Temperature Development?
Robert Jasiek
even in so called [global] ko fights?
--
robert jasiek
Bill Spight
> Does the temperature decrease monotonously in a perfect game,
> even in so called [global] ko fights?
Well, there is more than one way to view global temperature. One way is
to take the global temperature as the temperature of the whole board, as
a single game. That temperature does not decrease monotically.
E. g., in this game, {6 | 0 || -2}, the original temperature is 2. But
if Black plays to {6 | 0}, the temperature rises to 3.
But another way to look at the global temperature is as the background
or environmental temperature, i. e., as the temperature of those plays
on which we are not focusing. We can picture it like this.
A B t0
/ \ |\ C t1
/ \ | \ /|
------------------- T
Here, three plays are in focus. A and B have local temperatures of t0,
and C has a local temperature of t1. Below that, we have the environment
with a temperature of T.
Suppose that White to play plays C, producing this picture:
D t2
/ \
A B / \ t0
/ \ |\ / \
/ \ | \ / \
------------------------- T
The value of the hottest play has changed, but T remains the same. Over
the course of the game, T decreases monotonically.
T is a useful value, as an estimate of the cost of giving up sente after
the plays in focus have been played (or the gain from retaining it). The
temperature of the hottest play suggests what to play, and the gain from
playing it (or the loss from not playing it). Both temperatures have
heuristic value, but T is more useful for planning ahead.
Best regards,
Bill
Simon Goss
>Does the temperature decrease monotonously in a perfect game,
>even in so called [global] ko fights?
Just one thought: a "perfect" game would be played rather differently
from a normal game. In a perfect game, both players play optimally with
regard to the score; in a normal game they play to win.
If the result of perfect play by both is that Black wins by 7 points
(say), then, in a perfect game, White will accept a 7-point loss but
will play to ensure that he does not suffer worse. In a normal game, if
White is losing by 7 points, he will try to complicate things, even at
the risk of making the loss worse.
In a normal game, I feel that things like invasions raise the
temperature for quite prolonged periods. Just a feeling - no evidence
offered.
--
Simon
jum...@my-deja.com
From: Robert Jasiek <jas...@berlin.snafu.de>
> Does the temperature decrease monotonously in a perfect game,
> even in so called [global] ko fights?
An interesting question, but not one well-posed. You are already
implying -- by the phrase "a perfect game" -- that you acknowledge
the possibility of -multiple- (distinct) "perfect games." From most
positions we might also expect the -multiple- (distinct possibilities
of) "perfect continuations." This runs counter to Bill Taylor's idea
of "the best move" from a given position, since if we were to make
reversed extrapolation on Bill Taylor's notion then there might be
only -one- "perfect game" possible.
It's not clear whether there is any strong relationship between
the likelihood of increased temperatures within a "perfect game"
verses a "less perfect game." I suspect, however, that most games
of professionals -- we can observe today -- tend toward the cooler
temperatures since professionals are reluctant to drift into the
prospect of "losing control" implied by higher temperatures. Two
primary qualities are also implied by temperature, which may or
may not embody high "confusion factor." Certain "hot" positions
may be more easily analyzed than others, so among two positions
equivalently "hot" it makes sense to play on the position that
has less "confusion factor" so that one's opponent must burn up
time on the clock with the other "hot" position having a higher
"confusion factor." It's also more likely to play a wrong move
on a "hot" position with high "confusion factor." Now a "perfect
game" played between the (future) hypothetical "Deeper _Midori_"
of Go and a professional title-holder would likely involve higher
"confusion factors" more easily amenable to that machine design,
than we see in present professional games, so as to confound the
professional player. Therefore "more perfect games" between the
"Go _deus_ex_machina_" and professional players would more likely
involve higher temperatures due to the higher "confusion factors."
As for monotonic decreases, the Berlekamp experiment illustrated
intervals with no alternate point-value card drawn, indicating those
periods where game temperature drifted temporarily above the previous
temperature.
Has Bill Taylor discovered his "error" in the figure-8 _nakade_?
- regards
- jb
.
Sent via Deja.com http://www.deja.com/
Before you buy.
jum...@my-deja.com
http://www.theonion.com/onion3013/chess.html
--------------------------------------------
Chess Supercomputer Beaten Up By More Popular Computer
The Performa 6400, a popular PC, beat up IBM's Deep Blue Monday.
Insiders say the Performa may have been acting out of deep
personal insecurities over its sales figures, which historically
have lagged behind those of comparable IBM models.
KATONAH, NY--IBM's Deep Blue, the chess supercomputer that
recently contended with world chess champion Gary Kasparov, was
beaten up Monday by a Macintosh Performa 6400CD, one of the most
popular home computers on the market.
The attack occured at approximately 3 p.m., shortly after a 60
Minutes piece on Deep Blue finished taping at IBM headquarters.
The Performa reportedly entered Deep Blue's work station and
pounded aggressively at the cabinet housing the chess computer's
logic board, spilled coffee on its keyboard and inserted several
paper clips into its ventilation slots. Deep Blue was not badly
damaged.
Deep Blue's programmers expressed outrage over the incident.
"This kind of thing makes me furious, as Deep Blue is extremely
sensitive to teasing from more popular computers," said
programmer David Wembley. "Almost as sensitive as it is to
Capablanca gambits."
Added Wembley: "We are currently coding a subroutine into Deep
Blue explaining to it that when you're the best at something,
other computers sometimes have difficulty with that and feel
they have to take you down a notch."
Macintosh spokesman Guy Kawasaki described the beating as
"unfortunate," but added that "when you're as powerful and
popular as the 6400, with its huge 2.4GB hard drive,
lightning-quick 200MHz PowerPC 603e processor and sales topping
$150 million in the past three months alone, sometimes you wind
up stepping on some toes."
Some industry observers believe the Performa's bullying is
motivated by and indicative of deep personal insecurities.
"The Performa, one of the most popular home computers in the
history of the industry, has much to be proud of," Mac World
columnist and licensed therapist Mitch Gallagher said. "But for
all of its success, I believe the Performa still harbors a lot
of nagging self-doubt, because no matter what it does, its sales
figures still always seem to lag behind those of its
PC-compatible peers."
"Sometimes," continued Gallagher, "all the storage capacity in
the world isn't enough to make a computer feel good about
itself."
It is also rumored that things have not been going well at Apple
headquarters, leading some to believe that the Performa may be
under a good deal of stress. "Financial losses and layoffs at
Apple have probably made the Performa feel as though its world
has been turned upside-down," Wired's Ted Fraschilla said. "When
that happens, a computer can feel as though it has no control
over its environment. This may have caused the Performa to
commit what amounts to exercising control over Deep Blue."
Employees laid off in recent months include key members of the
Performa's development team, programmers the PC had known all
its life.
If the Performa is involved in more misbehavior, the Federal
Trade Commission may mandate a recall. Apple has urged the FTC
that such an action would only make things worse for the
Performa instead of better.
The last thing Performa needs right now is to be told that it is
a bad computer," Apple president Gilbert Amelio said. "A recall
would in effect do that. We are sure that Performa owners will
be pleased in the future by the performance of their PC, both in
its ability to perform assigned tasks and in how it gets along
with other machines."
© Copyright 1999 Onion, Inc., All rights reserved.
Masthead | Contact Information | Privacy Policy
D & A Klinkenberg
[skip
> The Performa reportedly entered Deep Blue's work station and
> pounded aggressively at the cabinet housing the chess computer's
> logic board, spilled coffee on its keyboard and inserted several
> paper clips into its ventilation slots. Deep Blue was not badly
> damaged.
[skip]
> © Copyright 1999 Onion, Inc., All rights reserved.
&&&
Hello all,
I hope no one is expected to take any of this seriously.
Dan in NY
Bill Taylor
|> Has Bill Taylor discovered his "error" in the figure-8 _nakade_?
No error there.
Please elaborate.
--------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
--------------------------------------------------------------------------
It is when we expect others to be reasonable, that we become unreasonable.
--------------------------------------------------------------------------
jum...@my-deja.com
> jum...@my-deja.com writes:
>> Has Bill Taylor discovered his "error" in the figure-8 _nakade_?
From: Bill Taylor <mat...@math.canterbury.ac.nz>
> No error there.
>
> Please elaborate.
Barely had room to reply because your .sig was five times as much
data as your message. Here's the definition for _nakade_ as found
in the Warkentyne/Jansteen literature:
nakade playing inside to reduce multiple
eyes to one eye and kill a group
of surrounded stones
So Bill, I'm going to be a real nice guy and give you another
chance to redeem yourself. You've made -two- errors, now, one in
your original post and another one in this post failing to see
your original error. I'll make certain that your employer doesn't
see this post, so don't worry about exposure.
- regards
- jb
.
John Fairbairn
>
>
>> jum...@my-deja.com writes:
>>> Has Bill Taylor discovered his "error" in the figure-8 _nakade_?
>
>From: Bill Taylor <mat...@math.canterbury.ac.nz>
>> No error there.
>>
>> Please elaborate.
>
> Barely had room to reply because your .sig was five times as much
> data as your message. Here's the definition for _nakade_ as found
> in the Warkentyne/Jansteen literature:
>
> nakade playing inside to reduce multiple
> eyes to one eye and kill a group
> of surrounded stones
>
of the time. Nakade (verb nakade suru; Chinese dian3) refers only to
playing inside a group at the vital point. It overlaps with oki/oku. The
end result could be seki or capturing part of a group.
The phrases gomoku nakade and so on are derivatives of the basic
meaning, but even here the end result could be seki.
Western players have corrupted the word to their own ends, and to that
extent the above definition is correct (in western usage only).
I posted a 16-point nakade position here recently and, as I recall,
Matthew Macfadyen mentioned another one (?)
--
John Fairbairn
Simon Goss
>> nakade playing inside to reduce multiple
>> eyes to one eye and kill a group
>> of surrounded stones
>>
>This definition is not really correct, although it covers reality most
>of the time. Nakade (verb nakade suru; Chinese dian3) refers only to
>playing inside a group at the vital point. It overlaps with oki/oku. The
>end result could be seki or capturing part of a group.
Oh! So, should the square 4 shape that is already dead as it stands not
be called nakade?
--
Simon
Eric Osman
Matthew Macfadyen mentioned another one (?)
Please post it again ! Thanks. /Eric
John Fairbairn
<si...@gosoft.demon.co.uk> writes
If you mean four empty points, "no" according to some dictionaries, but
others are more liberal and allow this as a derived meaning.
Here is an example of the main meaning from a Japanese go dictionary:
. . . . . .
. 0 . + . .
0 # 0 0 . .
# # # 0 . .
. . # . . .
1 . # . . .
. # # 0 . .
# # 0 0 . .
. 0 . . 0 .
. . . . . .
. . . . . .
This is the bottom left-hand corner of the board. 1 is played by 0 and
is called in Japanese gomoku nakade = a move played inside [at the vital
point of] a five-point [shape].
The other meaning is an ellipsis of derivative phrases such as gomoku
nakade no ishi.
The component parts of the word are naka = inside, te = move. Some
Japanese say nakate but this seems to be infra dig in the go world.
--
John Fairbairn
Bill Taylor
|> Barely had room to reply because your .sig was five times as much
|> data as your message.
Hey! This is Usenet! Remember the Usenet motto:-
"To hell with economy, someone else is paying for the bandwidth."
==============================================================
|> Here's the definition for _nakade_ as found
|> in the Warkentyne/Jansteen literature:
|>
|> nakade playing inside to reduce multiple
|> eyes to one eye and kill a group
|> of surrounded stones
Aha. So you want to trade definitions! I guess if there's nothing
of substance to add, it's OK to be nitpicky; though it's usual to start
off (or finish up) with a comment about "how I'm being nitpicky..."
OK, I'm just being nitpicky there.
The definition I've seen is
** Nakade: Unsettled eye shape.
As to whether either is what the Japanese precisely mean by the term,
I dunno; but hey, I can only work with the tools I've got? Maybe the term
in Japanese, like so many, can be used as either a noun, an adjective, or
a verb. Not that I would want to suggest there was anything imprecise about
anything Japanese! You know I would never utter anything so... so...
Anyway. As the shape involved is not fully unsettled, but merely
SEMI-unsettled, (as I first said, as I'm SURE you noticed), perhaps I should
call it a SEMI-nakade shape. But that would be being nitpicky, I guess.
|> So Bill, I'm going to be a real nice guy
Oh goody, give us a kiss then!
|> and give you another chance to redeem yourself.
I thought you chaps thought I was irredeemable?!
|> I'll make certain that your employer doesn't
|> see this post, so don't worry about exposure.
