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Ioannis
science forum Guru Wannabe
Joined: 24 Mar 2005
Posts: 246
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 Posted: Wed May 24, 2006 4:32 pm Post subject:
Geisler's Tetration Site Down?
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Does anybody know what happened to Daniel Geisler's "Tetration" page at
http://www.tetration.org/ ?
I've sent him a couple of emails, but no response so far.
Thanks much,
--
Ioannis |
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Dave L. Renfro
science forum Guru
Joined: 29 Apr 2005
Posts: 570
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| Posted: Wed May 24, 2006 5:00 pm Post subject:
Re: Geisler's Tetration Site Down?
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Ioannis wrote:
| Quote: | Does anybody know what happened to Daniel Geisler's
"Tetration" page at
http://www.tetration.org/ ?
I've sent him a couple of emails, but no response so far.
|
It's not working for me either, nor do I have any idea
why or if something has happened to him, but if
anyone wants access to his work, here's the latest
(March 23, 2005) internet archive version:
http://web.archive.org/web/20050323095218/http://www.tetration.org/
I realize you -- Ioannis -- are probably more interested
in *why* it's down than getting alternate access to it, but
I'm posting this in case others, who don't know about using
the internet archive, might be interested.
Dave L. Renfro |
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Ioannis
science forum Guru Wannabe
Joined: 24 Mar 2005
Posts: 246
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| Posted: Wed May 24, 2006 7:29 pm Post subject:
Re: Geisler's Tetration Site Down?
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"Dave L. Renfro" <renfr1dl@cmich.edu> wrote in message
news:1148490044.555421.155050@g10g2000cwb.googlegroups.com...
| Quote: |
Ioannis wrote:
Does anybody know what happened to Daniel Geisler's
"Tetration" page at
http://www.tetration.org/ ?
I've sent him a couple of emails, but no response so far.
It's not working for me either, nor do I have any idea
why or if something has happened to him, but if
anyone wants access to his work, here's the latest
(March 23, 2005) internet archive version:
http://web.archive.org/web/20050323095218/http://www.tetration.org/
I realize you -- Ioannis -- are probably more interested
in *why* it's down than getting alternate access to it, but
I'm posting this in case others, who don't know about using
the internet archive, might be interested.
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Thanks Dave. Yeah, it's true I am interested in what happened to him.
Tetration.org was a large personal project for him, in which he put a lot of
energy.
I sure hope Andrew Robbins' solution to analytic tetration didn't disappoint
him to the point of abandoning the entire project.
Ioannis |
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Dave Rusin
science forum Guru
Joined: 25 Mar 2005
Posts: 487
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| Posted: Wed May 24, 2006 11:24 pm Post subject:
Re: Geisler's Tetration Site Down?
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In article <1148498967.824308@athnrd02>, Ioannis <morpheus@olympus.mons> wrote:
| Quote: | I sure hope Andrew Robbins' solution to analytic tetration didn't disappoint
him to the point of abandoning the entire project.
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Could you clarify what you mean by "solution"? I am unfamiliar with what
Robbins has done. A brief web search found a page at
http://tetration.itgo.com/
which contains a paper apparently on this topic. But in the paper the
words "analytic" and "C^infinity" are used as synonyms, so I am not
inclined to read much in detail. (For those who came in late, it is
quite possible to have a nonzero function whose derivatives at a point
are all defined, and all equal zero --- that is, the Taylor series is
0 + 0 x + 0 x^2 + ... Such a function is "C-infinitey" but not "analytic".)
This really is an interesting mathematical question so if there has
been some resolution I'd like to hear about it. Four years ago you
and I had an exchange in this forum in which I wrote,
| Quote: | If anyone wishes to pursue this numerically, here is a test
question : when the base "x" is e=2.718..., and f(y) is
a smooth function with f(0)=1 and f(y+1) = e^ f(y), what
is the "correct" value of f'(0) ? In a paper by Walker
(Math Comp 57, 1991, 723-733) he shows that there is a
C-infinity solution for which f'(0)=1.09246 (approximately).
