‘Andrew, can an aeroplane fly at two-thousand miles per hour?’ asked Rodrigo.

Rodrigo sat at the end of the two tables that had been pushed together for dinner at TK’s restaurant. Andrew sat on his right-hand side. Rodrigo’s dad, Renato, sat to his left. To Andrew’s right sat Marcia. Across from Marcia, sat Monica, Rodrigo’s mum. Ruth sat at the end of the table opposite Rodrigo. The table was covered with dishes of spicy Asian food, chopsticks, pots of green tea, glasses of soda, and a glass of chocolate-milk for Rodrigo.

Andrew paused for a moment while he considered two supersonic aircraft brought
to mind by Rodrigo’s question. ‘I think the Anglo-French Concorde supersonic passenger aeroplane might travel close to that speed. I can’t remember exactly. I know it flies faster than one-thousand miles per hour.’

‘If it flew at two-thousand miles per hour, it would only take an hour to get from here to my home in Guatemala City,’ said Rodrigo in almost perfect English.

‘Yes, but that doesn’t take into account the time it takes to taxi, take-off, land, and taxi to the terminal.’

‘Can I fly on the Concorde?’

‘No, they took it out of service a few years ago because it had become too
expensive to fly. You can find out about the Concorde by connecting to the Internet from your computer and typing www.wikipedia.org into the address-bar of your web-browser.’

‘Oh!’ Rodrigo looked slightly disappointed. ‘How long would it take to fly from the Arctic to the Antarctic in the Concorde?’

‘That’s a good question. Do you know the circumference of the earth?’

‘No.’

‘Neither do I. Now I can’t remember. What else do I know about the earth?’ Andrew asked himself the question, looked out of the window and thought for a moment. ‘I understand the earth to be spherical; at least, mostly spherical. Scientists say that it isn’t perfectly spherical; they describe the earth as an oblate-spheroid—’

‘What does that mean?’

‘If you take a soccer-ball and put it on the ground and then press down on it hard enough to compress the ball, you have created an oblate-spheroid, which is a sphere that is squashed at the poles and fatter at the equator. But for the purpose of estimating the circumference of the earth, we will assume that the earth is a perfect sphere. How far around the earth would you go if you fly from the north-pole to the south-pole?’

Rodrigo considered this question for a moment and then said: ‘Half way around.’

‘Correct. So, how far around does the circumference go?’

‘All the way.’

‘Correct. So, how much of the circumference do you travel if you travel from the north-pole to the south-pole?’

‘Half?’

‘That’s right. So if we know the circumference of the earth and divide it by two, we will know how far it is from the Arctic to the Antarctic. Once we know that, we can calculate how long it will take to fly the distance at two-thousand miles per hour.’

‘But, we don’t know the circumference of the earth,’ said Rodrigo.

‘No, we don’t. Yet, I think you will agree that there are three-hundred and sixty degrees in a circle, which means that the circumference of the earth can be divided into the same number of degrees. Now, when we combine that fact with some other knowledge that I happen to have, we can compute the distance around the surface of a circular earth.’

‘What knowledge is that? What do you know? Tell me.’

Rodrigo was starting to get really interested in this Holmesian deduction and was,
by this time, paying close attention. Andrew, meanwhile, poured more Oolong tea into his cup and then took two, maybe three sips, savoring the fragrance and slightly nutty flavor; he looked into Rodrigo’s eyes then examined the details of Rodrigo’s face while he wondered if he should reveal this arcane piece of knowledge. Finally, he decided that he liked Rodrigo enough to share the special delights of discovery and knowing.

‘OK! I’ve studied navigation a little in the past—’

‘When?’

‘Oh! Let me see! You had your tenth birthday yesterday, didn’t you?’

‘Yes.’

‘I think I was eleven years old, perhaps I had twelve years when I started to learn about navigation. Then I lived on the south coast of England. At school I remember plotting courses from Portsmouth to Cap Gris Nez in France on nautical charts using parallel rulers and dividers. Since then I have learned other things about navigation.’

‘Like what?’

‘Well, the information we need is the distance between each degree of latitude on the surface of the earth. By the way, lines of latitude are used to divide the surface of the earth north and south of the equator. I haven’t thought about this for a long time, so I’m not sure, but I think the distance on the surface of the earth between degrees of latitude is six-hundred nautical miles; hmm! maybe it’s sixty miles, I can’t remember.

