The Mathematical Structure of Integrated Information Theory

Integrated Information Theory is one of the leading models of consciousness. It aims to describe both the quality and quantity of the conscious experience of a physical system, such as the brain, in a particular state. In this contribution, we propound the mathematical structure of the theory, separating the essentials from auxiliary formal tools.


Cytoscape is an open source software platform for visualizing molecular interaction networks and biological pathways and integrating these networks with annotations, gene expression profiles and other state data. Although Cytoscape was originally designed for biological research, now it is a general platform for complex network analysis and visualization. Cytoscape core distribution provides a basic set of features for data integration, analysis, and visualization.

Killing Science Fiction: Why Conscious States Cannot Be Copied or Repeated

Several philosophical problems arising from the physics of consciousness, including identity, duplication, teleportation, simulation, self-location, and the Boltzmann Brain problem, hinge on one of the most deeply held but unnecessary convictions of physicalism: the assumption that brain states and their corresponding conscious states can in principle be copied. In this paper I will argue against this assumption by attempting to prove the Unique History Theorem, which states, essentially, that conscious correlations to underlying quantum mechanical measurement events must increase with time and that every conscious state uniquely determines its history from an earlier conscious state.

Your Brain as Math: Part 1

In order to dive deeper into an exciting topic, we’re mixing up the format. Over the next three days, we’ll spend the next three episodes exploring an incredible application of seemingly purely-abstract mathematics: how algebraic topology can help us decode the connections among neurons in our brains, to help us understand their function.

Simplicial Complexes: Part 2

Last episode we saw that your neural network can be modeled as a graph, which — we’ll show in this episode — can be viewed as a higher-dimensional simplicial complex. So… what is a simplicial complex??

Your Mind Is Eight-Dimensional: Part 3

Last episode, we learned that your brain can be modeled as a simplicial complex. And algebraic topology can tell us the Betti numbers of that simplicial complex. Why is that helpful? Let’s find out.

The Case For Boredom

Neuroscientists will tell you that boredom gets a bad rap. Research is starting to show that the time we spend doing literally nothing could be extremely beneficial. Letting our minds wander could actually be the time we need to understand what we want from life, or spark the creative ideas that will move a long-stuck project forward. But if you’re always on your phone, whether it’s texting or checking Twitter, can you ever be bored enough for your mind to wander into brilliance?

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