They’re probably the only things that “create” information in the sense that you can always grab another slice. Thank you delicious pi!
Also did you ladies and fellas know that y=x^x is the ace of spades?
Irrational number do not “create” information, they simply contain every possible combination of digits. Given enought time you could find any pattern you wanted that represents some “information”, you could also find an infinite amount of patterns that represent false “information”. You cannot pick out a set of digits of pi and use that to learn something other than that set of digits.
🪙 🎲 ???!?
Any infinite group applies to this too. The group of integers, real numbers, etc. are infinite. Just add 1 👍
True although I would like to note that the digits of Pi are the heart of r-n jesus and the number line just does boring stuff like steadily increasing forever.
According to your reasoning, the Fibonacci numbers, or repeatedly applying a math operation to a number are infinite sources of information
As far as I see through context in science, anything is information. Matter. Energy. Numbers. Words. So an infinite number has to have infinite information, yeah?
No. sqrt(2) is an irrational number characterized as the positive solution to x^2 - 2 = 0. It’s described by a very small amount of data. Even its decimal expansion can be determined up to any precision by a simple algorithm.
Nah I replied to someone else with a similar thought. The Notorious Fibs sure I agree with you they are new information, similar to the primes but just adding +1 over an over again or even some repeating pattern doesn’t add new information beyond the initial pattern.
Is it actually information? I can give you the number two, but it’s not useful information until I also tell you which digit is significant and what the number means. Communicating information is still limited by the speed of light.
Is it actually information?
Yes. For every bit of number pi you get one bit of information.
I can give you the number two
You gave me log2(10) bits of information. Thanks.
but it’s not useful information until I also tell you which digit is significant and what the number means.
You are misunderstanding what informatiob is.
I can give you √2 which is 16-bits of information as characters. It’s also an irrational number. How you express something doesn’t change the amount of information is contained in the message.
How you express something doesn’t change the amount of information is contained in the message.
Welcome to the world of entropy coding.
I don’t see why not, it’s just numbers, which is all we store most data as.
You could use it as a source of pseudorandom numbers to encrypt an infinite data steam, e.g. we’ll encrypt using e, starting at position 40468.
Situationally, yes. “I want the next digit of pi” is information in that sense of the word. It’s not a particularly useful piece of information unless you’re building something that requires a circle with a circumferential precision larger than the width of our entire universe.
How many digits of Pi would you have to read for you to be able to reconstruct all of the information in the Universe up to this moment?
Does the set of all sets contain the Universe?
“uhm ackschually”: the thread
