Vibration · Part proven physics, part their idea
Sympathetic Resonance Simulator: Why Like Attracts Like
Strike a tuning fork and a matching fork across the room starts to sing with nothing touching it. William Walker Atkinson built his law of attraction on that image in 1906, and Neville Goddard was still reaching for tones and vibration in 1945. Tap a fork and see who answers.
Part one · Proven physics
Only the matching forks answer
Forks B, D and E are tuned to 432 Hz. Forks A and C sit at 288 Hz, and they are shuffled along the bench so that distance cannot explain who rings.
- Strike B. A and C stay dead while D and E slowly swell.
- Press grip to silence B. Whatever you still hear came through the air.
- Slide D one hertz sharp and strike B again.
Table view and live readings
| Fork | Tuned to | Now | Peak since strike |
|---|
| Detune | Peak answer |
|---|
“Just as a note of the violin will cause the thin glass to vibrate and "sing," so will a strong thought tend to awaken similar vibrations in minds attuned to receive it.”Atkinson, Thought Vibration, 1906
“Were the tones of health not contained within the consciousness of the one of whom they are affirmed, they could not be vibrated by the word which is sent.”Neville, Prayer: The Art of Believing, 1945
Part two · Proven physics
Nine metronomes, one loose board
Put metronomes on a board that can roll and each swing nudges the board, and the board nudges the rest. James Pantaleone did it with “two empty soda cans” for rollers. They start scattered, and with enough coupling they end up ticking as one.
0.00Scattered
Order 0 means scattered and 1 means perfect step, over the last 40 seconds. Critical coupling here is 0.48.
The line between
Which part is proven and which part is theirs
| Statement | Status |
|---|---|
| A tuned body picks up energy from a wave at its own frequency and hardly any from the rest. | Proven physics |
| Change its tuning a little and the response collapses. | Proven physics |
| Oscillators sharing a support pull each other into step. | Proven · Huygens to Pantaleone |
| “the difference is solely in the rate of vibration” between light, heat and thought. | Their idea · Atkinson 1906 |
| Minds sit in a sea of mind, the way forks sit in air, and thoughts cross it as waves. | Their idea · no such medium found |
| “You never attract that which you want, but always attract that which you are conscious of being.” | Their idea · Neville 1944 |
| The forks prove the law of attraction. | No · they illustrate it |
The first three rows will reproduce on any lab bench. The rest is a teaching, and people have lived by it for more than a century without a lab behind it. Our law of attraction page goes through what the studies do show about expectation and attention.
What the metal actually shows
Reception, more than attraction
Watch the bench closely and you will see that nothing moves toward anything. The wave from a struck fork reaches every fork in the room, the wrong ones included. What differs is what each fork does with it, because a matched fork adds up the pushes cycle after cycle and a mismatched one cancels them.
So the honest word for the effect is reception, and Atkinson comes close to saying this. His wireless example has sets that “receive the vibrations only from the sending instrument which has been attuned to the same key,” and that is a fair description of what Marconi had patented six years earlier. “Like attracts like in the Thought World” is the slogan that survived, though the argument under it is about tuning.
Neville never uses the word resonance, which is absent from all 320 texts we searched. His 1945 book gets closer to a mechanism than anything else we found in him. He says a state “persists until it awakens a corresponding vibration in the subject,” and that tones must already be present in a person for a word to vibrate them. A fork works the same way. It can only answer in a note it already has, which is why the picture appeals to anyone reading him.
Two more facts from the bench are worth keeping. The answer costs the struck fork energy, so it fades sooner when others are taking it. And all of this needs a carrier, which in the room is air. Their teaching needs one too, and its name for it is mind, or consciousness. The Neville Goddard section sets out what he meant by that in his own words.
Two different effects
“Synchronization differs from the well-known phenomena of resonance, where an oscillator responds to an external periodic signal.”Pantaleone, 2002
The forks are passive and only ring when something else drives them. Metronomes run on their own springs, so each one drives the rest. Both are real, and the page keeps them apart for that reason.
How the idea travelled
From Huygens’ clocks to a soda can
- 1665
Christiaan Huygens, kept to his rooms for some days, sees two pendulum clocks on one support fall into a shared rhythm, swinging opposite ways. In a letter he calls it “the sympathy of two clocks.”
- 1900
Marconi takes out patent 7777 for “tuned or syntonic telegraphy,” which lets stations share the air by working on different settings.
