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Comment by cs702 | Hacker News Reader

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 -- many important transcendental numbers, including π (Pi), are thought to be (but have not been proven to be!) normal.

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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-cont... for more details.

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

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.

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!

> most real numbers are normal

Which means that most real numbers violate all present and future copyrights.

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?).

This actually isn't known to be true afaict: https://www.askamathematician.com/2009/11/since-pi-is-infini...

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

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

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