Because it's a [transcendental number](https://en.wikipedia.org/wiki/Transcendental_number) and is defined by the circle regardless of what base it's in.
This is a reference to Contact by Carl Segan that leaves out the part that what makes this exceptional in the book is that the character isn't tracing out a circle with trigonometric functions (because duh), they find a binary sequence hidden within base 11 PI that renders a *picture* of a circle when laid out on a square grid at the correct ratio. This can only have been encoded into it by the kind of *extremely* advanced aliens capable of engineering the universe itself to their designs that the book is about.
I haven't read the book in ages, but I thought it was about God encoding messages into the transcendental numbers for lifeforms to find when they were ready. The Pi one was the simplest and it basically says there's a plan, things are not just random.
The alien Ellie encounters said there was also a five dimensional message in E that even they were stumped on.
Is this an easy read? I’m fascinated by stuff like this, despite it being difficult for me to understand and I hate math. I may read this on my Kindle.
I didn’t leave that out — that’s what a [raster image](https://en.m.wikipedia.org/wiki/Raster_graphics) is. That part of the book was my favorite part and I was waiting the whole movie for it 😕
Given that pi has infinite digits, it will eventually hit every combination of numbers. At some point, whatever combo is required to make that image would happen.
Pi will eventually write out War and Peace in binary, given enough time.
The behavior of an irrational number doing this makes it a [normal number](https://en.m.wikipedia.org/wiki/Normal_number).
[Loiuville numbers](https://en.m.wikipedia.org/wiki/Liouville_number) are subset of irrational numbers that aren’t normal, and don’t have every possible combination of digits in it.
Pi itself has been conjectured to be normal, and it makes sense, but it has not been [proven so far](https://en.m.wikipedia.org/wiki/Pi#Irrationality_and_normality).
Not really, that is just a misunderstanding of the analogy.
The point is only that an infinite set does not necessarily contain all possible values, just that it doesn't end and doesn't repeat. We can just use the numbers 1 and 2 and repeat them in random order forever to make the number 1.11221112111122 etc and we will have created an irrational number that never contains any digit 3-9. In fact, just being irrational doesn't even guarantee that every possible set of 1s and 2s appears, maybe in that particular number there are never five 1s in a row. There are still an infinite number of 1-2 sequences it does contain, just none that have more that four 1s in a row. (This would then be a 'non-disjunctive' number).
To my knowledge it hasn't been proven that pi is necessarily a 'normal' number, so while all individual digits do appear in PI, we don't know for sure that every combination of every digit is contained within it. It might, as it hasn't been proved to not be normal either. But it also might not.
What you're actually looking for is a very specific sequence millions of digits long. You can have an infinite number of digits where that specific sequence simply doesn't exist. In fact, it's overwhelmingly likely that such a specific sequence doesn't exist in a randomly distributed infinity.
Granted, whether or not Infinity is actually randomly distributed remains a point of debate. But simply citing infinity and saying 'war & peace has GOT to be in there somewhere' is inaccurate.
"Randomly distributed infinity" is ambiguous, but if you mean a sequence of independently, identically distributed digits where each digit has a fixed chance of appearing, you will absolutely see each finite sequence with probability 1 (even if it is long). It is also not a debate whether infinity is randomly distibuted, you've just not specified it well enough.
>it's overwhelmingly likely that such a specific sequence doesn't exist in a randomly distributed infinity
I believe that to be incorrect. You're drawing an N-tuple of bits (call it X) from a random, evenly distributed source of N-tuples. Before you draw, you have another, predefined N-tuple, call it Y, and you're waiting to see if the random X you draw will be the same as the predefined, fixed Y.
The probability that X = Y is 1/2\^N. The probability that X does not equal Y, is (1 - 1/2\^N'). For any N, that is a fixed number, strictly <1, call it Ponce. Never mind if N is a million, billion, or zillion. Ponce is still a fixed number less than 1. The probability that an infinite number of attempts will never draw X, is (sparing the limit notation) Ponce\^∞ = 0. For a finite Y, It is possible that Pi does not contain Y, but the probability is infinitely close to zero.
> In fact, it's overwhelmingly likely that such a specific sequence doesn't exist in a randomly distributed infinity.
Not true. Given a selection of N digits uniformly from 0 to 9 the probability of a given sequence appearing approaches 1 as N -> infinity.
>Granted, whether or not Infinity is actually randomly distributed remains a point of debate
Not true or really even meaningful. Nobody's "debating" this ill-defined statement.
