Re: [computer-go] Can Go be solved???... PLEASE help!

2007-01-13 Thread Nick Apperson

I would first just like to say, there have been many times in my life where
I have known 1000 times more than someone else and I didn't feel the need to
be an ass.  I'm sure you are a nice person, but please don't treat me like I
am a moron.  Some assumptions you made about me that aren't true:

1) you assume I didn't understand what solvable means in a mathematical
sense.  I think in a more important way, solvable means is able to be
solved and frankly that question is still able to be debated regarding go.

From a mathematical standpoint, any game with a finite set of states is

solvable.

2) You assume that I took 1 billion years literally...   Oh my, I would
venture to say that I have had a whole lot more physics than you have my
friend and I understand how people get those numbers.

3) You assume that I don't know that changing the board size doesn't
necessariyl change all the properties of the game.  I mean how dumb do you
think I am?

But, I am going to point out a couple problems in what you said since you
seem to be up for being an ass.

1) Multiple dimensions doesn't help at all.  Information processing ability
as well as informataion storing ability is proportional to a 2D surface
surrounding the area that is able to be used for the computation.  This is
the upper limit given with thermodynamics which is probably the only part of
physics that has laws that are well founded.

2) The reason I object to infinity as a concept is not because of my mental
inferiority.  In fact, infinity is a concept that comes quite readily to
me.  I learned it early in my youth and when I first saw a graph of velocity
versus time (age 12 maybe) I knew that the area under it was displacement.
I had taken calc 2 as a sophmore in highschool.  The problem I have with it
in regards to what you were talking about is that it has never been proven
to exist anywhere in the actual world and there is lots of evidence that it
doesn't exist.



That said, I have seen you post before and I enjoy reading your posts, but
please don't flame me.  Just because I am new to computer go doesn't mean I
am a moron.  I might bring something new.  If you all had it figured out
already, we wouldn't be having this discussion.  I have a lot to learn from
you and I look forward to that.  Please be more respectful.  I am sorry that
this was a harsh message, but I feel you were unfair to attack me as you
did.

Sincerely,
Nick

On 1/12/07, Don Dailey [EMAIL PROTECTED] wrote:


On Fri, 2007-01-12 at 15:43 -0600, Nick Apperson wrote:
 yeah, there are upper limits placed on computation rate by
 thermodynamics.  19x19 is way beyond those as Dave pointed out.  But,
 even if you believe that technology will improve and the most
 revolutionary change yet will come to understanding of physics and
 that change will give us signifigantly more computational power and
 time etc...  You can always make a bigger board.  If life comes to a
 point where go could be solved for any size board, you will no longer
 be in this world and solving things such as is go solvable? will
 have no meaning.

Yes, you can always make a bigger problem by making a bigger go board
but
that doesn't change the theoretical properties of the game.   The game
will always be solvable.

The game might be trivially solvable even now to a being not confined
to our 3 physical dimensions.   I hate to get philosophical like this,
but there are theories of other dimensions that (if true) say we live
in a multi-dimensional universe.There may be much more here than
we can sense and that we can perhaps take advantage of.

But it doesn't matter.   When Chris said 1 billion years you should
have instantly realized that he didn't mean this literally,   he just
meant a correct procedure exists for solving the game. Since no
one has proved how long the universe will last, I don't think you
can even prove that in a practical sense it's unsolvable.   If you
lack imagination you can simply say it's not solvable because you
believe it can't be done in your lifetime - as if science and math
cares about how long we live or even the universe.If the universe
will die in 10 trillion years does that mean the number 20 trillion
is an impossible number?

The concept of infinity is important in mathematics.   It's even useful,
but I suppose that it really should be considered meaningless since
we all die after 70 or 80 years.

- Don



___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/

___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/

Re: [computer-go] reign of terror

2007-01-13 Thread Sylvain Gelly

Hello,

It looks like most of these games are being won in the opening.  Doesn't

mogo have a big UCT opening book?  Is it learning from each game it plays
as
well?



unfortunately no for both. Its opening book is at maximum 4 ply (deepest
variation) and if you play first on a yoshi it is 2 ply (that is white
answer to your move and that's all).
Learning from each game would be great, but not so easy to do if you don't
have access to the strength of the opponent. And by the way, it would be a
little cheating, as the opening book would be then be overfitting the
players on cgos. For example I managed in some experiments to create on
opening book which gives a 100% winning rate against gnugo! But (i) there is
bad moves, and (ii) it would be an not interesting overfitting.

