From "forever unknowable" to "look at position 17,387,594,880"

[PseuTonym]

The intuitionists Brouwer and Heyting appealed to the “impossibility” of ever knowing whether and where the sequence 0123456789 appears in the decimal expansion of pi …

Yet it was found in 1997 by Kanada, beginning at position 17,387,594,880.

Depending on one’s ontological perspective, either

1. Nothing had changed, except for our state of knowledge. In other words, those digits were discovered in pi, and had always been there, or …

What should come next?

I will omit information about the source that I am quoting, because I think that the authors got a big sloppy there. I doubt that you will find a good answer by simply locating the text and copying what is there. However, after there have been some replies, I will certainly reveal the source in this thread if anybody makes such a request in this thread. In the meantime, send me a private message if you are interested.

 

[Crusaderbear]

By observing pi, humans created the sequence called the observer effect, a result of the heisenburg principle…or, stuff happens!

 

[GEddie]

If anything non-God is eternal, (which isn’t), certainly pi would be one of them!

ICXC NIKA

 

[Usagi]

Of course those digits were always in that position.

Well, we had to come up with a specifically decimal number system for pi to look that way, but “the relationship between a circle’s diameter and circumference” is a fixed thing, and doesn’t change as we become aware of more of it.

 

[Latias]

What should come next?

I will omit information about the source that I am quoting, because I think that the authors got a big sloppy there. I doubt that you will find a good answer by simply locating the text and copying what is there. However, after there have been some replies, I will certainly reveal the source in this thread if anybody makes such a request in this thread. In the meantime, send me a private message if you are interested.

I don’t know much about the mathematics of getting the precise digits or irrational numbers, but I would suppose that the string of digits are essentially random as Wikipedia says.

Since it is essentially random, then any digit could come next at an equal probability (10% for each digit).

Is there anything with greater profundity from the philosophy of mathematics than just the facile insight that they are essentially random?

 

[e_c]

Or they were only there because we had thought of that position.

The first option is the correct one.

 

[rossum]

If anything non-God is eternal, (which isn’t), certainly pi would be one of them!

There are a lot of things which are eternal and are not God: life, hell, heaven, love etc.

rossum

 

[GEddie]

There are a lot of things which are eternal and are not God: life, hell, heaven, love etc.

rossum

None of those items are eternal, as all were created.

Any created thing has a beginning.

ICXC NIKA

 

[rossum]

None of those items are eternal, as all were created.

• Is God alive, yes or no? (Psalm 42:2 applies)

• Is God created, yes or no?

You may want to rethink that statement.

Any created thing has a beginning.

So, God has not always loved; there was a beginning to God’s love. Was there a time when God was not present in heaven?

rossum

 

[Usagi]

• Is God alive, yes or no? (Psalm 42:2 applies)

• Is God created, yes or no?

You may want to rethink that statement.

Certainly not in the biological sense. But you do have a point there; anything that we say God “is” (existence, love, truth) is eternal because God is. I’m not sure that’s strictly the same thing as “things that are eternal but are not God,” though.

So, God has not always loved; there was a beginning to God’s love. Was there a time when God was not present in heaven?

rossum

In the broadest sense, Heaven is God’s presence, which would make it eternal but not distinct from God, like the concepts above. If we limit it to “the experience of God’s presence by a creature,” then Heaven did not exist as such until the first creature had that experience (but we would then also have to say that God Himself is not technically in Heaven). If there is a particular place (or place-analogue outside space as we know it) in which the afterlife generally occurs, then that would again be something created and not eternal.

 

[PseuTonym]

I don’t know much about the mathematics of getting the precise digits or irrational numbers, but I would suppose that the string of digits are essentially random as Wikipedia says.

Since it is essentially random, then any digit could come next at an equal probability (10% for each digit).

Is there anything with greater profundity from the philosophy of mathematics than just the facile insight that they are essentially random?

I believe that the decimal expansion of pi is almost completely non-random from the point of view of trying to use it as a one-time pad. Are you aware that a one-time pad that sender and receive have is thought to be an unbreakable code?

As a highly successful student once wrote (after earning both his undergraduate degree in chemical engineering, and his Ph.D. in mathematics at approximately the same time) …

Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.’
Link:
perlmonks.org/?node=Why%20aren%27t%20my%20random%20numbers%20random%3F

You might cook up your own home-made candidate for a one-time pad via a key generated from unpredictable atmospheric phenomena such as a highly precise registering of the timing of radioactive emission of a single hydrogen ion from a small sample of radium. Your computational device should generate a private key for use in a public key encryption system, with the registered information not stored in any removable secondary storage, but kept purely in volatile electronic storage, and the device powered down completely so that no trace will remain within the device of the timing information that was used to generate the private key.

You might want to look into Greg Chaitin and so-called Algorithmic Information Theory. It is said that Chaitin gave a rigorous proof of a vast generalization of Godel’s Incompleteness Theorem.

 

[rossum]

I believe that the decimal expansion of pi is almost completely non-random from the point of view of trying to use it as a one-time pad.

Putting my cryptographic hat on, it is (just) possible to use the expansion of pi, to any base, as a key to a One Time Pad. However, the binary number for the index of the first digit used would have to contain at least as many bits as the message being encrypted. Preferably a lot more. For the OTP to work, the key must be at least as long as the message. It is probably easier to use a true random source to generate the key.

Are you aware that a one-time pad that sender and receive have is thought to be an unbreakable code?

Yes, used properly (and the “properly” is absolutely critical) a One Time Pad is mathematically unbreakable. See “Venona” for the failings of a ‘Two Time Pad’.

As a highly successful student once wrote (after earning both his undergraduate degree in chemical engineering, and his Ph.D. in mathematics at approximately the same time) …

Anyone who attempts to generate random numbers by deterministic means is, of course, living in a state of sin.’
Link:
perlmonks.org/?node=Why%20aren%27t%20my%20random%20numbers%20random%3F

Very true, but deterministic pseudo-random numbers can be useful in places. Amateur cryptographers have a distressing tendency to imagine that using pseudo-random numbers can make a One Time Pad; they cannot. Their idea usually turns out to be a Stream Cipher, which is a different beast: more practical, but not mathematically unbreakable.

rossum