How do you wire a brain?

The Fractal Geometry of the Human Brain: An Evolutionary Perspective

The evolution of the brain in mammals is characterized by changes in size, architecture, and internal organization. Consequently, the geometry of the brain, and especially the size and shape of the cerebral cortex, has changed notably during evolution. Comparative studies of the cerebral cortex suggest that there are general architectural principles governing its growth and evolutionary development. In this chapter, some of the design principles and operational modes that underlie the fractal geometry and information processing capacity of the cerebral cortex in primates, including humans, will be explored. It is shown that the development of the cortex coordinates folding with connectivity in a way that produces smaller and faster brains.

Brain Computation Is Organized via Power-of-Two-Based Permutation Logic

There is considerable scientific interest in understanding how cell assemblies—the long-presumed computational motif—are organized so that the brain can generate intelligent cognition and flexible behavior. The Theory of Connectivity proposes that the origin of intelligence is rooted in a power-of-two-based permutation logic (N = 2ⁱ–1), producing specific-to-general cell-assembly architecture capable of generating specific perceptions and memories, as well as generalized knowledge and flexible actions. We show that this power-of-two-based permutation logic is widely used in cortical and subcortical circuits across animal species and is conserved for the processing of a variety of cognitive modalities including appetitive, emotional and social information. However, modulatory neurons, such as dopaminergic (DA) neurons, use a simpler logic despite their distinct subtypes. Interestingly, this specific-to-general permutation logic remained largely intact although NMDA receptors—the synaptic switch for learning and memory—were deleted throughout adulthood, suggesting that the logic is developmentally pre-configured. Moreover, this computational logic is implemented in the cortex via combining a random-connectivity strategy in superficial layers 2/3 with nonrandom organizations in deep layers 5/6. This randomness of layers 2/3 cliques—which preferentially encode specific and low-combinatorial features and project inter-cortically—is ideal for maximizing cross-modality novel pattern-extraction, pattern-discrimination and pattern-categorization using sparse code, consequently explaining why it requires hippocampal offline-consolidation. In contrast, the nonrandomness in layers 5/6—which consists of few specific cliques but a higher portion of more general cliques projecting mostly to subcortical systems—is ideal for feedback-control of motivation, emotion, consciousness and behaviors. These observations suggest that the brain’s basic computational algorithm is indeed organized by the power-of-two-based permutation logic. This simple mathematical logic can account for brain computation across the entire evolutionary spectrum, ranging from the simplest neural networks to the most complex.

Evolution of the human brain: when bigger is better

Comparative studies of the brain in mammals suggest that there are general architectural principles governing its growth and evolutionary development. We are beginning to understand the geometric, biophysical and energy constraints that have governed the evolution and functional organization of the brain and its underlying neuronal network. The object of this review is to present current perspectives on primate brain evolution, especially in humans, and to examine some hypothetical organizing principles that underlie the brain's complex organization. Some of the design principles and operational modes that underlie the information processing capacity of the cerebral cortex in primates will be explored. It is shown that the development of the cortex coordinates folding with connectivity in a way that produces smaller and faster brains, then otherwise would have been possible. In view of the central importance placed on brain evolution in explaining the success of our own species, one may wonder whether there are physical limits that constrain its processing power and evolutionary potential. It will be argued that at a brain size of about 3500 cm(3), corresponding to a brain volume two to three times that of modern man, the brain seems to reach its maximum processing capacity. The larger the brain grows beyond this critical size, the less efficient it will become, thus limiting any improvement in cognitive power.