In which Caleb finds out that Grandpa has made an Incredible Counting Machine

The contraption seemed to comprise a metal box with an old typewriter stuck to the front. There was no lid to the box, but instead an axle stretched from one side to the other and on it were mounted a great many metal discs. There was an electric motor at one end and various gears, some disappearing from sight into the box. A long slot was cut in the front of the box so that the nearest point of each disc was visible, each one displaying a number from 0 to 9. The discs were free to rotate such that if you gave them all a spin with your hand, when they came to a stop they would be showing a long and probably very large number. A car battery was connected to one end and a great many wires entered and exited the box in different places.

“What is it?” asked Caleb.

“This,” said Grandpa, with wide eyes and excitement in his voice, “is an Incredible Counting Machine!”

“A counting machine?” asked Caleb, thinking of the calculator in his school bag, which was a lot smaller and probably cleverer. “Does it do sums and things?”

“No, no – it doesn’t do any maths or anything like that,” said Grandpa. “It just counts!”

Caleb tried not to sound unimpressed. “What kind of things does it count?”

“Anything you can think of!” said Grandpa. “If there was ever something you wondered how many there were of, but knew it was impossible to count – now you can know. And it’s not just an estimate – it’s an actual count, down to the nearest whole number! Let me show you…”

Grandpa moved his cup of tea to one side and pulled his chair up the typewriter as though he was about to write a letter.

“Think of something there are a lot of… say, people. We type the word ‘people’ carefully into the typewriter. P – E – O – P – L – E.” Grandpa repeated as he hit each key in turn. Caleb was surprised to see that the word ‘people’ didn’t appear anywhere. There was no screen or display of any kind. Clearly Grandpa hadn’t watched enough films – displays with really good graphics are important for convincing people that something works.

“Now,” said Grandpa, “we flick this switch and wait for the capacitor to charge.” Caleb didn’t think it was the time to ask what a capacitor was. A quiet hum began to emerge from inside the box. “Then we turn the motor on.” Grandpa flicked another switch and the motor sprung to life. The discs started to move slowly, but soon they were spinning very fast indeed. “Now, when the capacitor is fully charged there will be a bit of a bang,” Grandpa warned.

And there was. Suddenly a huge spark reached out of the box and seemed to finger all of the discs. As it did they each came to an abrupt halt. There was a slight smell of burning.

Looking along the discs, Caleb could see a large number spelled out:

6,572,981,452

“There you have it,” said Grandpa, “six billion, five hundred and seventy-two million, nine hundred and eighty one thousand, four hundred and fifty two. That was exactly how many people there were in the world when you heard the bang.” Grandpa opened a notebook, looked at his watch and wrote down the number.

“You mean that isn’t always the number of people in the world?” asked Caleb.

“Well, no, with something like the number of people it is changing all the time – as more people are born and some people die. I’ll show you.”

Grandpa typed the word ‘people’ again, flicked the two switches and they waited for the bang. Hum… BANG, flash.

6,572,982,176

(Now at this point make sure the grown up who is reading to you reads the number properly, with all the billions and millions spelt out. This is the last time I’ll help: six billion, five hundred and seventy-two million, nine hundred and eighty-two thousand, one hundred and seventy six.)

“Isn’t it amazing?” beamed Grandpa. “We could only guess at these numbers before; apply our best scientific methods to come up with an estimate, all the time knowing that only God knew the actual answer – if only he would tell us! But now we can know.”

“Come on,” said Grandpa, “your turn. What would you like to know?”

“How many cars are there?” asked Caleb, looking at Grandpa.

“How the heck would I know?!” said Grandpa with a grin. “Let’s find out!”

Grandpa resumed his position at the keyboard and typed c-a-r-s. Click, click, hum, BANG, flash.

896,432,987

“Wow. Does that include ones that have been taken to the scrap yard?” asked Caleb.

“When does a car stop being a car?” Grandpa answered with a wink. “I expect it does, but not ones that have been crushed – you wouldn’t say they were a car anymore, would you? Another one?”

“How many stars are there?” asked Caleb.

Grandpa carefully typed s-t-a-r-s. Click, click, hum… BANG, flash.

7,195,987,392,656,539,143,775

(OK, if the person reading to you needs more help, remind them to look in the front of the book).

“Wow, that’s a lot,” said Caleb “I didn’t know you could have such big numbers.”

“You’re right. I had no idea there were so many either – that’s more than there are grains of sand in the whole world. I checked that earlier.” Caleb pondered this for a moment – they were not the easiest things to compare.

Grandpa went on, leaning towards Caleb as though telling a really exciting story, “And when you think that the nearest star to us is sixty six trillion kilometres away – which would take you 7 years to reach at the speed of light, it makes the universe a pretty big place.” He looked at Caleb who was now staring deep into his eyes, almost as though he could see the whole universe inside Grandpa’s head.

Grandpa sat back on his chair and brought them both back to earth.

“We need to be a bit careful, though,” said Grandpa. “There are only twenty-two discs, so the biggest number you can have is nine septillion.”

“What would happen if it went over?” asked Caleb.

“I’m not sure,” said Grandpa, “I think there might just be a bit missing from the start of your number and you wouldn’t know it.” This didn’t sound like too much of a problem to Caleb.

“How many hairs on my head?” asked Caleb.

Click, click, hum… BANG, flash.

172,119

“How many hairs on your head, Grandpa?” And then, with spectacularly good timing, Mum called up: “Supper’s ready!”