If you multiply two numbers there's only one possible product. But the product has at least one pair of factors. So there are more input states than output states - the calculation reduces entropy.
The multiplication calculation actually increases entropy (energy or information unavailable to the system). The size of the set of possible factors used as parameters to the multiplication operation has been infinitely increased. The number of possible factors is an uncountable infinity. In the Aristotlean tradition, a Cause cannot generate any Effect of greater energy than that of the Cause itself.
The problem I have with CA being proposed as a model of a reality is that the arrow of time in CA seems to be backwards. In our reality, we know the past, but the future is uncertain. In cellular automata, the future can be predicted perfectly, but the states which were used to get to the current state are ambiguous.
Actually, thermodynamics shows us that due to energy dissipation, there is also information dissipation, meaning that the History of the universe is (so far) inaccessible to us. How is this any different with cellular automata simulations?
Detectives may be able to come up with neat little stories to fit the details of a crime scene, but there are many possible causes that could have generated the effects over which the detectives peer and ponder.
Slashdot Mirror
The multiplication calculation actually increases entropy (energy or information unavailable to the system). The size of the set of possible factors used as parameters to the multiplication operation has been infinitely increased. The number of possible factors is an uncountable infinity. In the Aristotlean tradition, a Cause cannot generate any Effect of greater energy than that of the Cause itself.
Actually, thermodynamics shows us that due to energy dissipation, there is also information dissipation, meaning that the History of the universe is (so far) inaccessible to us. How is this any different with cellular automata simulations?
Detectives may be able to come up with neat little stories to fit the details of a crime scene, but there are many possible causes that could have generated the effects over which the detectives peer and ponder.