88.9 ThinkMinded Rooftop Meetup

Yesterday was the 88nine ThinkMinded Rooftop Meetup.

A lot of great Creative, tech startups, and entrepreneurially-minded individuals made it. For example, there were podcast recorders from Everyday Media, freelancers, Students working with The Commons, the RokkinCat team, and a representative from Spin Group (me).

Image result for 88.9 radio milwaukee rooftop thinkminded
I didn’t take this photo, but it’s a lot like what last night looked like.

Pilot Wave Theory: An Alternative Explanation to the Double-Slit Experiment

bouncing silicon droplets
An image of silicon droplets bouncing on oil, imitating the behavior of light particles according to Pilot Wave Theory

“Instead of non-real waves and real particles, why not just have real waves that push around real particles?” – Matthew O’Dowd, faculty at CUNY

There are a lot of weirdness in the quantum physics world. So much weirdness that quantum physics actually refers to some phenomena as quantum weirdness. And believe me, it lives up to it’s name. One example of very weird behavior is the wave-particle duality of light. The wave-particle duality is an explanation for how light behaves. Basically, it says that under certain circumstances, light is a particle. Under other circumstances, it behaves like a wave. Specifically, there is one experiment that is the “classic” case of demonstrating the apparent shift back and forth between the states called the double-slit experiment. The reason this topic gets attention is because of the outcome. Scientists expect electrons being shot through a double slit to behave like a particle — producing only two lines on a screen, but it behaves as a wave, producing a pattern of lines.

The current consensus explanation is that light can shift between particles and waves depending on the scenario. However, there is an alternative! The Pilot Wave Theory of light provides an excellent explanation for this experiment. It is also highly intuitive. Basically, it states that light does not shift between particle and wave, it is both at the same time. It is basically light particles riding on light waves, like surfers riding on ocean waves. This theory has a lot of traction in physics circles, but tragically is not accepted by mainstream science. This theory accurately explains the outcome of the double-slit experiment and challenges firmly held beliefs about the nature of light.

The double slit experiment shows how light behaves

Let’s zoom out here, and see exactly what the double-slit experiment is. The double slit experiment starts with the single-slit experiment. The single-slit experiment is basically setting up a particle beam that shoots either photons (small particles of light) or electrons through a slit in some kind of shield. The media shot through this is then observed on the other side.

1 Double slit Exp Single slit results | From the mid 1600 ...
The single-slit experiment produces results that we expect. A beam of light goes through a slit and produces a single strip of light on the other side.

Like the illustration shows, the single-slit experiment produces the expected result. This is how light acts as a particle. It travels straight through and produces a strip of light on the screen. Nothing really strange here at all, eh? But things get strange when another slit is added to the slit partition.

Superposition, Interference and Decoherence - Quantum ...
The double-slit experiment produces an interference pattern of light, similar to how a wave would behave.

Didn’t see that one coming, did ya? Well neither did a lot of scientists. However, when we now view light as a wave, the reason this happens is pretty clear. The waves are stacking on one another and producing an interference pattern on the screen. Essentially, waves of light are constructively and destructively interfering as they travel towards the screen, and producing the pattern of light and dark fringes. View the illustration below to see a visual of this.

As a wave goes through the two slits, it produces two waves that interfere with one another, producing an interference pattern and the resulting strips of light particles on the back screen

So what is the confusion exactly? Well, the confusion lies in the fact that the particles being collected on the back screen are behaving like waves. Remember in the beginning of the article when I talked about how the particles are collected on the back screen? Take a look at what they look like.

Strange! So it appears as though the light/electrons do in fact behave like both particles and waves. The particles are going through the slits, but they are distributed exactly like waves would be. But the current explanation is…they change between the two?

Enter Pilot Wave Theory

The alternative explanation to the wave-particle duality is to model the light particles as moving on waves. This is referred to as Pilot Wave Theory. This way, we don’t have to believe that light somehow flips between one state and another in a logic-defying way. Take a look at the animation below of the double-slit experiment. It accurately depicts a discrete light particle riding a light wave to it’s destination: one of the interference patterns bars on the back collection screen.

Pilot Wave Theory and Quantum Realism | Space Time | PBS Digital Studios
This animation from PBS Digital Studios provides a visual of the Pilot Wave theory. Light particles “ride” the waves of light, instead of transforming into them. The particle takes a specific trajectory (based on classical wave mechanics) and hits the screen as expected.

