> The river we step into is not the river we step out of. — *Heraclitus*

# On the Shape of What Is Lost

*Topological Affinity, Mythic Space, and the Mapping of Meaning*

## ✦ Introduction: The Affine Compass

Imagine dough spread across a countertop — thick, irregular, elastic. Scattered raisins hold their positions even as the whole mass stretches and deforms. This is affine transformation: change that preserves relational structure. What bends, what shifts, what remains fixed — these are the questions affine geometry answers.

Now imagine it’s not dough being stretched — but meaning.

This essay began as a response to an intriguing, if flawed, idea: that Tolkien’s Middle-earth is a *disguised* map of Ice Age Europe, as proposed by Andrew Henry in his blog *The Saxon Cross*. While initially compelling, Henry’s theory collapses under its own misapplied literalism. Yet beneath the geographic misreadings lies a more fertile question:

> What does it mean when fictional worlds resemble the real —
> not because they copy it, but because they share its shape?

This is not an attempt to debunk Henry, nor to replace one secret map with another. Instead, it offers an alternative lens — grounded in topology, symbolic cognition, and the metaphysics of affinity. It asks what becomes visible when we approach Tolkien’s Legendarium not as a cryptographic riddle, but as a **mythic field** resonating with memory, map, and mind.

To begin, we must clarify a foundational — and often misunderstood — distinction in the philosophy of measurement.

## ✦ Scales of Meaning: When Numbers Fail

Modern measurement theory distinguishes four levels: nominal, ordinal, interval, and ratio. Each determines what operations are meaningful on a dataset.

- **Nominal data**: Categories without order — apples and oranges, elves and dwarves. You can count them, but not rank them.
- **Ordinal data**: Ordered, but unevenly spaced — peasant to king, Maia to Vala. The gaps between ranks vary.
- **Interval data**: Allows comparison of differences (like Celsius), but lacks an absolute zero.
- **Ratio data**: Permits full mathematical operations — scaling, proportion, absolute comparison.

> Tolkien’s world belongs to the **nominal** and **ordinal** realms. It maps meanings, not measurements.

When someone overlays Tolkien’s maps onto Ice Age bathymetry, they reach for ratio-level correspondence where only topological affinity exists. The result isn’t revelation — it’s illusion: a confusion of scales that trades insight for the appearance of precision.

## ✦ Mapping the Invisible

Maps promise clarity: “Here is land. Here is sea. Here is border.” But mythic maps work differently. They are not tools of measurement, but of <ins>orientation</ins>.

Tolkien understood this deeply. His maps are not geographic instruments — they are moral projections, mythic renderings of memory, value, and loss. Middle-earth, with its drowned western lands and shadowed east, is shaped not just by terrain, but by **mythic gravity**.

Attempts to pin his world to Ice Age coastlines invert this logic. They flatten symbolic space into secret cartography, mistaking resonance for reference — a conceptual misstep we might call **concretized myth**.

Yet this mistake arises from a valid intuition: something in these stories echoes older shapes. Our task is not to silence the echo, but to interpret it correctly — topologically, not literally.

## ✦ Forms Without Facts: The Logic of Affinity

Topology studies forms that can bend, twist, or stretch — without breaking. A donut and a teacup are topologically identical: both have one hole. Details differ; structure endures.

Myth behaves the same way.

Atlantis. Númenor. The Flood of Gilgamesh. All are homeomorphic: different in content, identical in shape. They do not prove each other’s existence — they echo a common attractor.

To say Tolkien’s Númenor “is” Atlantis is a category error. Better to say both participate in the same **mythic attractor** — a pattern that recurs not because it is remembered, but because it is structurally inevitable.

## ✦ Learning to Read Myth Topologically

To walk the terrain of myth requires a new kind of literacy — symbolic, not technical; configurational, not empirical. This is not a rejection of rigor, but a call for a different kind: rooted in pattern recognition, symbolic resonance, and topological intuition.

