"What is intelligence" has been asked for two millennia. There is a more workable version of the question: if intelligence can be raised — human cognition through education, large models through more data — then what is the valve underneath that sets the level?
Our answer is a framework of four variables: information quality at the input layer (low entropy, high density, self-consistency) together with diversity, background integration efficiency at the processing layer, and metacognition on top. The level of intelligence is set by these four multiplied together, the first two accumulated over time.
Looking at carbon and silicon through that framework yields three things. First, both share one underlying mechanism: structure is extracted from information input by background integration, and new capability emerges once accumulated structure passes a critical point. Second, the brain's default mode network and large-model pretraining are functionally isomorphic; attention at inference time is a foreground operation, not background integration. Third, what family, education and culture do to a person is mechanistically isomorphic to what a pretraining corpus does to a model.
Boundaries: the framework is qualitative more than quantitative. The functional form of information quality, measurable indicators for integration efficiency, and a way to quantify metacognition are all still open. The six predictions span AI training, education design and individual cognition, and none has been tested.
Keywords: Intelligence Theory, First Principles, Pretraining, Background Integration, Information Quality, Emergent Abilities, Default Mode Network