Many people are familiar the the “upside-down tree” analogy in the 15th Chapter of the Gita. Recently, however, I learned this is a direct reference to Katha Upanishad (2.3.1). This is edifying to know, because we always say Vyāsa’s purpose in writing the Gita was to summarize and harmonize all the Upanishads.

Here is how the text appears in Katha Upanishad:

ऊर्ध्वमूलोऽवाक्शाख एषोऽश्वत्थः सनातनः ।
तदेव शुक्रं तद्ब्रह्म तदेवामृतमुच्यते ।
तस्मिँल्लोकाः श्रिताः सर्वे तदु नात्येति कश्चन । एतद्वै तत् ॥ १॥

ūrdhvamūlo ’vākśākha eṣo ’śvatthaḥ sanātanaḥ
tad eva śukraṃ tad brahma tad evāmṛtam ucyate
tasminl lokāḥ śritāḥ sarve tadu nāty eti kaścana 
etad vai tat .. 1..

Roots up, branches down, this eternal Pipal tree.

It is very bright,
it is consciousness,
it is certainly the deathlessness we speak of.

All realms and beings are auxiliaries of it
nothing could possibly be beyond it.

This is certainly that.

Shankara’s comments:

The goal is to understand Brahman (pure consciousness). We can achieve this goal by understanding our world (We can understand the health of a tree’s roots by examining its fruits and flowers).

The root of this tree is “Viṣṇu’s nature”.

The tree itself is the manifest universe, beginning from its potetial energetic state all the way down to its simplest, most inert solids.

A tree is called “Vṛkṣa” because it grows / changes / falls-dies. Describing the world as a “tree” indicates that it is in a state of constant change.

Brahman (pure consciousness) is the source of “sap” that nourishes “seed” of the tree (self-ignorance). It grows into desires and ambitions for deeds, and thus produces its trunk: the potential energetic form of the universe (“avyakta”).

The sprouting of this trunk is called “hiraṇyagarbha” (consciousness directed into matter).

The initial groth of the trunk constitutes the mental forms of all the living entities – their sense of pride-identity is established by the specifics of their desires.

The trunk produces branches, which produce buds – which represent the objectives that living entities wish to attain. The buds become leaves – which represent education about the objectives and the means to attain them. The leaves produce flowers – which represent execution of the various efforts. The flowers produce fruits – the goals of the efforts.

The desire for the fruits causes new roots to grow (a Pipal tree is like a banyan, it drops secondary roots from the branches). This increases the strength of the tree.

The creatures living in the tree build “nests” in it – which represent our bodies. Various nests on various branches represent various species in various worlds.

A lot of noise comes from all the creatures in this tree. All the sounds of joy and misery.

The tree always shakes, because the “winds” of our desires and deeds constantly buffet it.

The tree is “eternal” (sanātana) because it grows from our self-ignornce, which always existed.

Since the tree grew from the seed of self-ignorance, it can be cut down by the opposite of self-ignorance: self-knowledge. Shankar expresses this very nicely, “This tree is felled by the axe called “Ultimate-Self-Knowing” which is obtained by understanding Vedanta without reservation or resistance to it.”

Shankar says THE ROOT of the tree is very bright. (I dont see the Upanishad saying exactly that. To me it says the entire tree is very bright)

He explains “Nothing could possibly be beyond it” to mean that everything that exists is a modification of the root. So nothing could exist beyond the root. He says that although the tree is in constant change, Brahman, the nourishing root, is eternally unchanging.

“This is that” means “that tree symbolizes this world.” (I believe it also implies “this tree is analogus to our discussion of Brahman”)