In his article, published in the May 2003 edition of Scientific American, Tegmark explains that scientists are currently discussing four distinct kinds of parallel universes. He refers to the Level I multiverse as “the least controversial type.” As I understand it, this level is based on the idea that space is infinite even though only a small portion of it is currently visible to us. Even though the visible universe grows by one light year each year, we will never be able to come even close to seeing it in its entirety since it is without end. Because it is so vast, some physicists now speculate there are not only universes just like ours out there, but, as Tegmark explains, they are themselves as endless as space; “There are an infinite number of other inhabited planets, including not just one but infinitely many that that have people with the same appearance, name and memories as you, who play out every possible permutation of your life choices.”4 Assuming the uniform distribution of matter indicative of our universe is typical, cosmologists go so far as to predict your closest doppelganger is 10 to the 1028 meters away, and at 10 to the 1092 meters away there exists a solar system identical to ours, and at 10 to the 10118 meters away is an entire universe just like ours.
The Level II multiverse is considerably different than the Level I. In this model space is thought of as a mostly endless batch of rising dough containing bubbles in which a variety of universes exist. Because the dough continues to rise these bubbles grow farther and farther apart from each other so that it is impossible for us to ever see or visit them, even if, as Tegmark calculates, “you traveled at the speed of light forever.” What is interesting about Level II universes is the speculation that many, if not most, of them may operate under different physical laws than ours does. Some physicists theorize that our universe may have initially had nine dimensions that all functioned in symmetrical proportions. As the universe developed, however, only three of these dimensions participated in the cosmic expansion, which became our visible universe. The other six dimensions remain unseen.
The Level III multiverse also stands out from both the Level I and the Level II. In this multiverse, scientists speculate our universe is constantly branching into multiple other universes in which every possible outcome occurs. If you role a die, for example, and get a one, there are also at least five other universes in which you rolled a two, three, four, five and six. The difference between Level I and Level III multiverses is that in Level I your doubles simply live elsewhere in three-dimensional space. But in the Level III multiverse they live in another quantum reality altogether.
The Level IV multiverse may at first seem rather boring as compared to these others. It is the notion that every mathematical structure “corresponds to a parallel universe.” Tegmark himself refers to this as a “radical Platonism” that asserts these mathematical structures are physically real, though they exist outside of time and space. Although, for many of us, it might not seem like it would be much fun living in one of these mathematical universes, this may be just the sort of universe we need to explore from time to time if we’re going to get the bird’s eye view of reality. Many philosophers have speculated that truth is subjective, which is to say that for the frog on the lily-pad it doesn’t really matter that the stone has created a ripple effect because the frog can only experience one ripple at a time.