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Complexity mathematics systems

Rat on a Wheel: The Doughnut in your Mind

Recent research suggests that the underlying symmetry in neural patterns of geometric world mapping in the mammalian brain are toroidal. “(…) the Mosers discovered the activity structure of single grid cells. What they found was a hexagonal grid pattern that functions as the brain’s metric and coordinate system for space. Today they have uncovered the […]

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Philosophy

On things we can never know…

Context: Gödel’s Incompleteness Theorem, The Inherent Limitation Of Mathematics The discontinuous boundary condition at the edge of (as much as being that around which we built) logic, physics and mathematics is a global property, distributed across and as the complex hypersurface of a self-propagating, soliton-like hybrid matter/energy/information system. It is as though a logical vacuum, […]

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mathematics

Why is Mathematics Difficult?

A curious revelation of logic, mathematics and physics is that the concepts themselves are never really all that difficult and can usually be quite rapidly grasped if the method of education is sufficiently powerful. The difficulty lies in acquiring an aptitude to intuitively understand and leverage the relationships between the symbols that are used to […]

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Philosophy

Intelligence is Endemic to Biology

Context: Single-celled organism can ‘change its mind’ despite lacking a nervous system This is an example of entropy as degrees of freedom; intelligence as manifest choice. Not quite a solid vote for panpsychism but certainly heading in the direction of autonomously self-propagating biological computation being universal within observed biotic artefacts, entities and systems on Earth. […]

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Philosophy

AI: Big Data, Narrow Intelligence

Context: The False Philosophy Plaguing AI The (or at least a) problem here is that the ascendant technologies, frameworks, cultures and commercial incentives have inadvertently stumbled upon the constructive and recursively self-inflected sweet-spot through which those core assumptions themselves optimally self-propagate. If the incentives and rewards for developers, researchers and corporate or institutional entities find […]

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Philosophy

The Mystery of Mathematics

Context: Studying maths beyond GCSEs helps brain development, say scientists Mathematics is a truly wonderful mystery and I only wish that it had been taught as such when I was at school. The concepts are fascinating, mysterious and completely astonishing once a triangulation between the paradoxes of logic, physics and material reality is rendered intelligible. […]

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Philosophy

Beautiful Convergence

Beauty fascinates me although it is not at a purely aesthetic level or in any visceral approximation to emotional experience and desire with which our culturally-mediated experience of self and subjectivity endows us. Consider that there have been a number of cross-cultural and ethnically-diverse academic studies that demonstrate that the faces which are considered to […]

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Philosophy

Empty Universes of Endless Self-inflection

When we trade in Universals or concepts of substantive reality, we are engaging concepts of notionally “whole” or “complete” systems. The curious thing about any “totality” or aspirationally “complete” system is that there is no outside to that entity, no external conditions or properties. Everything is internal to that system. Why does this matter? Because […]

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Philosophy

Deep Dives into Holistic Philosophy

Our world is complex and yet as a matter of cognition and, beyond the confused and hollow or unthinking tribally-reflexive and adversarial impulse that humanity is prone to express, of intelligence – we are bound to assert or overlay simplicities, mnemonics and shortcuts or cartographies to interpret all of this effervescent noise in useful ways. […]

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Philosophy

Hidden Geometry of Life in the Cosmos

Beautiful… and the fact that these spiral symmetries are ubiquitous as (a) most energy-efficient method of maintaining adaptive structural complexity is magnificent. There are abstract, logical corollaries of this. Interesting how life possesses similarities to abstract geometric patterns like this – adaptive systems that (soliton-like) autonomously self-propagate by the sustainably continuous information and energy-processing gradient […]

Categories
Ontology

Mysteries of Higher Geometry

The greatest mystery of mathematics is, to me, that all of these patterns and logical systems appear to almost (and autonomously) seek higher-dimensional self-representations. In category theory or combinatorics we can relatively simply determine and demonstrate the way a set of properties or relationships seeks something of an implicit, intrinsic and endemic higher-dimensional geometry. The […]

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Philosophy

The world is Perfect Imperfection, but Why?

The world is so beautiful and perfect in all the glorious randomness and unexpected symmetry or beauty of it’s flow and form. Why is it that the perfection of this world deviates in the way it does from simple linearity to recurse itself into hidden patterns of mathematical complexity that displace this symmetry into opaque […]