David Hilbert raised the “Decision Problem,” or Entscheidungsproblem, in 1928. Turing Machines cannot solve Halting Problems, one specific type of decision problem.
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 […]
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, […]
Alan Turing (1912-1954) “invented” the Turing machine as a theoretical model for exploring the limits of rules-based mathematics. This purely theoretical device became a powerful tool in the minds of mathematicians, and modern computers still follow many of its principles. The Turing machine is even being honored via art at the Intuition and Ingenuity exhibit […]
Is there a new way to calculate a number’s cubed root? Recent news articles from India report that Mr. Nirbhay Singh Nahar has developed an algorithm to calculate the cube root of any number. Given an equation stating “y = x^3″, Nahar’s method would solve for “x = y^(1/3)” without the need to refine repeated […]
Richard’s Paradox demonstrated that a simple rule to define a set of numbers may lead to a paradox. Predecessors to the Richard Paradox In 1905, French mathematician Jules Richard shifted the focus from certain earlier mathematical paradoxes by showing that the definitions themselves might be at fault. In the very early 1900s, paradoxes in the […]
Confusing the “given” event (the event that you assume to have occurred) with the combined event (for which you are calculating probability) is a common pitfall with conditional probability. A Recap of Conditional Probability Recall that “the conditional probability of event ‘A’, given that event ‘B’ has occurred, is calculated as the probability that both […]
Despite the value of knowing the probability of an event before it occurs, it can be even more valuable to know how learning part of the outcome changes the conditional probability. The Foundation for Understanding Conditional Probability This article continues a series about probability, by introducing “conditional probability.” If the terms are unfamiliar, consider reviewing […]