Where is this theory from? A man name Louis de Broglie formulated this theory in the early 20th century. He modeled the light waves using the Schrödinger equation. [For information regarding the origin of the Schrödinger equation, please read this article]. However, his idea was ultimately rejected at the Solvay Conference. Mainstream academia’s strict adherence to Einstein’s general relativity and special relativity do not allow for light particles to travel on “guiding waves” as de Broglie describes. However, the elegance and brilliance of pilot wave theory has maintained many followers since it’s inception, and has lead many to abandon Einstein’s theories altogether in favor of de Broglie’s.

https://upload.wikimedia.org/wikipedia/commons/thumb/6/6e/Solvay_conference_1927.jpg/700px-Solvay_conference_1927.jpg
Einstein’s (fifth from right, bottom row) relativity theory overcast de Broglie’s pilot wave theory (third from right, middle row) at the 1927 Solvay Conference in Copenhagen, Denmark.

One person who pushed Pilot Wave Theory to a new height was David Bohm. David Bohm completed the Pilot Wave Theory. In fact, it was even renamed after his work in the 1950s, giving it it’s current name: de Broglie-Bohm Pilot Wave Theory.

David Bohm.jpg

There is a PBS Space Time publication that does an excellent job explaining the history of Pilot Wave Theory, and provides the back story of it’s formulation. In a nutshell, a scientist name Louis de Broglie came up with the theory in the early 20th century. His idea was rejected in Copenhagen quantum meetings, however. Other contemporary quantum leaders such as Neils Bohr and Werner Heisenberg were adamant about rejecting “classical” physics in their interpretation of quantum phenomena. Maybe they threw out the baby with the bathwater, though. but was revived by David Bohm in the 1950s.

The “life-sized” counterparts to pilot-wave theory

Analogous experiments that show Pilot Wave behavior can be reproduced at a human scale. Physicists like Yves Couder use silicon droplets bouncing on oil to demonstrate the particle-wave interaction. The particle bounces up and down, and generates a wave that pushes it. Below is a real example of silicon droplets in a double-slit experiment.

Yves Couder . Explains Wave/Particle Duality via Silicon Droplets [Through the Wormhole]
The appeal of Pilot Wave Theory is that it does not stray far away from classical physics—let alone throw it away like Einstein’s quantum theory. Scientists such as Yves Couder demonstrate the same double slit behavior with silicon particles visible to the naked eye.
As you can see in the footage (not an animation!), the bouncing silicon droplet picks a discrete trajectory. Staunch physicists may say “the quantum world does not behave like the human scale world.” But this kind of thinking is a hindrance to progress. After all, why shouldn’t it? Why do we need to weave stories about light particles transforming into waves when more intuitive  (or perhaps even obvious) explanations exist? I will leave that up to the reader to decide.

“In physics experiments, you only see what you are prepared to see.” – Researcher Yves Couder, University of Paris-Diderot, (producer of human-scale silicon droplet double-slit experiment)

Summary and looking deeper

Pilot Wave Theory is an elegant solution to the wave-particle duality problem. Instead of making mystical demands of scientists, and making ridiculous claims about wave particle transmutations, it gives an intuitive explanation for the double-slit experiment. The main reason it is rejected is due to political ignorance and orthodoxy surrounding Einstein’s flawed general relativity and special relativity doctrines. However, the theory has gained traction in circles mainly outside academia ever since it’s inception. Please investigate the theory for yourself and leave a comment with any errors or suggestions.

In a nutshell, Pilot Wave Theory suggests that light particles travel in discrete paths as particles, guided by waves.

Works Cited

Through the Wormhole – Wave/Particle – Silicon Droplets

Double slit GIF – By Lookang many thanks to Fu-Kwun Hwang and author of Easy Java Simulation = Francisco EsquembreOwn work, CC BY-SA 3.0, Link

Why don’t more physicists subscribe to pilot wave theory?

Bush, John. (2015). Pilot-Wave Hydrodynamics. Annual Review of Fluid Mechanics. 47. 269-292. 10.1146/annurev-fluid-010814-014506.

Pilot Wave Theory and Quantum Realism | Space Time | PBS Digital Studios

Particles on screens –

Description
English: Results of a double-slit-experiment performed by Dr. Tonomura showing the build-up of an interference pattern of single electrons. Numbers of electrons are 11 (a), 200 (b), 6000 (c), 40000 (d), 140000 (e).
Date
Source Provided with kind permission of Dr. Tonomura

Pomodoro Timer

Well golly-gee! Thanks for taking the time to take a peek at this!

