a0417z
Apr 27, 2014
(semantic, category theory)
Sergio Pissanetzky Micah, You seem to be asking about the famous binding problem: how things bind and become invariants, where semantics and scaling come from, why fractals and power laws are so abundant in nature. Here is what I can say. Take a causal set (S, w). It has a corresponding permutation groupoid, which induces a group-theoretical block system on S. In addition, and here comes the interesting part, partial order w induces a partial order on the blocks, and the block system itself becomes a (smaller) causal set. This property of recurrence should explain hierarchies, fractals, power laws, scaling, semantics, emergence, AGI.
Tom LaGatta: Why am I referring to nature? The fundamental principles of causality and symmetry describe information in its most fundamental and pristine state, and they apply to all physical systems, including the brain, human or otherwise, which is the only system where we observe the phenomena of intelligence. For any system described by a set S of boolean state variables with values {past, future}, the principle of causality is formalized by a causal set (S, w). And the principle of symmetry, or rather the breaking of symmetry which is necessary for structure to exist, is derived from the fact that partial order w breaks the original symmetry of S.
Yeah, that's a good place for the more AI-oriented parts of your question.
The specific question "is there any notion in category theory that indicates preferential logics" is about the only part which is well-suited for this forum. The answer is yes: preferences are well-modeled by partial orders (see the Stanford Encyclopedia of Philosophy entry on preferences). Because of the reflexivity and transitivity assumptions, a category can be modeled by a pre-order: we write x <= y if there is a morphism x -> y.
Being a partial order requires the antisymmetry constraint, which means that if x -> y and y -> x, then x and y are isomorphic (not necessarily equal).
Hope this helps. Even once you represent preferences computational, there is a host of other problems,including incomplete information, hierarchies of belief and bounded rationality.
/////////////////////////////////////////////// (Looking back on this note from 2022 I am pretty sure I saved this because the discussion barely begins to abstractly think about the binding problem https://www.sciencedirect.com/topics/neuroscience/binding-problem from the perspective of functions between categories that might contain sets or topologies.
The binding problem: "by Margaret Livingstone and David Hubel in 1988. These authors proposed that different visual features (specifically, color, motion, orientation, and retinal disparity) were analyzed in anatomically separate processing streams. These streams would originate in different types of ganglion cells in the retina, run through different types of layers in the visual part of the thalamus, and enter different layers of the primary visual cortex (V1). Staining patterns for cytochrome oxidase (CO), an enzyme whose presence is associated with increased metabolic demand, were supposed to provide the anatomical scaffold for further segregation in V1 and the adjacent area V2. For instance, color would be processed in the CO-rich ‘blobs’ of V1 and then passed on to the ‘thin stripes’ of V2 and finally the putative ‘color area’ V4. Similarly, the motion stream would run through the ‘thick stripes’ of area V2 and on to the putative ‘motion area’ MT. Early single-cell studies largely supported this model.
In the Livingstone–Hubel model, different visual features are segregated into different anatomical compartments, and each feature is processed by a specialized subset of cells. The visual system is thus viewed as disassembling incoming visual information into their component features. This model has been massively popular, and its central tenets are still taken for granted by many researchers. Accordingly, many reviews of the binding problem use the disassembly metaphor as a point of departure: If the system dismantles incoming information into its component features, how does it later reassemble the processed features into perceptual objects?
However, more recent research has undermined many of the central tenets of the Livingstone–Hubel model." The article goes on to say that the areas of the Visual Cortex are not really segregated as once imagined by researchers. Even so, the question might be well how does visual information combined with auditory information exactly? That is another perspective on the binding problem. Some information is going in through your ears, some is going in through your eyes, some is going in through your nose, your mouth, your skin, how does the brain bind it together into a conscious representation?
Ultimately the best way to think about how features detected by the neural networks of our brain are bound together comes from thinking about Neurons Syncing like Fireflies as discussed in the book Sync by Steven Strogatz and from thinking about big groups of oscillators interacting with other oscillators as discussed in the book Rhythms of the Brain by György Buzsáki combined the two books provide both a low level and a high level conceptual background for how information might be bound together in oscillations, with information clustering because of how the physics of oscillators work at all scales. At the level of regular cells coincident firing in receptors can trigger the cell to unlock some specific learned (or evolved) reaction (that might be encoded in dna, or it might result from the current state of the cells information configuration represented by its protein structure at that moment in time) at the neuron level that coincident firing is not just at the receptor level, but also at the dendritic level, and with pyramidal neurons also the soma might have its own sensory thresholds that are different from the dendrite, which make pyramidal neurons the most sensitive sensors in a sense, with the most flexbility for sensory representation, and signal transmission.
The key thought about where the observer is inside the mind, where is the person inside who is watching the brain's representations, is to think of the flow of information in the brain as a series of arrays, with each array seeing part of the picture, and the oscillating activity at different scales, from spikes to phase changes to big brainwaves and dipoles is the thing that binds together what each array in the brain is seeing as information passes through it, so you perceive what you perceive, and that includes a representation of your hands and your sense of self as the body of causation behind your hands.