Pressure on Women

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This is the Mother’s Day talk that I delivered in sacrament meeting.

Elder Christofferson said (in General Conference, 2013), “Sisters, I don’t want to overpraise you as we sometimes do in Mother’s Day talks that make you cringe. You don’t have to be perfect; I don’t claim that you are (with one possible exception who is sitting nearby at the moment).”

(I think it’s true that the talks and lessons we give are more for the speakers and teachers than for the people listening. That’s true for my talk. I’m not a mother. As I prepared for this talk, the most I dared pray for was that I would be able to feel the Spirit to give this talk. That means that it falls on each of you to pray that you will be able to feel the Spirit too.)

Sometimes we talk about Sisterhood and Motherhood at the expense of the actual, living sisters and mothers in the congregation. I will try not to create unattainable ideals in this talk. First I want to share my thoughts on one of the ways that women put pressure on themselves. Then I want to share some thoughts about the pressure that society places on women. Finally I’ll talk about the pressure that the church puts on women.

Woman of Valor

Let me tell you a story from the book A Year of Biblical Womanhood by Rachel Held Evans. Chapter 4 is about Proverbs 31. Proverbs 31 is about a “virtuous woman,” or “Eshet Ḥayil” in Hebrew. It’s the chapter that says, “Who can find a virtuous woman? for her price is far above rubies.”

The author of A Year of Biblical Womanhood, Rachel, talks about how intimidating Proverbs 31 is for a woman. It lists a ton of virtuous qualities that a Christian woman is expected to have. And it made her feel inadequate.

She asked an Orthodox Jew about that chapter, and whether it intimidates her too. The woman, Ahava, responded with an email that got printed in the book. One of the things Ahava said was, “Every week at the Shabbat table, my husband sings the Proverbs 31 poem to me. It’s special because I know that no matter what I do or don’t do, he praises me for blessing the family with my energy and creativity. All women can do that in their own way. I bet you do as well.” Rachel continued, “I looked into this, and sure enough, in Jewish culture it is not the women who memorize Proverbs 31, but the men. Husbands commit each line of the poem to memory, so they can recite it to their wives at the Sabbath meal, usually in song…. Eshet chayil is at its core a blessing—one that was never meant to be earned, but to be given, unconditionally. It’s like their version of ‘You go, girl!’”

In the spirit in which Proverbs 31 was intended, we can read it and listen for any one thing that you are doing that makes the Lord pleased. If you hear any one thing in this list that you have done, you can pat yourself on the back and say, “Eshet ḥayil, woman of valor.” If your mom or wife has done one of these things, then whisper to her, “Eshet ḥayil, woman of valor.” A little mental game to play is to find a way that every one of these applies to your mother, even if you have to stretch the definitions a bunch.

Proverbs 31:10–31

10 Who can find a virtuous woman? for her price is far above rubies.

11 The heart of her husband doth safely trust in her, so that he shall have no need of spoil.

12 She will do him good and not evil all the days of her life.

13 She seeketh wool, and flax, and worketh willingly with her hands.

14 She is like the merchants’ ships; she bringeth her food from afar.

15 She riseth also while it is yet night, and giveth meat to her household, and a portion to her maidens.

16 She considereth a field, and buyeth it: with the fruit of her hands she planteth a vineyard.

17 She girdeth her loins with strength, and strengtheneth her arms.

18 She perceiveth that her merchandise is good: her candle goeth not out by night.

19 She layeth her hands to the spindle, and her hands hold the distaff.

20 She stretcheth out her hand to the poor; yea, she reacheth forth her hands to the needy.

21 She is not afraid of the snow for her household: for all her household are clothed with scarlet.

22 She maketh herself coverings of tapestry; her clothing is silk and purple.

23 Her husband is known in the gates, when he sitteth among the elders of the land.

24 She maketh fine linen, and selleth it; and delivereth girdles unto the merchant.

25 Strength and honour are her clothing; and she shall rejoice in time to come.

26 She openeth her mouth with wisdom; and in her tongue is the law of kindness.

27 She looketh well to the ways of her household, and eateth not the bread of idleness.

28 Her children arise up, and call her blessed; her husband also, and he praiseth her.

29 Many daughters have done virtuously, but thou excellest them all.

30 Favour is deceitful, and beauty is vain: but a woman that feareth the Lord, she shall be praised.

31 Give her of the fruit of her hands; and let her own works praise her in the gates.


Rachel Held Evans reported that they used that chapter as a blessing in their household after that conversation.

