Rice - is 2E64 a lot or rice? Chinese chessboard thingie explained (a.k.a. neva diss da exponent)



Updated: January 19, 2009


Rice count
There's this story about an old Chinese man who came to the Chinese Emperor and asked for some rice. When the Emperor asked him how much he desired (how much thou desireth? he asked), the old Chinese man said he wanted twice as many grains of rice for each field on the chessboard (methinks, 2E64 and odds, he said). And the Emperor went mental.

Well, at first the Emperor gloated and laughed at the old man, thinking him for a fool. But after his advisers did a bit of quick math and discovered they owed 920% of their kingdom to the softly smiling old man, the Emperor decided to hire some ninjas to solve the problem for him. The morale of the story is never to underestimate old Chinese men. As a side dish, lesson two is about mathematics, the power thereof (sic).

So, the rice the old man asked for, is that a lot?

People have a really hard time understanding how mighty the exponent is. This mathematical little bugger is more than just a fancy superscript. It's one of the most powerful things in the Universe. To demonstrate, I'm going to show you just how much 2E64 grains of rice is. P.S. It's actually 2E63, as the first square starts with 1 grain, which translates into 2E0. But that's just big numbers, so we will neglect that for the same of this article. 2E64 sounds prettier.

Some basic math:

Chess

One kg of rice contains, let's say, 10E4 grains of rice. Note: Someone mailed me and claimed closer to 40,000 grains, so be it, but for the sake of math, let's argue a simpler number. One ton of rice contains 10E7 tons of rice. And so forth. Now, let's translate 2E64 into something more human-readable. Hint, if you are a computer user, the calculation should not be that difficult to you. 2E30 is 1GB (or 1E9 bytes). So, we have a billion billion grains - 10E18. Truth to be told we have 8 billion billion grains of rice, but that's just a multiplier.

OK, 10E18 grains of rice, 10E7 grains per ton. So, we have 10E11 tons of rice. For comparison's sake, the largest aircraft carrier in the world (one of the Nimitz-class) weighs about 100,000 (10E5) tons fully loaded. Therefore, we are talking about a million Nimitz-class carriers. Now, let's see how much space does this rice take.

Let's assume that rice displaces as much as water. Therefore, we can assume that a basic 10x10x10cm cube of rice weighs 1 kg and contains 10E5 grains. One ton of rice would then contain 10E9 grains and displace a full 1m3.

We have 10E11 tons, so we need 10E11 cubic meters of space for our rice. A possible solution would be a warehouse 10 km (10E4 m) long, 10 km (10E4 m wide) and 1 km (1E3 m) tall. That's one nasty warehouse! In fact, we would require a building 8 km tall, because we have 8 billion billion grains. In fact, we would need even more than that, because only the last field of the chessboard would be holding all this rice. The 63rd field would hold just 4 billion billion grains ... And so forth.

Architecturally speaking, a more reasonable solution would be a warehouse with a 25x25 km footprint and a mere height of 100 m. Again, if we take Nimitz as a standard unit of measure (mere 300 m long), we could neatly array some 75 aircraft carriers down each side of this behemoth warehouse without any problem. Weight aside, this warehouse could house approx. 10,000 Nimitz carriers inside. It would have an area of 625 km2, which is more than the territory of some 50 countries across the globe. Here's a would-be image; the tiny red thing is something approx. the size of a Nimitz aircraft carrier. The big blue thing is our rice warehouse. Probably unfathomable, even now.

Comparison

Conclusion

2E63 grains of rice is a lot. Quite a lot. Enough to feed 100 tons of rice to every single human on Planet Earth. That's 1 kg of rice per day per human for 275 long years. And economically speaking, more than a millennium worth of global rice production (we make approx. 100 million tons annually).

Therefore, if you ever encounter an old Chinese guy trying to make a deal with you while speaking in innocent riddles, exponent this, factorial that, do not ever, under any circumstances, agree. You may have to mortgage the Solar System just to pay him off.

Cheers.

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