Myth Math

Noah’s Ark is likely one of the biggest stories from the Bible. In this post I want to show that it just isn’t likely to have happened, and perhaps just couldn’t be possible.

And the flood was forty days upon the earth; and the waters increased, and bare up the ark, and it was lift up above the earth. And the waters prevailed, and were increased greatly upon the earth; and the ark went upon the face of the waters. And the waters prevailed exceedingly upon the earth; and all the high hills, that were under the whole heaven, were covered. Fifteen cubits upward did the waters prevail; and the mountains were covered.
-Genesis 7:17-20

So, we have a few very good math problems ahead of us. Not only are they just math, they aren’t even that complicated of a problem. Before we begin I will lay out the parts of the problem that are similar to each version.

First, the size of the Earth. NASA (clicky click) states that the volume of the Earth is 108.321 x 10^10 km³. These are big numbers, but I have all the room I need, it’s my blog. The average radius, the mean of the equatorial and polar radii, is:

(6378.1 km + 6356.8 km ) / 2 = 6367.45 km

That is the radius we will use to find the volume of the Earth and compare it to what NASA gave us.

V = 4/3 π r³
V = 4/3 * 3.14 * 6367.45 km³
V = 1.33 * 3.14 * 258164563961 km³
V = 1078146900000 km³
V = 1.0781469 x 10^12 km³

NASA reports the volume of the Earth to be 108.321 x 10^10 km³. I’d say a difference of 500 km is close enough, yay us!

15 Cubits Flood

So the text states that the waters went up 15 cubits. That is the first measurement we are going to work with. I am going to do the math to see how much water would be required to raise the sea level 15 cubits. But, how big is a cubit?

 

Because I want to give as much leniency to the story as possible I went to the group that takes the story most literally, Answers in Genesis.

They state that the cubit could range from 17.5 to 20.6 inches. I think the best bet for this problem is to take a middle point between the two.

(17.5 + 20.6) / 2 = our cubit
19.05″ = 1 cubit

15 cubits = 19.05 * 15
15 cubits = 285.75″
285.75″ = 23.8′

That doesn’t seem like a flood to me and it certainly doesn’t seem like it would cover the mountains. We are going to go with this measurement first.

So to find out the volume of water we simply find the volume of the Earth during the flood and take away the volume of the Earth. The 15 cubit flood raised the water level 23.8 feet so we add that to the mean radius we found earlier, a difference of only 0.00011%.

23.8′ + 6367.45 km = intra-flood radius
23.8′ = 0.00725424 km
0.00725424 + 6367.45 = 6367.45725424 km radius

If we then plug that radius into the equation to find volume during the flood, V(f):

V = 4/3 π r³
V(f) = 4/3 * 3.14 * (6367.45725424 km)³
V(f) = 1.33 * 3.14 * 258165446319.04806285631451844903 km³
V(f) = 1078150536917.6085 km³
V(f) = 1080852668589.0812231584367839066 km³

Then subtract the volume of the Earth, V,  from V(f) to find the volume of the water, V(w).

V(f) – V = V(w)
1080852668589.0812231584367839066 km³ – 1.0781469 x 10^12 km³ = V(w)
2705768589.0812231584367839065848 km³ = V(w)

That’s a really hard number to imagine, at least for me it is. Let’s make that volume into a sphere and see how it shapes up (I know it’s a bad/good pun however you see puns). If we take that volume and place it into the equation to find volume and work backwards we can find the radius of a sphere of water, r(w).

V = 4/3 π r³
r = ((3V)/(4π))^(1/3)
r = 0.62035 * V ^1/3
r(w) = 1188.4360369823730308866574874648 km
r(w) = 738.5 miles

That’s it. A sphere of water with a diameter of >1400 miles would be needed to raise the sea level to just 15 cubits. You know what else is about 1400 miles in diameter?

That’s right, a ball of water the size of Pluto would be needed to raise the sea level just 15 cubits. Like I said above though that’s only 23.8 feet of water, nowhere near covering the high hills or mountains.

Maybe we didn’t go by the Bible well enough. It does say “…and all the high hills, that were under the whole heaven, were covered. Fifteen cubits upward did the waters prevail; and the mountains were covered.”

“and the mountains were covered” Flood

The tallest mountain we know is Mt. Everest at 29,029′ above sea level. If we change our math enough to cover it, not even counting going over it by 15 cubits, how much water would be needed then?

