Relativity A Light Intro To Tensors A Framework For Defining Geometric Objects In Space Fractal Mandelbulb: Three Dimensional Fractals Searching For The Mandelbrot In Higher Dimensions Fractal Fractal Geometry From Gaston Julia to Benoit Mandelbrot Number Theory The Invention Of Zero Assigning Value To The Concept Of Nothing Automata Theory Elementary Cellular Automaton A Theory […]
The Monty hall problem became famous when Marilyn vos Savant published it in response to a reader’s question in her column in Parade magazine in 1990. It is as famous for the virulence with which Marilyn was mansplained as it is for the subtlety of the problem itself. Even the legendary Paul Erdos, one of […]
In the 19th century, many paradoxical statements, formed either in natural language or mathematics, caused concern leading to questions around the reliability of mathematical reasoning. Rigorous attempts were made to address such concerns. One of the most notable works in this regard is Principia Mathematica, written by Alfred North Whitehead (1861–1947) and Bertrand Russell (1872–1970) in the early 1900s, with […]
Kronecker Kronecker, God and the Integers Natural numbers were created by God, everything else is the work of men — Kronecker (1823–1891). Infinity There are Different Kinds of Infinities From Brilliance to Madness Logic Only So Much We Can Prove A Glimpse of Incompleteness Set Theory When Cantor Taught us to Count My theory stands […]
With nothing but a good model, a few definitions, and some math, we’ll derive a fundamental relationship of chemistry. Anyone who has ever taken a chemistry class has seen the Ideal Gas Law: Chemistry classes tend to teach the Ideal Gas Law as a combination of Boyle, Charles, Gay-Lussac, and Avogadro’s Laws. Although they derived […]
If asset prices in the short term show an identifiable pattern, won’t speculators find this pattern and exploit it, thereby eliminating it? Brownian motion or pedesis is the term used in physics to describe the random motion of particles (such as specs of dust) suspended in a fluid(such as a liquid or gas) resulting from collisions of such particles with […]
Let’s prove, using colour coded diagrams to follow the argument visually, why group decisions, from democracy to take-away choice, are always flawed. You’ll get a taste of advanced mathematical reasoning, presented in an accessible way! Primer Arrow’s Theorem invites us to consider how to make a decision as a group, when people have different preferences. […]
Approximating derivatives is a very important part of any numerical simulation. When it is no longer possible to analytically obtain a value for the derivative, for example when trying to simulate a complicated ODE. It is of much importance though, as getting it wrong can have detrimental effects on the solution. In this article, I […]
Exponential growth is a funny thing. It starts out real slow and then all of the sudden it shoots up big time. You know all about it, but how would you explain this topic to a fellow at a party? Doing It the Nerdy Way You could just grab a napkin and draw a little […]
Physics Another Approach To Understand Accelerated Motion Motion of a moving particle is considered to be one of the most instructive and useful physical systems one can study. In a real world case, such systems may exhibit immense complexity and intractability. But if we are lucky, we may be able to isolate the moving particle […]
Isaac Asimov once wrote [1] that all his discoveries in Math were either “completely correct findings that are quite old [or] completely new findings that are quite wrong.” I just had exactly the same experience, developing a totally new, greatly enhanced, surely unequaled method for finding square roots iteratively… to just end up realizing, after lots of […]
Philosophy Wittgenstein Didn’t Absolutely Agree with Gödel’s Theorems and Russell’s Paradox (and he was right) Gödel Gödel’s Constitutional Quarrel “The examiner was intelligent enough to quickly quieten Gödel and say ‘Oh god, let’s not go into this’ and broke off the examination at this point, greatly to our relief” — Oskar Morgenstern Kurt Gödel (1906–1978) […]
It describes the asymptotic nature of a system as the input grows. Usually, we are describing the runtime of an algorithm, but it can also be used to describe space complexity or even systems outside the realm of computer science. Here I will assume it describes the runtime of an algorithm unless stated otherwise. Asymptotic […]
Puzzle A Quick Mathematical Puzzle: Calendar Dice What numbers do they need to contain to display all days of the month? Probability Theory The Two Envelopes Problem or Necktie Paradox Should I switch or should I stay? The Switching Paradox Probability Theory Bayes’ Theorem and (Corona-) Virus Testing With the current Corona Crisis going on […]