Artists and thinkers are already creating informal laboratories to explore this symbolic space — not to decode myth, but to shape with it. ***Mythic First*** is one such initiative: a research project investigating how form precedes function in the stories that shape us, and how affine cognition — visual, poetic, structural — might model myth without reducing it.

These are not quests for secret coordinates. They are inquiries into the shape of the invisible — and how our stories bend toward it.

## ✦ When Myths Collapse: From Orientation to Conspiracy

If myth is a cognitive tool for navigating eternal form, then misuse begins when we mistake orientation for explanation.

When functioning properly, myth arises through symbolic intuition. It echoes the internal structure of psyche and culture — not to explain the world away, but to orient within it. The enduring myths are those that reflect deep affordances: patterns of transformation, love, exile, loss, return.

Misuse occurs when myth is treated as blueprint — when symbolic structures are flattened into literal record, recurrence mistaken for repetition, affinity confused with identity.

This is the domain of conspiratorial thinking — not as caricature, but as epistemological collapse. A myth misused becomes a surjective mapping read as bijective: many sources project onto one symbol, interpreted as a one-to-one code. The result? Fixation on uncanny correspondences without interpretive humility.

> “It may be true, but it isn’t a fact.” — Stephen Hoeller
> {[audio lecture on YouTube](https://www.youtube.com/watch?v=5rZ3N3upJwU)}
> {[transcript](https://westofwest.org/docs/jrr_tolkiens_gnosis_for_our_day.pdf), PDF}

## ✦ What Returns, What Remains

If the mythic field is eternal, and if we move through it not temporally but configurationally, then the key question is not *when* something occurred — but *how often* its shape returns.

Not whether it is factually true — but whether it <ins>resonates</ins>.

In a world obsessed with precision and proof, myth invites a return to poetic perception. Some truths are not literal, but structural. Some memories survive not as records, but as patterns.

To navigate such terrain, we need different tools — not rulers and coordinates, but topological intuition, symbolic reasoning, and attuned imagination.

This is not relativism. It is a call to disciplined mythopoeia: to shape with care, to trace the invisible architecture that returns across minds, histories, and dreams.

And so we return.
Not to the same point — but to the same *shape*.
Not to sameness — but to *resonance*.

In this way, the mythic becomes a mode of perception — not a lie we once believed, but a form we still remember.

And if we are careful — if we are honest — perhaps we can ***remember forward***.

## ✦ Doggerland Remembered: An Affine Imagination

Some readers, having followed this far, may wonder — *what about Doggerland?*
What of the claim that Tolkien's maps are not pure invention, but submerged memory?

This paper began in dialogue with Andrew Henry’s thesis — that *Middle-earth is a reimagining of Ice Age Europe*, with Doggerland occupying the symbolic heart of the North. In his reconstructions, the **Dogger Hills** become the **Hills of Evendim**, and the **Silver Pit Lake** becomes **Lake Nenuial**. The Shire, he proposes, lies nestled in what is now the North Sea basin — submerged, forgotten, but once real.

It’s a compelling vision — not because it is cartographically precise, but because it speaks in the grammar of *affinity*, not identity. In Henry’s overlays, what we see is not evidence of deliberate concealment, but a kind of affine memory mapping: **stretching**, **rotating**, and **symbolically reconfiguring** real landscapes to preserve their mythic function, not their coordinate position.

### ✦ Insert: *Locally Bijective Worlds*

When we compare the coastlines of Doggerland to Tolkien’s maps, the resemblance is not one of copying but of **correspondence**. In mathematical terms, we might call it a *locally bijective surjection* — a mapping that covers the whole field, yet aligns perfectly only in certain regions.

Imagine tracing two coastlines: one geological, one mythic. Most of the time they drift apart — stretched, rotated, folded through time. But here and there, for a moment, they match: a bay curves like a remembered river; a hill echoes a name lost to sound but not to shape. Those are the **local bijections** — small windows where myth and memory coincide, not by design but by continuity.

