I have picked two colors. They shall shine in the dark. ~~~ Another version of my series Reality and Imagination. I used artistic license when tweaking the color values.

# Tag: Complex Analysis

# 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 … Continue reading Boosted

# Complex Alien Eclipse

My colorful complex function lived in a universe of white light. I turned off the light. Turned it into its negative. Expected it to look bleak. Like thin white bones on black canvas, cartoon skeletons of imaginary alien creatures. But it is more like the total solar eclipse I watched in 1999. There is interference, … Continue reading Complex Alien Eclipse

# Spins, Rotations, and the Beauty of Complex Numbers

This is a simple quantum state ... |β> = Ξ±|β> + Ξ²|β> ... built from an up |β> state and a down state |β>. Ξ± and Ξ² are complex numbers. The result |β> is in the middle, oblique. The oblique state is a superposition or the up and down base states. Making a measurement, you … Continue reading Spins, Rotations, and the Beauty of Complex Numbers

# 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

# 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

# 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

# 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. $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