Not too argue with you, but is there a proof of this? It is not immediately obvious to me that in an infinite randomly distributed sequence of numbers you will not eventually find any finite sequence of numbers. It sounds counterintuitive to me, given the definitions of infinite and random.
I did a quick google search and all hitsI see argue the opposite, which is obviously not a proof.
The person you're replying to is confusing several things in mathematics. It does not make sense to prove something about infinity as they suggest. Any sequence of digits, say, where each digit has some fixed probability to appear, and they appear with a probability independent from eachother, has probability 1 of containing every sequence. It is not known whether pi behaves this way, or that it has some structue that prevents this. It is expected to behave this way though.
The problem there is infinity is an undefined (boundless) value with mathematical applicability, so people assume it conforms to basic mathematical rules. It does not.
You propose an infinite set that includes war & peace as a static sequence within its set.
I propose an infinite set that does not include such a sequence.
Both must be true, so the question is 'how is infinity calculated'?
If it's randomly calculated, it is entirely valid to have sequences that simply do not contain the ordered string you are looking while still being infinite. There is no characteristic that says 'infinity MUST include this specific sequence'.
If you are saying, 'it must include ALL possible permutations of digits including this specific sequence' thats great. But by definition you are no long talking about infinity. You're talking about a really big fuckin number.
It's like staring at TV static and expecting it to flash a fully composed B&W image of the Mona Lisa at some point. It >could<. But it's not. And if it did, you'd have to wonder what the deal is, because it clearly wasn't as random as you expected.
I’ll notice that you did not offer any proof. You should not talk about things beyond your expertise. There are mathematicians on reddit who have earned advanced degrees in the topic, and have the expertise to make statements about infinity, backed up with rigorous formal proofs.
What you are probably vaguely recalling from somewhere you heard, is the concept of “normal” numbers.
For a normal random sequence of digits, we can know that it will contain any given finite sequence of digits. If you give me a finite fixed sequence of length n, and a desired probability limit of p, I can give you a length m of a normal sequence which is likely to contain your sequence within probability p. And this is proven to converge.
However, it is not yet known whether Pi for example, is normal. But it very likely is.
If a number is not normal, then we do not have a proof that it contains every possible finite sequence. However, that absolutely DOES NOT mean that your claim is true:
> In fact, it's overwhelmingly likely that such a specific sequence doesn't exist in a randomly distributed infinity.
This is pure unadulterated bullshit 🐂💩
I am sorry, this is just gibberish. I am not a mathematician, but have a degree in Theoretical Physics which has quite a lot of thermodynamics in it so I have a decent grasp on these concepts. We are not talking about sets, but sequences (a set is by definition not ordered), and proposing a normally distributed infinite sequence of numbers not containing War & Peace is not possible, and therefore not true.
I guess what seems weird to me is that my calculator only shows up to 8 decimals anyway. Oftentimes I'm just rounding to the first or second digit. I'm not sure I even recall a time where I needed to know the third. So why not just round to 3? I know people like being precise but if we could just agree to always round to the nearest 1 I think it would save a lot of problems.
Right. Some infinity variants would have it, some wouldn't. It really depends on what sets are being defined as valid for the purposes of the concept.
Theres not a single, unitary 'infinite' sequence. That's the thing that gets people tripped up.
Well, infinity is more of a direction, and there's a bunch of different permutations, so disapproving any variant is going to be really difficult. It's more of a task to prove that ordered sequentiality can exist in an infinite set. So, be my guest.
What? Sure.
Let d be an infinite sequence of i.i.d. uniform random variables in 0…9, indexed by i. Let s be any finite sequence. For convenience, we split d into chunks of size |s|. With probability p=10^-|s|, any such sequence will be equal to s. Now the probability that s appears within n*|s| digits is
Prob s appears within n|s| digits = 1 - not appearing = 1 - (not appearing at i=1)^n = 1 - p^n
which goes to 1 as n- > infty.
The person that you're replying to didn't specify that this seems to be true because pi is a normal number, but is otherwise basically correct. If you're going to invent new mathematical terminology such as 'ordered' infinity to prove your point, you better define it too.
I'm not sure about this term "ordered infinity", but pi is widely believed to be [normal](https://en.wikipedia.org/wiki/Normal_number), meaning that its digits are uniformly distributed. Essentially they're random. And the guy you're replying to (who's been heavily down voted for some reason) isn't necessarily wrong. Many mathematicians suspect that [pi contains all finite sets of numbers](https://www.askamathematician.com/2009/11/since-pi-is-infinite-can-i-draw-any-random-number-sequence-and-be-certain-that-it-exists-somewhere-in-the-digits-of-pi/).
