Electromagic ~~~ Appeal of Antique Scientific Instruments

A collage of images and a collage of words. The images are public domain technical drawings related to electromagnetism. The lines of the poem are my prompts, followed by phrases from the first Google search results prompted by it.   ~~~ Electromagic explore the illuminating history seamless and unforgettable Metal and Wood memory building work…

They Shall Shine in the Dark

On February 24 I wrote: They shall shine in the dark. I use this sentence as a seed for Twitter search poetry – interlacing poetry with temperature waves again . ~ ~~ ~~~ ~~~~ They shall shine in the dark The interstellar void going down much faster determined to take over under renewed attack under…

Plural Form

Take a figure of a historical patent, meticulously drawn before there was software. It’s a Plural Grating Spectrograph. Wonder about the appeal of antique technical drawings. So modest, so sublime. Copy it, multiply it. Slowly rotate the color wheel, until the purples meet the reds again. This is an impossible spectrum. There are no purples…

Tribute to a Pragmatic Swiss Solar Pioneer – Who Called to Action in 1989

He is called a pragmatic doer, knowing his physics and engineering, devoid of ideology. This is how Josef Jenni is introduced in the preface to his document called How can we achieve the energy transition (Wie erreichen wir die Energiewende). It’s a manifesto and a technical overview – by the pioneer whose company had built…

Loops Near the surface. Lumped Together in Space.

There was a time, when most articles here looked like lab reports or chapters of a thesis. Occasionally, there was a weird poem thrown in. Now is the time for art only, and the thesis-like postings provide for raw material. Temperature waves beneath the ground, driven by the oscillation of the temperature on the surface…

Innovation and Scarcity (and Panic)

I tried to avoid such words. They sounded like hollow buzzwords in times of abundance, used by advertizers playing on fears. But our complacent world is taught a lesson, right now, at furious speed. I am following news as everybody else, I am reading about gloomy forecasts. An Austria paper mill has announced today it…

Jellyfish of Diffraction

Diffraction patterns, again. But this time I tack them to an imaginary semi-circular screen. Screens grow bigger in radius with increasing wavelength – growing more reddish. If every wavelength would be diffracted in the same way, all peaks would lie on a radius of the circle. But as red is diffracted more, maxima move to…

Newton’s Space Probes Investigate my Ribbons of Diffraction

I have been calculating diffraction patterns for visible light. Curves are displaced to turn the whole structure into a wavy ribbon built from colored wires or threads. I have turned these images into collages, adding Isaac Newton’s drawings from Opticks (1704). The more I moved Newton’s figures around, and the more I twisted the ribbons…

Transforming the Celestial Sphere

A spherical spaceship swooshes by at 99% of the speed of light. What will it look like? Squashed because of Lorentz contraction – like an ellipsoid? No. The outline of a moving sphere will remain spherical. Roger Penrose explained this first in 1958 – 50 years after Einstein’s formulation of the theory of special relativity….

Boosted

I have been playing with the geometry of special relativity again! The light cone signifies the invariance of the speed of light. There is a notion of length in four-dimensional spacetime, defined as c2t2 – x2 – y2 – z2. Surfaces of constant length are 4-dimensional hyperboloids. Light rays are null rays, as light travels…

Joys of Geometry

Creating figures with math software does not feel like fabricating illustrations for science posts. It is more of a meditation on geometry. I want to literally draw every line. I am not using grid lines or rendered surfaces. I craft a parametric curve for every line. A curve is set of equations. Yet, playing with…

Spins, Rotations, and the Beauty of Complex Numbers

This is a simple quantum state … |➚> = α|↑> + β|↓> … built from an up |↑> state and a down state |↓>. α and β are complex numbers. The result |➚> is in the middle, oblique. The oblique state is a superposition or the up and down base states. Making a measurement, you…

Galaxies of Diffraction

These – the arrangement of points in the image below – are covectors, sort of. I wrote about them, some time ago. They are entities dual to vectors. Eating vectors, spitting out numbers. Vectors are again ‘co’ to vectors; they will eat covectors. If vectors live in a space with axes all perpendicular to each…

