The development of the system of measurements

Origins of the system of measurements >> (Entwicklung der massysteme)
 

Click the arrow which will appear in the bottom right corner of the window if you hold your cursor over it. You will see that the “seamless” ascending series of bars is divided into types of sizes. This subdivision is increasingly refined. If you want to go back you can click the arrow in the bottom left corner of the window. 
 

What happens at each step?
 

1. After the first click on the arrow you see that the seamless rising sequence is divided in groups. These can be compared to the groups which you created in the experiment. These are bars which belong together as a particular type of size. That type is limited by two threshold sizes which form the transition to a smaller and larger type of size. 
 

2. And 3. Here you only see the threshold sizes, thus omitting the intermediate bars. 
 

4. The difference between the eighth and tenth bar is as large as the seventh bar. 
 

5. The difference between the sixth and fourth bar is as large as the third bar. What is not yet demonstrated here – which is fifteen clicks away – is that the difference between the fourth and second bar is equal to the size of the first bar. The reason for this is the formula of the plastic number: this proportional number creates a range where the addition of two consecutive sizes creates the fourth size in the range. That is different from the sequence of Fibonacci which provides the golden ratio; there the addition of two sequential sizes always creates the third size in that sequence. 
 

6. Here you see how the bars as characteristic types of size contrast with the “seamless” ascending sequence.