Before trying to catch up answering some of the previous posts (thanks for your nice words, Taffer, it's a pleasure to have these discussions with all of you), I would like to make some more general statements, to be able to refer to them later.
Definitions
Down to the pits of terminology and definitions:
A universe shall be, for the sake of this post, a totality of all that exists. Depending on the concept and definition, this does or doesn't include mathematics.
A world shall be, for the sake of this post, an entity that has no informational input after its creation, that is, a world is something for which physicalism is true.
I choose this definition to permit a simulated reality to be a world. Within a world, it is possible to simulate another world, which depends only on its "physical" laws and initial conditions; therefore, it received input only at creation time; on the other hand, such a simulated world has output, since it is possible to observe it.
So a world can be contained within another world, or be caused by another world, or depend on another world. A world that is not contained in another world (that doesn't depend on another world or exports information to another world) may be called a root world. This doesn't mean that there has to be a root world: it is conceivable that all worlds are contained worlds (imagine an infinite chain of worlds, one contained within the other).
The universe, according to this definition, has to exist. It is therefore useless to ask why the universe exists. But I don't know of any principle that could tell us how many worlds the universe contains. Since we exist, it must contain at least one world; but it still could be possible that the universe contains just one world, or infinite many of them.
This allows a reformulation of the question of the opening post: why does the universe contain at least one world, and not none?
The Anthropic Principle And Reasons To Be
If we assume that there are lots of different worlds, it is easy to explain why our world has conditions favorable for the development of life. This is no longer true if we assume that there is just one world: in this case, it is an open question why this world is favorable for the development of life.
Furthermore, we can imagine an alternative universe that contains no world. But since there is, per definition, only one universe, we can't pick and choose among different alternatives: we can't argue that among all those universes, one has to contain a world, since there is only one.
If we, based on whatever reason, rule out the possibility that randomness plays any role in the number of worlds the universe contains, then the number of worlds must be the number that it is, necessarily. There couldn't be more or less. But that is not an explanation: based on the assumption of missing randomness, we can assume that there must be a reason why there is the number of worlds there is, but that doesn't tell us the reason, so it doesn't provide us with an answer to the question why the universe contains as many world as it contains.
Alternative Physics
Case 1: Slight Variation
The image above shows a perpetuum mobile. It consists of a locomotive (a), and a pair of magnets (b), connected with a bar. The locomotive (called Emma), being made of iron, is attracted by the magnets and moves forward, thereby pushing the magnets.
Why doesn't this work in our world, but only in Lummerland? The magnets would be attracted by the locomotive, and therefore, the total system of locomotive and magnets would not move. This, it seems, is not just an accidental property of magnets; it is expressed in the idea that each actio equals an opposite reactio; more fundamentally, such a machine would violate the rule of conservation of energy. And that means that not only this specific, but any kind of perpetual motion machine is impossible in our world.
So although the variation of physics in this alternative world depicted above seems innocent and slight, it inevitably touches fundamental principles of our world.
Instead of saying "Any alteration of physical laws, be it as drastic as one wishes, is bound to be a mere cosmetic and superficial change", one could say: "even the most slightest and seemingly harmless change of physical laws leads to a world that is fundamentally different from our world".
Case 2: Synthetic Variation
This time, the image depicts an object of a world that looks far less familiar. This world is a certain cellular automaton, namely, Conway's Game of Life. It is an infinite orthogonal two-dimensional lattice with states of "on" and "off", and a rule to go from one discreet "tick" in time to the next. The image above shows a breeder, a structure moving to the right and leaving, like a puffer, a trail of guns, each gun shooting gliders. The pattern therefore shows quadratic growths.
It is also possible to built a pattern that replicates itself. It is also possible to built a universal turing machine (in fact, a universal computer has been built by Paul Chapman, although it is not a turing machine, but a Minsky Register Machine). If physicalism is correct and dualism is wrong, then it would be possible to built self-replicating, conscious beings within the world of life (although, one has to admit, it is uncertain whether natural selection would work very well within the Game of Life: small errors often have dramatic consequences, so a single mutation could not only kill its carrier, but an entire ecosystem; there are also problems with perception, since it is difficult within the world of the Game of Life to perceive something without destroying it).
It would also be possible to built a giant computer within the Game of Life that runs a giant simulation, one that simulates a world similar to our world — or maybe our world is just a simulation, computed on a machine that has been built in a world with the physics of the Game of Life.
Unlike the previous example, the physics of this world is not just the physics of our world, with some twist added. Instead, it is built from scratch. Therefore, it is no surprise that fundamental rules of our world, like the conservation of energy, don't hold in this world.
