The Puranic Ganapati Sloka
The Puranic Ganapati derived its form and shape from the Rg Veda Ganapati. Probably people depicted the form and shape of Ganapati from the descriptions of Ganapati. The below sloka depicts the form and shape of Ganapati
Mooshika vahana modaka hasta
Chamara karna vilambita sootra
Vamana roopa Maheswara putra
Vigna-vinayaka paada namaste
Mushika - Small Crucilble, Small box, Mouse
Mushika Vahana - That is carried in a small Crucible
Carried in a small crucible OR carried in a mouse
Modaka - Sweetball in which the core (sweet) is hidden inside the layers
Modaka hasta - One that possesses the sweetball
Possessing a layered ball like structure that hides its core OR Possessing a sweetball
Chamara - Big fan-like
Karana - from behind, behind, Ear
Chamara Karna - Big fan-like (structure) from behind
Big fan-like structure that emerges from behind OR Big fan-like ears
Vilambita - hanging down, pendulous
Sutra - the thread (Yarn, Wire) that connects everything, rule or laws (as the thread that connect everything)
Vilambita Sutra - One that has a hanging down thread that connects everything
Hanging down pendulous structure that connects everything or Big threaded
Vamana - Short and Stout
Rupa - form/shape
Vamana Rupa - One who is of the form of short and stout
Short and Stout structured
Eswara - One who is the reason/source
Sarva - Eswara - One who is the reason/source of everything
Viswa -Eswara - One who is the reason/source of Universe
Maha - Eswara - One who is the Greatest reason/Source
Putra - Scion, descendant
Maheswara Putra - One who is the scion of the Greatest Reason/source
Scion of the Great Reason/source OR scion of Lord Maheswara
Vigna Vinayaga - The Lord of all actions
The Lord of all actions
Pada Namaste - I submit to you
I submit to you
The Shape and Structure of Brain
Carried in Small Crucible, Possessing a ball-like structure that hides its core, Big-fan like structure that emerges from behind, Hanging down pendulous structure that connects everything, Short and Stout one, The descendant of the Great Reason, I submit to you.
Brain is carried in a small crucible made of Skull bones on all sides. Thus the brain is the Mushika Vahana.
The Cerebellum of Brain is shaped like Modaka. It is placed like a Modaka as a separate structure to the brain. It is also exactly formed like Modaka. Cerebellum has a thick layer of tissues hiding a set of neurons that gives massive signal processing capability, which themselves are around a core cerebellar nuclei.
Like a Modaka that is formed with layers and layers of flour hiding the sweetness inside, cerebellar nuclei and nuerons are deeply embedded inside the layers and layers of tissues of cerebellum. Thus the brain is Modaka Hasta.
The cerebrum of Brain is shaped like a Big fan that emerges from behind. Thus the brain is Chamara KarNa.
The Spinal cord is connected to Brain as a hanging down pendulous thread-like structure that connects to all the nerves of the body and thus controls all the body. Thus Brain becomes Vilambita Sutra.
The Brain is itself short and stout. Thus it is Vamana Rupa.
As the Rg Veda Ganapati Mantra says, brain is the evolver and the evolved. It carries all the logic and reasoning. It is the REASON for all our actions.
The Universe got formed due to the Reasoning of the Maha-Eswara. Vedas say it is the 'Thought' of the Atman or the Reasoning of the Atman or the Desire of the Atman to realize itself through Evolution (BrAhman) that Universe if formed.
Thus the Atman or Supreme consciousness is the Maha-Eswara or the Great Reason. Our Brain is the descendant/scion of that Atma as it carries on the Legacy of thought and reasoning. Thus Brain is the Maheswara Putra.
Brain is the Lord of of all our actions. Hence it is Vigna Vinayaga.
Thus this sloka aplty describes our brain, the Vinayaga (Lord of all actions) or Ganapati (Guide of all attendants).
The Puranic descriptions of Ganapati
In the Puranic times, as several of our devas were given human forms or forms/shapes that human beings could understand, the current structure of Ganapati would have evolved.
From this sloka, if one just looks at the depiction, it is easy to portray a Vinayaga with a person who travels on mouse (who travels on crucible does not make sense), a person who carries sweetball in hand, a person with fan-like ears (which else has got a fan-like ears except elephant, hence elephant-headed), a person with a thread wrapped all around the body (a long pendulous structure that connects everything is not possible unless a thread is wrapped around the body), a short and stout person (hence pot-bellied) and a son of Siva.
Thus a Vinayaga who is elephant-headed, who has fan-like ears, who is pot bellied, who wears thread around the body/belly, who travels in a mouse, who carries sweetball in hand is born.
The actual depiction, in my view, is about our brain.
This does not mean we should not worship the Lord Ganapati as we see it now. Please invoke the Ganapati, but remember to aspire for that intelligence that evolves your brain and also gets evolved.