We are going to add 29,029′ to the radius of the Earth from above. Because water levels itself it would need to be at this level around the entire planet to cover any part of it. If you hold that the Earth was covered by a layer of water 15 cubits deep like a film over all the mountains and hill then I can’t do anything for you, that’s ridiculous (and I’m the one doing math to figure out Noah’s flood).

The radius of the Earth from earlier plus the added distance to the top of Mt. Everest:

r = 6367.45 km + 29,029 ft
r = 6376.2980392 km

An addition of just 0.1389%. If we then use that in the volume formulas from above we get the volume during the flood (I cut out the math but you are welcome to check for accuracy):

V(f) = 1085360995411.5541311496090510458 km³

To find the volume of the water, V(w):

V(w) = V(f) – V
V(w) = 7214100000 km³

Now, let’s find the radius of the sphere of water that would be required for that volume:

r = 0.62035 * V ^1/3
r = 1198.6641207880081840568342435861 km
r = 744.8 miles , d = 1490 miles

Isn’t that interesting? I know I am shocked. It’s less than 100 miles difference. That being said, that amount of water is staggering. Where did it come from and where did it go. Those are the big questions.

I know immediately the believer would bring up:

…all the fountains of the great deep broken up, and the windows of heaven were opened.
-Genesis 7:11

There just isn’t that much water underground, nor in the clouds, nor in the ice caps, nor in all of those combined. According to the USGS, all combined, there is about 1409560910 km³ of water on the Earth. That’s about 20% of the water needed to cover the Earth above the mountains.

Another theory I remember hearing is that the water came from an asteroid or some such object. Like we found the object would need to be nearly the size of Pluto to contain enough water, and that still leaves the question of where the water went after the genocide was complete.

The water couldn’t have been absorbed into the planet. Our planet is powered by a magmatic engine that would solidify if cooled by water. Without the core spinning we lose both our magnetic cover and our atmosphere.

It simply didn’t happen. I’m sorry if you can’t accept this point, but I feel like I have shown very clearly that the evidence just isn’t there to accept your claim of a global flood.

Well, that’s it. That was actually fun for me. I messed up the math in a few places because of the exponents and units but I feel this final post is error free. If you disagree with the math I urge you to do it for yourself and see that the only way Noah’s Ark would have actually happened is by magic. Be truthful to yourself and align your beliefs with those things that are provable. And let’s not even get started on the animals.

Exodus 2

Exodus 2 – Moses is Born, Kills, and Marries

 

Moses is born to a man from the house of Levi and a woman from the house of Levi. We don’t know his parentage? After all of the droning genealogies one of the absolute main characters has unnamed parents?

Remember that the pharaoh charged all of his people at the end of Ex. 1 to kill the sons of the Hebrews. The woman from above had a son and quote ‘when she saw he was a goodly child, she hid him three months.’ I wonder what would have happened if the kid had had something wrong, probably wouldn’t have been hidden I’m thinking.

She hid the child for three months but eventually couldn’t keep it a secret so she took him and made a boat to set him in in the river. After attempting to hide the child for three months she decides to give it up?

And guess who finds the child? The pharaoh’s daughter.

Who is v.7 speaking of? It says, ‘then said his sister to Pharaoh’s daughter…’ who is the male? The story only talks of the daughter, her servants, the mother and the sister, and of course the baby boy being at the river. I could concieve that it is speaking of the baby’s sister; one of the servants. This could be the reason that when the pharaoh’s daughter calls for a milk maid, the child’s actual mother is chosen; because it is that servant girl’s mother too.

Pharaoh’s daughter gets a Hebrew woman to nurse the baby for her who turns out to be the child’s actual mother. Apparently the name Moses means to come from the water from what the Pharaoh’s daughter says in v.10.

We don’t know how much time passes between v.10 and v.11 but he must then be in his teenage years judging by his actions in the rest of the chapter.

Moses is grown and joins his brethren, likely working under the slave drivers, when he sees an Egyptian ‘smiting’ one of the Hebrews. When he saw the Egyptian alone and that no one was looking he ‘slew’ him and hid his body. Premeditated murder, pretty wrong but no response from god.

The next day he returned to the work site to find that two Hebrews had been placed in charge of the slaves and were treating them just as the Egyptian had. Moses confronted them asking why they would smite their brethren. One of them responds asking who made you boss basically and asked if Moses was going to kill them just like had killed the Egyptian the day before. Moses got scared knowing that it was known that he had been the one to kill the guy so he fled to Midian. It pretty clearly states that the Pharaoh was angry at Moses and Moses fled ‘from the face of Pharaoh.’

