Even cooler, at 75 digits you can calculate the circumference of your mom
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
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
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.
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 inO(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 :)
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.”
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.
