How many is really a lot?
Thomas Schmelzer
Portfolio construction and technology @ ADIA | Commodities and LS Equities | Visiting Scholar at Stanford.
Last weekend we celebrated reunion at Balliol. I had the pleasure to be placed across a young man running a shipping company -- shipping as in container ships. To illustrate how quickly powers of 2 grow I asked him an old favourite question of mine: How many modern container ships would I need to transport the rice needed to cover the chessboard --- according to the legend we are talking about 2^{64} - 1 grains. You may remember: 1 grain on the first field, 2 grains on the 2nd, 4 on the 3rd, 8 on the 4th, ...
We assume a modern container ship can take 20000=2e4 containers. The latest generation can actually take 27000 containers. Each container is supposed to carry approx. 30t but being generous we say we can load each container with 100t or 1e5 kg. Such ships are massive, and my table neighbour argued that one ship is probably enough. So, we could load our ship with 2e9kg of rice (1e6=million, 1e9=billion).
To take the step from weight to number of grains I counted the grains in a 1kg pack of rice I bought at Tesco. I counted close to 50000=5e4 grains. So, our ship can take 1e14 grains of rice (e.g. 100 trillion). That's a lot of rice.
It remains to estimate 2^{64}-1. I use 2^10 = 1024 approx. 1e3. And hence 2^{64} \approx 1e18 * 2^4 = 1.6e19. Therefore, we need approx. 1.6e5 ships or 160000 ships each with 20000 containers and each container with 100t of rice.
Unfortunately, there are neither enough ships (I have learnt there are only 5000 container ships globally) nor enough rice.
Global Investment Leader | Expert in Private Equity, Capital Markets, & Real Estate.Driving Growth & Risk Mitigation.PhD in Business & Management. Certified by Columbia, IBM, Erasmus, Gies College,UNIGE, LBS & HEC Paris.
4 周Thomas, I really enjoyed the way you illustrated the scale of exponential growth with the rice-and-chessboard analogy. The mental exercise of visualizing 160,000 container ships packed with rice really drives home how quickly powers of 2 grow. It’s fascinating that even with the massive capacity of modern ships, we'd need 32 times the global fleet to transport such an amount. Thanks for a great perspective on scale!
Portfolio construction and technology @ ADIA | Commodities and LS Equities | Visiting Scholar at Stanford.
1 个月Russia is doubling a fine on russia every week, see https://www.dhirubhai.net/posts/irinaheaver_technology-law-activity-7257655500194856960-4XNk?utm_source=share&utm_medium=member_desktop
Turnleaf Analytics / Visiting Lecturer at QMUL
1 个月That’s a lot of rice puddings!
Systematic Trader (Quant-Algo)
1 个月gut gemacht :)
Consultant | Director
1 个月The container owned should have given the Monty Python Holy Grail reply, "African or European, grains?'