NITAAI-Veda.nyf > Soul Science God Philosophy > Science and Spiritual Quest > Section 2 Machine, Mind and Consciousness > MOLECULAR INTELLIGENCE > 4.3 Diophantine Equations |

**4.3 Diophantine Equations**

Consider the following Diophantine equation (the polynomial
equations, in any number of variables, for which all the coefficients and all
the solutions must be integers [13]):

6w + 2x2-y3 =0

5xy - z2 + 6 = 0

w -w+2x-y=z-4=0

When solved, the solution comes out to be: w = 1; x = 1; y =2; z=
4;

Now consider another Diophantine equation:

6w + 2x2-y3 = 0

5xy-z2+6 = 0

w -w+2x-y-z-3=0

This equation has no solution (because by its first equation, y
must be even, by second equation z must be even also but this contradicts its
third equation: whatever w is, because w2 - w is always even, while 3 is an odd number).

The first equation can be solved by writing a computer algorithm,
which just slavishly tries all sets of integers one after another, and after a
certain number of trials, it finds: w= l;x= l;y=2;z = 4isthe solution. When the second equation is
given to the same algorithm, it will never halt for it will not get any
combination of numbers which solve the equation.

While human being using his conscious brain can easily tell
whether such an equation has solution or not, no computer algorithmusing
artificial intelligence can do this.

While human being using his conscious brain can easily tell
whether such an equation has solution or not, no computer algorithm using
artificial intelligence can do
this. If consciousness could be simulated on
a computer, then there
must exist a computational algorithm for the above
mathematical problem, which could tell in yes/no that such numbers can exist
or not.Russian mathematician Yuri
Matiyasevich [14] demonstrated that there can't be any computer algorithm which
decides yes/no systematically to the question of whether a system of Diophantine equation has a solution.