measuring value of broken tools (memorandum)

NOTICE

• DO NOT TRUST THE FOLLOWING

MOTIVATION

• a la Heidegger, we could say tools notice us when they do not work properly
• think direct sum decomposition of tool: tool = broken tool + its functionality
• other than its functionality, value of broken tool might be zero
• repairer might price broken tool as >0

(added) KNOWLEDGE AND NON-COMMUTATIVITY

• determining (valuation) of broken tool is dependent on repairer's knowledge and available repair process (both are continuously changing)
• some repair depends on too specific supply of spare parts recycled from another broken tool

Statistical Dynamics of Radioactive Pollution (memorandum)

NOTICE

• DO NOT TRUST THE FOLLOWING

Motivation

• Any event occurs in this universe minimize the statistical Lagrangian of the universe
• What is minimized, or how is it minimized, in spacial scattering of unstable isotopes as consequence in huge diastrophism (displacement of crustal plates)?
• scattering of magma (containing heavy elements like thorium and uranium) and nuclear fuel works in same way
• solar neutrinos and beta-decay isotopes might affect local Higgs field
• and they all, more or less, modify state of so-called causality (time asymmetry)

Recent Scientific Findings

• Existence of Higgs boson was confirmed (Mar 2013)
• A report that say stem cells are reduced from differentiated cells easily and more reversibly (Jan 2014)

Potential background effect of more symmetric vacuum physics

• crazy idea, I agree

Harmless to time arrow?

• even if it is so, who cares? or who could care?
• If our universe is really infinite dimensional, you always find another force and blame it for still remaining errors, so the time still flows
• If our universe is finite dimensional and you find the very last force, the universe might stop: no one would feel nor think any more

Cardinal Geometry (memorandum)

NOTICE

• DO NOT TRUST THE FOLLOWING

Cardinal Geometry

• Desirable geometric view/interpretation for set-theoretic elementary embedding of universe into universe, not new math
• Infinite dimensional analogue of Riemannian embedding
• Ignoring finite sets, set-theoretic universe consists of ordinal "lines"
• Measurable cardinals or $\aleph_\omega$ (first singular cardinal) might work as "vanishing lines" or "horizon"
• But why ZFC? Categorical topology actually works and needs no additional concern about cardinality. Continuous geometry was invented for vaguely same objective, but disappeared abandoned

So what?

• Just thinking

Update: curse of dimensionality, integrability and chaos

• the very first result in dimension theory (Cantor(1877)): $card(\mathbb{R}^2) = \mathfrak{c}$
• existence of discontinuous mapping between 1-d real line and 2-d real area
• generally speaking, elementary embedding of universe into universe does not conserve information of dimensionality
• as change of topology, it changes continuity into singularity (making neighbors apart), it might also change singularity into continuity (making new neighborhood with aliens from distant galaxy)
• if you change order of enumeration, measure is not conserved (see summation of infinite series)
• curse of dimensionality: with requirement of conserving dimensional order information (for integrability) elementary embedding require further huge universe (if GCH holds it must be the power of current universe)
• continuum problem in numerical context: can you find measure-conserving chaotic (turbulent) circumstance characterized as having fractional dimensionality?