This is one of two ambitious pieces of writing that I wish to complete in the next year. For now, only a table of contents exists.
To begin understanding the endeavor of science, we must descend into its origins in the unscientific. One step removed is statistics, another is mathematics, another philosophy, and finally we arrive at empirical observation and our biological sensory-cognitive world.
1. Science as a Framework
a. The statistical bridge between the empirical and the arithmetic in Random Variables. Hypotheses Tests as mathematical falsifiability. The apriori assumptive parametrization required for inference and estimation
b. The Quantized, Stable, and Platonic Nature of Symbols and Language: an object is not its representation, the map is not the territory.
c. Is Mathematics Invented or Discovered: The intrinsically empirical nature of mathematics. Mathematical Operators are precisely transformations in the real world (logic is physics) and we generalize these observations in the mass of our brains with an anthropological architecture.
d. The Bridge between Algebra and Geometry: Variables and Dimensionality, Change of Basis and Principal Component Analysis, How to navigate Data, World, and View space in Computer Graphics
e. Scientific Instruments and Human Observability: Anthropological contortion of signals and contrived artifacts from data analysis (Machine Learning, Convolution, Visualization, Fourier Decomposition, Taylor Approximation)
f. Precision versus Accuracy, Partitioning and Granularity, Attributes/Units (e.g. RGB versus HSV) and Dimensional Analysis
2. Experimental History of Alchemy
3. Experimental History of Mechanics and Relativity
4. Experimental History of Electricity, Magnetism, Waves