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It’s always nice when people independently reinvent good ideas! This poster’s more or less come up with up-arrow notation and a shot at its inverse. edit: actu

It’s always nice when people independently reinvent good ideas! This poster’s more or less come up with up-arrow notation and a shot at its inverse. edit: actually meant https://en.wikipedia.org/wiki/Tetration https://en.wikipedia.org/wiki/Tetration https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation

ColinWright 7y ago
As is pointed out further down, it does effectively invent tetration, which is cool, but that's not Knuth's arrow notation. Edited: I've removed the original and replaced it with the above because clearly my original comment wasn't being understood the way it was intended. Possibly this is no better, but it's worth a try. To provide context, the comment by elil17 is in response to my original, in which I asked what this had to do with Knuth's arrow notation.
- acollins1331 7y ago
  I wouldn't worry much when your e-rep takes a few hits from people with nothing better to do.
  - perl4ever 7y ago
    You're not supposed to discuss voting...but I've noticed a couple times that sometimes when I make two related comments on the same thread expressing basically the same opinion, one gets upvoted a lot and one gets downvoted a lot, and that's just weird. Maybe the exact timing determines if the upvoters see it.
    - acollins1331 7y ago
      Yeah, this is just one reason why I wouldn't be super concerned with your hacker news points.
- elil17 7y ago
  a@2 = a↑↑2
  - ColinWright 7y ago
    Except the essence of Knuth's up-arrow notation is the recursive nature. This is going one step, and while I agree that it's a first step, it doesn't actually get the recursive nature. So this is a notation for a single thing, not a general thing. It's good, but i's missing the generalisation step that is what makes Knuth's notation particularly special. Maybe I know too much about the field, maybe I don't know enough, but I've looked over this many times and it doesn't seem to me to be making "the step." Maybe I'm just expecting too much, but it feels like the heart of Knuth's notation is missing. <fx: shrug /> I'll leave it at that. Feel free to disagree, perhaps it's an interesting talking point.
    - Sharlin 7y ago
      Maybe it's more accurate to say that the poster had invented tetration. https://en.wikipedia.org/wiki/Tetration https://en.wikipedia.org/wiki/Tetration
    - perl4ever 7y ago
      I find it hard to focus on this stuff, but is there really any ultimate generalization? Like, you always can recurse once more - once you define up arrows, then why not iterate them? ↑n means n up arrows, so why not have an operator that applies up arrows a number of times defined with up arrows? It seems like it's just dipping your toe into large numbers, no matter how far you go.
      - dahart 7y ago
        > why not have an operator that applies up arrows a number of times defined with up arrows? That is exactly what up arrows do, isn’t it? Up arrows are iterated up arrows. I learned this in college but still didn’t fully understand up arrows for a long time, they grow unimaginably bigger and faster than I first thought. This video explains it pretty well: https://youtu.be/GuigptwlVHo https://youtu.be/GuigptwlVHo I don’t know about ‘ultimate’ but there are some generalizations of up arrows: https://en.m.wikipedia.org/wiki/Hyperoperation https://en.m.wikipedia.org/wiki/Hyperoperation https://en.m.wikipedia.org/wiki/Conway_chained_arrow_notation https://en.m.wikipedia.org/wiki/Conway_chained_arrow_notatio...

ColinWright 7y ago

As is pointed out further down, it does effectively invent tetration, which is cool, but that's not Knuth's arrow notation. Edited: I've removed the original and replaced it with the above because clearly my original comment wasn't being understood the way it was intended. Possibly this is no better, but it's worth a try. To provide context, the comment by elil17 is in response to my original, in which I asked what this had to do with Knuth's arrow notation.

acollins1331 7y ago
I wouldn't worry much when your e-rep takes a few hits from people with nothing better to do.
- perl4ever 7y ago
  You're not supposed to discuss voting...but I've noticed a couple times that sometimes when I make two related comments on the same thread expressing basically the same opinion, one gets upvoted a lot and one gets downvoted a lot, and that's just weird. Maybe the exact timing determines if the upvoters see it.
  - acollins1331 7y ago
    Yeah, this is just one reason why I wouldn't be super concerned with your hacker news points.
elil17 7y ago
a@2 = a↑↑2
- ColinWright 7y ago
  Except the essence of Knuth's up-arrow notation is the recursive nature. This is going one step, and while I agree that it's a first step, it doesn't actually get the recursive nature. So this is a notation for a single thing, not a general thing. It's good, but i's missing the generalisation step that is what makes Knuth's notation particularly special. Maybe I know too much about the field, maybe I don't know enough, but I've looked over this many times and it doesn't seem to me to be making "the step." Maybe I'm just expecting too much, but it feels like the heart of Knuth's notation is missing. <fx: shrug /> I'll leave it at that. Feel free to disagree, perhaps it's an interesting talking point.
  - Sharlin 7y ago
    Maybe it's more accurate to say that the poster had invented tetration. https://en.wikipedia.org/wiki/Tetration https://en.wikipedia.org/wiki/Tetration
  - perl4ever 7y ago
    I find it hard to focus on this stuff, but is there really any ultimate generalization? Like, you always can recurse once more - once you define up arrows, then why not iterate them? ↑n means n up arrows, so why not have an operator that applies up arrows a number of times defined with up arrows? It seems like it's just dipping your toe into large numbers, no matter how far you go.
    - dahart 7y ago
      > why not have an operator that applies up arrows a number of times defined with up arrows? That is exactly what up arrows do, isn’t it? Up arrows are iterated up arrows. I learned this in college but still didn’t fully understand up arrows for a long time, they grow unimaginably bigger and faster than I first thought. This video explains it pretty well: https://youtu.be/GuigptwlVHo https://youtu.be/GuigptwlVHo I don’t know about ‘ultimate’ but there are some generalizations of up arrows: https://en.m.wikipedia.org/wiki/Hyperoperation https://en.m.wikipedia.org/wiki/Hyperoperation https://en.m.wikipedia.org/wiki/Conway_chained_arrow_notation https://en.m.wikipedia.org/wiki/Conway_chained_arrow_notatio...