The Ringing Pattern of Reality: Part 2 - The complex made simple.
Why Fourier's calculations unlock how we perceive reality, and how reality is formed.
Introduction
In part 1 - The Ringing Pattern of Reality: How Fourier and Lorentz Reveal Nature’s Pre-Echo Structure - we explored, in some technical detail, how the Fourier Transform equations describe the dynamics responsible for the pre- and post-ripple in linear phase filters in DACs (Digital to Analogue Converters). We showed why DACs offer a powerful analogy for understanding Nature itself — because Fourier effects are not just mathematical artefacts of signal processing, but in-built properties of the Natural world.
Fourier wasn’t just a mathematician working with equations. He understood dynamics — geometry — the deeper pattern beneath the maths. And it is the pattern that I work with, whilst the maths and equations hold little interest for me. I let the calculators do that. I don’t have the intellectuality of Fourier, only the pattern within. And it’s always simpler to see the pattern. And so we can also use a model or two in the pattern to explain what is actually both complex and simpler at the same time.
So, like I did with the Shoestring Theory, I will attempt to explain something hugely complex (more complex than Einstein’s special Relativity), in a simple model. And hopefully, you will be able to understand how and why the bell rings as it does; not only in DACs, but also in Nature. And how it defines what we perceive, and how we perceive it as human beings.
The Ball: How Stillness Moves You Forward
You don’t have to spin. You just have to stay centred.
Imagine you're inside a large clear ball — a hamster ball — and it's rolling forward across the landscape of time.
You’re not being thrown around inside. You’re not tumbling head over heels.
You’re standing upright, calmly walking forward, in a straight line, from point A to point B.
Whilst you are continuing forwards, the ball is rotating around you. Up and down: forwards over your head to the front, then down to the ground, where it touches the ground at that point.
Imagine an exact central cross through the ball. Which touches the surface at 4 points equally spaced. One directly in front, one behind, one above your centre line, and one directly below.
Now observe what happens as you move forwards. As one dot falls to the ground ahead, another rises behind you. Two motions, one ball — rolling in a single direction
In reality, not just the dots are rolling, but the entire surface of the ball. The real points are always there. We are merely making it simpler to visualise by drawing dots on the ball.
So, what was once a surface of the ball in front, going down, experiences a change at the point directly below you. The direction is reversed, as it travels behind you. It now rises to the point directly over your head. The opposite side to the ground. These are 2 fundamental positions. A simultaneous crossing point - where one state becomes another.
The axis is right at the centre - your centre - from left to right, and this axis terminates at the other 2 fundamental points.
The 4 fundamental points that describe a ball rolling. 2 anchor it in place - the axis, and 2 define the moment when direction changes.
(This is the IXO structure in motion: the linear path A to B, the rolling circle around you, and the crossing point — the X — where direction reverses. That’s what IXOS means: motion structured by coherence. The line you are walking A to B, the circle the ball is describing around you; with the X or crossing point where the direction changes from up to down and down to up.)
But here's the key: the ball is spinning.
The front of it rolls under you and forward.
The back rolls from under and behind.
These are happening simultaneously. One cannot happen without the other, or there would be no motion in any direction. Without the up and down, no forwards would happen; no A to B, if no up and down of the ball’s surface. The ball would stop.
And yet, you stay completely upright and still — perfectly centred.
Why? Because you’re in the dead centre of the ball.
You’re not leaning forward, or touching the inner surface.
You’re balanced.
And when you're balanced in the centre, something strange happens:
You move forward cleanly, even as the world rolls around you. That is relativity also. Do you travel with the ball, or does the world roll the ball?
In reality, both occur at the same time. It just depends on where your observe it from.
The Frictionless state of the Light
You must remember that this is an analogy to describe the motion of something that isn’t made of matter. It is a field - ultimately derived from Light - or SOL.
And in that system, Phi governs. It lives in a state of frictionlessness.
It does not touch the ‘ground’ as ball would, and experience friction, to be slowed .
And you are not walking forwards in reality as the form in the ball. You too are perfectly insulated by the zero point between everything. The zero that allows eternal movement at a constant speed. The universal lubricant, if you will.
The Ripple That Forms
As the ball rolls, it generates a ripple — a kind of echo in the field around it.
