How does the Morkov Network work and what is without memory?

Question

How do Markov chains work? I read wikipedia for the Markov chain , but I do not get without memory. Vastness says that:

The next state depends only on the current state, and not on the sequence of events preceding it.

If the Markov chain has this property, then what is the point of using the chain in the Markov model?
Explain this property.

Answer 1

, , . , (-) . Ai Aj j. , .

, , Ai Aj , . , , .

Answer 2

. , . , , . http://www.americanscientist.org/issues/pub/first-links-in-the-markov-chain

. , , . , ( ) - . , ( , ).

, .. . , . , (, , !), - , - , . 3 3, ( I, , "" J),

, "" . "" . 9 , , 9 9. , .

, , , , , , , . , . 9 9, . , , , : () , - "", , , . . ( ), , .

, : ( , - ). 3 3 , ( , , ), . 9 9, 3 , , 18 . , .

, , , , . , . , , , " " .

, ( ), , , . () ( ) . n- n- , . , , , ( ) http://en.wikipedia.org/wiki/Hamiltonian_mechanics

, . (, ) . , . , . (, ) . ( , "" ).