Blue night is the dark mystery within, the journey into self, that place to which you can always retreat to garner the gifts of your process subjectively. You are being asked to enter into and explore your process subjectively. Blue Night is the immense field of potential found in the depths of human emotion and feeling. The touch of Blue Night is like the moment you crawl into bed and feel yourself surrounded by warmth, darkness and peace.
Blue Night's abyss holds the potent evolutionary playing field of all possibility. Here, as in the aboriginal dreamtime, there are no distinctions between then and now, real or imagined, dream or dreamer. In this expanded field, all things are not only possible but are constantly in the process of creation. In the framework of dreamtime, limiting constructs of "ordinary reality" such as time, space, and linear causality are freed into an expanded system, with unlimited access to ALL realities.
Dreamtime holds powerful opportunities. It is a field where potential, past, and future are held in the same matrix as the present moment. If such a construct is foreign to you, stretch your mind and entertain the possibility that you could help to dream a different reality into being. Enter into the mystery where reality is actually created.
In becoming a conscious dreamer, you can assist in literally creating a new reality for yourself, as well as constributing to the larger dream that is emerging. By focusing on this creation, your thoughts and intentions are projected at superluminal speeds across the crystal grid network that encompasses universes. This energetic field seeds, supports, and empowers the creation of an unfolding reality.
At a certain point, when a critical threshold of energy has been focused on a clear intent such as world peace, the underlying constructs of reality shift and a new reality begins filtering into human experience. Make no mistake: great change is seeded by conscious dreamers who understand and know that they are co-creating the larger dream.
Among other things, the dreamfield will bring to the surface your psychological polarities and core issues. These are the belief constructs you learn from society and experience, such as likes and dislikes, values and attitudes. You naturally attract the situation that promises integration, but through conditioning and habitual behaviour, you may choose to compensate, staying in a fixed pattern to protect your position. This choice will create only momentary relief, because the issues will keep being drawn back to be integrated. Thus, you may often find whatever is blocked or hidden manifesting into your consciousness through a dream, a body symptom, or a relationship. Often you may resist the new and the unknown. You may avoid going over your "growth edge", because it may be asking for a shift in your underlying belief structures. Yet profound growth is possible through working with this charged material. Through following it into the darkness, you bring into the dreamfield the light that will carry you to wholeness and fulfillment.
In working with the growth edge in your dreamfield, often it is important to catalyze enough energy to free the stuckness and fixed patterns. By following or amplifying the feeling, your increased awareness will lead to the root of the issue thas has been separated from consciousness. Hidden within the unused channels of your perception are clues to the mystery that will integrate and release the restrictive pattern.
A meditation for Blue Night is, "I am the darkness that is the light and the stillness that is the dancing." This meditation perfectly describes the paradoxical energy of Blue Night, the place of darkness from which all light emanates, the no-form abyss that contains all possibility. In finding this still point of Blue Night, you can access any expression of the light. The energy of Blue Night simply asks you to be still, to allow that expression to take shape from the darkness. From the darkness of Blue Night emerges the Essence Self. Sit in stillness, embracing the journey of insight and integration.
The colour of Blue Night is black, which represents the womb of the larger self, the receptive condition necessary to receive the light fully. Black is also an access route to the wisdom of the unconscious, the mystery of the abyss where you can tap into the collective dreamfield for insight and creative ideas. Blue Night also includes the shades of gray, symbolic of the merging of light with the darkness. If you wish to work with the energy of Blue Night, visualize black.
Blue Eagle is your Higher Self & Guide.
Blue Eagle reminds you to step powerfully into your commitment as a planetary server! Your assignment includes whatever furthers your personal evolution and the evolution of global mind. You are an awakener, a transformer, an empowered gloal visionary. In your vision, you have compassion for others, and your decisions are made in the light of global consciousness. Ask yourself how you might experience compassion toward self, the Earth, and others. Be guided towards types of work, relationships, places to live, and projects that will benefit the Earth and her creatures. Allow your spirit to expand. Soar on your spreading wings and planetary perspective. Affirm: "Through your, Gaia, I am also transformed! I am awakening as the return of divine love and light. We are all one. Gaia, as you awaken, I heal myself. As I awaken, you are healed, and together our petals open ecstatically to the new Sun of Flowers."
It is up to each one of us to hold a positive vision and affirmation, for the means by which this miracle will occur is through changes in the one affecting the greater whole.
Imagine the profound impact your loving thoughts have on planetary mind. You do make a difference! As you connect individually with the larger crystal grid network, your power is multiplied exponentially. This galactic grid is also known as the Mayan cobweb.
The greatest gift you can offer to the planet is to simply be the love. Believe in yourself and your dreams and visions! Remember your special gifts, your path of service on Earth, your promise to serve the light. Everything you are connects to the greater whole. You are starseeded! You have the vision of the eagle. Believe in your dreams. You are the hope and the vision revealed.