I am posting a link here to a project I wrote on CodePen.io. It’s a pomodoro timer. For those who aren’t familiar, the pomodoro technique is a method that helps people fight procrastination and the fear of starting a project. It does this by challenging someone to only spend 25 minutes on a task, rather than hours. This helps break the “fear barrier” of starting a project (the “aw shit I gotta spend all day on this” mentality). In addition, it helps with focus because the other rule to using a pomodoro timer is that you work distraction-free for 25 minutes. No cell phones, no talking to other people, just 25 minutes of solid effort toward a specific goal. It has worked wonders for me and many other people. Please check out, and use the pomodoro timer I created!

Rules:

  1. Decide on the task to be done.
  2. Set the pomodoro timer (traditionally to 25 minutes).[1]
  3. Work on the task disctraction free, no cell phones, notifications, pointless email checking, Facebook, etc.
  4. End work when the timer rings and put a checkmark on a piece of paper.[5]
  5. If you have fewer than four checkmarks, take a break (5 minutes), then go to step 2.
  6. Do as many pomodoros as is comfortable, usually 1-4. If exceeding 4, take a long break after 4th (usually 15 mins).

 

Sonoluminescence Video

Hello!

Please check out a video made collaboratively with Thunderbolts project. It covers the material in the article with additional commentary from Thunderbolts. Cheers and happy Friday!

The Border of Death

A human skull

This article is dedicated to the memory of Victor Mikecz (6-20-1926 – 4-13-2018), who passed away during the writing of this article.

Death seems like a black and white subject. There is not much middle ground between alive and dead. Or is there? The law has strictly defined definitions of death that are used during examinations and in making medical decisions for those kept alive by external life support. However, the border between life and death has many shades of gray. For those in states of persistent unconsciousness, life becomes a condition ranging from hope for full recovery to death only being a matter of time. For healthy individuals going through cardiac arrest, they may have “near-death experiences” with previously unexplained “lights.” New research in these subjects is giving humanity greater insight into both conditions of unconsciousness and the electrical nature of near death experience. Though death is defined legally, our understanding of human conditions near the border of death continues to grow with advances in brain research and electrical technology.

Background, The UDDA Death Document

In the United States, death is defined by the Uniform Determination of Death Act. The National Conference of Commissioners on Uniform State Laws wrote the document in 1980 for adoption across all 50 states, and is currently adopted by 37 US states, Washington D.C., and the U.S. Virgin Islands. The American Medical Association (AMA), the American Bar Association (ABA), and President’s Commission on Medical Ethics all approved this document. The document was necessary because medical methods throughout the 1970s were clashing with out-of-date legal standards of death. Simply put, at that time death was still defined by common law as the cessation of the cardiorespiratory system. The UDDA builds on the old common law by extending the definition of death to include complete not only heart and lung failure, but termination of all brain function, including the brain stem.

This is an important point, because the brain stem is a very tough little bugger,

The brain stem of a human brain
The three parts of the human brain stem.

and will continue to function under harsh circumstances. It is the most primitive part of the human brain. It handles some very core aspects of human functioning. Among other things, the brain stem controls the cardiovascular system, respiratory function, alertness, and consciousness. Therefore, loss of brain stem function is the end of the road for a human being. This total loss of function in the brain is a brain death.

Hello…? Any controversy in there?

Where exactly is the issue? The difference between between brain death and persistent vegetative states is critical in understanding how the US defines death and how patients are treated in each condition. Think of the term “brain-dead,” and the type of person it is used to describe—someone in a coma, someone unresponsive. This layman’s word is similar to brain-death but does not mean the same thing. Well, what many think is a brain death could be a persistent vegetative state (PVS). In a persistent vegetative state, medical care usually consists of nothing more than a feeding tube. People who have suffered severe brain trauma typically are the ones who suffer with persistent vegetative states. The condition is one in which the patient retains some function of consciousness. They exhibit sleep-wake cycles, and often can use some motor function such as use of their eye-lids. What is the difference, exactly between PVS, a brain death and a coma? The key difference is that people in PVS still retain function of their brain stem, whereas in a brain death, the brain stem has lost all function and the patient has to be supported by external equipment. Lastly, in a coma, the patient has lost all consciousness, and will not respond at all to touch, speech, or any other form of contact.