Sylvain

PS: by the way, I set limited version of MoGo playing on cgos, with
extension _xk, which means making x thousands of simulations per move.
Currently, there are 3k and 10k playing.


David


 -Original Message-
 From: [EMAIL PROTECTED]
 [mailto:[EMAIL PROTECTED] On Behalf Of Don Dailey
 Sent: Friday, January 12, 2007 6:41 PM
 To: computer-go
 Subject: [computer-go] reign of terror


 Someone needs to get their bot on CGOS and end Mogo's reign of terror.

 A version of MoGo has achieved a CGOS rating of well over 2300!



 - Don


 ___
 computer-go mailing list
 computer-go@computer-go.org
 http://www.computer-go.org/mailman/listinfo/computer-go/



___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/

___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/

Re: [computer-go] Can Go be solved???... Komi

2007-01-13 Thread alain Baeckeroot
Le vendredi 12 janvier 2007 23:45, Chrilly a écrit :

 It would be interesting if the empirical Komi depends on the playing 
 strength. 
It seems that for nearly random players, the komi is close to 0 (or maybe 1
under chinese rules to compensate for 1 more stone)

Gunnar reported komi = 0.05 for brown (random except does not fill eyes) and
Aloril reported komi = 1.5 for his veryweakbot.

Also stats on even games, shows this for amateur players
http://gemma.ujf.cas.cz/~cieply/GO/statev.html
Playing even game against 1 rank stronger (so give W 6.5 komi instead of 0.5)
shows very significant difference only for strong dan players, not before.

For pro, i have been told that Lee Chang Ho is 2 points stronger than one of
his opponent, and achieves nearly 70% wins against him (in even games)

I would assume,that the tempo of Black is worth more for strong  
 players.
You seem to be right :)

 But there is on the other side the law of the balance of stupity. 
 Also white loosed due too his lack of skills tempo/sente and the net effect 
 is for all playing levels the same. Monte-Carlo Go is based on this law.
 
 Chrilly 

Alain.
___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/


Re: [computer-go] Useless moves in the endgame and slow move in beginning

2007-01-13 Thread alain Baeckeroot
Le mercredi 10 janvier 2007 10:32, Sylvain Gelly a écrit :
 Hello,
 
  Also on 19x19 mogos plays also some very slow moves in the beginning of
  7 handicap game.
[...]
 In 19x19, MoGo only considers local moves, near the move you 
 just played or the last move it played. It even doesn't look at other moves,
 so the slow moves are mandatory.
So placing handicap ala japanese (= on star points) would be an easy
improvement. This placement is optimal repartition of strenght on the board,
it would avoid over-concentration of handicap stones, and makes local moves
better (as global advantage is already done with handi).
But i find free placement more fun for white, even if it often gives easier
game due to black misplacement of handi (very often overconcentrated)

 I did not try something like plays globally until the xxx move then
 locally. Perhaps it should help.
Hmm its probably rather difficult to find the balance, local answer are
very often needed. Good stuff would be : when no local answer is needed,
then take initiative and play one big/global move.

 I agree there is lt to do in 19x19 :).
Mogo is already very impressive :)
Alain

___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/


Re: [computer-go] Useless moves in the endgame and slow move in beginning

2007-01-13 Thread Sylvain Gelly

I did not try something like plays globally until the xxx move then



 locally. Perhaps it should help.
Hmm its probably rather difficult to find the balance, local answer are
very often needed. Good stuff would be : when no local answer is needed,
then take initiative and play one big/global move.



Yes you are right. Yet, answering the when no local answer is needed
question is hard. I tried something like consider global at the root and
local at deeper nodes. But MoGo is still too weak at local fights to afford
spending simulations to global search. I hope in the future it will become
stronger in local fights so that it can afford looking global at the root.

I agree this is a big issue. Perhaps some has already much better
solutions/ideas in mind.

Sylvain
___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/

Re: [computer-go] Can Go be solved???... PLEASE help!

2007-01-13 Thread Unknown
On Fri, 2007-01-12 at 15:51 +, Mehdi Ahmadi wrote:
 Hello  thank in advance for any interests/ responses.
 
