Ganesh hands usually hold objects. These objects symbolize powers or functions of the God. Some of these objects represent weapons that Ganesha used to fight demons and negative forces. Traditional scriptures describe Ganesh with four raised arms, a broken tusk, an axe, a closed lotus and a plate of sweets. Other scriptures quote, for instance, a goad (to control an elephant), a snake, and a trident. From time to time, Ganesh holds a fruit in one hand. For example, in Srilankan depictions, he holds a mango, a lime, or a jambose fruit.
The axe (parashu) is a very common emblem of Ganesh. Most times, he holds it in the upper right hand. The axe originally comes from Shiva (one among the three Lords of Hindu community i.e. Brahma, Vishnu and Shiva) and is vested in the Shaiva deities (except for Parashurâma, a Vishnu avatar, who receives it from Shiva). The axe symbolizes the destruction of desires and attachments, and all their results like troubles and sorrows.
As the “Lord of Obstacles”, Ganesh holds a lasso or a noose (pasha), in order to catch delusions (moha), which are obstacles to Truth seekers. The noose also means eagerness (raga), soul slavery, and hearing. Like a knot, eagerness binds us. This noose permits the spiritual seeker to lift himself up, beyond his human limitations, and connect to the everlasting bliss of his own self. This noose is sometimes shown like a tightly coiled snake.
His elephant goad or hook (ankusha) is used to conduct elephants and is the symbol of his sovereignty over the world. This goad also symbolizes anger (krodha). Anger injures us like a hook. Anger also represents touch and, surprisingly, the higher knowledge which allows human beings to free themselves from ermits to set oneself free from furor.
The plate of sweet (modaka) is the most famous and most ubiquitous among Ganesh attributes (at least in India). Held by the lower left hand, modakas are like cakes. The trunk of Ganesh touches this sweet because it is said that Ganesh is fond of it. The modaka is also the joyful reward of the Truth seeker. Offerings of modaka represent the germs of all the universes kept within the huge belly of Ganesh. According to the Padma-Purâna (a religious textbook of Hindus), the modaka is the symbol of the supreme wisdom (mahâbuddhi).
Before the sixth century, but also more recently, during the 9th to 12th century period, one may find, mostly in Orissa and Bengal, representations of Ganesh holding an object which can be identified, without any doubt, as a radish or a turnip (moolakakanda). Some specialists have written that this vegetable could also be a horse-radish and they have supposed that the broken tusk would always be a vegetable.
Some ancient scriptures like the Yâjñavalkyasmrti state that the radish is an appropriate emblem for Ganesh because this vegetable was an offering to Vinâyaka, like sweets are. In ancient times, the Vinâyaka were the names of demons of tantric nature and they were supposed to be very fond of tubers, like radish and also onion and garlic, because they use to live underground.
Various texts have talked about Ganesh holding a radish:
A text from the 5th century, the Bharat Samhita, mentions Ganesh holding a radish
The Yâjñavalkyasmrti (about 300 BC) states that the radish is an adequate offering to Vinâyaka, another form of Ganesh
The Grhyasutra too indicates the radish as an offering
In addition, Ganesh holds a mâlâ : or akshamâlâ made of 50 rudra grains in his lower right hand. It corresponds to the 50 letters of the Sanskrit alphabet and symbolizes sound and hearing.
The above mentioned attributes are the most common ones. Sometimes they may be difficult to identify them on ancient stone statues. For example the axes may look like sticks or big clubs.
Other Ganesh emblems are:
The only just opened lotus, which represents the supreme goal of the human spiritual evolution that Ganesh, offers to his worshippers,
The raising blue lotus (utpala ) associated with the moon,
The kamandalu (a pot for sacred water),
The lute (Vina) ,
Some rice ears,
The vajra ,
A book, etc.
Esoteric forms of Ganesh hold also other emblems like the water pot called kalasha, the discus (chakra), the bow (dhanus) and the arrow (bâna).
All these objects are symbols used in Hindu mythology to refer to tools and weapons that represent defeating common vices in human beings. Within these stories lie valuable lessons, applicable to the modern world and the mankind in the 21st century.