not edited it before this reply ...
Your first question is
Why does digital mechanism work "without collapse" and not 'with collapse'? In other words, what is the significance of "without collapse"?
Answer: in quantum mechanics we can add "classical physical states" and get a new physical state. The best known example is Schroedinger's cat. We can (and later I might explain how) put a cat in the state "DEAD + ALIVE". Here DEAD and ALIVE are the two classical states, and QM says that we can manage the cat to be in a state DEAD + ALIVE. By doing so we can predict correctly many results that we can obtain about possible observations made for the cat. In particular, if we decide to just observe if the cat is DEAD or ALIVE, we will see it DEAD or ALIVE with a probability equal to 1/2.
You might then think that the state DEAD + ALIVE is just in reality a classical state like "DEAD or ALIVE". The cat would be either dead or alive when in the state DEAD+ALIVE. Later I can explain why this will not work (we can do other observations on the cat which would contradict this). Yet, looking just to the state ALIVE/DEAD, we do find the cat either alive or dead.
Today, there is no unanimity among physicists, about what means DEAD+ALIVE, and what happen when we look at the cat. But there are two main very different answers. I will call them COPENHAGEN and EVERETT. "Copenhagen" is the standard answer, very often exposed in the textbook. It says that when we look at the cat in the state DEAD+ALIVE, the observation destroys the state "DEAD + ALIVE" into either the state DEAD, or the state ALIVE, with the probability 1/2. This works fine in practice, as indeed subsequent observation will not lead to contradictions. But there is a big problem: the wave equation, which is the core of Quantum Mechanics, does not allow this to happen. This means that the observation cannot itself be described by the wave equation, and somehow it leads to the idea that QM describes differently the observed and the observers.
The vocabulary is that the wave "DEAD+ALIVE" collapses into DEAD, or collapses into ALIVE, with the relevant probability.
This has led to many different explanation why it could be like that: from: - 'the macroscopic device does not obey to the wave', to - 'consciousness does not obey to the wave'.
But such kind of explanations by "collapse" have many drawbacks, and "COPENHAGEN" appears to be like a rule of thumb that nobody understands. It cannot be used in field theory, quantum cosmology (where the wave is applied to entire galaxies or black hole), quantum computing, etc.
In 1957, Everett proposed a much simpler explanation. It consists very simply to apply QM, purposefully to, not just the cat, but to the entire system of the observer looking at the cat. In that case the wave equation describes the following. If *YOU* look at the cat, in the state DEAD+ALIVE, the wave describes:
YOU * (DEAD + ALIVE) = YOU*DEAD + YOU*ALIVE.
With YOU*DEAD = YOU in front of a dead cat, and YOU*ALIVE = you in front of the alive cat.
The superposition (as the "+" is called, here) of the cat state becomes contagious to its environment, including the observer. This leads to a ... "parallel reality". It explains why "YOU" found the cat in either a dead, or an alive state, despite the superposition has not disappear (as the wave describes).
Now you can see the relation with COMP. Looking at a superposition state (like DEAD+ALIVE), duplicates yourself in two examplars "You seeing the cat alive" + you seeing the cat dead". Everett makes the QM probabilities, similar to the probabilities we can find with "usual" (non quantum) duplication of a person.
I hope this can help a little bit.
Your second question:
How do universal numbers relate to "many dreams"?
There is one thing, already explained a bit to kedabra in his thread, which will be tough to explain to you; not because you are a dummy, but because it asks for some work. A part of that work is needed for UDA step 7, and a bigger amount is needed for step 8 (but the whole thing is needed only for the Arithmetical UDA, not for UDA itself).
So a short answer is that a universal number is just a computer. logicians have discovered the computer in arithmetic, well before the engineer build sort of physical approximation of them in "nature". How could a number acts like a computer? Well, I will not try to explains this here and now, but we will come back on this. Just keep in mind that a universal number is just a 'mathematical" computer, and a computation done by that computer will appear to be related to a sequence of number. If you assume computationalism, when you dream (or even are awake), your brain/computer (by assumption) does a computation, and some subjective experience (the 'dream') can be associated to that computation.
Then it is possible to define (and build) a universal dovetailer. This is a program which makes the computer generating all possible programs (virtual machines) and executing them all, by a dovetailing procedure (that I will explain probably in step 7). That is: one program generates all possible computations. That will give the many dreams.
SL, why do you set apart quantum teleportation and digital teleportation? What's the difference? I wonder why the original has to be destroyed?
Well, again, this is not needed for UDA. Just keep in mind that in classical teleportation (like in UDA) you are scanned, destroyed, and reconstituted elsewhere, BUT: you don't have to be destroyed. In Quantum teleportaion, a completely different technic is used, based on the existence of the quantum superpositions, and it happens that with such technic we have to destroyed the infomartion. This we can explain and discuss later, it is more demanding on Quantum Mechanics.
Here's a stupid question:
Let's say Jack is pasted a year later. During that time the solar system has moved a long distance through space. Does Jack's different place in the cosmos have any effect on the infinite numerical associations going on in Jack's brain?
As you notice, the answer should be "no", as the movement of the solar system can't change the content of the information that has been read during the scanning. Of course, fater the reconstitution, if Jack look at the star, he might slowly realize that some time has gone through. The point is that without such evidences, he cannot be aware of any delay. OK?
Maybe I'm just a dummy, but there seems to be a 100 percent, 1st person chance that X- Jack will end up in W, and a 100 percent, 1st person chance that X- jack will end up in M.
You are right, but this is a third person description of the situation. After the duplication you are in W, *and* you are in M. But from the first person point of view of 'both of you', you feel like you are in only one city. In W, the you in W, feels being in W and has only intellectual knowledge that he has a doppelganger in M, and vice versa. The probabilities we are interested in are the one bearing on the future first person points of view. You know in advance, (because you assume comp) that whatever happens in that experience, you will feel to be in only one city, with some doppelganger in the other city. And you cannot predict which one in advance, as if you say "W", you know that the guy in M will refutes this, and vice versa. If you iterate that experience (with both of "you" coming back from W and M, and redoing the same experience), there will be four stories:
described in each individual diaries. None of them could say "I am WM, and I predicted this in advance". All right? In fact, in this case, the probability to be the one with the "story" "WM" is 1/4 (if you accept the 50/50 for the single duplication) OK?