 I'm unfortunately (or not) doing a dissertation as part of my final year
 project (undergraduate) on the game of Go. The exact title is: Can the game
 of go be solved? Analysis of computational methodologies for go. And I have
 included my overall objectives below. 
 
 I have many works from different people on different aspects of Computer Go
 which would make for great inclusion at different parts - but overall I am
 still gravely struggling. In reviewing some of these my greatest difficulty
 is in understanding exactly how say Monte-Carlo-UCT or even Alpha-Beta
 testing (pruning, etc) occur so as to be able to give a simplified depiction
 (illustrated or otherwise) of the process. Can this be done without having
 to go through the source code of say something like GNU Go?
 
 Also another difficulty I've had is in trying to get further information on
 the commonly referred top ranking packages, Handtalk, Go++, Many Faces of
 Go, etc due to their commercial nature? (the only thing I've been able to
 find which is a bit outdated:
 http://www.inventivity.com/OpenGo/Papers/EditedGoPapers.html).


If they still exist online, most of these papers are suggested reading,
IMHO

WRT classic methods (alpha-beta, evaluation, Zobrist hashing, etc) a lot
of material can be found in computer-chess publications.

Another source of links can be found at Markus Enzenberger's online
bibliography:

http://www.cs.ualberta.ca/~emarkus/compgo_biblio/


Most of the computer go authors have posted on this mailing list, and
discussed their views and methods, and the design of their programs.

The archive of this mailinglist can be found at:

http://computer-go.org/pipermail/computer-go/



This archive starts at approx 2003. I have an archive of older stuff
(1993-) from this mailinglist stored on my personal website:

http://nngs.ziar.net/cgml/


HTH,
AvK


___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/


Re: [computer-go] Can Go be solved???... PLEASE help!

2007-01-13 Thread Don Dailey
Ok Nick,   

The funny thing about this,  is that I was originally defending someone
who
after making a simple post got flooded with all the stale size of the
universe
and grains of sands arguments - presumably to prove he was wrong when he
made
a simple statement which was correct.   He made the horrible mistake of
saying 1 billion years and I guess that's where he went wrong.
Everyone
jumped in as if he was an idiot for thinking it would only take 1
billion years.

I also admit I got annoyed with those arguments about the size of the
game,
I felt it was pretty redundant and I don't know of anyone on this group
that needed a refresher course on this - everyone knows how huge this 
problem is.

I'm sure you understand physics much more than I do.   However, I
disagree about dimensionality and if I'm wrong I have a thick skin and
you can explain it to
me and I will believe you.   One of the theoretical limitations to
computing power (which was layed out in someones posts) and I have
always understood to be the case, is related to
space - the physical size of the universe.If a computer can exist in
3 
dimensions,  couldn't an infinite number of them exist with 1 more
dimension?
Couldn't one be constructed that is far more highly parallel that what
we
can construct in our 3 physical dimensions?


- Don




On Sat, 2007-01-13 at 03:38 -0600, Nick Apperson wrote:
 I would first just like to say, there have been many times in my life
 where I have known 1000 times more than someone else and I didn't feel
 the need to be an ass.  I'm sure you are a nice person, but please
 don't treat me like I am a moron.  Some assumptions you made about me
 that aren't true: 
 
 1) you assume I didn't understand what solvable means in a
 mathematical sense.  I think in a more important way, solvable means
 is able to be solved and frankly that question is still able to be
 debated regarding go.  From a mathematical standpoint, any game with a
 finite set of states is solvable. 
 
 2) You assume that I took 1 billion years literally...   Oh my, I
 would venture to say that I have had a whole lot more physics than you
 have my friend and I understand how people get those numbers.
 
 3) You assume that I don't know that changing the board size doesn't
 necessariyl change all the properties of the game.  I mean how dumb do
 you think I am? 
 
 But, I am going to point out a couple problems in what you said since
 you seem to be up for being an ass.
 
 1) Multiple dimensions doesn't help at all.  Information processing
 ability as well as informataion storing ability is proportional to a
 2D surface surrounding the area that is able to be used for the
 computation.  This is the upper limit given with thermodynamics which
 is probably the only part of physics that has laws that are well
 founded. 
 
