Andrius Kulikauskas

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Understandable FFFFFF

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Time: A moving point is a line, a moving line is a plane, a moving plane is a volume... Time is the addition of a scalar (from a field), thus the addition of choice. Time relates affine and projective space. Compare time with space. A moving "center" is a point: the center is what moves, thus what has time.

Function can be partial, whereas a permutation maps completely.

Derangements. Interpret? Not likely...

Symmetry group relates:

  • Algebraic structure, "group"
  • Analytic (recurring activity) transformations

Axiom of infinity - can be eliminated - it is unnecessary in "implicit math".

The factoring (number of simplexes n choose k - dependent simplex) x (number of flags on k - independent Euclidean) x (number of flags on n-k - independent Euclidean) = (number of flags on n)

What kind of conjugation is that?

Relate triangulated categories with representations of threesome

Kan extension - extending the domain - every concept is a Kan extension

Express the link between algebra wnd analysis in terms of exact sequences and Kan extensions. Explain why category theory not relevant for analysis.

What is Mathematical Music Theory?

Consider the connection between walks on trees and Dynkin diagrams, where the latter typically have a distinguished node (the root of the tree) from which we can imagine the tree being "perceived". There can also be double or triple perspectives.

The mind is augmented through the "symmetric group" which is the system that augments our imagination.

Matematikos įrodymo būdai

  • 6 matematikos irodymo budai skiriaisi nuo issiaiskinimo budu taciau kaip jie susiję

Apibrėžti "gebėjimus" ir kaip matematinis mąstymas suveda skirtingus gebėjimus suvokti kelis, keliolika, keliasdešimts, tūkstančius ir t.t. daiktų

Kodėl yra tiek daug būdų įrodyti Pitagoro teoremą?

Gramatika visada turi prasmę. Matematika yra tai, kas pavaldu logikai, bet nebūtinai turi prasmę.


  • A variable is an "atom" of meaning as in my paper, The Algebra of Copyright, which can be parsed on three different levels, yielding four levels and six pairs of levels.


  • Protas apibendrina. Kaip nagrinėti apibendrinimą? Suvokti neurologiškai (arba tinklais). Jeigu keli pavyzdžiai (ar netgi vienas) turi tam tikras bendras savybes, tada tas apibendrintas savybes gali naujai priskirti naujoms jų apibudintoms sąvokoms.
  • Apibendrinimas yra "objekto" kūrimas.

Differentiability of a complex function means that it can be written as an infinite power series. So differentiation reduces complex functions to infinite power series. This is analogous to evolution abstracting the "real world" to a representation of it. And differentiation is relevant as a shift from the known to focus on the unknown - the change.

How do special rim hook tableaux (which depend on the behavior of their endpoints) relate to Dynkin diagrams (which also depend on their endpoints)?

Study the duality between 1^N and N in symmetric functions (Young tableaux) but also Catalan numbers, etc.

Analysis is based on the "looseness" by which a local property (the slope locally) may not maintain globally. And this looseness is of different kinds:

  • nonlooseness of path - discrete (integer, rational) affine
  • looseness of line - reals - projective
  • looseness of angle - complexes - conformal
  • looseness of orientation (cross product) - quaternions - symplectic

So looseness is the flip-side of invariance. We see the role of equivalence as based on limits. And also we see the qualitative distinction based on the nature of the limiting process - so taking the limit in all directions for the complexes relates to preserving angles.

What would be the notion of differentiation for a function on the quaternions?ähler_manifold

Dyson's threefold way R C H Freeman J. Dyson, The threefold way: algebraic structure of symmetry groups and ensembles in quantum mechanics, Jour. Math. Phys. 3 (1962), 1199–1215.


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Puslapis paskutinį kartą pakeistas 2018 sausio 18 d., 00:02