The __________ dual

This name "the dual" for any val or monzo or whatever is kind of
confusing, because there are lots of duals. It's sort of like Hodge
duality but not quote, and another type of duality I've been looking
into a lot is Pontryagin duality, which I think will be useful in
understanding contorted systems. So to say "the dual" is fine
basically only for now, until some other useful type of dual comes up.

Can we just call it the (something) dual? Maybe the Smith dual? I get
Gene didn't invent the exterior algebra concept, but as far as I know
he's the first to recognize it's importance in music theory and use it
everywhere. And if there is ever worked out a sort of canonical dual
that leaves contorsion alone, maybe that could be the Breed dual or
something. But in this case I'm specifically talking about the one
that uses exterior algebra and just tells you if there is contorsion,
but not the specific way in which things are contorted.

I get that people don't like to name things after themselves, but I
still think it's a good idea because we're going to have to qualify
what type of duality it is eventually.

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> This name "the dual" for any val or monzo or whatever is kind of
> confusing, because there are lots of duals.

http://en.wikipedia.org/wiki/List_of_dualities

> Can we just call it the (something) dual? Maybe the Smith dual?

The Battaglia dual! Or maybe the multidual, sending multivals to multimonzos and vice versa.

On Thu, Jan 19, 2012 at 8:00 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > This name "the dual" for any val or monzo or whatever is kind of
> > confusing, because there are lots of duals.
>
> http://en.wikipedia.org/wiki/List_of_dualities

That's a lot of duals.

> > Can we just call it the (something) dual? Maybe the Smith dual?
>
> The Battaglia dual! Or maybe the multidual, sending multivals to multimonzos and vice versa.

Haha! Not my dual. Multidual? Exterior dual?

Is there really no name for this dual? It's never been given a name?

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Is there really no name for this dual? It's never been given a name?

Just the regular duality between a vector space and the dual space doesn't have any better name than "dual" so far as I know, but I suppose that is an argument not to just call our thing "the dual". But I could try asking if it has a name.

On Thu, Jan 19, 2012 at 10:42 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Is there really no name for this dual? It's never been given a name?
>
> Just the regular duality between a vector space and the dual space doesn't have any better name than "dual" so far as I know, but I suppose that is an argument not to just call our thing "the dual". But I could try asking if it has a name.

You can do that? There are people who you ask stuff about math? Who
are these people? Where are they? Is this like the illuminati? Can I
ask questions too?

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Jan 19, 2012 at 10:42 PM, genewardsmith
> <genewardsmith@...> wrote:
> >
> > --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > Is there really no name for this dual? It's never been given a name?
> >
> > Just the regular duality between a vector space and the dual space doesn't have any better name than "dual" so far as I know, but I suppose that is an argument not to just call our thing "the dual". But I could try asking if it has a name.
>
> You can do that? There are people who you ask stuff about math? Who
> are these people? Where are they? Is this like the illuminati? Can I
> ask questions too?

You could try here:
https://groups.google.com/forum/#!forum/sci.math.research

It's moderated to keep the riff-raff out so try not to sound like riff-raff.