- 1906
Thought Vibration appears in Chicago and borrows both pictures, the singing glass and the wireless set, for the mind.
- 1941 to 1945
Neville writes of things in tune with consciousness, then of corresponding vibrations awakened in another person.
- 1975
Yoshiki Kuramoto publishes the simple model of many oscillators pulling on each other that the board above runs on.
- 2002
James Pantaleone shows that metronomes on a light board are a working version of that model, with two empty cans for wheels.
Under the hood
What the simulator computes
The forks
x″ + γx′ + ω²x = 2gω Σ xothers
- Each fork is a damped oscillator driven by every other fork, stepped 44,100 times a second.
- Damping γ is 0.5 per second, which gives a Q near 5,400 at 432 Hz.
- Coupling g is 0.42 per second, far stronger than real air, so you see it in seconds.
- The curve comes from a separate calculation of the slow envelope. We ran both at nine detune settings and they agreed to within 2 percent.
- Sound is one sine per fork with loudness set by its amplitude, plus a brief strike tone at 6.25 times the pitch, the overtone a real fork gives.
The metronomes
θ′ᵢ = ωᵢ + K r sin(ψ − θᵢ)
- This is the Kuramoto model with nine oscillators, the form Pantaleone derived for metronomes.
- Natural rates spread 6 percent either side of one swing a second.
- The order reading r is the length of the average of all nine phases.
- Critical coupling is K = 4Δ/π for evenly spread rates, about 0.48 here. Nine is a small crowd, so the change is softer than the formula suggests.
- The board’s sway is drawn from the swings and is for show. The coupling term does the work.
The ripples behind the forks use true wavelength ratios, so 288 Hz waves are 1.5 times as long as 432 Hz waves. Their speed and scale are slowed for the eye. The sim stops when you scroll away to save your battery.
Questions
Resonance, sync and the law of attraction
What is sympathetic resonance?
A body starts to vibrate because a nearby sound matches a frequency it already has. Strike one of two matched tuning forks and the second begins to ring with nothing touching it, driven by pressure waves in the air. A fork tuned elsewhere feels the same air and barely moves.
Does sympathetic resonance prove the law of attraction?
No. It proves that a tuned object takes up energy at its own frequency. Nobody has shown that thoughts are waves of that kind, or that a sea of mind carries them. The forks are the best picture of what Atkinson and Neville claimed, and a picture is all they supply.
Why does a fork go silent after such a small detune?
A fork is a narrow filter. In this model a detune of one hertz, about a quarter of a percent, cuts the answer from 39 percent of the strike to about 11, and six hertz leaves 2. Each cycle of the wave arrives slightly out of step with the fork, so the pushes begin to cancel.
Why did Atkinson compare thoughts to a violin and a wireless set?
Those were the tuned systems he reached for. A violin note could make a thin glass sing, and Marconi’s sets could pick out one sender from the traffic in the air. Both gave him a visible model of selective reception, and he applied it to the mind.
Do metronomes on a board always fall into step?
Not always. On a light board that can roll, James Pantaleone found the sync is generally in phase, with antiphase only under special conditions. He also found that with a large enough difference between metronomes no synchronization occurs. The slider here lets you find that edge from the other side, by weakening the coupling.
How accurate is the simulator?
The equations are the standard ones and they are integrated properly, at 44,100 steps a second for the forks. The numbers are chosen for your eyes. Real forks ring longer and couple more weakly through air, and the speed of the ripples on screen is slowed so that you can see them.
Sources
The record behind this page
The Atkinson and Neville lines above were checked by script against the book and corpus text before they went in.
- William Walker Atkinson, Thought Vibration, or the Law of Attraction in the Thought World, 1906.
- Neville, Prayer: The Art of Believing, 1945, and Your Faith Is Your Fortune, 1941.
- James Pantaleone, “Synchronization of metronomes,” American Journal of Physics 70, 992 (2002).
- Kuramoto model, Wikipedia, for the equation, the order parameter and the critical coupling.
- Sympathetic resonance and tuning fork, Wikipedia, for the effect and the overtone ratio.
- “The secret of the synchronized pendulums,” Physics World, for Huygens and his letter.
- Marconi biography, Nobel Prize, for patent 7777, and Electronics Notes on what tuning allowed.
- An Odd Kind of Sympathy, Idols of the Cave, for the translated 1665 letters.
For teachers
Use the simulator in a lesson
Physics teachers and study groups can drop both benches into their own page with this code.