When interpreting a hexagram I sometimes replace the trigrams with planets (including the moon).
Although the "fit" is of course not perfect, this trick often sheds new light on possible meanings of a hexagram.
I will give a few examples later on.

First the replacement scheme that I use:

* Sun: no trigram
(The sun represents undifferentiated life energy; when we are "talking" trigrams we are on the level of differentiated life. I read the "sunny" trigram fire as jupiter)

* Moon: water

* Mercury: wood/wind
(I think this trigram has more affinity with the introverted virgo-mercury than with the more extroverted gemini-mercury)

* Venus: lake

* Mars: thunder

* Jupiter: fire
(Jupiter is the biggest planet in the solar system; a Dutch astrologer (Ram) once wrote that jupiter acts as a mediator for the life energy (prana) that comes from the sun)

* Saturn: mountain
(Mountain feels lighter than the rather "heavy" saturn of astrology. But astrologers perhaps tend to over-stress the heavy side of saturn)

* Uranus: heaven

* Neptune: earth

* Pluto: no trigram
(Pluto is beyond life as we know it)


A few examples

- Hexagram 7, the army
Moon + neptune, the personal soul and the collective or universal soul. Neptune is "on top", dominant (well, that's one way to read it).
With this combination, we could expect that the personal is invaded by, or willingly surrenders to collective or universal influences.
The result would be a loss of individuality, depersonalization.
This is indeed something that happens in an army, or more generally in a situation of war. Individuals don't count ...
But there are many other possibilities, ranging from total chaos (for example a crowd that goes mad, pathological depersonalization, and so on) to the mystical at the other side of the spectrum (surrender to the universal)

- Hexagram 8, unity
Again moon + neptune, but now the moon is on top.
It could indicate an individual that personifies (or acts as a personal channel for) the collective or the universal.
Not an easy job ...
The text talks about the need to re-examine oneself, as if the writers wanted to say: are you really up to this?
The reference to divination perhaps means: look for signs that can guide you.
The commentary on the fifth line is also interesting. I think it means: don't try to own or control this completely, you can't, it is really too big for you.


Perhaps this is enough for now.
I will add more examples later.


Martin

More examples ...

- hexagram 55
Jupiter + mars with mars on top.
Mars and Jupiter are both energy planets. The energy of mars is physical-emotional, jupiter is more subtle, a higher frequency, emotional-mental.
Thoughts on the level of jupiter are colored by emotion, they are beliefs, convictions.
One way to read 55 would be: conviction (jupiter) into action (mars).
In other words, action in accordance with what one believes to be right or true.
"there is no occasion to be anxious" and "let him be as the sun at noon" (from the Legge
translation) seem to say:
Do it, express yourself, regardless of the consequences, now is the moment, it's now or never.

- hexagram 21
Jupiter + mars with jupiter on top.
The other way round. The mars-energy cannot express itself directly. It has to go upward and inward to the more subtle jupiter level. Sublimation is called for and frustration is not impossible.
The text suggests that "legal constraints" might be necessary. Mars in prison!
Imagine a schoolboy who wants to play soccer, but he has to sit still and learn.
Or imagine that you want to make love to your lover, but she/he is not in the mood, she/he wants to talk ..


And a note ...

For the sake of clarity (and because I like to exaggerate) I sometimes interpret hexagrams on a rather high energy level, so to speak.
Hexagram 55, for example, doesn't necessarily imply that one has to become reckless, "regardless of the consequences".
The message (on a lower energy level) could also be: "live as you like to live" or "feel free to express yourself, don't worry too much about consequences"

Hi Martin,

I do not agree with your attribution of planets to trigrams.

I always tent to look at things from their own perspective. In this case we
should keep in mind that ancient Chinese knew about five planets, Mercury -
water star (shuixing), Venus - metal star (jinxing), Mars - fire star
(huoxing), Jupiter - wood star (muxing ) and Saturn - earth star
(tuxing), plus Sun - great yang (taiyang) and Moon - great yin (taiyin). Uranus, Neptune and Pluto are out of the question, as they were unknown
of. We could open an discussion about to which trigrams they should be
attributed, but I'll refrain of this.

According to their wuxing attribution we can connect them with relevant
trigrams. But we should also keep in mind two basic arrangements of the
trigrams, as well as their attributes they have in "Yijing".

