Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2009

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: I broke the sum into pieces

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105149] Re: I broke the sum into pieces
  • From: Roger Bagula <roger.bagula at gmail.com>
  • Date: Sun, 22 Nov 2009 06:11:09 -0500 (EST)
  • References: <4B0551F8.1050308@sbcglobal.net> <144987c90911190624s3f42b7e7g6545e37062631d1f@mail.gmail.com>

On Nov 21, 12:33 am, Daniel Lichtblau <d... at wolfram.com> wrote:
> Roger Bagula wrote:
> > Alexander Povolotsky wrote:
> >> Did you verify that with your friend - that guy who runs Mathematica g=
roup ?
> >> On 11/19/09, Roger Bagula <rlbag... at sbcglobal.net> wrote:
>
> >>>  [...]
>
> > Alexander Povolotsky,
>
> > No I haven't reported this.
> > Since the Mathematica guys ( Trott and Wolfram himself) put up my Beta
> > cube fractal
> > without giving me any credit for it, they are on my list, ha, ha...
> > [...]
>
> I think this calls for a response.
>
> First, let me agree that it is unfortunate you were not given
> appropriate credit for your work. That said, I will point out both that
> there are ways in which the damage was self inflicted, and that there
> have been (and continue to be) efforts to rectify it.
>
> Here is the demonstration in question.
>
> http://demonstrations.wolfram.com/BetaCube/
>
> As you have found (and posted to MathGroup), it now cites "Based on work
> by: Roger Bagula". This came about on October 27 of this year. I had
> received a request to get your name added on October 25, a Sunday, added
> it Monday, and the automated update publication took place early on the
> 27th. So I'd say it was handled quickly, at least from the time it came
> to the attention of someone on the Demonstrations Team (myself, in this
> instance).
>
> We all agree the demonstration is based on work from a MathGroup post of
> yours:
>
> http://forums.wolfram.com/mathgroup/archive/2004/Jul/msg00509.html
>
> Your original version predates the arrival of Manipulate, and moreover
> would not run fast enough in the original form. So people here reworked
> it to fit the framework of the then-under-development Demonstrations
> project. This was in fact done at the request of Stephen Wolfram--who I
> gather had seen the MathGroup post--and I guess that's how the
> "Suggested by:" field came to bear his name.
>
> Here is where things start to come back to you. People in the Wolfram
> Demonstrations project are reluctant to get mixed in anything involving
> yourself. I expect you know why, and I'll not discuss that further.
> Suffice it to say, they have sound reasons, and hence made no comment
> regarding the authorship. I question my own judgement in responding now,
> but as I take responsibity for trouble-shooting such issues involving
> Demonstrations, I feel it is something of an obligation.
>
> I will also mention that there are ways to bring improper citation to
> our attention. Best at the time of your note (last month) was to fill
> out the "Give us your feedback" form at the bottom of the
> demonstration's web page. More recently the pages have been revised, and
> there is now also a button "Report an issue", which also brings up the
> comment box. The difference being, it is even more obvious that a
> comment can be in the form of reporting problems such as missing
> attribution. In any case, we have had issues raised with other
> demonstrations, both in terms of correctness and citation. And we have
> endeavored to address such issues.
>
> Back to the matter at hand. I've spent more time today than I care to
> recall in going over the original code in the MathGroup post, the
> various stages of development of the final product, who contributed what
> when, etc. My conclusion is that the authorship should change to give
> credit to you. Below that it will also state "Additional contributions
> by: The Wolfram Demonstrations Team". I will take the liberty of
> assuming this is a desirable outcome from your point of view.
>
> Daniel Lichtblau
> Wolfram Research

The whole point of the post was the infinite sum fault
that plagues me in trying to get a scale 1/64 in five parts BBP
like approximation of Pi.
This is important because of my conjecture:
The z Transform of rational Polynomials:
P[n,k] and Q[n,k] exist such that:
A[z,n]=Sum[(P[n,k]/Q[n.k])/z^k,{k,0,Infinity}]=Sum[W[n,k]*z^k/k!,{k,
0,Infinity}] ( Taylor expansion of A[z,n])
Such that at the scale:
z=scale[n]
A[scale[n],n]=Pi
( essentially this is a conjecture that BBP  Pi sums exist for
different levels of n
besides those already known and calculated).
It also gives a hunting license  for higher binary scales , I think).

This conjecture is related to the idea that the probability
p[n,k]=(P[n,k]/Q[n.k])/(P[n,0]/Q[n.0]):
(normalized so that the first value
is still a probability)
has finite entropy at the scale[n]:
Infinity>Sum[-p[n,k]*Log[p[n,m]]/Log[scale[n]],{k,0,infinity}]>0
That states that the  information involved in producing Pi is finite.

The constant Pi exists at all scales and in all Euclidean dimensions.

The Poincare conjecture was proved so that all the 3d manifolds reduce
to a circle
( hyperbolic included), so up to 4 dimensions 3 d manifolds Pi should
be
the same constant in our universe.
I think that conjecture was already proved true in higher dimensions.

An effort to give some analysis to this:
The Taylor expansion if true term by term:
(P[n,k]/Q[n.k])/z^k=W[n,k]*z^k/k!
Where (D[A[z,n],{x,k}]/.z->0)=W[n,k]
(P[n,k]/Q[n.k])=W[n,k]*scale[n]^(2*k)/k!=(D[A[z,n],{x,k}]/.z->0)*scale
[n]^(2*k)/k!

Experiments show that in 32th and 64th the very first term
n=0 has to be closer to Pi...but below it.

Why don't we try to put this Beta Cube behind us?
A representative of Wolfram solicited my submission of
said Beta Cube, and then rejected it.
Later, much later, I find that it is a demonstration
while trying to find in Google pictures to show a friend
of the Beta Cube.
Since I did that originally in a demo version of Mathematica 3.0
about 1997 or so
while I was working on cuboid versions of Pascal triangles in 3d
and also active in fuzzy logic,
the result is unique, new and probably important as a fractal.


  • Prev by Date: Re: Re: Undo in Mathematica
  • Next by Date: Re: More Efficient Method
  • Previous by thread: Re: Re: I broke the sum into pieces
  • Next by thread: Re: Re: I broke the sum into pieces