1928 - Alderson High School - 1968

 

A. A. MEETS A PARADOX

Alice Ann Asbury

PROLOGUE

Recall that when Boozer and Three Eight Ball were camping out in Saw Mill Hollow in search of Big Foot, Boozer fell down a rabbit hole and found himself in Wonderland where he met Alice Ann Asbury, the twin sister of A. A. Asbury. It wasnít long after that that Boozer ďbumpedĒ into Alice at the Big Wheel in Alderson.

Boozer: Youíre Alice arenít you? I guess you found your way out of Wonderland.

Alice: Yes, but Iím not sure that it all wasnít just a dream.

Boozer: Same here. I woke up the next morning in my sleeping bag and I donít know how I got out of Wonderland. However, I do remember you, so something strange must have happened somewhere between the two of us.

Alice: I guess so. By the way, I spoke with A. A. about a week ago and I am now positive that he is dead.

Boozer: I donít understand, if you spoke with him, surely he is alive.

Alice: Well, not really. I went to a friend of mine who is a medium and she was able to put me in touch with A. A.

Boozer: Come on Alice, you must be kidding.

Alice: Well, I didnít believe it either at first, but A. A. told me things about our childhood that the medium couldnít possibly have known.

Boozer: O.K. Did he say anything about Wireís teeth?

Alice: Yes, he is very disappointed that he let the Freemasons of Alderson down. As you know, A. A. was killed in Scotland and this put an end to his search for Wireís teeth. A. A. told me that after his death he found himself in a strange land, where he met an old man that he called the Librarian. The Librarian told A. A. that if he could complete a simple task successfully, then he would tell A. A. where to find Wireís teeth. Letís have dinner together and Iíll tell you about the task that A. A. was to complete. Since the story involves the thoughts of A. A. and since the conversation is between A. A. and the Librarian, Iíll tell it to you that way.

A. A. MEETS THE LIBRARIAN

A. A. knew that he was dead and he didnít know exactly where he was. A. A. also knew that he had been wandering around for a couple of years since he died, but this didnít bother him since he was at peace with himself and quite content. A. A. thought that maybe his magic underwear had worked and he was on a planet that he had been given to rule. While A. A. was pondering this and reflecting on his life, he was approached by a frail old man who appeared to be hundreds if not thousands of years old. The old man, who had a flowing white beard, was dressed in a golden robe and he walked with a long staff.

A. A.: Hello, where am I?

Old Man: Where you are makes no difference. I know you from past history.

A. A.: Past history?

Old Man: Yes, I know how you were killed in Scotland and that you were on a quest to find Wireís teeth. After your death, the fact that a clue to the location of the Treasure of King Solomonís Temple was hidden in Wireís teeth became known throughout the world. Many countries and groups of people were interested in his teeth and over the next 200 years many hundreds of expeditions were launched in search of Wireís teeth. Many searches were launched by The Catholic Church, by the Freemasons, by the Illuminati, by Scientologists, and by Middle Eastern Countries, to name just a few. None of the searches were successful.

A. A.: 200 years? But isnít this 2011?

Old Man: No, you are in a different world now and 200 years have passed since you died. Itís now early 2211, but you will have no memory of the passage of time from 2011 until now.

A. A.: What is your name?

Old Man: I am called Librarian. I am the keeper of all the books that have been written in the Universe since the beginning of time. Come with me and I will show you the library.

At this point the Librarian waved his hand and, as if by magic, they found themselves in a very large building. A. A. had never seen as many books before, and he was stunned that so many books could be collected and held in one place. A. A. was amazed that the Librarian could point to a book and it would float off the shelf and slowly settle in his hand.

Librarian: I have a task for you to do.

A.A.: A task?

Librarian: Yes, I want you to do a library search for me. If you can complete it successfully, then I am prepared to tell you where you can find Wireís teeth. But remember, the task must be carried out exactly, exactly as instructed with no exceptions.

A. A.: What kind of search?

Librarian: Well, the library contains several catalogues each of which is a list of books and each book on the list tells of a particular search for Wireís teeth. These books were written over the past two centuries by various groups who were searching for his teeth. For example, one of these catalogues is a list of all books in the library that were written about the searches for Wireís teeth launched by the Catholic Church from 2011 through 2050. Another catalogue is a list of books in the library that deal with those searches conducted by Iran from 2175 through 2200.

A. A.: You mean each of the catalogues contains nothing else, just a list of books?

Librarian: Nothing other than a short introduction explaining what the catalogue contains.

A. A.: I see. You want me to make a list of these catalogues for you?

Librarian: Well, not exactly. Some of the authors of the catalogues decided to list their own catalogue in the catalogue they compiled.

A. A.: What do you mean?

Librarian: The catalogue that lists books that deal with the searches for Wireís teeth by the Catholic Church from 2011 through 2050 lists itself. The author, realizing that her catalogue itself was a book about these searches included its own name in the list.

A. A.: The catalogue lists itself?

Librarian: Yes.

A. A.: What about the catalogue that gives a list of books dealing with searches conducted by Iran from 2175 through 2200, does it list itself?

Librarian: No, it doesnít.