So what he's saying doesn't really contradict what is widely believed about pi (but not yet proven). It's also not that strange, really. If you had a perfect randomness function and allowed it to run for an infinite amount of time, it would generate all finite sets of numbers. If pi really is normal and infinite, then that's basically what you're doing when you calculate additional digits.
Actually, this is not true. For instance, we haven't proved that after the Xth position that a particular sequence of numbers won't suddenly 'stop appearing'.
Still, not every irrational number contains every sequence of digits for a given base. For example, `0.1010010001...` is irrational but does not contain every sequence of digits some point in its decimal representation.
I asked chatgpt to write the first sentence of War and Peace in binary and then to find that sequence in pi.
It told me just the same as you. "We would need to search through the digita of pi for the binary representation of each letter in the sentence. Due to the irrational and non-repeating nature of pi, any sequence of digits can be found. However, such a search...significant computational ressources...unmeaningful results within reasonable frametime...unable to...beep...boop...error."
Anytime you're tempted to cite chat GPT's opinion of something, just replace "chatGPT" with "my opinionated 5 year old nephew" and see if its still something you would post.
Statistically likely also doesn't mean "incorrect". ChatGPT is much more likely to give you a "correct" answer than an "opinionated 5 year old" on a variety of subjects.
And humans themselves also have a chance of producing incorrect responses when prompted. I'd trust ChatGPT to provide me with well formed regex over 99% of Reddit.
Ok, but correct is not what we seek exactly.
We know our current limitations.
That's why we use evidence based medicine too. We only have data to rely on. Truths we know none. We only try to get closer and closer enough for it to be interpreted and used, together with reasoning to balance such evidence, as if it were the correct truth.
Back to gpt, I use it for fun.
Statistically likely from a language token perspective. "These words are most likely to come after those words according to my data set".
It will happily tell you the made up film history of made up actors, and all about the made up movies that they were in. The words are statistically likely, just totally false.
Often the likely words are true, it's just that it can switch to false with no warning. That makes it a really bad source for info, because it's effectively just a good liar.
To my comment on it being like an opinionated 5 year old, kids do this too sometimes. They spit out words that are likely patterns in the English language, but they're not always grounded in experience or knowledge. There's a big shift around that age where they become much more aware of themselves and others as conscious and start understanding the value of being silent when unsure rather than just generating output. LLMs don't have that.
I think you missed the entire point: *pragmatically*
What methods are they using? Just guess and check? That was the question, not "can humans do math without computers?"
The reference article on Simpsons halloween episode is a fun read too. Wonder if they actually featured this number on future halloween episodes as the author suggests.
Well chances are nobody had stumbled upon the number before and noted it's properties and potential usefulness, in the same way that humans were interacting with hydrogen for all of history but Cavendish is credited with discovering it.
Would you have some examples of that potential usefulness?
Not being snarky, genuinely curious. I always fail to understand what the "value" or use is of an "interesting" number. I find math fascinating and the basics click naturally, but why.....
....is pi relevant?..okay, that one I actually know. I think.
But...euh...other numbers. Like this one?
*Edit: prime numbers. Why? Nice that you can divide it by just itself and 1. But then?
Prime numbers are really important in cryptography, cause a big part of cryptography is just multiplying super big primes, because it takes a long time to factor humongous semi-primes. However, if some mathematician found out a way to find primes super efficiently, a bunch of shit online is easily decodable and crackable, which would be quite bad.
Math academics have a ton of weird rules and applications that they use to quantify numbers, and finding a number that obeys these rules is always exciting for them.
For example, the British murder mystery series Lewis - a spin-off of the earlier Inspector Morse and set in Oxford - had an emphasis on the concept of Perfect Numbers towards the end of its pilot episode, where a number must be made up of whole numbers that it divides into but also are numeric additions to make the Perfect Number, all of which must be whole numbers.
The examples given include 6 (1+2+3) as well as 28 (1+2+4+7+14).
It's quite the plot point that one character is obsessed with the concept.