When my blog sold enough ads to become profitable, he looked up from the computer, smiled, and declared, “Woman of valor!” When I finally got around to cleaning out the guest room closet, he high-fived me and shouted, “Woman of valor!” When I stumbled through the front door after a long day with nothing but takeout pizza to show for dinner, he stretched out his arms in absolute delight and cried, “Pizza? Woman of valor!”

It’s amazing what a little poetry can do for a marriage.

Gender Bias

Let me switch subjects, and talk about one way that society places pressure on women. It concerns me.

Three days ago I gave a presentation at work about a new project that I’m pitching. I’m going to tell you the story that was on my first slide in that presentation.

There was a sociology study in 2012. Researchers sent out 127 résumés for a lab manager position. Half of the résumés were for men and half were for women. Then they collected information on how qualified the applicants were. Participants in the study said that the male applicants averaged at 4.0 out of 5 for competence. They said that the female applicants averaged 3.3 out of 5.

This study was super interesting, because they actually sent the same résumé to all 127 participants. The only thing they changed was that half of the résumés were for John and the other half were for Jennifer. Everything else was equal. And yet the female applicants were less qualified.

Participants were asked what they would pay the applicants. The average salary offered to a male was $30,200. The average salary offered to a female was $26,500. That’s what is known as the gender pay gap. I presented this information at work and then I presented a plan for how our business could combat that kind of bias.

Death by a Thousand Cuts

This world creates obstacles for our women. Little instances of resistance are everywhere, and they cut our girls. I worry that they suffer death by a thousand cuts.

One tiny incident was on a day I volunteered at the elementary school. The other volunteer split the class into pairs with one boy and one girl. Then he requested, “Girls, go to a table and wait. Boys, go get the heavy art bins at the back and carry one to your table.” Death by a thousand cuts.

A 2009 book described thousands of hours of research in elementary school classrooms, and the researchers measured that teachers would spend up to two-thirds of their time talking to boys. The teachers were more likely to interrupt girls and not boys. Death by a thousand cuts.

5 years ago I was in great a ward with a great bishop. When the kids turned 12, the bishop interviewed them. Then he presented them to the congregation and congratulated them on entering the young men or young women’s programs. He would say a word or two about each boy or girl. He would say how the young men were hard workers and good examples. He invariably said the same thing about each of the girls, though. He said they were beautiful. Every time a girl was graduating primary, I’d wait for it, and when he said that the young woman was beautiful, I’d wonder whether he wasn’t able to learn anything about their personalities, like he had done for the boys. Death by a thousand cuts. (I hesitated to tell this because I don’t want to make the bishop self-conscious. This happened five years ago, and he really was a good bishop).

Church Evolution

With that, I want to switch from talking about societal pressure, to talking about the pressure that women get from church.

I’ve spent some time at the temple contemplating what manhood and womanhood mean to me. The world outside tells us that there aren’t supposed to be any differences in the way we treat men and women. I have a lot of thoughts about how in the church we learn to treat the men and women very differently. Right now, the women are in the congregation. The men are up here, blessing the sacrament and leading the meetings. For me, trying to figure out what the purpose of those differences could be, is all very confusing.