He also proposes a definition for a real-analytic solution and
while he fails to show it exists, he provides numerical data
to suggest that it does and has f'(0)=1.091767352...,
which is slightly but definitely different. Another definition
which supports either of these two answers would be of interest.
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So if Robbins has a C-infinity solution to the recursion f(y+1)=e^f(y),
that's nice but not new. If he has proved there is only one such,
that's "new" but false (I'm pretty sure). If he has proved that there
is an _analytic_ solution, that's new and very interesting. If he
has proved in addition that the analytic solution is unique, that's
fantastic.
To clarify just what claim has been made, it would be nice to
know what his value of f'(0) is. Bonus points if it's expressible
in terms of "standard" functions.
dave |
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Ioannis
science forum Guru Wannabe
Joined: 24 Mar 2005
Posts: 246
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| Posted: Thu May 25, 2006 12:40 am Post subject:
Re: Geisler's Tetration Site Down?
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"Dave Rusin" <rusin@vesuvius.math.niu.edu> wrote in message
news:e52pvp$l5d$1@news.math.niu.edu...
| Quote: |
In article <1148498967.824308@athnrd02>, Ioannis <morpheus@olympus.mons
wrote:
I sure hope Andrew Robbins' solution to analytic tetration didn't
disappoint
him to the point of abandoning the entire project.
Could you clarify what you mean by "solution"? I am unfamiliar with what
Robbins has done. A brief web search found a page at
http://tetration.itgo.com/
which contains a paper apparently on this topic. But in the paper the
words "analytic" and "C^infinity" are used as synonyms, so I am not
inclined to read much in detail.
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[snip]
From what I understand from his solution, he constructs an on demand C^k, k
in N, series solution to a function he calls superlog (slog), which
satisfies:
x^^slog_x(y) = y
Then he uses slog to define tetration via Abel's linearization equation. So
his solution always preserves the functional equation F(y+1)=e^F(y)
His site has the paper in 4 parts and the graphics for some reason are
garbled. Here's the entire paper in one chunk, with nice Mathematica
graphics, hosted on my website (courtesy of him):
http://misc.virtualcomposer2000.com/TetrationSuperlog_Robbins.pdf
| Quote: | So if Robbins has a C-infinity solution to the recursion f(y+1)=e^f(y),
that's nice but not new. If he has proved there is only one such,
that's "new" but false (I'm pretty sure). If he has proved that there
is an _analytic_ solution, that's new and very interesting. If he
has proved in addition that the analytic solution is unique, that's
fantastic.
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I am not exactly sure how he uses the term "analytic". I suspect he uses it
as "real analytic". His method seems to give as many coefficients for the
series of slog as one wants, so "in the limit" his slog function solution is
real analytic. He uses a rough heuristic argument for uniqueness I think,
but it hasn't convinced me, because the area of convergence of the
aforementioned series for slog, appears to be quite erratic and can be
determined only by visual inspection.
| Quote: | To clarify just what claim has been made, it would be nice to
know what his value of f'(0) is. Bonus points if it's expressible
in terms of "standard" functions.
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He has such numerical estimates at the end of the paper, although I don't
see any for f'. You might also be interested in the following thread which
was his original announcement, in which Edgar, Andrew and me participated
and on which he gives some more numerical estimates:
http://tinyurl.com/nrxjh
Ioannis |
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G. A. Edgar
science forum Guru
Joined: 29 Apr 2005
Posts: 470
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| Posted: Thu May 25, 2006 12:41 pm Post subject:
Re: Geisler's Tetration Site Down?
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In article <1148517621.457415@athnrd02>, Ioannis
<morpheus@olympus.mons> wrote:
| Quote: | I am not exactly sure how he uses the term "analytic". I suspect he uses it
as "real analytic". His method seems to give as many coefficients for the
series of slog as one wants, so "in the limit" his slog function solution is
real analytic.
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Provided the power series converges (which he doesn't prove).
| Quote: | He uses a rough heuristic argument for uniqueness I think,
but it hasn't convinced me, because the area of convergence of the
aforementioned series for slog, appears to be quite erratic and can be
determined only by visual inspection.
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--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/ |
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