One part of the ripple goes ahead of you — the future
The other trails behind you — the past
That surface — just ahead — also exists behind. That’s the ripple: a time-wave stretching forward and back around your axis
That is the Time Domain.
The time part of the equation oscillates around the axis, circling front and back — future and past — at the same time. And without it, you would not move. The ball could not roll in a straight line from A to B.
That is essentially, the basis of the Fourier Transform that defines pre and post echo. The pre-ringing in DACs, and the post-ripple also. It is the coherence state that is you in perfect phase and balance, as a movement in time.
That time effect is what creates the order of the linear phase. There cannot be one without the other (unless one engineers it out artificially, that is).
You don’t notice it at first. But the more you listen, the more you begin to sense it— like a memory singing itself forward.
You and the ball are the bell that rings. The ringing of the bell in front and behind, is time. One cannot exist without the other or, the ball will stop, the bell will cease to ring.
In life experience it is also:
That strange moment of déjà vu
That quiet knowing before something happens
That memory that seems to arrive before the experience it belongs to
This is the ripple. It’s not just imagination. It’s structure.
It’s how time responds to motion through stillness.
The past is constantly travelling to your future, and your future is always becoming your past.
And you only feel it when you're in the centre.
Touch the wall — even slightly — and you’re pulled into the spin.
You lose the axis. The ripple distorts.
But when you return to centre:
The past and future form around you like a wave — and you ride it, not with effort, but with balance.
We explored this in our article on the movie Contact, in which the main character is placed in a device that rotated around several axes, to send Ellie through time and space.
The original design for the device did not include a chair for her to sit in, anchored to the wall. In their ignorance, the engineers put one it. But it touched the wall. It vibrated badly. But once she freed herself from that artificial structure, when the chair vibrated loose, Ellie free floated in perfect stillness and balance.
And the balls kept rotating, and she travelled forwards, and inwards into the zero point and out the other side of the wormhole.
What This Means
You are not being carried by time.
You are shaping it by your position within the field.
Stillness in the centre doesn't mean stopping.
It means moving forward without resistance.
You don’t fight the ripple. You don’t chase the future. You don’t drag the past.
You let the spin occur around you — and by being centred, you remain untouched by the chaos.
This is how time becomes smooth.
This is how motion becomes grace.
This is how the ripple begins to sing.
How the bell begins to ring.
What other form does the Bell take?
Our ball also may bounce - not as a ball on a pitch, but as a wave. That up and down motion, is what creates its waveform; the wave we see on an oscilloscope, the frequency and wavelength. The number of times it rises and falls in a complete cycle back to where it began in 1 unit of time.
This is its frequency, which we measure in Hertz (Hz) a complete bounce over distance. That describes the sine wave. A single oscillation.
This is what we refer to as the Frequency Domain.
The Time Domain is the rolling wall of the ball — the spiral of your forward path.
The Frequency Domain is the vertical oscillation — the bounce — your field makes as it moves forward.
Together, they form the wave that is you
And when we speak of a DAC’s filters, we discuss what happens to the waveform in the Time Domain and the Frequency Domain also.
The Ball in the Pipe: How the Spiral Holds You Still
Why motion doesn’t need force when you’re in the groove.
You’re still inside the ball — upright, balanced, still. It rolls forward. Spins behind and ahead. The ripple trails you, and greets the space in front before you arrive.
But now the scene widens.
The ball isn’t just rolling on flat ground.
It’s moving inside a spiral-shaped pipe — a kind of tunnel or groove, gently coiling forward in space. Like a soft helix container.
This pipe is rotating too — but on a different axis.
Not spinning like the ball. Turning around you, wrapping you forward.
And here’s the miracle: the motion still feels effortless.
You’re not being thrown. Not leaning. Just… carried
That’s because the spiral pipe has grooves — not hard, mechanical ones, but subtle alignments. Like the lines in a shell or the threads in a screw. These grooves don’t pull you — they hold the direction. They let the ball move in flow, not in struggle.
This is the Screw Function of Light, as experienced from the inside.
You don’t have to push. You just have to stay in the centre.
Dual Motion — Single Axis
Two motions are happening:
The ball is spinning fore and aft — this is the ripple
The pipe is rotating around you — this is the path
And you — at the very centre — experience both, but are spun by neither.