White Mirror is your Subconscious Self and Hidden Helper.
White Mirror represents the Hall of Mirrors, where you can face your own reflection and see the truth about yourself. As a mirror, White Mirror merely reflects what is, whether truth, beauty or illusion. Here you can face unfinished business, the dissonance of difficulties, or charged issues that would keep you from the full expression of your Divinity. Become aware of any illusions or distortions within yourself; your clarity of perception will transform them. Take a moment to see yourself as you actually are, shadow and all, freed from the maze of mental illusion.
Sometimes you may find yourself reacting rather than freely responding to a situation or person. If you have charged reactions such as frustration, anger, fear, judgement or jealousy, look at how you might be projecting these issues onto someone else. The world is the mirror for you to truly see. Any strong reaction to a person or event signals an issue to work on in yourself. Be willing to examine and utilize what you see in your mirrors, in order to transform dysfunctional belief systems, negative thoughtforms, and fixed patterns.
In the Hall of Mirrors there is no good or bad, no right or wrong - there is only the reflection of what is. As you learn to see yourself, you begin to see your emotional reactions as signs indicating where to focus your awareness for growth.
On this quest, come prepared to face White Mirror's sword of truth and purification. The wisdom of this sword penetrates, exposes, and ultimately heals your illusions. Discrimination is tempered with love cleanly cuts away everything that does not serve your evolution. To the Maya, White Mirror is the flint that hones your sword.
The greatest gift of the sword is the power of forgiveness. A profound freedom emerges from forgiveness, the releasing of the illusion of cause and effect. Use the great gifts offered in this blad of truth and light to forgive and release anything you may judge or see as imperfect.
You are already an Enlightened Being!
The colour for White Mirror is reflective silver. Silver symbolizes the lunar intelligence of intuition and receptiveness, the mirrored illusions of duality and multiplicity. In the larger pattern, all thigns are reflections of the greater reality. Silver offers a glimpse of the Great Mystery, the reflection of things as they really are. To access the qualities and teachings of White Mirror, utilize silver.
White Mirror's are able to clearly reflect others back to themselves once their own mirror is clear.
Red Skywalker represents your Challenge and Gift. With maturity and awareness this challenge will turn into a Focus. This is what you desire to learn in this lifetime.
In the shadow of Red Skywalker is the tendency to hold onto the limited reference points of your beliefs, patterns, and identities. Your reality is maintained by these beliefs, which may be viewed as set reference points. When your reference points change, so does your reality. As you explore unfamiliar territory, your points of reference become open and fluid. This can be perceived either as frightening or exciting. Experiencing fluid reference points can feel like floating weightless in space. However, you also feel delight as you discover the depth of your changed perspective, knowing that you have been touched by the Divine.
In the shadow of Red Skywalker, you may also feel anxious, uncomfortable, or fearful of moving into the unknown. You may have issues of looking at the shadow of self. The word courage in French means being 'at heart.' Find the courage to move through what seems difficult or uncomfortable. Take heart, skywalker! Red Skywalker offers a loving hand to lead you into the unknown. Being anchored in a secure sense of self and Source creates a lifeline for the journey.
Another shadow of Red Skywalker may be the desire to withdraw from the world. Once you have been deeply touched by the light, you may yearn for the experience again. You may feel difficulty coping with the "abrasive edges" of daily life created by old perceptions. Do you feel like a hermit? Perhaps you find yourself spending much of your time in isolation, withdrawing into meditative, intellectual, artistic, or fantasy pursuits. If so, look deeply at your hidden needs, the root source underlying your issues or reactions.
Learn to create a balance between solitude and service. Discover and satisfy your true spiritual desires, and create joy in your everyday work and play. Help to bring the light of heaven into the world. If you feel discouraged, draw even more light into yourself. An angelic messenger offers you unconditional strength, love, and courage. If you feel isolated, walk into service, sharing the compassion of your light and love.
The transformation offered in this shadow has to do with balance. Take time in solitude for your own inner work and spiritual nurturance, and fulfill the commitment to outer work and service. Create a balance between being in the world and being a skywalker.
Yellow Warrior is your Compliment - something that comes naturally to you.
Yellow Warrior, the galactic guide, is a mystic ferryman on the return path to the stars; allow Yellow Warrior's staff to ferry you to the spiraling vortex of cosmic consciousness. Yellow Warrior is the grace of the descent of the dove. Embody the mystic gift of trust in direct guidance. Through trust, you journey to the place of 'no time' and limitless light. There you will undergo the transformations to embody solar heart and mind.
