CAIA as a mathematician (Part 3)

All in all, the explanation given for CAIA’s solution of the Saint-Exupéry problem is very simple. It includes only two important choices: what disjunction for the backtrack, and what value for L. For all the other steps of its proof, CAIA uses a combinatorial method: it applies every of its mathematical rules that can be […]

CAIA as a mathematician (Part 2)

Let us consider the beginning of the proof given in Diophante site. Three new unknowns appear, defined by: M/N=(C-A)/B=B/(C+A) the parities of M and N being different. This gives: A/(M2-N2)=B/(2*M*N)=C/(M2+N2)=D D is an integer because two denominators have never a common factor. Therefore, one has to solve: 2*M*N*(N-M)*(N+M)*D2=311850*P As either M or N is even, […]

CAIA as a mathematician (Part 1)

It is interesting, to compare the solutions found by CAIA with those found by a human mathematician. Diophante is a very useful site, which proposes many mathematical problems, with one, and sometimes several, solution. I will consider the solution found by CAIA, and the one given by Diophante for the same problem. One finds it […]

Bootstrapping CAIA Part III

 For the realization of a General Problem Solving system, a number of meta-problems arise. The main idea of bootstrapping is that these meta-problems will be solved by the system itself, in the same way as it solves the problems for which it was designed. CAIA is quite an elaborate system; however, it is not yet […]

CAIA is not a good magician

 Too often, IA researchers describe the successes of their system, but they keep a lower profile when they get poor outcomes. I do not want to comply to this bad habit. I describe here CAIA’s behavior when success does not come, in the present case, the magic square problem. An order N Magic Square has […]

CAIA surprised me Part I

 An AI researcher can always arrange his system so that it can find a solution that he already knows. To do that, he chooses a formulation well adapted to this solution, he includes all the methods necessary for this solution, and he indicates to avoid the roads that do not lead to the right direction. […]