Alain Badiou (1937-) is a French philosopher. At one point he was the chair of Philosophy at the École normale supérieure (ENS) and founder (with Michel Foucault, Gilles Deleuze and Jean-François Lyotard) of the Faculty of Philosophy at the Université de Paris VIII. He’s now René Descartes Chair and Professor of Philosophy at The European Graduate […]
The following piece explains a particular symbolic expression (or version) of Kurt Gödel’s first incompleteness theorem. It also includes a particular expression (or example) of a Gödel sentence (i.e., “This statement is false” — this link takes you to a humorous entry!). In terms of the actual symbols used, this representation of the theorem expresses a (slight) philosophical […]
Hardy occasionally let slip that I am an academic great-grandchild of G.H. Hardy, whose non-technical writings about mathematics, in particular A Mathematician’s Apology are often quoted in general discussions of the nature of mathematics. Here I give my personal thoughts related to four of these well known quotations. These of course reflect my own background, with a research career in […]
Group Theory Modeling this construction using GAP I sometimes pick up a math book that I can’t put back down. A year ago, it was Conway and Sloane’s Sphere Packings, Lattices, and Groups. In this post I’ll describe a neat connection between the sporadic Mathieu group M12 and the icosahedron that they describe. I’ll use GAP […]
History AI since Artistotle (Part 3) 20 Nov 2020 — 12 min read Photo by Greg Rakozy on Unsplash hat happened when there was neither direct evidence nor any eye witness in an ancient Greek court? A juror could not rely on Aristotlelian logic, since neither the acussor nor the accused used logic to reveal the truth; rather, […]
Relativity Deriving Einstein’s Gravity Equations From Thermodynamics Is Gravity Just an Average of the Behavior of Unknown “Atoms” of Spacetime? 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” — […]
The architectural symmetry of Cubic polynomials supports many root approximation methods, helping intuitive understanding and with a little work, can be transposed to higher orders to minimise more complex math. This post expands on an earlier post, Cubic Polynomials — Using Similar Triangles to Approximate Roots, which promoted the use of Similar Triangles derived from Turning and […]
The significance of prime numbers, in both everyday applications & as a subtopic pertinent to all branches of math, cannot be overstated. We quietly rely on their special properties to carry the backbone of countless parts of our society — all because they are an irreducible part of the very fabric of nature. Resistant to any further factorization, […]
Relativity How to Compute the General Relativistic Correction to Time General relativity is one of the most technically difficult physics theories, as it requires uncommon knowledge and mathematical skills. However, it is possible to calculate the relativistic effects induced by the curvature of space-time with good precision, and even to derive its formula, with a […]
A couple of things before we start, I’m not writing this as an attack, these are just personal view based on some facts. I’ll be using a little bit of math in the part of Game Theory nothing too crazy, I think if you have studied class 12th math you’ll understand it. And finally, please […]
What one would do to find the representation of a number written in one base to some another would probably be to take a look at the Euclidean algorithm: Dividing the number by a new base, writing down the integer part, then divide it again, and again, until it will not reach 0. The order formed […]
Emergent gravity is an idea in quantum gravity according to which the fabric of spacetime is not fundamental but emerges as a coarse-graining approximation of underlying (still unknown) microscopic degrees of freedom (similarly to a gas emerging from a large sampling of atoms or molecules). In the words of Huggett and Wuthrich, emergent gravity is the view that gravity arises due to the […]
When you think of knots, you might think of your double-knotted shoelaces or your hopelessly tangled earbuds. I personally think of garlic knots. However, these sorts of knots are different from mathematical knots. What kind of snob wouldn’t consider garlic knots valid knots? Well, the difference is that “knots” like shoelaces have loose ends, meaning […]
Puzzle What numbers do they need to contain to display all days of the month? Photo by Iga Palacz on Unsplash Calendar Dice are a popular gadget on German office desks. Two dice can be moved in a small box to display the current day of the month. They’re decorative and it’s not even clear that it is […]