When I was growing up, I saw the way the church meetings are run, and I just took for granted that that’s the way things should always be. Now I know that some of the things I took for granted are pretty modern inventions. There are scriptures that make me wonder, did God treat the genders differently at different points in history versus now? That seems possible. To take one example, there are references from the Bible about prophetesses. Miriam was a sister to Moses and she was introduced as a prophetess in Exodus 15. We don’t use the word “prophetess” in the modern church. Something has changed.

What if we go back just 100 years? A hundred years ago, we didn’t have the Proclamation on the Family yet. A hundred years ago, the Relief Society had the power to draw up their own curriculum, deciding what books and lessons to study. They had the power to spend their own budget. The women had the power to administer blessings of health. Now, in 2017, The Lord has said that all those jobs are only for men. Something has changed in the last 100 years—not the Lord, because the Lord hasn’t changed. But maybe something has changed in us.

I believe that the Lord needs to give some commandments that are temporary, for a certain time and place and circumstance. When the Lord commanded that the women in the Relief Society hand over their authority to the Presiding Bishopric, I think it’s worth considering that it could be a temporary change. Maybe someday the Lord will issue new commandments, and women will be given more autonomy and more leadership positions, like they had in the past. If you watch General Conference, you know that since the 1980s, the Lord has wanted women to speak to us in the general session. That was not always the case. That’s an example of how we believe in this church that the Lord needs to continuously give us new commandments, to update our knowledge, and steer the church in a better direction.

I don’t want to be the kind of person that tells girls that they can never hold certain positions in the church, because I don’t know what the future holds; only God does; and in the meantime, I’d prefer not to be negative. I just hope that, whatever happens, we are doing a good job of preparing our girls to reach their full potential, and become generals in the fight against Satan.

Sex Difference

More important than studying the things that have changed in the modern church, I have questions about what things have always been the same. What does God himself say about the sexes? What messages has God delivered eternally, to all his followers, across all eras and cultures?

There is a German saying that, “All stories begin with Adam and Eve.” So we’ll go back to the creation of the world, to the time when God created a garden in Eden. There were animals in the garden. And from the very beginning, those animals were divided into the male and female sexes. Something about the sex difference was important enough to God that it became part of the foundation of our world.

The interesting thing for me is not just knowing that there were males and females created by God in Eden, but in asking, what does God want us to learn from the fact that he divided up the animals into males and females? If God had wanted us to treat men and women the same, then he didn’t have to create that distinction in the first place. I am a believer that scriptures are given to us with a purpose. We don’t get scriptures revealed to us to tell us about Adam and Eve in the Garden of Eden, unless we also get a responsibility to study it, and to find out what God wants us to do with that information. So what does God want us to do with the information about males and females? There are probably a lot of answers. But I am totally inadequate to being able to address that question today. (I think it’s OK to ask questions that we don’t know the answers to).

Role Play

I do know that gender differences are hardwired into us from a very young age.

I substitute taught the 8-year-olds last week, and the lesson talked about setting apart someone with the Priesthood. “What is setting apart?” Some of the kids didn’t know. I asked a few to role-play it for the class. Three boys and one girl raised their hands to volunteer. They came up to the front of the room. One boy sat in a chair. The others gathered in a circle around him. And at that point, something felt wrong to all of them. They quickly rearranged so that the girl was in the chair and the three boys were standing. The boys spread themselves out in a circle around the girl. Then they all laid their hands on the girl’s head.

After that I asked them about all the decisions they made during the role play. Why did they need a single chair? Some of them didn’t know. Some suggested that it was a rule to give the blessing while standing and receive it while sitting. Someone else thought it was a rule for the boys to spread out evenly in a full circle around the chair. I gave an explanation that those things are normal but not required, because it’s an arrangement that just makes it easier for everyone to reach.

Why did they all put their hands on the person’s head? We talked about it for a minute. I don’t know why physical touch is important to the blessing, so I didn’t offer any explanation. We only know that Jesus sometimes did the same thing.

Even when the kids are too young to be told about the rules for giving blessings, they seem to notice all the rituals that we have. Kids mimic the adults, to a fault.