You're all heart. :) Me too. Yours and mine together!
..8888888.. ..8888888..
.8:::::::::::8. .8:::::::::::8.
.8:::::::::::::::8:::::::::::::::8.
.8:::::::::::::::::::::::::::::::::8.
8:::::::::::::::::::::::::::::::::::8
8::::::::::/` \/ `\:::::::::::::::::8
8::::::::::\ /` \/ `\:::::::::::8
`8:::::::::::. .\ /::::::::::8'
`8:::::::::::\/:::. .:::::::::::8'
`8::::::::::::::::\/:::::::::::8'
`8:::::::::::::::::::::::::8'
`8:::::::::::::::::::::8'
`8:::::::::::::::::8'
`8:::::::::::8'
`8:::::8'
`8'
BTW, speaking about wasting bandwidth, which we almost were, I seem
to recall a few posts by your good self that were incredibly long,
and, well, and... not altogether fully... well... to the point...?
No no... that can't be right. I must be misremembering!
-----------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
-----------------------------------------------------------------------------
Q: What's the difference between Bill TAylor and MArgaret Thatcher?
A: One goes in for nit picking and the other goes in for...
-----------------------------------------------------------------------------
Thiele Everett
: Maybe the term in Japanese, like so many, can be used as either a noun,
: an adjective, or a verb.
Rather like English then, English also being notoriously flexible in that
regard.
As regards go-terms in English, I would say always listen to Fairbairn's
explanations: they are interesting, shed light on the game, and seem very
reliable and authoritative. Having done so, just go on using the terms
with the customary meanings they have taken on in English. Making up
a bunch of new translations just spreads confusion. In the case of nakade,
then, that would mean: a nakade, in ENGLISH, is an unsettled or dead large
eye. (Often brought about through sacrificing stones inside the opponenent's
group)
What could be more simply, reasonable or practical?
--Rett
RedIron Studios
> The phrases gomoku nakade and so on are derivatives of the basic
> meaning, but even here the end result could be seki.
I was just wondering "gomoku nakade" would not simply be a derivative of the
basic meaning would it? It is actually more specific no? gomoku meaning 5,
so this would be a 5 space nakade correct?
Cheers,
RedIron Ceramic Studios,
Vancouver, BC, Canada
>
> Western players have corrupted the word to their own ends, and to that
> extent the above definition is correct (in western usage only).
>
> I posted a 16-point nakade position here recently and, as I recall,
> Matthew Macfadyen mentioned another one (?)
>
> --
> John Fairbairn
Stijn van Dongen
>The component parts of the word are naka = inside, te = move. Some
>Japanese say nakate but this seems to be infra dig in the go world.
Curious what you mean by 'infra dig'. Is it some grunge band the
sprouting of which I missed? Something to do with underground?
What should I make it of? Please help :!
Regards,
Stijn
--
Stijn van Dongen
Centrum voor Wiskunde en Informatica (CWI)
Kruislaan 413 1098 SJ Amsterdam @ _ @
tel: +31 20 5924180 sti...@cwi.nl <_`'/_/ _>
Orne Batmagoo
> John Fairbairn <J...@harrowgo.demon.co.uk> writes:
>
>>The component parts of the word are naka = inside, te = move. Some
>>Japanese say nakate but this seems to be infra dig in the go world.
>
> Curious what you mean by 'infra dig'. Is it some grunge band the
> sprouting of which I missed? Something to do with underground?
> What should I make it of? Please help :!
It means "beneath the dignity of" someone. Its etymology is from the
Latin _infra_dignitatem_. Here are a few literary references:
"Of course one couldn't!" echoed Arthur. "Any more than one could
argue with a potato. It would be altogether--excuse the ancient
pun--infra dig.!"
-- Lewis Carroll, _Sylvie_and_Bruno_
"If a fellow gets up, the papers make a great ado over his having
been a woodchopper, or a bobbin-boy, or something of that kind, but
I doubt if the fellow himself likes it; he doesn't if he's got any
sense. The rest of us feel that it's infra dig., and hope nobody will
find out that we ever worked with our hands for a living."
-- W. D. Howells, _A_Traveller_from_Altruria_
Is this ma milieu where I must
[How grahamgreeneish! How infra dig!]
Snatch from the bottle in my bag An analeptic swig?
-- W. H. Auden, "On the Circuit"
I note that Carroll, quite the pedant when it came to punctuation (he
wrote "ca'n't" and "sha'n't"), has included a period (Br. "full stop")
before the exclamation point. Howells, a nineteeth-century American
author, has done the same (before a comma). Perhaps that was appropriate
at one time, "infra dig." being thought of as an abbreviation of the Latin
phrase which was its source, but modern English dictionaries simply list
the phrase in its own right, without such punctuation. I reckon that's
because -- though it used to be the cornerstone of a liberal arts edu-
cation -- the study of classical languages isn't as prevalent as it once
was, so what's the point of that funny-looking dot? Dig it.
--
Orne Batmagoo
Eric Osman
Here's the first part of "everlasting story" from web page
http://miaka.com/satou_akemi/ever.html .
Hoshi furu oka no ueni Hitoride tachitsukushi ta
Hitotsu dutsu madoni tomoru akariga
Daremoga egao no oku Itamio kakae ta mama
Ikite iruyo Kono hoshi no nakade
..........................
Note that hoshi no nakade appears in that last line of first stanza.
Who here knows japanese and can tell us nani o imi desu ka ?
My guess is "star space" or "universe" ? /Eric
Eric Osman
For a nice list of go terms, including "nakade", which it defines as "dead
shape",
see
http://www.cwi.nl/people/jansteen/go/dict/GIF/technical.html
Bill Spight
> defines as "dead shape",
Oy!
And in chess, I suppose that "castling" is another name for a rook, and that a zwischenzug is a diversionary tactic. And in bridge, that a squeeze is a bad discard. And in poker, that a bluff is a weak hand.
Bill
Stijn van Dongen
>>>The component parts of the word are naka = inside, te = move. Some
>>>Japanese say nakate but this seems to be infra dig in the go world.
>>
>> Curious what you mean by 'infra dig'. Is it some grunge band the
>> sprouting of which I missed? Something to do with underground?
>> What should I make it of? Please help :!
>It means "beneath the dignity of" someone. Its etymology is from the
>Latin _infra_dignitatem_. Here are a few literary references:
[excellent explanation and citations snipped]
Thank you Orne,
that was an excellent explanation, even with citations included. Remarkable
that it goes such a long way back, it sounded like hip slang to me,
due to the 'dig' part. Given the history of the phrase,
I am not surprised to find it in the Oxford dictionary (which gives
the example
*dancing in the street seemed rather infra dig for a bank manager*),
but I never even thought of looking there before your article. But then again,
I should have surmized that John Fairbarn does not exercise MTV speak,
or that infra is not a likely word to crop up in hip slang.
Still, I like the idea of a band called 'infra dig'. It's just what some
bands aspire to be, and the phrase has a good ring.
I dug it :)
Mike Vaughn
Dongen) wrote:
> John Fairbairn <J...@harrowgo.demon.co.uk> writes:
>
> >The component parts of the word are naka = inside, te = move. Some
> >Japanese say nakate but this seems to be infra dig in the go world.
>
> Curious what you mean by 'infra dig'. Is it some grunge band the
> sprouting of which I missed? Something to do with underground?
> What should I make it of? Please help :!
>
> Regards,
> Stijn
I think 'e means that to say 'nakate' instead of 'nakade' is some sort
of lower class Japanese equivalent of a certain London dialect ;-)
Jean-Pierre
http://www.fin.or.jp/~igo/yougo/yougo.htm) give naka"te" (as in sen"te")
in the furigana column (pronunciation).
I wonder where the naka"de" comes from ?
If your browser can view the katakana characters :
nakade ’†?è
sente —¼?æ?è
Could any distinguished japanese speaker explain this ?
> Mike Vaughn a écrit:
Mike Vaughn
<jpve...@atthis.com> wrote:
> Actually all the japanese/english glossary (see
> http://www.fin.or.jp/~igo/yougo/yougo.htm) give naka"te" (as in sen"te")
> in the furigana column (pronunciation).
> I wonder where the naka"de" comes from ?
> If your browser can view the katakana characters :
> nakade ’†?è
> sente —¼?æ?è
> Could any distinguished japanese speaker explain this ?
Perhaps, but I can also try:
'naka' means 'middle', or 'center'
'te' means 'hand' (by itself) or 'play' in a game context
hence 'nakade' (pronunciation change normal) means 'to play in the middle'
(of the eye space).
'sen' means 'before' == 'go' means 'after' -- hence 'sente' and 'gote'
John Fairbairn
>Actually all the japanese/english glossary (see
>http://www.fin.or.jp/~igo/yougo/yougo.htm) give naka"te" (as in sen"te")
>in the furigana column (pronunciation).
>I wonder where the naka"de" comes from ?
Both nakate and nakade are correct. The word nakate, however (same
characters), exists in non-go language and means either a kind of rice
or the metacarpus. In these senses nakade never seems to be used.
In go, perhaps to emphasise it is a go word and not the above, the
reading nakade is usual. It would not be wrong to say nakate, but you
might not be seen as part of the "in" crowd (if you'll allow a subtle
pun).
You will find this sort of stuff in standard dictionaries such as
Kojien.
--
John Fairbairn
Simon Goss
>For a nice list of go terms, including "nakade", which it defines as "dead
>shape",
Well, that definition is around, but it's appalling. All but one of the
nakade are not dead, but unsettled.
--
Simon
Mike Vaughn
<J...@harrowgo.demon.co.uk> wrote:
> In article <37FCBD91...@atthis.com>, Jean-Pierre
> <jpve...@atthis.com> writes
> >Actually all the japanese/english glossary (see
> >http://www.fin.or.jp/~igo/yougo/yougo.htm) give naka"te" (as in sen"te")
> >in the furigana column (pronunciation).
> >I wonder where the naka"de" comes from ?
> Both nakate and nakade are correct. The word nakate, however (same
> characters), exists in non-go language and means either a kind of rice
> or the metacarpus. In these senses nakade never seems to be used.
"mid-season rice" or "the summer rice crop", according to my Kenkyusha,
whihc does not mention 'nakade' at all.
> In go, perhaps to emphasise it is a go word and not the above, the
> reading nakade is usual. It would not be wrong to say nakate, but you
> might not be seen as part of the "in" crowd (if you'll allow a subtle
> pun).
> You will find this sort of stuff in standard dictionaries such as Kojien.
Thanks for the enlightenment.
> --
> John Fairbairn
Richard Hunter
>Nakade (verb nakade suru; Chinese dian3) refers only to
>playing inside a group at the vital point.
> Here is an example of the main meaning from a Japanese go dictionary:
>
> . . . . . .
> . 0 . + . .
> 0 # 0 0 . .
> # # # 0 . .
> . . # . . .
> 1 . # . . .
> . # # 0 . .
> # # 0 0 . .
> . 0 . . 0 .
> . . . . . .
> . . . . . .
>
> This is the bottom left-hand corner of the board. 1 is played by 0 and
> is called in Japanese gomoku nakade = a move played inside [at the vital
> point of] a five-point [shape].
Thank you John for this clear explanation and your previous informative
comments. I hope readers will take note. I'm interested in nakade
because I'm thinking of writing a series in the British Go Journal on
nakade and ishi no shita when I've finished my current series on
counting liberties.
One cause of people's misunderstanding of nakade is that there are
several wrong or misleading definitions in English go books. The most
wildly inaccurate one I know of is in All about Life and Death by Cho
Chikun. This is a fine book in Japanese. If you handle it in the right
way, the English version is still very useful, despite numerous errors
and misconceptions that seem to have crept in during the translation. I
suggest you treat it as a book written in a foreign language that you
don't understand. Study the diagrams and ignore the text. Anything that
reads strangely is probably wrong.
In the glossary added for the benefit of English readers, nakade is
defined as "a big eye". This is totally wrong. A nakade is not an eye in
itself, and has nothing to do with a big eye. Nakade is a move not a
shape. This misconception is the cause of numerous mistranslations
throughout the text.
For example, in vol. 1, page 48 for solution 2,
. . . . . . . . .
. . . . . . . 0 .
. . . . . . . . .
