3 ms·

Fun read. But if we allow ourselves as much precision as we need, we don't even need a parameter. Any constant that is a normal number should suffice. Such cons

by cs702 5y ago

Fun read. But if we allow ourselves as much precision as we need, we don't even need a parameter. Any constant that is a normal number should suffice. Such constants already contain every possible sequence of digits you could muster -- i.e., they already contain every possible dataset. EDIT: I replaced "transcendental" with "normal" after reading Scarblac's comment below: https://news.ycombinator.com/item?id=28699622 https://news.ycombinator.com/item?id=28699622 -- many important transcendental numbers, including π (Pi), are thought to be (but have not been proven to be!) normal.

Scarblac 5y ago
I don't believe just being transcendental is sufficient for that property. E.g. I can't imagine that pi with all the '1' digits replaced by '2' isn't transcendental, but it clearly doesn't contain every sequence of digits. I think you mean normal numbers.
- cs702 5y ago
  You're right: normal, not transcendental. IIRC, most real numbers are normal, and many important transcendental numbers are thought to be (but have not been proven to be) normal. I edited my comment. Thank you for the correction!
  - amelius 5y ago
    > most real numbers are normal Which means that most real numbers violate all present and future copyrights.
KerrickStaley 5y ago
It's not true that any transcendental number would work. A transcendental number is a number which isn't the root of any polynomial with rational coefficients. This property doesn't imply that it contains all number sequences. It hasn't even been proven that pi contains all number sequences. See https://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations https://math.stackexchange.com/questions/216343/does-pi-cont... for more details.
- cs702 5y ago
  You're right. I edited my comment. Thank you for pointing it out!
creddit 5y ago
This actually isn't known to be true afaict: https://www.askamathematician.com/2009/11/since-pi-is-infinite-can-i-draw-any-random-number-sequence-and-be-certain-that-it-exists-somewhere-in-the-digits-of-pi/ https://www.askamathematician.com/2009/11/since-pi-is-infini...
- cs702 5y ago
  You're right. I edited my comment. Thank you for pointing it out!
gnramires 5y ago
Right, but any constant doesn't "encode" this information. To use a normal constant to encode information, you need to encode the location of the substring of interest. Generally, the location of the substring of interest needs to require as many bits as the substring itself (unless there's an intimate relationship between the number and the substrings of interest). So arguably it's the location that encodes the data, the number is irrelevant (and why not encode the data directly into this location?).
analog31 5y ago
You could use the digits of pi as an end-of-file marker, which would indeed make it transcendent. ;-)

by cs702 5y ago

Scarblac 5y ago

I don't believe just being transcendental is sufficient for that property. E.g. I can't imagine that pi with all the '1' digits replaced by '2' isn't transcendental, but it clearly doesn't contain every sequence of digits. I think you mean normal numbers.

cs702 5y ago
You're right: normal, not transcendental. IIRC, most real numbers are normal, and many important transcendental numbers are thought to be (but have not been proven to be) normal. I edited my comment. Thank you for the correction!
- amelius 5y ago
  > most real numbers are normal Which means that most real numbers violate all present and future copyrights.

KerrickStaley 5y ago

It's not true that any transcendental number would work. A transcendental number is a number which isn't the root of any polynomial with rational coefficients. This property doesn't imply that it contains all number sequences. It hasn't even been proven that pi contains all number sequences. See https://math.stackexchange.com/questions/216343/does-pi-contain-all-possible-number-combinations https://math.stackexchange.com/questions/216343/does-pi-cont... for more details.

cs702 5y ago
You're right. I edited my comment. Thank you for pointing it out!

creddit 5y ago

This actually isn't known to be true afaict: https://www.askamathematician.com/2009/11/since-pi-is-infinite-can-i-draw-any-random-number-sequence-and-be-certain-that-it-exists-somewhere-in-the-digits-of-pi/ https://www.askamathematician.com/2009/11/since-pi-is-infini...

cs702 5y ago
You're right. I edited my comment. Thank you for pointing it out!

gnramires 5y ago

Right, but any constant doesn't "encode" this information. To use a normal constant to encode information, you need to encode the location of the substring of interest. Generally, the location of the substring of interest needs to require as many bits as the substring itself (unless there's an intimate relationship between the number and the substrings of interest). So arguably it's the location that encodes the data, the number is irrelevant (and why not encode the data directly into this location?).

analog31 5y ago

You could use the digits of pi as an end-of-file marker, which would indeed make it transcendent. ;-)