 2) The reason I object to infinity as a concept is not because of my
 mental inferiority.  In fact, infinity is a concept that comes quite
 readily to me.  I learned it early in my youth and when I first saw a
 graph of velocity versus time (age 12 maybe) I knew that the area
 under it was displacement.  I had taken calc 2 as a sophmore in
 highschool.  The problem I have with it in regards to what you were
 talking about is that it has never been proven to exist anywhere in
 the actual world and there is lots of evidence that it doesn't exist. 
 
 
 
 That said, I have seen you post before and I enjoy reading your posts,
 but please don't flame me.  Just because I am new to computer go
 doesn't mean I am a moron.  I might bring something new.  If you all
 had it figured out already, we wouldn't be having this discussion.  I
 have a lot to learn from you and I look forward to that.  Please be
 more respectful.  I am sorry that this was a harsh message, but I feel
 you were unfair to attack me as you did. 
 
 Sincerely,
 Nick
 
 On 1/12/07, Don Dailey [EMAIL PROTECTED] wrote:
 On Fri, 2007-01-12 at 15:43 -0600, Nick Apperson wrote:
  yeah, there are upper limits placed on computation rate by
  thermodynamics.  19x19 is way beyond those as Dave pointed
 out.  But,
  even if you believe that technology will improve and the
 most 
  revolutionary change yet will come to understanding of
 physics and
  that change will give us signifigantly more computational
 power and
  time etc...  You can always make a bigger board.  If life
 comes to a 
  point where go could be solved for any size board, you will
 no longer
  be in this world and solving things such as is go
 solvable? will
  have no meaning.
 
 Yes, you can always make a bigger problem by making a bigger
 go board 
 but
 that doesn't change the theoretical properties of the game.
 The game
 will always be solvable.
 
 The game might be trivially solvable even now to a 

Re: [computer-go] Testing against gnugo

2007-01-13 Thread Eduardo Sabbatella Riccardi
It seems that you GTP implementation doesn´t implements the 
command final_score.

About the passes. I found that pass move is not sent by twogtp.py to the 
other player. 

So, from a black player point of view, you will receive: genmove black, you 
will process and return your move. If you receive ANOTHER genmove black it 
means: play white pass, then genmove black.

It works for me, my gtp implementation works agains gnugo, agains itself and 
with the KGS client.

I hope it helps,
Eduardo

On Friday 12 January 2007 16:47, Peter Drake wrote:
 I used the Python version and it worked almost perfectly on the first
 try -- thanks!  Here's the command I used:

 python /Applications/gnugo-3.6/interface/gtp_examples/twogtp.py --
 black 'path to my program here' --white '/usr/local/bin/gnugo --
 mode gtp --quiet --level 1 --never-resign --chinese-rules --capture-
 all-dead' --verbose 2 --komi 7.5 --size 9

 It played out the game, but at the end this happened:

 Black passes
 A B C D E F G H J
 9 O O . O . O O O . 9
 8 O O O O O O . O O 8
 7 . O O . O O O . O 7
 6 O O O O O . O O . 6
 5 O O O O O O . O O 5
 4 . O O . O . O O . 4
 3 O O + O . O O . O 3
 2 O . O O O O O O . 2 WHITE (O) has captured 51 stones
 1 . O . O . O . O O 1 BLACK (X) has captured 0 stones
 A B C D E F G H J

 Game 1: W+88.5 ERROR: GTP Command failed: unknown command
 Game 1: ERROR: GTP Command failed: unknown command W+88.5
 White: 3.400s CPU time

 I interpret this to mean that the script sent W+88.5 as a GTP
 command to my program, which of course didn't understand it. Is this
 standard GTP or something specific to GNU Go? Would a reasonable
 response be to silently acknowledge any command whose second
 character is +?

 (Lest Orego's honor be besmirched, I should clarify that I was only
 allowing Orego one second per move while testing out the protocol.
 Hopefully it won't get wiped off the board by GNU Go level 1 if I
 give Orego more time.)

 Peter Drake
 Assistant Professor of Computer Science
 Lewis  Clark College
 http://www.lclark.edu/~drake/

 On Nov 20, 2006, at 3:44 AM, alain Baeckeroot wrote:
  Le vendredi 17 novembre 2006 18:41, Peter Drake a écrit :
  Orego speaks GTP, as does gnugo. I'd like to run a bunch of games
  (say, 50) between them to see how many Orego wins. Does anyone have a
  handy script (ideally bash or Python) for this?
 
