05/26/2021, 11:17 PM
(05/26/2021, 10:50 AM)MphLee Wrote: What do you think about the centrality of hyper-operations chain-like objects and their possible continuous extension to non-discrete chains (paths?)?
How do you think the reception of these ideas was and what was the atmosphere around those chain objects? Did they treat them as exotic and niche items?
Honestly, their reaction was mostly; that this is some really wacky and weird stuff. But they thought it was cool. They were more interested in taking matrices and arbitrary operators and doing things like this:
\(
\frac{d^{z}}{dw^z} e^{Aw} = A^z e^{Aw}\\
\)
Honestly, I don't see what's so cool about that; a fractional power of matrix seems easy to do; but apparently they like that
go figure.They were more receptive than you may think. A lot of them would already have brushed on these things; especially comp sci people. They're more of the boat, that this looks way too hard, there's no way we could ever do that; than, it's unimportant or niche. They especially like the \( \Gamma \) which pops up everywhere, lol.
Honestly; I still have no idea how to construct a function like \( \alpha \uparrow^s z \); and it's not so much that you have to prove the thing converges; it's the domain arguments needed to show the functional equation that are a real problem. I gave up a long time ago trying to make that work. But I still believe it to be a very important subject.
Sincere Regards, James
