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.
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.
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 :)
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.
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.
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.
At my last job I was bored so I wrote sql server functions to perform standard math operations on varchar(max) and used them to build factorial tables which I then used to iteratively calculate pi. I think I got up to around 100 digits before I got yelled at for bogging down the server and had to stop.
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.
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.
That's fascinating. Obviously, there's a series of repeating numbers in there, and one of the numbers would have a highest number of repeats... until further places of pi are determined and another number knocks it off... I assume there's a repeating 1, or 2 that repeats 7 or 8 times,etc... at some point...
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"
Well I thought that at first, but it has to be less than infinite since other numbers have to repeat in there as well with at least some occurrence so it's infinite minus something, but since pi goes on infinitely, it's obviously some high number...
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
I did read it, I also wrote it. Wasn't trying to put you down or anything just sharing a bit of knowledge I found interesting. I know many people (my self included at one point) assumed pi would have to include everything when that just isn't true. Apologies if I did a bad job explaining it though
You get that level of precision in a standard "double" floating point number. So that's basically the normal level of precision you get without trying.