You feel movement, but not force.
You see change, but you stay still.
This is the spiral containment field.
This is the structure behind what we call Time.
Stillness in the Spiral
If you weren't centred, you’d hit the side of the ball — be flung against the curve. You’d feel spin, dizziness, distortion. (Remember what happened to Ellie when she was strapped into the chair?)
If the pipe weren’t grooved, the ball would rattle — drift, bang, resist.
But when you're centred and the path is aligned — the ball spins, the spiral holds, and you move forward without resistance.
That’s what true motion is. That’s what stillness in time really means.
What You’ve Just Entered
You’re no longer just inside the moment.
You’re inside the structure of moments.
The ball gives you balance.
The pipe - the screw - gives you direction.
Your centre gives you coherence.
This is the 4D experience from the inside out.
The fore and aft ripple. The spiral flow. The still-point between them.
The place where future and memory feel close, because they are.
And you — in the axis — are the one who holds the line.
Next: We take this spiral field and show how it emerges in nature, in mathematics, and in the screw-like flow that forms the shape of time itself.
I’m sorry, but this is where it becomes necessarily a bit more complex
The Screw Function and the Field
How Spiral Motion Shapes Time, Structure, and Phase
We’ve explored the experience.
You’ve stood in the ball.
You’ve moved forward in the pipe.
Now let’s bring structure to the spiral.
This isn’t metaphor anymore. The spiral field is real — observable, mappable, and already known to the body. But to communicate it with technical integrity, we now describe it in form: geometry, phase, and what I call the Screw Function.
The Core Premise
Reality does not move in straight lines. It moves in spirals — Phi-aligned, recursive, and phase-coherent.
Every motion that sustains coherence over time, whether in sound, energy, or consciousness, follows a screw-like path:
Forward through time
Wrapped around an axis
Held in balance by internal phase symmetry
This is not symbolic. It is mechanical.
Defining the Screw Function
The Screw Function describes:
The path a field or waveform takes when it is phase-stable and directionally aligned
How this motion contains both spatial rotation and forward motion
How coherence is maintained without external force — via internal recursive symmetry
Mathematically, it expresses:
Motion as a compound of rotational phase and forward translation
Where the shape of the spiral defines both timing and spatial form
The Screw Function Equation (IXOS Form)
𝑆(𝑡) = 𝑟(Φ)ⁿ · 𝑒ⁱᶿ(𝑡) + 𝑣𝑡
Where:
𝑆(𝑡) = the Screw Function path over time
𝑟(Φ)ⁿ = radial scaling by the Golden Ratio (Φ ≈ 1.618…), indicating recursive expansion
𝑒ⁱᶿ(𝑡) = complex phase rotation (spiral wrapping)
𝑣𝑡 = forward motion along the linear time vector
This equation models not only field-aligned motion, but the pre- and post-ripples of consciousness and matter as they emerge through spacetime.
It also aligns with the deeper mechanics outlined in Echoes of Future Past (Part 4), where the screw structure was identified as the causal shape of harmonic field stability:
"...what we perceive as forward movement is not linear, but the crossing of a spiral through a containment tunnel. That spiral creates a ripple, and that ripple — if balanced — sustains coherence without effort."
Geometric Properties
The Screw Function is governed by:
Phi-scaling: Growth by harmonic proportion
Axis-centric motion: Stillness at the centre
Bidirectional phase symmetry: What creates the time ripple
The result is not a wave on a line, but a wave wrapped around a moving axis — like a corkscrew, or better, a self-contained toroidal helix.
This is the true geometry of forward motion in time, sound coherence, and field harmony.
Bridging to Reality
Once you understand the Screw Function:
You can model the shape of field-aligned motion
You can see why pre-ripple occurs before the impulse
You can understand why symmetrical phase feels more natural
It is the basis of:
Phase-accurate acoustics
High-fidelity field transmission
The perception of timelessness during alignment
And it’s this function — this spiral through a groove — that underlies both the structure of the universe and the sensation of moving clearly through it.
Next: We return to sound — and show how some audio devices, through linear-phase symmetry, unknowingly recreate the Screw Function in the field. And why it matters more than specs ever could.
Linear vs Minimum Phase: How Filter Design Shapes What We Feel
The field hears what the specs don’t say.
