The digital divide has expanded into a broader intelligence gap, marked not only by disparities in technology access but also by unequal abilities to engage with data-driven systems like AI. This gap reflects imbalances in technology literacy, decision-making autonomy, and the capacity to harness digital intelligence for personal and societal benefit. This study introduces a multidimensional hierarchy of the intelligence gap, structured around four key dimensions: access, knowledge, choice, and empowerment. By examining how individuals and communities interact with data-driven systems, the research reveals systemic barriers that restrict equitable participation in an increasingly algorithmic world. Addressing this gap requires a holistic, layered approach that accounts for technical, cognitive, and structural factors to foster inclusive and just technological integration across diverse contexts.