Edward Lorenz: The Butterfly Man
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Edward Lorenz was a meteorologist who discovered the butterfly effect in the 1960s. While working at MIT, he created a simplified computer model of weather patterns. One day, he restarted the model from a midway printout instead of from the beginning, and noticed the results diverged significantly. This led him to realize small changes in initial conditions could dramatically affect the long-term outcome, hence the metaphor of a butterfly's wings causing a hurricane. Lorenz's discovery helped establish the field of chaos theory and showed weather is inherently unpredictable in the long run due to its chaotic nature.
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Nikola Tesla detected faint radio signals in 1899 while experimenting in Colorado that he believed came from Mars. He published several accounts over subsequent decades reiterating his conviction that the signals were of planetary origin and not from any known terrestrial source. Researchers Kenneth and James Corum analyzed Tesla's receivers and experiments, finding that under certain conditions there exists an ionospheric window that could allow detection of signals in the lower very low frequency range Tesla's receivers functioned in. They believe Tesla may have made the original pioneering achievement in radio astronomy by detecting the first signals from another planet.
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The iDeal Reader Jacob Bronowski, ‘‘The Nature of Scientific.docx
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Lattice Energy LLC-LENRs ca 1950s-Sternglass Expts-Einstein & Bethe-Nov 25 2011
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The Pre-History of the Two Black Hole Collision Problem
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The britannica guide to relativity and quantum mechanics (physics explained)
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Nikola tesla and the electrical signals of planetary origin
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More from Abhranil Das
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Theoretical description and MATLAB code for depth estimation from stereo image pairs using the simple technique of block-matching.
Derivation of the Boltzmann Transport Equation
A physical derivation of the Boltzmann Transport Equation of kinetic theory, using only basic scattering theory.
The Moore-Spiegel Oscillator
This document discusses the Moore-Spiegel oscillator, a nonlinear oscillator model used to study chaos. It provides the system equations, finds periodic and chaotic solutions using numerical integration, and analyzes the dynamics through phase space plots, Poincare sections, bifurcation diagrams, and Lyapunov exponents. The analysis reveals transitions from periodic to chaotic behavior as the control parameters are varied.
Are Randomly Grown Graphs Really Random?
A paper that discusses whether randomly grown graphs, as opposed to static random graphs, are truly random.
Active Matter and the Vicsek Model of Flocking
Active matter consists of active units that take in and dissipate energy, often leading to large-scale organization. Examples include cytoskeleton with molecular motors and schools of fish. The Vicsek model simulates flocking through particles that maintain a fixed speed but align their direction of motion based on nearby particles, with some random perturbation. It exhibits a phase transition from disorder to global coherence as noise is reduced. While simple, it demonstrates self-organization in self-driven systems and similarities to models of magnetism. However, it is a minimal model that requires more biological realism and tuning of parameters like neighborhood size.
Stochastic Neural Network Model: Part 2
A stochastic computer model for hippocampal brain activity exhibits behaviour earlier identified as deterministic chaos, and hence raises doubts over the techniques of identifying chaotic dynamics.
Lyapunov Exponent of Time Series Data
The document discusses the Lyapunov exponent, which is a measure of the rate of divergence of infinitesimally close trajectories in a dynamical system. It provides the example of calculating the Lyapunov exponent for the logistic map and an interbeat interval time series, finding the exponent to be approximately 0.75 for the logistic map and demonstrating independence and randomness for variables in the interbeat interval time series.
Diffusion-Limited Aggregation
A simulation of diffusion-limited aggregation (DLA) processes that give fractal shapes to mineral dendrites, electrodeposition etc.
Simulating Evolution and Behaviour
The document describes a program called monkey.py that simulates evolution through natural selection to generate a desired phrase or quote. The program starts with a random or user-defined initial phrase and then iteratively mutates the phrase, judges fitness compared to the destination phrase, selectively breeds the most fit phrase, and repeats over generations. Within a few generations, the program is often able to generate complex phrases like Shakespearean quotes that would be nearly impossible through random chance alone. The program demonstrates how natural selection is able to guide evolution in a directed manner to produce complex outcomes in a small fraction of the time compared to an unguided random process.
Stochastic Neural Network Model: Part 1
A stochastic computer model for hippocampal brain activity exhibits behaviour earlier identified as deterministic chaos, and hence raises doubts over the techniques of identifying chaotic dynamics.