After talking about the other aspects of the role play, I asked about how they decided who should sit in the chair. I wanted to know about the shuffling that had happened. The kids said that the girl couldn’t be in the circle. So she had to be the one sitting down. Why couldn’t she be in the circle? Because she doesn’t have the Melchizedek Priesthood. I looked at those 8-year-old boys and I asked, “Oh, so you have the Melchizedek Priesthood?” They knew that was a silly question. The boys can get the Melchizedek Priesthood when they grow up. The girl will never be able to have the priesthood, so she didn’t belong in the circle for the role play.

Even when kids are too young to be told about the rules for giving blessings, they seem to notice that the boys are the ones who give blessings and the girls are the ones who watch. Kids learn what girls are capable of by mimicking adults. We show our women what we think their place is, by how we act and what we pay attention to.

Dangerous Ideas

Now, sometimes there are parents of 8-year-olds who must like to fill their kids’ heads with ideas. Our class last week had at least one parent who causes trouble. Because one student in the class raised a hand and said, “Actually, my mom has given priesthood blessings before. It’s something that girls are allowed to do in the temple. My mom worked in the temple. She got to give a special blessing to people and it uses the priesthood.”

I said, “Good point, Eden.” Because of course it was my daughter. You can bet that if there is a group of parents filling their kids’ heads with dangerous ideas, I’m going to be one of them.

I next asked the kids, “Who in this room is authorized to set people apart with a priesthood blessing?” They all answered that only I was, since I was the only Melchizedek Priesthood holder in the room. I clarified that even that wasn’t correct, because I hadn’t been authorized by the bishop to set anybody apart. If I went ahead and set someone apart without permission, then it wouldn’t be valid.

So the question of who is allowed to set someone apart gets pretty complicated, after you start talking through those issues. The interesting thing about that is the way that the kids strip away all that complexity. They didn’t summarize the rules by saying, “Only someone authorized can give blessings.” Instead, their world consisted of the simple rule, “Girls are not allowed.” It makes me wonder what we do and say as adults that causes the kids to see harsh battle lines drawn between the sexes. Of the dozen different ways kids could describe who has priesthood authority, they chose a mental model that leaves out the girls.


Eden was right. Girls can be allowed to give blessings. Women officiate in the initiatory ceremony in the temple. Women give an important priesthood blessing to the female initiates. For some reason we don’t talk about that very much in the church. Sunday School teachers sometimes accidentally say that only men can exercise the priesthood. When we say things like that, we are telling the women in our lives what they can’t do. It can sound like we’re telling women what we don’t want them to do. In 2015 the Church published an essay about women and the priesthood that explained, “The priesthood authority exercised by Latter-day Saint women in the temple and elsewhere remains largely unrecognized by people outside the Church and is sometimes misunderstood or overlooked by those within.”

With a little extra effort, we can find ways to speak that don’t limit the role of women to being subordinate to men. We can find ways to emphasize the things that we believe that women and men do together. The future mothers in the congregation are watching us very closely, and so I believe our efforts will be noticed. I have a testimony, that the priesthood power in our family is exercised by Elisa and by me together, as a partnership. I wouldn’t want my kids misunderstanding that priesthood power is something the guys do, alone.


As we honor our wives and mothers today, let’s make it a priority to be inclusive about what we believe about women, what they are allowed to do, and what we can praise them for. Let’s be careful about the thousands of ways that we tell women what they can’t do. Let’s watch for opportunities when we can get to know our boys and girls, so we don’t accidentally treat someone as flat stereotype of a typical boy or a typical girl. Let’s remember that husbands and wives are sealed together, and blessed to exercise priesthood power together. Let’s celebrate our favorite women with praise. Please find a chance today to say to the special women in your life, “Eshet ḥayil, woman of valor!”