Therefore the division would be (in Xiantian bagua):

1. Qian = Heaven, Sun
2. Dui = Venus
3. Li = Mars
4. Zhen = Great Laddle (Great Bear)
5. Xun = Jupiter
6. Kan = Mercury
7. Gen = Pole Star
8. Kun = Earth, Saturn

As "Yijing" is based on Houtian bagua, I would suggest following
arrangement:

1. Kan = Moon, Mercury, Great River (Dachuan) (Milky Way)
2. Kun = Saturn
3. Zhen = Northern Ladle (Beidou) or Great Dipper (Tiangangxing)
(part of Great Bear constellation)
4. Xun = Jupiter
5. (no trigram) = Earth (point of observation) - earth was not considered as
a planet
6. Qian = Heaven
7. Dui = Venus
8. Gen = Pole Star (Jixing or Tianhuang dadi), and
9. Li = Sun, Mars, meteors

I would not comment use of planets in hexagram interpretation as it's out of
scope of my interests and comprehension.

Boyler
www.hidden-city.net

Hi Robert,

It's true that the planets Uranus, Neptune and Pluto were probably unknown in ancient China, but that doesn't mean that the corresponding principles or qualities were unknown.
For example, from the viewpoint of (western) astrology we can say that Taoism is in many ways "neptunian" (receptive, fluid, embracing, mystical, and so on).
Confucianism, on the other hand, is more "saturnial" (more rigid, structured, judging, and so on).

The neptunian and saturnial qualities are there, we can recognize them, and I assume that the ancient Chinese also recognized them, although they didn't associate them with planets.
(In the case of Neptune that wasn't even possible, because they were - as far as we know - not aware of the existence of Neptune)
They saw those different qualities through other lenses or prisms, so to speak.
They used trigrams and hexagrams, among other things.

The "prisms" of trigrams and western astrology are rooted in very different traditions and cultures.
We cannot expect that they reveal exactly the same. As I wrote earlier: the "fit" is not perfect.
In some cases (the trigram wood and the planet mercury, for example) we can even say that it is far from perfect.

On the other hand, the basic principles or qualities of human life seem to be more or less independent of place and time. What we see through different lenses or prisms is not altogether that different.

Still, the question remains: what corresponds with what?
The scheme that I use sometimes sheds new light on the meaning of a hexagram, sometimes it doesn't.
I haven't tried your scheme yet, but I will look into it.

Thanks for your response.

Martin

I was interested in the comment that the Chinese were unaware of the outer planets in ancient times. In my own studies of ancient culture I have become aware of information like this that supposedly didn't exist , that at the time did exist but was considered 'secret' or was only taught to a few special students who also retained these secrets. For example in kabbalistic mysticism there were secrets that pertained to knowledge of the universe that is only now being understood. Kabbalistic 'secrets' included the age of the universe, approx 14-15 billion years. (The latest information based on the big bang theory is that the universe is approx 13-14 billion years old). The concept of multiple universes was another 'secret'.(This is now being discussed as probably correct). The kabbalists also discussed other universal races, the no. of stars in the galaxy etc. in quite an exacting way.
I suppose the point Im trying to make is that when western science or culture looks back at ancient culture they often see less of the real scope of knowledge that was available to the chosen few in these times. This is because 1. the information was secret and 2. because the methods used to obtain this type of information were also kept secret or not acceptable to western scientific minds.

I see in the above discussion also the 'holographic' theory coming into play. This theory says basically that all things are connected and that all things can be known through the study of one thing. For example by studying the foot or the ear we see the correlation of parts of the ear or foot to other parts of the body. So by studying astrology astromomy or the Yi we see the connections between them as we learn more. Connecting the planets to the trigrams hence is no different than connecting plants to trigrams or galaxies to trigrams. All knowledge gained leads to the ultimate knowledge of universal unity and interconnectedness. From this base all things can be known.

Yes, we often underestimate ancient cultures. Not only, I think, because the ancients kept part of their knowledge secret, but also because we tend to overestimate the achievements of our own culture.
We have all this technology, we know how to build airplanes, computers and so on.
Fine, great, but in other areas we are not at all that "advanced".

Even technologically the difference is perhaps not so big. Someone told me that the Romans knew how to build steam engines and that the old Chinese (I don't know when) had steam trains.
The Romans didn't develop their steam engines, because it was economically not interesting, slaves were cheaper ...
And the Chinese saw their steam trains merely as a curiosity!

