Computer programs exist that can tell you what the next digit is. That means it’s deterministic, and running the program will give you a prediction for each digit (within the memory constraints of your computer).
The fact that it’s deterministic is exactly why pi is interesting. If it was random it would typically be much easier to prove properties about it’s digits.
There’s no way to predict what the next unsolved pi digit will be just by looking at what came before it. It’s neither predictable nor deterministic. The very existence of calculations to get the next digit supports that.
Note: I’m not saying Pi is random. Again, the calculations support the general non-randomness of it. It is possible to be unpredictable, undeterministic, and completely logical.
Note Note: I don’t know everything. For all I know, we’re in a simulation and we’ll eventually hit the floating point limit of pi and underflow the universe. I just wanted to point out that your example doesn’t quite fit with pi.
As I said, you can’t predict the next number simply based upon the set of numbers that came before. You have to calculate it, and that calculation can be so complex that it takes insane amounts of energy to do it.
Also, I think I was thinking of the philisophical definition of “deterministic” when I was using it earlier. That doesn’t really apply to pi… unless we really do live in a simulation.
This might just be my computer-focused life talking, but I’ve never heard of deterministic meaning anything but non-random. At best philosophic determinism is about free will and the existence of true randomness, but that just seems like sacred consciousness.
I also don’t know why predictability would be solely based on the numbers that came before. Election predictions are heavily based on polling data, and any good CEO will prepare for coming policy changes, so why ignore context here? If that’s a specific definition in math then fair enough, but that’s not a good argument for or against the existence of arbitrary strings in some numbers. Difficult is a far cry from impossible.
Yeah, but your number doesn’t fit pi. It may not have a pattern, but it’s predictable and deterministic.
Pi is predictable and deterministic.
Computer programs exist that can tell you what the next digit is. That means it’s deterministic, and running the program will give you a prediction for each digit (within the memory constraints of your computer).
The fact that it’s deterministic is exactly why pi is interesting. If it was random it would typically be much easier to prove properties about it’s digits.
There’s no way to predict what the next unsolved pi digit will be just by looking at what came before it. It’s neither predictable nor deterministic. The very existence of calculations to get the next digit supports that.
Note: I’m not saying Pi is random. Again, the calculations support the general non-randomness of it. It is possible to be unpredictable, undeterministic, and completely logical.
Note Note: I don’t know everything. For all I know, we’re in a simulation and we’ll eventually hit the floating point limit of pi and underflow the universe. I just wanted to point out that your example doesn’t quite fit with pi.
π isn’t deterministic? How do you figure that? If two people calculate π they get different answers?
What π is, is fully determined by it’s definition and the geometry of a circle.
Also, unpredictable? Difficult to predict, sure. Unpredictable by simple methods, sure. But fully impossible to predict at all?
As I said, you can’t predict the next number simply based upon the set of numbers that came before. You have to calculate it, and that calculation can be so complex that it takes insane amounts of energy to do it.
Also, I think I was thinking of the philisophical definition of “deterministic” when I was using it earlier. That doesn’t really apply to pi… unless we really do live in a simulation.
This might just be my computer-focused life talking, but I’ve never heard of deterministic meaning anything but non-random. At best philosophic determinism is about free will and the existence of true randomness, but that just seems like sacred consciousness.
I also don’t know why predictability would be solely based on the numbers that came before. Election predictions are heavily based on polling data, and any good CEO will prepare for coming policy changes, so why ignore context here? If that’s a specific definition in math then fair enough, but that’s not a good argument for or against the existence of arbitrary strings in some numbers. Difficult is a far cry from impossible.