Edited to add: a missing "Case 2:"
Definitions
Down to the pits of terminology and definitions:
A universe shall be, for the sake of this post, a totality of all that exists. Depending on the concept and definition, this does or doesn't include mathematics.
A world shall be, for the sake of this post, an entity that has no informational input after its creation, that is, a world is something for which physicalism is true.
I choose this definition to permit a simulated reality to be a world. Within a world, it is possible to simulate another world, which depends only on its "physical" laws and initial conditions; therefore, it received input only at creation time; on the other hand, such a simulated world has output, since it is possible to observe it.
So a world can be contained within another world, or be caused by another world, or depend on another world. A world that is not contained in another world (that doesn't depend on another world or exports information to another world) may be called a root world. This doesn't mean that there has to be a root world: it is conceivable that all worlds are contained worlds (imagine an infinite chain of worlds, one contained within the other).
The universe, according to this definition, has to exist. It is therefore useless to ask why the universe exists. But I don't know of any principle that could tell us how many worlds the universe contains. Since we exist, it must contain at least one world; but it still could be possible that the universe contains just one world, or infinite many of them.
This allows a reformulation of the question of the opening post: why does the universe contain at least one world, and not none?
The Anthropic Principle And Reasons To Be
If we assume that there are lots of different worlds, it is easy to explain why our world has conditions favorable for the development of life. This is no longer true if we assume that there is just one world: in this case, it is an open question why this world is favorable for the development of life.
Furthermore, we can imagine an alternative universe that contains no world. But since there is, per definition, only one universe, we can't pick and choose among different alternatives: we can't argue that among all those universes, one has to contain a world, since there is only one.
If we, based on whatever reason, rule out the possibility that randomness plays any role in the number of worlds the universe contains, then the number of worlds must be the number that it is, necessarily. There couldn't be more or less. But that is not an explanation: based on the assumption of missing randomness, we can assume that there must be a reason why there is the number of worlds there is, but that doesn't tell us the reason, so it doesn't provide us with an answer to the question why the universe contains as many world as it contains.
Alternative Physics
Case 1: Slight Variation
The image above shows a perpetuum mobile. It consists of a locomotive (a), and a pair of magnets (b), connected with a bar. The locomotive (called Emma), being made of iron, is attracted by the magnets and moves forward, thereby pushing the magnets.
Why doesn't this work in our world, but only in Lummerland? The magnets would be attracted by the locomotive, and therefore, the total system of locomotive and magnets would not move. This, it seems, is not just an accidental property of magnets; it is expressed in the idea that each actio equals an opposite reactio; more fundamentally, such a machine would violate the rule of conservation of energy. And that means that not only this specific, but any kind of perpetual motion machine is impossible in our world.
So although the variation of physics in this alternative world depicted above seems innocent and slight, it inevitably touches fundamental principles of our world.
Instead of saying "Any alteration of physical laws, be it as drastic as one wishes, is bound to be a mere cosmetic and superficial change", one could say: "even the most slightest and seemingly harmless change of physical laws leads to a world that is fundamentally different from our world".
Case 2: Synthetic Variation
This time, the image depicts an object of a world that looks far less familiar. This world is a certain cellular automaton, namely, Conway's Game of Life. It is an infinite orthogonal two-dimensional lattice with states of "on" and "off", and a rule to go from one discreet "tick" in time to the next. The image above shows a breeder, a structure moving to the right and leaving, like a puffer, a trail of guns, each gun shooting gliders. The pattern therefore shows quadratic growths.
It is also possible to built a pattern that replicates itself. It is also possible to built a universal turing machine (in fact, a universal computer has been built by Paul Chapman, although it is not a turing machine, but a Minsky Register Machine). If physicalism is correct and dualism is wrong, then it would be possible to built self-replicating, conscious beings within the world of life (although, one has to admit, it is uncertain whether natural selection would work very well within the Game of Life: small errors often have dramatic consequences, so a single mutation could not only kill its carrier, but an entire ecosystem; there are also problems with perception, since it is difficult within the world of the Game of Life to perceive something without destroying it).
It would also be possible to built a giant computer within the Game of Life that runs a giant simulation, one that simulates a world similar to our world — or maybe our world is just a simulation, computed on a machine that has been built in a world with the physics of the Game of Life.
Unlike the previous example, the physics of this world is not just the physics of our world, with some twist added. Instead, it is built from scratch. Therefore, it is no surprise that fundamental rules of our world, like the conservation of energy, don't hold in this world.
Edited to add: a missing "Case 2:"