Martin

Martin, I agree with you that we often underestimate ancient cultures. Hominid brains are seven times larger than other mammals of approximately our size. That evolutionary stage took place about 160,000 years ago. And yet, we modern humans only use 10% of that brainpower. What survival benefit did all that extra brain matter contribute to our species? Were the ancients able to use their brains in ways that are unknown to us now? If so, can we learn to regain those lost capabilities? I think the answer is yes.

I dont think it makes much sense to link Astrology with the I Ching. The Oracle is a work of profound Philosophy while Astrology is an unproven pseudo science. Of course, not everyone is overly concerned with making sense....

Ricky x

Astrology an unproven pseudo science?
What a delicious statement!
Perhaps I'll post it in an astrology forum ..

About making sense and that "work of profound philosophy", I don't remember any other book with so much nonsense in it.
The writers must have laughed their head off.

Martin

Ricky,

Astrology is like the I Ching - a metaphor founded on initial recursion of a dichotomy thus:

[1]earth/heaven (air)
[2]earth,water / fire, heaven (air)

At this point Astrology goes off into its own little world, mixing categories from different levels into 'one' - thus 8s become 12s etc etc The I Ching, rooted in the same development process, keeps going, maintaining the structure (and we see it reflect 12s as 2^12 ;-)). In the link below is identified the derivation of Astrology terms from recursion and the shift from 8s to 12s etc. (and dont forget the different types of Astrology)

Behind the labels used in any specialisation are feelings and it is to those feelings people respond and derive 'meaning'. Thus all 'esoteric' systems will be found to be of 'value' to the users since the meaning is in the feelings generated, not the labels - but people can confuse this, taking the label as the thing.

The 'problems' with Astrology have been with taking certain metaphors within astrology as 'real' - recognise the metaphors and Astrology can serve as a typology system just as the MBTI etc etc etc and understanding how our brain works allows for the 'restructuring' of Astrology!

The more 'approximate' the thinking the more the need to use IMPLICIT identifications to derive meaning. Thus the development of prediction systems using geometric formats - charts, card spreads, patterns in stones, tealeaves, etc etc etc. - we 'link dots' to IMPLY something.

As a species, the development of precision shifted our mappings to a more algebraic perspective and so into 'hard core', more parts oriented, Logic, Mathematics, and overall Science.

BUT these are still all metaphors, even with their precision, in that the language is a set of labels for the same feelings all specialisations share - the general set of qualities used by the species to derive meaning.

See the essay "The logic of the esoteric" .. http://pages.prodigy.net/lofting/esoter.html

See the IDM pages for the mapping of neurocognitive processes to consciousness and map making -

http://pages.prodigy.net/lofting/idm001.html

We cannot teach Astrology in high school etc due to its 'gaga-land' element, we could teach the I Ching and it is that that makes the I Ching more useful, more universal, than Astrology or Tarot or Rune - it is not as 'extreme' as other esoteric disciplines and its A/NOT-A format is attractive to the more 'science-oriented' individuals. (but better still, teach the reasons how/why esoteric systems have developed and so teach about our species nature, how we derive meaning, link labels, and create our own little worlds!)

If you applied hexagram 23 to Astrology etc you would end-up with something close to what the I Ching does ;-) - the problem is that Astrology being rooted in a few thousand years of belief not many would appreciate such a 'refinement' process. Better to keep going with I Ching, Logic, Mathematics etc, improve those and the over-metaphorised will become increasingly marginalised and even fade-away - evolution at work ;-) (but will take a LONG time ;-))

Note in modern times the need for precision means that the over-rich metaphor systems, such as Astrology, become too specialist and so too esoteric in terms and so a need to maintain the sense of 'waving of hands' and go 'wide', we intuitively recruit other systems and form hybrids - Astro-Tarot or Astro-Runes or Astro-I Ching or Tao-stones etc etc etc

The 'need' to do this reflects the lack in 'scientific' precision in esoteric disciplines and a focus on the labels, on linking labels to form new analogies/metaphors, rather than focus on the neurocognitive roots of these disciplines - which we have not been able to do until recent times and the data derived will take time to filter-in to society in general.

Evolution at the LOCAL level focuses on REPLACEMENT, be it through aggression (kill the others) or sex (flood with copies of self and so dilute the influence of others).

Evolution at the GENERAL level focuses on INTEGRATON, on keeping everything in that some context can come along where we need an 'Astrology' perspective or a 'I Ching' perspective or a 'Logic' perspective etc etc

Thus we keep everything and time will make some things 'fade away' OR refurbishment with new 'facts' can give something new 'life' ;-)

Chris.