The Infinite Library

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Jorge Borges’ “The Library of Babel” talks about an incomprehensibly large Library that contains every possible book. Even though there are 25 characters in the Library’s alphabet, Borges points out that transliterations or more complex encodings could represent any language. Each book is limited to exactly 410 pages. A shorter work could still be found in the Library, since later pages are allowed to contain only spaces. A longer work could presumably exist, although critics disagree about the best way that could be done. Very long books get to be important when working with any strange language where the Library’s meager alphabet needs dozens of pages for a single foreign phrase. A collection of serialized two-megapixel photographs would run into a book each.

Steven Peck proposed in A Short Stay in Hell that two books together could be considered as one large book. A character explained, “War and Peace would be in multiple volumes.” That is not accurate, strictly speaking, because there are some books that can exist in our Universe but not in that library. Imagine a monotonous book with three million repetitions of the letter “A.” This would take more than two 410-page books all filled with “A.” However, Peck’s library only contains one copy of each permutation, so two books that are both full of “A” could never be found.

The philosopher W. V. O. Quine noticed that repetition would be necessary to resolve the problem. In “Universal Library” he said that even if a library only contained two-inch strips of seventeen characters each, all literature could be expressed. Further, even if a library only contained a single dot and a single dash, their correct combination could create any book in Morse code or a binary encoding.

The totality of truth is now reduced to a manageable compass. Getting a substantial account of anything will require extensive concatenation of our two-inch strips, and re-use of strips here and there. But we have everything to work with.

The ultimate absurdity is now staring us in the face: a universal library of two volumes, one containing a single dot and the other a dash. Persistent repetition and alternation of the two is sufficient, we well know, for spelling out any and every truth.

Borges is deliberately ambiguous about the details of the Library and whether it has an end. Of all the different formulations of the Library, the most romantic descriptions are where every possible book exists, regardless of length. Quine’s repetition is unattractive, because a library with only two overused symbols is utterly lacking in mystery. We are already familiar with our Universe, where all books are assembled by humans. Quine’s use of intelligent composition makes the Library too much like our Universe. Borges foresaw the argument and mentioned that it is “blasphemous” (“blasfema“) for librarians to write books. The Library is interesting because it is the Library itself that has prepared all possible permutations. Logically, this should extend to large works. To honestly say that any 820-page book appears in the Library, it should be produced by the Library itself, with the two volumes naturally adjacent, not needing the intervention of a librarian.

Somewhere in the Library, two adjacent volumes can tell any possible 820-page story, just as one volume tells any possible 410-page story. That means that a given volume must appear an infinite number of times in the Library, but in different contexts, as part of an infinite number of larger works. A volume at the end of a shelf could be considered adjacent to the first volume of the next shelf, and the last volume in a gallery is followed by the first volume in the next gallery. It’s not obvious which gallery should be chosen to be next. The hallway leading to the nearest gallery cannot always be chosen, because a complete path ought to visit other floors. A strategy is needed that can collapse the several dimensions of character, line, page, volume, shelf, side, gallery, circuit, and floor into a single ordered list of coordinates. The tool for this is called a pairing function. A simple example is a sequence that visits all the neighbor galleries, left then right then above then below, and then recursively revisits each of those galleries in the same order while also visiting their respective neighbors. Within books, an order of left to right and top to bottom could be assumed, or a different exhaustive path could be chosen. This is a form of breadth-first traversal, and it gives the librarian an unambiguous way of stringing together volume after volume throughout the entire Library, although it still needs to be examined whether any one traversal is the “correct” one. Also, if a librarian wants an unambiguous way to determine where one multi-volume work stops and another starts, then an encoding scheme needs to be defined, but that issue will be ignored here since encoded representations are well understood and this essay is concerned with the organization of the Library’s information rather than its interpretation.

