Organizing the Bible and the Talmud


My latest blog post for The Jewish Journal:

Do you know what it says in the Book of Deuteronomy, Chapter 8, verse 3?

Unless you’re a rabbi or a savant, you probably don’t. Neither do I. But we know how to look it up. We just open the Torah, turn to the Book of Deuteronomy, and flip to Chapter 8, verse 3.

In ancient times, people couldn’t do that. There were no chapters or verses in the Bible.

If you wanted to refer to a passage, you just quoted it and hoped that your listeners knew its origin. You might have told them which book of the Bible you were talking about, but that was as much as you could do.

People needed a certain level of Biblical literacy to understand what you were talking about. Some of them, like most people today, just didn’t have it. They were left out of the conversation.

That got easier in the 13th century CE, thanks to the efforts of Stephen Langton, who was the Archbishop of Canterbury in England. He worked through both the Tanakh and the Christian scriptures, and divided the text into the chapters and verses we (both Jews and Christians) use today. Now, if we want to refer to a Bible passage, we need only give the book, chapter, and verse.

Langton is better known in history for his role in forcing King John to sign the Magna Carta, which limited the powers of the king and gave rights to the people. Back then, “the people” meant mainly the landed nobility. However, the idea evolved over the centuries to mean that ordinary people had rights the government should not violate.

Therefore, Langton changed history in two ways: He gave us a new way of looking at the Bible, and he gave us a new way of looking at the relationship between people and their government. Langton’s principled stands got him into trouble first with King John and then with the Pope.

Despite his scholarship, Langton’s parsing of the Biblical text is not perfect. One strange division occurs between the two creation stories given by the Book of Genesis. The first creation story occupies all of Chapter 1 and the first three verses of Chapter 2. It has a cosmic viewpoint and refers to God as “Elohim.”

The second story occupies the rest of Chapter 2 and Chapter 3. It has a ground-level viewpoint and adds the Tetragrammaton to God’s name. Langton knew it, but for some reason decided not to put the chapter break at the end of the first story.

The Talmud also benefited from Gentile assistance. The page layout we use today originated in the 16th century with a Catholic printer in Venice, Italy. Before then, the text of the Talmud and the text of commentaries often appeared in separate documents copied by hand. That made it more difficult to flip between them for reference and study.

Venice did not allow Jews to own printing presses, so we had to depend on Christian printers to print the Talmud and other books. Daniel Bomberg, a Christian printer from Belgium, printed a complete edition of the Babylonian Talmud and used the layout that is now familiar. The Talmud text is the middle column, Rashi’s commentary is on one side of it, and additional commentaries (Tosafot) are on the other side.

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Biblical Writers Were Math Nerds


My latest blog post for The Jewish Journal:

We normally look to the Bible for morals, religious inspiration, and history. But are you excited to learn that there’s some mathematics in there, too?

If you’re a nerd like me, the answer is yes. It’s very exciting. Only chocolate syrup and whipped cream could make it better.

Most people’s favorite number is pi because it’s one of the only things they remember from geometry class in school. Pi is the ratio between the circumference and diameter of a circle, about 3.14159. The decimal digits actually go on forever because pi is irrational, meaning it can’t be written as a ratio of whole numbers. One book explains that:

“An almost cultlike following has arisen about pi. Web sites report its ‘sightings’, clubs meet to discuss its properties, and even a day on the calendar is set aside to celebrate it, that being March 14, which coincidentally is also Albert Einstein’s birthday.” (Pi: A Biography of the World’s Most Mysterious Number)

The Bible refers to pi in two places. They seem to give the same number for pi. However, their wording differs slightly, by just one letter. The Vilna Gaon thought the discrepancy concealed a mystery.

The first reference to pi is in 1 Kings 7:23:

“Then he made the tank of cast metal, 10 cubits across from brim to brim, completely round; it was 5 cubits high, and it measured 30 cubits in circumference.”