. . . . 0 0 0 0 . X Black
. . . . 0 X X X 4 0 White
. . 0 0 X X 7 1 3 1 = White
. . . X 5 6 . 2 .
we get the sentence "... White 5 and 7 make a three-space big eye." This
is incomprehensible, but an experienced go player could probably guess
what it actually means by looking at the diagram. White is not making
an eye at all. Moreover, a three-space eye is a small eye not a big
eye.[1] The original Japanese is "... shiro 5, 7 de sanmoku nakade ni
natte iru." Although I don't claim to be a professional translator, I
would render this as something like "... White 5 and 7 reduce Black to a
single eye." unless you prefer the more literal " ... with White 5 and 7
it becomes a three-point nakade." Neither White 5 nor 7 is the actual
nakade move played on the vital point of the eye-space.
The san-moku nakade under discussion is the position that will
inevitably be reached if Black tries to claim he is not dead and
continues to play on. The meaning here is: once all the outside
liberties are filled:
. . . . . . . . .
. . . . . . . 0 .
. . . . . . . . .
. . . . 0 0 0 0 O X Black
. . . . 0 X X X X 0 White
. . 0 0 X X O O O
. . O X X X . X .
Black will be in atari, but if Black captures the white stones in his
eye before the outside liberties are filled, White will be able to play
a knockout move on the vital point (W1 in the first diagram) of Black's
subsequent three-point eye space, leaving Black with only one eye. This
future move on the point W1 is the nakade. In other words, Black is dead
by the technique of san-moku nakade, because he cannot prevent White
from playing this killing move. In an actual game, the position would
not get that far.
[1] Perhaps one source of confusion is the expression:
"oo-naka, ko-naka" meaning big eye versus a smaller eye. Here oo-naka
refers to a 4-point or larger nakade. So maybe a secondary meaning of
nakade is eye space, but certainly not the primary meaning.
-----------------------------------------------------------
Richard Hunter (hunter at gol dot com), Tokyo, Japan
Thiele Everett
: In the glossary added for the benefit of English readers, nakade is
: defined as "a big eye". This is totally wrong. A nakade is not an eye in
: itself, and has nothing to do with a big eye. Nakade is a move not a
: shape. This misconception is the cause of numerous mistranslations
: throughout the text.
As I mentioned before, I don't think that that is a mistake, but rather
shows awareness on the part of the translator that go terms imported
from Japanese have taken on a life of their own in English. I think
it is unwise to start campaigns to re-define terms which people already
use in meaningful ways, as it will only spread confusion, with different
books using entirely different terminology. On the other hand, articles
describing how the terms are used in Japanese can be very interesting
and useful, so I do appreciate your contribution here.
: For example, in vol. 1, page 48 for solution 2,
: . . . . . . . . .
: . . . . . . . 0 .
: . . . . . . . . .
: . . . . 0 0 0 0 . X Black
: . . . . 0 X X X 4 0 White
: . . 0 0 X X 7 1 3 1 = White
: . . . X 5 6 . 2 .
: we get the sentence "... White 5 and 7 make a three-space big eye." This
: is incomprehensible, but an experienced go player could probably guess
: what it actually means by looking at the diagram. White is not making
: an eye at all.
It makes perfect sense. White is making _what we call in English_ a
"nakade shape" inside the black group. I understood that immediately,
based on my having learned go in an English speaking context.
: Moreover, a three-space eye is a small eye not a big
: eye.[1]
I don't see the point of that distintion. A three-space eye can divide
into two eyes, hence it has a vital point in its center. That is what
is the issue here.
The original Japanese is "... shiro 5, 7 de sanmoku nakade ni
: natte iru." Although I don't claim to be a professional translator, I
: would render this as something like "... White 5 and 7 reduce Black to a
: single eye." unless you prefer the more literal " ... with White 5 and 7
: it becomes a three-point nakade." Neither White 5 nor 7 is the actual
: nakade move played on the vital point of the eye-space.
No, because English speaking go players don't think of nakade as a 'move'
but rather as a 'shape'. So what you are calling a mistake, is actually
a case of intelligent translation.
Please don't get me wrong, I found your article, and Fairbairn's very
interesting and useful. But when it comes to the terms we use in producing
go books and articles, these kinds of reform movements don't seem very
important. I'm pretty sure we are able, with the go-language we already
possess, to express all the key ideas in life and death. Who cares if the
English go-language doesn't _precisely overlap_ with the Japanese langauge.
I'll bet the Japanese doesn't perfectly overlap with the Chinese and Korean
either. (Though Kanji might make up a pretty strong common ground). The
point is, don't remain hung up on the _words_, but stick to the meanings.
In the event that there are important go concepts in any other language
which lack any English terms to express them, then by all means import
or invent words for us, and explain them. But as for the terminology
we already have: if it ain't broke, don't fix it. (and it ain't broke
just because it doen't slavishly conform to the original Japanese usage)
We know what we mean by terms like sente, tesuji, hane, miai, nakade,
etc. Redefining them, or inventing English equivalents at this stage
of the game is probably only going to be counter-productive.
So I repeat: NAKADE, in English usage, means an unsettled or dead large
eye shape, often created by sacrificing stones inside the enemy group.
regards,
--Rett
P.S. if you are planning an article series on Nakade and Under-the-stones
you will find many examples in Yutopian's new book _Art of Capturing:
Sacrifice Techniques_.
P.P.S. Half of the English language consists of words imperfectly
imported from other languages. That's how languages develop and grow.
Why fight nature?
Bill Spight
> Half of the English language consists of words imperfectly
> imported from other languages. That's how languages develop and
> grow.
> Why fight nature?
I agree with you whole-heartedly about English. But "nakade", "hane", "kosumi", "yoseko", "nobi", etc., are go terms, not English proper. If you are playing chess, "J'adoube" is not French, "Zugzwang" is not German, they are chess terms. Whether you are a native speaker of French, German, English, Russian, Pahlavi, or Urdu, in a chess context you should use these terms the same way as everybody else uses them, regardless of their native tongue. "Rabbity six" is a go term. It originated from English, but if Japanese, Chinese, Korean, German, or Polish go players use the term, they should use it the same way as English speakers do.
> But when it comes to the terms we use in producing
> go books and articles, these kinds of reform movements don't
> seem very important.
What reform movement? Who decided that go terms should mean something else for English speakers than for the rest of the go world? Nobody. The original explicators (there is no translation here) thought that they were giving correct explanations. Correcting their errors is not reform. It enables us to communicate without confusion with the rest of the go world.
Best regards,
Bill
jum...@my-deja.com
Load these pages for their pretty diagrams ---
http://www.innerx.net/personal/tsmith/ichgene6.html
---------------------------------------------------
I Ching Genetic Code HyperDiamond Physics
Tony Smith's Home Page
I Ching (Ho Tu and Lo Shu),
Genetic Code,
Tai Hsuan Ching,
and the D4-D5-E6-E7 Model
Chinese cosmology begins with
the undivided Tai Chi,
illustrated here as o, a scalar point of origin.
| |
| |
_____|_____|_____
| |
| o |
_____|_____|_____
| |
| |
| |
Then add 4 vector directions of Physical Spacetime:
1, i, j, k of the quaternions
to get the 5 Elements:
| |
| i |
_____|_____|_____
| |
j | o | 1
_____|_____|_____
| |
| k |
| |
Then add 4 vector directions of Internal Symmetry Space:
E, I, J, K of the octonions,
which are the basis for the D4-D5-E6-E7 physics model,
to get 9 directions:
| |
J | i | I
_____|_____|_____
| |
j | o | 1
_____|_____|_____
| |
K | k | E
| |
The 10th direction is Yin-Yang reflection
of the 8 vector directions 1, i, j, k, E, I, J, K.
Now, identify the 3x3 square with the Magic Square
| |
4 | 9 | 2
_____|_____|_____
| |
3 | 5 | 7
_____|_____|_____
| |
8 | 1 | 6
| |
whose central number, 5, is also
central in the sequence 1,2,3,4, 5, 6,7,8,9
which sequence corresponds
to the octonions 1,i,j,k, 0, E,I,J,K
whose total number for each line is 15,
the dimension of the largest Hopf fibration
and the dimension of the imaginary sedenions.
If you take into account the direction in which you add each
of the 8 ways, and add all directed ways together
you get a total of 16x15 = 240
which is the number of vertices of a Witting polytope.
The total of all 9 numbers of the Magic Square is 45,
the dimension of the D5 Lie algebra Spin(10)
that is used in the D4-D5-E6-E7 physics model
in which
the D4 Spin(8) subgroup of Spin(10) corresponds
to 28 bivector gauge bosons
and the 16-dimensional homogeneous space
Spin(10) / Spin(8)xU(1)
corresponds to an 8-dimensional complex domain
whose Shilov boundary is RP1 x S7
corresponding to an 8-dimensional spacetime.
Perhaps about 5,300 years ago, China's first emperor, Fu Xi,
saw, rising from the Yellow River, a dragon-horse
with markings of the
Ho Tu,
shown here in its ancient and modern forms:
Fu Xi interpreted the 4 directions and 4 diagonal directions
of the Ho Tu in terms of the Earlier Heaven arrangement
of the 8 trigrams of the I Ching:
The 8 trigrams of the I Ching are similar to
the 16 tetragrams of Ilm al-Raml (the Science of the Sands)
attributed to the third Islamic prophet, Idris,
which were preserved from the Global Early Civilization
as the FA of the Fon people of Benin (Dahomey).
When the 8 trigrams are combined in pairs
according to the Fu Xi Earlier Heaven Ho Tu arrangement
to make 64 hexagrams of the I Ching,
you get a very symmetrical I Ching pattern
Although the Earlier Heaven arrangement of the 8 trigrams
does not exactly correspond to the binary number
sequence from 0 through 7
(it is 0,1,2,3,7,6,5,4 instead of 0,1,2,3,4,5,6,7),
the Earlier Heaven arrangement of the 64 hexagrams
does correspond to the binary number
sequence from 0 through 63.
Katya Walter has shown that the Fu Xi Earlier Heaven
Ho Tu arrangement of the 64 hexagrams
can represent the DNA genetic code:
Since the DNA genetic code can be represented by
4 things taken 3 at a time,
or (2x2) x (2x2) x (2x2) = 64,
and since the I Ching (which is based on 6 bars,
each of which can be in 2 states - broken or unbroken)
can be represented by 2 things taken 6 at a time,
or 2 x 2 x 2 x 2 x 2 x 2 = 64,
and since pairs of octonionic half-spinors of the Spin(0,8)
Clifford algebra Cl(0,8) on which the D4-D5-E6-E7 physics model is based
can be represented by 8 things taken 2 at a time,
or (2x2x2) x (2x2x2) = 64,
the genetic code, the I Ching, and the D4-D5-E6-E7 physics model
are all just different representations
of the same fundamental structure.
The fundamental structure of 8 trigrams can not only be extended
to 8x8 = 2^6 = 64 hexagrams,
but also to 24-grams, of which there are 8^8 = 2^24 = 16,777,216.
24-grams are directly related to Golay codes and the Leech lattice.
In that connection,
the hexacode H6 is related to Golay codes and the Leech lattice.
The hexacode H6 can be used to construct
quantum-error-correcting codes that are based on GF(4),
and
an RNA code is based on 4 nucleotides UGAC, taken 3 at a time.
Katya Walter has shown that
the I Ching representation of the DNA genetic code
can be transformed in a natural way to
an I Ching representation of the RNA genetic code.
The same fundamental structure is also shared
by Penrose tilings and musical sequences.
Further,
you can represent genetic information by
DNA sequence music (215k wav).
Katya Walter has shown that the representation of the DNA code
by Fu Xi's Ho Tu arrangement of the I Ching is not superficial.
The 55 points of the Ho Tu diagram can be divided into
27 SouthEast points and 28 NorthWest points,
if the central point is put into the NorthWest part.
The G-C base pair has 15 ring atoms and 12 other atoms,
just as the SouthEast part has 15 even points and 12 odd points.
The T-A base pair has 15 ring atoms and 13 other atoms,
just as the NouthWest part has 15 even points and 13 odd points.
If the central point is allowed to remain central,
and represent a U(1) propagator phase,
then both the SouthEast and NorthWest parts
have 15 even points and 12 odd points,
so that they represent
the 15 generators of the Spin(6) that gives
conformal gravity and the Higgs mechanism
and
the 12 generators of the SU(3)xSU(2)xU(1) standard model,
that is,
all the gauge bosons of the D4-D5-E6-E7 physics model
after dimensional reduction to 4-dimensional spacetime.
Note that, to represent physical structures
such as the DNA code and the D4-D5-E6-E7 model gauge bosons,
the proper axis for the Ho Tu diagram is NorthEast-SouthWest,
which is different
from the North-South axis used to represent abstract Yin-Yang
binary math structure.
