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Other Minds & Shared Reality Interpretation

Here is the oldest worry in philosophy, sharpened by everything before it. If reality is always read from a private frame, and my frame is the only one I can occupy, what stops the picture from collapsing into solipsism? The theory’s reply is a two-layer argument — a part that is nearly a theorem and a part that is frankly geometric — and its honesty is in keeping the two of deliberately unequal strength.

Two solipsisms

“Solipsism” names two theses. The weak one — my experience is given directly to me alone — the source grants outright: “we would not need to tell each other how we feel if feeling were public.” The strong one — only I exist — is, as Schopenhauer noted, held by no one outside an asylum. The problem has felt perennial only because we slide between them. The strategy is not to argue outward from private experience to a world (every such argument can be met with a shrug) but to show the strong thesis is not even coherent.

The argument from partiality, and where it honestly stops

Grant the solipsist only his own premises. He has a perspective (he states his thesis from one); it is private; and it is partial — it presents objects one-sidedly, with horizons, the far side of a cup “present as hidden,” co-intended without being seen. This is the phenomenologists’ adumbration, following Husserl, and the point is that it is a feature of experience, not a theory about it. A partial presentation, just by being partial, points beyond itself to a fuller whole it does not contain. The conclusion (the paper’s Theorem 3.1, the “weak structure”): a perspective is a disjoint, partial presentation of a shared whole that exceeds it. And so strong solipsism is not false but incoherent — “a perspective with nothing beyond it would present everything from nowhere with no horizon, which is not a perspective at all.” It asserts a perspective that is not a perspective, incoherent the way “I am the only word in this sentence” is.

Then the source flags its own seam. Partiality forces the excess to be larger — but not yet shared. A solipsist in retreat can relabel the excess “the rest of my own possible experience” and slide into idealism, and idealism is not solipsism. So a second, harder wedge is needed, and it is error (Theorem 3.3): the solipsist admits he can be wrong — surprised, corrected, resisted. But a reading that can fail requires a corrector it did not author; “a self-authored stream cannot be the source of its own being-wrong.” The last refuge — “the corrector is my own unconscious, still me” — fails, because an inner otherness that genuinely constrains the ego is “a second reading wearing the first one’s name.” Error forces an independent reference. And there it stops, with discipline: error forces only that something independent exists, not that it is other minds in particular and not realism over idealism. That last step — that the independent thing is other observers with this geometry — is evidence, not proof: the structure of forced agreement is the same $(B^4, S^3)$ whose boundary integral returns $\alpha^{-1} = 137.036$, and a contentless private theatre is the one hypothesis under which that coincidence has no explanation at all.

The bundle, and the theorem

The geometric layer makes the observers precise. The carrier is the three-sphere as the unit sphere of $\mathbb{C}^2$, and the Hopf map collapses each phase orbit to a point:

$S^3 = \{(z_1, z_2) \in \mathbb{C}^2 : |z_1|^2 + |z_2|^2 = 1\}, \qquad \pi : S^3 \to S^2, \qquad M_q = \pi^{-1}(q) \cong S^1.$

The total space $S^3$ is the shared world; a fiber $M_q$ is one observer; the base $S^2$ is the space of perspectives, one per point. From this the Anti-Solipsism Theorem reads off four facts. (a) Privacy: distinct fibers are disjoint, $M_i \cap M_j = \varnothing$, so experience is fiber-local. (b) Embedding: each fiber is a proper subset of the one $S^3$, which carries continuum-many fibers — to be a perspective is to be a fiber of the bundle, which presupposes the shared arena. (c) Enforcement: disjoint fibers admit no direct path, so the only channel between two observers is the shared boundary, $M_i \to S^3 \to M_j$ — intersubjective consistency is topologically enforced. (d) Linking: any two distinct fibers are linked, with linking number one.

Synchronicity, on a short leash

That last fact is the surprising one, and the source quantifies it. The linking number of two disjoint closed curves is the Gauss integral

$\mathrm{lk}(\gamma_1, \gamma_2) = \dfrac{1}{4\pi} \oint_{\gamma_1}\oint_{\gamma_2} \dfrac{(\mathbf{x}_1 - \mathbf{x}_2)\cdot(d\mathbf{x}_1 \times d\mathbf{x}_2)} {|\mathbf{x}_1 - \mathbf{x}_2|^3},$

and for two Hopf fibers it evaluates to $1$, while for the trivial bundle $S^2 \times S^1$ it is $0$ (both checked to machine precision in the corpus). Read into the interpretation, linking is correlation without contact — a structural tie that is not a causal tie, no path running between the fibers, nothing transmitted — which is exactly the shape Jung was reaching for with “synchronicity,” an acausal connecting principle: “acausal, yet not accidental; connecting, yet not transmitting.” Crucially, parts (a), (b), (c) — and the entire dissolution of strong solipsism — hold on any realization of the weak structure, including the trivial bundle with linking zero. Only part (d), the synchronicity, needs the specific Hopf geometry. A reader who doubts the Hopf identification loses synchronicity and keeps the dissolution intact — and the source is emphatic that even the synchronicity “makes no paranormal claim,” certifies no particular coincidence, and is “if anything, a constraint on enthusiasm.”

One ethical shape aligns with the geometry here — one the author held independently of the mathematics, not a claim to derive ethics from physics. One can act on one’s own fiber — its phase, its trajectory — but the shared $S^3$ changes only by action upon it; “correlation is not a handle.” To force the shared world without acting on it is not difficult but geometrically impossible, blocked by the very disjointness that secures privacy. To change what we share, we must act in what we share. The chapter’s verdict, in a line: “solipsism is a category error — it mistakes the privacy of a fiber for the privacy of the bundle.”

First-Edition sources & full derivations: P42