I have said more than once, that I hold space to be something purely relative, as time; an order of coexistences, as time is an order of successions. (Leibniz)
If you follow the path, you will with satisfaction discover that you have learned to master powerful mathematics, which in traditional teaching is viewed far too advanced to serve as school mathematics.
Be confident that these two short codes will carry you long way! It is the computational-constructive aspects of DigiMat which allows you to take this leap even if you are not a math freak. Be confident that the path is open to you!
Take as a first goal, for example, to construct your own Angry (Math) Birds.
- First the natural numbers are constructed by repetition of the basic operation of +1 according to a basic prototype of all computer programs of DigiMat of the form n = n + 1, which starting with n = 1 generates 2 = 1 + 1, 3 = 2 + 1, 4 = 3 + 1, and so on. Similarly the negative integers are constructed with repetition of the operation -1.
- Once the integers have been constructed, representation in binary or decimal form is specified and the basic algorithms of addition, subtraction, multiplication and division are defined and then expressed as computer programs taking the form of a pocket calculator programmed by the student, which in a next step is extended to rational numbers in binary or decimal form.
- With rational numbers at hand Newton/Leibniz’ world of Calculus and Linear Algebra, can be constructed as spatial and temporal variation expressed by numbers. The prototype program then takes the form x = x + v*dt and v = v+a*dt, where x is spatial position, v is velocity and a is acceleration, which can depend on x and v, and dt is a time step. This is the time stepping version of Newton’s Laws dx =v*dt, dv=a*dt and a=f/m.
- The next step is to extend to cover all aspects of the world as solid/fluid/quantum mechanics, thermodynamics, electromagnetics, biology, geoscience, economy, and more, all in constructive form based on computer programs of the prototype form.
Here you find more material in the form of earlier versions of DigiMat: