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Andrius Kulikauskas

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See: Geometry perspective, Divisions


Understand how mathematics defines a perspective.


Defining perspectives

  • Study fixed point theorems, such as Brouwer's fixed point theorem, and the inverse function theorem and implicit function.
    • In studying perspective: How is homology used to prove the Brouwer fixed point theorem?
  • How is exactness (the image of f1 matching the kernel of f2) related to perspectives, for example, the notion of the complement?
  • Relate sheaves and vector bundles.
  • How do observables relate to perspective?
  • Relate to perspectives: Homology groups measure how far a chain complex is from being an exact sequence.
  • How might adjunction express the inversion of perspective and various other transformations of perspective?
  • Consider how a black hole is like a sphere and how its collapsing may be like a mapping to itself that yields various perspectives, as with divisions of everything or the Bott periodicity theorem.
  • Relate cones, limits and perspectives.

Algebra of perspectives

  • When are perspectives associative and when are they nonassociative?
  • Does the relations between the components of polytopes give an algebra of perspectives?

Areas of math that express perspectives

  • Projective geometry
  • Dimensions of the n-sphere are the perspectives in a division of everything
  • Bott periodicity relates the eight divisions of everything
  • Category theory expresses the composition of perspectives. Perspectives are arrows.
  • Logic defines quantifiers and the sevensome.
  • Fixed points ground perspectives.
  • Two-dimensional complex numbers express the truth of the heart. One-dimensional real numbers express the truth of the world.
  • Dimensions
  • Parameters (real or complex)

What is a perspective in mathematics?

  • A perspective is a bundle. It expresses (with the fiber) the regularity of choice available for any point (in the base).
  • A perspective is a dimension with a varying scalar.
  • A perspective is a map with a fixed point.

More ideas

  • There is no quantum frequency. Photons are "perspectives". Bosons are "force carriers", "relationships", they "don't exist".
  • Perspectives are (multidimensional) arrays. The number of array dimensions is the number of divisions of everything.
  • Think of the nullsome as the point at infinity (the eye that sees the perspective). And think of it going beyond itself and then returning back to itself, making a big circle around. And think of that circle as a discrete line with four places.

Bundles

  • Perspective relates intrinsic and extrinsic geometry by way of ambient space. Ambient space relates base and fiber (perspective) as a bundle.
  • Vector bundles: Identity and self-identity (like the ends of a regular strip or a Moebius strip). Identity of a point, identity of a fiber - self-identity under continuity. How does a fiber relate to itself? Is it flipped or not? 2 kinds of self-identity (or non-identity) allows the edge to be flipped upside down.
  • Bundle. Geometry relates analysis (continuum) and algebra (discrete) as a restructuring. When the discrete grows large does it become a continuum?
  • Bundle = restructuring (base = continuum -> fiber = discrete). A number that is "large enough" can essentially model the continuum.
  • Normal bundles involve embedding in an extrinsic space.

Readings

Notes

  • Ker/Image - the kernel are those that can relate, that can take up the perspective
  • The Axiom of Choice is based on the notions of a perspective (a bundle) in that we can assign to each set a choice. The set is fiber and the set of sets is the base.
  • {$K_0$} and {$K_1$} perhaps express perspectives, like God's trinity and the three-cycle, the two foursomes in the eight-cycle.
  • The possibilities for a complex plane (extra point for sphere, point removed for cylinder) are relevant for modeling perspectives.
  • The six ways of restructuring relate the unconscious's continuum (large number) with the conscious's discrete (small number) and express the relations between the two. Consider these relations in the house of knowledge for mathematics, and how they relate to the six geometrical transformations.
  • Comma category can help model perspectives. The anchor object is the vantage point.
  • A cone models a perspective on structure (of perspectives). An object is a perspective.

Perspectives - dimensions

  • Požiūris išreiškiamas lauku (field). Nes tai leidžia keisti proporciją, santykį, didinti ir mažinti. Nes galima išversti, galima didinti ir mažinti, taip pat didėjimas ir mažėjimas vyksta dvejopai - dauginant ir sudedant. O skirtingus požiūrius derina vektorių laukas.
  • Koordinatės: Bazę parinkus vektorių ir matricas galim išrašyti atvaizdu, reprezentacija. Be bazės negalime juos suvokti konkrečiai, tik abstrakčiai. Tačiau tada jie nėra sukonkretinti, jie laisvai mąstomi.
  • Specialajame reliatyvume priskiriame dalelytei (ar kūnui) koordinačių sistemos centrą. Tačiau tai negalime padaryti kvantų fizikoje kadangi yra pozicijos ir judesio kiekio paklaidos. Tada tenka naudoti kitą (tyrimo) koordinačių sistemą kuri laikoma iš esmės pastovi.
  • Fotonos ar kita dalelytė keliaujanti šviesos greičiu neturi jokio požiūrio - nėra kaip priimti jos požiūrį - ji nebendrauja su aplinka - tiktai kelionės pradžioje ir pabaigoje. Jeigu jinai atsimuša į kažką tai nauja išsispinduliuoja, tai naujas fotonas.
  • Įsijautimas - galime įsijausti tik į tai kas gali tarnauti koordinačių sistemos centru.
  • Step out, atsitokėjimas - tai yra išorinė koordinačių sistema kuria matuojame kitus reiškinius, jie gali būti netikslūs, kvantiniai, išteplioti.
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Šis puslapis paskutinį kartą keistas March 07, 2021, at 02:06 PM