Hi Chris,

A lot of what you say seems to be based on the belief that we understand how our brain works.
Do we?
The ideas, models and metaphors that we derive from computer science are interesting and may help
us to understand the workings of our brain or at least some aspects of it.
We will see how far we can get with them. Time will tell.
But how far are we at the moment, really?
I think we are mostly speculating, guessing, and that's fine, but ...
And even if the brain is somewhat like a computer on a neurological level, what about the mind? That's again another level.

Another point, are we heading toward more and more precision?
There seems to be a kind of optimum: beyond a certain point more precision may lead to a loss of meaning.
No, I am not talking quantum mechanics, I really don't want to get into that now ...
What I mean is, well, we need a certain amount of poetry and fuzzy metaphors in our lives, don't we?

Last but not least ..
From the viewpoint of astrological typology I would say that your approach is "mercury + uranus". Right?

Martin

Hi Martin, I think the following should cover your questions etc....

> Hi Chris,
>
> A lot of what you say seems to be based on the belief that
> we understand how our brain works.
> Do we?

Close enough to identify fundamental patterns in meaning derivation. You will need to go through the IDM material:

http://pages.prodigy.net/lofting/idm001.html

or just go through the reference material:

Abstracts (you will need some exposure the brain terms etc):
http://pages.prodigy.net/lofting/neurorefs.html (warning, BIG file at the moment (400Kb))
http://pages.prodigy.net/lofting/dencerefs.html
http://pages.prodigy.net/lofting/formrefs.html

some of the above abstracts have short annotations, my intent is to eventually have a paragraph or two for each abstract to aid in understanding the link to the IDM material.

General refs:
I Ching etc - http://pages.prodigy.net/lofting/irefs.html

Basic neuroscience/cogsci/semiotics/psych:
http://pages.prodigy.net/lofting/brefs.html

I have not updated the general refs for a while but the above is useful. There is also a small set of refs in the page "The Dance of the Neurons" - http://pages.prodigy.net/lofting/ideal.html

> The ideas, models and metaphors that we derive from computer
> science are interesting and may help
> us to understand the workings of our brain or at least some
> aspects of it.

Wrong way around ;-) My IDM work started from psychology, neurosciences and cognitive science. ;-) The common error is to say 'the brain is like a computer', no - a computer is like a limited brain ;-) subtle difference but important, thus material from neurosciences aid in developing computer science etc.

I think this is the problem with computer science, it can be too quick in abstractions and so miss influences of emotion on meaning derivation etc - but I am attempting to 'refine' that perspective re giving computer systems a sense of feeling - see http://pages.prodigy.net/lofting/emote.html (and there are more references at the end of that page)

> We will see how far we can get with them. Time will tell.
> But how far are we at the moment, really?
> I think we are mostly speculating, guessing,

The IDM material shows a pattern of meaning derivable from known brain dynamics. Those patterns correlate well with meanings asserted in such disciplines as I Ching, MBTI, Mathematics etc (the "logic of the esoteric" page also covers likely roots of categories used on Western Astrology etc)

> and that's
> fine, but ...
> And even if the brain is somewhat like a computer on a
> neurological level, what about the mind? That's again
> another level.

See the distinctions made in IDM re our species-nature vs our consciousness-nature, more so the diagram and text in the introduction page - http://pages.prodigy.net/lofting/idm002.html as well as the links. (e.g. a page that makes comparisons of brain/mind interpretations etc - http://pages.prodigy.net/lofting/light.html)

Overall the properties and methods of the brain that equate with local derivation of meanings have been recruited and abstracted at the mind level to be used as 'universals' - so we see the same patterns, the same feelings, different labels where the labels serve to tie the universal feelings with a local context. This act can lead to creating illusions and delusions (illusions we live by ;-)). Can be useful LOCALLY but comes up with problems when we try to generalise.

>
> Another point, are we heading toward more and more
> precision?

Our consciousness-nature is more precise than our species-nature and also able to relabel basic feelings and so create specialisations, same feelings but different labels due to context. The prime drive in Mathematics has been on the 'discretisation' of Mathematics - reduces things down to a 'dot' perspective - the dimensionless - that can then be built-up. Thus the geometric, with its dependencies on dimensions, is reduced to the dimensionless in the form of algebra that is THEN applied to the geometric and so 'refines' the geometry, makes it more realistic rather than too idealistic.

