Saraswati is the Goddess of knowledge and learning. She sometimes appears alone on this chakra [Swadhisthan], and Her image appears to convey to human beings the real meaning of all knowledge. In one hand She often holds a veena symbolizing that the one who has knowledge (Gyani) must be a person who knows the music of the Divine. Indian classical music is based on the original Primordial Sound (Brahma Nada). So at this chakra, the Goddess appears with a veena to suggest that if you are a scholar you must also have the knowledge of music. Moreover a scholar should not be a dry personality but someone who enjoys the beauties of creativity (Madhurya).
In another hand She holds a rosary suggesting that a seeker after knowledge has to be a devotee of God and appreciate His eternal love. The seeker therefore must be well-versed in the devotional aspect of learning. The main purpose of his studies must be the search for eternal truth. That is the mark of a true bhakti: one who seeks wisdom and not just superficial knowledge. In a third hand the Goddess Saraswati carries books of knowledge to suggest that the scholar must create books out of the eternal truths discovered during his pursuit of knowledge.
Saraswati wears a white sari with a red border edged in goldwork. Her conveyance (Vahana) is a peacock (Mayura), the national bird of India. It is a fabulous bird with magnificent plumage. The choice of a peacock suggests that a scholar must be gifted with a complete sense of aesthetics. When clouds appear in the sky peacocks start to dance which is a peculiar habit exhibited by this bird. It depicts the poet or the dancer who sings or dances with joy when it sees the clouds. It interprets this as the news of future blessings, just like farmers feel joy at the sight of impending rain. Peacocks and farmers are united in collective consciousness at this manifestation of nature. The peacock is just like the scholar who sees God's grace appearing as clouds of joy in the sky, and dances with joy after seeing this vision of his yearning in the sky. The symbol of a peacock further suggests that like the peacock a scholar should be a visionary. It is the female peacock who dances not the male. Female peacocks are disgusted when males fight among themselves, and it falls to her to choose the victor in such a fight. This suggests that scholars are not to fight over dogmas as this is the action of undignified people.
H.H.Shri Mataji Nirmala Devi, [the unpublished first book]