Even cooler, at 75 digits you can calculate the circumference of your mom
this post was submitted on 22 Jan 2024
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Why would you miss the opportunity to make the web page continue computing pi to as many digits as you feel like scrolling down to expose though
Whoa. No spoilers for Contact please.
Turns out that's not possible because the complexity of computing pi becomes exponentially harder the more digits you add.
That is definitely not true. Pi has been computed to way more digits than would be feasible if it were exponential. Looks to me like it's O(n log(n)^3) with n=the number of digits, which sounds basically fine for any number of digits any human is going to have the patience to scroll down to.
There was a recent post asking what the self-taught among us feel we are missing from our knowledge base. For me, it's being able to calculate stuff like that for making decisions. I feel like I can spot an equivalence to the travelling salesman problem or to the halting problem a mile away, but anything more subtle is beyond me.
Of course, in this situation, I'd probably just see if I could find a sufficiently large precalculation and just pretend :)
Just put up a little spinning it’s-loading icon with an increasing delay. Then, when you run out of precalculated data, make it spin forever.
“It’s infinte scrolling man, you just didn’t wait long enough. It’s not my fault you can’t be more patient.”
Okay, maybe exponential is the wrong math term, but my point is, the complexity grows with number of digits. Infinite scrolling is therefore impossible because eventually it will become too slow to keep up with scrolling. You may be right that it may go farther than any human is willing to scroll, but that depends on the human and if they're on a potato phone.
As far as I know, the current fastest algorithm is the Bailey–Borwein–Plouffe formula,, which is O(n log n) to calculate the nth digit (not even the whole number). Infinite scrolling is only possible if we can calculate the nth digit in O(1) time.
Oh shit! Yeah, it looks like as of 2022 that article I linked to needs to be updated. It should say O(n log n), yes.
That said, scrolling ever-farther on a web page will always get slower the further down you go, and eventually fail, because of memory allocation. If you ignore some of the factors that make all truly-infinite pages impossible, and require an O(1) algorithm to generate numbers within the inherently-more-than-O(1) process of rendering the page in the first place, then sure, it’s impossible. My point is, the asymptotic complexity is low enough that you can make a page that does it and it’ll work in practice.
At work we have a scale sensitive to the 1/10,000 of a gram. 4 decimal digits. It's so sensitive it needs to be encased in a box so tiny connection currents don't make it go frantic! Even in the box the number changes a lot. 15 0s is nutty.
connection currents
Convection currents?
Yes. Heckin Gboard.
Mine can tell if I'm sitting next to it's desk or not. I've come to the conclusion it's the deformation of the ground the desk is sitting on.
It's really a silly amount of precision for what I use it for. But It's so fun to lock g on .0000, even if only for a few seconds. Anyone who has a target of a specific amount of 0s can do it themselves. After the first 2 shits pretty random.
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Haha 3 go brr
Diameter of a hydrogen atom is all well and good, but how many digits of pi will we need to be accurate to a Planck Length?
Honestly probably not that many more. My guess since I'm too lazy to do the math is less than 100.
The diameter of a hydrogen atom is over 10,000,000,000,000,000,000,000,000 plank lengths.
So based on this post I have no idea.
Well that's only 26 more digits, so we're probably good at 100 digits of pi. [citation needed]
log_10(size of observable universe / planck length) = 61.74... so like 63 digits of precision for everything are enough
The width of a hydrogen atom is 3.1*10^24 Planck lengths. So, yeah, 65 digits of pi ought to do it.
Dope. I just memorized it to 50 digits. Good to know for my intents and purposes it doesn't matter at all anyway.
Hey, cheer up, it doesn't matter for anyone's intents and purposes.
No no no. The error compounds every time you math so if you math a lot at 40 digits you might end up with like 30 digits of correct precision. Totally unacceptable. Literally unplayable.
Still, we can't proof that Pi^Pi^Pi^Pi is an integer or not, since we don't know enough digits.
It's definitely not an integer seeing as it has a fractional component. Do you mean if it's rational or not?
