Let us pretend that we can go back to a time two hundred centuries ago. We're going to pay a visit to a little girl in a land across the sea. The girl's name is Nom. She and her family are Stone Age people. In the last story you began to understand what life was like for the cave man.
Like every other member of the family, this little girl, Nom, has many jobs to do. She helps her mother and brother find food for the family to eat. They gather nuts, berries, roots, and seeds.
Nom's mother has a way of grinding seeds by using two stones. After the seeds are ground, Nom's mother adds water to make a thick paste. The she bakes the paste in the sum to make a cake.
The cave people dress in animal hides. Nom helps to clean the hides with a stone scraper.
Nom's brother has a fishhook made of an animal bone. He has made a string out of animal skin. He can help the family by catching fish in the stream.
The biggest job for the cave people is finding food. So everyone must help. Life isn't easy. In fact, just keeping alive is quite a big job itself.
One day Nom's father sets out on a hunting party with a number of other cave men. The hunting party works as a team. Teamwork is better than one person working alone. This hunting party is going after deer meet. A herd of deer was seen not far away.
At sunrise the hunting party starts off. Later that day the cave men are back, carrying a big fat deer with them. Everyone is pleased; there is plenty of deer meat to go around.
Little Nom decides to keep track of the number of deer which the cave men bring back. She has a way of keeping track of numbers with pebbles. After dinner Nom digs a small hole with a sharp stone near the mouth of the cave.
Next to the small hole, she places a pile of pebbles. Nom thinks to herself, "I'll let one of those pebbles stand for one deer. The hunting party got one deer today, so I'll drop one pebble into the Ones' Hole."
Nom isn't thinking with those English words exactly. Her language is not English; her language is an ancestor of English. Every language has ancestors just as every person has ancestors. In order to think, we need language. Nom has a language, and with it she can do her number thinking.
At sunrise the next day, Nom is up and helping her mother. The hunting party is setting out to track the herd of deer. They hope to get another deer. Nom her mother and her brother work on several jobs while the men are away. When the hunting party returns, the men are carrying another deer.
After dinner, Nom runs to the place where she is keeping her record. She thinks, "That's deer number two. I'll drop pebble number two into the Ones' Hole."
The cave men are very lucky in their deer hunting. At the end of the sixth day, Nom has six pebbles in the hole where she keeps her ones. Six pebbles stand for six deer.
On the seventh day Nom stands at the mouth of the cave watching the hunters leave together. She begins to think of a very important plan. The little girl of the cave family says to herself, "If the men bring back one more deer, that will make seven deer all together – one dear every day for seven days. But I don't think I'll drop the seventh into the Ones' Hole. I've got a better plan."
The seventh day is another lucky hunting day. The hunting party of cave men bring back another deer. That nught there will be plenty of meat for everybody.
After dinner Nom goes to the place where she keeps her record. "Let's see," she says. "Before, I was letting one pebble stand for one deer. Why can't I just as well let one pebble stand for seven deer? Yes, I can. But if one pebble stands for seven, I can't drop it into the Ones' Hole. I'll dig another small hole to the left of the Ones' Hole. I'll call it the Sevens' Hole."
Nom digs another hole next to the Ones' Hole on the left. Then she takes the six pebbles from the Ones' Hole. It's empty. She drops one pebble into the Sevens' Hole and tells herself, "There's my record and it's easy to read. It says one seven and no ones. That means seven deer so far. Maybe there will be more later."
On the next day the hunters return with still another deer. After dinner Nom wants to bring her record up to date. She drops a pebble into the Ones' Hole. The record tells her that there is one seven and one one. Every day for one week and one day the cave people had a deer to eat.
Can you think of another way to say the number of deer which Nom counted?
The people two hundred centuries ago didn't write as we do today. Here's a way to write nom's record:
11seven
It means one seven and one one. The cave man's little girl had found a way of counting by sets of sevens.
Today we count by sets of tens. When you see 11, you can think, "That means one ten and one one."
Let's see if you understand. What is the meaning of each of these records?
11three 11five 11nine
Nom never went to an arithmetic class. She never had a teacher to help understand numbers. But Nom was a very smart, very bright little girl. She invented a way of counting and keeping a record.