Such a diagonal axis will be used in the Lo Shu diagram,
which is more oriented to representations of physical structures,
as opposed to abstract structures.
China's third emperor Huang Di started the
present Chinese calendar on 10 February 2697 BC.
About 4,200 years ago, when Comet Hale-Bopp last appeared,
Yu (father of the first emperor of the Xia dynasty)
saw, rising from the Lo River, a turtle
with markings of the
Lo Shu,
shown here in its ancient and modern forms:
Yu interpreted the 4 directions and 4 diagonal directions
of the Lo Shu in terms of the Later Heaven arrangement
of the 8 trigrams of the I Ching:
Note that the Yu Later Heaven Lo Shu arrangement of the 8 trigrams
is not very symmetrical with respect to abstract Yin-Yang
binary structure,
but is very symmetrical with respect to a NorthEast-SouthWest axis
and the physical representation of the 5 Elements.
The NorthEast-SouthWest axis is Earth-Earth-Earth,
SouthEast and East are Wood,
NorthWest and West are Metal, and
South is Fire and North is Water.
Although the Lo Shu is not very symmetrical with respect
to abstract Yin-Yang binary structure,
the Lo Shu diagram does have the interesting mathematical
structure of a Magic Square:
In addition to Square tilings of the plane,
there are Hexagonal tilings.
The only Magic Hexagon that exits also has central number 5:
15
14 13
9 8 10
6 4
11 5 12
1 2
18 7 16
17 19
3
There are 15 sums, 5 parallel to each of its 3 axes.
Each sum is 38 = 2x19, and there are 1+6+12 = 19 cells.
19x19 is the dimension of the lattice of a WeiQi board.
Perhaps because of its lack of abstract Yin-Yang binary symmetry,
the Later Heaven Lo Shu arrangement of the 8 trigrams
did not lead Yu to make
a corresponding arrangement of the 64 hexagrams.
It was not until about 3,100 years ago
that Wen-wang (father of the founder of the Zhou dynasty)
made a Lo Shu arrangement of the 64 hexagrams.
Since Wen-wang's son Wu-wang named him (posthumously) as
the first emperor of the Zhou dynasty,
Wen-wang is known as King Wen,
and his arrangement of the 64 hexagrams
often called the King Wen arrangement.
King Wen created his arrangement while imprisoned by
the Shang emperor. It was not an arrangement to describe
abstract principles, but to describe his life and how it
could be useful in overthrowing the corrupt Shang emperor
and setting up a better government.
The 64 King Wen hexagrams are arranged in 32 dual pairs.
For 28 of the pairs, one is the other turned upside down.
8 hexagrams are the same turned upside down,
so they make up 4 pairs of opposites.
The 28 upside-down symmetric pairs have a similar symmetry
to the 28-dimensional antisymmetric real 8x8 matrices
that represent Spin(0,8) of the D4-D5-E6-E7 physics model.
King Wen's arrangement is designed for life in our physical world,
beginning with pure Yang, forward moving Heaven,
and ending with a hexagram described by two characters
that mean "not yet across (a river)",
so that its ending is really also a beginning,
just as in real life.
Perhaps that is why the King Wen arrangement is the one
most often seen in present-day I Ching books.
Another son of King Wen was the Duke of Zhou,
the brother of King Wu (Wu-wang).
When King Wen wrote about the 64 hexagrams,
he wrote for each entire hexagram a Judgment.
The Duke of Zhou wrote a poetic text, the Line Text,
for each hexagram Judgment.
Each poem line corresponds to a hexagram line,
and each whole poem goes with
the Chinese characters for each hexagram Judgment.
Much later commentaries, such as the Ten Wings,
have been added to the present-day I Ching books.
My opinion about such later commentaries is
the same as that of Rosemary and Kerson Huang:
"The poetic aspect of the I Ching,
however, has been obscured by the Ten Wings.
How can you enjoy poetry if every line is followed
by government regulations on how to read it?"
Of course, it is possible to make other arrangements
of the 8 trigrams and 64 hexagrams of the
I Ching
than the Fu Xi and King Wen arrangements.
The 8 trigrams can be arranged in 8! = 40,320 different orders.
As well as ordering the 8 trigrams differently,
you can pick subsets of the 8 trigrams.
That can also be done in many ways:
there are 2^8 = 256 subsets of the 8 trigrams.
The number of subsets of the 8 trigrams is
the dimension of the Cl(0,8) Clifford algebra
that is used in the D4-D5-E6-E7 physics model
and
is related to ordering the 8 trigrams
by the Clifford sequence corresponding
to the binary numbers from 0 through 7
You can arrange the 64 hexagrams
in 64! (about 1.27 x 10^89) different orders.
As well as ordering the 64 hexagrams differently,
you can pick subsets of the 64 hexagrams.
That can also be done in many ways:
there are 2^64 (about 1.844 x 10^19) subsets of the 64 hexagrams.
The number of subsets of the 64 hexagrams is
useful in estimating the Planck mass.
If you want more possibilities,
consider the (2^64)! possible orderings
of all 2^64 subsets of the 64 hexagrams.
If you want still more,
consider the possible orderings
within each of the 2^64 subsets of the 64 hexagrams.
The ordering of the 64 hexagrams in the Mawangdui Silk Text
may be related to historical events of the time period
from 613 BC (Emperor Zhuang of Chu)
to the time the manuscript was copied,
probably about 202-195 BC (Emperor Liu Bang of Han).
A natural ordering of the 64 hexagrams is
the I Ching lattice of Billy Culver
in which the 64 hexagrams are in groups of
4 + 16 + (12+12) + 16 + 4 = 4 + 16 + 24 + 16 + 4 = 64
This can be seen as a 4-fold expansion of the
1 4 6 4 1
level of the Su Meru triangle.
Another order is based on the
1 6 15 20 15 6 1
level, with 2^6 = 64 elements, of the Su Meru triangle:
(Here, the hexagrams are denoted by numbers representing them in the
binary Fu Xi Earlier Heaven sequence, as binary numbers from 0 through
63, with broken lines denoted by - -.)
----------------------
0 1 hexagram with 0 - -
----------------------
1 2 4 8 16 32 6 hexagrams with 1 - -
----------------------
3 6 12 24 48
5 10 20 40
9 18 36 15 hexagrams with 2 - -
17 34
33
----------------------
7 14 28
11 22
13 26
19
21
25
====================== 10+10 = 20 hexagrams with 3 - -
38 = 63 - 25
42 = 63 - 21
44 = 63 - 19
37 50 = 63 - 13
41 52 = 63 - 11
35 49 56 = 63 - 7
----------------------
30 = 63 - 33
29 46 = 63 - 17
27 45 54 = 63 - 9 15 hexagrams with 4 - -
23 43 53 58 = 63 - 5
15 39 51 57 60 = 63 - 3
----------------------
31 47 55 59 61 62 = 63 - 1 6 hexagrams with 5 - -
----------------------
63 = 63 - 0 1 hexagram with 6 - -
----------------------
Still another interesting order for the hexagrams
uses the order of this 8x8 Magic Square whose sum is 260.
It is constructed by writing the numbers 1...64 in sequence
and then reversing the order of the green entries:
64 2 3 61 60 6 7 8
9 55 54 12 13 51 50 16
17 47 46 20 21 43 42 24
40 26 27 37 36 30 31 32
32 34 35 29 28 38 39 25
41 23 22 44 45 19 18 48
49 15 14 52 53 11 10 56
8 58 59 5 4 62 63 1
Since 8x8 = 64 = 4x4x4 is both a square and a cube
(the smallest such number greater than 1)
you can use the same numbers and a similar method
to construct a 4x4x4 Magic Cube with sum 130.
Here is such a cube as constructed by Meredith Houlton:
1 63 62 4
60 6 7 57
56 10 11 53
13 51 50 16
48 18 19 45
21 43 42 24
25 39 38 28
36 30 31 33
32 34 35 29
37 27 26 40
41 23 22 44
20 46 47 17
49 15 14 52
12 54 55 9
8 58 59 5
61 3 2 64
The sum of the 8x8 Magic Square, 260,
is twice the sum (130) of the 4x4x4 Magic Cube.
The Maya calendar uses a period of 260 days, the Tzolkin,
as well as a period of 365 days, the Haab.
A version of the
Tai Hsuan Ching
was written by Yang Hsiung,
who lived from about 53 BC to about 18 AD.
As the I Ching is based on hexagrams of binary lines,
for a total of 2x2x2x2x2x2 = 8x8 = 64 hexagrams,
the Tai Hsuan Ching is based on tetragrams of ternary lines,
for a total of 3x3x3x3 = 9x9 = 81 tetragrams.
The progression from the I Ching to the Tai Hsuan Ching
is similar to a number of things:
Duchamp changed from 8 Malic Moulds to 9 Malic Moulds;
the Hermetic Ogdoad progressed to the Ennead;
45-dimensional D4 progresses to E6 in the D4-D5-E6-E7 physics model
(45 is the total number of the I Ching Magic Square and the
27-dimensional representation of E6 is like the 27x27 Magic Square
version of the Tai Hsuan Ching Magic Cube.);
the 8 Immortals plus Lao Zi are 9;
my Lo Pan contains the 8 trigrams of the I Ching, and references to
the 9 Moving Stars of the Big Dipper;
Plato's Timaeus described cosmogony and music with both powers of 2
and of 3; and
Chinese Buddhism increased the original 16 Lohan to 18 Lohan.
The numbers shown in the arrangement below
are the ternary numbers plus 1,
as the ternary numbers go from 0 to 80
instead of from 1 to 81.
The ternary number arrangement is similar to
the Fu Xi binary number arrangement of the I Ching.
The 81 tetragrams correspond to the 81 verses
of the Tao Te Ching.
The Tai Hsuan Ching may be at least as
old as the King Wen arrangement of the I Ching,
since such tetragrams have been
found on Shang and Zhou dynasty oracle bones.
To construct the Tai Hsuan Ching,
start with the 3x3 I Ching Magic Square
| |
4 | 9 | 2
_____|_____|_____
| |
3 | 5 | 7
_____|_____|_____
| |
8 | 1 | 6
| |
whose central number, 5, is also
central in the sequence 1,2,3,4, 5, 6,7,8,9
which sequence corresponds
to the octonions 1,i,j,k, 0, E,I,J,K
whose total number for each line is 15,
the dimension of the largest Hopf fibration
and the dimension of the imaginary sedenions.
If you take into account the direction in which you add each
of the 8 ways, and add all directed ways together
you get a total of 16x15 = 240
which is the number of vertices of a Witting polytope.
The total of all 9 numbers is 45,
the dimension of the D5 Lie algebra Spin(10)
that is used in the D4-D5-E6-E7 physics model
in which
the D4 Spin(8) subgroup of Spin(10) corresponds
to 28 bivector gauge bosons
and the 16-dimensional homogeneous space
Spin(10) / Spin(8)xU(1)
corresponds to an 8-dimensional complex domain
whose Shilov boundary is RP1 x S7
corresponding to an 8-dimensional spacetime.
Notice that the 3x3 Magic Square gives
the gauge bosons and the spacetime
of the D4-D5-E6-E7 physics model
but
does not contain the spinor fermions.
The 3 generations of spinor fermions
corresond to a Lie Algebra Magic Square.
The Tai Hsuan Ching construction will
give us the spinor fermions,
and therefore corresponds to
the complete D4-D5-E6-E7 physics model.
To construct the Tai Hsaun Ching,
consider the Magic Square sequence as a line
3 8 4 9 5 1 6 2 7
with central 5 and opposite pairs at equal distances.
If you try to make that, or a multiple of it,
into a 9x9 Magic Square whose central number
is the central number 41 of 9x9 = 81 = 40+1+40,
you will fail because 41 is not a multiple of 5.
However, since 365 = 5x73 is
the central number of 729 = 364+1+364 , you can
make a 9x9x9 Magic Cube with 9x9x9 = 729 entries,
each 9x9 square of which is a Magic Square.
The Magic Cube of the Tai Hsaun Ching
gives the same sum for all lines parallel to an edge,
and for all diagonals containing the central entry.
The central number of the Magic Cube, 365,
the period of a Maya Haab.
The total number for each line is 3,285 = 219 x 15.
The total of all numbers is 266,085 = 5,913 x 45.
Since 729 is the smallest odd number greater than 1
that is both a cubic number and a square number,
the 729 entries of the 9x9x9 Magic Cube with central entry 365
can be rearranged to form
a 27x27 Magic Square with 729 entries and central entry 365.