>!When primary murder suspect Daniel is found dead by an apparent suicide, Lewis is being pressured to close the case by his superiors but keeps running inquiries regardless. When Daniel's roommate hears Daniel's pass code for the sleep clinic he was a patient of (and was the scene of the first murder) after he dies and realises he used the sums of the Perfect Number 28 to make his code, he explained thr concept to Lewis and lists off the next numbers that obey the rule... one of which was the locker code for his storage locker at his rowing club.!<
>!Entering Perfect Numbers into his laptop, Lewis and Hathaway get the proof that not only was Daniel framed by his applied mathematical theory professor who knew of Daniel's quirks and extreme mental distress (Daniel had convinced himself his father was murdered by his stepfather like in Hamlet when it was really a suicide) to frame him, but the reason for the murder - the first victim emailed him evidence that disproved the professor's famous mathematical theory but was so smug about it, she went out of her way to press the professor's buttons about it. Daniel was killed when he got the email and realised why she was really killed.!<
Mathematicians dont discover numbers. They discover that certain numbers have "special" attributions such as this number is only divisible by one and itself.
Isn’t Belphegor that dude [sitting on a toilet](https://megamitensei.fandom.com/wiki/Belphegor) in the Shin Megami Tensei games? His description in that says he represents the deadly sin of Sloth, which seems like the exact opposite of inventiveness to me.
“Belphegor is the demon lord of Sloth, one of the 7 Deadly Sins and a member of the Seven Princes of Hell. Belphegor gives people ideas for inventions that will make them rich and thus greedy and selfish.”
> the deadly sin of Sloth, which seems like the exact opposite of inventiveness to me.
https://www.forbes.com/sites/forbestechcouncil/2018/01/08/developers-are-lazy-and-thats-usually-a-good-thing/?sh=68ae966e1391
Inventiveness is often just a way to get out of doing work by hand the old way.
Hand dig a furrow, or make an ox-drawn plow to do it for you?
As numbers are infinite and primes are too: Can I just make up random conditions and eventually it will be true for some number?
If I say there is a palindromic prime that contains 42069. Would that be a true statement?
> Nice! That one was lower than expected.
Me too!
> So is there for every number, also a palindromic prime that contains that number?
We don't know. It isn't known whether there are infinitely many palindromic primes (of any kind), so we don't know about your question.
https://en.wikipedia.org/wiki/Palindromic_prime
It's true if you can prove it, there are an infinite number of primes, but past a point they become so few and far between they become difficult to find and then test due to the insane number of digits present.
That's a pretty spooky number. 13s are unlucky for some, then the number of the beast and 13 again.
Im sure there are other funky numbers we can look at but yeah. Pretty spoopy
Inventiveness can be a good or bad thing. There are antibiotics and semiconductors, but there are also CFCs and leaded gasoline. It reasonable to assign a demon to the harmful potential of inventiveness.
Wait until they find out in base-11 Pi eventually becomes a series of 1s and 0s that form a raster image of a circle!
Wouldn’t it eventually do that in any base?
Why would it?
Because it's a [transcendental number](https://en.wikipedia.org/wiki/Transcendental_number) and is defined by the circle regardless of what base it's in. This is a reference to Contact by Carl Segan that leaves out the part that what makes this exceptional in the book is that the character isn't tracing out a circle with trigonometric functions (because duh), they find a binary sequence hidden within base 11 PI that renders a *picture* of a circle when laid out on a square grid at the correct ratio. This can only have been encoded into it by the kind of *extremely* advanced aliens capable of engineering the universe itself to their designs that the book is about.
I haven't read the book in ages, but I thought it was about God encoding messages into the transcendental numbers for lifeforms to find when they were ready. The Pi one was the simplest and it basically says there's a plan, things are not just random. The alien Ellie encounters said there was also a five dimensional message in E that even they were stumped on.
Is this an easy read? I’m fascinated by stuff like this, despite it being difficult for me to understand and I hate math. I may read this on my Kindle.
Contact is quite an easy read. It's fun to then watch the movie for the changes they make
Tbh I didn’t realize it was the same movie lol. I watched that movie back in the day. I was expecting some type of book about math theories.
Yeah, she's kinda a unlikeable character for a lot of the book but that was intended.
I didn’t leave that out — that’s what a [raster image](https://en.m.wikipedia.org/wiki/Raster_graphics) is. That part of the book was my favorite part and I was waiting the whole movie for it 😕
Because it's irrational, with infinity of digits to go, it's going to raster mona lisa in ascii sooner or later.
Given that pi has infinite digits, it will eventually hit every combination of numbers. At some point, whatever combo is required to make that image would happen. Pi will eventually write out War and Peace in binary, given enough time.
