Supposing there is nothing in the universe outside of time, such that everything that can exist (the "universe"), exists in time, and that time has no beginning or end, then we can make some statements about eternity. If time itself has a beginning and an end, then there is no eternity. We cannot know whether eternity exists, but if it exists we can deduce its possible structures.
We can deduce that, if eternity exists, the three possible types of generally non-random eternities are linear, circular, and spiral. We can deduce that we exist in a generally non-random universe, because we observe that the universe changes, at least some of the time, non-randomly. Each state of the universe is correlated to a prior state in a way that preserves information, for at least our epoch. So if eternity exists, it is generally non-random at least some of the time.
A linear eternity is one in which whatever has happened before, never happens again in exactly the same way. One can roll snake-eyes twice in a row, or a million times in a row, but the universe changes in countless ways between each roll of the dice. Cycles can exist, but the universe never repeats the same pattern of successive states, unless for a finite period by random happenstance. Generally, the universe never obtains exactly the same state as any prior state. However, if the universe is finite while time is infinite, it is inevitable that prior states will be replicated in the future. In a linear eternity, there is no predictable pattern to replication, if replication occurs. Occasionally, randomness or something indistinguishable from randomness must occur between successive states, breaking correlation of the state to its parent state. For example, at the instant of a big bang, randomness (or some other force, e.g., "infinite creativity" or "free will") can give rise to a new and different cycle unlike any previous cycle.
A circular eternity is one in which each state of the universe is repeated forever and ever at successive times. For example, every "big bang" is followed by a "big crunch" (or by some other destiny), after which there is a new big bang and everything that happened in the earlier universe is replicated exactly again. A never-ending series of big bangs each leading to an everlasting expansion and nested inside one another is another example of a circular eternity. This would be a structure a bit like a perpetual ripple on the surface of a pond. Whatever its structure, the characteristic feature of a circular eternity is that every state that the universe obtains is identically repeated at successive later times. There is no randomness because every state of the universe is perfectly correlated to every other state. There is no randomness, no creativity, no free will; only the pulsing of a never ending wave.
A spiral eternity is one in which states of the universe are repeated in successive cycles, but each successive cycle differs from its most recent prior counterpart in some correlated way. There is loss of information between cycles injected by forces such as randomness or free will, but not a total loss. The next cycle remains a recognizable child of its most recent parent. Like the linear eternity, there is no discernible pattern to replication (if replication occurs); like the circular eternity, successive cycles are discernibly related.
Besides linear, circular, and spiral eternities, eternity could also behave like combination of these types, for example linear sometimes, and circular or spiral sometimes, but in the ultimate analysis it must be one of these three. This conclusion follows from the starting assumptions that time has no end, time is necessary to enable change, and that at least some changes in the universe are not random. If time has a beginning but no end, then the eternities are the same as for time without beginning or end, once begun. If time has an end but no beginning, that is an impossibility. Although we can deduce the possible structures of eternity, we cannot discover empirically whether or not eternity is linear, circular, or spiral.
We (i.e., finite beings) cannot ever know by empirical science whether eternity is linear, circular, or spiral, or whether eternity exists at all. No matter how long our period of scientific observation endures, it is always finite. Therefore we can never know whether what we observe will remain so forever, or only for a temporary phase. For example, if we observe the universe expanding, we cannot know that it will never contract later on. If we see entropy always increasing, we cannot know that universal laws will not change so that entropy seems to be always decreasing during some future time.
To empirically determine the structure of eternity, it would be necessary for a part of the universe to exist outside of time, and for communication to be possible between the part of the universe subject to time, and that part outside of time. More on this in a subsequent post.
Knowledge of whether eternity exists, and if it exists is linear, circular or spiral, are rather small examples of knowledge beyond all possible reach of empirical observations. For convenience, we might refer to things that we know must be real, but cannot be known scientifically, as holy things. This is not inconsistent with the biblical meaning of "holy." In the biblical sense, holy means set apart from the mundane, empirical world.
In modern times, most people spend almost no time thinking about or discussing holy things. It feels a bit strange and useless. Many people profess the rather bleak belief that everything about our existence can be known empirically, but this belief cannot be true. There are many things that logically must be real, but cannot be known empirically. For example, we can know we exist, but we cannot know whether we exist in a time dimension that is eternal, or if eternity exists, whether its structure is linear, circular, or spiral. Although logical hypotheses about eternity are not empirically testable, they are no less logical for that. And being no less logical, they are no less possible and true.
Mathematicians have spent a great deal of time thinking about infinities, if not eternities, and practical applications have even been developed from such thinking. Mathematical infinities are not exactly the same as eternities, however. Eternities deal with the destiny of the universe, and the human race as part of that universe. Holy eternities have a special significance to ethics, because eternities enmesh related concepts like free will, predestination, and destiny, that are important in ethics. In other words, metaphysics is not entirely useless. In future posts, we will attempt to derive some use from it.
