On 23 Jun 2014, at 05:46, Platonist Guitar Cowboy wrote:
On Mon, Jun 23, 2014 at 3:59 AM, LizR <lizj...@gmail.com> wrote:
On 23 June 2014 04:51, Bruno Marchal <marc...@ulb.ac.be> wrote:
I apply math on the mathematician (the dreamer) like Everett applied
physics on the physicians.
I suspect you meant to say physicists. Physicians are doctors :-)
Somebody should start a cipher thread for Bruno's consistent uhm...
English typing habits. Been reading this place for too long, I
didn't even notice that. Are they recursively enumerable?
Yes. But only when defined at, or below, the (my) correct substitution
level. This need comp + some level choice/bet.
Russell mentioned something about Brent referencing quarternions in
relation to QM. Can somebody point to or mention the thread/
reference as I missed that?
On that note I wonder if there is any kind of number/algebra beyond
the sedenian?
They are but are completely degenerated. Octonions have application in
quantum gravitation. Baez wrote interesting papers on that topic. 8
is my favorite divisor of 24! (and I love 24 for his crazy role in the
counting of number partition).
I'd guess there isn't much more to "relax" beyond alternative, power
associativity, and flexibility properties, right?
From complex to real, you lose nothing and get n solution for all
degree n polynomial equation. Some function, like exponentiation and
logarithm get multivalued though.
From complex to quaternion, you loose commutativity, but that is
natural in the quantum context where observable, or heisenberg matrix,
don't commute. This gives rise to commutator [AB] - [BA], which have
interesting algebra.
From quaternion to octonion, you lose associativity, and get
associator [(AB)C] - [A(BC)], which again provides quite interesting
algebras. But I should revise a bit to be sure not saying something
inadequate.
I have not met a convincing use of quaternion in QM per se, but
octonion seems to me more indispensable somehow.
Do sedenians find some application in QL still, as the octonians do?
I have not heard of an application of the sedenians.
Not looking for some comprehensive serious response, just curious
about types of numbers, algebra, their application etc. PGC
It is a very interesting subject, but quite a large topic. The
relation between the natural numbers, and the other numbers, and
geometry, is a quite vast and interesting subject.
Bruno
http://iridia.ulb.ac.be/~marchal/
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to everything-list+unsubscr...@googlegroups.com.
To post to this group, send email to everything-list@googlegroups.com.
Visit this group at http://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