In topology, such mappings are called *local homeomorphisms*: they are *faithful in the small*, even if the large picture is transformed beyond recognition. The mythic and the historical touch in passing — enough to remind us that what is lost is not gone, but merely translated. These are not overlays of geography, but **echoes in configuration space**: regions of resonance across the manifold of time.

> In affine space, distances deform — but relations endure.

So it is with Doggerland, Beleriand, and Arnor: realms lost in their turn, each remembered in fragment and in exile. Beleriand was drowned in the age of myth, Arnor faded in the ebb of legend, and Doggerland sank beneath the seas of the world in substantiated proto-history. Yet all lie west of shadow, east of the sea, drawn toward the same mythic attractor: the quiet country at the edge of memory, pastoral and doomed. What Henry senses is not a secret geography, but a resonant topology — a space remembered through *transformation*.


**Figure: The Europe That Was**
A reconstruction of northwestern Europe at the end of the last Ice Age, showing the extent of **Doggerland** before its submergence. Ancient rivers such as the Thames, Rhine, and the so-called [Shotton River](https://www.researchgate.net/figure/Location-of-the-Shotton-River-in-relation-to-the-British-Isles-and-Mainland-Europe-Image_fig5_32117145) once coursed through this lowland plain, linking Britain to the continent. Though this map is scientific in origin, it resonates with the mythic memory of drowned realms — lands west of shadow, east of the sea — that persist in story long after their coastlines have vanished.

Perhaps that is the truest shape of what is lost:
Not gone, but **transfigured** —
Not mapped, but **remembered** —
Not measured, but **returned to**, again and again, in altered shape.

Just as Doggerland lies beneath the waves,
so too does its mythic echo lie beneath the text —
folded into story,
waiting...

------

## Appendix I: On Atlantis and Númenor

Many claim Tolkien “borrowed” Númenor from Plato’s Atlantis. But their structures reveal key differences:

- Plato’s Atlantis is moral allegory — a critique of Athenian decline, wrapped in political philosophy.
- Tolkien’s Númenor is mythopoeic memory — less about prescribing virtue, more about mourning lost wisdom and the corruption of pride.

Or put another way:

Plato’s Atlantis exists to *prove a point*.
Tolkien’s Númenor exists to *break your heart*.

Their resemblance is affine, not derivative. Both express the universal attractor of the sunken golden age — not because one copied the other, but because certain mythic shapes recur when civilizations confront the limits of their hubris.

## Appendix II: Surjective Maps, Mythic Forms, and the Illusion of Origins

*Why not every echo has a single voice*

Myths projected onto real-world geography are often misread as one-to-one encodings — as if each story must “mean” one specific event or place. But myths rarely work that way. They’re not bijective functions (one input, one output), but usually surjective: many origins map to one symbolic form, which in turn radiates into many interpretations.

So when readers claim Tolkien “copied” Atlantis, or that Middle-earth “is” Ice Age Europe, they confuse symbolic projection with literal encoding.

This isn’t to say the mapping is arbitrary. It’s shaped by topological affinity — preserving pattern and relation, not distance or identity.

### Narrative Attractors in Tolkien’s Drafts

Tolkien’s own revisions illustrate this vividly.

In early drafts of *Beren and Lúthien*, Sauron’s role was played by Tevildo — a giant, demonic, talking cat. Wildly different in form, identical in function: threshold guardian, captor, tester of will.

In the first draft of *Fellowship*, hobbits hide in woods not from a Ringwraith — but from Gandalf, whom they plan to ambush in jest. Within pages, Tolkien changed it: they flee an ominous Black Rider, a moment thick with dread.

Despite surface upheaval, each version falls into the same mythic attractor basin: journey into unknown, peril of the watcher, test of courage. This is myth’s logic — not replication of form, but preservation of pattern through transformation.

### 📐 Formal Interpretation (for mathematically inclined readers)

To clarify these symbolic mappings, we can borrow from function theory and measurement scales.

#### 1. Levels of Measurement

- **Nominal**: Categories without order (race, archetype, culture).
- **Ordinal**: Ordered, but without measurable intervals (peasant < king).
- **Interval/Ratio**: Measurable, scalable; Ratio includes absolute zero.

