Functionality, nondeterministic. But oddly even if the universe was deterministic, that doesn’t mean it’s computable, so even if you knew every single state of every single atom and everything was deterministic, you still couldn’t make accurate predictions
This is a weird application of the Halting Problem
Suppose that the universe is absolutely deterministic, and we have an omniscient machine that can 100% accurately predict the future because of this
Now, imagine we have another much much simpler machine that just inverts whatever input it has; when given input A, it outputs B. This can be a single if statement or even a simple electronic NOT gate, but the functionality of this machine is completely known
Now, connect the determining machine to the inverting machine, and ask the omniscient machine “what will the inverter machine output?”
Although the universe is deterministic and the machine is omniscient, it’s impossible to accurately predict the future without being wrong.
If the determiner says “A”, then the inverter says “B”, and if the determiner says “B”, then the inverter says “A”
Even though the inverter machine is highly simple in construction and it’s functionality is completely known, it’s still enough to make accurate predictions in a deterministic universe impossible, even for an omniscient machine, since simply making a prediction changes the outcome
The only way for the omniscient machine to be accurate is if it doesn’t at all interact with the universe that it’s predicting, at which case it ceases to be useful
So nothing within the universe can 100% accurately predict the future, regardless if it’s deterministic or not
Functionality, nondeterministic. But oddly even if the universe was deterministic, that doesn’t mean it’s computable, so even if you knew every single state of every single atom and everything was deterministic, you still couldn’t make accurate predictions
This is a weird application of the Halting Problem
Suppose that the universe is absolutely deterministic, and we have an omniscient machine that can 100% accurately predict the future because of this
Now, imagine we have another much much simpler machine that just inverts whatever input it has; when given input A, it outputs B. This can be a single if statement or even a simple electronic NOT gate, but the functionality of this machine is completely known
Now, connect the determining machine to the inverting machine, and ask the omniscient machine “what will the inverter machine output?”
Although the universe is deterministic and the machine is omniscient, it’s impossible to accurately predict the future without being wrong.
If the determiner says “A”, then the inverter says “B”, and if the determiner says “B”, then the inverter says “A”
Even though the inverter machine is highly simple in construction and it’s functionality is completely known, it’s still enough to make accurate predictions in a deterministic universe impossible, even for an omniscient machine, since simply making a prediction changes the outcome
The only way for the omniscient machine to be accurate is if it doesn’t at all interact with the universe that it’s predicting, at which case it ceases to be useful
So nothing within the universe can 100% accurately predict the future, regardless if it’s deterministic or not