[seqfan] followup Re: Floretions CKD

[Robert Munafo]

Thank you Bob and Kevin and Richard.

Bob Lyons wrote:
> I'm not familiar with floretions.
> But back in March, Neil and I discussed the FAMP programs and the fact that there doesn't seem to be an easy way to run these programs.
> Neil asked me to move all the FAMP programs from the PROG section to the COMMENTS section.

Thank you. Later (after my previous message to seqfan) Creighton
Dement (CKD) wrote back to me, stating that some of the early OEIS
sequences were "not meant to be published" even though they were on a
website. My notes from 15 years ago indicate that at the time, he had
told me that the sequences came from a website whose contents were
lost somehow (and had no backups). Neither CKD nor anyone else seems
to have performed the automated search to re-discover how to calculate
the mystery sequences. I guess if they're still in the OEIS after all
these years then they can stay.

Kevin Ryde wrote:
> > integers taken 3 bits at a time
> That's A308496 (mentioned in the PDF). The material there is still controversial.
>
> > quasi ring-like algebraic system with 16 basis elements (but not normal sedenions).
> That might be "order 2".
> I thought the intention was what might be called a direct product of some number of quaternions.  The algebraists in the house will probably say that's badly wrong terminology. (Is "Clifford algebra" closer?)

Okay, that seems to explain what CKD meant, saying that "order 2" was
the result of doing some kind of construction once (and that each
subsequent application of the construction multiplies the number of
basis elements by 4). I personally think CKD has recently invented an
iterable construction, vaguely like Cayley-Dickson in principle, that
repeats a pattern that he recognised in his earlier work; and I think
he now considers the earlier work to (retroactively) be part of the
series.

Richard Mathar wrote:
> Back in 2010 Floretions were an algebra defined on a group of order 32. I tried to put the group into a standard perspective then: https://oeis.org/A173343/a173343.pdf .

Thanks for reminding me, yes I do have that paper and I've just linked
to it from my old Floretions-related web page.
(mrob.com/pub/seq/floretion.html)

I see that it hasn't gotten any more well-understood, and the new
stuff is too confusing for me: using 64 or 256 or more real numbers at
a time, somehow using integers as indices to the basis vectors, and
using the same noun "floretions" to refer to the integer and to a
compound of many reals.

--
  Robert Munafo, mrob27 at gmail.com