Models of Addition

SzucsModel

 

Isn't addition like this: 1 + 2 = 3 ? If your technology is a typewriter, it is. This is certainly true for this blog since my human-machine interface is quite limited. And that is an interesting aspect of modeling: all models are tied to the technologies used to design and create them. So, if you have a marble quarry, then all of your models will look like stone. And if you use a typewriter or, equivalently, the modern keyboard, then your models will look like Arial, Helvetica, Times Roman, or whatever font family you happen to employ. For Szücs (Similitude and Modeling, 1980), the above mechanical components are models of addition. It is a way of thinking about mathematics using the technologies required to make gears and pulleys. There is nothing magical about typography in mathematics--it is just cheap and therefore useful for communication and standardization. Something that is not immediately apparent, but important, is that the models of addition contain the parameter of time. The addition using standard notation for simple addition is S(t) = a(t) + b(t).