Found this article by mistake a while ago while coding my infinite canvas drawing application. It's not exactly what I was looking for but it brought me to a place that I'd never have expected....
Found this article by mistake a while ago while coding my infinite canvas drawing application. It's not exactly what I was looking for but it brought me to a place that I'd never have expected.
The question is simple but I think it quickly takes a philosophical turn.
Man I just love early 00's writing. I don't know what it is specifically, maybe just the underlying optimism andcuriosity. Reminded me of being young and devouring internet blogs and articles,...
Man I just love early 00's writing. I don't know what it is specifically, maybe just the underlying optimism andcuriosity. Reminded me of being young and devouring internet blogs and articles, growing fascinated with all the thibgs that fascinated everyone else.
Took a look at the rest of his blog and immediately I'm met with the modern paradigm. Jebus Chrysler, modern internet writing is quite fearful and despondant. I think it an understandable response to modern times (although something feels feedbacky in all this). But damn, I miss the older more calm interwebz.
Can we have a bit more of those nice faelike wibes tpday plz?
Another one that gives me a similar vibe is https://prog21.dadgum.com/. I was so sad when he decided to stop posting. I still didn't find another blog like that except maybe the one in the OP.
Another one that gives me a similar vibe is https://prog21.dadgum.com/. I was so sad when he decided to stop posting. I still didn't find another blog like that except maybe the one in the OP.
Thank you for that. I knew vaguely about busy beavers in the context of big numbers, but I had no idea of why they were so big. And it all being written in a very digestible way. It was also...
Thank you for that. I knew vaguely about busy beavers in the context of big numbers, but I had no idea of why they were so big. And it all being written in a very digestible way. It was also interesting to see this ending up being about growth of sequences. It would've been interesting to know more about some of the larger numbers/sequences and how they compare and relate.
This Numberphile video about subcubic graphic numbers gets to big numbers using (in my opinion) a much more interesting method than just continuing to recursively repeat operations. I like the...
This Numberphile video about subcubic graphic numbers gets to big numbers using (in my opinion) a much more interesting method than just continuing to recursively repeat operations.
I like the notion of ideas that we can define yet also defy the scale of numbers we can write down.
I think TREE is a function, not a number? Also, if you're using the TREE function, I'm pretty sure TREE() grows faster than exponentials, e.g. TREE(TREE(3)) is immensely much bigger than...
I think TREE is a function, not a number? Also, if you're using the TREE function, I'm pretty sure TREE() grows faster than exponentials, e.g. TREE(TREE(3)) is immensely much bigger than TREE^TREE(3) with about the same amount of typing.
There is a common notation of "iterated functions" where it does make some sense with a small adjustment. f^1 (x) = f(x) f^2 (x) = f(f(x)) f^3 (x) = f(f(f(x))) and so on. Hopefully you see that...
There is a common notation of "iterated functions" where it does make some sense with a small adjustment.
Hopefully you see that tree^tree(3) (3) is more immense than any of the computable numbers mentioned in the article (but still grows slower than the busy beavers).
Note you could also write BB^BB(100) (100).
You could also define the Ackermann hierarchy for this, and get function tetration, pentation, and so on. Plug BB into any of those and that will win, but still grow slower than the "higher level busy beavers" mentioned in the article.
TIL. No i didn't know about that notation and yes, in that case tree^tree(3) (3) as you say is obviously larger. As for the article, I think the main purpose wasn't actually typing out a big...
TIL. No i didn't know about that notation and yes, in that case tree^tree(3) (3) as you say is obviously larger.
As for the article, I think the main purpose wasn't actually typing out a big number, but rather teaching people like me about the different classes of numbers and functions.
Yeah, I deleted the part of my comment that I think this is in response to because, after further thought, I think it missed the point of the article and also the point of the busy beavers themselves.
As for the article, I think the main purpose wasn't actually typing out a big number, but rather teaching people like me about the different classes of numbers and functions.
Yeah, I deleted the part of my comment that I think this is in response to because, after further thought, I think it missed the point of the article and also the point of the busy beavers themselves.