27 = 3x3x3 = 13+1+13 is a cubic number with central number 14,
and there is a 3x3x3 Magic Cube with central entry 14
(14 is the dimension of the exceptional Lie algebra G2)
and sum 42:
10 24 8 26 1 15 6 17 19
23 7 12 3 14 25 16 21 5
9 11 22 13 27 2 20 4 18
The lowest dimensional non-trivial representation
of the Lie algebra E6 is 27-dimensional,
corresponding to the 27-dimensional Jordan algebra
of 3x3 Hermitian octonionic matrices.
E6 is the 78-dimensional Lie algebra
that is used in the D4-D5-E6-E7 physics model
in which
the 32-dimensional homogeneous space
E6 / Spin(10)xU(1)
corresponds to a 16-dimensional complex domain
whose Shilov boundary is two copies of RP1 x S7
corresponding to Spin(8) spinors, representing
8 fermion particles and 8 fermion antiparticles.
All 4 components of the D4-D5-E6-E7 model,
arising from the 4 fundamental representations of Spin(8),
are contained within E6:
8 half-spinor fermion particles;
8 half-spinor fermion antiparticles;
8-dimensional spacetime
(4 Physical Spacetime dimensions and
4 Internal Symmetry dimensions);
and 28 gauge bosons
(12 for the Standard Model,
15 for Conformal Gravity and the Higgs Mechanism, and
1 for propagator phase).
The Lie algebra E6 is 72+6 = 78-dimensional,
and has Weyl group of order 72x6! = 51,840
which is the symmetry group of the 6-dimensional polytope 2_21
with 27 vertices and 27+72 faces
which is also the symmetry group of the 27 line configuration:
The 78 dimensions of E6 correspond to the 78 Tarot cards.
Since E6 as used in the D4-D5-E6-E7 physics model
represents the two half-spinor representations of Spin(8),
For Spin(n) up to n = 8,
here are is their Clifford algebra structure
as shown by the Yang Hui (Pascal) triangle
and the dimensions of their spinor representations
n Total Spinor
Dimension Dimension
0 1 2^0 = 1= 1x1 1
1 1 1 2^1 = 2= 1+1 1
2 1 2 1 2^2 = 4= 2x2 2 = 1+1
3 1 3 3 1 2^3 = 8= 4+4 2
4 1 4 6 4 1 2^4 = 16= 4x4 4 = 2+2
5 1 5 10 10 5 1 2^5 = 32=16+16 4
6 1 6 15 20 15 6 1 2^6 = 64= 8x8 8 = 4+4
7 1 7 21 35 35 21 7 1 2^7 = 128=64+64 8
8 1 8 28 56 70 56 28 8 1 2^8 = 256=16x16 16 = 8+8
Since each row of the Yang Hui (Pascal) triangle
corresponds to the graded structure of an exterior algebra
with a wedge product, call each row a wedge string.
In this pattern, the 28 and the 8 for n = 8 correspond
to the 28 gauge bosons of the D4 Lie algebra
and to the 8 spacetime (4 physical and 4 internal symmetry)
dimensions that are added when you go to the D5 Lie algebra.
The 8+8 = 16 fermions that are added when you go to E6,
corresponding to spinors, do not correspond to any single
grade of the n = 8 Clifford algebra with graded structure
1 8 28 56 70 56 28 8 1
but correspond to the entire Clifford algebra as a whole.
The total dimension of the Clifford algebra
is given by the Yang Hui (Pascal) triangle
pattern of binary expansion (1 + 1)^n,
which
corresponds to the number of vertices of
a hypercube of dimension n.
The spinors of the Clifford algebra of dimension n
are derived from the total matrix algebra of dimension 2^n
with pattern
n
0 1
1 2
2 4
3 8
4 16
5 32
6 64
7 128
8 256
This can be expanded to a pattern
n
0 1
1 2 1
2 4 2 1
3 8 4 2 1
4 16 8 4 2 1
5 32 16 8 4 2 1
6 64 32 16 8 4 2 1
7 128 64 32 16 8 4 2 1
8 256 128 64 32 16 8 4 2 1
in the same form as the Yang Hui (Pascal) triangle.
Call each row a spinor string.
For a given row in the binary (1+1)^n Yang Hui (Pascal) triangle
the string product of a spinor string and a wedge string
(2^N, 2^(N-1), 2^(N-2), ... , 2^(N-J), ... , 4, 2, 1)
(1 , N , N(N-1)/2,...,N^k J^(N-k)/(k!(N-k)!)J),...,N(N-1)/2,N,1)
gives the rows of the ternary (1+2)^n power of 3 triangle
n
0 1 3^0 = 1
1 2 1 3^1 = 3
2 4 4 1 3^2 = 9
3 8 12 6 1 3^3 = 27
4 16 32 24 8 1 3^4 = 81
5 32 80 80 40 10 1 3^5 = 243
6 64 192 240 160 60 12 1 3^6 = 729
7 128 448 672 560 280 84 14 1 3^7 = 2,187
8 256 1024 1792 1792 1120 448 112 16 1 3^8 = 6,561
Just as the binary (1+1)^n triangle corresponds to the I Ching,
the ternary (1+2)^n triangle corresponds to the Tai Hsuan Ching.
The ternary triangle also describes
the sub-hypercube structure of a hypercube.
The ternary power of 3 triangle is not only
used in representations of the spinors in the D4-D5-E6-E7 model,
it was also by Plato in describing cosmogony and music.
The 9x9x9 Magic Cube of the Tai Hsuan Ching
has central entry 365,
and 365 = 73 x 5 is the whole number of days in a solar year.
The corresponding Maya 365-day period is called the Haab.
The 8x8 Magic Square and 4x4x4 Magic Cube of the I Ching
have sums 260 and 130 = 260/2,
and 260 = 13 x 5 x 4 is the number of days in a Maya Tzolkin.
The common period of the Maya Haab and Tzolkin
is 73 x 5 x 13 x 4 = 18,980 days or 52 Haab.
The synodic period of Venus is 584 = 73 x 8.
The common period of the Maya Haab and
the synodic period of Venus
is 73 x 5 x 8 = 37,960 days or 104 Haab.
The common period of the Maya Haab and Tzolkin and
the synodic period of Venus
is 73 x 5 x 8 = 2,929 days or 8 Haab.
Since the 8x8 = 4x4x4 = 64, and 584 = 2 x 260 + 64.
the synodic period of Venus is naturally expressible in
terms of the 8x8 Magic Square and the 4x4x4 Magic Cube.
Here is the 9x9x9 Magic Cube:
1
543 179 616 252 689 397 33 470 106
107 544 180 617 244 690 398 34 471
472 108 545 172 618 245 691 399 35
36 473 100 546 173 619 246 692 400
401 28 474 101 547 174 620 247 693
685 402 29 475 102 548 175 621 248
249 686 403 30 476 103 549 176 613
614 250 687 404 31 477 104 541 177
178 615 251 688 405 32 469 105 542
2
97 534 170 607 324 680 388 24 461
462 98 535 171 608 316 681 389 25
26 463 99 536 163 609 317 682 390
391 27 464 91 537 164 610 318 683
684 392 19 465 92 538 165 611 319
320 676 393 20 466 93 539 166 612
604 321 677 394 21 467 94 540 167
168 605 322 678 395 22 468 95 532
533 169 606 323 679 396 23 460 96
3
452 88 525 242 598 315 671 379 15
16 453 89 526 243 599 307 672 380
381 17 454 90 527 235 600 308 673
674 382 18 455 82 528 236 601 309
310 675 383 10 456 83 529 237 602
603 311 667 384 11 457 84 530 238
239 595 312 668 385 12 458 85 531
523 240 596 313 669 386 13 459 86
87 524 241 597 314 670 387 14 451
4
6 443 160 516 231 589 306 662 370
371 7 444 161 517 234 590 298 663
664 372 8 445 162 518 226 591 299
300 665 373 9 446 154 519 227 592
593 301 666 374 1 447 155 520 228
229 594 302 658 375 2 448 156 521
522 230 586 303 659 376 3 449 157
158 514 231 587 304 660 377 4 450
442 159 515 232 588 305 661 378 5
5
361 78 434 151 507 224 580 297 653
654 362 79 435 152 508 225 581 289
290 655 363 80 436 153 509 217 582
583 291 656 364 81 437 145 510 218
219 584 292 657 365 73 438 146 511
512 220 585 293 649 366 74 439 147
148 513 221 577 294 650 367 75 440
441 149 505 222 578 295 651 368 76
77 433 150 506 223 579 296 652 369
6
725 352 69 425 142 498 215 571 288
280 726 353 70 426 143 499 216 572
573 281 727 354 71 427 144 500 208
209 574 282 728 355 72 428 136 501
502 210 575 283 729 356 64 429 137
138 503 211 576 284 721 357 65 430
431 139 504 212 568 285 722 358 66
67 432 140 496 213 569 286 723 359
360 68 424 141 497 214 570 287 724
7
279 716 343 60 416 133 489 206 643
644 271 717 344 61 417 134 490 207
199 645 272 718 345 62 418 135 491
492 200 646 273 719 346 63 419 127
128 493 201 647 274 720 347 55 420
421 129 494 202 648 275 712 348 56
57 422 130 495 203 640 276 713 349
150 58 423 131 487 204 641 277 714
715 351 59 415 132 488 205 642 278
8
634 270 707 334 51 407 124 561 197
198 635 262 708 335 52 408 125 562
563 190 636 263 709 336 53 409 126
118 564 191 637 264 710 337 54 410
411 119 565 192 638 265 711 338 46
47 412 120 566 193 639 266 703 339
340 48 413 121 567 194 631 267 704
705 341 49 414 122 559 195 632 268
269 706 342 50 406 123 560 196 633
9
188 625 261 698 325 42 479 115 552
553 189 626 253 699 326 43 480 116
117 554 181 627 254 700 327 44 481
482 109 555 182 628 255 701 328 45
37 483 110 556 183 629 256 702 329
330 38 484 111 557 184 630 257 694
695 331 39 485 112 558 185 622 258
259 696 332 40 486 113 550 186 623
624 260 697 333 41 478 114 551 187
References:
Andrews, W. S., Magic Squares and Cubes (Dover 1960).
Arguelles, Jose, Earth Ascending (3rd ed) (Bear 1996).
(Jose Arguelles noticed similar correspondencies between
8x8 Magic Squares, the I Ching, and the Mayan calendar, at
least as early as the first edition of Earth Ascending in 1984.)
Coxeter, H. S. M., Math. Z. 200 (1988) 3-45.
Huang, Kerson and Rosemary, I Ching (Workman 1987).
Lau, Kwan, Feng Shui for Today (Tengu 1996).
Schele, Linda and Freidel, David, A Forest of Kings
(Quill, William Morrow 1990).
Shaughnessy, Edward, I Ching (Ballantine 1996).
Walter, Katya, Tao of Chaos (Element 1994).
Walters, Derek, Chinese Astrology (Aquarian 1992).
Walters, Derek, The Alternative I Ching (Aquarian Press 1987),
originally published in 1983 under the title The Tai Hsuan Ching.
Wells, David, The Penguin Dictionary of Curious and
Interesting Numbers (Penguin 1986).
Williams, C. A. S., Chinese Symbolism and Art Motifs (Tuttle 1974).
Wong, Eva, Feng Shui (Shambhala 1996).
Wong, Eva, Taoism (Shambhala 1997).
An I Ching web site from UCLA.
The I Ching web site of Chris Lofting, which has a lot of very
interesting philosophical discussion.
The I Ching web site of Christopher Garrity, which relates the 8x8 I
Ching Matrix to a Matrix of the 8 Colors of the SU(3) Color Force:
white; red, blue, and green; and their complementary colors.
Tony Smith's Home Page
......
jum...@my-deja.com
http://www.innerx.net/personal/tsmith/ficw.html#weiqi
-----------------------------------------------------
Wei Qi,
Cellular Automata,
Ising Model,
Feynman Checkerboard
Tony's Home
Feynman Checkerboards
in 1+1 dimensions are isomorphic to 1-dimensional
Ising Models
which can be represented by
Cellular Automata
which are like
Wei Qi
Feynman Checkerboards
A single FEYNMAN CHECKERBOARD configuration is one of all possible
ways for an electron to go from an initial point to a destination point.
Choice of a particular single configuration is a RANDOM quantum choice.
Feynman's Relativistic Chessboard as an Ising Model,
by H. A. Gersch (Int. J. Theor. Phys. 20 (1981) 491),
shows that the (1+1)-dimensional Feynman Checkerboard,
which describes the (1+1)-dimensional Dirac equation,
is equivalent to the 1-dimensional Ising model.
