look at these towers Using the map creating a distorted image projected up to the sphere All connecting rays follow this rule Imaginary number i makes an appearance that borders on the poetic It’s nothing more than a whisper construct the proof for yourself something of a dying art avoid thinking about anything there has … Continue reading Elliptical Poetry

# 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 … Continue reading My Elliptical Cone

# 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 … Continue reading Circles to Circles

# 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 … Continue reading Lines and Circles

# 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 … Continue reading Looking Back: Hacking and Defending Windows Public Key Infrastructure (ADCS)

# 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 … Continue reading Reality and Imagination

# 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

# Super Motivational Function

I've presented a Motivational Function, a while back. $latex f(z) = e^{\left(-\frac{1}{z^{2}}\right)}&s=3 $ It is infinitely flat at the zero point: all its derivatives are zero there. Yet, it manages to lift its head - as it is not analytic at zero! If you think of it as a function of a complex argument, its … Continue reading Super Motivational Function

# Construct the Labyrinth from Which You Plan to Escape

Found Poetry found me. I started this website as a science blog, but then I saw poetry in mundane texts - just as you see faces in things. I created poems from spam comments, from search terms, from physics textbooks, from book spines, from error messages, from Facebooks ads, from any text anywhere in the … Continue reading Construct the Labyrinth from Which You Plan to Escape

# Secure Poetry: “I have been quite confident”

A poem from snippets of two postings on cybersecurity. Trying to carve words out of jargon. Details on the creative process at the bottom of the post. I have been quite confident I have been inspired In this simple way to find both options take note of an extra stealth factor I hardly ever … Continue reading Secure Poetry: “I have been quite confident”