I don't want to play games if it doesn't make me feel like a kid in a candy store. And saying "what you said but +1" is quintessential kid stuff. (But yes I know I just couldn't resist)
I don't want to play games if it doesn't make me feel like a kid in a candy store. And saying "what you said but +1" is quintessential kid stuff.
TIL I can no longer correctly spell googolplex... thanks Google.
I think it was Milton Sirotta who spelled it wrong.
Found this article by mistake a while ago while coding my infinite canvas drawing application. It's not exactly what I was looking for but it brought me to a place that I'd never have expected.
The question is simple but I think it quickly takes a philosophical turn.
Man I just love early 00's writing. I don't know what it is specifically, maybe just the underlying optimism andcuriosity. Reminded me of being young and devouring internet blogs and articles, growing fascinated with all the thibgs that fascinated everyone else.
Took a look at the rest of his blog and immediately I'm met with the modern paradigm. Jebus Chrysler, modern internet writing is quite fearful and despondant. I think it an understandable response to modern times (although something feels feedbacky in all this). But damn, I miss the older more calm interwebz.
Can we have a bit more of those nice faelike wibes tpday plz?
Another one that gives me a similar vibe is https://prog21.dadgum.com/. I was so sad when he decided to stop posting. I still didn't find another blog like that except maybe the one in the OP.
Thank you for that. I knew vaguely about busy beavers in the context of big numbers, but I had no idea of why they were so big. And it all being written in a very digestible way. It was also interesting to see this ending up being about growth of sequences. It would've been interesting to know more about some of the larger numbers/sequences and how they compare and relate.
I really enjoyed the idea that writing 11111... is better than 99999... if you're trying to type out a large number, it tickles something within me =)
It's better for handwriting large numbers, for typing 9's are still better.
Sure, you got me, english is not my native language.
This Numberphile video about subcubic graphic numbers gets to big numbers using (in my opinion) a much more interesting method than just continuing to recursively repeat operations.
I like the notion of ideas that we can define yet also defy the scale of numbers we can write down.
This reminds me of a recent little Joel video.
I always think of Graham's Number when big numbers are discussed.
Aleph^(aleph^(aleph^.....))etc.
Pretty sure I win.
The article excludes infinities when laying out the rules of the game, though my mind also went to Aleph at first.
Tree ^ Tree valid?
I think TREE is a function, not a number? Also, if you're using the TREE function, I'm pretty sure TREE() grows faster than exponentials, e.g. TREE(TREE(3)) is immensely much bigger than TREE^TREE(3) with about the same amount of typing.
Ahh right. I have very very little knowledge in this area other than trivia, but that makes sense.
There is a common notation of "iterated functions" where it does make some sense with a small adjustment.
and so on.
Hopefully you see that
tree^tree(3) (3)is more immense than any of the computable numbers mentioned in the article (but still grows slower than the busy beavers).Note you could also write
BB^BB(100) (100).You could also define the Ackermann hierarchy for this, and get function tetration, pentation, and so on. Plug
BBinto any of those and that will win, but still grow slower than the "higher level busy beavers" mentioned in the article.The bignum bakeoff is in this vein and had some incredible ideas. https://youtube.com/playlist?list=PL-R4p-BRL8NR8THgjx_DW9c92VHTtjZEY
TIL. No i didn't know about that notation and yes, in that case
tree^tree(3) (3)as you say is obviously larger.As for the article, I think the main purpose wasn't actually typing out a big number, but rather teaching people like me about the different classes of numbers and functions.
Yeah, I deleted the part of my comment that I think this is in response to because, after further thought, I think it missed the point of the article and also the point of the busy beavers themselves.
ah dang, I missed that.
This.. but +1.
A brilliant move, but unfortunately infinities are disallowed by the rules of the "game".
I don't want to play games if it doesn't make me feel like a kid in a candy store. And saying "what you said but +1" is quintessential kid stuff.
(But yes I know I just couldn't resist)