The Feynman Checkerboard for an electron in 1+1 dimensional spacetime
can be represented as a 1-dimensional Cellular Automaton
evolving in 1 time dimension.
The initial state is a point in the t=0 initial time,
the initial location of the electron in 1-dimensional space.
Each possible state at time t=N is a point locating the electron on
the spatial line at t=N.
All possible paths from the initial state at t=0 to the state at t=N
are summed (the Quantum Sum Over Histories) to get the amplitude
for the electron to go from the initial state at t=0
to each of the possible states at t=N.
The Cellular Automaton evolves to time t=N+1
by considering all possible paths that go from t=0 to t=N+1.
In terms of amplitudes (rather than probabilities),
the paths to t=N+1 are just the extensions of the paths to t=N.
Here is a rough diagram of one such possible path
to one such possible point, up to time t=N+1 :
t=N+1 --------------*----------------------------
\
t=N ----------------*--------------------------
/
t=N-1 --------------*----------------------------
\
..................................................
..................................................
..................................................
/
t=3 -------------------*-----------------------
\
t=2 ---------------------*---------------------
/
t=1 -------------------*-----------------------
/
t=0 -----------------*-------------------------
Each Initial State of the Feynman Checkerboard,
or point on the space-like 1-dimensional line at t=0,
can be represented on the real line interval [0,4]
by a binary semi-sequence of +/- signs in the form of
2 +/- sqrt(2 +/- sqrt(2 +/- sqrt(2 +/- ... )))
Such sequences of length M are the zeroes
of the Chebyshev polynomials of degree 2^M.
Simlarly to this way that the binary sequences
can represent the spatial part of the 1+1-dim Feynman Checkerboard
as points on a line segment,
the spatial part of the 1+1-dim Feynman Checkerboard can also
be represented as a 1-dimensional sphere S1.
This is analogous to the S7 space of the RP1 x S7 spacetime
of the D4-D5-E6-E7 physics model,
which is discussed below as an Octonion Julia Set.
Intervals containing those zeroes
form Mth order Borel sets for [0,4].
The corresponding Borel measure is the singular measure
concentrated at the zeroes with value 2^(-M) at each zero.
As M goes to infinity,
the Chebyshev measure goes to the arccosine measure.
The Bernoulli Scheme of the right shift operator
acting on such semi-infinite sequences of +/- signs.
is isomorphic to the Bernoulli Scheme for Lebesgue measure
and the usual Borel sets on the unit interval,
as shown by Barnsley, Geronimo, and Harrington
in Comm. Math. Phys. 88 (1983) 479-501.
Consider such a binary semi-sequence of length KM.
Then,
a Bernoulli shift of length PN for P less than K
takes a
sequence whose initial M elements correspond to one Initial State
to a
sequence whose initial M elements correspond to another Initial State,
described by the Pth set of M elements in the original sequence.
Consider such a sequence of length KM with K = 2^M
such that
all subsequences of length M beginning with 0, M, 2M, ...
are distinct.
Such a sequence contains All Possible Initial States
for the Feynman Checkerboard at t = 0.
Therefore:
a Bernoulli Scheme of shift operator of length M
acts on such sequences of length KM
which describe
the Ensemble of all Possible Initial States.
By extending the process to include all possible states
at each time up to time t=N,
you get that
a compound Bernoulli Scheme of a shift operator of length KM
and a second shift operator of length M
acts on such sequences of length NKM
which describe
the Ensemble of All Sums Over Histories
of all paths from all initial states to all final points,
or, equivalently,
of All Ensembles of All Possible Initial States.
Generalize the binary semi-sequence of +/- signs in the form of
2 +/- sqrt(2 +/- sqrt(2 +/- sqrt(2 +/- ... )))
to the binary semi-sequence of +/- signs in the form of
L +/- sqrt(L +/- sqrt(L +/- sqrt(L +/- ... )))
where L is in the real interval (0,2],
and extend the result to L=0 by continuity.
Then, as discussed by Barnsley, Geronimo, and Harrington
in Comm. Math. Phys. 88 (1983) 479-501,
sequences of +/- signs of length N correspond to
points on the Julia Set JL of N-th order iterations of F(z,L),
where z is a complex number and F(z,L) = (z - L)^2,
which form a Bernoulli Scheme as described above.
Such a Julia Set JL is defined as the boundary of the region
in z-space for which all iterations of the map F remain bounded
(for that value of L).
For F(z,0), the the Julia Set J0 is the unit circle S1,
the limit of the sequence representations as L approaches 0.
In that way,
the spatial part of the 1+1-dim Feynman Checkerboard
can be represented by the binary sequences
as a 1-dimensional sphere S1.
This is analogous to the S7 space of the RP1 x S7 spacetime
of the D4-D5-E6-E7 physics model,
which is discussed below as an Octonion Julia Set.
Here are some images of Julia sets for various values of L,
ranging along the real axis from L = 0 to L = 2:
If L is greater than 2, the Julia set JL
is a set of points on the real axis,
is perfect (all its points are limit points
and it contains all its limit points),
is compact, non-denumerable. and contains no intervals,
is of Lebesgue measure zero,
and can be regarded as a dust of disconnected points.
If L is allowed to take values in the entire complex plane,
the region in L-space for which all iterations of the map F
remain bounded (for z = 0) is the Mandelbrot Set.
An equivalent definition is the set of values of L
for which the Julia set JL is connected, and not a dust.
Here is a web page about the Mandelbrot Set images.
Here is a Fractal FAQ.
Note that instead of the map F(z,L) = (z - L)^2
others often use the closely related map G(z,L) = z^2 + L.
For F(z,L) = (z - L)^2 the Mandelbrot set look like this:
The conventional Feynmand Checkerboard has 1 space dimension.
The Quantum Cellular Automaton of Iwo Bialynicki-Birula
is fundamentally a Feynman Checkerboard with 3 space dimensions,
and is similar to
the Penrose-Rindler light-cone formulation of massive fields
and
a frequency-cubed power spectrum Background Field.
In the D4-D5-E6-E7 physics model,
the generalized HyperDiamond Feynman Checkerboard has
3 physical space dimensions
plus 4 internal symmetry space-like dimensions,
for a total of 7 space dimensions.
If z in F(z,L) is quaternion or octonion instead of complex,
you get similar figures in each 2-dimensional subspace
containing the real axis. Also:
For complex z J0 = S1 and J2 = [0,4]
The correspondence between J0 and J2 is 1-1,
based on sequences and limits of the form
L +/- sqrt(L +/- sqrt(L +/- sqrt(L +/- ... )))
and the fact that the only square roots of -1
are i and its negative.
For quaternion z J0 = S3 and J2 = [0,4]
Denote by J0basis the 3 "basis" unit circles in S3
corresponding to the imaginary quaternions i, j, k.
The correspondence between J0basis and J2 is 3-1,
based on sequences and limits of the form
L +/- sqrt(L +/- sqrt(L +/- sqrt(L +/- ... )))
and the fact that the square roots of -1
include i, j, k and their negatives.
For octonion z J0 = S7 and J2 = [0,4]
Denote by J0basis the 7 "basis" unit circles in S3
corresponding to the imaginary quaternions i,j,k,E,I,J,K.
The correspondence between J0basis and J2 is 7-1,
based on sequences and limits of the form
L +/- sqrt(L +/- sqrt(L +/- sqrt(L +/- ... )))
and the fact that the square roots of -1
include i, j, k, E, I, J, K and their negatives.
HOWEVER,
if you look at discrete octonion lattices,
you see that there are 7 distinct E8 lattices,
and that they all have the same real axis,
and that they correspond 1-1 with the 7 imaginary octonions.
Therefore:
If you include all 7 distinct E8 lattices,
you get 7 distinct lattice representations of the real axis,
which correspond 1-1 with the 7 imaginary octonions,
so you get
a 7-7 (or, equivalently, 1-1) correspondence
between
J0basis (in each of the 7 E8 lattices)
and
J2 = [0,4] (in each of the 7 E8 lattice real axes).
Therefore there is
a 7-7 (or, equivalently, 1-1) correspondence
between
J0 = S7 (in octonion space spanned by the real axis
plus the 7 imaginary octonions)
and
J2 = [0,4] (in the space spanned by
the 7 E8 lattice real axes).
As to the general properties of Bernoulli Schemes,
an interesting web page describing Bernoulli Numbers
is maintained by S. C. Woon, who also wrote a paper
Analytic Continuation of Bernoulli Numbers,
a New Formula for the Riemann Zeta Function,
and the Phenomenon of Scattering of Zeroes.
The Riemann zeta function is
zeta(s) = SUM( 1 / (N^s) )
sum over N from 1 to infinity
It is also equal to
zeta(s) = PROD( 1 / (1 - P^(-s)) )
product over all prime numbers P
Note that zeta(1) = SUM(1/N) is the harmonic series.
The fact that the harmonic series diverges
shows that
the sum over all primes P SUM( 1/P ) also diverges,
which also shows that the number of primes is infinite.
(There is a theorem that if PROD( 1 + K ) converges,
then SUM( K ) converges.)
(see Introduction to Calculus and Analysis,
vol. 1, by Courant and John, Springer 1989)
You can also use zeta functions and generalizations
to calculate distributions of prime numbers, and
to do calculations for sum-over-histories path
integrals in quantum theory, and
for a lot of neat poorly understood stuff.
According to the 18 May 1996 issue of the New Scientist,
(see also Science 274 (20 Dec 96) 2014-2015)
Michael Berry and Jon Keating have seen correspondences
between the spacing of the prime numbers
and the spacing of energy levels
of quantum systems that classically would be chaotic.
They would like to find a chaotic system that,
when quantized, would have energy levels that are
distributed exactly as the prime numbers.
Since energy levels are positive numbers,
and so should correspond to a straight line in the complex plane,
such a zeta function - quantum system correspondence
could be used to verify the Riemann hypothesis,
that all the nontrivial zeroes of the zeta function
are on the straight line Re(z) = 1/2 in the complex plane.
Thus, the quantum harmonies in the music of the primes
could prove the Riemann hypothesis.
Bernoulli Shifts and Bernoulli Numbers
can be seen as coming from binary decision trees,
similar to
the binary decision trees that produce Markov Processes
and
the binary decision trees that produce the Surreal Numbers:
Bernoulli Numbers are also related to Homotopy Theory.
Ising Models
A single ISING MODEL STATE configuration is one of all possible
spin configuration states.
Choice of a particular single configuration is a RANDOM
statistical choice.
Feynman's Relativistic Chessboard as an Ising Model,
by H. A. Gersch (Int. J. Theor. Phys. 20 (1981) 491),
shows that the (1+1)-dimensional Feynman Checkerboard,
which describes the (1+1)-dimensional Dirac equation,
is equivalent to the 1-dimensional Ising Model.
There are interesting relationships among Ising Models
and Cellular Automata and Spin Networks.
Generalized Ising Models based on E8 lattices
and octonions might accurately represent
the HyperDiamond Feynman Checkerboard picture
of the D4-D5-E6-E7 physics model.
Cellular Automata
A single CELLULAR AUTOMATON STATE configuration is one of all possible
initial states.
Choice of a particular single configuration is a RANDOM choice.
Alexander Schatten (e-mail address: asc...@fbch.tuwien.ac.at)
has written a Tutorial on Cellular Automata.
The Properties of Cellular Automata are described
on a web page by Santa Fe A-Life.
Cellular Automata have been classified by Wolfram
into 4 classes:
Class 1 - After a finite number of time-steps, going to a unique state
from (nearly) all possible starting conditions.
Class 2 - Usually creating patterns that repeat periodically
or are stable. They can be seen as a kind of filter.
Class 3 - From nearly all starting conditions,
creating aperiodic chaotic patterns.
Class 4 - more complex behaviour, capable of universal computation.
They show a high level of irreversibility,
and usually die after a finite number of time steps.
Langton has also classified Cellular Automata,
using his Lambda parameter, which is the probability
that a cell will live to the next generation in time.
As described in The Global Dynamics of Cellular Automata,
Santa Fe Institute Reference Volume I,
by Andrew Wuensche and Mike Lesser (Addison-Wesley 1992),
another parameter,
the Z-parameter, is defined as the probability that
the next cell of a partial pre-image has a unique value.
For Binary rules,
as Z varies from 0 to 1,
Lambda varies from 0 to 1/2 and conversely from 1 to 1/2.
