Showing posts with label Exodus. Show all posts
Showing posts with label Exodus. Show all posts

Friday, August 2, 2019

The Weight of Mystery


In the popular 1981 action film, Raiders of the Lost Ark, Indiana Jones battled Nazis seeking the lost Ark of the Covenant. As described in the Bible, the Ark was a gold-covered box of acacia wood with a lid of solid gold, built as a container for two stone tablets on which were written the Ten Commandments. It was carried ahead of the people during the days in the wilderness when the Hebrews were en-route from Egypt to Canaan. But when it wasn’t in-transit, it sat in the inner sanctum of the Tabernacle and, later, the Temple in Jerusalem.

A Seemingly Simple Question

The instructions for how the Ark was to be constructed are provided in Exodus 25:10-22. A few weeks ago I was reading a commentary on Exodus and, thinking about the slab of gold forming the lid and all the other gold used in its construction, I had a very simple question: How much would it have weighed? Could it have been easily carried by four men?

It seems like it should be easy to calculate an answer. We know the density of acacia wood (0.54 g/cm3) and gold (19.3 g/cm3). Exodus 25:10-22 provides dimensions for the Ark’s length (2.5 cubits), width and height (both 1.5 cubits). But how long is a cubit?

A cubit is the distance between elbow and fingertips and the definition varies in different cultures and time periods (anywhere from 17.5 to 20.8 inches). A commonly-cited value is 18 inches (45.7 cm).

My thinking is that the Hebrew artisans who built the Ark for Moses would have learned their craft in Egypt. We know the length of the ancient Egyptian cubit from measuring rods discovered in New Kingdom tombs that are roughly contemporary to the time the Exodus is supposed to have taken place. The Egyptian cubit is about 52.4 cm so I’ll use that as the base measurement. This gives me 131 cm (51.6”) for the length and 79 cm (31”) for the width and height.

I am now able to calculate the surface area but to calculate the volume I’ll need to know the thickness of the wooden walls and Exodus doesn’t provide that measurement. Neither does it tells us the thickness of the solid gold lid nor the dimensions of the cherubim atop the lid.

Scene from Raiders of the Lost Ark. You can actually purchase a kit (http://goldenarmor.com/arkhomepage/) that allows you to build a replica of the prop from the movie


Feast of the Assumptions

What have others come up with in estimating the missing dimensions? A simple Google search for “how heavy was the ark of the covenant” returned wildly varying answers.

WarrenMyers is one of the first results that pops up in Google, which is unfortunate because his assumptions are unsupported and his math is questionable. For example, he assumes the walls are 2” thick but calculates the wooden part of the Ark weighs only 25 lbs (based on Myers’ assumptions my math says the wood should weigh over 240 lbs). He estimates 104 lbs for the cherubim and guesses 1/32 inch (0.8 mm) for the thickness of the gold plating, eventually determining a total weight of 615 lbs.

Another of the top hits, JacquesGauvin uses some ridiculous assumptions. He assumes 3” thick walls, making the wood portion 413 lbs. His carrying poles are 6” diameter, more like fence posts. His cherubim are 1000 lbs. He guesses 0.125” (3.2 mm) for the thickness of the gold plating. His Ark finally weighs in at a whopping 4763 lbs. That’s more than twice the weight of all the gold Exodus 38:24 says was used in construction of the entire Tabernacle!

These two examples illustrate a couple of points: 1) unconstrained assumptions can vary wildly and 2) gold is the major determining factor in the weight. In Gauvin’s example, even if the weight of the acacia wood is reduced to almost nothing, you would still have an Ark weighing in excess of two tons due simply to the amount of gold used in his estimates.

Scientific Wild-Ass Guesses

A more thoughtful exercise is taken by ElihuSchatz. I found his Jewish Bible Quarterly article well after I had already started working through the issues on my own and was pleasantly surprised to see that Schatz had also identified gold as the key factor. Schatz’s Ark weighs in at 183 lbs mainly because his gold overlay is only 0.2 mm thick. But unlike the wild guesses of Myers and Gauvin, Schatz arrived at this thickness through deduction.

Exodus 38:24 tells us that 29 talents and 730 shekels of gold were used in the construction of the Tabernacle. This includes not only the Ark, but also an incense altar, table, lampstand, and the walls of the Tabernacle.A talent was 3000 shekels and archaeological evidence tells us a shekel weighed 11.3 g. In modern measures, 994 kg (2187 lbs) of gold were used for all the items in the Tabernacle.

Schatz writes (p. 116), “I calculated the total weight of the gold for all the vessels [in the tabernacle], and had to use a thickness for the gold overlay of 0.02 centimeters in order to approximate the value.” He cites the calculations made in his commentary (in Hebrew) on the book of Exodus, so I’m not able to see how he arrived at his conclusion but independently I had run some numbers on my own and arrived at the same figure. I originally was concerned that it might be too thin and would scrape off, but subsequent research told me that 0.02 cm (0.2 mm) is twice the thickness of the side of an aluminum can, so it seems that a gold overlay of that thickness would be durable.