The ratio of the circumference to the diameter gives pi a value of 3. Kind of close, but not very.

The second reference in 2 Chronicles 4:2 is almost identical, but the Hebrew text omits the letter “heh” at the end of the word (qof, vav, heh) for circumference.

And there’s where the mystery arises. Using gematria, the Vilna Gaon calculated the first spelling’s value as 111 and the second as 106. Dividing 111 by 106 gives 1.0472. Multiplying the Bible’s pi value of 3 by 1.0472 gives — wait for it! — 3.1416, which is the rounded value of pi. Just as you’d expect if, as some scientists argue, “God is a mathematician.”

The Bible has some other mathematical references, but that one is the most interesting. And as long as we’re talking about the Ancient Near East, the Egyptians had a neat way to calculate the area of a circle, and that also gives a value of pi.

You might remember that the formula for the area of a circle is pi times the square of the radius, and that the radius is half the diameter.

Ancient Egyptians didn’t have a science of mathematics, but they had a lot of practical tricks to calculate land areas for surveying. To calculate the area of a circle, they drew a square whose sides were eight-ninths of the circle’s diameter. Then the area of the square was close enough to the area of the circle that they couldn’t detect any difference.

And if you work it out, they had a value for pi that was, like the Bible’s, pretty darned close:

  • The diameter of a circle is two times the radius, so each side of the square was 8/9ths times twice the radius, or 16/9ths times the radius.
  • The area of the square was 16/9ths of the radius multiplied by 16/9ths of the radius, which gives 256/81 times the radius squared.
  • And 256/81 equals 3.1605, a little off the rounded pi value of 3.1416. But as they say in Washington DC, “it’s close enough for government work.”

If the Egyptians had thought of their method as a mathematical formula, theirs was 3.1605 times the radius squared — very close to ours.

Other Biblical references to mathematics are little strained. In life, the Golden Ratio (1.618..) occurs frequently, especially in art and architecture. In the Bible, Exodus 25:10 says that God commanded Noah to build the Ark of the Covenant measuring 2.5 by 1.5 cubits, and 2.5 divided by 1.5 is 1.666. Some writers say it refers to the Golden Ratio, but unless the Vilna Gaon came up with something like he did with pi, it doesn’t look like it to me.

And the Bible just doesn’t have my favorite number, Euler’s number (2.71828..). I’ve learned to live with that little disappointment.

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Tisha B’Av Turns Tragedy into Victory


My latest blog post for The Jewish Journal:

“They tried to kill us. We won. Let’s eat.”

According to the late comedian Alan King, that’s the explanation of most Jewish holidays.

It’s particularly relevant to the fast day of Tisha B’Av, which is a few days from now. On Tisha B’Av, we mourn the destruction of the First and Second Temples, along with other tragedies that have befallen our people.

But this year, the approach of Tisha B’Av has me thinking of — Dunkirk. A big-budget movie about it is scheduled for release next summer.

If you’ve never heard of Dunkirk, or what makes it significant, don’t worry. About half of the U.S. population thinks that World War II occurred shortly after the Civil War. You’re way ahead of the game if you can find France on a map.

In May 1940, the German Army trapped 10 divisions of the British Army at Dunkirk, an area in the North of France that was directly across the English Channel. Hitler ordered the Luftwaffe to destroy the British forces, which had no way to escape from the French coast back to England. If the Luftwaffe had succeeded, Germany might have won the war.

Instead, the British people set sail in their own private boats — fishing boats, cargo ships, rowboats, anything that could make it across the channel and back — to rescue “their boys” from the beaches of Dunkirk. Almost 800 boats made the trip, over and over, under heavy fire from German planes and artillery. They rescued almost 340,000 British soldiers from certain death. Many of the rescuers died in their heroic mission.

By military standards, the Battle of Dunkirk was a crushing defeat. But “Dunkirk!” became a symbol of British people’s courage, unity, and determination to prevail against any odds.

