The “Two Envelope Paradox” is an intriguing puzzle that some prefer to solve using the logic of Bayesian probability. Can we avoid Bayes with a classic solution or a realistic experiment?

## A Brief Guide to the Euclidean Postulates Found in Euclid’s Elements

## Elements of Geometry: A Brief Guide to the Euclidean Axioms

Euclidean geometry is based on Euclid’s axioms and postulates. What do the Euclidean axioms say, and why are they so important in math?

## Euclid Laid the Foundations of Geometry for Mathematics

## T Cells, Predators and Finances all Walk the Levy Walk

## The Turing Machine versus the Decision Problem of Hilbert

## Algorithm to Solve Arranged Marriages via the Hall Theorem

## Is it Possible for Turing Machines to Solve the Halting Problem?

## The Special Case of Non-Deterministic Turing Machines

Alan Turing (1912-1954) “invented” the Turing machine (TM) as a powerful theoretical model for mathematicians exploring rules-based mathematics. The Non-deterministic Turing machine, or NTM, extends the basic concept by permitting multiple instructions for one state-input combination. The Deterministic Turing Machine A Turing machine has a finite number of states, symbols and instructions. A pattern of symbols are presented on […]

## Examples of Turing Machines: Loops, Halts, and Rewriting

A Turing machine, or TM, is a theoretical model devised by Alan Turing to explore the limits of rule-based math. The model has a finite number of rules, states and symbols, and an infinite tape with cells, each of which can contain a single symbol. The TM can either read the current cell, rewrite it, […]