The classic novel Slaughterhouse-Five by Kurt Vonnegut explores the concept of time as linear and unchanging. In it the main character, Billy Pilgrim becomes “unstuck” in time. His conscious mind moves back and forward through his life such that he experiences it out of order. He encounters an alien species that experiences all of time simultaneously. From them, he learns that human beings are oddly handicapped in being unable to experience more than one moment.
Vonnegut’s concept of consciousness is not that far off from Descartes’ dualistic view of the soul. In this concept, the soul carries a lot of information around with it giving it the sense of where it has been before. In reality, the mind is likely devoid of information, dependent on the brain to provide all knowledge and experience. This means that your mind could be moving around through time randomly but you wouldn’t notice because your brain would not be going with you. Your brain progresses, instead, according to the laws of thermodynamics to provide sensory experience and memory one moment after another.
For proof of this, if you were to develop a degenerative disorder where you lose memory and sensory abilities, your mind would cease to experience these. Brain injuries to short-term memory have been shown to cause people to experience time as disjointed.
If time is two-dimensional, however, there is the possibility of moving not only from past to future but from, e.g., left to right in time. Since the brain is localized in time and space, it is likely localized in the second time dimension as well, meaning that only one moment is experienced at any given time coordinates.
The difference is that we now can have multiple pasts, not just one. If we think of history as a line through space that all the atoms in our bodies follow, then in two-dimensional time that line becomes a plane or sheet.
Nevertheless, our conscious minds perceive neither the line nor the sheet directly but only the single moment. The line is inferred, of course, from memories of past events and a sense that more events will unfold in the future.
If we can infer the line, how do we infer the sheet?
Much depends on the nature of the sheet. We remember the past because of the 2nd law of thermodynamics. In a closed system, entropy must always increase. Entropy is equivalent to the amount of disorder in a system, but it is also equivalent to how much information a system stores. If a system is very ordered, then it cannot store much. For example, suppose I have three playing cards each drawn from three different decks. If I carefully arrange all those cards so that they are all the same, the ace of spades, they have low entropy. I can only represent 1 out of 52 possibilities. If, however, I allow them to be different cards, the ace of spades, the two of diamonds, and the jack of clubs, they can represent 3 times more information or 1 out of 156.
The flow of entropy from past to future is a law of our universe that we don’t quite understand, yet it is responsible for our perception of the flow of time and change. It is why we can store information about the past but not the future.
With two-dimensional time, to understand what that is like, we have to understand how entropy flows in two dimensions.
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