Perspective: the maths of seeing
This is the two-part seminar I gave in college on my book that is being published. Hope you like it, although a lot of the information was delivered verbally and is not contained in the slides.
Transposons: the jumping genes
Transposons are segments of DNA that can move within a genome and sometimes cause mutations. They were first discovered by Barbara McClintock in maize plants while studying how transposition affected kernel color, work for which she later won a Nobel Prize. There are two main types of transposons: retrotransposons, which copy and paste via an RNA intermediate using reverse transcriptase; and DNA-only transposons, which cut and paste directly using a transposase enzyme without an RNA intermediate. Transposons can cause target repeats when they insert into new locations in the genome and can contain their own transposase gene, making them self-sufficient. Some transposons contain additional genetic material flanked by insertion
The DNA Double Helix
1) The DNA double helix structure has two helical strands that are skewed and not directly opposite each other, resulting in a distance between the strands at any cross-section that is less than the diameter of the helices.
2) The structure of the two helical strands can be defined mathematically using parametric coordinates, where the angle θ increases by 2π with each turn of the helix.
3) The pitch of the helix, or vertical rise of one complete turn, can be calculated using the parametric coordinates and angles of the two helical strands.
Cellular automata
Cellular automata are self-operating systems where cells on a grid update in discrete time steps according to a set of rules based on the states of neighboring cells. John Conway invented the Game of Life, a famous 2D cellular automaton where cells are either alive or dead and change states based on how many neighboring cells are alive. Common patterns in the Game of Life include static shapes, oscillators that repeat patterns over time, and gliders that move across the grid.
Hyperactivation
Hyperactivation is a form of increased sperm motility characterized by high amplitude movements, deep bends in the tail, and frequent changes in swimming direction. It occurs after capacitation as calcium levels in the sperm rise, opening ion channels that allow for stronger tail movements. Hyperactivation helps sperm penetrate the zona pellucida surrounding the egg by providing greater propulsion through the female reproductive tract and increasing the chances of finding the egg.
Cellular Automata
On cellular automata, which are artificial systems that develop according to simple rules, but sometimes amazingly emulate nature and life.
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The narrative then shifts to a captivating exploration of prominent desktop OSs, Windows, macOS, and Linux. Windows, with its globally ubiquitous presence and user-friendly interface, emerges as a cornerstone in personal computing history. macOS, lauded for its sleek design and seamless integration with Apple's ecosystem, stands as a beacon of stability and creativity. Linux, an open-source marvel, offers unparalleled flexibility and security, revolutionizing the computing landscape. 🖥️
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Overview
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7. What is Prometheus?
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12. Jupyter Notebooks with Code Examples
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Edward Lorenz: The Butterfly Man
- 1. Edward Lorenz The Butterfly Man Abhranil Das
- 2. Sunrise on 20 Nov 2031: 5:52 AM [1] Weather on 20 Nov 2011: ? [1] : timeanddate.com
- 3. Edward Norton Lorenz Born in Connecticut Studied Mathematics at Dartmouth and Harvard Served as a forecaster in the US Army Air Corps from 1942-46 Returned to study meteorology at MIT, published good orthodox papers Kept thinking about forecasting
- 4. The situation in the 1960’s Forecasting isn’t science; it’s guesswork. MIT: Work on problems that have solutions. Don’t trust computers.
- 5. “The machine, a Royal McBee, […] broke down every week or so. It had neither the speed nor the memory to manage a realistic simulation of the earth’s atmosphere and oceans. Yet Lorenz created a toy weather in 1960… Every minute the machine marked the passing of a day by printing a row of numbers across a page… Digitized cyclones spun slowly around an idealized globe.” - Chaos, James Gleick
- 6. Newtonian determinism + the computer: Weather problem solved. Or not.
- 7. “One day in the winter of 1961, wanting to examine one sequence at greater length, Lorenz took a shortcut. Instead of starting the whole run over, he started midway through. To give the machine its initial conditions, he typed the numbers straight from the earlier printout. “Then he walked down the hall to get away from the noise and drink a cup of coffee. When he returned an hour later, he saw something unexpected, something that planted a seed for a new science.”
- 8. The Butterfly Effect 0.506127 → 0.506 Lorenz had a gut feeling it wasn’t the computer. And that it held true in the real atmosphere.
- 9. Lorenz was a meteorologist, and no one thought to look for chaos on page 130 of volume 20 of the Journal of the Atmospheric Sciences.
- 10. References Chaos: the making of a new science James Gleick