The way the author solved this shares a lot of the problem space with compression algorithms. You could model what they did as effectively creating a highly compressed encoding for Waldo, which then reduced the entropy needed to produce it, thereby bringing the Pi index within a reasonable searching range.
This is the kind of thing that ignites the imagination of students and gets them into entire fields of discipline.
We don’t know for sure: pi is believed to be a normal number. Normal numbers have the pattern that all single digits are equally likely to appear, all pairs are equally likely, all triplets, etc. If this holds, any sequence of digits of length n, represented in base b will appear with probability 1/b^n.
An example of a normal number formed by construction is Champernowne’s constant. In base 10, it is 0.12345678910111213(...) - a concatenation of all natural numbers. As you can see, any natural number you can name is guaranteed to appear inside this constant.
Normal numbers are interesting because it’s been proven that almost all real numbers are normal; however, outside of numbers explicitly constructed to be normal, very few reals have been proven to be normal.
e: u/sinic is actually more correct than I; all normals are disjunctive but not all disjunctives are normal.
There was this entry a few years ago about using π as a storage device. It does contain all data that could exist.
Can’t find the link right now.
Here’s a fun idea for a weekend project:
A javascript library that implementing a tag that displays a fixed size image based on a π offset passed as a parameter. A script like the one in this post could be used to find the image. Perhaps even allowing for a certain error level for performance reasons.
Thinking out loud. We may be able to get to GDPR compliance by rounding Pi down to 3. Yes, we’ll lose some data but we’re really down to the wire here.
LOL, this is absolutely what my company did when GDPR hit.
How long till the authorities find child pornography (or Critical Race Theory) in pifs and get π shut down, or possibly censored to an innocuous value like 22/7? That could break everything that depends on π, like for example wheels…
Re verification: you do not need to download whole billions of digits for that! If wikipedia is right, Bailey–Borwein–Plouffe formula could be used instead for the verification stage (and also for finding stage as well, since it gives the nth hex-digits).
This put a big grin on my face :D
The way the author solved this shares a lot of the problem space with compression algorithms. You could model what they did as effectively creating a highly compressed encoding for Waldo, which then reduced the entropy needed to produce it, thereby bringing the Pi index within a reasonable searching range.
This is the kind of thing that ignites the imagination of students and gets them into entire fields of discipline.
Love this energy.
Is every possible sequence of digits found somewhere in π?
That property is called disjunctive, and, while a widely held belief, it’s unknown whether π is in fact a disjunctive number.
We don’t know for sure: pi is believed to be a normal number. Normal numbers have the pattern that all single digits are equally likely to appear, all pairs are equally likely, all triplets, etc. If this holds, any sequence of digits of length n, represented in base b will appear with probability
1/b^n.An example of a normal number formed by construction is Champernowne’s constant. In base 10, it is
0.12345678910111213(...)- a concatenation of all natural numbers. As you can see, any natural number you can name is guaranteed to appear inside this constant.Normal numbers are interesting because it’s been proven that almost all real numbers are normal; however, outside of numbers explicitly constructed to be normal, very few reals have been proven to be normal.
e: u/sinic is actually more correct than I; all normals are disjunctive but not all disjunctives are normal.
Thanks to this thread I understand today’s SMNC! https://www.smbc-comics.com/comic/normal
That’s an open mathematical question. No one has proven it, but I think the consensus guess is yes.
There was this entry a few years ago about using π as a storage device. It does contain all data that could exist. Can’t find the link right now.
Here’s a fun idea for a weekend project: A javascript library that implementing a tag that displays a fixed size image based on a π offset passed as a parameter. A script like the one in this post could be used to find the image. Perhaps even allowing for a certain error level for performance reasons.
Is it https://github.com/philipl/pifs by any chance?
This is pure gold. Don’t forget to look at the issue tracker. There are valuable gems like this one:
GDPR compliance #56
LOL, this is absolutely what my company did when GDPR hit.
How long till the authorities find child pornography (or Critical Race Theory) in pifs and get π shut down, or possibly censored to an innocuous value like 22/7? That could break everything that depends on π, like for example wheels…
Yes, thank you.
Re verification: you do not need to download whole billions of digits for that! If wikipedia is right, Bailey–Borwein–Plouffe formula could be used instead for the verification stage (and also for finding stage as well, since it gives the nth hex-digits).
The dialog in the referenced SMBC is, with a few minor substitutions, the punchline of the epilogue of Carl Sagan’s Contact (the novel, not the film).
If you’re interested in visualisations of PI, see Martin Krzywinski http://mkweb.bcgsc.ca/pi/ He recently did some music based on Pi with Gregory Coles, Numberphile2 did a podcast on it: https://www.youtube.com/watch?v=JXyO8GB_mkw (The first and last digits of PI)