The Electric Brain

Advances in medical instrumentation now help determine the cognitive functioning of patients in PVS states. For example, in a recent article published in New England Journal of Medicine, researchers used fMRI to ask questions to a patient, and then measure the response using fMRI equipment. The article called Willful Modulation of Brain Activity in Disorders also states that

“…a small proportion of patients in a vegetative or minimally
conscious state have brain activation reflecting some awareness and cognition.”
-Martin Monti et. al,, New England Journal of Medicine
fMRI of brain
fMRI (functional Magnetic Resonance Imaging) allows doctors to view brain activity in real time.

The article states that scientists could ask questions and patients responded “yes” or “no” via measurement with fMRI. These researchers also state that new methods are required to make diagnoses of conditions of consciousness such as comas and persistent vegetative states. The article states that 40% of these conditions are misdiagnosed!

fMRI of yes/no answer
Actual “yes” and “no” responses of patients correspond with similar brain activity of control patients. Source: New England Journal of Medicine

Despite these scans appearing promising for all PVS patients, it is important to note that only a minority of PVS patients in this study exhibited this ability to “communicate” via fMRI in this study. Specifically, five of fifty-four patients (~9%) could do so. This is important to note, as fMRI is by no means a miraculous means of communicating, but can be effective for investigating the state of a patient’s conscious state.

On that same token, vegetative states encompass a wide range of conditions. The definition of the state is rather broad in most contexts. The Royal College of Physicians defines vegetative states as “A state of wakefulness without awareness in which there is preserved capacity for spontaneous or stimulus-induced arousal, evidenced by sleep–wake cycles and a range of reflexive and spontaneous behaviours.” In plain English, aside from sleep-wake cycles and some motor movement, vegetative states can be applied to a very broad range of states of consciousness after a traumatic brain injury. This is probably why fMRI communication does not work with all patients, some simply have more damage than others and are in lowered states of consciousness.

Life After Death for a Healthy Brain

Aside from other states of consciousness that linger near death, healthy human brains actually exhibit strange electrical activity after death. In a article published in PNAS called “Surge of neurophysiological coherence and connectivity in the dying brain,” researchers at the University of Michigan state that their research partially explains why many cardiac-arrest patients have “near-death experiences.” Their research shows that when rats clinically die, and blood flow stops to the brain, the brain actually exhibits electrical activity similar to that in conscious perception.

Jimo Borjigin
Jimo Borjigin
“High-frequency neurophysiological activity in
the near-death state exceeded levels found during the conscious
waking state. These data demonstrate that the mammalian brain
can, albeit paradoxically, generate neural correlates of heightened
conscious processing at near-death.”

Jimo Borjigin, et al., University of Michigan

The quote above paints a picture different from what researchers expected. After a clinical death, they expected brain activity to slow down to a halt. However, what they saw was quite different. Researchers found that the brain activity actually increased for a period after the death, resulting in a heightened state of consciousness processing. The brain scientists state that this electrical activity could account for the “lights” that people experience during near-death experiences of cardiac arrest patients.

Looking Deeper

The human brain is a miraculous work. Lingering states before death can be confusing for all involved, and education is critical to making decisions regarding loved ones. Currently, the US law has very specific rules for handling patients in comatose, PVS, and brain-death conditions. Current law also accounts for legal statements made before the patient fell into their condition.

Advances in fMRI technology are allowing doctors to make more accurate decisions in diagnosis. Physicians achieve this by comparing fMRI imagery of patients with severe brain trauma with control patients. Are some PVS patients capable of even more communication beyond yes or no questions? Will the use of this technology change our medical procedures and law? It is hard to say, but the future looks promising for using more advanced communications methods with brain damaged patients on the border of death.

Our understanding of near-death experience continues to give credence to reports of cardiac arrest patients. How will this body of research continue to grow? If electrical activity in the brain really is responsible for the “lights” experienced in death, can we officially include this experience in medical texts? Readers are encouraged to continue to push the boundaries of our current understanding of death. Doing so will not only increase our understanding of the ultimate commonality among creatures, but can bring feelings of peace when we or a loved one has to face it.

Legal Docs

UDDA Document

Scientific Articles

Monti, Martin, et al. “Willful Modulation of Brain Activity in Disorders of Consciousness | NEJM.” New England Journal of Medicine, www.nejm.org/doi/full/10.1056/NEJMoa0905370.