The size of this Library is now certainly unbounded. Not only are all the 2580×40×410 possible 410-page books present, but also all the possible multi-volume works that are 2580×40×410 volumes long and longer. Every volume has a volume that follows it in an unending sequence. Such a sequence is described by the technical term “disjunctive.” It is impossible for the sequence to be periodic, frustrating the narrator’s hope for a cyclical “Order.” There are many ways to arrange letters into a disjunctive sequence, and some can produce all sorts of heterogeneous structures for librarians to discover. However, in Borges’ story, there is only a mystical lack of structure. All the letters appear with equal frequency, and the books still don’t reveal any structure when interpreted as coded messages in other alphabets. Such a sequence is called by the odd name “absolutely normal.”

There are an uncountably infinite number of possible libraries that are absolutely normal. One simple example is that there are libraries where everything is uniformly random. Another possibility is a library that has a central gallery that contains all works of one letter, followed by all works of two letters, and so on, forever. That sequence is known as the Champernowne constant. Paradoxically, a random library must also have a gallery somewhere that contains all works of one letter followed by all works of two letters and so on for as long as a librarian could imagine following. There are no end of ways that the library could be organized, but it matters very little how it is organized, because every library can mimic every other. Although all the possible libraries are distinct from each other, they each contain arbitrarily large overlaps. Note that an arbitrarily large overlap is not as complete as an infinite overlap, which is what would be required to call two libraries equivalent. An arbitrarily large overlap is just enough to make it impossible for the librarians in any finite amount of time to prove or disprove a postulated order to the library.

With that theory in place, it is possible to investigate whether some paths through the Library will work better than others. The only criterion for a path to be admissible is that it must reach every work eventually. To illustrate the concern, suppose that a path only traverses a single floor. If the Library were generated with a random sequence, then that path would work as well as any other path. But if the Library were mostly random except for a single floor filled only with the letter “A,” then that path may be unlucky and never find anything except “A.” There would be other paths where the Library would behave absolutely normal despite the floor with fixed contents, because one floor has an infinitesimal effect on the Library as a whole. For the same reason, the probability of a librarian accidentally starting on that floor would be zero. A path that covers all galleries on all floors would eventually exit such an area of fixed contents and would be guaranteed to be absolutely normal. A more damaging scenario is if it were possible that the Library has fixed contents spaced out at intervals that frustrate the breadth-first traversal, but that exhibit absolutely normal behavior in some alternative “correct” path. For example, suppose that the correct path is a breadth-first traversal that skips every other gallery, and suppose that the skipped galleries contain fixed contents. Those fixed contents would not be part of the absolutely normal sequence, but they would poison the librarian’s breadth-first traversal. This example can be dismissed, however, since the correct path ought to visit every gallery eventually. The model is that the correct path was used by the Library to generate the books, and so galleries not on the path would therefore not have books. The question concerns the order of the galleries, not which galleries are included. That means that asking whether all paths are correct is equivalent to asking whether an absolutely normal sequence can survive permutation. Clearly it is possible to find a permutation that is not absolutely normal: replace every instance of “ABC” with “ACB,” guaranteeing that “ABC” never appears. But such a permutation could not be created accidentally, because absolutely normal numbers are so much in the majority that for every incorrect path there are an infinite number of correct paths. If the Library was generated randomly, then the probability of a particular breadth-first search being incorrect is zero. It could only have been incorrect if the Library itself had singled out that traversal to not contain all possible works. If that were the case, it would comprise a message from the Library to the librarians, showing them one path that is exceptional among paths. Since the Library fastidiously does not create order from the chaos, such communication is unrealistic. Therefore, the librarian is free to choose any path that traverses the entire library. It is known that any configuration of the Library will still have paths that do not contain every possible work, but they are outnumbered in infinite proportions by paths that will succeed.