In Midian Moses was sitting by a well when seven women and their flocks came to get water. Some shepherds came and took over the well and tried to shoo the ladies but Moses stood up to the shepherds and drew the water from the well for the women.

When the women returned to their father Reuel and told him the story he told them they should have brought Moses with them for the good deed. Within the same verse, v.21, Moses moves in and receives Zipporah as his wife and then his son Gershom is born in v.22.

‘…in process of time,’ the Hebrews in bondage in Egypt sighed because of the bondage. OK, they didn’t complain about the slavery until now? Anyways, they cried to god to release them. It says then that god remembered his covenant with Abraham, Isaac, and Jacob and he looked unto the children and had respect unto them. I thought god saw everything, did he not see them in slavery all this time? Did he forget his covenant until now?

Exodus 1

Exodus 1 – Israelites Multiply and are Enslaved

The story of the life of Joseph and his brothers is wrapped up pretty quickly in v.6.

We are told that the generations of the children of Israel become more numerable than the people of Egypt. The timeline of BibleHub gives about 100 years span between the death of Joseph (1800 BCE) and the enslavement (1700 BCE). Think about that in a mere 100 years the Israelites go from about 70 people (v.5) to outnumbering the Egyptians (v.9).

v.8 talks of a new king coming to power in Egypt who doesn’t know Joseph. It doesn’t say how many kings have taken the throne since the famine only that this is the king who didn’t know of Joseph. Two things must be questioned:

1-Similar to Jacob/Israel, why is this king called king and not Pharaoh? The most likely answer is that the word Pharaoh is an anachronism. It is the title that WAS used for the ruler of the Egypt but we must look at the fact that the title wasn’t in use until about 1400 BCE.

2-How does this ‘king’ not know of Joseph? Joseph saved the country from a seven year famine with a dream interpretation and was placed in power over all the land. Even if the king hadn’t met Joseph in person, he would be familiar with the story of that person, its only been about 100 years after all.

The new king warns his people that if the Israelites continue to multiply and they side with an enemy that Egypt would fall. As a result the Egyptians enslaved the children of Israel. Is it correct to think now that the ratio of slaves per capita is greater than 1:1? The population of slaves is greater than the population of the country of Egypt? That would definitely be something that would be recorded in history in more than this single source, but in fact it can’t be found in any of the records of the Egyptians.

The lives of the children of Israel were made rough, it says everything they were made to do they had to do with rigour. In this instance the bible speaks of the harsh parts of servitude that were never covered when it was the Hebrews that had the slaves.

The king tells the midwives (only two midwives for all of them) that when they birth a baby they are to kill the boys. But the midwives feared god above the king and did not obey him. The king brings the midwives back to ask why they have not listened to him. They responded with little jab at the Egyptians saying that the Hebrew women weren’t like the Egyptians, they give birth to their children before the midwife gets there. Because the king couldn’t get the midwives to kill the sons he commands all of the people to kill the sons and save the daughters.

It seems that he was trying to keep this little bit of infanticide under cover if possible but the midwives wouldn’t listen to him so he had to make it public. Perhaps this is why he didn’t punish the midwives more than talking to them as we would expect him to.

 

Genesis 50

Genesis 50 – The Death of Joseph

Jacob has died, Joseph weeps and then commands that his father be embalmed which took 40 days back then. It even says the Egyptians mourned for him.

Joseph goes to Pharaoh to tell him of the oath he made with his father to bury him in the land of his fathers. Pharaoh accepted and told Joseph to go and to do as he had sworn.

Joseph didn’t go alone though. He took with him everyone from his father’s house, everyone from his house, his brothers (and likely their families), the elders of the land of Egypt and all the servants of Pharaoh.

It says they left only the herds, flocks, and the little ones in Goshen. Undoubtedly they also left the women but they just aren’t notable enough to the authors of the bible.

v.9, It was a very great company. No doubt, with all of those people the group was likely no less than 100 people.

On the journey Joseph had the group stop for seven days to mourn again, but the group and the sons of Jacob fulfilled their obligation and buried him in the cave.

After returning from the burial Joseph’s brothers were afraid that Joseph would change. They feared that since their father was gone Joseph do them like they had done him. Because of their fear they sent a message to Joseph containing a message that Jacob had supposedly wanted Joseph to receive before his death.

The message was for Joseph to forgive his brothers for the evil they had committed against him.

The brothers came to Joseph and bowed before him and said they were his servants but Joseph responded by telling them that he is no god. He explained that the evil they committed against him was god’s plan for good to save the people from the famine. He reassured them that he would take care of them and their families.

