Expressions Of Pj Problems

Pj Problems - Overview

Celestial Stars

The Number Line

Geometries

7 Spaces Of Interest - Overview

Triadic Unit Mesh

Creation

The Atom

Survival

Energy

Light

Heat

Sound

Music

Language

Stories

Work

States Of Matter

Buoyancy

Nuclear Reactions

Molecular Shapes

Electron Configurations

Chemical Bonds

Energy Conversion

Chemical Reactions

Electromagnetism

Continuity

Growth

Human-cells

Proteins

Nucleic Acids

COHN - Natures Engineering Of The Human Body

The Human-Body Systems

Vision

Walking

Behaviors

Sensors Sensings

Beauty

Faith, Love, Charity

Photosynthesis

Weather

Systems

Algorithms

Tools

Networks

Search

Differential Calculus

Antiderivative

Integral Calculus

Economies

Inflation

Markets

Money Supply

Painting

Statistical Triad - Groups, Data, Inference

Figure 118.1 illustrates the conceptual essence of statistic.

(a) What is statistics?

(b) Describe its triadic components.

**The strings**:
S_{7}P_{6}A_{64} (Grouping - Multi-criteria).
**The math**:

Pj Problem of Interest is of type *grouping* (multi-criteria). *Grouping* is at the heart of statistics. The grouping may be permutational or combinational, single criterion or multi-criteria grouping.

(a) Only 7 types of problems (P_{1}, P_{2}, P_{3}, P_{4}, P_{5}, P_{6} and P_{7}) constitute the core of existential problems. However, these problems are variedly manifested in form and complexities. Social and biological problems are replete with such complexities. The search for a reliable method for extracting pertinent information from complex problems not amenable to precise solutions was the impetus for the discovery of *statistics* which is in essence the quantification and extraction of non-deterministics (probabilistic) information from a population of interest. In other words, statistics exists because of lack of precise information.

John Graunt (1620-1674) is credited with the founding of *statistics*. Graunt's 1662 book *Natural and Political Observations ... upon the Bills of Mortality* initialized the quantitative inquiry into the social sciences. William Petty (1623-1685), L.A.J Quetelet (1796-1874), Francis Galton (1822-1911) and Karl Pearson (1857-1936) were early contributors and developers of *statistics*. Today, statistical information is ubiquituous.

(b) **Grouping**: no population, no statistics. It is from a given population that a group of interest is extracted. Graunt knew this very early on when just out of curiosity, he was studying the death records in English cities. He categorized the percentages of death due to accidents, suicides, and various diseases and noticed that the variations were not significant.
**Data**: the purpose of the grouping is to collect and analyze data of interest. Graunt was interested in percentages of death due to accident, suicides and various other diseases.
**Inference**: the purpose of the data collection and analyses is to extract quantitative information (not otherwise available by standard scientific method) about the groups of interest.

A primary characteristic of statistics is that it provides reliable information about large groups and do not provide definite prediction about any individual case.

Math

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

Single Variable Functions

Conics

Ordinary Differential Equations (ODEs)

Vector Spaces

Real Numbers

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

More Pj Problem Strings