"This article is supposed to have pretty graphics, but I have yet to get around to doing that. It shall be updated at a later date."
At one point in my life, I read a short story that went something like this,
A farmer and her child were shelling their rice (that’s what people do to rice right?) after a bountiful harvest, when they dropped a grain of rice. Instead of continuing their work, the mother spent an inordinate amount of time searching for the grain. This puzzled her child very much, who asked for an explanation. Her mother then spun a tale of how a single grain could produce seven shiploads of grain in a span of seven years.
The story ended with them finding the errant grain and living happily after ever. Unfortunately for my credibility, I’ve scoured the web for this story to no avail, so you’ll just have to take my word for it.
This seven shiploads in seven years adage has left an impression on me since then. The moral was probably something along the lines of “don’t waste food” or “everyone is precious”. That being said, all I could think of was the seemingly impossible growth of rice. It was only recently, armed with upgraded knowledge banks, did I decide to calculate this once and for all.
We know that rice can be harvested twice a year. Doing a quick search for the number of grains of rice an average stalk produces ranges from one to three hundred grains. So I just grabbed a picture and did a rough count, and got something around 150. Let us also assume that every last grain of rice is used for the next cultivating cycle (as each grain is precious).
The number of grains we get after each harvest is defined as 150n where n is the number of harvests, i.e. after the first harvest we get 150 grains, after the second, 150 × 150 and so on…
The first year
Well, we are only at two cycles, so our farmer family will only have 22500 grains of rice in their rice bank. A cup of rice is around 7000 grains, that would mean our family will have just above three cups of rice to eat.
Unfortunately for them, we’re going to need that rice for planting and they’ll have to seek out an alternative source of food.
The second year
At four cycles our family has 506 250 000 grains of rice in their bank, assuming they haven’t starved already. But on the bright side, that roughly translates to 72 321 cups of rice, way more than enough to feed them and their their entire village for a year! (They live in a small village.) But this is all going to be used for cultivation and they’ll have to wait another five years before they can feast.
The third year
At six cycles, I’m going to have to use scientific notation in order to display the number. We have 1.14×1013 grains in our rice bank. (That’s a 1 followed by thirteen zeros behind it.)
Each kilogram of rice contains about 50 000 grains of rice. That means we now have 228 000 metric tonnes of rice in our bank. By this time, if our family has not starved to death, they would have drowned in the rice itself. We shall assume there are some other means of cultivating the rice from now on.
The fourth year
At this juncture, our rice bank would have 2.56×1017 grains, which is equivalent to 5.13×1012 kg. We would have produced ten times more rice than the entire of China produced in 2009, which is about 200 million tonnes or 2×1011 kg of rice.
The fifth year
In year five, we’d have passed yet another important number mi lestone, 5.77×1021. What’s so special about this I hear you ask? Well according to assorted online estimates, the number of grains of sand on earth is somewhere within the range of 1018 to 1021. That means we will have more grains of rice in our bank than there are grains of sand on our planet. Of course, how a single grain of rice can be cultivated on a single grain of sand is a topic for another post.
The sixth year
1.29×1026 grains = 2.59×1021 kg
The mass of all water on earth roughly equivalent to the mass of the rice we have. And since rice should be about 25% moisture, 25% of our earth’s water supply should have been sucked up and stored in the rice. Of earth’s entire water supply, only about 2.5% is fresh water. We would have used up all the freshwater ten times over just to cultivate this year’s harvest.
The seventh year
Finally, we end up with 5.84×1025 kg worth of rice.
For comparison, the estimated mass of the earth is 5.97×1024.
So we have almost 10kg of rice for every kilo the Earth is made of. Of course, we will not be able to store all this rice here, since that would technically add to the weight of earth. We would have to store it off planet somehow, maybe like orbiting the planet. Wouldn’t it be nice to look up in the sky and see ten massive planetoids orbiting ours?
There are similar stories that demonstrate the power of powers that can be found online through a simple search.
Paper space travel
Exponention has proven to be almost magical, so it should come as no surprise if I were to proclaim that if I were to take a sheet of paper, and fold it in half fifty times, it will easily reach the moon. Since we’re already here, let’s just do the calculations.
Firstly, let’s figure out the thickness of a sheet of paper. According to Google, that’s around 0.1mm per sheet. We define a single fold as folding the sheet of paper exactly in half, and we assume that this sheet can be folded much more than the alleged seven times maximum (a topic which MythBusters covered in one of their episodes). Since each time we fold the paper doubles it’s thickness, folding it n times will give us the nth power of 2 sheets’ thickness.
A sheet’s thickness is 0.1mm, or 10-4 m.
10-4 m × 250 = 1.13×1011 m.
For comparison, 1AU (the average distance from Earth to the Sun) is 1.5×1011 m.
If we fold the sheet just two more times, we will easily get a tower stretching from Earth to Mars. Had Mark known this, that whole struggle in The Martian could haven been easily avoided. Of course, acquiring an infinitely foldable sheet may prove a challenge…