I’m sure you see where this is going. If anything on earth has preserved the Jewish people for millennia, it’s courage, unity, and determination to prevail against any odds. Tisha B’Av, just like Dunkirk, takes something bad and turns it into something good.

According to our tradition, the first tragedy to occur on Tisha B’Av was in 1313 BCE when the Israelites failed to trust God during the Exodus. As a result, they had to wander for another 38 years before entering the promised land. On Tisha B’Av in 423 BCE, the Babylonians destroyed the First Temple, and on the same date in 70 CE, the Romans destroyed the Second Temple. It was on that date in 1290 CE that our people were expelled from England and on the same date in 1492 that they were expelled from Spain.

We must allow tradition a bit of poetic license, since archaeology finds no evidence of the 1313 event and says that the First Temple was destroyed in 586 BCE instead of 423 BCE. Only about 2,000 of us were expelled from England, peacefully, and the Spanish expulsion edict wasn’t issued on Tisha B’Av. The value of a religiously helpful story trumps (pardon the expression) a few minor factual inaccuracies.

Tisha B’Av, just like Dunkirk, shows how a people can turn tragedy into victory by telling a new story about it and giving it a new meaning. Instead of being a weakness, the tragedy becomes a source of strength:

“A story told by English Jews, perhaps apocryphal, tells of a prominent nineteenth-century British politician who was walking near a synagogue on Tisha B’Av and heard wailing coming from inside. He looked in and was informed that the Jews were mourning the loss of their ancient Temple. Deeply impressed, the politician remarked, ‘A people who mourn with such intensity the loss of their homeland, even after two thousand years, will someday regain that homeland.’” (Joseph Telushkin, Jewish Literacy, p. 669)

What applies to groups also applies to individuals. You can turn your personal tragedies into victories by telling yourself a new story about them: a story in which you are no longer a passive victim but are instead a survivor, who suffered but became a better and stronger person as a result.

They tried to kill us. We won. Let’s eat (just not on Tisha B’Av).

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Is It Moral to Have Children?


My latest blog post for The Jerusalem Post:

The question is strange but not crazy: Should we have children? Are there cases when we shouldn’t?

Judaism and common sense agree that generally we should and sometimes we shouldn’t.

But there are bigger issues involved. In her book The Risk of a Lifetime: How, When, and Why Procreation May Be Permissible, philosopher Rivka Weinberg seems to over-think all of them.

The essence of her argument is that life can be pretty darned awful, and we should not impose that risk on an unsuspecting would-be child without sufficient moral justification. Two things can justify it:

  • Correct motivation: You should have “the desire to engage in the parent-child relationship as a parent.” She argues that you can’t do it to benefit the child because the child doesn’t yet exist, and you may not do it to benefit society because that treats the child as a means to something else.
  • Reasonable risk: Having children “is permissible when the risk you impose [on the child] would not be irrational for you to accept as a condition of your own birth.” This is a fancy re-statement of Rabbi Hillel’s advice: “If you wouldn’t want it done to you, then don’t do it to anybody else.” Philosopher John Rawls made a similar argument more generally in his classic book A Theory of Justice.

I don’t mean to make light of Weinberg’s arguments. They’re totally legitimate from a philosophical point of view. Anything we do should be justifiable in principle, even if we rarely get challenged to justify it. However, it would not occur to most people that activities in which we have engaged since the dawn of the species require justification, unless some obvious harm is involved.

The big-picture answer to Weinberg’s concern involves trees, forests, and what it means to believe in God, if you do.

Which is real, the trees or the forest? Most people today unconsciously think that only the trees are real. The forest is just something we made up.

Likewise, contemporary attitudes enshrine the individual person’s desires and welfare above all else, even above biological reality. As a result, the idea of having children to benefit nation, society, or family seems vaguely suspect, perhaps even fascist.