Yellow Warrior is a conduit for cosmic communication, offering access to the universal web of consciousness. This is the web of the Mayan mystic spider that weaves intergalactic threads, the conduit of interconnected consciousness. Yellow Warrior is the spider in the web, the grid connection for divine communication. Receive these ripples of knowing from Yellow Warrior's web through the central axis in your spine, your staff. Accept this gift of knowing in grace, as you would receive the morning light by turning your face to the Sun. Grace is an unexpected touch, a blessing given in love, a natural gift from the universe. Use the power of love like an electrical current to serve the light. Open fully to feel and receive it!
The number for Yellow Warrior is sixteen, the number of unity with the cosmic foundation of resonant evolution. As you embody the ferryman's staff, you become anchored in your connection to cosmic consciousness. Holding within you the foundational steps of the trinity, you carry the "Christed one" into the world. As a living mystic, you are the conduit of the spiraling galaxies that creates a union with cosmic consciousness. Sixteen may also be seen as the beginning of another octave - a higher octave characterized by organic balance and the new Earth under your feet.
Yellow Warrior's colours are indigo and gold, combining the limitlessness of the night sky with the freedom of the daytime Sun. If you desire to access grace and trust, focus on these colours.
Your Tone is Tone 12 - Crystal
Stability in expansion, greater constellation, union of polarity, framework of connectedness.
Twelve is the ray of Complex Stability, the foundation of self and the foundation of essence in union with the mystical truth of polarity. All things are interwoven in the dance of yin and yang. All parts make up a greater whole. Draw on the wisdom, strength, and stability you derive as a member of the greater coucil. No matter what your experience, there is a complex stability in the larger pattern that invites you to feel stable as you expand and evolve. Living in a world of polarities, yet knowing that all parts are one in the unified whole, creates the underlying framework of connectedness. The hologram of polarity is simply the structure, the loom upon which worlds and realities are woven.
Stability is a matter of perception. Find where you can openly flow and expand in the midst of seeming complexity. Utilize the relationships created by polarity to explore and expand any self-limiting construct. Open your perceptions. Through you, the mysterious balance of the cosmos is fulfilled.
These excerpts were taken from the book, "The Mayan Oracle - Return Path to the Stars" by Ariel Spilsbury & Michael Bryner - Click here to email Ariel and purchase a signed copy!
Okay - I think I got it.
Set of all subsets (power set*) is exactly the right way to think about this. The state space is the set of all states.
1) Definition of state:
"A state contains all of the information necessary to predict the effects of an action and to determine if it is a goal state." (http://artint.info/html/ArtInt_48.html)
The actions in this scenario are simple: They are the possible movements a bug could make.
2) Definition of solution:
Solutions are sequences of actions that lead to the goal test being passed.
If we only permitted states, one for each possible starting position the bug was in, then we would have a state space that gave solutions that were valid only for discrete starting positions. But, the solution must be valid regardless of the initial state of the bug. This means the solution must work for scenarios in which the bug could occupy any of the available squares.
In other words, the solutions must be valid for each and every subset (combination) of possible starting spaces, which yields the power set of , which is .
Why? Because solutions that are valid for a given start state may not be valid for all other start states. And the problem requires us to find solutions that are valid for all start states. This is also why the state space is much larger than even though in reality our bug only occupies of the positions upon initialization. Just because a solution (sequence of moves) works when the bug starts at doesn't mean that solution (sequence of moves) will also work for the bug starting at .
Bonus Question: Why isn't the state space just 1, the full set where each of the squares 'has' a bug (and bugs are permitted to move on top of each other)?
I was tempted to say that just because a sequence of moves gives a goal state when the bug can start at all of the possible positions, that doesn't mean that same sequence of moves gives a goal state when the bug starts at or at or etc. possible positions. But by definition it must (a solution over all starting points must be a solution over every finite subset of starting points).
So I think the reason you evaluate starting states other than "all boxes have a bug" is because the solution generated by evaluating only that state may not be optimal. And in fact this interpretation is borne out by what the homework gives as admissible heuristics for this problem:
The maximum of Manhattan distances to the goal from each possible location the insect could be in.
The minimum of Manhattan distances to the goal from each possible location the insect could be in.
The case where we just have one starting state with bugs on all the boxes (with the magic ability to be on top of each other) is the relaxed problem we use to define our heuristic. Again by definition of admissibility, since the heuristic must not overestimate the true (arc) cost of an action, and since arc cost is given by Manhattan distances, both the heuristics above are admissible. (The maximum case is admissible because each possible location for the bug is, in fact, possible - thus the max cost is possible).
*If you don't know what power set means, all you need to know is that the power set is the set of all subsets of a given set. It is given by .
In other words, if I have a set of three balls and I want to know how many different subsets I have, I can calculate it as follows. A subset either has the element in it (1), or it doesn't (0). So would be the subset of only the green ball, would be the subset of all the balls (yes, technically this is a subset) and would be the subset of none of the balls (again, technically a subset). So we see that the number of all subsets is . Or in our problem, .