Borjigin, Jimo, et al. “Surge of Neurophysiological Coherence and Connectivity in the Dying Brain.” PNAS, National Academy of Sciences, 27 Aug. 2013, www.pnas.org/content/110/35/14432.abstract.

Photos

Top Skull Photo – Title: Memento Mori!, Author: Milan Nykodym, from Kutna Hora, Czech Republic,

fMRI (first)- John Graner, Neuroimaging Department, National Intrepid Center of Excellence, Walter Reed National Military Medical Center, 8901 Wisconsin Avenue, Bethesda, MD 20889, USA

fMRI (second) – Photo sourced from “Willful Modulation…” by Monti, Martin et. al.

Update

Recently most of my time has been dominated by both my work and by writing articles for Thunderbolts.info. Both of these endeavours are going pretty well in my opinion. Thunderbolts has published two articles now, and my work at Spin Group is really engaging.

However, I would like to take some time to reflect on my own perspectives and progress outside of my work. The reason is that often I am having to make compromises in my writing in order to make things fit, and I am often working on projects that are more or less handed to me. This is not bad, but I would like to take time to re-affirm my own reasons for learning web development.

First and foremost, I want to state what a fun technical challenge it can be. Solving the puzzles of building websites takes use of special tools and processes, and it can be a joy to solve in itself.

Secondly, it is a career path with promising outlooks. This does not exactly go without saying, as many technical fields are ephemeral. There are niches within web development (like the use of HubSpot) that will continue to grow, and the field of front-end web development still has a large market for new developers.

Third, it has a creative bend to it. Unlike the engineering field I left behind, web development is a creative field. I use photoshop, I make style changes, I use different typefaces/fonts to convey different messages. In this sense, I am able to use some creative force in my work instead of strictly making calculations and charts.

Prepare an Excel file as ODBC source for Data Advisor ...
This was a lot of what engineering was. Data science is cool, but an endless stream of *.xls BS gets old fast man.

Lastly, I have had more practice doing copywriting. The only regret with copywriting is that I am saying things that are for other people most of the time, in some way squashing my own voice. That is part of the reason I am writing this post, is to simply exercise my own voice and say what I really think.

Cymatics: Vibrating plates to the Hydrogen Electron Shell

I say that when a table is struck in different places, the dust that is upon it is reduced to various shapes of mounds and tiny hillocks …

― Leonardo Da Vinci,  early “cymatic” research.

Double Hexagon Cymatic Image, made with CymaScope, an advanced cymatic research instrument.

Cymatics is the study of acoustically generated modal vibrations—standing wave systems. Examples of cymatic research include subjecting water, sand, or other semi-solid media to sound frequencies or music and observing the pattern in the media. Depending on the media used and the frequency applied, the patterns that emerge assume a variety of forms. This fascinating field of acoustic research has yielded a myriad of scientific and mathematical breakthroughs. Cymatic research continues to reveal more insights into the nature of our electric universe by aiding scientists understanding of wave phenomena. Though cymatic research crosses over into many scientific fields, this article takes a brief look into one discovery born from cymatic research—the Schrödinger equation. Mathematical models born out of cymatics lead to our current understanding of the electron shells of atoms, thereby increasing our understanding of the nature of electricity itself.

What Is Cymatics?

 

cymatic image at 1760 hz
Cymatic image produced with 1760hz vibration

Cymatic research is the study of visual and mathematical patterns in standing wave systems. Look at the image above and notice the enigmatic pattern that is produced with nothing more than a tone generator, metal plate, and some sand. What exactly creates these visual forms? The “pictures” or patterns that emerge are the result of standing waves. When a tone is applied to a plate or other media, the media resonates and produces an up and down motion on fixed places on the plate. These waves occur between stationary nodes.

Standing wave image.
This disc is an excellent example of a standing wave. Notice how the waves do not travel longitudinally, they only oscillate up and down.

When media such as sand is added to one of these vibrating plates, it arranges itself along the stationary nodes of the standing wave. Similarly, patterns emerge from media like water because the vibrations can be easily viewed in the water itself and there is no need for any other additional media. The vibrating metal plate is a very popular means of producing cymatic images. These metal plates that are subjected to vibration with either tone generators or other means attached are called Chladni Plates, after 19th century acoustician and physicist Ernst Chladni. View the video below to see a Chladni plate vibrated with a violin bow string.

