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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. 