12/18/2022, 02:20 AM
(12/17/2022, 01:37 PM)MphLee Wrote: There is alot to unpack here but this already projects some light on my fragile understanding of your old attempt of turning Bennet into Goodstein.
If possible, it would be interesting to see if Gottfried/Sheldon can somehow manage to extract some efficient truncated matrix black magic out of this... so to have some run-able pariGP.
Also, I wonder if using the Limit trick for hyperoperations would produce easier finite order truncations matrices... then we could just have something that evaluates in human amount of time and just leave formal convergence proof for another day, just like Sheldon and Gottfried codes.
In fact.... I don't think a pc would take too much to work with 5 or 6 order square matrices... or maybe it does?
I believe, if I could transport my knowledge and understanding into Gottfried or Sheldon; they'd be able to write this for 100 terms. And it should converge fast. The only reason I stuck to \(3\times 3\) matrices in my experiments, is because that's about all my brain can handle. I am quite literally handicapped when it comes to matrices. They are unintuitive, ugly, disgusting things in my brain--and nothing makes sense. If you ask me to bruteforce a \(3 \times 3\) matrix, I can do it, but it takes me wayyyyyyyy longer than it should. You ask me to do it with \(100 \times 100\), and I am instantly crushed under the weight of that many terms.
I am still confident the Bennet-Goodstein approach is the correct approach to semi-operators. And I understand that I need working code to empirically justify it. I need more time though. Luckily I have 2-3 months come Jan 10th--and I plan to buckle down and rip this apart!
Regards.