I do have quibbles about some of Schatz’s other assumptions. For example, he estimates the walls of the Ark were 1.0 cm thick. This seems too flimsy and 2.0 cm would be more realistic. An article from the Metropolitan Museum of Art references (p. 130) an ancient Egyptian royal coffin from 2680 BCE “made of plywood, the six layers arranged with the grain running in alternate directions for strength and to prevent warping.” Each of the six layers was an eighth of an inch thick, giving a total thickness of ¾” (1.9 cm).

Also questionable is Schatz’s assertion that a 1-mm layer of gold for the cover “would have sufficient structural strength” (p. 117) to hold up his 25-kg (55 lb) cherubim. Gold has about the same elasticity of aluminum. A 1-mm piece of gold the size of a stick of chewing gum could be easily bent in your hands, so I have my doubts about its structural integrity. The inner coffin in King Tut’s tomb is made of solid gold with a thickness of 2.5-3.0 mm. My reasoning is that the ancient Egyptian goldsmiths knew what they were doing, so 3 mm seems a more realistic estimate for the thickness of the Ark’s cover.

On the bright side, I consider Schatz’s estimate of 25 kg for the two cherubim realistic. I base this on the fact that King Tut’s famous gold mask is 54 cm tall and 39 cm wide and weighs 10 kg. For comparison, the angels on the Raiders prop are 16.5” (42 cm) long and 8.75” (22 cm) tall. I think the cherubim may have been standing figures instead of crouching as in the angels from Raiders. The cherubim may also have been bigger than what the moviemakers had in mind. No one knows. But I think an estimate of 25 kg for the two cherubim puts us in the right neighborhood.


Multiple views of King Tut's gold death mask.

Putting it All Together

To arrive at an estimate for the weight of the Ark, I need to determine the weight of the acacia wood used to construct the chest, add the weight of the gold overlay, then the estimates for the solid-gold cover and cherubim. There’s also supposed to be a gold molding around the edges and rings to hold the carrying poles, but those comprise only a minor fraction of the total weight. Considering all the estimations and approximations, we can only hope to be in ballpark range for the total weight anyway.

The weight of the acacia wood using my preferred 2-cm thickness comes out to be 47 kg and the gold overlay of 0.2-mm thickness is 33 kg. The weight of the solid gold lid is 60 kg and the cherubim 25 kg. Almost half the weight is in the chest and the other half in its cover. The center of gravity would be around the point where the lid comes in contact with the chest.

The total weight using my estimations is 165 kg (362 lbs) and more than 70% of that weight (118 kg) comes from the gold. Four men could lift it but couldn’t be expected to carry it very far for very long.

Using a shorter cubit (such as the 18” cubit) dramatically reduces the estimate to 131 kg (289 lbs). Decreasing the thickness of the gold overlay to 0.1 mm further reduces the weight to 119 kg (261 lbs). Using 2.5 mm for the thickness of the cover marginally reduces the estimated weight to 111 kg (244 lbs).

As you can see, small changes in the variables can increase or decrease the estimated weight by 33% or more. You can come up with various reasons to tweak the numbers to get the weight of the Ark (and its contents) down to 180 lbs, and it might work if you only consider the Ark in isolation, but any of these tweaks will affect how much gold you end up using for all the Tabernacle items. Reducing the length of the cubit, for example, reduces the surface area of not only the Ark but all the other Tabernacle items and the amount of gold that would be needed to cover them.

Now that I have an idea how much the Ark could have weighed, in my next article I will discuss some observations I drew from this analysis and examine the question as to whether the Ark ever existed at all.

Wednesday, December 6, 2017

Out of Egypt, I am Called Yahweh

Previous articles have discussed evidence for multiple sources in the creation and flood stories. In the final version of these stories that appears in our bibles, the Bible’s editor (called the “redactor”) sometimes keeps the sources intact (as in the two separate creation tales) and other times interweaves them (as in the combined flood story). Scholars can identify the separate strands based on terminology, consistent themes, and narrative flow. One of the themes that sets one source apart from the other is when God’s name is revealed.

What’s in a Name?

According to the source known as the “Yahwist” or “J”, God revealed his name around the time of Adam’s grandson:
To Seth also a son was born, and he named him Enosh. At that time people began to invoke the name of YHWH.” (Gen 4:26)
Thereafter, the J source exclusively uses the name YHWH (usually translated as “the Lord” in modern bibles) in narration. That is why this source was named the “Yahwist.” Ancient Hebrew consisted of only consonants, so we don’t know for sure exactly how it was pronounced, but scholars believe it would have been “Yah-WEH” (accent on last syllable).

