If you have a garden of rocks, it is possible that no rock has the same weight as the average. ~Carl Jung


AI models train with a huge number of initially random parameters (you can include architecture search). The information contained in the outputs of an untrained (random) network must be miniscule relative to the dimensionality (number of paths) of the search space. That means that the models are very low complexity even though the number of parameters is high.

Conjectures

Our hands have many degrees of freedom, nodal and distributed.

I am doing research into how we can use our hands like an abacus.


Addition, Subtraction, Multiplication and Division Practice


Another Derivation of the Quadratic Formula

Generalization of the Pigeonhole Principle

Theoretical Physics of Spring

Hyper Tetrahedron Invariants

Honeycomb Trigonometry

Fuel Loop Problem Proof Sketch (with extension to applied problem)


Research Programs (see Imre Lakatos)

Geometric Connection Theory

Game Integration / Game Theory Alternatives

Example of a Classical Game (can be a collaborative game)

Non Standard Set Theory

Statistics

Loss Functions Seminar

Loss Functions Seminar 2 (showing maximum likelihood estimate is optimal given large number of samples)

There is a common misconception that data typically is normally distributed.

Analysis of Coincidence

Causality

Quantification Problem 1

Quantification Problem 2 with Safety Applications

Multiple Sensor Averaging can Reduce Error

(As a note, sometimes too much input to an algorithm can make a problem harder to solve. For example, if too many people in a car are giving the driver instructions, that can make driving more difficult.)

Exponential Linear Region (for quick risk calculations given pressure)


Group Theory

Definitions of Group


Number Theory

Arithmetic Hacks

Real Number Subtraction Theorem

Rational Number Theorem

Induction with Examples

Multiplicative Commutativity (inductive proof and non axiomatic proof)

Euclid's Division Lemma

Exponentiation Lesson

Basis Representation Theorem

Basis Representation Theorem optional material

Quantifier Chains

Introduction to Prime Numbers

Largest Public Prime Number code reference