Octonion Hyper-Operations Catullus Fellow Posts: 213 Threads: 47 Joined: Jun 2022   06/11/2022, 04:04 AM (This post was last modified: 07/11/2022, 10:59 PM by Catullus.) How does tetration work for quaternions? What about for octonions? How do pentation and higher hyper-operations work for those? Please remember to stay hydrated. ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\ tommy1729 Ultimate Fellow Posts: 1,703 Threads: 374 Joined: Feb 2009 06/12/2022, 01:56 PM We try to walk before we can run We do not even understand tetration well for octonions ( or even complex numbers lol ) And there are many tetrations and many hyper-operators. So I assume it might be case specific. I like the question , but it seems very very general. Wish I could say more ... sorry. regards tommy1729 tommy1729 Ultimate Fellow Posts: 1,703 Threads: 374 Joined: Feb 2009 06/12/2022, 02:12 PM I think most (known) methods rely on properties such as commutative associative etc. So that might imply they all fail for most non-complex numbers. Note that it is also problematic to define derivatives for non-complex functions. ( zero-divisors , depending on the type of infinitesimal , ... )  so that makes formulas that use calculus concepts * uncomfortable *.  Functional composition is associative ... but if we plug in non-associative numbers as parameters ... feels * delicate *. Also we might get extra fixpoints in say the quaternions and such that harrass our convergeance domains and such. Or as we learned before ; functions do no agree on the fixpoint. ( see the bummer thread ) There are also issues with combinatorial interpretations/methods but those are complicated. Best I hope for is that the taylor series expansions of the solutions we have can be used ; plug in a power-associative number x instead of the complex z and just compute the values. ... It should agree with the complex solution and by extension also the field/ring/whatever of x. hopefully. regards tommy1729 Catullus Fellow Posts: 213 Threads: 47 Joined: Jun 2022   07/05/2022, 08:53 AM (This post was last modified: 07/11/2022, 10:59 PM by Catullus.) How do they work for matrices? Please remember to stay hydrated. ฅ(ﾐ⚈ ﻌ ⚈ﾐ)ฅ Sincerely: Catullus /ᐠ_ ꞈ _ᐟ\ « Next Oldest | Next Newest »

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