Re: I broke the sum into pieces
Roger Bagula
> Did you verify that with your friend - that guy who runs Mathematica group ?
> On 11/19/09, Roger Bagula <rlba...@sbcglobal.net> wrote:
>
>> Alexander Povolotsky
>>
>> This is the part Mathematica fails on:
>> Sum[(1/(64^n))*(1/(32*n + 333333)), {n, 0, Infinity}]
>> for some reason.
>> In[36]:=
>> N[333333/64,100]
>>
>> Out[36]=
>> 5208.3281250000000000000000000000000000000000000000000000000000000000000000000\
>> 00000000000000000000000
>>
>> In[39]:=
>> b[5]=Sum[(64^(-n-1))*(1/(n/2+5208.328125)),{n,0,Infinity}]
>>
>> Out[39]=
>> \!\(\(-2.05555574498401916904809250313`15.954589770191003*^18796\)\)
>> It just gives the wrong answer for that part.
>> Respectfully, Roger L. Bagula
>> 11759 Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
>> http://www.google.com/profiles/Roger.Bagula
>> alternative email: roger....@gmail.com
>>
>>
>>
>>
>
>
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...
In trying to get a 5th term I tried:
$MaxExtraPrecision = 200
b[5] = Sum[(1/(64^n))*(1/(32*n + 3*1097)), {n, 0, Infinity}];
N[%, 100]
0.0003086349990279674310845177265991859681618864099951680507521205061977799618\
089309382536127817971331870245951164951`99.99999999999999
I'm pretty sure that is wrong too.
I'll cc this to him.
I can't use this approach to get closer to Pi at this rate.
Clear[b]
b[1]=Sum[(1/(64^n))*22/(32*n+7),{n,0,Infinity}];
b[2]=Sum[(1/(64^n))*(-1/(32*n+114)),{n,0,Infinity}];
b[3]=Sum[(1/(64^n))*(-1/(32*n+394)),{n,0,Infinity}];
b[4]=Sum[(1/(64^n))*(1/(32*n+781)),{n,0,Infinity}];
Sum[b[m],{m,1,4}];
N[%,100]
3.1415920104768860463819395769548831674912014189966869630288247319187743718795\
561171365118029140148452540476917807442`99.99999999999999
%-Pi
-6.431129071920807038063246197167059679803784188579461198603890420344066528814\
91523022428102222728100394732538`93.31113744211372*^-7
Respectfully, Roger L. Bagula
11759 Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
http://www.google.com/profiles/Roger.Bagula
alternative email: roger....@gmail.com
Daniel Lichtblau
> Alexander Povolotsky wrote:
>> Did you verify that with your friend - that guy who runs Mathematica group ?
>> On 11/19/09, Roger Bagula <rlba...@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
Roger Bagula
> Roger Bagula wrote:
> > Alexander Povolotsky wrote:
roup ?
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.
Andrzej Kozlowski
On 22 Nov 2009, at 20:11, Roger Bagula wrote:
> he 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.
This is a fantastic mi-statement of the Poincare conjecture and its
solutions. It is absolutely not true that all 3d manifolds "reduce to a
circle" in any sense whatever. This is even less true in higher
dimensions!
The original Poincare conjecture in dimensions 3 states that a simply
connected manifold which is a homology sphere is homeomorphic to the
standard sphere. The 3-d case is rather special since any simply
connected closed manifold always is a homology sphere so the conjecture
can be stated in the form: every simply connected closed 3-manifold is
homeomorphic to a sphere. This however certainly does not mean that all
3 manifolds "reduce" to a sphere (not a circle) as there are infinitely
many non-simply connected ones!
The 3 dimensional Poincare conjecture was proved several years ago by G.
Perelman, building on ideas introduced by Richard Hamilton.
In higher dimensions the conjecture is even more different from what was
implied in this post. It states that a homotopy n-sphere is homomorphic
to an n-sphere. The condition that something is a homotopy n-sphere is a
very strong one - relatively few manifolds are homotopy spheres! To say
that this somehow implies that *all* manifolds "reduce" to spheres is a
comical travesty.
Just for completeness: the Poincare conjecture in dimensions >=5 was
proved in 1961 by Stephen Smale. The Poincare conjecture in dimension 4
was proved in 1982 by Michael Freedman. He actually only proved the so
called topological Poincare conjecture - the smooth version still
remains unproved. (Dimenion 4 is thought to be very special. The four
dimensional Euclidean space is the only one in which the topological
structure does not determine the smooth structure - in other words,
there exist exotic smooth structures on R^4).
Smale, Freedman and Perelman received Fields medals for their solutions
but Perelman refused to accept his.
Andrzej Kozlowski
Andrzej Kozlowski
On 23 Nov 2009, at 20:52, Andrzej Kozlowski wrote:
> In higher dimensions the conjecture is even more different from what was
> implied in this post. It states that a homotopy n-sphere is homomorphic
> to an n-sphere. The condition that something is a homotopy n-sphere is a
> very strong one - relatively few manifolds are homotopy spheres! To say
> that this somehow implies that *all* manifolds "reduce" to spheres is a
> comical travesty.
In fact the conjecture is like: "if it quacks like a duck, it is a duck". And the "comical travesty" is presenting this as stating that "all birds are ducks".
Andrzej Kozlowski