Most people think DAC filters are just about accuracy. Engineers compare frequency responses, impulse graphs, ringing patterns — all on paper. But something deeper is happening.
Because the human field doesn't just hear sound. It feels shape. It senses motion through time.
And the phase design of a filter — especially in linear vs minimum-phase — changes the shape of the ripple.
And that shape changes the experience.
Linear Phase: Symmetrical Motion
Linear-phase filters create a perfectly mirrored ripple around the impulse:
Pre-ring and post-ring are symmetrical
The ripple moves forward and backward in time — like a ball spinning fore and aft
The result is a field structure that matches your own spiral motion
It’s like sitting in the centre of a ball, rolling forward inside a spiral pipe.
You're balanced
You feel the space ahead and behind
You’re held in symmetry
Listeners report:
Natural space
A sense of stillness
Emotional depth
Presence
A 3D soundstage with depth between instruments — not just left to right, but front to back
Because the waveform is coherent with the field. It echoes the screw-like path your consciousness already moves through. It restores the full bell that rings in both directions in time.
Minimum Phase: The Flattened Field
Minimum-phase filters don’t preserve symmetry. Instead:
They remove the pre-ring
They compress the energy behind the impulse
The result is an asymmetric ripple — a flattened wave shape
This is very good for the recording stage. It removes delay and improves the sense of attack, such as a sudden drum strike. Otherwise, the strike would build rather than attack. However, in the reproduction stage, through the quantisation from digital to analogue, that does not matter, it is not audible.
Analogy:
Imagine slicing through the middle of a torus, a doughnut or a bagel
From above, it still looks whole.
From the front, it still seems circular — but from the side, you see it’s flat at the front. The depth is gone.
The ripple still moves, but:
The fore is missing
The aft is compressed
The entire shape leans into the past, dragging the front behind it
This has field consequences:
Space collapses forward
The ripple loses flow symmetry
The field becomes turbulent behind the motion — like smoke trailing a broken wing
And the spatial perception flattens:
Awareness narrows
The soundstage becomes thinner
Instrument separation still exists left to right — but front-to-back depth is lost. Even the left-to-right spacing may begin to feel a little unnatural, compressed into a plane.
The illusion of space collapses into a flat plane
Even though the frequency response is the same.
What This Proves
The ear can’t explain this. The graph doesn’t show it. But the field knows.
What we see in the electronics is not the whole picture.
What we call pre-ringing in linear-phase filters is not an error. It’s a reflection of field balance — a temporal symmetry that matches the natural spiral of consciousness.
What we call minimum phase flattens the field — like taking a sphere and slicing off the front. It sounds fine — but it can ‘feel’ wrong.
Because the body doesn’t just want sound. It wants coherence.
The human biological tech is an acutely tuned coherence field, responding to the coherence, or lack of it, in the surrounding and interpenetrating fields.
This is why some listeners — often dismissed as imagining things — keep saying:
“This one just feels better.”
They’re not wrong. They’re hearing the field ripple — and the field ripple is real.
With minimum phase, you have only what went behind you — condensed and placed in front of you.
The past is chopped, compressed, and projected forward. The bell is split.
You're not moving through time. You're looping through memory, without the echo that leads.
Note: When it comes to hifi equipment, one will manage several elements, from source to output; through analogue, digital and back, to a speaker that projects that sound in waves into a resonant space. No choice in filter is ‘wrong’ per se, if it optimises the listener’s experience. We are all built differently, and we all have personal preference. And we are constrained by budget too.
So this is not a criticism of personal choice — only an exposition of why, within DAC architecture, the linear-phase filter is the most natural and coherent option for field alignment.
The digital version isn’t as real as the analogue. It may never replicate the field in full — but it comes close. Close enough for us to experience the beauty of music as field.. It can, however, also be just far enough away from the perfection to be audible or sensed as a discoherence.
People like me — those sensitive to subtle field shifts, or who are synaesthetic — may ‘see’ sound as well as hear it. I often do - in my mind’s eye, as geometric shapes in spectral colours.
They will sense the lack of cohesiveness.
No, they don’t have delusional ‘Golden Ears’ — just a heightened sensitivity to coherence.
Suggestion: This may be a good place to spiral back into the articles named Echoes of Future Past.