Vintage Covectors

Covectors in the Dual Space. This sounds like an alien tribe living in a parallel universe hitherto unknown to humans. In this lectures on General Relativity, Prof. Frederic Schuller says: Now comes a much-feared topic: Dual vector space. And it's totally unclear why this is such a feared topic! A vector feels familiar: three numbers … Continue reading Vintage Covectors

Dirac’s Belt Trick

Is classical physics boring? In his preface to Volume 1 of The Feynman Lectures on Physics, Richard Feynman worries about students' enthusiasm: ... They have heard a lot about how interesting and exciting physics is—the theory of relativity, quantum mechanics, and other modern ideas. By the end of two years of our previous course, many … Continue reading Dirac’s Belt Trick

Motivational Function

complex-exp-1-z2

Deadly mutants are after us. What can give us hope? This innocuous-looking function is a sublime light in the dark. It proves you can always recover. If your perseverance is infinite. $latex e^{\left(-\frac{1}{x^{2}}\right)}&s=3 $ As x tends to zero, the exponent tends to minus infinity. The function's value at zero tends to zero. It is … Continue reading Motivational Function

Heat Conduction Cheat Sheet

I am dumping some equations here I need now and then! The sections about 3-dimensional temperature waves summarize what is described at length in the second part of this post. Temperature waves are interesting for simulating yearly and daily oscillations in the temperature below the surface of the earth or near wall/floor of our ice/water … Continue reading Heat Conduction Cheat Sheet

Consequences of the Second Law of Thermodynamics

Why a Carnot process using a Van der Waals gas - or other fluid with uncommon equation of state - also runs at Carnot's efficiency. Textbooks often refer to an ideal gas when introducing Carnot's cycle - it's easy to calculate heat energies and work in this case. Perhaps this might imply that not only must the … Continue reading Consequences of the Second Law of Thermodynamics

Computers, Science, and History Thereof

I am reading three online resources in parallel - on the history and the basics of computing, computer science, software engineering, and the related culture and 'philosophy'. An accidental combination I find most enjoyable. Joel on Software: Joel Spolsky's blog - a collection of classic essays. What every developer needs to know about Unicode. New terms … Continue reading Computers, Science, and History Thereof

Tinkering, Science, and (Not) Sharing It

I stumbled upon this research paper called PVC polyhedra: We describe how to construct a dodecahedron, tetrahedron, cube, and octahedron out of pvc pipes using standard fittings. ... In particular, if we take a connector that takes three pipes each at 120 degree angles from the others (this is called a “true wye”) and we … Continue reading Tinkering, Science, and (Not) Sharing It

Spheres in a Space with Trillions of Dimensions

I don't venture into speculative science writing - this is just about classical statistical mechanics; actually about a special mathematical aspect. It was one of the things I found particularly intriguing in my first encounters with statistical mechanics and thermodynamics a long time ago - a curious feature of volumes. I was mulling upon how … Continue reading Spheres in a Space with Trillions of Dimensions

You Never Know

... when obscure knowledge comes in handy! You can dismantle an old gutter without efforts, and without any special tools: Just by gently setting it into twisted motion, effectively applying ~1Hz torsion waves that would lead to fatigue break within a few minutes. I knew my stint in steel research in the 1990s would finally … Continue reading You Never Know

Ploughing Through Theoretical Physics Textbooks Is Therapeutic

And finally science confirms it, in a sense. Again and again, I've harping on this pet theory of mine: At the peak of my immersion in the so-called corporate world, as a super-busy bonus miles-collecting consultant, I turned to the only solace: Getting up (even) earlier, and starting to re-read all my old mathematics and … Continue reading Ploughing Through Theoretical Physics Textbooks Is Therapeutic