See the concept of the 'dimension of precision' in the IDM material. As the precision increases so all becomes a space filled with 'dots' and each 'dot' is connected to all others - IOW the dots are 'nodes' in an integrated whole - we are back at the 'beginning' ;-) This gets into issues of holographic concepts and phase-space concepts.

The realm of the qualitative is less precise than the quantitiative when dealing with 'dots'. The qualitative is more into 'fields' ;-) - intuitive areas. implicit identifications. Thus E=MC^2 is REALLY precise and to a physicist its implications are huge. To the untrained so a more qualitative communication is required - such as a two-hour+ documentry on Hiroshima/Nagasaki as the 'dark side' and the 'lighter side' as the ability to supply power for extended periods of time on small amount of fuel (e.g. nuclear powered aircraft carriers, spaceships etc).

Thus 'field' precision goes 'wide' to make links with a range of emotions etc that are in fact 'compressed' into E=MC^2, the 'dot' precision.

In the brain the 'clearest' images etc are 'left brained' reflecting an FM bias in processing data (like FM radio etc). The more 'right brained' is more AM oriented. See text in http://pages.prodigy.net/lofting/general.html - oldish but still valid re FM/AM biases.

> There seems to be a kind of optimum: beyond a certain point
> more precision may lead to a loss of meaning.

Sort of. The differences in brain/mind (and so species/consciousness) reflect 'reality' as at the level of our species-nature, a realm of integration with the environment over thousands of years and so interaction through WHOLES. The interaction is through instincts/habits and as such is unconscious, immediate.

Our consciousness seems to have emerged out of the ability to go past the species-nature WHOLES and into PARTS processing. The interactions of individual with reality 'slow down' a bit but are more precise and allow us to 'refine' the instincts/habits and exploit and 'take over' the context. From this, we as a conscious species, are creating our own reality - a hybrid of the ideals of our consciousness and the materialism of the universe. We then need to be wary as to which reality we are dealing with, that of the universe or that of our conscious species (or the interface of the two ;-)) and also recognise what came first - the material. IOW our consciousness has to be careful in that its freedom to imagine can threaten the realm of the material - we dont think of the consequences of our actions as in corrupting the planet etc etc.

The problem is that our consciousness, until recent times, has been unaware of these brain/mind differences such that our consciousness creates experiments based on PARTS perspectives and then gets 'confused' in interpretations when it comes across reality as WHOLE (IOW symmetric, non-local - the state vector).

Our species-nature, being integrated with reality will reflect symmetry concepts and so a non-local reality. In our brain this is reflected in parallel processing, A AND B. The development of consciousness takes us PAST the level of reality 'as is' into details, into PARTS, and a focus on A XOR B - the realm of the exclusive or and of the asymmetric, distortions, exaggerations.

See the page on consequences of sensory systems structure and our maps - http://pages.prodigy.net/lofting/vision.html

Also see the page covering the 'problem' with species-nature and consciousness-nature getting 'confused' - we experience paradox : http://pages.prodigy.net/lofting/paradox.html


> No, I am not talking quantum mechanics, I really don't want
> to get into that now ...

see above links ;-) Our interpretations of QM are based on 'confusion' ;-)

> What I mean is, well, we need a certain amount of poetry and
> fuzzy metaphors in our lives, don't we?
>

Sure. The mentioned dimension of precision has the realm of the unary at one 'end' - focus on symmetry and so no distinctions, no highs, no lows. At the other end is the realm of the binary - very A/NOT-A. Put in more energy at the A/NOT-A and things get 'unstable' and you enter the realm of complexity/chaos and so of emergence concepts. We can as such be over-precise and so become 'unstable'. BUT that process reflects the source of consciousness, of multiple minds in the one brain, of the instinct to 'transcend' (as such it is both creative but also linked to issues of psychosis)

High precision focus is A/NOT-A but also PARTS oriented when seen from the species-nature perspective. As such our consciousness is an exaggeration, a distortion, an 'excess' of our species-nature. Pour-in energy and out pops 'transcendences'.

