I must begin this article with a disclaimer. There have been entire books written on each of these ancient symbols, and I cannot presume to include all of the information, or all of the esoteric theories, in these few paragraphs. I propose here to discuss the one theme which they all share in common: each of these figures is a three-tiered representation of the levels of Creation.

1)  The first figure is sometimes called the Star of David, but it is not exclusively Jewish; you will see it carved in Hindu temples and used by Rosicrucian alchemists. In actual fact it is not a "star" at all, but two interlacing triangles, one pointing up (symbolizing human aspirations toward the Divine) and the other pointing down (symbolizing the Divine's willingness to meet humankind half way). The space where they intersect indicates the creation of a third state: the moment when Divine Consciousness manifests in human flesh. This is the state of Grace. It is Enlightenment. It is Samadhi.

 The sacred triangles represent the union of heaven and earth, spirit and matter. They embody the metaphysical principle, As Above, So Below.

 If the atomic "stuff" of Creation was different or unique at each level, there could be no communication or exchange of energies between higher and lower. But one of the most important esoteric teachings is that energy is the same throughout all the realms of Being; the only difference is in how fast that energy vibrates. Slower vibration makes it heavy and brings it down into physical form. Faster vibration makes it lighter, bringing it up into gaseous states; and the fastest vibration of all elevates it into pure Spirit. The form may change, but the energy doesn't. And energy is never lost.

 The conservation of energy is a law of Physics; but it was intuited hundreds of years ago by European alchemists. And the concept existed before that, with Greek philosophers and Indian yogis.

 2)  The Vesica Piscis shares much of the same symbolism, but in place of two triangles it interlaces two circles. As with the triangles, the bottom circle represents the human realm and the upper circle symbolizes the Divine; and the sacred space where they intersect - forming an oval with pointed ends - creates the third state of Divine manifestation in human affairs. This figure, too, represents the union of heaven and earth, spirit and matter. It, too, embodies the metaphysical principle, As Above, So Below. 

 As its name suggests, the oval shape is reminiscent of a fish. The Christian fish symbols which are often displayed on cars are derived from the Vesica Piscis, though it is doubtful whether most drivers of those cars are aware of the fact. They probably do know that the fish was an early secret code for Christians, who were hunted by the authorities and went about in fear for their lives; for the Greek word for "fish" - ICHTHUS - is an acronym containing the first letters of the phrase, "Jesus Christ, God's Son, Savior."

But the Vesica Piscis has a more hidden esoteric significance, which the early Church understood very well but modern Christians have all but forgotten. This significance is seen when the symbol is turned on its side. Now the central oval shape is vertical, reminiscent of the female vulva - and the crescents on either side suggest the waning and waxing moon. It is Goddess symbology! Paintings of Christ depicted him standing inside the central oval (called a mandorla), as a constant reminder to the viewer that Jesus was conceived in, and born from, a Mother's womb. Although the new religion continued the Hebraic domination of masculine theology, the Goddess was not completely forgotten. The essential role which she had always played was now delegated to the Virgin Mary. 

3)  The World Tree differs considerably in its iconography from the sacred triangles and the Vesica Piscis; yet it, too, depicts three levels of Creation. The Tree's branches contain the realm of the Gods; its roots contain the Underworld; the connecting trunk is the realm of humankind - we know it as Middle Earth - joining the branches and roots together. It is understood that both the Divine realm and the Lower Depths can manifest in the affairs of Men. (Few would argue with that notion, as history affords plenty of instances in which men have behaved like both gods and demons!)

So, again, we have a symbol which represents the coming together of heaven and earth, spirit and matter, and embodies the metaphysical principle, As Above, So Below. While diverse cultures developed their own ways of expressing this principle, all of these models declare that Reality - both cosmic and mundane - manifests in terms of the number Three. The commonality of this revelation over thousands of years and thousands of miles is extraordinary.

To be sure, the geometric philosophers did not concern themselves with levels below our earthly existence; they were only interested in the relationship between God and Man. Also, they proposed that the confluence of the two opposite levels - Divine and human - brought about the creation of the third. In the World Tree, however, the three realms are always existent from the beginning, as parts of the whole.

Another distinction is in the divergent ways in which Mathematicians and Naturalists view the world. Triangles and circles are geometric extrapolations of what the human brain observes in Nature. Trees, on the other hand, are Nature personified. They have been in our psyches ever since the beginning.

The Old Testament speaks of two other trees, the Tree of Life and the Tree of the Knowledge of Good and Evil. Readers of J.R.R. Tolkien know the deep significance he attached to trees; for him they became the very embodiment of what we now call the struggle to save the Environment. James Cameron brilliantly extended both the environmental and the spiritual issues into Avatar, in which the gargantuan Home Tree actually contains the soul energies of all of the Na'vis' ancestors. 

Whichever of these human constructions appeals most to you - whether you are a Germanic heathen, a metaphysical alchemist or a devotee of the Chalice Well at Glastonbury - take comfort in knowing that more souls are in like-minded accord with you, at least within the privacy of their own minds, than you may have ever suspected. You are not alone, my friend! It is only words that keep us apart.