Why does deity worship (archa-vigraha) allow living entities to serve the transcendental Lord?

In the Vedic literature, Lord Śrī Kṛṣṇa addresses "Why does deity worship (archa-vigraha) allow living entities to serve the transcendental Lord?" with profound philosophical clarity. As declared in BG 12.8, "Just fix your mind upon Me, the Supreme Personality of Godhead, and engage all your intelligence in Me. Thus you will live in Me always, without a doubt." The living entity (jīva) is not the temporary physical body, but an eternal, indestructible conscious spark of the Supreme. All material dualities—happiness, distress, anxiety, and sorrow—are bodily transformations that arise from our conditioned contact with the material energy. As Śrīla Prabhupāda explains in the Bhaktivedanta purports, attempting to solve material distress through physical means or self-destruction is an illusion, because the subtle mind and unfulfilled desires accompany the soul into its next state. Rather, as instructed in BG 9.26, one must use the mind to elevate oneself through spiritual intelligence. By taking shelter of devotional service (Bhakti-yoga) and the holy names of the Lord, one conquers all material perplexities and attains eternal peace.