To get a simpler comparison between Z and Lambda,
you can use another parameter,
the Lambda Ratio, which for a binary rule is:
Lambda Ratio = 2 Lambda if Lambda is not greater than 1/2, and
Lambda Ratio = 2 (1 - Lambda) if Lambda is greater than 1/2.
The Lambda Ratio is never smaller than the Z parameter.
Some important characteristics of Cellular Automata are:
array length L
maximum pre-maging mp
maximum period of attractor cycles mc
maximum length of transient trees ml
number of separate basins in the field nb
Consider mc, ml, and nb:
Since a preponderance of any one will tend to diminish
the other two, these three parameters vary together.
Wuensche and Lesser give examples of varying characteristics
of 1-dimensional binary nearest neighbor (n=3) Cellular Automata:
Class 1 typically has Z = 0.25,
a lot of ambiguous permutations in the rule table,
mp diverges exponentially with L,
mc, ml, nb are either fixed or vary arithmetically with L.
cycles and transients are short.
Class 2 typically has Z = 0.5,
many basins separated from the uniform attractor,
mp diverges exponentially with L, but less than for Class 1,
mc, ml, nb are either fixed or vary arithmetically with L,
cycles and transients are short.
Class 4 typically has Z = 0.75,
complex behavior,
mp and some combination of mc, ml, nb are finely balanced,
mp diverges by intermediate function of L,
mc, ml, nb diverge by intermediate function of L,
cycles and transients are moderately long.
Class 4 has been called the Edge of Chaos,
the area of universal computation and possible life,
because at lower Z values things are too simple
and at higher Z values things are too chaotic.
Harold McIntosh has a web page at Santa Fe about Class 4.
Class 3 typically has Z = 1.0,
chaotic behavior,
mp is fixed,
some combination of mc, ml, nb diverges exponentially with L.
As Wuensche and Lesser note, there are some exceptions to
the general characterizations.
A web page by Timothy Keitt has illustrations of all 256 types of
2-state 1-dimensional Cellular Automata that
have nearest neighbor (3-cell neighborhood) rules.
As to which of the 256 rules
have Class 4 behavior, Harold McIntosh says:
"It's generally accepted that
the following "elementary" (2 state, radius 1) rules
have typical class IV (or "complex") behaviours,
because they feature emergent coherent propagating structures
(analagous to gliders in Life, but 1-D).
These gliders move and interact on periodic backgrounds;
collisions between gliders produce new gliders.
Rule 54 (and the equivalent Rule 147).
Rule 193 (and equivalent Rules 124, 137 and 110)."
Interesting examples of Cellular Automata are
forms of the Binomial Triangle sometimes known as
the Yang Hui Triangle or the Pascal Triangle,
as discussed in the web pages of Andrew Granville,
which cover such things as
Binomial Triangle patterns modulo prime numbers.
HISTORICAL NOTE: The Binomial Triangle known to Europeans as Pascal's
Triangle was known to the Southern Song Chinese mathematician
mathematician Yang Hui (1261 AD). Here are some references to even
earlier discovery of the Binomial Triangle: 1100-1109 AD: Jia Xien
states the method of forming the Pascal triangle; the triangle was
probably known before his time.
(from The Timetables of Science, A. Hellemans and B. Bunch, Simon and
Schuster (1988)) ca. 1100-1180 AD: As-Samaw'al ibn-Yahya al-Maghribi
wrote The Luminous Book on Arithmetic, which contained an illustration
of the Binomial Triangle up to order 11.
He was he son of a Moroccan Rabbi. He moved to Baghdad and coverted to
Islam. He did not claim to have discovered the Binomial Triangle, but
to have gotten it from Al-Karaji, who in turn may have gotten it from
another source.
(from From One to Zero, G. Ifrah, Penguin (1985) English translation
of 1981 French book) ca. 300-200 BC: The Jaina mathematician Halayudha
has been given credit for discovering the Binomial Triangle by John
McLeish (The Story of Numbers, Fawcett Columbine (1991)). McLeish says
that it should be called the Meru-Prastera rule.
The Binomial Triangle is a basic structure in Clifford Algebras,
such as are used in the D4-D5-E6-E7 physics model.
Cellular Automata are related to Ising Models
and to Spin Networks.
Some threads from Santa Fe A-Life discuss connections
between Wei Qi and Cellular Automata.
(Wei Qi is sometimes known by its Japanese name, Go.)
Iwo Bialynicki-Birula has formulated Dirac and Weyl equations
on a cubic attice as Quantum Cellular Automata.
Generalized Cellular Automata based on E8 lattices
and octonions might accurately represent
the HyperDiamond Feynman Checkerboard picture
of the D4-D5-E6-E7 physics model.
Wei Qi
A single WEI QI STATE configuration is one of all possible
states of placement of stones on the board lattice.
Choice of a particular single configuration is a CONSCIOUS choice.
Some threads from Santa Fe A-Life discuss connections
between Wei Qi and Cellular Automata.
(Wei Qi is sometimes known by its Japanese name, Go.)
Wei Qi moves are not made by predetermined rule
or at random, but by Conscious Intelligence that:
observes an incomplete state of the board;
perceives which more complete states are likely;
and makes a move that tends to produce favorable states.
Progress in the Wei Qi game is defined
as going from less complete states to more complete states,
and NOT by going from earlier in time states to later states.
The objective is defined as producing
a more complete state that is more favorable.
Here favorable means maximizing the area controlled,
or, in Cellular Automata terminology,
maximizing the desired basins of attraction
by using the move to alter the Cellular Automaton.
The Wei Qi board is not 19x19 lines in a square pattern,
but 19x19 lines in a rectangular pattern,
suggesting a distinction between the vertical lines
and the horizontal lines.
If the vertical lines represent time,
and the horizontal lines represent one space dimension,
then the entire board might represent (1+1)-dimensional spacetime.
Therefore, the Conscious Intelligence of the Wei Qi player
perceives the relevant 19x19 region of spacetime all at once,
in its entirety,
as a lightcone being lifeform might perceive
a region of the spacetime in our universe.
From that perspective,
the Wei Qi moves of the Conscious Intelligence would
be like a lightcone being making moves at various
points of our spacetime to alter its structure
so as to maximize the favorable basins of attraction
in the ensemble of possible Many-Worlds.
In order to make its move, such a lightcone being
might have to interact with a massive spacelike being
in order to actually execute the move.
By making its move, and so affecting the Many-Worlds,
such a type of lightcone being might be acting
as an abstract Many-Worlds being.
This perspective seems to indicate a relationship between
Randomness of Cellular Automata, Ising Models,
and Sum-Over-Histories Feynman Checkerboards
and
Consciousness of the Wei Qi player.
The pattern-principles (Li) by which the next Wei Qi move
is determined might be represented by
the I Ching and the Tai Hsuan Ching as though
the I Ching and Tai Hsuan Ching show how to move in Wei Qi.
The interactions among the basins of attraction
would be in accord with the principles of Zhen-Shan-Ren.
Generalized Wei Qi based on E8 lattices
and octonions might accurately represent
the HyperDiamond Feynman Checkerboard picture
of the D4-D5-E6-E7 physics model.
Wei Qi could have begun with a 16x16 pattern corresponding to the 256
elements of IFA and the Cl(8) Clifford Algebra that is the basis of
the D4-D5-E6 physics model
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x
The 256 elements are in four 8x8 blocks of 64 elements each. The
division into 4 blocks is a natural Clifford Algebra subdivision. Each
of the 8x8 blocks of 64 elements looks like the I Ching.
Now, add 33 elements of a central row and column to form the 17x17
pattern of 289 elements, the new elements corresponding to the
Symmetric Space E6 / Spin(10)xU(1) (and its U(1), marked as o)
representing the CL(8) Spinors of the D4-D5-E6 physics model.
Acccording to Needham (Science and Civilization in China, Cambridge
Un. Press, vol. III, page 139) Shen Kua refers to old Wei Qi boards
with 17 rows and columns.
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x o x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x
To get to the 19x19 Wei Qi board, add an outer border of 72 = 17 + 28
+ 27 elements,
17 of which correspond to the Symmetric Space Spin(10) /
Spin(8)xU(1) (and its U(1), marked as o) representing Vectors in the
D4-D5-E6-E7 physics model,
28 of which correspond to the Spin(8) gauge group (whose 4 Cartan
Subalgebra elements are marked as o) of the D4-D5-E6-E7 physics
model, and
27 of which correspond to the Complex dimensionality of the
Symmetric Space E7 / E6xU(1) (with its 3 rank elements marked as o)
representing the MacroSpace of the Super Implicate Order of the
D4-D5-E6-E7 physics model.
o x x x x x x x x o x x x x x x x x o
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
o x x x x x x x x o x x x x x x x x o
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
o x x x x x x x x o x x x x x x x x o
Now we have added a total of 33 + 72 = 105 elements to the original
256, and produced the Wei Qi board with 19x19 = 361 elements.
Since 105 = 78 + 27, you can say that
78 of the new elements are the 78-real-dimensional Lie group E6
that, in the D4-D5-E6-E7 physics model, corresponds to the
SpaceTime, Fermions, and Gauge Bosons of one World of the
Many-Worlds, and
27 of the new elements are the 27-complex-dimensional symmetric
space E7 / E6xU(1) that, in the D4-D5-E6-E7 physics model,
corresponds to the MacroSpace of Many of the Worlds of the
Many-Worlds.
The 9 elements at the center and the ends of the new rows and columns
have been marked with o. They correspond to the total rank of the 105
new elements, since
the 78-real-dimensional Lie Group E6 has rank 6 and
the 27-complex-dimensional symmetric space E7 / E6xU(1) has rank 3.
Therefore, the 19x19 = 361 elements of Wei Qi correspond to:
the 256 elements of IFA and Cl(8), made up of four copies of the
I Ching;
the 78 elements of Tarot and E6, which in turn are made up of
the 28 elements of Spin(8);
the 16+1 elements of Spin(10) / Spin(8)xU(1) plus the 1 U(1);
the 32+1 elements of E6 / Spin(10)xU(1) plus the U(1);
the 27 elements of the Sri Yantra, the 22 Hebrew Letters plus 5
Finals, and MacroSpace E7 / E6xU(1).
Another way to describe the Wei Qi board is to put the 27 MacroSpace
elements and the 6 E6 Cartan Subalgebra elements in the 33 inner
central row and column spaces, and then put the 72 E6 root vector
elements in the 72 outer row and column spaces:
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x o x x x x x x x x x
x x x x x x x x x o x x x x x x x x x
x x x x x x x x x o x x x x x x x x x
x x x x x x x x x o x x x x x x x x x
x x x x x x x x x o x x x x x x x x x
x x x x x x x x x o x x x x x x x x x
x x x x x x x x x o x x x x x x x x x
x x x x x x x x x o x x x x x x x x x
x x x x x x x x x o x x x x x x x x x
x x x x x x x x x x x x x x x x x x x
Tony's Home
Thiele Everett
: > But when it comes to the terms we use in producing
: > go books and articles, these kinds of reform movements don't
: > seem very important.
: What reform movement? Who decided that go terms should mean something
: else for English speakers than for the rest of the go world? Nobody. The
: original explicators (there is no translation here) thought that they
: were giving correct explanations. Correcting their errors is not reform.
: It enables us to communicate without confusion with the rest of the go
: world.
Your viewpoint seems also a valid one even though I disagree.
All along I have said that listening to what they have to say
about the Japanese language is a good idea, especially if you want
to be able to talk about go with Japanese people. The kind of reform
movement I am talking about is when translators start reforming the
language of go books, and try to avoid words like 'hane' and 'tesuji'
which are very well established in the English go-vocabulary. The
results are unsatisfactory and confusing IMO. This has taken place,
I believe in some of the books John Fairbairn translated for Yutopian.
(If anyone can correct this, or provide examples I'd be grateful, as
I don't have the books at hand right now).I think it can be seen as
an interesting experiment, and who would be better equipped to carry
such a task out than such a learned, veteran translator as Fairbairn?
Still, my feeling is that the results are counterproductive. My
opinion is not very important, and the historical sweep of the matter
will decide in the end anyway.
regards,
--Rett
dmsi...@my-deja.com
<1999101010...@tc-1-177.ariake.gol.ne.jp>,
Warning!s...@sig.for.address wrote:
> John Fairbairn <J...@harrowgo.demon.co.uk> wrote:
> >Nakade (verb nakade suru; Chinese dian3) refers only to
> >playing inside a group at the vital point.
>
> > Here is an example of the main meaning from a Japanese go
dictionary:
<snip>
>
> Thank you John for this clear explanation and your previous
>informative comments.
<snip>
I second that thought!