> Tolkien’s mythos operates primarily at **nominal** and **ordinal** levels — worlds of names, roles, relationships. Trying to “calculate” the Silmarils or “weigh” Númenórean morality in metric terms is a category error.

#### 2. Surjection, Not Bijection

A surjective function $f: X \rightarrow Y$ means every $y \in Y$ has *at least one* $x \in X$ mapping to it — but multiple $x$’s can map to the same $y$.

In myth:

- The **motif** (e.g., the Fall, the Flood) = $Y$
- The **sources** (Atlantis, Doggerland, Mesopotamian myth, psychological descent) = $X$

Many origins converge on one symbolic form. To insist one $x_0$ is the “true” source ignores this structure — and invites confirmation bias.

#### 3. Category Error Example

As I’ve said privately:

> “People often treat mythology like a political poll — saying ‘7.4 Americans prefer Trump’ — applying ratio logic to ordinal or nominal data. Generating nonsense.”

Similarly, claiming “Númenor is Atlantis” collapses symbolic structure into literal equivalence — a semantic flattening.

### 🌀 Symbolic Memory and Myth as Compression

Cognitively, myths act like compressed fields. They preserve not exact events, but meaningful relations. Thus Elros’s choice of mortality echoes Jonathan yielding the throne to David, and even Karna’s loyalty to Duryodhana in the *Mahābhārata* — all stories where allegiance reorders destiny. Ar-Pharazôn’s proud defiance finds its mirror not only in the builders of Babel but also in Icarus’s fatal ascent, each a parable of hubris undone. The cycle of exile and return, embodied by Beren, recalls Odysseus’s homecoming to Ithaca and Rama’s return to rule in the *Rāmāyaṇa* — journeys where absence deepens the meaning of restoration. Yet not all exiles end in return: Elendil flees Númenor never to see it again, just as Adam and Eve are barred from Eden, and as Gilgamesh grasps the plant of immortality only to lose it forever.

These patterns echo across cultures not through copying, but because human experience folds into similar shapes under shared pressures. Multiple inputs → same symbolic attractor.

## Appendix III: Platonia — A Timeless Landscape

This exploration of topological mythography aligns with physicist Julian Barbour’s radical view: time is not real. What we call time is an illusion born from sequencing static configurations. He calls this timeless set *Platonia*.

Here’s the idea, rendered accessibly.

### The Core Problem: What Is Time?

Newton: “Time is what clocks measure.”
Einstein: “Time bends with gravity.”
Thermodynamics: “Time is entropy’s arrow.”
Barbour: **“There is no time.”**

Only change — or rather, the *appearance* of change. What we experience as time is motion across a vast landscape of possible configurations — Platonia.

### Platonia as the Eternal Library

Imagine an infinite bookshelf. Each book is a “Now” — a complete snapshot of the universe. All books already exist. None evolve. We live inside one — but that book contains *records* of other “Nows”: fossils, memories, ruins.

The illusion of time? It’s cognitive. We trace paths through the shelf — not because time flows, but because configurations resemble each other.

### What We Experience as Time Is Pathfinding

Change isn’t movement through time. It’s relational reconfiguration — stepping from one “Now” to a nearby one. Like walking among stones in a field: no path preexists, but some stones cluster by shape. The path emerges from the terrain.

“Before” and “After”? Features within a single Now — not bridges between them.

### Implications for Mythic Structure

If Platonia is real, [mythic recurrence](https://publicdomainreview.org/essay/same-as-it-ever-was/) isn’t cyclical. It’s structural proximity.

Certain configurations — exile, fall, redemption — cluster together. Myths return not because time loops, but because we step into adjacent Nows that hold similar shapes.

To understand myth is not to recall history. It’s to recognize a configuration — to become aware of the shape of now.

