This is great! It reminds me a bit of ordinal arithmetic, in which addition is non-commutative. The ordinal numbers begin with all infinitely many natural numbers, followed by the first infinite ordinal, ω. The next ordinal is ω+1, which is greater than ω. But 1+ω is just ω.
Subtraction isn’t canonically defined for the ordinals, so ω−1 isn’t a thing, but there’s an extension of the ordinal numbers called the surreal numbers where it does exist. Sadly addition is defined differently on the surreals, and here it is commutative.ω×−1=−ω does exist though, and as with Norahatsω×−1×−1×−1 does equal ω.
The surreals also contain the infinitesimal number ϵ, which is greater than zero but less than any real number. it’s defined as the number between 0 on the left and all members of the infinite sequence 1,12,14,18,… on the right. Not exactly Norklet (ω−1≠ϵ), but not too far away: ω−1=1ω=ϵ :)
(h/t Alex_Altair, whose recent venture into this area caused me to have any information whatsoever about it in my head)
Yeah, agreed :) I mentioned ω−1 existing as a surreal in the original comment, though more in passing than epsilon. I guess the name Norklet more than anything made me think to mention epsilon—it has a kinda infinitesimal ring to it. But agreed that ω−1 is a way better analog.
That was mainly the motivation for my counting question but the answer isconsistent with Noranoo invoking transfinite induction to get counted.
I think the pattern of—”Is it possible to count to Noranoo?” -yes and—”Can I count to Noranoo?” -no would isolate only transfinite induction.
Another way this could be asked as a dad joke is if ever one is tired and being asked about it claim that “I spent the night counting to Noranoo”. If this story is incredile then it is recognised as a supertask. If there is a reaction like “wow you count fast” that would point to it being some very high finite integer.
I guess I am trying to fish for a scneario that would prompt a resonpce that would clearly support that. Another approach that would more strongly differentiate against googol-likeness would be to start counting and then increasingly blur the words together and then slow down ”… norklet, noranoo” the thinking going that even if your mouth was perfectly dexterous the counting might detect “cheating detection” as it migth not be respectful of the vastness of the number.
But to be frank it was more that I thought I kinda understood the difference but I find myself struggling to figure out what would be a fair operationalization, suggesting I don’t understand it.
This is great! It reminds me a bit of ordinal arithmetic, in which addition is non-commutative. The ordinal numbers begin with all infinitely many natural numbers, followed by the first infinite ordinal, ω. The next ordinal is ω+1, which is greater than ω. But 1+ω is just ω.
Subtraction isn’t canonically defined for the ordinals, so ω−1 isn’t a thing, but there’s an extension of the ordinal numbers called the surreal numbers where it does exist. Sadly addition is defined differently on the surreals, and here it is commutative.ω×−1=−ω does exist though, and as with
Norahatsω×−1×−1×−1 does equal ω.The surreals also contain the infinitesimal number ϵ, which is greater than zero but less than any real number. it’s defined as the number between 0 on the left and all members of the infinite sequence 1,12,14,18,… on the right. Not exactly
Norklet(ω−1≠ϵ), but not too far away: ω−1=1ω=ϵ :)(h/t Alex_Altair, whose recent venture into this area caused me to have any information whatsoever about it in my head)
ω-1 does exist as a surreal and is way better direct analog for Norklet
Yeah, agreed :) I mentioned ω−1 existing as a surreal in the original comment, though more in passing than epsilon. I guess the name Norklet more than anything made me think to mention epsilon—it has a kinda infinitesimal ring to it. But agreed that ω−1 is a way better analog.
One big difference, I think, is that you can’t get to ω by (finite) counting, but you can get to Noranoo?
That was mainly the motivation for my counting question but the answer isconsistent with Noranoo invoking transfinite induction to get counted.
I think the pattern of—”Is it possible to count to Noranoo?” -yes and—”Can I count to Noranoo?” -no would isolate only transfinite induction.
Another way this could be asked as a dad joke is if ever one is tired and being asked about it claim that “I spent the night counting to Noranoo”. If this story is incredile then it is recognised as a supertask. If there is a reaction like “wow you count fast” that would point to it being some very high finite integer.
I mean, she may think that it is such a large number that it is unrealistic that I could count that high overnight? Or even in my lifetime?
For example, if you claimed to have counted to a googol overnight I wouldn’t believe you, but it’s still finite.
I guess I am trying to fish for a scneario that would prompt a resonpce that would clearly support that. Another approach that would more strongly differentiate against googol-likeness would be to start counting and then increasingly blur the words together and then slow down ”… norklet, noranoo” the thinking going that even if your mouth was perfectly dexterous the counting might detect “cheating detection” as it migth not be respectful of the vastness of the number.
But to be frank it was more that I thought I kinda understood the difference but I find myself struggling to figure out what would be a fair operationalization, suggesting I don’t understand it.