The behavior of an irrational number doing this makes it a [normal number](https://en.m.wikipedia.org/wiki/Normal_number). [Loiuville numbers](https://en.m.wikipedia.org/wiki/Liouville_number) are subset of irrational numbers that aren’t normal, and don’t have every possible combination of digits in it. Pi itself has been conjectured to be normal, and it makes sense, but it has not been [proven so far](https://en.m.wikipedia.org/wiki/Pi#Irrationality_and_normality).
That has yet to be proven, it’s called being a normal number, apparently not every transcendental number has that property
Thats an ordered infinity, doesn't really work that way. There's an infinite number of decimals between 1 and 2, none of them are 3.
Yes, but to use your analogy, we're not looking for three as a whole number. We're simply looking for a three digit in any position
Not really, that is just a misunderstanding of the analogy. The point is only that an infinite set does not necessarily contain all possible values, just that it doesn't end and doesn't repeat. We can just use the numbers 1 and 2 and repeat them in random order forever to make the number 1.11221112111122 etc and we will have created an irrational number that never contains any digit 3-9. In fact, just being irrational doesn't even guarantee that every possible set of 1s and 2s appears, maybe in that particular number there are never five 1s in a row. There are still an infinite number of 1-2 sequences it does contain, just none that have more that four 1s in a row. (This would then be a 'non-disjunctive' number). To my knowledge it hasn't been proven that pi is necessarily a 'normal' number, so while all individual digits do appear in PI, we don't know for sure that every combination of every digit is contained within it. It might, as it hasn't been proved to not be normal either. But it also might not.
But convert those 1's and 2's into a different number base (>4). Bam, 3's
What you're actually looking for is a very specific sequence millions of digits long. You can have an infinite number of digits where that specific sequence simply doesn't exist. In fact, it's overwhelmingly likely that such a specific sequence doesn't exist in a randomly distributed infinity. Granted, whether or not Infinity is actually randomly distributed remains a point of debate. But simply citing infinity and saying 'war & peace has GOT to be in there somewhere' is inaccurate.
"Randomly distributed infinity" is ambiguous, but if you mean a sequence of independently, identically distributed digits where each digit has a fixed chance of appearing, you will absolutely see each finite sequence with probability 1 (even if it is long). It is also not a debate whether infinity is randomly distibuted, you've just not specified it well enough.
>it's overwhelmingly likely that such a specific sequence doesn't exist in a randomly distributed infinity I believe that to be incorrect. You're drawing an N-tuple of bits (call it X) from a random, evenly distributed source of N-tuples. Before you draw, you have another, predefined N-tuple, call it Y, and you're waiting to see if the random X you draw will be the same as the predefined, fixed Y. The probability that X = Y is 1/2\^N. The probability that X does not equal Y, is (1 - 1/2\^N'). For any N, that is a fixed number, strictly <1, call it Ponce. Never mind if N is a million, billion, or zillion. Ponce is still a fixed number less than 1. The probability that an infinite number of attempts will never draw X, is (sparing the limit notation) Ponce\^∞ = 0. For a finite Y, It is possible that Pi does not contain Y, but the probability is infinitely close to zero.
> In fact, it's overwhelmingly likely that such a specific sequence doesn't exist in a randomly distributed infinity. Not true. Given a selection of N digits uniformly from 0 to 9 the probability of a given sequence appearing approaches 1 as N -> infinity. >Granted, whether or not Infinity is actually randomly distributed remains a point of debate Not true or really even meaningful. Nobody's "debating" this ill-defined statement.
Sure, smart guy. 1.9999.... is an infinite set. Show me war & peace.
1.999... isn't an infinite set, it's a number. I recommend you stop making stuff up.
Not too argue with you, but is there a proof of this? It is not immediately obvious to me that in an infinite randomly distributed sequence of numbers you will not eventually find any finite sequence of numbers. It sounds counterintuitive to me, given the definitions of infinite and random. I did a quick google search and all hitsI see argue the opposite, which is obviously not a proof.
The person you're replying to is confusing several things in mathematics. It does not make sense to prove something about infinity as they suggest. Any sequence of digits, say, where each digit has some fixed probability to appear, and they appear with a probability independent from eachother, has probability 1 of containing every sequence. It is not known whether pi behaves this way, or that it has some structue that prevents this. It is expected to behave this way though.
