Information mismatch

[questfortruth]

The square root of 2 is an irrational number. Any irrational number contains infinitely many bits of information.
For example, the Pi has infinitely many digits. The Pi is an infinitely long number. To describe it thoroughly, one needs an infinitely huge file. Same for the root of 2. But, on the other hand, the amount of information is small and finite, just the sentence "root of 2."
Why, in the first presentation, infinitely much independent information, but in the second presentation - very little information?
This means that information is not invariant.
Hence, the information does not conserve like a physical energy saving. This is a solution to the Black Hole Information Loss Paradox of Steven Hawking.

Author: Dmitri Martila, 20. October 2022.

 

[Altfish]

The square root of 2 is an irrational number. Any irrational number contains infinitely many bits of information.
For example, the Pi has infinitely many digits. The Pi is an infinitely long number. To describe it thoroughly, one needs an infinitely huge file. Same for the root of 2. But, on the other hand, the amount of information is small and finite, just the sentence "root of 2."
Why, in the first presentation, infinitely much independent information, but in the second presentation - very little information?
This means that information is not invariant.
Hence, the information does not conserve like a physical energy saving. This is a solution to the Black Hole Information Loss Paradox of Steven Hawking.

Author: Dmitri Martila, 20. October 2022.

You've lost me,

 

[exchemist]

No, an irrational number does NOT require infinitely many bits of information to specify it. If that were true we would be unable to define it. But you just have. Durrh.

 

[questfortruth]

No, an irrational number does NOT require infinitely many bits of information to specify it. If that were true we would be unable to define it. But you just have. Durrh.

There are two definitions of root of 2. One is with infinitely much information.

 

[questfortruth]

You've lost me,

Can you see the first-class idea when it is there?

 

[Heyo]

The square root of 2 is an irrational number. Any irrational number contains infinitely many bits of information.
For example, the Pi has infinitely many digits. The Pi is an infinitely long number. To describe it thoroughly, one needs an infinitely huge file. Same for the root of 2. But, on the other hand, the amount of information is small and finite, just the sentence "root of 2."
Why, in the first presentation, infinitely much independent information, but in the second presentation - very little information?
This means that information is not invariant.
Hence, the information does not conserve like a physical energy saving. This is a solution to the Black Hole Information Loss Paradox of Steven Hawking.

Author: Dmitri Martila, 20. October 2022.

I think you need to read up on how "information" is defined in information theory.

 

[questfortruth]

I think you need to read up on how "information" is defined in information theory.

Please tell me, friend. I have no access to school.

 

[Heyo]

Please tell me, friend. I have no access to school.

In a very short way, information is only that what remains when you strip the noise. Most messages contain redundancies, those don't add to the information.