The Shiva lingam belongs to the class of "natural" Hindu symbols, which are usually mathematical in form. Such symbols are called "natural" because they not only represent a reality, but to some extent are the actual vehicles of the power within that reality. The lingam is an ellipsoid. It symbolizes Shiva-Shakti; that is, the primary polarity principle of positive and negative forces. On this principle of opposites the whole universe is founded.
Why is an ellipsoid used to symbolize the polarity principle? The ultimate reality, the Absolute or Brahman or God, or whatever we care to term it, has no polarity, no pairs of opposites: all principles are balanced and harmonized within it. Therefore the ultimate reality is represented by the most perfect mathematical figure, the sphere.
If the center or the one focal point of the sphere divided itself into two, we get the ellipsoid. So this figure gives a symbolic representation of the primary pair of opposites out of the original harmonious one. And from this first duality, comes all manifestation, all creation, all the multiplicity of things in the universe. The lingam is therefore the basic form lying at the root of all creation, as "Aum" is the basic sound.
In Hindu terms, from the one Bramha emerges Shiva-Shakti, the father and mother of all that is. In this connection, Shiva is not only an aspect of the Triune Godhead - the destruction-regeneration aspect - he is also the highest God, the father of all gods, the cosmic logos.
Like all the gods of Hindu thought, Shiva has his consort, Shakti, or female aspect. And whereas the male or positive aspect represents consciousness, the female or negative aspect symbolizes power. Both are necessary for creation or manifestation in the planes of matter.
It is significant too, that the ellipsoidal or lingam form, which symbolizes the Shiva-Shakti principle, plays a fundamental part in the structure and working of the universe. It lies, for instance, at the base of all matter within the atom, where electrons move in elliptical courses around the central nucleus. Again, at the solar level, we find the planets describing not circular, but elliptical orbits around the sun.
The lingam is also considered the symbol of a phallus, yet another representation of the god Shiva's dual nature. Worshipped as the most vivid symbol of sexual energy, the lingam as a phallus symbol remains forever erect because it swells with potential creation which never sheds, but always retains his semen. Even before the full emergence of the Tantric movement which uses sexual imagery to represent the union of opposites, the lingam was depicted arising from the yoni, a symbol of the vulva or of female energy. The lingam and the yoni denote the union of male and female, heaven and earth, and are a powerful representation of creativity and the totality of existence.
The lingam as a manifestation of the Shiva-Shakti principle is demonstrated in all the pairs of opposites, and nothing can exist in this phenomenal universe without its opposite or contrast. In fact, the concept of opposites is basic to our very thinking at this level of consciousness; we cannot know light without darkness, and so forth.
The word lingam, in Sanskrit, simply means a symbol or emblem, which in itself suggests that it is a basic, primary symbol. In fact, representing in concrete form the fundamental principle and power of creation, it is considered the highest object of worship on the physical plane, and as it has a true mathematical relationship to the reality it symbolizes, it can bring the worshippers en rapport with that reality. In the Uttara Gita, Lord Krishna says that lingam is from the word lina which means to unite. This is because the lingam makes possible the union of the lower self with the higher self and with God - with Jivatma and Paramatma.
Nevertheless, this sacred ellipsoid of stone or metal does have the occult property of creating a channel between man and the divine power on the inner plane it represents. Through such a channel, many blessings, benefits and auspicious conditions will flow to the worshippers. But the mystic link must be established by someone with the necessary understanding of the principles, and knowledge of the forms of the ritual required. It is essential for regular and specific poojas, or ritualistic worship, to be performed for such a sacred symbol.