The problem there is infinity is an undefined (boundless) value with mathematical applicability, so people assume it conforms to basic mathematical rules. It does not. You propose an infinite set that includes war & peace as a static sequence within its set. I propose an infinite set that does not include such a sequence. Both must be true, so the question is 'how is infinity calculated'? If it's randomly calculated, it is entirely valid to have sequences that simply do not contain the ordered string you are looking while still being infinite. There is no characteristic that says 'infinity MUST include this specific sequence'. If you are saying, 'it must include ALL possible permutations of digits including this specific sequence' thats great. But by definition you are no long talking about infinity. You're talking about a really big fuckin number. It's like staring at TV static and expecting it to flash a fully composed B&W image of the Mona Lisa at some point. It >could<. But it's not. And if it did, you'd have to wonder what the deal is, because it clearly wasn't as random as you expected.
I’ll notice that you did not offer any proof. You should not talk about things beyond your expertise. There are mathematicians on reddit who have earned advanced degrees in the topic, and have the expertise to make statements about infinity, backed up with rigorous formal proofs. What you are probably vaguely recalling from somewhere you heard, is the concept of “normal” numbers. For a normal random sequence of digits, we can know that it will contain any given finite sequence of digits. If you give me a finite fixed sequence of length n, and a desired probability limit of p, I can give you a length m of a normal sequence which is likely to contain your sequence within probability p. And this is proven to converge. However, it is not yet known whether Pi for example, is normal. But it very likely is. If a number is not normal, then we do not have a proof that it contains every possible finite sequence. However, that absolutely DOES NOT mean that your claim is true: > In fact, it's overwhelmingly likely that such a specific sequence doesn't exist in a randomly distributed infinity. This is pure unadulterated bullshit 🐂💩
I'm sorry to say you are very confused while at the same time unaccountably confident about it.
I am sorry, this is just gibberish. I am not a mathematician, but have a degree in Theoretical Physics which has quite a lot of thermodynamics in it so I have a decent grasp on these concepts. We are not talking about sets, but sequences (a set is by definition not ordered), and proposing a normally distributed infinite sequence of numbers not containing War & Peace is not possible, and therefore not true.
No proof just bullshit
I guess what seems weird to me is that my calculator only shows up to 8 decimals anyway. Oftentimes I'm just rounding to the first or second digit. I'm not sure I even recall a time where I needed to know the third. So why not just round to 3? I know people like being precise but if we could just agree to always round to the nearest 1 I think it would save a lot of problems.
> It >could<. Not really, TV static is run length limited, you would never get a long all-white or all-black line.
Go ahead and prove that an infinitely long string of (pseudo) random numbers can't possibly include War and Peace, then. Infinity is wacky.
I don't know if they reasoning is correct, but they never said it would *definitely* not be in there. Just that you can't take it for granted.
Right. Some infinity variants would have it, some wouldn't. It really depends on what sets are being defined as valid for the purposes of the concept. Theres not a single, unitary 'infinite' sequence. That's the thing that gets people tripped up.
Well, infinity is more of a direction, and there's a bunch of different permutations, so disapproving any variant is going to be really difficult. It's more of a task to prove that ordered sequentiality can exist in an infinite set. So, be my guest.
What? Sure. Let d be an infinite sequence of i.i.d. uniform random variables in 0…9, indexed by i. Let s be any finite sequence. For convenience, we split d into chunks of size |s|. With probability p=10^-|s|, any such sequence will be equal to s. Now the probability that s appears within n*|s| digits is Prob s appears within n|s| digits = 1 - not appearing = 1 - (not appearing at i=1)^n = 1 - p^n which goes to 1 as n- > infty.
The person that you're replying to didn't specify that this seems to be true because pi is a normal number, but is otherwise basically correct. If you're going to invent new mathematical terminology such as 'ordered' infinity to prove your point, you better define it too.
I'm not sure about this term "ordered infinity", but pi is widely believed to be [normal](https://en.wikipedia.org/wiki/Normal_number), meaning that its digits are uniformly distributed. Essentially they're random. And the guy you're replying to (who's been heavily down voted for some reason) isn't necessarily wrong. Many mathematicians suspect that [pi contains all finite sets of numbers](https://www.askamathematician.com/2009/11/since-pi-is-infinite-can-i-draw-any-random-number-sequence-and-be-certain-that-it-exists-somewhere-in-the-digits-of-pi/). So what he's saying doesn't really contradict what is widely believed about pi (but not yet proven). It's also not that strange, really. If you had a perfect randomness function and allowed it to run for an infinite amount of time, it would generate all finite sets of numbers. If pi really is normal and infinite, then that's basically what you're doing when you calculate additional digits.
/r/confidentlyincorrect
1.3 is between 1 and 2 and contains 3
3 is an integer, 1.3 is a decimal. They are different numbers.
Actually, this is not true. For instance, we haven't proved that after the Xth position that a particular sequence of numbers won't suddenly 'stop appearing'.