  Thanks,
 
  Peter Drake
  Assistant Professor of Computer Science
  Lewis  Clark College
  http://www.lclark.edu/~drake/
 
   Hi
  In GNU Go package you have tools interface/gtp_examples/twogtp.xyz
  in various
  languages.
 
  my 2 cents
  Alain
  ___
  computer-go mailing list
  computer-go@computer-go.org
  http://www.computer-go.org/mailman/listinfo/computer-go/

 ___
 computer-go mailing list
 computer-go@computer-go.org
 http://www.computer-go.org/mailman/listinfo/computer-go/





__
Preguntá. Respondé. Descubrí.
Todo lo que querías saber, y lo que ni imaginabas,
está en Yahoo! Respuestas (Beta).
¡Probalo ya!
http://www.yahoo.com.ar/respuestas

___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/


Re: [computer-go] Can Go be solved???... PLEASE help!

2007-01-13 Thread Eduardo Sabbatella Riccardi
On Friday 12 January 2007 16:16, Chris Fant wrote:
 Seems like a silly title.  Any game of perfect information that has a
 clear rule set can be solved.  Plus, some would argue that any Go
 already is solved (write simple algorithm and wait 1 billion years
 while it runs).  A better question is, Can Computer Go Surpass Human
 Go?  But again, clearly it will.  It's just a question of how long
 until it occurs.

Don´t be rude. I understood what he means.
Game of go for is not solved for me. (19x19).

The thing is, nobody found an optimisation good enough that is able to calc 
the perfect game in human time.

You changed the topic of the disertation to humans vs machines.

Eduardo





__
Preguntá. Respondé. Descubrí.
Todo lo que querías saber, y lo que ni imaginabas,
está en Yahoo! Respuestas (Beta).
¡Probalo ya!
http://www.yahoo.com.ar/respuestas

___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/


Re: [computer-go] Can Go be solved???... PLEASE help!

2007-01-13 Thread Hideki Kato
CM-1's processing element is not a transputer but a custom (CMOS) 1-bit
ALU with 4Ki bit of RAM. I know this is not essential but believe this
kind of correction is old men's role :-).

alain Baeckeroot: [EMAIL PROTECTED]:
Le samedi 13 janvier 2007 15:06, Don Dailey a écrit :
  If a computer can exist in 3 
 dimensions,  couldn't an infinite number of them exist with 1 more
 dimension?
 Couldn't one be constructed that is far more highly parallel that what
 we
 can construct in our 3 physical dimensions?
 
 

The first Connection-Machine CM1 (from Thinking Machine Inc) was
65 536 transputer connected on a 12d hypercube (one transputer at each corner)

Itw was quite hard to program, but i think it could be a very good hardware
for a strong go program :) Sadly it is now in museum.

Alain
___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/
--
[EMAIL PROTECTED] (Kato)
___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/


Re: [computer-go] Can Go be solved???... PLEASE help!

2007-01-13 Thread alain Baeckeroot
Le samedi 13 janvier 2007 16:46, Hideki Kato a écrit :
 CM-1's processing element is not a transputer but a custom (CMOS) 1-bit 
 ALU with 4Ki bit of RAM. I know this is not essential but believe this 
 kind of correction is old men's role :-).
 

oops, true, my memory mixed up some old stuff :)
Also 2^12 != 65536
but still CM1 was 12d, with 16 tiny proc at each corner of the hyper cube.

Alain 

___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/


[computer-go] Can Go be solved???... PLEASE help!

2007-01-13 Thread Nick Apperson

oops, accidentally sent to just Don Dailey

-- Forwarded message --
From: Nick Apperson [EMAIL PROTECTED]
Date: Jan 13, 2007 5:11 PM
Subject: Re: [computer-go] Can Go be solved???... PLEASE help!
To: [EMAIL PROTECTED]

Here is a link for anybody that is interested in why I say 2 dimensions.
There are ofcourse many papers on it, but this is the basic idea.
Essentially says that the maximum amount of information is proportional to
the 2D surface around it.  Even if we live in a many-dimensional world (I
happen to believe we do), the area surrounding it would still be 2
dimensional as long as these are small dimensions.  Sorry to get off track I
just thought someone might find it interesting.  For us we are no where near
the theoretical limit of computing power, but if we had enough of it we
would be subject to the theoretical maximum.  Essentially, if you had enough
computers to reach this limit, they would collapse into a black hole.