An important detail about the Champernowne constant is that there is no proof that it is absolutely normal. So it may not meet the minimum requirements to be the mystical Library. Likewise, if all books were generated from the digits of tau (or pi), then it is conjectured to be absolutely normal, but no one really knows. Absolutely normal numbers are strangely elusive: it is known that there are an uncountably infinite number of them, (even more than the number of books in the Library), and it is known that almost all numbers are absolutely normal, but it took until 2002 for mathematicians to figure out how to come up with a single concrete example! This is one of those strange areas of science where simple ideas are maddeningly difficult to prove. A consequence of this is that it would be impractical for a computer program to generate the volumes that could appear in the library. The only deterministic process that has been discovered is prohibitively expensive. It would be necessary to cheat by using a sequence that merely gives the mystical appearance of being random. In the future, the state of the art may advance so that a computer could accurately simulate the Library.

Another paradox is that there must be a region in the Library where only the letters “A” and “B” and “C” appear. A librarian born in such an area would wander for a lifetime and never get an inkling that other letters existed. Likewise, the narrator could have been born in such an anomalous region. An enormous distance away there could exist an infinite number of books with a larger alphabet, or illustrated books in colorfully-painted galleries. It is allowed for the Library to have freedom with a countably infinite number of typefaces and of bindings and of any number of other characteristics, because the possible permutations would still be countably infinite. The important point is that it would be plausible for a librarian to describe an enormous region as having different letters from the narrator’s in Borges’ story, or as having a pattern that is not absolutely normal, yet the same Library can encompass both realities. This justifies the cheating that a computer would need if it generated a library. No librarian would be able to determine whether a given computer program is doing a good job or not, because there must be somewhere in the Library that mimics the computer’s output, however artificial it looks.

All these hypotheses allow one to accurately simulate the Library in our own Universe, such as the online “Library of Babel” does. A classifying system is necessary for distinguishing books and galleries. Borges uses natural numbers when describing “circuit fifteen ninety-four” (“circuito quince noventa y cuatro“). One possible catalog would start with an arbitrary pseudorandom gallery and call the first book #1, and continue numbering all books from that point. A pseudorandom sequence is already cheating because it is periodic. Jonathan Basile proposed using truncated entries from the quasi-random Halton sequence so that the library would be searchable, which is elegant and may one day be proved to be absolutely normal. Another possible catalog would fill all the books by using the digits of tau (or pi). Yet another possible catalog would locate a book that only contains the letter “A” and call that book “A.” The book next to it only contains the letter “B” and is named book “B,” and so on. After all the one-letter works would come the book containing “AA” and named “AA.” This library is generated by the Champernowne constant. This is the simplest ordering because each book near the start is named the same as its contents. Far enough away, when book names are already 80×40×410 characters long and books start to repeat themselves, the books can still be ordered by the length of the multi-volume work, and then in alphabetical order. The names then need a prefix to distinguish different copies of each book. Somewhere in the Library there must exist such a convenient ordering of books, so it is no trick to define a coordinate system with that gallery at its center. In fact, no matter what classifying system is desired, there is a gallery somewhere that acts as an appropriate origin and that follows the pattern for an arbitrarily large distance. The Champernowne constant is just as plausible a choice as the digits of tau (or pi) or of any given random sequence. This supports the story’s assertion of symmetry, “The Library is a sphere whose exact center is any one of its hexagons and whose circumference is inaccessible” (“La Biblioteca es una esfera cuyo centro cabal es cualquier hexágono, cuya circunferencia es inaccesible“). Even if the catalog is cheating, it is impossible for a librarian to ever catch it. Creating a catalog of the Library is therefore as easy a task as the author desires to make it. It is more of an artistic choice than a mathematical one. No matter what catalog a librarian invents, the Library obliges by providing a gallery somewhere that fulfills the catalog’s criteria.

In summary, the Library is a never-ending sequence that contains every possible work of every possible length. As long as there is one path through the Library that finds every work, any path is almost certain to succeed. Simulating the Library with a computer program is unfeasible with current technology, because not much is known about absolutely normal numbers. At present, computers must resort to cheating with sequences that are not guaranteed to include all works. As long as cheating is acceptable, no strategy is more or less plausible than the others, because every possible pattern appears somewhere in the Library.