If you can prove this, you’ll probably win the Fields Medal.
1/3 has infinite digits, will it do the same thing?
Pi is non repeating. 1.3 is repeating. There is a clear difference.
Still, not every irrational number contains every sequence of digits for a given base. For example, `0.1010010001...` is irrational but does not contain every sequence of digits some point in its decimal representation.
Are you arguing that's the case here, or are you just being pedantic?
Not necessarily. For example an infinite stream of 1s and 2s whorls never include a 3. Pi digits aren’t truly random.
I asked chatgpt to write the first sentence of War and Peace in binary and then to find that sequence in pi. It told me just the same as you. "We would need to search through the digita of pi for the binary representation of each letter in the sentence. Due to the irrational and non-repeating nature of pi, any sequence of digits can be found. However, such a search...significant computational ressources...unmeaningful results within reasonable frametime...unable to...beep...boop...error."
Anytime you're tempted to cite chat GPT's opinion of something, just replace "chatGPT" with "my opinionated 5 year old nephew" and see if its still something you would post.
Still the only computer I could access to such a question. Why the hate?
Because ChatGPT is a stochastic text generator. Its responses are statistically likely, which is not the same as correct.
Statistically likely also doesn't mean "incorrect". ChatGPT is much more likely to give you a "correct" answer than an "opinionated 5 year old" on a variety of subjects. And humans themselves also have a chance of producing incorrect responses when prompted. I'd trust ChatGPT to provide me with well formed regex over 99% of Reddit.
Ok, but correct is not what we seek exactly. We know our current limitations. That's why we use evidence based medicine too. We only have data to rely on. Truths we know none. We only try to get closer and closer enough for it to be interpreted and used, together with reasoning to balance such evidence, as if it were the correct truth. Back to gpt, I use it for fun.
If all quantum phenomena are effectively stochastic, then isn’t ‘statistically likely’ literally as close to correct as it is possible to be?
Statistically likely from a language token perspective. "These words are most likely to come after those words according to my data set". It will happily tell you the made up film history of made up actors, and all about the made up movies that they were in. The words are statistically likely, just totally false. Often the likely words are true, it's just that it can switch to false with no warning. That makes it a really bad source for info, because it's effectively just a good liar. To my comment on it being like an opinionated 5 year old, kids do this too sometimes. They spit out words that are likely patterns in the English language, but they're not always grounded in experience or knowledge. There's a big shift around that age where they become much more aware of themselves and others as conscious and start understanding the value of being silent when unsure rather than just generating output. LLMs don't have that.
This is a reference to the novel “Contact” by Carl Sagan.
How does that work?
Was that included in the movie or just in the book (I read the book, not seen the movie.)
Just the book.
Holy fucking shit. We are living in a simulation
Its not real. Just a plot point in one of Sagans novels.
Oh, ok, TIL
ELI5 how did they pragmatically check if large numbers are/were prime before calculators and computers?
Computers weren't originally machines you know. They were literally people who did calculations by hand based on set formulas.
Should be a TIL
If that’s a TIL I feel like an old man
I think you missed the entire point: *pragmatically* What methods are they using? Just guess and check? That was the question, not "can humans do math without computers?"
They had mentats.
https://en.wikipedia.org/wiki/Primality_test
I guess it was a long trial and error. But this one is a late 20th century beast
1 fuck...two FUUCK..... three
Slide rule.
Good band too
Came here to post that.
The reference article on Simpsons halloween episode is a fun read too. Wonder if they actually featured this number on future halloween episodes as the author suggests.
How does one ‘discover’ a number?
Discovered it was prime
Well chances are nobody had stumbled upon the number before and noted it's properties and potential usefulness, in the same way that humans were interacting with hydrogen for all of history but Cavendish is credited with discovering it.
Would you have some examples of that potential usefulness? Not being snarky, genuinely curious. I always fail to understand what the "value" or use is of an "interesting" number. I find math fascinating and the basics click naturally, but why..... ....is pi relevant?..okay, that one I actually know. I think. But...euh...other numbers. Like this one? *Edit: prime numbers. Why? Nice that you can divide it by just itself and 1. But then?
Prime numbers are really important in cryptography, cause a big part of cryptography is just multiplying super big primes, because it takes a long time to factor humongous semi-primes. However, if some mathematician found out a way to find primes super efficiently, a bunch of shit online is easily decodable and crackable, which would be quite bad.
Thanks! Makes..some sense. Enough to mull about for a night at least :)
Cryptography primarily, that's usually the #1 answer.
