I ate The Onion
There’s no way the copyright office is actually going to approve this right?
According to Dr. Calibri, there’s a 99.9999% chance they will approve it :)
This just in: Measurements are now limited to ~3M decimals.
Science is ruined!
Welp, time for quectoquectoquectoquectoquectometers.
Actually, a plank length seems to be 10 microquectometers, so my first guess might only be necessary for interpretation of the world, and not physical accuracy.
Including relevant XKCD as demanded by internet law: https://xkcd.com/10/
If pi is truly infinite, then it contains all the works of Shakespeare, every version of Windows, and this comment I’m typing right now.
That’s not how it’s works. Being “infinite” is not enough, the number 1.110100100010000… is “infinite”, without repeating patterns and dosen’t have other digits that 1 or 0.
If it’s infinite without repeating patterns then it just contain all patterns, no? Eh i guess that’s not how that works, is it? Half of all patterns is still infinity.
Not, the example I gave have infinite decimals who doesn’t repeat and don’t contain any patterns.
What people think about when said that pi contain all patters, is in normal numbers. Pi is believed to be normal, but haven’t been proven yet.
An easy example of a number who contains “all patterns” is 0.12345678910111213…
No. 1011001110001111… (One 1, one 0, two 1s, two zeros…) Doesn’t contain repeating patterns. It also doesn’t contain any patterns with ‘2’ in it.
But pi is believed to be normal. https://en.m.wikipedia.org/wiki/Normal_number
So it should contain all finite patterns an infinite number of times.
In some encoding scheme, those digits can represent something other than binary digits. If we consider your string of digits to truly be infinite, some substring somewhere will be meaningful.
to be fair, though, 1 and 0 are just binary representations of values, same as decimal and hexadecimal. within your example, we’d absolutely find the entire works of shakespeare encoded in ascii, unicode, and lcd pixel format with each letter arranged in 3x5 grids.
Doesn’t, the binary pattern 10101010 dosen’t exists on that number, for example.
Actually, there’d only be single pixels past digit 225 in the last example, if I understand you correctly.
If we can choose encoding, we can “cheat” by effectively embedding whatever we want to find in the encoding. The existence of every substring in a one of a set of ordinary encodings might not even be a weaker property than a fixed encoding, though, because infinities can be like that.
Still not enough, or at least pi is not known to have this property. You need the number to be “normal” (or a slightly weaker property) which turns out to be hard to prove about most numbers.