Graham definitions for geometric complexity and badness

I gave a definition of geometric complexity using natural logs;
Graham suggested log base 2 instead. He also proposed taking the dth
root of this, where d is the codimension of the wedgie--that is, the
number of commas used to define it.

If G is the Graham geometric complexity under this definition, R is
(rms or minimax, etc.) error, and n = pi(p) is the number of primes
in the p-limit we are looking at, the formula for geometic badness
now becomes

B = R G^n

which is pretty nice. Does anyone have a concern about switching
definitions to the Graham version, which looks to me like a good idea?

i suggest we use the name "Breed complexity".
feedback please.

-monz

> -----Original Message-----
> From: Gene Ward Smith [mailto:gwsmith@svpal.org]
> Sent: Friday, August 01, 2003 8:12 PM
> To: tuning-math@yahoogroups.com
> Subject: [tuning-math] Graham definitions for geometric complexity and
> badness
>
>
> I gave a definition of geometric complexity using natural logs;
> Graham suggested log base 2 instead. He also proposed taking the dth
> root of this, where d is the codimension of the wedgie--that is, the
> number of commas used to define it.
>
> If G is the Graham geometric complexity under this definition, R is
> (rms or minimax, etc.) error, and n = pi(p) is the number of primes
> in the p-limit we are looking at, the formula for geometic badness
> now becomes
>
> B = R G^n
>
> which is pretty nice. Does anyone have a concern about switching
> definitions to the Graham version, which looks to me like a good idea?

>i suggest we use the name "Breed complexity".
>feedback please.

No, no, Graham is a cool first name, and first names
should be used when possible. :)

-C.

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >i suggest we use the name "Breed complexity".
> >feedback please.
>
> No, no, Graham is a cool first name, and first names
> should be used when possible. :)

What's wrong with just calling it geometric complexity? You are going
to get this mixed up with Graham's complexity for linear temperaments.

>> No, no, Graham is a cool first name, and first names
>> should be used when possible. :)
>
>What's wrong with just calling it geometric complexity? You are going
>to get this mixed up with Graham's complexity for linear temperaments.

It was you who called it that! But you're right.

-Carl

hi Gene,

> From: Carl Lumma [mailto:ekin@lumma.org]
> Sent: Saturday, August 02, 2003 11:05 AM
> To: tuning-math@yahoogroups.com
> Subject: Re: [tuning-math] Re: Graham definitions for geometric
> complexity and badness
>
>
> >> No, no, Graham is a cool first name, and first names
> >> should be used when possible. :)
> >
> > What's wrong with just calling it geometric complexity?
> > You are going to get this mixed up with Graham's complexity
> > for linear temperaments.
>
> It was you who called it that! But you're right.

OK, i'll make a Dictionary entry for "geometric complexity".

if you give me an opening paragraph describing what it is,
i can just use the rest of your previous post for the definition.

-monz