What texts or images have we found in pi?

[Learjeff]

@septimus

as well as trillions of faulty versions of Rush’s Rise and Fall in which 9-11 was a CIA plot and Sarah Palin becomes President in 2010.

Oh the horrors! :-o

@Indistinguishable

For what it’s worth, it’s possible that π is not normal but still contains every finite string of digits in its decimal expansion (i.e., that it is “disjunctive”). Not that anyone has any particular reason to suspect this, but it could happen…

Good point. Any random digit distribution satisfies the requirement, as do some nonrandom ones (like the Champernowne constant mentioned above).

Disjunctive is the property that makes the premise true by definition.

[Indistinguishable]

@Learjeff

Any random digit distribution satisfies the requirement, as do some nonrandom ones (like the Champernowne constant mentioned above).

Minor nitpick, but the Champernowne constant is normal.

(One concrete example of a non-normal, disjunctive number in base b is given by taking the Champernowne constant in base (b + 1) and identifying two of its digits to get a base b digit-sequence where everything shows up, but one digit appears twice as often as the others).

[brujaja]

Reading all of this, I become idly curious as to whether the endless iteration of pi could be correlated in any way to the GATC sequences in DNA, with some kind of scheme for having the four letters represent all ten digits by, say, changing their value depending on their neighbors.

[cmyk]

@brujaja

Reading all of this, I become idly curious as to whether the endless iteration of pi could be correlated in any way to the GATC sequences in DNA, with some kind of scheme for having the four letters represent all ten digits by, say, changing their value depending on their neighbors.

You could simply assign a letter to multiple digits, like so:

G=1,2,3 T=4,5 C=6,7,8 A=9,0

Granted the base-pairs wouldn’t have equal representation though, unless you assigned each letter two digits and rotated the 9 and 0 between them consecutively.

[Chronos]

Or just express pi in base 4.

[cmyk]

True dat.

[Indistinguishable]

Or take two decimal digits at a time, assigning 25 digit-pairs to each of GATC.