While Augustine was working on his book On the Trinity, he was walking by the seaside one day, meditating on the difficult problem of how God could be three Persons at once. He came upon a little child. The child had dug a little hole in the sand, and with a small spoon or seashell was scooping water from the sea into the small hole. Augustine watched him for a while and finally asked the child what he was doing. The child answered that he would scoop all the water from the sea and pour it into the little hole in the sand. ‘What?’ Augustine said. ‘That is impossible. Obviously, the sea is too large and the hole too small.’ ‘Indeed,’ said the child, ‘but I will sooner draw all the water from the sea and empty it into this hole than you will succeed in penetrating the mystery of the Holy Trinity with your limited understanding.’ Augustine turned away in amazement and when he looked back the child had disappeared. The Child By The Seaside: A Medieval Story About Saint Augustine
… what Gödel’s famous proof shows is that arithmetic can’t be formalized. Any formal system of arithmetic is either going to be inconsistent or incomplete … any formal system that is rich enough to express arithmetic will have a proposition which is true and unprovable. Rebecca Goldstein
Marisol was bothered by her dream, the same dream she’d had for the past several weeks, a dream of anxiety because she could not accomplish an important task no matter how hard she tried.
The odd thing was that she knew she was dreaming but that knowledge did not alleviate the stress she felt. The dream was about a book, an assignment from a teacher that was required for the final course in the last class she needed to graduate. That made no sense. She graduated long ago, was not taking any class and was not under the guidance of any teacher. Or, so she thought. She was aware of this even while she dreamed but it gave her no relief. She had this enduring sense of unease whether she was asleep or awake.
Because the book was central to the dream, it occurred to Marisol that she should try while dreaming to find out as much as possible about the book. Even a sentence or two might give her a hint as to what she was supposed to glean from this dream that had taken over her life.
The problem was that when she dreamed she saw only blank pages and when she was awake the book, but not the anxiety, disappeared.
Marisol took long walks to sort out this mystery that eluded her. How could she be so bothered by a dream, by a book with blank pages and a story that disappeared whenever she tried to grasp its meaning?
On one particular walk Marisol encountered a strange building in the shape of a hexagon. Above the entrance in capital letters each separated by a period was B.L.O.B. She immediately became curious. Ten stairs led to the entrance. When she stepped on the first stair, a new stair emerged between the first and second stair. Thus, she found herself still ten stairs from the top and one eleventh of the way to the top instead of one tenth. As she continued to climb this odd phenomenon continued so that the absolute distance (in number of stairs remaining) to the entrance remained the same while the relative distance (in percentage of stairs remaining) diminished in an orderly fashion. Needless to say, Marisol was confused by this odd situation. She wondered if there was some similarity between the stairway and her dream.
She reversed course and stepped down. Immediately the step just below her disappeared and this continued until she was back on the ground having taken exactly the same number of steps down as she took up. The distance to the top remained at ten stairs.
Marisol knew there must be some lesson to be learned, something related to her dream. That night her dream slightly changed. Something about Zeno’s paradox crept in. She was convinced that she had made progress and her anxiety diminished.
The next day Marisol returned to B.L.O.B. This time the stairs were gone. She was able to walk right through the front door. It was odd but Marisol had grown accustomed to oddities since the dream had taken over her life.
When she entered, Marisol stepped into a space that formed a giant beehive with hexagonal cells (or rooms) leading in all directions, up, down, left, right. Whichever cell (or room) she chose appeared to be at the center of an infinite space of identical cells.
“Welcome to the Library of Babel,” said a disembodied voice. “You may have heard about the library from a man called Borges. Every book that has been, every book that will be, every book that could be is housed here. Each cell (or room) in the library (of which some believe there is an infinite number) is presided over by a teacher who is a specialist in the books of that cell. One such teacher you have encountered in a dream. That is why you are here. A healthy library is like a beehive. If you destroy one cell, everything else survives, not only survives but in the case of this library reconstitutes the cell that was destroyed. An unhealthy library is a sack tied with a knot. Once a hole appears anywhere, all the books and teachers fall out.”
When she fully realized what the voice told her, Marisol was at first confused and then terrified. She gazed into infinite darkness as the library was not well lit. This (almost) infinite library contained all of Marisol’s past and all of her future—her entire life. Theoretically it was possible for her to discover the totality of her life, but mathematically it was almost impossible. An equivalent event would be for the pieces of a shattered glass to reassemble into an unshattered glass. It could happen but it was very, very unlikely.
Marisol was sure the meaning of her dream was shelved somewhere in this library. She was so repelled at first by the thought that the entirety of her life lay on a shelf somewhere in the strange Library of Babel that she tried to leave, but she was confronted once again by the strange stairs. There were ten stairs down, but with each step she took another stair appeared. The absolute distance to the ground remained at ten stairs while the relative distance based on the number of steps taken diminished in an orderly fashion. It was impossible to leave.
Marisol reversed direction. She resolved to return to the library and search for the book of her life no matter how unlikely it might be that she would find it and no matter what the book might say. She managed to reenter the cell (or room) of her first encounter in the library. She knew immediately that the teacher in this cell was not the teacher from her dream, so she moved on to another cell without even looking at the books. She continued in this organized fashion and she continues still. Marisol’s dream became her life.
Like the Sisyphus of Camus, Marisol ultimately accepted her fate. During her endless search, she came upon a book by Calderon de la Barca, La Vida es Sueño (Life is a Dream).
¿Qué es la vida? Un frenesí. What is life? A frenzy.
¿Qué es la vida? Una ilusión, What is life? An illusion,
una sombra, una ficción, A shadow, a fiction,
y el mayor bien es pequeño. And the greatest good is small;
¡Que toda la vida es sueño, For all of life is a dream,
y los sueños, sueños son! And dreams, are only dreams.
Acceptance gave her sort of peace in the face of the absurdity of life. Her search was unending, futile, but in that search she found happiness and ultimately relief from her anxiety.
Living is only a dream and experience teaches me that a man who is living dreams what he is until he awakens. Life is a Dream, Calderon de la Barca