My Elliptical Cone

I’ve still been thinking about this elliptical cone! It has been the main character in my geometric proof on stereographic projection mapping circles to circles. The idea has been to reduce a three-dimensional problem to a two-dimensional one, by noting that something has to be symmetric. A circle on a sphere is mapped to some…

Circles to Circles

Using stereographic projection, you create a distorted image of the surface of a sphere, stretched out to cover an infinite plane. Each point on the sphere is mapped to a point in the equatorial plane by a projection ray starting at a pole of the sphere. Draw a circle on the sphere, e.g. by intersecting…

Lines and Circles

I poked at complex function 1/z, and its real and imaginary parts look like magical towers. When you look at these towers from above or below, you see sections of perfect circles. This is hinting at some underlying simplicity. Using the map 1/z, another complex number – w=1/z – is mapped to z. Four dimensions…

Looking Back: Hacking and Defending Windows Public Key Infrastructure (ADCS)

I live at the fringes of the cybersecurity community. I have never attended infosec conferences. There will be a talk on PKI hacking at Blackhat 2021 soon: Top AD offensive security gurus are presenting comprehensive research on abusing ADCS (Active Directory Certificate Services). I only know about that, because I noticed backlinks from their article…

Reality and Imagination

Grey and colorful. Cutting through each other. Chasing each other. Meeting in the center, leaning on each other, forming an infinite line. ~ Reality and Imagination: Real and imaginary part of complex function 1/z: ~ The real part of 1/z is painted in shades of grey, the imaginary part in rainbow colors. Plots are created…

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…

Injecting an EFS Recovery Agent – and Let the Virus Scanner Help You!

How can you read files encrypted with Windows’s Encrypting File System if you neither have access to the owner’s encryption certificate and key and nor that of a legit data recovery agent (DRA) … but if you are a local administrator? This work is still inspired by the hackthebox machine Helpline. You were able to…

Peter M. Schuster on History of Science

The late Dr. Peter M. Schuster was a physicist and historian of science. After a career in industry, he founded a laser technology startup. Recovering from severe illness, he sold his company and became an author, science writer, and historian. He founded echophysics – the European Center for the History of Physics – in Pöllau…

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…

Motivational Function

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. As x tends to zero, the exponent tends to minus infinity. The function’s value at zero tends to zero. It is a zero value…

Infinity

New Year’s Eve 2019 seems infinitely far in the past. It was the first day news about this mysterious disease had been published in my country. Yet it seems infinitely far away at that time, somewhere in China. Today we see something glowing at the end of a weird long corridor. Despite horrible news, I…

Gödel’s Proof

Gödel’s proof is the (meta-)mathematical counterpart of the paradoxical statement This sentence is false. In his epic 1979 debut book Gödel, Escher, Bach Douglas Hofstadter intertwines computer science, math, art, biology with a simplified version of the proof. In 2007 he revisits these ideas in I Am a Strange Loop. Hofstadter writes: … at age…

Enthalpy

When you move from fundamental principles (in physics)  to calculating something ‘useful’ (in engineering), you seem to move from energy to enthalpy. Enthalpy is measured in Joule, as well as energy. It is assigned to a ‘system’, a part of the physical world separated from other parts by interfaces. The canonical example is a vessel…

Statistical Independence and Logarithms

In classical mechanics you want to understand the motion of all constituents of a system in detail. The trajectory of each ‘particle’ can be calculated from the forces between them and initial positions and velocities. In statistical mechanics you try to work out what can still be said about a system even though – or…

Integrating The Delta Function (Again and Again) – Penrose Version

I quoted Nobel prize winner Paul Dirac’s book, now I will quote this year’s physics Nobel prize winner Roger Penrose. In his book The Road to Reality Penrose discusses not-so-well-behaved functions like the Delta Function: They belong in the category of  Hyperfunctions. A Hyperfunction is the difference of two complex functions: Each of the complex…

The RSA Algorithm

You want this: Encrypt a message to somebody else – using information that is publicly available. Somebody else should then be able to decrypt the message, using only information they have; nobody else should be able to read this information. The public key cryptography algorithm RSA does achieve this. This article is my way of…