If it’s infinite without repeating patterns then it just contain all patterns, no? Eh i guess that’s not how that works, is it? Half of all patterns is still infinity.
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.
This might just be my computer-focused life talking
I’m a software eng too, but I have broad interests. Like I said, the philosophic use doesn’t really have a place in this discussion and I messed up by bringing it in. The only way it would be relevant is if the universe is a simulation because, as you guessed, then free will itself becomes part of the equation.
I also don’t know why predictability would be solely based on the numbers that came before
There’s a miscommunication happening here, and I’m wondering if I’m not explaining myself well. Election predictions use polling as their dataset, and there are no calculations that really go into predicting the results other than comparing the numbers within those sets. That’s why they’re notoriously garbage (every single pollster had Hillary winning in late October 2016, for example). Also, there aren’t any calculations that go into a CEO/Boardroom’s intuitions on how shareholders will react to policy changes, so I’m not sure about the relevance here. In the case of pi, there is no dataset that you can use that tells you what the next unknown number in pi is. The only way to get that number is to run a very complex calculation. Calculations are not predictions.
However, as the name implies, this is nothing special about pi. Almost all numbers have this property. If anything, it’s the integers that we should be finding weird, like you mean to tell me that every single digit after the decimal point is a zero? No matter how far you go, just zeroes forever?
If it’s infinite without repeating patterns then it just contain all patterns, no? Eh i guess that’s not how that works, is it? Half of all patterns is still infinity.
No. 1011001110001111… (One 1, one 0, two 1s, two zeros…) Doesn’t contain repeating patterns. It also doesn’t contain any patterns with ‘2’ in it.
But pi is believed to be normal. https://en.m.wikipedia.org/wiki/Normal_number
So it should contain all finite patterns an infinite number of times.
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.
I’m a software eng too, but I have broad interests. Like I said, the philosophic use doesn’t really have a place in this discussion and I messed up by bringing it in. The only way it would be relevant is if the universe is a simulation because, as you guessed, then free will itself becomes part of the equation.
There’s a miscommunication happening here, and I’m wondering if I’m not explaining myself well. Election predictions use polling as their dataset, and there are no calculations that really go into predicting the results other than comparing the numbers within those sets. That’s why they’re notoriously garbage (every single pollster had Hillary winning in late October 2016, for example). Also, there aren’t any calculations that go into a CEO/Boardroom’s intuitions on how shareholders will react to policy changes, so I’m not sure about the relevance here. In the case of pi, there is no dataset that you can use that tells you what the next unknown number in pi is. The only way to get that number is to run a very complex calculation. Calculations are not predictions.
However, as the name implies, this is nothing special about pi. Almost all numbers have this property. If anything, it’s the integers that we should be finding weird, like you mean to tell me that every single digit after the decimal point is a zero? No matter how far you go, just zeroes forever?
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Not, the example I gave have infinite decimals who doesn’t repeat and don’t contain any patterns.
What people think about when said that pi contain all patters, is in normal numbers. Pi is believed to be normal, but haven’t been proven yet.
An easy example of a number who contains “all patterns” is 0.12345678910111213…