The Mathematics of Becoming: Adaptation, Attention, Awareness, Learning, Memory, and Knowledge

How does a vulnerable system detect change, select what matters, regulate response, learn from error, preserve memory, and build knowledge that remains open to correction?The Mathematics of Becoming: Adaptation, Attention, Awareness, Learning, Memory, and Knowledge develops a disciplined mathematical and constitutional architecture for these questions. The volume moves through feedback and feedforward control, plasticity, recovery, signal detection, resource allocation, relevance, integration, belief states, representation, prediction error, generalization, transfer, storage, attractors, consolidation, reconstruction, inference, calibration, consistency, and revision.Aston Gustavous Farquharson keeps every domain boundary visible. Similar mathematics may appear in organisms, nervous systems, persons, machines, institutions, and civilizations, but shared form does not establish shared mechanism. Adaptation is not survival at any cost; attention is not a moral ranking; awareness is not equated with one unproven mechanism; learning may be harmful or maladaptive; memory may distort; and knowledge remains accountable to provenance, uncertainty, evidence, and reality.The volume continues the human foundation of the SDAE Canon: the spiritual inheritance of parents and grandparents and decades of face-to-face work with thousands of NuSpecians and their families confronting illness, suffering, caregiving, recovery, dying, and grief. These lived realities motivate questions and moral responsibility without substituting for empirical validation.Six source-locked figures make the argument visible: Adaptation and Recovery; Attention and Selection; Awareness and Representation; Error, Update, Generalization, and Transfer; Encoding, Retention, Consolidation, and Reconstruction; and Evidence, Consistency, Calibration, and Revision. This third public volume can be read independently while permanent identifiers connect it to the wider fifteen-volume Mathematics of Becoming sequence. Reality remains the measure.SHORT DESCRIPTIONAdaptation, Attention, Awareness, Learning, Memory, and Knowledge develops a disciplined mathematical architecture for feedback, control, plasticity, signal detection, resource allocation, integration, prediction error, generalization, memory consolidation, representation, inference, calibration, and revision. It distinguishes adaptation from change, attention from worth, awareness from a completed consciousness theory, learning from automatic improvement, memory from perfect storage, and knowledge from certainty. Six canonical figures connect this independent volume to the wider Mathematics of Becoming sequence.