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Diversity Improves Machine Learning
For the last two years, the Nonlinear Artificial Intelligence Lab and I have labored to incorporate diversity in machine learning. Diversity conveys advantages in nature, yet homogeneous neurons typically comprise the layers of artificial neural networks. In software, we constructed neural networks from neurons that learn their own activation functions (relating inputs to outputs), quickly…
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Neural network does quantum mechanics
A particle confined to an impassable box is a paradigmatic and exactly solvable one-dimensional quantum system modeled by an infinite square well potential. Working with Bill Ditto, Elliott Holliday and I recently explored some of its infinitely many generalizations to two dimensions, including particles confined to regions that exhibit integrable, ergodic, or chaotic classical billiard…
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The Ringed Planets
When I was a kid, Saturn was the ringed planet. But today, we know that all of the outer planets have rings. The James Webb Space Telescope has now imaged each of them in infrared revealing their distinctive structures, including Jupiter‘s very faint ring (located by the arrow and dashed curve). The planet images below…
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Simplest Chaos
The motion of one of the simplest dynamical systems, a torqued, damped, nonlinear pendulum, can be infinitely complicated. Consider a simple pendulum of length and mass rigidly connected to an axle of radius wrapped by a rope that hangs down one side with a mass climbing up and down it, as in the attached animation.…
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Vampire Ein Stein
Just a couple of months after announcing the remarkable discovery of a single shape that forces a non-periodic tiling of the plane, Smith, Myers, Kaplan, and Goodman-Strauss have announced an improved aperiodic monotile or ein stein. (Ein stein is “one stone” in German.) The hat and turtle shapes tile the plane only non-periodically, but with their…
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The Temperature of the Vacuum
Quantum field theory predicts that the temperature of empty space should depend on the observer’s motion, increasing proportionally with acceleration. Here I attempt an accessible introduction to this striking effect, related to Hawking radiation and discovered independently by Fulling, Davies, and Unruh, assuming only sophomore-level physics (including hyperbolic functions) with some assistance from Mathematica. Hyperbolic…
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A Century of Compton Scattering
One hundred years ago today the Physical Review published research on light scattering electrons that would earn its author, Wooster graduate Arthur Compton, a Physics Nobel Prize. By relativistically conserving spacetime momentum, as in the diagram below, and treating light as particles now called photons, Compton discovered that deflecting an electron through an angle stretches…
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We Are Going
After half a century confined to low-Earth orbit, and as soon as late next year, humans will once again leave Earth and voyage to Moon. The reality of this exciting adventure crystallized earlier this month when NASA announced the diverse and inspiring Artemis II crew: Clockwise from left in the photo below are Christina Koch,…
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Behold, an Ein Stein!
This academic year has been thrilling: first nuclear fusion breakeven, now an ein stein! Last week, a preprint at arxiv.org by David Smith et al. announced an “ein stein”, or one stone, a shape that forces a non periodic tiling of the plane, ending a half-century quest by many researchers, including me. A retiree and…
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Generalizing Coulomb’s Law
The forces between two electric charges in arbitrary motion are complicated by velocity, acceleration, and time-delay effects. The forces need not even lie along the line joining the two charges! Suppose a source charge is at position with velocity and acceleration , and a test charge is at position with velocity and acceleration . Let…
Author: John F. Lindner
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Nice post, John! Thanks for writing these. I always enjoy them.
David Smith’s ein stein is an awesome shape!
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Thanks, Mark! I enjoy reading your posts as well.