? harmonic entropy

I've mentioned the Minkowski ? function, and have put up a Wikipedia
article about it:

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

I used this for "poor man's harmonic entropy", but I also mentioned,
and keep thinking I ought to compute, a smoothed derivative using
Stieltjes
integrals, but I never do; Maple is not that great at heavy computing
and I don't want to write Fortran code or something. In case someone
else wants to try, and by way of documentation, consider this.

Stieltjes integrals: http://en.wikipedia.org/wiki/Stieltjes_integral

If M is a smooth distribution, for instance

M(x) = 1/(sqrt(2pi)a) exp(-x^2/(2a^2))

then we can define a smoothed derivative for ? by

f(t) = int_-\infty^\infty M(x-t)d?

We can evaluate that by integrating by parts, which gives us the
convolution of ?(x) and M'(x)

f(t) = - int_-infty^\infty ?(x)M'(x-t)dx

which we could evaluate by the Trapezoidal rule, which amounts to
simply a finite sum.

We can do the same thing with respect to something which probably
makes more musical sense, the function w(x) = x 2^(-x)?(2^x), which is

By the way, I'm tired of posting things and then having them not
appear. I was using coolgoose as a bitbucket address, which would
simply accumulate postings for me not to read, but things started
bouncing again. Does anyone know a nice email address which is willing
to dispose of the junk instead of bouncing it? I need a way to send
email to /dev/null, basically.

>We can do the same thing with respect to something which probably
>makes more musical sense, the function w(x) = x 2^(-x)?(2^x), which is

Did you intentionally break here?

>By the way, I'm tired of posting things and then having them not
>appear. I was using coolgoose as a bitbucket address, which would
>simply accumulate postings for me not to read, but things started
>bouncing again. Does anyone know a nice email address which is willing
>to dispose of the junk instead of bouncing it? I need a way to send
>email to /dev/null, basically.

Er, if you accept the mail it won't bounce... don't understand the
question. You're getting a lot of junk and you want to abandon an
address, but you don't want it to bounce...?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >We can do the same thing with respect to something which probably
> >makes more musical sense, the function w(x) = x 2^(-x)?(2^x), which is
>
> Did you intentionally break here?

No, but I was pretty much done. I don't know what I wanted to say.

> Er, if you accept the mail it won't bounce... don't understand the
> question. You're getting a lot of junk and you want to abandon an
> address, but you don't want it to bounce...?

If I get bouncing email, then Yahoo will stop my posting priviledges.
Posts just dissappear. However, I am not interested in reading the
spam generated from Yahoo, so I want a /dev/null email address; one
which never bounces anything, and never checks to see if you actually
read anything.

>> Er, if you accept the mail it won't bounce... don't understand the
>> question. You're getting a lot of junk and you want to abandon an
>> address, but you don't want it to bounce...?
>
>If I get bouncing email, then Yahoo will stop my posting priviledges.
>Posts just dissappear. However, I am not interested in reading the
>spam generated from Yahoo, so I want a /dev/null email address; one
>which never bounces anything, and never checks to see if you actually
>read anything.

My solution was to filter anything sent to the admin addresses
directly to my trash with my e-mail client. I announced to the
list that I couldn't be contacted there.

If you're getting mail on the web, I would just create a dummy
gmail account and go there however often it takes for a gigabyte
of spam to accumulate and clean it out. You can probably
invite yourself at this point, but I have like 50 invites if you
want one.

-Carl