We had meatballs for dinner last night, and as Max was eating his, he got thoughtful, and asked:

If you took all the food that all humans have ever eaten, and mashed it into one giant ball, would it be as big as the Earth?

Good question. It called for a quick series of incredibly inaccurate back of the envelope calculations:

• We estimated that one person’s daily food would be a ball about 10cm in diameter, or about 524 cm³.
• Times 365 days/year, one person’s yearly food ball would be 191250 cm³.
• Times 6.5 billion people on Earth, today’s humans consume 1.25×10⁹ m³ of food each year.
• Now comes the tricky part, estimating over the whole course of human history. Humans have been around for let’s say 200,000 years, but the growth has been exponential over that time, making it hard to flatten it out for simple calculations. (Probably some of my forgotten calculus would help here, but did I mention it’s forgotten?) A good estimate is that there have been 100 billion humans ever.
• If we take a yearly intake of 191250 cm³, times an aggregate average lifespan of 50 years, times 100 billion people, we get a total all-time human consumption of 9.5×10¹¹ m³.
• The Earth has a radius of 6372 km, giving it a volume of 1.1×10¹² km³ or 1.1×10²¹ m³.

So, rounding a little further, humans have eaten 10¹² cubic meters of food, and the Earth is 10²¹ cubic meters in volume, so we’re only off by a factor of a billion!