how they Seme
August 27th 2026
The Seme (pronounced “seem”)
When an equation becomes an object of semantic entitlement
A curious thing happened in a recent discussion in the IPI email group about two mathematical formalisms.
The original interest was similarity (they were identical) in a written formula.
Two independently developed constructions appeared to produce a physically related algebraic structure. The tempting question was therefore whether similarity in mathematical form implied similarity in physical meaning.
The discussion revealed it did not.
A subsequent calculation made the distinction unusually sharp. One vacuum computation was mathematically correct, but it had been assigned to the wrong vacuum object for the intent of the other. The object actually calculated and the object it was claimed to represent occupied orthogonal rays. The mathematics survived; the attribution did not. Both intentions survived, the idea they said the same thing did not.
This produced a useful methodological observation:
correct mathematics does not by itself determine what object that mathematics is entitled to represent.
But there is another feature of the episode that interests me.
Consider the relation that was being exposed in both pieces of work (the object):
V² = −64V
In the particular complex representation being tested, that relation is computationally recoverable. Johann Pascher’s verification gives V as proportional to the relevant Pn-sector product and verifies V² = −64V; under the stated mod-3 treatment, −64 ≡ −1.
Look at the equation, however, not first as physics but as writing.
It contains remarkably little.
V
²
=
−
64
V
Yet none of those marks arrives empty.
Take only 64.
The written numeral is already entitled, within ordinary arithmetic, to participate in relations such as:
64 = 2⁶ = (2³)².
To understand that statement is to inherit a considerable formal constitution.
2 must already possess standing as a numerical object.
3 must possess standing.
Repeated multiplication must be permitted.
Exponentiation must be permitted.
Parentheses must establish order.
Equality must preserve an accepted equivalence between the objects produced by these different constructions.
The resulting 64 is therefore not merely two glyphs.
It is an object sitting inside a network of licensed transformations.
Its identity is partly given by the relations in which it can legitimately participate.
That becomes interesting when 64 is placed into:
V² = −64V.
The syntax surrounding V now exhibits a strangely similar generative structure.
There is an object:
V
There is an admissible operation:
V → V²
And there is a return relation:
V² → −64V
or, more abstractly:
V² ∝ V.
The equation therefore does not merely name V.
It gives V an identity through an action.
It tells us what happens when a particular permitted transformation is performed upon it, and it tells us how the resulting object remains related to the object with which we began.
The numerical object and the represented object consequently occupy different semantic domains, but they participate in the same written architecture.
The arithmetic standing of 64 is inherited from the relations that make 64 a meaningful mathematical object.
The standing of V is being established through another relation that makes V a meaningful object within the particular algebra.
There is a kind of formal mirroring:
2⁶ = (2³)² = 64
and
V² = −64V.
These statements do not say the same thing.
Nor do they possess identical evidential status.
What they share is a syntax in which identity is carried through licensed transformation.
That is the feature I want to isolate.
The spun object
One way of thinking about such an equation is as a spun object.
The equation begins with an object, passes it through an operation, and returns a relationship to that same object.
It therefore contains both:
state
and
licensed consequence.
V is not merely located by the visible symbol V.
Its mathematical identity is further constituted by what may legitimately be done to it and by what relation survives the doing.
This is familiar mathematics. Objects are constantly characterised by their invariants, transformations, eigenrelations, symmetries, closure properties and equivalence relations.
But written as an equation, the whole operation can itself become a new object.
We can quote it.
Store it.
Transmit it.
Compare it.
Use it as a premise.
Apply another operation to it.
Ask whether another formalism exhibits the same relation.
And, most importantly, begin attaching physical interpretations to it.
At that moment something has happened which is not simply algebra.
The equation has begun to carry meaning beyond its syntax.
From equation to Seme
I propose calling such an object, when it acquires this additional role, a Seme (pronounced “seem”.
The word is deliberately close to meme and gene.
A gene is capable of carrying biological inheritance.
A meme is capable of carrying culturally repeatable content.
A Seme, in the sense proposed here, would carry semantic entitlement.
The term already has a history in linguistics and semiotics, where a seme can denote a minimal feature or unit of meaning. That existing usage is useful and congruent rather than inconvenient.
