A brief article written for pupils about mathematical symbols.
There are no right and wrong answers to this
problem; the drawings could be up to $25.000$ years old, so we
cannot ask the people who drew them! What it does definitely show
us, however, is that the people living all of those years ago had
some sort of system for encoding information. This is what we need
to communicate - we use codes all of the time. Numbers are codes,
and so are letters; put together in a meaningful way, we can then
decode this, and work out what the message is. Symbols can also be
used to transmit information. For example, a smiley face shows that
you are happy, a plus sign means that you add numbers together and
Some great suggestions for the "meaning"
of the drawings were submitted. If we can understand the code the
cave men were using, we can then de-code this and read the message
Although this is posed as a mathematical
problem, we must also bear in mind that the drawings may not be
directly maths-related. Lauren, from the Princess Elizabeth School,
suggested that the drawings could be a map of an area, possibly
with directions. For example, the line on top of the vertical
lines, joining them all together, could represent the direction you
should walk in. The number of vertical lines, dipping down below,
represent the number of steps to take in that direction. The
"curvy" lines show a more complicated, curved path.
Lauren also made another suggestion:
Other people suggested that the drawings
could be some form of early counting system. Joe, from Meridian
Primary, and Lauren from Princess Elizabeth, thought that the lines
could represent a certain quantity. In the simplest case, each line
could mean "one". Then, to work out the total number, you would
just count the number of lines. As Ewan, from Sofrydd Primary
wrote, this a bit like the "tallying" that we use nowadays.
Although it is simple, writing large numbers using simply "ones"
may take a long time, and is very inefficent. So, perhaps
combinations of these lines could mean different things? Perhaps
some of the different symbols represent larger numbers? Read on
The code could
be more complicated; each line could mean two, or ten, or $100$.
Or, as Grant from the Village School suggested, the lines could
mean different quantities in different contexts. For example, when
there are six lines joined together by a horizontal line across the
top, this could represent $30$ or another number. A single line on
its own could still mean "one", but when it is grouped together
with other lines, it can mean something different.
This is actually similar to the way that the
numbers, which we use today, work. A number $2$ on its own means
"two". However, if the "$2$" is accompanied by other numbers (like
having more lines in the cave drawings), its place (i.e. its
context) in the number is important as it can mean different things
in different places/contexts. In the number $236$, the "$2$" now
means "two hundred". In the number $56721$, the "$2$" now means
Sam, from Village Elementary, thought that the
drawings in the cave may be some form of numeral system:
Different numeral systems have different
advantages and disadvantages. As mentioned above, the Arabic
numeral system uses the position of a number to encode different
meanings. This is good because we need fewer numbers for our code
(less to remember!). Also, it is quicker to write (and read) these
numbers than, let's say, Roman numerals. Compare "$1998$" (Arabic)
to MCMXCVIII (Roman)!
As well as being easier to write and read, the
Arabic numeral system also means that calculations are easier to
do. The "changeover" from the Roman to Arabic numeral system meant
that scientists and mathematicians could do more complicated sums
and come up with more complex theories.
Think about the advantages and disadvantages
of using the system seen in the cave (if the drawings do indeed
show some form of counting!).
What could the cave men be counting? Sam, from
Village Elementary, had a suggestion:
Maia, from Culford was also thinking this way.
She thought that the lines may be used to count sheep. Ethan
thought that the lines may represent years, as part of a
Overall, there is no definite answer for what
the drawings mean. People have different suggestions, or different
versions of a similar suggestion. As long as the reasoning is good,
then this is great! It is fantastic to have lots of different
theories to choose from!