Other sources – the “Elohist” (E) and “Priestly” (P) – hold that the divine name YHWH was first revealed to Moses. Before Moses, God was known to the ancestors under different names. For example, in the P account of the covenant with Abram, we read,
When Abram was ninety-nine years old, YHWH appeared to Abram, and said to him, “I am El Shaddai.” (Gen 17:1)
The P source explains in this verse that Abram only knows the deity by the name El Shaddai (“God Almighty” in most English translations). But when YHWH speaks to Moses, the text reads:
God also spoke to Moses and said to him: “I am YHWH. I appeared to Abraham, Isaac, and Jacob as El Shaddai, but by my name ‘YHWH’ I did not make myself known to them.” (Ex 6:2-3)
These verses are taken from the P version of the call of Moses (Ex 6:2-12). God’s commission to Moses to lead his people out of Egypt is a “triplet,” a story recounted in three sources: P, J, and E. The P version is isolated and intact, but the J and E versions are combined in an earlier passage (Ex 3:1-4:23). The E source predominates in this longer passage:
But Moses said to God, “If I come to the Israelites and say to them, ‘The God of your ancestors has sent me to you,’ and they ask me, ‘What is his name?’ what shall I say to them?” God said to Moses, “am who am.” He said further, “Thus you shall say to the Israelites, ‘am has sent me to you.’” God also said to Moses, “Thus you shall say to the Israelites, ‘YHWH, the God of your ancestors, the God of Abraham, the God of Isaac, and the God of Jacob, has sent me to you.’ (Ex 3:13-15)
There’s a lot going on in this passage that doesn’t concern us at this point. The key thing to note is that, as in the P version, the ancestors knew the deity under different names but God first reveals his true name to Moses. Both E and P agree on this point: the name YHWH only came into use after the exodus from Egypt.

Could this be a clue that refugees from Egypt brought the worship of YHWH with them to Canaan?

Charlton Heston as Moses learns the name of God in the burning bush scene from Cecil B. DeMille's 1956 version of The Ten Commandments.

The Midianite Connection

In my last article, we saw that archaeology revealed the early Israelites were Canaanites, speaking a Canaanite dialect and practicing the Canaanite religion. In that religion, the main god was known as “El” (as in El Shaddai). Of the hundreds of city names in Canaan, many include the name El (for example, Beth-el, for “house of God”) but none include the name YHWH. Yet the worship of YHWH eventually became synonymous with Israel (etymology uncertain, perhaps means “God rules”).

How did Canaanites go from worshipping El to YHWH? Let’s go back to Exodus 3-4 and the commission of Moses. Other than Moses being told God’s true name, we also have the indication of where this occurred:
Moses was keeping the flock of his father-in-law Jethro, the priest of Midian; he led his flock beyond the wilderness, and came to Horeb, the mountain of God. (Ex 3:1)
Both J and E tie Moses to Midian, even going so far to say that Moses’ father-in-law was a Midianite priest. Both also locate God’s mountain (called Sinai in J and Horeb in E) in or near Midian. It is reasonable then to look for the origins of the cult of YHWH in Midian. (Midian was located east of the Gulf of Aqaba, south of present-day Jordan, in what would now be the extreme northwest corner of Saudi Arabia.)

We also have Egyptian texts from the 14th-13th centuries BCE that mention semi-nomads called the “Shasu of yhw3” who were located in the general vicinity of Midian. Egyptologists derive the name “Shasu” from an Egyptian verb meaning “to wander.” The Egyptian hieroglyphs transliterated as “yhw3” would probably have been pronounced “Yahu” and is strangely similar to the name of Israel’s God, YHWH. It may have been a place name or it could have been their patron god.

The pieces seem to fit together. Let’s say you have a small group who escape from Egypt – perhaps captured Canaanites or Midianites who had been enslaved – and, on their way to eventually settling in the hill country of Canaan, they pass through Midian. When they finally arrive in the central hill country, they bring with them their story of deliverance from Egypt and attribute their freedom to the god they followed in Midian, who they now call Yahweh.

Certainly the Midianite connection is strong, but so are the Egyptian connections. There are Egyptian details in the story that may go back to the original story told by those who escaped Egypt. We’ll look at those in the next article.

Tuesday, November 21, 2017

Absence of Exodus

The one event from the Bible for which we should be able to find ample evidence in extra-biblical sources is the exodus from Egypt. According to the biblical account, various plagues wracked the nation of Egypt over the course of several months. This was then followed by the exit of 600,000 men and their families (estimated population of over 2 million) from Egypt. When the pharaoh attempted to stop them with a squadron of 600 chariots, they were drowned in the Red Sea. The 2 million people wandered the desert for 40 years before finally settling in the land of Canaan after defeating the indigenous population in a series of battles.

