The linked Voyager PDF pages show the *Voyager I* spacecraft and some of
the images encoded on a golden record placed on board. *Voyager
I* was launched by NASA on September 5, 1977, and it still
transmits data about the outer reaches of our solar system. A team of
scientists created the golden record in case intelligent life forms
find the spacecraft. The record contains many pages of information
about life on earth. The surface of the record contains symbols that
will hopefully help someone finding the record to play it. The
scientists felt that it was important to explain our number system and
arithmetic symbols at the beginning so that numbers could be used to
describe other items throughout the record.

Look at the page that introduces our numbers. What do you think the scientists are trying to explain? Why did they choose the examples shown?

What do you think the scientists are explaining on the other pages? Do you think that intelligent beings would be able to understand something about life on planet earth after seeing these? If you were going to add one more page, what would you include in this message to the cosmos?

We have made contact with intelligent aliens from another solar system! Our ambassadors think that it would be a nice gesture if we help some of the alien school children with their homework. The alien teachers transmitted the linked worksheets to us. The first two problems on each page are worked out as examples for the alien children.

We know that one of the pages is addition, one is subtraction, one is multiplication, and one is division, but we do not know which is which. We also do not understand what their symbols mean. The ambassadors have a feeling that the aliens do not use our base ten number system to represent numbers, but they are not certain what system they are using.

Your mission is to discover as many things about these worksheets as possible. Can you tell what operation is shown on each page? Can you tell what the symbols mean and make a key? Can you tell how their number system works? Can you understand how to translate these numbers into our system? How would you translate one of our numbers into their system? Finally, can you work out the alien math problems using their symbols?

Through the ages people have invented many different ways to name, write, and compute with numbers. Our current number system is based on place values corresponding to powers of ten. In principle, place values could correspond to any sequence of numbers. For example, the places could have values corresponding to the sequence of square numbers, triangular numbers, multiples of six, Fibonacci numbers, prime numbers, or factorials.

The Roman numeral system does not use place values, but the position of numerals does matter when determining the number represented. Tally marks are a simple system, but representing large numbers requires many strokes.

In our number system, symbols for digits and the positions they are located combine to represent the value of the number. It is possible to create a system where symbols stand for operations rather than values. For example, the system might always start at a default number and use symbols to stand for operations such as doubling, adding one, taking the reciprocal, dividing by ten, squaring, negating, or any other specific operations.

Create your own number system. What symbols will you use for your numbers? How will your system work? Demonstrate how your system could be used to perform some of the following functions.

- Count from 0 up to 100
- Compare the sizes of numbers
- Add and subtract whole numbers
- Multiply and divide whole numbers
- Represent fractional values
- Represent irrational numbers (such as π)

What are some of the advantages of your system compared with other systems? What are some of the disadvantages?

If you met aliens that had developed their own number system, how might their mathematics be similar to ours and how might it be different? Make a list of some math facts and procedures that you have learned. Which items on the list would probably be the same no matter what number system was used? Which facts and procedures would depend on the number system?

This work placed into the public domain by the Riverbend Community Math Center.

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http://riverbendmath.org

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This work placed into the public domain by the Riverbend Community Math Center.