More advanced instrumentation has recently been developed to produce cymatic imagery. One instrument is the Cymascope. This instrument uses ultra-pure water to produce standing-wave imagery. The reason ultra-pure water is used is because of the surface-tension properties. According to it’s developers, the water’s high flexibility and fast-response to vibration make it well suited for vibrational research. The cymascope was used to capture the first image of the article, as well as the one below.

Cymascope image
Another example of a cymatic image captured with a cymascope.

Cymatic Research Leads to 2D Wave Model

At first glance, cymatic research usually appears curious but with no obvious applications. However, Ernst Chladni recognized the potential mathematical implications of two-dimensional standing waves.  Eventually, later mathematicians pushed these solutions to three dimensions.

The story begins with the acoustician named Ernst Chladni, who experimented with cymatic plates, as mentioned earlier. He thought that the wave forms that were produced must have some mathematical relationship to the vibrational tone he applied. He came up with approximate solutions to model the cymatic image shape but never solved the 2D wave function completely.

cymatic data from Chladni in german
In a publicly available lecture from Yale University, Dr. James McBride shows Chladni’s original cymatic data

After the Math was Solved, Schrödinger could model the electron shell

Despite Chladni being unable to solve the puzzling mathematical problem posed by his plates, others eventually did. Chladni’s 2D mathematical problems attracted a lot of eminent mathematicians like Leonhard Euler, Daniel Bernoulli, and Joseph-Louis LaGrange. Building upon the rough approximations between frequency and nodes that Chladni described, these mathematicians pushed the mathematics to the point of solving both 2D and 3D wave functions. Later, other mathematicians like Edmond LaGuerre and Adrien-Marie Legendre continued to perfect wave function mathematics. Professor McBride of Yale University explains how cymatic disks were used to help solve wave functions in this YouTube video.

In this way, cymatic research was the impetus for mathematicians to study the field of 3D waveform research, and this research was used by Schrödinger to write his famous wave equation.

 

“The solutions we get involve what are called spherical harmonics, and they’re 3D analogues of Chladni’s 2D figures….[Speaking of 3D wave functions] Schrödinger didn’t find these, he just looked them up. These guys had already done it from acoustics.”

-Professor John Mcbride, Yale University

Are current electron models accurate?

It should be clear by now that cymatics has lead to accurate generalized mathematical formulas for 2D and 3D waves. Whether or not these equations are being applied correctly is open to debate. Mainstream science is confident that the hydrogen electron shell can be modeled by a 3D wave equation. Alternatively, other scientists like Edwin Kaal believe that atoms take on geometric forms. In his view, the electron “shell” would not exist at all, and the modeling of electron shells with 3D wave models would not be accurate whatsoever.

Bearing this in mind, are there any scientific problems that the 3D wave model could explain? Our current understanding of light could be better explained with wave models. This topic falls outside the scope of this article in particular, which serves to lay a foundation for our understanding of 2D and 3D standing waves born out of cymatic research.

 

Cymatics Will Continue to Open Doors

Cymatics is a curious subject. Many have been enchanted by it’s ability to produce novel forms. In fact, many find the Chladni plate images and forms so mystifying that they find no need to research deeper. However, the more scientifically inclined researchers have taken the 2D waveforms and produced brilliant mathematical formulas with it. It is clear that cymatic research played a critical role in the development of the Schrödinger equation. The 2D waveforms produced on Chladni plates were the first rough-sketch of the formulas that embody our current models of both 2D and 3D waves. Where does the story end? Cymatics may be applicable in another field, light research.

In the next article, we will look at other standing wave phenomena, and plausible explanations for wave-particle duality. Specifically, we will see how scientists are using particle-wave behavior to create life-size analogues of some quantum behavior. This research takes a remarkable look at one of the most puzzling “quantum weirdness” phenomena to date: the double slit experiment.

Readers are encouraged to send comments, questions, or inaccuracies to the author.

Attributions

Violin bow Chladni plate video – A demonstration of sand forming cymatic patterns on a metal plate. From the film Inner Worlds Outer Worlds. Author: SpiritFilms

Video from Yale Open Courses – Chladni Figures and One-Electron Atoms, Professor James McBride, 2009

http://www.cymatics.co.uk/author/john/

John Stuart Reid Quote -sourced from cymascope.com