> In the glossary added for the benefit of English readers, nakade is
> defined as "a big eye". This is totally wrong. A nakade is not an eye
> in itself, and has nothing to do with a big eye. Nakade is a move not
> a shape. This misconception is the cause of numerous mistranslations
> throughout the text.
>
<snip>
> Richard Hunter (hunter at gol dot com), Tokyo, Japan
>
I think that there is a significant difference between using the *main
meaning* as John describes it and being totally wrong (or right). As a
counter example I offer diagram 1 from page 102 of Otake's *Shodan e no
Kihon Tesuji* which uses both the shape and play meanings in successive
sentences - in Japanese naturally:
(White to play)
. . X . . 2 1 . .
. O X . 3 . X O .
. O X X X X X O .
. O O O O O O O .
. . . . . . . . .
The comment is *Kuro 2 to utta kata ha 5 moku nakade desu* - roughly -
the shape after black 2 is 5 moku nakade. The next sentence is *Shiro 3
to nakade sare, 1 me ni saremasu* - (black) is reduced to 1 eye by
white's nakade at 3.
I don't think that there is anything wrong with the tendency to use the
shape meaning in English. I would say it is more interesting that the
secondary meaning has been promoted to primary in translation. Is this
an East/West thing? Or is it perhaps the difference between amateurs'
love of good shape and pros' love of dynamics which John has written
about in the past?
Dave
Bill Spight
> As a
> counter example I offer diagram 1 from page 102 of Otake's *Shodan e no
> Kihon Tesuji* which uses both the shape and play meanings in successive
> sentences - in Japanese naturally:
> (White to play)
>
> . . X . . 2 1 . .
> . O X . 3 . X O .
> . O X X X X X O .
> . O O O O O O O .
> . . . . . . . . .
> The comment is *Kuro 2 to utta kata ha 5 moku nakade desu* - roughly -
> the shape after black 2 is 5 moku nakade.
>
I do not believe that this shows that "nakade" also means a shape. Rather, "5-moku nakade" is a predicate nominative which modifies the sentence topic "kata" (subject in English, topic in Japanese. Slight difference). I. e., it is equivalent to "Kuro 2 to utta kata wa 5-moku nakade no kata desu." "The shape after B 2 is a 5-moku nakade shape." The test is that you cannot switch the predicate nominative and the topic. "5-moku nakade [no hitotsu] wa kuro 2 to utta kata desu."* ("[One instance of] 5-moku nakade is the shape after B 2."*)
Ask Otake, "Nakade wa katachi desu ka?" ("Is a nakade a shape?") and he'll reply, "Tondemo nai!" ("No way!") (Actually, he'll probably be polite and say, "Maybe not," or even, "Possibly so." ;-))
What say you, Sir John?
Best,
Bill
Bill Spight
> Am I correct to understand that you agree that however you analyze the
> sentence, it is not using the term nakade in reference to the subsequent play
> by white - the main meaning - but rather the result after black 2 - the usage
> more commonly carried over into English?
Let's stick to English usage. The Japanese is similar.
If I say, "This is a nakade position," I am using a noun (nakade) to modify another noun (position). I do not mean that the position is itself nakade, but that in that position a nakade is correct play. With the same meaning, I may also say, "This position is nakade." Similarly, in American football I may say, "Third and fifteen is a pass," meaning, not that third down with fifteen yards to go for first down is the same thing as throwing the ball, but that in that situation, a pass is almost always the right play. Or in contract bridge I may say, "that hand is a double," meaning that I think that double is the right call with that hand, not that the cards held constitute a kind of call. Or in Hold'em poker I may say, "AQ on the button is a raise," meaning that if I hold those cards as dealer, I think that the correct play is to raise the pot.
I am saying that Otake is using language in essentially the same way. When he says that the shape is 5-moku nakade, he means that in that shape, the correct play for one player (White in this case) is a 5-moku nakade. In that position, there are 5 nakade. Only one is correct, and that is the one called 5-moku nakade. There is a relation between the shape and the correct play, of course. But the shape is not the play.
Best,
Bill
Eric Osman
I think there's an inaccuracy here:
> Here is an example of the main meaning from a Japanese go dictionary:
>
> . . . . . .
> . 0 . + . .
> 0 # 0 0 . .
> # # # 0 . .
> . . # . . .
> 1 . # . . .
> . # # 0 . .
> # # 0 0 . .
> . 0 . . 0 .
> . . . . . .
> . . . . . .
>
> This is the bottom left-hand corner of the board. 1 is played by 0 and
> is called in Japanese gomoku nakade = a move played inside [at the vital
> point of] a five-point [shape].
If it's truly the BOTTOM LEFT-HAND corner, as stated, then it's nonobvious.
Afte O plays the "1" move, suppose # clamps, like this:
. . . . . .
. . . . . .
. . . . . .
. . . + . .
. . . . . .
. . . . . .
. . . . . .
. . . . . .
. # . . . . Can O contain X and kill, after this clamp ????
. 0 . + . .
0 # 0 0 . .
# # # 0 . .
. . # . . .
1 . # . . .
. # # 0 . .
# # 0 0 . .
. 0 . . 0 .
. . . . . .
. . . . . .
Perhaps O's best defense is connecting, then # takes one stone, then
O starts pushing ? Looks like this:
. . . . . .
. . . . . .
. . . . . .
. . . + . .
. . . . . .
. . . . . .
. . O . . .
. # . . . .
. # O . . .
# 0 0 + . .
. # 0 0 . .
# # # 0 . .
. . # . . .
1 . # . . .
. # # 0 . .
# # 0 0 . .
. 0 . . 0 .
. . . . . .
. . . . . .
Will O be able to kill ?
/Eric
David Sigaty
Bill,
I bow to your greater linguistic knowledge, or more accurately - you lost me!
:-). Am I correct to understand that you agree that however you analyze the
sentence, it is not using the term nakade in reference to the subsequent play
by white - the main meaning - but rather the result after black 2 - the usage
more commonly carried over into English?
Dave
Richard Hunter
> I think there's an inaccuracy here:
You're right. There's a stone left off. The diagram in the dictionary
has a hanging connection which prevents any escape.
. . . . . .
. . O . . .
> > . 0 . + . .
> > 0 # 0 0 . .
> > # # # 0 . .
> > . . # . . .
> > 1 . # . . .
> > . # # 0 . .
> > # # 0 0 . .
> > . 0 . . 0 .
> > . . . . . .
> > . . . . . .
> >
> If it's truly the BOTTOM LEFT-HAND corner, as stated, then it's nonobvious.
> Afte O plays the "1" move, suppose # clamps, like this:
-----------------------------------------------------------------
Richard Hunter
> I think that there is a significant difference between using the *main
> meaning* as John describes it and being totally wrong (or right).
Thanks for your stimulating response.
Personally, I am happy with expressions like "This position becomes a
five-point nakade" although others might disagree. The question is how
to translate that into clear English. I think "White reduces Black to a
single eye" is acceptable, but a skillful translator might find
something better.
My original complaint was that the English words "... White 5 and 7 make
a three-space big eye." do not meaningfully describe the diagram. The
problems are:
1. make
2. eye
3. big
1. White is not making an eye. The diagram below is an example of what I
would visualize for "make an eye". Here, White 1 makes a three-space
eye. But since it is then Black's turn, Black can kill him.
. . . . . . . . . .
. . . . . . . . . . X Black
. . X X X X X X X . 0 White
. . X O O 1 O O X . 1 = White
. . X O . . . O X .
Instead, it should perhaps have been "White 5 and 7 give Black a (single
killable) eye." Readers should not be required to puzzle out the
inverted meaning of the words by understanding the diagram.
2. Slightly better would be "White 5 and 7 make a three-point nakade",
but since the nakade arises in the future, how about "White 5 and 7 lead
to the position becoming a three-point nakade." However, every instance
of nakade in the book is incorrectly substituted by "big eye". Although
all three-point eye-spaces can be killed by nakade, but this is not true
of all four- and five-point eye-spaces. Yet the same expression is still
used with no hint that the eye given to the opponent is killable. See
for example, vol. 2, page 173.
3. A big eye is conventionally defined as four points or larger.
Therefore, a three-space eye is a small eye. This distinction is
essential in order to understand semeai, especially in applying the
proverb "big eye versus a smaller eye" to see who the inside liberties
belong to. The incorrect definition of nakade as "a big eye" incorrectly
uses the adjective big to mean monolithic or single undivided eye-space.
David Sigaty
the
> > sentence, it is not using the term nakade in reference to the
subsequent play
> > by white - the main meaning - but rather the result after black 2 -
the usage
> > more commonly carried over into English?
>
>
> If I say, "This is a nakade position," I am using a noun (nakade) to
modify another noun (position). I do not mean that the position is
itself nakade, but that in that position a nakade is correct play. With
the same meaning, I may also say, "This position is nakade." Similarly,
in American football I may say, "Third and fifteen is a pass," meaning,
not that third down with fifteen yards to go for first down is the same
thing as throwing the ball, but that in that situation, a pass is almost
always the right play. Or in contract bridge I may say, "that hand is a
double," meaning that I think that double is the right call with that
hand, not that the cards held constitute a kind of call. Or in Hold'em
poker I may say, "AQ on the button is a raise," meaning that if I hold
those cards as dealer, I think that the correct play is to raise the
pot.
>
> I am saying that Otake is using language in essentially the same way.
When he says that the shape is 5-moku nakade, he means that in that
shape, the correct play for one player (White in this case) is a 5-moku
nakade. In that position, there are 5 nakade. Only one is correct, and
that is the one called 5-moku nakade. There is a relation between the
shape and the correct play, of course. But the shape is not the play.
>
> Best,
>
> Bill
>
Bill,
Thanks for a very clear explanation.
Jan van der Steen
>> For a nice list of go terms, including "nakade", which it
>> defines as "dead shape",
> Oy!
> And in chess, I suppose that "castling" is another name for a
> rook, and that a zwischenzug is a diversionary tactic. And in
> bridge, that a squeeze is a bad discard. And in poker, that a
> bluff is a weak hand.
This is the second time the Internet Go Dictionary *) is quoted
wrongly, not to say that the definition for "nakade" in there
is entirely correct though:
Nakade
------
Large shape that can be reduced to one eye leaving the
surrounding group dead
*) http://www.cwi.nl/people/jansteen/intergo/index.html
Jan van der Steen
--
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
Jan van der Steen Jan.van....@cwi.nl
Centre for Mathematics and Computer Science (CWI)
The World Wide Web "http://www.cwi.nl/~jansteen/"
Milton N. Bradley
For what it's worth, The Ishi Press "Go: International Handbook and
Dictionary, Summer 1970", gives the following definition:
"nakade (lit. 'central placement'): the placing of stones inside a group
to reduce the shape to one eye".
Milt
--
"Better to light one small candle than to curse the darkness."
Visit my web page at http://www.villagenet.com/~bradleym
Eric Osman
Yes, I totally agree that some of yutopian's books ended up
with very awkward-sounding english.
I in fact reviewed the rooster book (I forget what it eventually
got called).
The book kept using the term
equivalent options
instead of
miai
even though my review comments tried to convince them to keep the term
maia.
Their reasoning was that to be "fair" they tried not to use
any japanese terms.
I tried to convince them that "equivalent options" and "miai" are
not equivalent options !
Points A and B are miai if we agree that if white takes A, black will
take B, and vice versa. but that does *not* make them equivalent options.
Consider, for example (this is a 2x11 board!) :
O O O O X X X X X X X
. O . O . . X . . . X
A B
We would say A and B are miai so X is alive. But they're definitely NOT
equivalent options. If O plays A and X plays B, O WINS by 1/2 point komi.
But if O plays B and X plays A, O LOSES by 2 1/2 .
So A and B are NOT equivalent options even though they are miai.
Thanks. /Eric
Dr. Ruthless
"Milton N. Bradley" <brad...@villagenet.com> wrote:
> All:
>
> For what it's worth, The Ishi Press "Go: International Handbook and
> Dictionary, Summer 1970", gives the following definition:
>
> "nakade (lit. 'central placement'): the placing of stones inside a group
> to reduce the shape to one eye".
>
> Milt
>
Glad to see somebody got it (almost) right.
"Naka" means "central" or "inside"; "de" or "te" means "move". In the
case of "nakade", the appropriate literal translation should be "tesuji
inside" a group. "Nakade" is a MOVE inside an area seemingly secure but
liable to be reduced to one eye; or it could mean a move that starts
building a live group inside opponent's territory.
Nakade is a MOVE, not a GROUP'S SHAPE.
Dr. Ruthless