But in fact forests do exist, albeit not in the same way as individual trees. So do nations, societies, peoples, and families have an existence beyond that of their individual members. It’s just as reasonable to consider the welfare of society or the Jewish people as to consider the welfare of an individual not-yet-conceived child who might have a pleasant life or a difficult one. And valuing the welfare of the child as an individual is entirely consistent with also valuing the contributions he or she might make to society.

But what about God? Where does He come into the equation?

Well, if you’re an Orthodox believer, it’s pretty straightforward: “To sire children is to fulfill a mitzvah, the Biblical commandment ‘Be fertile and increase.’ … to avoid having children is to negate a Divine commandment.” (To Be a Jew: A Guide to Jewish Observance in Contemporary Life)

If you’re not an Orthodox believer, it’s a little more complicated but not impossibly so. What does it mean to say that you believe in God, if God is a Being utterly transcendent and incomprehensible?

Believing in the existence of dogs or houses is easy: You can see them and understand them. If you say “I believe in the existence of houses,” it’s perfectly clear what you mean. But believing in God isn’t like that. You can’t see God and you can’t understand Him. If believing in God means anything, it means that you believe the universe is moral and that good is more powerful than evil.

A moral universe means that the chance of a child’s life being good or bad is not 50-50: It’s more likely to be good (in some way) than to be bad. Under normal circumstances, not having children more probably deprives them of goodness than subjects them to evil.

Of course, circumstances aren’t always normal: Even the Bible has God warning Jeremiah not to have children because of the dire fate they would suffer (Jeremiah 16:1-4). If you’re in a war zone or would pass on a hereditary disorder, you have to think seriously about the risks for your child.

But in circumstances that are more benign, having children is not only moral but is a blessing: to them, to you, to the Jewish people, and to the God who loves them.

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“Why is everybody wrong except me?”


My latest blog post for The Jewish Journal:

“These are the times that try men’s souls,” wrote American founder Thomas Paine.

Our own times are more likely to try people’s patience than their souls. We can’t stop shouting at each other. If it’s not about the presidential election, it’s about Israel. If it’s not about Israel, it’s about Ukraine. If it’s not about any of those things, it’s about who gets to use which bathroom.

Many people today are full of passionate intensity, and not only, as William Butler Yeats said, “the worst.” Good people, educated and reasonable, disagree about issues of consequence. In the most tragic cases, argument descends into bitterness. Friendships and family relationships are sundered.

We cannot eliminate disagreement, nor should we try. But if we understand why we disagree, we can minimize the bitterness and become more tolerant of others.

Consider an example that’s on many people’s minds: Who should be elected president? There are two main choices. Choosing one requires assessing the candidates’ personal character, the merits of their proposed policies, and how accurately they understand the world.

Most of us rely on the campaigns’ carefully crafted images and sound bites to assess the candidates’ character. We assess their policies based on what we think is desirable, moral, and achievable. We decide the latter mostly through memes and mental images, but also with one eye on what our peer group regards as acceptable opinion.

In the best case, you and a friend disagree. You both respect evidence, respect each other, and sincerely want to discover the truth. You both start with unreliable information, simplified mental pictures, and biases about issues of which you have little or no first-hand knowledge. Your most fundamental beliefs are so much a part of you that you don’t even realize you hold them.

Think about it. Is Hillary Clinton or Donald Trump a good person? A bad person? Given that a small army of propagandists stands between you and them, how sure can you be? Should you support policy X? Making that decision requires you to understand policy X, know the relevant facts, predict reliably about X’s results, and assess its morality when all factors are considered.

If you have a day job — or even if you don’t — you probably can’t do it. At best, you can learn a few things to support what you believe on instinct. And what you believe on instinct is influenced dramatically by your brain.

The troubling fact is that human intelligence didn’t evolve to analyze and evaluate complex political or economic issues. It evolved to help us survive and pass on our genes to the next generation. Period.

Biologists call it “the evolutionary legacy principle:” Our brains evolved to cope with prehistoric and pre-technological situations. We use essentially the same cognitive methods to cope with modern situations, and it often works poorly for them.

