The following fun exercises appeared on p. 134 of Hofstadter's Metamagical Themas, a collection of his Scientific American articles from the early 1980s (the title is a play on Martin Gardner's column, "Mathematical Games").

I have not sought permission to reprint them here, although I doubt he would be upset if more people explored—and became fluent with—really big numbers. I encourage you to buy the book, which has the same *élan vitale* that made GEB a classic.

**Note: ** In case anyone is interested I have posted my "solutions." If you don't care about my thought process, you can grab my results as a list of tuples for easy processing; it might be interesting to aggregate people's answers.

I would suggest to interested readers that they attempt to build up their own numeracy in a very simple way. All they need to do is to get a sheet of paper and write down on it the numbers 1 to 20. Then they should proceed to think a bit about some large numbers that seem of interest to them, and try to estimate them within one order of magnitude (or two, for the larger ones). By "estimate" here, I mean actually do a back-of-the-envelope (or mental) calculation, ignoring all but factors of ten. Then they should attach the idea to the computed number. Here are some samples of large numbers:

- What's the gross state product of California?
- How many people die per day on Earth?
- How many traffic lights are there in New York City?
- How many Chinese restaurants are there in the U.S.?
- How many passenger-miles are flown each day in the U.S.?
- How many volumes are there in the Library of Congress?
- How many notes are played in the full career of a concert pianist?
- How many square miles are there in the U.S.? How many of them have you been in?
- How many syllables have been uttered by humans since 1400 A.D.?
- How many "300" games are bowled in the U.S. per year?
- How many stitches are there in a stocking?
- How many characters does one need to know to read a Chinese newspaper?
- How many sperms are there per ejaculate?
- How many condors remain in the U.S.?
- How many moving parts are in the Columbia space shuttle?
- How many people in the U.S. are called "Michael Jackson"? "Naomi Hunt"?
- What volume of oil is removed from the earth each year?
- How many barrels of oil are left in the world?
- How much carbon monoxide enters the atmosphere each year in auto exhaust fumes?
- How many meaningful, grammatical, ten-word sentences are there in English?
- How long did it take the 200-inch mirror of the Palomar telescope to cool down?
- What angle does the earth's orbit subtend, as seen from Sirius?
- What angle does the Andromeda galaxy subtend, as seen from earth?
- How many heartbeats does a typical creature live?
- How many insects (of how many species) are now alive?
- How many giraffes are now alive? Tigers? Ostriches? Horseshoe crabs? Jellyfish?
- What are the pressure and temperature at the bottom of the ocean?
- How many tons of garbage does New York City put out each week?
- How many letters did Oscar Wilde write in his lifetime?
- How many typefaces have been designed for the Latin alphabet?
- How fast do meteorites move through the atmosphere?
- How many digits are in 720 factorial?
- How much is a brick of gold worth?
- How many gold bricks are there in Fort Knox? How much is it worth?
- How fast do your wisdom teeth grow (in miles per hour, say)?
- How fast does your hair grow (again in miles per hour)?\
- How fast is Venice sinking?
- How far is a million feet? A billion inches?
- What is the weight of the Empire State Building? Of Hoover Dam? Of a fully loaded jumbo jet?
- How many commercial airline takeoffs occur each year in the world?
These or similar questions will do. The main thing is to attach some concreteness to those numbers from 1 to 20, seen as exponents. They are like dates in history. At first, a date like "1685" may be utterly meaningless to you, but if you love music and find out that Bach was born that year, all of a sudden it sticks. Likewise with the secondary meaning for small numbers. I can't guarantee it will work miracles, but you may increase your own numeracy and you may help to increase others'. Merry numbers!