Surely, events on such a scale should have left a record in either Egyptian texts or archaeological strata that would allow us to assign them to an appropriate point in world history.

Getting the Date Right

According to the Bible (1 Kgs 6:1), work on Solomon’s Temple began in the 480th year since the Exodus. Since we know that date with some degree of confidence, a simple calculation would give us 1447 BCE for the date of the exodus. But that places the exodus during the reign of Thutmose III when Egypt was at the height of its powers and Canaan was firmly under his control. Egypt’s power over Canaan only began to weaken in the 13th century BCE.

The Bible also provides a clue that suggests the 15th century is not the right era. Ex 1:11 reports that the enslaved Hebrews were forced to construct the supply cities of “Pithom and Rameses.” Most experts identify the biblical city of “Rameses” as the old Hyksos capital of Avaris (modern-day Tell ed-Dab’a). The city was destroyed in 1530 BCE and long abandoned until it was rebuilt as the royal city of Pi-ramesse during the reign of Ramesses II (1279-1213 BCE). The construction referenced in Ex 1:11, therefore, could only have taken place in the 13th century.

We also can’t look at Egypt in isolation, but have to consider what happened in Canaan once the Israelites arrive. All the experts agree that a major break in the archaeological record indicating a shift from an urban “Canaanite” to a rural “Israelite” culture occurred at the end of the Bronze Age, ca. 1250-1150 BCE. If a large number of people suddenly settled in Canaan from elsewhere, it could only have happened in this period.

Therefore, the mid-13th century is the era in which we need to situate the biblical stories of exodus.

Missing Evidence

We can’t quite yet call it a day, though. The big events recounted in the Book of Exodus should have left plenty of evidence in both the written and in the archaeological record, but many have searched and found nothing. There are no Egyptian records of a series of plagues that would surely have destroyed the economy and killed thousands. No records of a mass migration of 2 million former slave workers. No record of a major military defeat in a freak tidal wave.

The typical counter-argument is that Egyptians do not record their defeats. True, Egyptians did put a positive spin on things, but we don’t see that, either. Where are the boasts of a pharaoh who forcefully expelled troublesome aliens from his land or bravely rescued his soldiers from a flood? Sure, there could have been Egyptian texts or inscriptions that did not survive, but we have to make judgments based on the evidence we do have.

And there’s no archaeological evidence of the desert wanderings, either. Two million people could not have passed through the Sinai desert and left behind no evidence behind. It’s certainly not because people weren’t motivated to look or looked in the wrong places. Any discoverers of sunken Egyptian chariots or ruins of ancient Israelite desert encampments would have their names written in the history books, but alas! At some point you have to admit that nothing has been found because there’s nothing there to find.

The First Thanksgiving 1621 by Jean Leon Gerome Ferris (1899) shows many common misconceptions such as the outfits worn by the Pilgrims and the Wampanoag.

Where Does That Leave Us?

While many scholars believe the exodus story was invented by the Israelites as their own rags-to-riches tale, there are some biblical clues that some portion of Israel recalled once having lived in Egypt. For example, several of the individuals named in the biblical story of the exodus – Moses, Hophni, Hur, Phinehas – have Egyptian names. The description of the Tabernacle (or Tent of Meeting) has architectural parallels with the war tent of Ramesses II and the Ark of the Covenant has parallels with ritual Egyptian barks. (I hope to go into more detail on this in a future article.) These details could have been invented hundreds of years later to provide Egyptian color to the story, but they could also be relics of memories handed down for hundreds of years.

The prophet Amos wrote in the 8th century BCE, “Did I not bring Israel up from the land of Egypt, and the Philistines from Caphtor?” (Amos 9:7) Caphtor is the area of Cypress and Crete and historians agree that the Philistines did arrive in Canaan from there in the 12th century BCE. If Amos knew where Philistines originated 400 years previously, why would we not expect him to know the origins of his own people?

It is not inconceivable that a relatively small group of Semite immigrants left Egypt during the time of Ramesses and settled in the hill country of Canaan, bringing with them tales of having once lived as strangers in an alien land. We would not expect Egyptians to record the departure of a small group nor would we find traces of them in the desert unless we knew exactly where to look. No plagues, no miracle of the sea, just one of many quiet migrations in and out of Egypt.

But if this theory is true, then only a fraction of the people who became Israel would be able to trace their story back to Egypt. How did the entire nation of Israel come to see themselves as having been brought up from the land of Egypt?

Americans can look to Thanksgiving as an example. While very few Americans can trace their ancestry back to one of the 102 passengers on the Mayflower, we teach our children the story of Pilgrims sharing food with Native Americans every Thanksgiving as though it were our story. The Pilgrims’ desire to flee religious persecution in Europe became a central theme in American history and culture.

And what happened once the Egyptian pilgrims arrived in their promised land? We’ll look at the stories of the conquest of Canaan in my next article.