Saraswathi is depicted as the embodiment of Knowledge. Knowledge is obtained in three ways.

1. Through listening: We hear and learn. Right from childhood from parents and saraswathyteachers we learn through listening. This continues even in professional training also. We also like to get the training in a meldoy form.  This is why Saraswathi holds the veena instrument which gives melodious sounds for listening. The greatest wealth according to Thruvalluvar is the is the wealth of listening.

Hearing is different from listening. Hearing is a sesnual activity. When we connect our mind to the information we hear, then it becomes listening. We may interpret anything we hear according to our personality, which may be true or not true (yad bhaavam tad bhavati (you perceive according to your mental framework). Our views are biased because they are based on our likes and dilikes, like the blind men.  Only a reference standard (wholistic view like Shasthras) can tell us whether our understanding synchronizes with the Universal Truth.

2. Reference: We always need reference books for two reasons. Reference material is to confirm our understanding and also for advancing more knowledge. This is why Saraswathi holds the Veda Shashtras (Science) in her hands. The Veda Shasthras is a reference of Unviersal Truth, which means true to all being at all times. 

3.  Practical Repeating and Contemplation: The knowledge has to be experienced which can happen only when it sink deep in our mind. So we need repetition. or practice (Abhyasa).  As children, we imbibed many things by constantly repeating what we learnred. This is the reason why Saraswathy constantly rotates  Roseary beads (Rudhraksha) in her hand to symbolize practical repetition and contemplatation.

White Sari: The three modes of getting knowledge depicted as Saraswathi image then symbolize the white color Sari she wears. When knowledge becomes Universally applicable it is pure which is depicted in white color. Unadultered, unquestionable is Pure.

Left foot down and Right foot folded: We have earlier discussed that right part of the body stimulates the left part of the brain which is the region of intelligence. The left part of the body stimulates the right part of the brain centers involved in emotions. 

Hands represents doing action, in other words, knietic Energy in action. Legs represents moving or transforming Energy. Saraswathi draws her right leg inwards to represent inner transformation using knowledge.  When there is inner transformation, our emotional mind is very relaxed. This is why Saraswathi's left leg is at ease. 

Swan or Hamsa is a bird with the unique quality of drinking only milk leaving out water. Similarly our mind should always drink happiness leaving out adultering unwanted watery thoughts surrounding us.

Purpose of life is to be happy and ultimately Ananda.