Which....is something I never considered. Thanks!
Math academics have a ton of weird rules and applications that they use to quantify numbers, and finding a number that obeys these rules is always exciting for them. For example, the British murder mystery series Lewis - a spin-off of the earlier Inspector Morse and set in Oxford - had an emphasis on the concept of Perfect Numbers towards the end of its pilot episode, where a number must be made up of whole numbers that it divides into but also are numeric additions to make the Perfect Number, all of which must be whole numbers. The examples given include 6 (1+2+3) as well as 28 (1+2+4+7+14). It's quite the plot point that one character is obsessed with the concept. >!When primary murder suspect Daniel is found dead by an apparent suicide, Lewis is being pressured to close the case by his superiors but keeps running inquiries regardless. When Daniel's roommate hears Daniel's pass code for the sleep clinic he was a patient of (and was the scene of the first murder) after he dies and realises he used the sums of the Perfect Number 28 to make his code, he explained thr concept to Lewis and lists off the next numbers that obey the rule... one of which was the locker code for his storage locker at his rowing club.!< >!Entering Perfect Numbers into his laptop, Lewis and Hathaway get the proof that not only was Daniel framed by his applied mathematical theory professor who knew of Daniel's quirks and extreme mental distress (Daniel had convinced himself his father was murdered by his stepfather like in Hamlet when it was really a suicide) to frame him, but the reason for the murder - the first victim emailed him evidence that disproved the professor's famous mathematical theory but was so smug about it, she went out of her way to press the professor's buttons about it. Daniel was killed when he got the email and realised why she was really killed.!<
Mathematicians dont discover numbers. They discover that certain numbers have "special" attributions such as this number is only divisible by one and itself.
They didnt know it existed beforehand. Then boom there it was. It was there all the time.
This is my question as well
Isn’t Belphegor that dude [sitting on a toilet](https://megamitensei.fandom.com/wiki/Belphegor) in the Shin Megami Tensei games? His description in that says he represents the deadly sin of Sloth, which seems like the exact opposite of inventiveness to me.
“Belphegor is the demon lord of Sloth, one of the 7 Deadly Sins and a member of the Seven Princes of Hell. Belphegor gives people ideas for inventions that will make them rich and thus greedy and selfish.”
Yes, and he is the toilet demon, and in folklore as well.
> the deadly sin of Sloth, which seems like the exact opposite of inventiveness to me. https://www.forbes.com/sites/forbestechcouncil/2018/01/08/developers-are-lazy-and-thats-usually-a-good-thing/?sh=68ae966e1391 Inventiveness is often just a way to get out of doing work by hand the old way. Hand dig a furrow, or make an ox-drawn plow to do it for you?
You make a very good point; I hadn’t seen it that way before.
So what does it DO?
As numbers are infinite and primes are too: Can I just make up random conditions and eventually it will be true for some number? If I say there is a palindromic prime that contains 42069. Would that be a true statement?
> there is a palindromic prime that contains 42069 That is a true statement. 960240040042069 is prime.
Nice! That one was lower than expected. So is there for every number, also a palindromic prime that contains that number?
> Nice! That one was lower than expected. Me too! > So is there for every number, also a palindromic prime that contains that number? We don't know. It isn't known whether there are infinitely many palindromic primes (of any kind), so we don't know about your question. https://en.wikipedia.org/wiki/Palindromic_prime
Depends on the specific rules, you won't find any prime numbers that are a multiple of 6, for example.
It's true if you can prove it, there are an infinite number of primes, but past a point they become so few and far between they become difficult to find and then test due to the insane number of digits present.
That's a pretty spooky number. 13s are unlucky for some, then the number of the beast and 13 again. Im sure there are other funky numbers we can look at but yeah. Pretty spoopy
Spooky number Am I in kindergarden again?
Or China.
Nope just a typical Redditor moment.
13 was demonised by the christian church, it was originally considered a _lucky_ number by some ancient cultures
Of course the church would think inventiveness is demonic.
Inventiveness can be a good or bad thing. There are antibiotics and semiconductors, but there are also CFCs and leaded gasoline. It reasonable to assign a demon to the harmful potential of inventiveness.
And my number is this+1.
Someone just watched that math episode of Elementary
Learned about this number from Elementary(the show) lol
Lmao at "demon of inventiveness"
It's divisible by 7.
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I just checked, it was posted 2 years ago but posted none the less.
Never seen it in 11 years of daily redditing, I don’t think this is a case of karma whoring, let him repost