A. A.: O.K., so what do you want me to do?

Librarian: I want you write a new catalogue which is a list of all the catalogues in the library that deal with searches for Wireís teeth that do not list themselves. Name it the Catalogue of Catalogues that do not List Themselves, write a short introduction to the list, bind the list together with the introduction, leave one copy in the library and bring me a copy. When you have completed this task successfully, I will tell you where to find Wireís teeth. I know that you will communicate with your twin sister Alice Ann sometime in the future through a medium, so if you complete the task successfully, then you can tell her where to find Wireís teeth.

A. A.: But how could you know that that I will communicate with Alice in the future?

Librarian: Oh, I know, donít worry about that.

A. A. was excited about the task the Librarian had given him, so excited that he danced a little jig as he began to make a list for his Catalogue of Catalogues that do not List Themselves. He felt confident that he could complete such a simple task successfully. If the Librarianís prediction of the future was correct, he could tell Alice where to find Wireís teeth and she could pass this information on to the Freemasons of Alderson. A. A. spent the next year completing his catalogue of catalogues and when he finished he went looking for the Liberian. A. A. spotted him sitting on what appeared to be a small cloud hovering above the ground. A. A. climbed a set of stairs leading to the cloud, where the Librarian invited him to take a seat.

A. A.: Well, Mr. Librarian, Iím finished with the task.

Librarian: O.K., letís see what youíve got.

A. A.: Hereís a bound and complete list of all appropriate catalogues in the library that do not list themselves. As you instructed, I named it The Catalogue of Catalogues that do not List Themselves. Also, as instructed, I have written a short introduction and bound it with the list.

Librarian: Did you put a copy in the library as I instructed and does your catalogue list itself?

A. A.: Yes, I put a copy in the library, and no, my catalogue does not list itself.

Librarian: Iím sorry, but you have failed to complete the task successfully.

A. A.: What do you mean? I have done everything exactly as instructed.

Librarian: Your list is incomplete!

A. A.: But it is complete. I am sure that I found every catalogue in the library that lists books dealing with searches for Wireís teeth. My catalogue of catalogues lists only those catalogues that do not list themselves and I am sure that my list is complete.

Librarian: No, itís not, think about it.

A. A. thinks to himself, this old man is trying to put one over on me. I know that I finished the task correctly, but I donít want to antagonize him. Maybe I can convince him later that I am correct.

A. A.: Well, ok, but I still think that I am correct.

Librarian: You must reflect on this task and see if you can understand why you didnít complete it successfully. Since you were unable to complete the task successfully, I canít tell you where to find Wireís teeth. However, I will give you your own planet to rule. Good luck to you.

As A. A. was about to leave the Librarian, he turned and spoke again.

A. A.: Does the task present a trick problem or is it some kind of paradox?

Librarian: Itís a paradox, a very fundamental one.

A. A. was disappointed and he still didnít understand why he hadnít completed the task successfully.

ALICE EXPLAINS EVERYTHING

Back at the Big Wheel Alice and Boozer continue their conversation.

Alice: Remember that I told you that I spoke with A. A. about a week ago; well, he also told me that he was unable to complete his task successfully. The Librarian didnít give him any clues as to how it could be completed, but the Librarian did tell him that it was a paradox.

Boozer: But itís 2211 where A. A. is, so how were you able to speak with him since itís only 2011 here?

Alice: Well, I donít understand that either. It must be some kind of Einsteinian time warp thing. Donít you remember the little jingle, there was a young lad named Bright who traveled faster than light. He departed one day in an Einsteinian way and came back on the previous night. Maybe, itís something like that.

Boozer: O.K., I guess that could happen, but do you understand why A. A. was unable to complete the task?

Alice: Yes, I have thought about it quite a bit and I think I do. Remember that A. A. was instructed to leave a copy of his Catalogue of Catalogues that do not List Themselves in the library. Remember also that he told the Librarian that his catalogue of catalogues did not list itself. So A. A.ís catalogue of catalogues is a catalogue in the library that does not list itself. So if the list within his catalogue of catalogues is to be complete, it must list itself.

Boozer: Why didnít A. A. just add the name of his catalogue of catalogues to the list within the Catalogue of Catalogues that do not List Themselves while he was with the Librarian?

Alice: Well, if he did that, then his catalogue of catalogues would list itself, so its name wouldnít belong on the list of Catalogue of Catalogues that do not List Themselves.

Boozer: Let me see if I understand this correctly. Since A. A.ís catalogue of catalogues does not list itself, its name belongs on the list within his catalogues of catalogues. But if the name of his catalogue of catalogues is on this list, then it lists itself and so its name doesnít belong on the list. This just leads us in circles: if the name is not on the list, then it must be on the list and if the name is on the list, then it cannot be on the list.

Alice: Exactly! That Librarian is a sneaky old devil. His task cannot be completed successfully, so I guess that we wonít be able to tell the Freemasons of Alderson where to find Wireís teeth.

Boozer: Well, at least A. A. got his own planet to rule.

Alice: Yes, I guess that A. A. did benefit from the experience, but itís disappointing that the search for Wireís teeth must continue. Do you think Wireís teeth will ever be found?

Boozer: Probably not.

Alice: It just goes to show that not all problems can be solved, even when they appear to be very simple!

Boozer: Yes, we can often be trapped by our own logic, and it can sometimes lead us to behave like a cat chasing its own tail.

Alice: Exactly, but sometimes considering a paradox can lead to great fun and, as Hercule Poirot would say, ďto an exercise for the little gray cells.Ē

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