The Kaṭha's portrait of Ātman through paradox: smaller than the smallest, greater than the greatest, hidden in the cave of the heart. The self cannot be found by looking outward — because it is what is looking.
The Kaṭha gives the self two paradoxical descriptions simultaneously: it is smaller than the smallest — more subtle than any atom, more interior than any inner thing. And it is greater than the greatest — more encompassing than any large thing, without boundary, without edge.
These are not contradictions. They are the same description from two directions. What is infinitely subtle is not located anywhere — it has no location to be smaller than. What has no location is not bounded — it extends beyond any boundary. The self that cannot be found anywhere (because it is not an object) is also everywhere (because everything appears within it).
The phrase nihito guhāyām — hidden in the cave of the heart — is the Kaṭha's spatial metaphor for a non-spatial reality. The heart here is not the physical organ. It is the hṛdaya — the centre of being, the innermost point of the person, the place where awareness seems to arise from. The self is hidden there not because it is located there but because it is closest to recognition there — the movement inward reaches it sooner than the movement outward.
The condition for seeing it: akratu — free from desire, free from wilful striving. The self is not seen by those who are looking for it with desire, because desire implies the self is an object to be acquired. It is seen by those who have ceased looking — in whose inquiry the grasping has quieted, leaving only the bare attention that is already the self looking at itself.
The verse 1.2.20 is one of four places in the Kaṭha where the self is described through paradox rather than through positive attributes. This is the Kaṭha's version of the Bṛhadāraṇyaka's neti-neti method: instead of negating inadequate descriptions one by one, it places two apparently contradictory descriptions side by side, forcing the mind to let go of both and rest in what they are both pointing at.
Verse 2.1.10–11 adds the cosmological claim: "The Puruṣa, of the size of a thumb, dwells in the middle of the body, as the lord of the past and future. One who knows this is not afraid of anything. This indeed is that." The "size of a thumb" is not literal. Śaṅkara reads it as the most interior point of the body — the locus of the subjective sense of being. The self appears to be located there for practical purposes; ultimately it has no size.
The phrase dhātuḥ prasādāt (by the grace of the Creator) has been debated in the tradition. Śaṅkara reads it not as divine grace in a theistic sense but as the grace that comes from the purification produced by karma and upāsanā — the preparation that makes the mind clear enough to see what was always present. The "Creator" here is the principle of order that ensures that a prepared mind is ready to recognise the self.
The paradox of "smaller than the small, greater than the great" recurs in many Upanishadic descriptions of Brahman and appears also in later Advaita commentarial tradition as a standard example of the kind of statement that cannot be held in the mind as a concept but can only be pointed toward. The statement's function is not to describe the self as an object with unusual size properties. Its function is to defeat the mind's attempt to locate or bound the self — any mind that takes the statement literally will be puzzled (what kind of thing is both the smallest and the largest?), and that puzzlement is the intended response. The puzzlement breaks the habit of treating the self as an object among other objects.
This makes the verse a practical instrument, not just a poetic description. Meditating on aṇoraṇīyān mahato mahīyān — holding both simultaneously without resolving the paradox — is the nididhyāsana practice the verse is designed to occasion. The mind that holds both without collapsing into either is the mind that is approaching the recognition the verse is pointing at.