Joseph stayed in Egypt and lived long enough to see the third generation born. Joseph tells his family that even though he was to die god would bring them out of the land to the land that he had promised to Abraham and then to Isaac and then to Jacob and then to himself.

Four generations of promises that THEY and their children would control that land and they have yet to. How many promises can be made and not followed through and still be believed?

Joseph dies at 110, he is embalmed and laid to rest in a coffin in EGYPT.

So, not only the promises about the land but also about getting out of Egypt. Jacob was promised just like Joseph that god would deliver them from the land but now both have died in Egypt. Jacob’s body was at least taken out and buried with his fathers’ but Joseph was laid to rest in Egypt.

Genesis 49

Genesis 49 – Jacob Blesses his Sons

Jacob’s death is really being prolonged.

Jacob calls his sons to him to explain what will come to be and bless them.

Reuben – Firstborn, mighty, dignity, power, but also unstable and will not excel because of his affair with Bilhah.

Simeon/Levi – brothers of cruelty

Judah – his brothers will bow to him and praise him, a lion among prey, king among the people until Shiloh comes. Jacob explains him as the ruler and lawgiver with the scepter and also the details about his clothing being dyed purple. A strange detail about his eyes being red with wine but I think it was less about the color of his eyes and more about being wealthy enough to have lots of wine; something like ‘I’ve drank so much my eyes are swimming’.

Zebulun – will live by the sea bordering Zidon.

Issachar – strong and stubborn. And something I don’t understand in v.15

Dan – the judge

Gad – will be overtaken but will come back

Asher – will be rich with bread and will yield ‘royal dainties’

Naphtali – a smooth talker

Joseph – fruitful, hated by the archers because of his skill and strength, blessed of the air, the sea, the breast, and children.

Benjamin – will share his spoils.

These are described as the twelve tribes of Israel. The sons of Jacob whose descendants would populate the country of Israel. Along with the blessings he gave them he tells them to bury him in the cave with Leah and Isaac/Rebekah and Abraham/Sarah.

These blessings weren’t very good. A blessing should be used to make people better, to increase the good in the world. He just told his sons about the future and some of them weren’t something to look forward to, except for his favorites Jacob and Benjamin of course.

Immediately after having this conversation with his sons he died.

 

Genesis 48

Genesis 48 – Jacob Blesses Joseph and his Sons

Even though the end of Gen. 47 seemed to end with the death of Jacob, the beginning of Gen. 48 Joseph learns that his father is ill.

Joseph took his two sons to Jacob on his deathbed and Jacob blesses them. Jacob tells Joseph of the promise god had made to him about the land belonging to his descendants and the death of Rachel.

The blessing is pretty basic with one change in the ritual. Joseph tried to move his father’s hand when he was placing his hands on the boy’s heads. The right hand was for the first born but Jacob was placing that hand on Ephraim, not Manasseh. Joseph tried to correct this but Jacob said he knew what he was doing and the younger would be greater than the older one.

Jacob tells Joseph that he himself is going to die but god would be with Joseph and bring him out of Egypt to the land of his fathers. This is much like the promise god made to Jacob to have him return out of Egypt but he is dying now there so what happened to that one?

Jacob also reiterates that Joseph was his favorite son saying that he had given him a portion above his brothers which he took by force from the Amorites.

Genesis 47

Genesis 47 – Jacob Blesses Pharaoh

Joseph brings five of his brothers to Pharaoh to present them and let him know that they had gotten there and settled in. Whats the first question Pharaoh asks of them? What they do for a living. They answer with the truth even though Joseph had told them directly to lie. They tell the Pharaoh that they are shepherds.

They explain that they have brought their herds to stay in the land because of the famine. Pharaoh tells Joseph that they can live in the land of Goshen in the best part of the land. He even offers that if any of them are good with cattle they should be placed in charge of the Pharaoh’s herds.

Joseph then brings his father to Pharaoh and Jacob blesses him. This verse is usually cited as a problem because it says Jacob blessed Pharaoh in v.7 and also again in v.10. I can easily explain this because of the many times the bible repeats and repeats itself with single verses used to unnecessarily sum up something that will be explained just after. But in this case the two verses are actually nearly the same thing and don’t actually explain the blessing at all.

Pharaoh inquires about Jacob and his age. Jacob responds that he is 130 and that he hadn’t yet reached the age of his fathers.

Joseph gets the land for his father and brothers and gives them bread to settle them in.

When the bread runs out because of the famine the people of the country come to Joseph because he had collected all the money that had been given to buy corn. The people ask for bread but Joseph tells them they must sell their cattle in exchange for the bread. Thank goodness god placed someone in charge of the food so people wouldn’t die from the famine, someone less worthy may have used this as an opportunity to get rich.

