穴居人是如何记数和书写数字的？

"Cavemen" is a very vague term. But many early life forms would use body parts, like fingers, to count.

Tally marks became one of the first early systems of counting. They are a more ancient alternative to the number line.

Depending on where you're from, there are many different ways to tally. In the United States, we use lines up to four and then a slash through it to represent five. This repeats itself no matter how big a number we're tallying, even for very large positive integers. However, we cannot use tally marks to represent fractions because each line represents a $1$. It is not standard to break the lines into pieces.

In the Paleolithic era, the tally system was discovered on bones called tally sticks. They simply used lines to represent numbers, i.e. ||||||.

The tally system is also related to multiples of numbers. Each group of slashed tallies represents $5$. That means:

1. Two groups will represent the number $10$
2. Three groups will represent the number $15$
3. Four groups will represent the number $20$

and so on.

This also means you won't have more than four sticks with no slash through them. The ticks with no slash can be thought of as the remainder when dividing by $5$.

Cavemen Counting

Cavemen counting is an easy way to keep count by drawing lines.

Cavemen counting is essentially drawing a vertical line for each count.

For example, $4$ can be represented as |||| and $8$ can be represented as ||||||||.

Let’s take a look at an example.

You are conducting a survey and asking people what their favorite subject is. $5$ people said English, $8$ people said Math, $6$ people said Science, and $4$ people said Art.

Let’s summarize this data using cavemen counting.

Now, we can write the totals on the right side.

We are now going to take a look at a problem you might encounter about cavemen counting.

You can represent 'four' using cavemen counting by drawing $4$ vertical lines or $4$ tallies, ||||.

(Video) Tally Marks (Cavemen Counting)

by Don’t Memorise

Here is a Youtube video by Don’t Memorise that covers Cavemen Counting.

$\large{\text{Summary}}$

This video uses a survey to demonstrate how cavemen counting can be used in real life.

Instead of writing numbers, we can draw a vertical line to represent $1$ person, or $1$ unit. Each person is a whole quantity. Thus it should make sense that we only use tally marks to represent positive numbers.

When you get to five, draw a slanted line going through $4$ vertical lines to represent the $5$th person, or the $5$th unit. It is easier to count this pattern than a group of only vertical lines bunched up together. For instance, try counting the number of lines in this picture:

$$||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||$$

If you're like me, your eyes probably hurt!