No, we can't proof if its an integer or not. If you can proof it, you are up for a great career in mathematics: https://www.spektrum.de/kolumne/ist-pi-hoch-pi-hoch-pi-hoch-pi-eine-ganze-zahl/2203268
(Unfortunately only found this german article, but maybe translation works)
Memory Masters destroying the last of their childhood memories so they can add another 80,000 digits of pi to their mind palace.
context
Memory Mastery is a technique where you force your brain to remember random information by formatting it in a certain way, some people have gone on to use this trick to memorize millions of digits of pi. A study recently came out confirming that every time you make a new memory it destroys an old one, so every time someone makes a "memory palace" it comes at the cost of older memories, such as in childhood.
A study recently came out confirming that every time you make a new memory it destroys an old one
If that was true, babies would forget their first memory every time they remember their second memory. There's no way it's true. It might be partly true, but it can't be completely true.
Well the way memory works is that it allocates certain clusters of neurons to storing information. When you're young there's a lot of blank space that you can store stuff in but as you get older you start having to pick and choose as more and more brain space gets taken up.
Here's a cool video on the subject: https://www.youtube.com/watch?v=X5trRLX7PQY Fun fact: because of how memories are formed in chains you can tell if you're on the precipice of forgetting something if you try to recall it and you start trailing into another memory. You can experience this for yourself by trying to recall the beat of an old song and note when it starts morphing into the beat of a newer song. It's also worth noting that every time you recall a memory you destroy the original and rewrite it, bringing it back to the top. That little asshole is like 90% of the reason why our memories suck so much shit and are so prone to outside manipulation.
You wouldn't happen to have that study close at hand?
I often nerd into new hobbies and learn new stuff. I also don't feel like I remember as much of my early childhood as people around me does.
I have no idéa if this is what's happening to me, but it'd be interesting to read about.
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Math is just runes and you can't convince me otherwise.
There's a 9 repeating 6 times in there which I'd think is a pretty rare occurrence in pi. I wonder what the longest occurrence of a repeating digit is.
Pi is infinite so every combination/string of numbers is in there, if we calculated enough you could find a billion 2s next to each other
You can look through the first trillion here
https://archive.org/details/pi_dec_1t
Though it’s a bunch of downloading
Not necessarily. It could just become a series of 1's repeating forever. Nothing would require it to contain all strings of numbers.
It could just become a series of 1’s repeating forever
If that happens in a number, then it is rational. Pi is not rational, so that will never happen in pi.
The point of pi is that it’s non-repeating
Take a look at 0.101001000100001... This number is also non-repeating, but obviously doesn't contain all numbers with finite digits.
The property you're looking for is called to be a normal number. Pi is assumed to be one, but it hasn't yet been proven.
However, in a sense this is an unremarkable property as almost all real numbers are normal. :)
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At work at the moment so can't go deep into it. But I think you misunderstand what non repeating numbers mean. Of course there are repeating numbers within pi which is fine, the issue would be if ALL the digits were to simply cycle over and repeat themselves. If however there are a few trillion digits then a series of 1's and 0's for ever, pi is still non repeating
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Looked it up, and it's apparently called the Feynman point after Physicist Richard Feynman (though the story behind that attribution is disputed). https://en.wikipedia.org/wiki/Six_nines_in_pi?wprov=sfla1
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On a long enough string I'm guessing... Infinite? Pi isn't a pattern so does it follow the same "if monkeys hade an infinite amount of time to type at a typewriter they'd type Shakespeare"
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So it's just a standard double precision floating point? Makes it seem like 15 decimal places was hand selected.
Why stop at 1 billion?... Let's go for a trillion, just because we can.
we do what we must because we can
For the good of all of us, except the ones who are dead
But there's no sense crying over every mistake
Idk how much the original gif weighted, but a gif that's thousand more than that would be an absolute pain to load.
I memorized it to a hundred digits for a bet so I'm set for life.
Just one more digit bro, imagine how many things youd discover bro, just one more, one more and it will be so much safer bro, It would help all mission just use 16digits bro
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