It is indeed a surprising and fortunate fact that nature can be expressed by relatively low-order mathematical functions. (Rudolf Carnarp)
The objective of DigiMat is to lead students climb a staircase of construct/model-simulate-explore-understand-predict/control the World, through the following steps:
- Construct Natural Numbers 1, 2, 3, 4,…
- Construct Rational Numbers
- Construct Space and Position
- Construct Time and Motion
- Construct Particles/Bodies interacting by Forces
- Construct Models of the World using 1-5.
- Simulate-Explore-Understand-Control the World by 1-6.
The construction of the mathematical objects is realised by execution of computer codes with basic template of the form
- n = n + 1;
which when executed repeatedly starting with n=0 on the right, successively the natural numbers as 1 = 0 +1, 2 = 1 + 1, 3 = 2 + 1, 4 = 3 + 1, and so on. Here +1 represents stepwise construction where an object is built by adding piece after piece, like building a house brick by brick. The World is so constructed by repetition of +1 in various forms: bodies adding piece-by-piece like in MineCraft, motions of bodies by time-stepping from one moment to next moment like in a movie.
Recall that ordinary language is used to create models of the World with the ultimate goal of controlling the World by forming predictions of different scenarios allowing a more ore less rational decision of what action to take. DigiMat offers a specific precise language to use for specific purposes, with the ultimate goal of controlling the World (more or less) by a capability of predicting the World.