As you move from the unary to the binary so patterns that are 'meaningful' develop. The initial patterns being rooted in the fibonacci sequence that develops into the binary sequence. You can 'stop' on any point on the dimension and develop 'vertically' - and so a discipline can develop on finding meaning in 'fibonacci' patterns as revealing 'god' (as found in the early days with their focus on 'spiritual geometry' where PHI was the closest you could get to 'god' etc). as precision has improved so we have moved past that point, to the point of the binary. but many can, and will, develop their everyday life on some other point on the dimension of precision. the LESS precise you are so the more identifications are made by implications, approximations, and are more prophetic in form rather than predictive where prophetic is "X will happen if you keep doing Y" allowing you to change X. Predictive is "X will happen [these days qualified with "with probability W"] regardless of what you try to do"

> Last but not least ..
> From the viewpoint of astrological typology I would say that
> your approach is "mercury + uranus". Right?

no idea. I am not interested in high-precision Astrology typology these days. Did a lot of work on it in the 70s/80s with Gauqualin's work etc and came up with identifying the basic patterns identified in IDM as being 'in' Astrology etc. For demonstrating the IDM material reasonably 'clearly' the I Ching, MBTI, and Mathematics is 'easier', more acceptable universally ;-)

In the MBTI my usual 'type' is XNTP. This correlates with an I Ching 'totem' of the trigram of Thunder. In the enneagram it is more type 5 (note my focus on issues of meaning etc). In the IDM template of Astrology I map to fire signs (and as it so happens in my birth chart am an Aries with Virgo rising - but gauqualin's work is more interesting ;-)) - Behind all of these specialisations is the generalisation of a focus on expansive binding.... I did do some rough associations a while ago with the I Ching and Tarot/QBL - see

http://www.ozemail.com.au/~ddiamond/taro.html

the associations reflect the tarot as having three levels - major aracana, and two levels of minor, court cards (map to 16 types) and the numbered cards.

Chris.

Hi Chris,

Your approach reminds me of a book that I once read, "The Language of the Lines" by Nigel Richmond.
I think he was more or less on the same track. His unconventional interpretations of the hexagrams are very interesting.

Another association (I'm not in high precision mode at the moment ):
According to classical mathematical logic we have A and ~A and ... that's it, nothing in-between.
But according to Brouwer's intuitionism "A or ~A" is not true. ~~A is another possibility and ~~A
doesn't imply A.
Perhaps intuitionism comes closer to the actual workings of our brains (and/or minds) than classical mathematics.

Martin

Hi Martin,

you wrote:

> According to classical mathematical logic we have A and ~A
> and ... that's it, nothing in-between.
> But according to Brouwer's intuitionism "A or ~A" is not
> true. ~~A is another possibility and ~~A
> doesn't imply A.
> Perhaps intuitionism comes closer to the actual workings of
> our brains (and/or minds) than classical mathematics.
>

The IDM work focuses on the structure of dichotomies as being (a) oppositional and (b) cooperative.

Thus A/NOT-A is not necessarily 1:1, more often 1:many with the '1' being an exaggeration out of the 'many' - this reflects bifurcation.

In the process of recursion we can identify different logics etc emerge:

[0] undifferentiated whole
[1] A / ~A [Propositional, use of ALL]
[2] AA, A~A / ~AA, ~A~A [predicate, use of ALL and SOME]
[3] AAA, AA~A .... / ...~A~AA, ~A~A~A [modal/indicative/fuzzy etc]

The IDM analysis of meaning derivation shows A/NOT-A as 1:1 reflecting exaggeration. With it comes a subjective time distortion such that thermodynamic time is converted to mechanistic time and so slowable, stoppable, reversible. This method is useful in identifying 'static' forms but has some problems when we generalise it to reflect the whole of the universe!

See my page on Logic as a blend of analytical and dialectical concepts of logic -

http://pages.prodigy.net/lofting/logic.html

In the I Ching, the analysis from a perspective of lines is A/NOT-A, 1:1, all or nothing. Move to digrams and you move to introducing SOME. Move to trigrams and you introduce a focus on both objects and relationships and move into modal (necessary/possible), fuzzy (probabilities), and indicative (true, false, imaginary, fantasy - see Spencer-Brown's work and the extensions of that work by Varela and Kaufmann)

The IDM "dimension of precision" favours an intuitive perspective being more 'species' oriented, a sudden 'stretching', and such notions as 'not this, not that' is a valid concept in the descriptions.

Our rigid A/NOT-A perspectives reflect the exaggerations of consciousness in making maps, we are, for the species, over-precise. Thus maps from consciousness can be very precise but cause paradox when we try to interpret from our species-nature. If we recognise this 'problem', stemming for the embodyment of mind, we can get on with things without being distracted by an anomoly caused by two mechanisms for interpretation sharing the same space. ;-)

Chris.