The biggest single flaw in our cognitive machinery is “us versus them” thinking.

In small primitive tribes, it was helpful to cooperate with “us” and to be hostile or suspicious toward “them” — that is, toward outsiders who weren’t members of our group. Compassion was reserved for other members of our own group, since compassion toward outsiders could get us or other group members killed.

In modern societies, it’s much more difficult and much less useful to decide who is “us” and who is “them.” But our caveman cognitive machinery still putters along as if nothing had changed. If we feel that people who believe X or support candidate Y are “them,” then we tend to disbelieve anything they say. We consider them so despicable or morally unworthy that their feelings and welfare are unimportant. Then we are in danger of becoming cruel and vindictive, as are they.

Our best option is to remember that all of us have flaws and biases, but none of us deserves to be presumed evil and unworthy of consideration.

Let’s listen to each other, pay attention to each other’s concerns, and respect even those with whom we strongly disagree.

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Pianko and Peoplehood


My new blog post for The Jewish Journal:

Are we not one people, but many?

Today’s Jewish population is incredibly diverse. World Jewry includes people of all races and nationalities. It includes “honorary members” such as interfaith spouses and children who are not Jewish and don’t intend to convert. We disagree, often bitterly, about belief and observance. The headline “Orthodox rabbi says Reform isn’t Jewish” has become a regular occurrence.

It’s hard to find the unity in all that diversity. Some influential writers say we shouldn’t try.

We commonly think that Jewish peoplehood is an old idea, but Jewish Studies scholar Noam Pianko argues that it’s a new one. In his book Jewish Peoplehood: An American Innovation, he traces the term’s origin to American Zionist Mordecai Kaplan in the 1940s.

Kaplan wanted to build support for Zionism, and until 1942 he did it by talking about Jews as a nation. However, he worried that calling Jews a nation would invite accusations of dual loyalty. He needed an alternative term without the anti-Semitic implications. By 1948, “peoplehood” had become his term of choice. Pianko observes that it was hardly used at all before then, and it did not appear in English dictionaries until the late 1960s.

In Pianko’s view, the idea of peoplehood was too closely related to that of nationhood. It misled us into looking for a Jewish unity that wasn’t there. To replace it, he proposes “peoplehood in a new key” that doesn’t require unity.

Instead of asking who is Jewish, what values unite us, and how we differ from non-Jews, he would ask what we do in the Jewish community and what parts of Judaism are meaningful to us. Pianko sees it as a decentralized “neighborhood model” of Judaism:

“A neighborhood model [seeks] to build collective consciousness by recognizing the organizing power of specific groups to develop different, and sometimes even mutually incompatible, visions of what it means to be part of the Jewish people. A sense of connection to a larger entity is generated most authentically— and enduringly— from the bottom up.” (Jewish Peoplehood)

“Different neighborhoods, with incompatible values, doing different things.” That suggestion made me uneasy. It sounded too much like something from another book, this one by renowned biologist Ernst Mayr:

“What happens in the isolated population? There may be new mutations, certain genes may be lost owing to accidents of sampling, recombination results in the production of a diversity of new phenotypes … The isolated population will diverge increasingly from the parental species. If this process continues long enough, the isolated population changes enough to qualify as a different species.” (What Evolution Is)

In biology, the neighborhood model results in the evolution of new species and the possible disappearance of the parent species. In the case of the Jewish people, it might not work out that way, but the analogy is uncomfortably close.

To understand each other, people must have something in common. To be loyal to each other, they must have a relationship. Explicitly separate Jewish neighborhoods, doing different things and holding incompatible values, do not have that kind of relationship. They will not long remain united by nothing but a name. Soon, the name itself will disappear. And then what is left?

Why should we care if our people continue to exist as a distinct group? Does it really make a difference?