‘Can I have your notebook and pencil?’ asked Rodrigo, looking at Andrew’s shirt pocket where he could see the wire-spiral of the notebook and the pencil-clip.’

‘Here you are,’ said Andrew, taking them from his pocket and offering them Rodrigo.

Rodrigo turned to a fresh page, extended the pencil lead and started making a
calculation. This is what he wrote:

       360 degrees multiplied by
       600 nautical miles
216,000 nautical miles

‘There,’ said Rodrigo turning the notebook toward Andrew, ‘the circumference of the earth.’

‘That number looks too big to me. I think my first thought was an order of
magnitude too big. Now that I am thinking of it, I remember the definition of a nautical mile; it is the distance on the surface of the earth at the equator subtended by one minute of arc from the center of the earth. How many minutes are there in one degree?’

‘Sixty?’

‘Yes. So, multiply the number of degrees in a circle by sixty.’

Taking the notebook and pencil, Rodrigo performed this calculation:

     360 degrees multiplied by
       60 nautical miles
21,600 nautical miles

‘There,’ said Rodrigo showing his result.

‘That looks like a more reasonable answer. However, we have another problem.’

‘What?’ said Rodrigo, his face clouded by a frown.

‘You asked about flying at two-thousand miles per hour whereas we have just
calculated the distance in nautical miles which are longer than statute miles used for everyday measurement. When using nautical miles, speed is computed in knots. Nautical miles and knots are a legacy from the days of the sailing ship. There are approximately 6,060 feet in a nautical mile. In a statue mile there are 5,280 feet.’

‘Oh!’ said Rodrigo, whose expression had changed to one of glum resignation at the prospect of arithmetic likely to give him indigestion.

‘Don’t worry, I won’t ask you to convert from nautical miles to statute miles. We just need an approximate idea of how long it would take to fly from pole-to-pole at two-thousand miles an hour, give or take a few minutes. You know what to do now that you have found the circumference of the earth, divide it by two to find the distance from the Arctic to the Antarctic, assuming we are going from geographic pole to geographic pole.’

Once again Rodrigo took the notebook and, this time, turned to a fresh page. Here
is what he wrote:

2)21600 nautical miles

   10800 nautical miles

Next, Rodrigo divided the distance by the speed of two-thousand miles per hour,
which he did in his head by moving the decimal point three places to the left and dividing the result by two, thus:

10.800 or 10.8 divided by 2 = 5.4 hours

Rodrigo wrote down the answer and underlined it twice.

‘Well done indeed,’ said Andrew, reaching out to give Rodrigo a congratulatory pat on the shoulder. ‘What do you notice about the time it takes to fly at two-thousand miles per hour from pole-to-pole and the time it takes to fly from here to Guatemala City?’

‘Oh!’ said Rodrigo, ‘It takes a little more than five times as long to fly the poles.’

‘Why is that?’

‘Because it is five times as far.’

‘Excellent! But it is not exactly five times as far, is it?’

‘No.’

‘So, how far is five-times farther than Guatemala City from here?’

Rodrigo thought about this for a moment while he multiplied two-thousand miles
by five in his head and said: ‘Ten-thousand miles.’

‘Yes, that’s right. And if it takes one hour to fly to two-thousand miles, it will take five hours to fly ten-thousand miles at two-thousand miles an hour. Won’t it?’

‘Yes.’

‘So how many miles are accounted for by that fractional four tenths of an hour above five hours that you calculated a little while ago?’

Rodrigo looked at his calculations on the sheets of notepaper and, in his head,
subtracted ten-thousand miles from ten-thousand eight-hundred and replied: ‘Eight-hundred miles.’

‘Good man! Now, are you going to have dessert?’

‘No, I’m full. I want to go to the concert in Utica Square.’

‘Marcia and I have to go home. When you get home, check the wikipedia for
information on the Concorde. Also, look up the SR-71 Blackbird. Be careful using the wikipedia; there is no editorial control other than the people who use and contribute to it, so compare what it says against what you know. If what you see there doesn’t make sense, check the facts purported against other sources of information, just as we have done this evening. Be skeptical about what you read and hear. If information doesn’t feel correct, verify it against other sources and, if possible, perform your own tests and experiments for truth and accuracy. Be skeptical about what you think you know because you might be in error.’

The waitress brought the bills for Andrew and Renato to pay. Each of the diners
ate a fortune cookie. Inside Rodrigo’s cookie the fortune said: ‘You will have interesting conversation and learn new things.’

Rodrigo went to attend the concert. Andrew went home.