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 par