Yes, it makes a big difference. Goodness in human life never appears in the abstract. It always appears in specific social, religious, and historical contexts.

Our people and tradition have brought goodness into the world in unique ways that no other group can replace. For us to give up existence as a separate people and forsake our unique tradition would deprive not only us but everyone else in the world of something precious that only we can provide. “Peoplehood” might be a new word, but our people have been around for millennia. That’s not new at all.

All humans band together in groups that provide a safer, richer, and happier life than being alone. It gives both our families and us as individuals a better chance to survive and prosper. Our ancestors struggled to give us that chance. We should pay it forward to our children and to the generations that follow.

Political philosopher Edmund Burke said it well: “History is a pact between the living, the dead, and the yet unborn.”

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Gloomy Gus Mendelssohn


My latest blog post for The Jerusalem Post:

Do we survive bodily death?

There are reasons to think so, but nothing that qualifies as proof. Perhaps the most sensible attitude (because it’s mine) is that if we do survive death, then we’ll find out someday. If we don’t survive death, then we’ll never know, so it won’t bother us.

A kind of proof was offered by Moses Mendelssohn (1729-1786), the German Jewish philosopher whose fame was such that he was nicknamed “the Socrates of Berlin.”

However, Mendelssohn seemed so distressed by the subject of death that it reminded me of another nickname: “Gloomy Gus,” applied to people who obsess about the negative side of life.

He wrote about death in his 1767 book Phaedo, or Concerning the Immortality of the Soul (Phädon oder über die Unsterblichkeit der Seele). “Phaedo” refers to a dialogue by Plato in which Socrates, while he is dying, discusses the issue with his students.

Mendelssohn has two main arguments for the immortality of the soul. The first is metaphysical, but since it’s both complicated and unconvincing, I won’t inflict it on you. Immanuel Kant gives a fairly good summary of the argument in his Critique of Pure Reason (B-413).

The second argument is where Mendelssohn turns into a Gloomy Gus of major proportions. His argument isn’t very convincing either, but at least it’s interesting and you can understand what he’s talking about.

He seems to worry about death a lot more than a psychologically healthy person should:

“During happy times, the dreadful thought of nonexistence winds its way through the most delightful representations like a snake through flowers, and poisons the enjoyment of life. During unhappy times, such a thought dashes a man to the ground in complete hopelessness …”1

His basic argument, as far as I can tell, is this:

  1. If death is the end of us, then life is our ultimate good.
  2. If life is our ultimate good, then we have a right to do whatever is necessary to protect and prolong our lives.
  3. Each country has a right to demand that its citizens sacrifice their lives for their country.
  4. Our right to life conflicts with our countries’ right to demand that we sacrifice our lives.
  5. There are no irresolvable conflicts of rights.
  6. Therefore, death is not the end of us.

In this argument, Mendelssohn deduces a metaphysical conclusion (the soul is immortal) from a moral conundrum: if the soul isn’t immortal, then there are conflicts of rights.

The problem is that all of his premises are highly debatable. He might believe in them, but they require a lot more argument to convince anyone else.

I’m not sure that Mendelssohn himself thought his argument was valid. He might have thought that belief in immortality promoted happiness and moral behavior, so it was justified for him to use heavy-breathing rhetoric to convince people it was true.

In his “Open Letter to Lavater” (1769), he said that when truth conflicts with the social good, we should sometimes support the social good instead of the truth:

“Whoever cares more for the welfare of mankind than for his own renown will keep a rein on his opinions concerning … erroneous religious opinions that are accidentally connected to the promotion of the good.”2

Mendelssohn seems to have been a wise man: indeed, wiser than we might think from reading his shaky argument in favor of human immortality.

Works Cited

Gottlieb, M., editor (2011), Moses Mendelssohn: Writings on Judaism, Christianity, and the Bible. Lebanon: Brandeis University Press.


  1. Gottlieb, M. (2011), p. 246. 
  2. Gottlieb, M. (2011), p. 12. 
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