what can you see?

This shows the proportional relationship between 3 entities without specifying number. The ‘wavefunction’ is whole.


If you decide to ‘collapse’ this ‘wavefunction’ you will see specific relationships.

If you call the black rod 7, the others are 5 and 2.

If you call the black rod 70, the others are 50 and 20.

If you call the black rod 6, the others are two sevenths of six and five sevenths of 6.

If you measure them with a 1-rod then you can see these:

5 + 2 = 7

2 + 5 = 7

The above shows an extremely powerful law of algebra

7 – 5 = 2

7 – 2 = 5

The above mentioned law doesn’t work with this pair

If you call the black rod 1 you can see that:

five sevenths and two sevenths make one

1 minus five sevenths is two sevenths

1 minus two sevenths is five sevenths

If you call the yellow rod 1 you can see that:

seven fifths take away two fifths is one

one is equivalent to five fifths

If you call the red rod one you can see that:

seven halves less five halves is two halves

five halves plus two halves is seven halves


seven divided by five is one remainder two

seven million divided by five million is one remainder two million

The image is a CLASS. It is INFINITE as it is not collapsed.

The specific cases are INSTANCES. They appear when you measure the image.


The cuisenaire way


“The outstanding results achieved by the Cuisenaire-Gattegno method have made the present primary school curriculum and courses of study in mathematics completely out of date.” Madelaine Goutard, 1963