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

- Nick

P.S.  Sorry I was going ape last night.

On 1/13/07, Don Dailey [EMAIL PROTECTED] wrote:


Ok Nick,

The funny thing about this,  is that I was originally defending someone
who
after making a simple post got flooded with all the stale size of the
universe
and grains of sands arguments - presumably to prove he was wrong when he
made
a simple statement which was correct.   He made the horrible mistake of
saying 1 billion years and I guess that's where he went wrong.
Everyone
jumped in as if he was an idiot for thinking it would only take 1
billion years.

I also admit I got annoyed with those arguments about the size of the
game,
I felt it was pretty redundant and I don't know of anyone on this group
that needed a refresher course on this - everyone knows how huge this
problem is.

I'm sure you understand physics much more than I do.   However, I
disagree about dimensionality and if I'm wrong I have a thick skin and
you can explain it to
me and I will believe you.   One of the theoretical limitations to
computing power (which was layed out in someones posts) and I have
always understood to be the case, is related to
space - the physical size of the universe.If a computer can exist in
3
dimensions,  couldn't an infinite number of them exist with 1 more
dimension?
Couldn't one be constructed that is far more highly parallel that what
we
can construct in our 3 physical dimensions?


- Don




On Sat, 2007-01-13 at 03:38 -0600, Nick Apperson wrote:
 I would first just like to say, there have been many times in my life
 where I have known 1000 times more than someone else and I didn't feel
 the need to be an ass.  I'm sure you are a nice person, but please
 don't treat me like I am a moron.  Some assumptions you made about me
 that aren't true:

 1) you assume I didn't understand what solvable means in a
 mathematical sense.  I think in a more important way, solvable means
 is able to be solved and frankly that question is still able to be
 debated regarding go.  From a mathematical standpoint, any game with a
 finite set of states is solvable.

 2) You assume that I took 1 billion years literally...   Oh my, I
 would venture to say that I have had a whole lot more physics than you
 have my friend and I understand how people get those numbers.

 3) You assume that I don't know that changing the board size doesn't
 necessariyl change all the properties of the game.  I mean how dumb do
 you think I am?

 But, I am going to point out a couple problems in what you said since
 you seem to be up for being an ass.

 1) Multiple dimensions doesn't help at all.  Information processing
 ability as well as informataion storing ability is proportional to a
 2D surface surrounding the area that is able to be used for the
 computation.  This is the upper limit given with thermodynamics which
 is probably the only part of physics that has laws that are well
 founded.

 2) The reason I object to infinity as a concept is not because of my
 mental inferiority.  In fact, infinity is a concept that comes quite
 readily to me.  I learned it early in my youth and when I first saw a
 graph of velocity versus time (age 12 maybe) I knew that the area
 under it was displacement.  I had taken calc 2 as a sophmore in
 highschool.  The problem I have with it in regards to what you were
 talking about is that it has never been proven to exist anywhere in
 the actual world and there is lots of evidence that it doesn't exist.



 That said, I have seen you post before and I enjoy reading your posts,
 but please don't flame me.  Just because I am new to computer go
 doesn't mean I am a moron.  I might bring something new.  If you all
 had it figured out already, we wouldn't be having this discussion.  I
 have a lot to learn from you and I look forward to that.  Please be
 more respectful.  I am sorry that this was a harsh message, but I feel
 you were unfair to attack me as you did.

 Sincerely,
 Nick

 On 1/12/07, Don Dailey  [EMAIL 

Re: [computer-go] Can Go be solved???... PLEASE help!

2007-01-13 Thread Erik van der Werf

On 1/14/07, Nick Apperson [EMAIL PROTECTED] wrote:

From: Nick Apperson [EMAIL PROTECTED] 
...
Essentially says that the maximum amount of information is proportional to
the 2D surface around it.  Even if we live in a many-dimensional world (I
happen to believe we do), the area surrounding it would still be 2
dimensional as long as these are small dimensions.


I don't understand why that boundary would necessarily be 2
dimensional. Isn't the boundary of an N dimensional hypervolume simply
an N-1 dimensional hypersurface?

E.
___
computer-go mailing list
computer-go@computer-go.org
http://www.computer-go.org/mailman/listinfo/computer-go/