The proposed extension is more specific:
A Seme is a minimally reproducible informational object that carries forward a licensed relation between formal representation and meaning.
It is not merely something that means.
It carries a rule about what something is presently entitled to mean.
That distinction matters.
Consider again:
V² = −64V.
At one level it is an algebraic expression.
At another it may become a statement about a vacuum object.
At another it may participate in a comparison between two theories.
At another it may be offered as evidence that two frameworks share some underlying structure.
And, eventually, it may be enlisted in an argument that a particular formalism has standing as a candidate representation of substrate reality.
Those are not equivalent operations.
The same written equation can travel through all of them.
The Seme is the informational object through which that travel becomes possible.
Formulaic similarity, semantic difference
This returns us to the original problem in the discussion.
Two expressions can be formally similar without being semantically equivalent.
Indeed, that was precisely what the comparison exposed.
The order-three structures may resemble one another.
The vacuum constructions may occupy comparable formal territory.
But similarity of syntax does not automatically constitute identity of represented object, still less identity of physical meaning.
Johann himself subsequently accepted the distinction explicitly: a mathematical representation having physical standing for particular operations is not the same thing as granting that representation candidate substrate standing. He also accepted the vacuum correction as showing that mathematical correctness and entitlement to represent a particular object are distinguishable questions.
This means the Seme can fail.
And that is essential.
A useful unit of semantic entitlement cannot simply transmit meaning indefinitely by repetition.
Its entitlement must remain accountable to the constitution under which it obtained that meaning.
The original vacuum error gives us almost the perfect example.
The computation had one standing:
mathematically correct for object A.
It was then semantically transmitted as:
representation of object B.
That second entitlement failed.
The mathematics did not disappear.
The Seme had crossed an inadmissible bridge.
Underconstitution
This suggests another way of understanding what happens when mathematics is used in fundamental physics.
The problem is frequently not that the terms are badly defined mathematically.
Quite the opposite.
They may be defined as completely as the mathematical operation requires.
The underdefinition arises somewhere else.
They are constitutionally underdefined relative to the stronger burden subsequently placed upon them.
V may be perfectly defined as a formal object.
64 may be perfectly defined arithmetically.
The exponent may be perfectly defined operationally.
The equality may be perfectly valid.
Nothing more need be added in order for the mathematics to be mathematics.
But the moment we say:
this V is the physical vacuum
the burden changes.
And when we say:
this formal structure is evidence about substrate reality
the burden changes again.
The terms have not suddenly become mathematically incomplete.
They have been asked to carry a new kind of standing.
That is what “constitutionally underdefined” means here.
Not:
we haven't defined the mathematics well enough.
But:
the constitution presently governing the representation does not yet account for the additional semantic role we are asking the representation to perform.
The Seme therefore marks a boundary.
It is where an already valid mathematical object is being prepared to carry something additional.
The strange case of zero
This becomes particularly obvious with 0.
Mathematically, zero requires no rescue.
It is a perfectly legitimate object within the relevant structures.
But physically, 0 can carry radically different meanings.
No signal.
No occupation.
No measured value.
A chosen origin.
A cancellation.
A null eigenvalue.
Absence within the model.
Absence in the physical world.
Those are not the same thing.
Yet science frequently carries the numeral smoothly from the formal system into the physical representation.
The written symbol survives while its ontological burden changes.
Again, the issue is not whether 0 is mathematically real.
The issue is:
what is 0 presently truthfully entitled to mean?
That is a constitutional question.
And it is exactly the kind of question a Seme would need to preserve.
Minimum writable tension
There is perhaps an even more interesting way to read:
V² = −64V.
The equation may be approaching a kind of minimum writable tension.
On the left:
an object acted upon.
On the right:
the same object recovered through a scalar relation.
Between them:
equality.
The complete expression records, in an extraordinarily compressed way, the tension between identity and transformation.
V is itself.
V is acted upon.
The result is not simply V.
Yet the result remains formally bound to V.
One object is simultaneously the origin and the endpoint of a permissible transformation.
That is what I mean by a spun object.
