*This gallery contains 6 photos.*

nerves of cell complexes

7-WAY VENN via peano, wowgreat

multiplicities of freedom demonstrates Chaos Theory in Excel. If he filled in more initial values, you would see a thick bar—like a picture of white-noise. Butterflies flapping their wings in Vermont to change the wind in Hangzhou? A drop of … Continue reading

If you don’t read the n-category café’s wiki project, you are missing out. Definition. A Frobenius algebra in a monoidal category is a quadruple (A,δ,ϵ,μ,η) such that (A,μ,η) is a monoid, (A,δ,ϵ) is a comonoid, and the Frobenius laws hold: (1⊗μ)∘(δ⊗1)=δ∘μ=(μ⊗1)∘(1⊗δ). In terms of string diagrams, this definition says: The first line here … Continue reading

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Tagged algebra, Georg Frobenius, mathematics, TQFT, visualisation
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If you don’t read Sketches of Low-Dimensional Topology already, your personal astrologer advises that you start doing so before the next ecliptic. Sample pics and text: ctctstr4, originally uploaded by epsilon_is_afraid_of_zeta. View this 3-manifold as an interval of concentric spheres where … Continue reading

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Tagged geometry, imagination, Ken Baker, mathematics, topology, visualisation
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visualisation of how the kernel trick makes a non-separable collection of points linearly separable. I guess the kernel mappings really add a dimension, rather than replacing a dimension, don’t they. (Source: http://www.youtube.com/)

My interpretation of [Leland Wilkinson’s] grammar [of statistical graphics]: —Data is the most important thing, and the thing that you bring to the table. —Geometric objects … what you actually see on the plot: points, lines, polygons, etc. —Statistics transform … Continue reading