------

## Suggested Resources

> 🎥 Watch: *Julian Barbour | The End of Time* — The Institute of Art and Ideas.
> [Watch on YouTube, (runtime: 44 min)](https://www.youtube.com/watch?v=GoTeGW2csPk)
> A lecture in which Barbour outlines his radical thesis: that time is an illusion, and reality is a timeless configuration space he calls *Platonia*. With clear metaphors and philosophical depth, he explains how the “flow” of past to future arises only from relations among static “Nows,” and why this changes how we think about physics, memory, and existence.
>
> 🎥 Watch: *The Physicist Who Says Time Doesn’t Exist* — Closer to Truth (2024).
> [Watch on YouTube, (runtime: 1:54 hrs)](https://www.youtube.com/watch?v=bprxrGaf0Os)
> A recent interview with Julian Barbour, offering a concise overview of his ideas on the illusion of time, Platonia, and the Janus Point. This video complements his earlier *End of Time* lecture, adding clearer explanations and accessible metaphors while situating his work in dialogue with broader debates about the nature of time.
>
> 📄 Read: *The Core Problem – What is Time?* — Companion note.
> [Read on HackMD](https://hackmd.io/@EriolElwin/H1AfIiaoll)
> A short essay expanding on Barbour’s ideas with accessible metaphors, the definition of Platonia, and a clear distinction between Platonia and the pop-cultural “multiverse.” Serves as a conceptual bridge between physics and myth.
>
> 📄 Read: *Shamanic Visions, Insights, and the Illusion of Time* — HackMD note.
> [Read on HackMD](https://hackmd.io/@EriolElwin/Sk5cpUisA)
> An exploration of shamanic metaperception, automatic thought, and entheogenic insight, showing how shamanic visions provide specific, actionable guidance distinct from symbolic divination. Connects Inuit practices, Salvia experiences, and Julian Barbour’s thesis on the illusion of time, situating shamanic knowing within a broader topology of temporality.
>
> 🎥 Watch: *Cave of Forgotten Dreams* — Directed by Werner Herzog (2010).
> [Watch on Dailymotion, (runtime: 1:28 hrs)](https://www.dailymotion.com/video/x9jn1rm)
> A documentary exploring the Chauvet cave paintings, some 30,000 years old. Herzog reflects on how Ice Age memory endures through image, gesture, and imagination. Though not about Doggerland directly, the film resonates with its themes: submerged worlds that survive in symbolic form, reaching us across vast spans of time.
>
> 🎥 Watch: *How Doggerland Sank Beneath the Waves (500,000–4000 BC)* — Short BBC documentary overview.
> [Watch on MEGA, (runtime: 50 min)](https://mega.nz/file/vuRF0YRT#CXBNhM9uIvuaJxgKGdAhPcnWOErIV-N1k2LVKSJ0JSk)
> A concise historical-geological survey tracing Doggerland’s submergence over half a million years, from Ice Age lowlands to the drowned North Sea basin. Useful for situating the mythic discussion within its scientific frame.

------

## Endnotes & References:

1. Andrew Henry, *How Tolkien Disguised Ice-Age Europe as Middle-Earth*, [Part 1](https://thesaxoncross.substack.com/p/tolkien-ice-age-europe-and-middle), [Part 2](https://thesaxoncross.substack.com/p/tolkien-and-ice-age-europe-pt-2)
2. Stephen Hoeller, *J.R.R. Tolkien’s Gnosis for Our Day*, [Audio](https://westofwest.org/audio/lectures/hoeller-tolkien.mp3)
3. S. S. Stevens, “On the Theory of Scales of Measurement” (1946)
4. Vogt & Johnson, *The SAGE Dictionary of Statistics & Methodology* (2015)
5. Agresti, *Statistical Methods for the Social Sciences* (2018)
6. Claire Hall, “Same as It Ever Was? Eternal Recurrence in Ancient Greek and Roman Philosophy,” [Public Domain Review](https://publicdomainreview.org/essay/same-as-it-ever-was/)
7. See Appendix III above for Barbour references. Julian Barbour’s official website [Platonia.com](http://platonia.com/index.html) introduces his research into the foundations of physics, including Shape Dynamics, and provides access to his publications, collaborations, and talks.