V space is defined by base vectors (basic functions). In conventional vector spaces, basis vectors are linearly independent. This idea should be expanded to V space, meaning that functionalities of basic functions shouldn’t overlap. It was said yesterday that each base vector should do one thing only. This condition is necessary to ensure functionalities won’t overlap. However, this is not a precise condition. Conditions for base vectors should be specified. Functions get a set of inputs and produce an output based on some procedure. Procedures contained in functions specify whether functionalities of base vectors overlap or not (for example consider F_1 (x)= g(x)/h(x) = x and F_2(x)= k(x)/j(x)=x, but F_1(x) and F_2(x) may be totally different procedures, although both functions output x, so output doesn’t specify whether functionalities overlap).
For this purpose, a network of nodes will be defined. Then it is required that each base vector connects one node to another node. This means each functionality starts from some initial state or position to the final position (with no intermediary node). This condition ensures no function (or base vector) is reducible.
So now functionalities are constructed based on nodes. The next question is what those nodes are. In previous writings, complex problem-solving was discussed. Each problem should be divided into its constituent parts then the collection of solutions to those parts provides a solution to the main problem. However, it was said that this wasn’t a unique process.
In this setting, each constituent part is a node. So a complex problem might consist of many nodes. So a programmer write down the problem they try to solve. The AI system divides the problem into its constituent parts, and those parts will be the base vectors of that V space. Then if another programmer writes another problem, the AI system will try to divide that problem with existing base vectors. If new base vectors are necessary, the AI system will generate new base vectors, and this process goes on and on.
UPDATE 1:
I was advised to make it a game. Good suggestion. It’s cool to invent an encoding language and try to decode other teams’ messages. It will be an evolutionary game, the best encoding languages (methods) will be selected. So the platform provides means for this competition, players will build the encoding systems. Anyone can play this game, not only researchers, etc.
Networking is essential in this game. people should form teams. this is not a solo game.