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Skeptic: Math of Noah's Ark

In response to Conversations with a Skeptic Podcast.

At one point when the Pastor is talking about evidence. He very quickly mentions Noah and the Ark. He asserts:

If you want to study it from a mathematician's standpoint, it's pretty obvious. You can take 2 of every species and you can put them in that dimensions and have plenty of room left over. You could even take 2 of every dinosaur. You could put every single species we're aware of and you could put them 2 by 2 in that.

When he said this it struck me as strange, because that's an awfully bold claim to put forward without any support. I really had no idea how the math would work out, so I thought it might be fun to sit down with some back-of-the-envelope calculations to see if he's just repeating some claim he's heard before without checking it. So, let's check it! What follows is a SUPREMELY ROUGH AND ARBITRARY SET OF NUMBERS. Got it? :)

I did some quick web searches and found four different sites that gave numbers for the number of species on the planet:

Mammals Birds Fish Amphib Reptiles Arthropods
Wikipedia.org 5,400 10,000 28,000 6,347 8225 1,170,000
About.com 5,000 9,000 23,500 5,400 7,984 1,115,500
funtrivia.com 4,300 9,000 27,000 3,000 8,000 800,000
worldstory.net 15,000 9,000 20,000 1,000 6,000 1,000,000

Obviously there would be no need to include Fish in our equations, because they could just continue swimming. We'll also assume that Amphibians would be able to survive the storm without needing to be on the ark. Insects present another problem to the equations... you can't really bring two of each insect and expect them to survive a full year on the ark (it rained or 40 days, then the water remained for 150 days, then during another 150 days the waters receeded before everyone was let out of the ark). Many insects don't even live that long and some need queens, etc, so the calculations involving insects and other arthropods are a little complicated for now. Let's leave that until later. I'm going to use the Wikipedia numbers because those numbers are sourced while the other web pages aren't (and they aren't radically different anyway).

There were also 8 people on-board. Noah and his wife, Noah's three sons and their wives.


Mammals - Mammals range from the size of mice to the size of elephants, but the distribution of sizes is going to weigh more heavily toward the smaller. I'm going to arbitrarily choose my cat as the "average mammal" size. She's about 6" wide and about 14" long. I'm also going to assume that each mammal will require some space to move around in. We'll be charitable to the math and horribly cruel to the animals by giving them double their body size, so my theoretical average mammal will get 12" x 28" of floor space in which to exist.

Reptiles - Reptiles range in size from 0.5" to 20' and again the distribution of sizes is going to weigh more heavily toward the smaller. Adult iguanas are about 4-6' long, but that seems too large for my assumed small size. I'm going to use the same calculations I did with my cat. 6" wide and about 14" long. My guess is that is smaller than the average.

Birds - I was originally not going to include birds in my calculations, because I figured that birds could just fly around and land on top of the ark when needed. However, the Scriptures clearly state that birds were to be brought into the ark. Birds range in size from 2" to 10' in length (Ostrich). We'll go with parakeet-ish size about 8" in length. They are only about 3" wide, but with wing-span they'll be more like 10".

Now let's talk ark dimensions. 450' x 75' and it had 3 stories (45') which is 101,250 sq ft. Obviously with smaller animals it will be possible to stack several of them on one deck so we'll need a 3 dimensional calculation to get a closer number. Let's stick with 2 dimensions for now and we'll make the equations more complex as we move forward.

Mammals: 5,400 x (12" x 28") x 2 = 25,200 sq ft
Reptiles: 8,225 x (12" x 28") x 2 = 38,384 sq ft
Birds: 10,000 x (20" x 16") x 2 = 44,444 sq ft

Assuming these 2 dimensional numbers, that is 108,028 sq ft which is 6,778 sq ft larger than the above ark dimensions. As stated before, we need to do some compression and move to 3 dimensional numbers. Since we know that not all animals are the size of my cat. Let's use an 75%/20%/5% split for small/medium/large. For Mammals we'll roughly go with cat, dog, and horse for small, medium and large. Remember we're giving them a highly constricting space that is only double their body size for a full year.

Mammals (Small): (5,400 * 75%) x (12" x 28" x 16") x 2 = 25,200 cubic ft
Mammals (Medium): (5,400 * 20%) x (24" x 72" x 72") x 2 = 155,520 cubic ft
Mammals (Large): (5,400 * 5%) x (72" x 168" x 144") x 2 = 544,320 cubic ft
Reptiles (Small): (8,225 * 75%) x (12" x 28" x 16") x 2 = 38,383 cubic ft
Reptiles (Medium): (8,225 * 20%) x (16" x 96" x 32") x 2 = 93,582 cubic ft
Reptiles (Large): (8,225 * 5%) x (72" x 120" x 48") x 2 = 197,400 cubic ft
Birds (Small): (10,000 * 75%) x (20" x 16" x 20") x 2 = 55,556 cubic ft
Birds (Medium): (10,000 * 20%) x (30" x 24" x 30") x 2 = 50,000 cubic ft
Birds (Large): (10,000 * 5%) x (60" x 72" x 60") x 2 = 150,000 cubic ft
1,309,961 cubic ft

That leaves us 94,961 cubic ft over the limit. I really had no idea how these numbers were going to pan out and please let me state once again they are entirely based on guesses of animal size and distributions of sizes throughout the species. On the surface of these incredibly loose numbers, my feeling is that there isn't "plenty of room to spare." The above numbers are based on a very restrictive amount of space...

... they don't take into account the structures necessary to partition all the animals which would take up more space...

... they don't take into account that you would need walkways among each of the animal pens so that you could care for them...

... they don't take into account the immense volume of animal dung that would need to be scraped out of the ark and tossed overboard daily or weekly for an entire year...

... they don't take into account the immense amount of food you'd have to bring on to the ark to feed 8 humans and almost 24,000 animals for an entire year...

... they don't take into account the common misconception that only 2 of each animal were brought on-board. 2 of each unclean animal was brought on board, but 7 of each clean animal was brought on-board...

... and we didn't even include all of the PLANT species that Noah had to bring on board as commanded by God...

... and we didn't even include all of the insects, spiders and other arthropods that should have been included!

My point here is not "the ark is mathematically impossible" because as I've stated several times so far, these numbers are REALLY ROUGH. Like, super duper rough. :) My point is that the Pastor's simple assertion of "plenty of room left over" isn't so simple. Especially when you complicate ALL of the above factors in with his assertion that "You could even take 2 of every dinosaur."

The true goal of my post is in the heart of the title. Skepticism. How many people listening to this Pastor preach or listening to the podcast afterward heard him make this HUGE assertion in two simple little sentences and didn't even think twice about it? He said it, passed it off and moved on in the span of like 15 seconds as if it was no big deal. It's true, there ya have it, let's move on. That's not the kind of intellectual caution and verification that comes along with a skeptical mindset.

If we put together a sufficiently complex mathematical model and were able to gather all of the data needed to properly feed that model (real animal sizes, quantities of food, etc), perhaps the numbers would work out. Perhaps it is possible to house that many plants and animals in that size structure for an entire year. I don't really know. The point is that I'm asking those questions along with questions about the other fantastical stories in the Bible.

If you believe the Bible is correct... if you believe that these stories are all true... then you should have no fear in asking these questions because you'll always come back with the answer that you are right. You have to do it honestly though. You can't approach the question without honestly accepting the possibility that you might be wrong. To answer the questions honestly, when you are presented with a finding or an answer that indicates you might be wrong, the appropriate response is to delve further and discover the truth instead of saying "God is all-powerful, so if He wanted to then He could make it work like that."

Being right is not the goal. Finding the truth is the goal.

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