The year after this the people return but tell Joseph that he has their money from buying corn and their herds from buying bread. They explain that they have nothing left but their land and their bodies.

The people ask for bread and seeds in exchange for their land and their servitude. Joseph takes the land of all the people for the Pharaoh. He did not take the land of the priests because the land and their stuff was already Pharaoh’s.

Joseph moved all of the people whom he had bought to cities around the land of Egypt and gave them seeds to sow. They are made to work the land and anything they get from the crops is theirs less one fifth that they must give to Pharaoh.

Jacob lived 17 years after moving to Goshen when he died at 147. What happened to that promise god made that said he would get him out of Egypt? Unless you count Joseph taking Jacob’s body back.

Genesis 46

Genesis 46 – Jacob Reunites with Joseph

On his way to Egypt to see if Joseph really is alive and well Jacob, or Israel whichever you are feeling like at the moment, came upon Beersheba and gave sacrifices to god.

Within the very same verse (v.2) the text talks about Israel but god calls him Jacob. Not even god follows his renaming of Jacob. God tells Jacob to not fear going to Egypt that he will go with him and he will bring him out safely. They leave Beersheba and make their way Egypt.

v.8-27 detail the family that came with Jacob including Joseph and his wife and kids, a total of 70 people.

A tear-filled meeting between Jacob and Joseph. Jacob/Israel said he could now die having seen his son alive after all this time.

Joseph says he will go tell Pharaoh that his family had arrived but he warns his family that if they are asked about what they did they were to explain that they took care of the cattle just as their fathers had because shepherds were an abomination to the Egyptians. Really? If they had god on their side why must they lie about what they do? I guess lies aren’t so bad huh?

Genesis 45

Genesis 45 – Joseph Reveals Himself

Joseph was unable to control himself during the meal and began to cry. He shooed everyone out of the room except for his brothers whom he revealed himself to.

His brothers were troubled when he told them of his true identity but he reassured them to not be mad at themselves for what they had done. He said that their selling him as a slave was part of god’s plan to save life.

This is a strange thing to think about; god had a person sold into slavery for many years to help the Egyptians make it through the famine that he was going to cause. What about the other millions of people around the world that were affected, are we to believe that the Egyptians saving just one fifth of their harvests for seven years would have saved enough food to supply the world for another seven years? I may digress but these questions need to be asked and answered if the bible is to be taken as a literal account of historical events.

Joseph tells his brothers to go to his father and tell him that ALL of his sons are alive and well and to make his way to Egypt too. He tells them to bring every person and every animal nearer to Egypt to the land of Goshen so they would be close enough to survive the remaining five years of the famine.

The Pharaoh heard of the reunion and was pleased that his Zaphenathpaneah had family and they were going to be closer to live through the famine. Pharaoh tells the brothers of Joseph to take supplies and return with the house of their father, he even tells them to take his wagons so the women and children wouldn’t have to walk.

Joseph gave his brothers the wagons and supplies and a change of clothing each except for Benjamin. To Benjamin he gave 300 pieces of silver and five changes of clothing. He even sent supplies for his father and his trip.

The brothers made their way to Jacob and told him of everything about Joseph. He didn’t believe them until he saw all of the supplies that the brothers had brought along with them. Jacob, well Israel in this particular verse, said that was enough evidence and he believed them and agreed to go and see before he died.

 

 

Genesis 44

Genesis 44 – The Silver Cup

As Joseph is sending off his brothers for the second time, he has their sacks filled and their money returned again, he also has his silver cup put into Benjamin’s bag.

After they left Joseph had his servant go unto them and find the cup and accuse them of stealing it.

The brothers explain that they wouldn’t steal and had even brought back the money from the first time they tried to buy food. They even offer that if it is found the one who had it could be killed and the others made into servants.

As the search continued, the cup was found in Benjamin’s bag.

They all returned to Joseph’s house. Joseph demands that the one who was found with the cup become his servant and the rest could leave in peace. Judah explains that one of their father’s children had died (Joseph) and the youngest was supposed to have stayed with their father.

Judah explains what happened when they told Jacob that they couldn’t return to Egypt to buy more food unless Benjamin came with them and how Jacob had reacted to his youngest son having to leave. He explains that Jacob would surely die if they returned without Benjamin.

Judah explains that if Benjamin was not returned Judah would bear the blame of it. Because of this Judah asks to take the place of Benjamin in servitude.