> But according to Brouwer's intuitionism "A or ~A" is not
> true. ~~A is another possibility and ~~A
> doesn't imply A.

Martin and Chris, I don't know why, but that reminds me of a funny story about an English grammar teacher. He was lecturing the class about double negatives. He said there were many languages, including English, in which a double negative equals a positive. But there is no language, he said, in which a double positive equals a negative. At that point a voice from the back of the room called out, "Yeah, right."

ok, first of all I dont know how to get that wavy line symbol on my PC, but I take it to mean 'not' in everyday language.
now, 'not not A' clearly does logically imply 'A'.
If any of you people has a concise explanation of how 'not not A' can not imply 'A' I'd love to see it.
chris, I love your work but could you please try to be more concise?
Ricky x

Joan, yeah, right, . Who was that guy in the back of the room? Lao Tzu?

Ricky, I will give an example:

"Proposition: There exists a natural number n that has a certain property P.
Proof: Suppose that such a natural number doesn't exist. I.e. suppose not P for all natural numbers n.
We will derive a contradiction:
<bla bla>
<ba bla bla>
.........
<bla bla>
1=2! contradiction!
This proves our proposition. QED."

This proof is based on "not not A implies A" (if not A is false A must be true) and it is acceptable in classical mathematics.
But intuitionists (and also the so called "constructivists") would say: wait a moment, where is this number n for which P is true? You have not given me a method to calculate that number. You say that it "exists", what do you mean? You will have to specify what you mean, otherwise I cannot accept your proposition.

This example is perhaps more constructivistic than intuitionistic, but I think it can give you a rough idea of what Brouwer had in mind.
If you want to know more, please Google ..

Martin

Ricky, I did a Google myself and found this link:

http://plato.stanford.edu/entries/brouwer/

Sums it up quite well, I think.

Martin

Hi Chris,

How does your "dialectical" logic relate to intuitionistic logic? Hard to say.
As far as I know intuitionism has no problem with "not (A and not A)" (your version of the law of the excluded middle) , but it does have a problem with "A or not A" and "not not A implies A"!



Martin

Joang - LOL! ;-)

Martin, Ricky,

The problem with Western perspectives is that they are high precision and so focused on differentiations.

In differentiation the precision is down to the ONE.

BUT our species-nature is more integrating and as such the precision issue is not reducable past a PAIR.

Thus a 'pure' integration state can be only described in a differentiating mode as 'not this, not that' in that (!) at the level of intergration there is no 'this' or 'that' since these terms reflects differentiations ;-)

This gets us into issues of topology, a qualitative description of reality where a finite space (such as the sensory cortex of the brain) is distorted rather than cut.

In the process of recursion the basic distinctions that work as a template is differentiation/integration.

WE can trace this root back from our consciousness to the beginnings of the universe re categories of 'fermions/bosons' - see the page

http://pages.prodigy.net/lofting/symmetry.html

Analytical logic is very precise down to the unit level, down to asserting a 'universal', but to do that requires a distortion of time, we make time mechanistic and so out pops a sense of the 'eternal' etc etc etc

Dialectial logic is not as precise when it comes down to 'dot' precision, time is thermodynamic and as such the logic contains the 'arrow of time' and so a focus on approximations.

The integration focus in dialectical logic means that the law of identity in analytical logic, the law of A=A is not valid, we deal with A != A, IOW there is always change. (see table of categories given in my previous email link to logic.html)

The combination of analytical and dialectical gives us a logic that 'fits' reality better than either analytical or dialectical.

The DYNAMICS of analytical, from a neurocognitive perspective, reflects the analytical as an exaggeration out of the dialectical.

This gets into the dynamics of exaggerating from the species-nature to consciousness and then 're-inserting' the now refines exaggeration back into the species-nature -

Wu Chi -> T'ai Chi -> yin/yang -> T'ai Chi -> Wu Chi.

The second T'ai Chi is not the same as the first in that it now has a label, refined analysis from the perspective of OUR species etc etc and we are creating our own reality - a hybrid everyday.

In the sense of description, it is possible to describe something from a differentiating perspective OR (!) an integrating perspective - and so from a sense of precision, the ONE=PAIR

Now go back to the IC and look at pairs ;-)

Chris.