And once written, the spun object can itself become the thing operated upon intellectually.
We no longer need to execute the matrices every time we discuss the relation.
We can write:
V² = −64V
and carry the result forward.
Compression has occurred.
But compression also creates epistemic danger.
The equation now looks self-contained.
Its provenance disappears.
Its representation disappears.
Its assumptions disappear.
Its object attribution disappears.
Its admissibility conditions disappear.
All of those may nevertheless be silently inherited when someone later reads the equation.
This is exactly how semantic entitlement can become memetic.
A result is repeated more easily than the constitutional process that warranted it.
The Seme names that problem.
Semantic replication
A meme survives by being repeatable.
A Seme survives by being meaningfully repeatable.
But meaningful repetition requires something stronger than copying the characters.
For a Seme to preserve its scientific standing, enough of its constitution must remain recoverable to answer questions such as:
What formal object did this expression concern?
Under what representation?
What operations were valid?
What was actually demonstrated?
What physical object was it attributed to?
Who or what made that attribution?
What evidence licensed the attribution?
What stronger claims were not established?
What would revoke the entitlement?
Without those conditions, semantic repetition can outrun evidential standing.
The characters remain stable while the meaning drifts.
This may be one of the central problems of scientific communication.
The Seme and scientific reality
We frequently say that something becomes scientifically real when we know what it is made of, how it behaves, how it relates to other things, or how to reproduce its effects.
That need not mean that science creates the physical reality.
It means science constitutes an informational object capable of standing for that reality.
And what gives such an object its scientific identity is rarely its name alone.
It is a network of relations:
**form
permitted operation
invariant behaviour
physical attribution
evidential warrant.**
The first three may be mathematical.
The fourth is semantic.
The fifth is epistemic.
Together they may eventually support an ontological claim.
The scientific object is therefore less like an isolated noun than a constrained relational structure.
In this respect the syntax of mathematics is unusually revealing.
64 is not meaningful merely because somebody once decided to call a quantity sixty-four.
Its place in arithmetic is sustained by a dense, repeatable web of permitted relations.
64 = 2⁶ = (2³)²
is one tiny visible fragment of that web.
Likewise, V acquires formal identity through its relations.
V² = −64V
is one fragment of that web.
The temptation of fundamental physics is to allow the stability of the first kind of relation to lend authority silently to the second, and then to allow both to lend authority to a third:
therefore this describes what reality fundamentally is.
That third transition may be justified.
But it is not contained automatically in the first two.
It requires constitution.
The Seme as an accountable semantic object
This leads to a possible definition.
Seme
A reproducible symbolic object that preserves, or purports to preserve, the entitlement by which a formal relation may carry a specified meaning into subsequent operations.
A scientific Seme would ideally contain, either internally or by recoverable reference:
formal identity
→ operative relation
→ admissibility conditions
→ represented object
→ evidential standing
→ permitted semantic consequence.
Under that definition,
V² = −64V
is not automatically a Seme merely because it is an equation.
It becomes one when it is used as a carrier of a claim about what V stands for.
Its scientific integrity then depends upon whether the entitlement survives repetition.
The vacuum correction is precisely a case in which the formal object survived but one semantic entitlement did not.
That may make it a particularly good first example.
Seme-ing
There is one final linguistic accident I rather like.
Seme sits close to seem.
To seem is to appear under a relation of similarity without yet guaranteeing identity.
That is almost exactly where this discussion began.
Two formalisms seemed alike.
Some structures genuinely converged.
Some meanings did not.
The useful scientific response was neither to declare them identical nor to dismiss the resemblance.
It was to ask:
In what respect do they seem the same?
What operation establishes that similarity?
What meaning is the similarity entitled to carry?
And:
where does the entitlement stop?
Perhaps that is what a Seme should ultimately preserve.
Not merely meaning.
Not merely resemblance.
But the accountable boundary between what something formally seems to say and what science is presently entitled to say that it means.
That boundary may be one of the smallest writable objects from which scientific reality is built.
Not physical reality itself.
Scientific reality:
the recoverable, transmissible and criticisable world of things to which our representations have been given permission to refer.
Describing the semantically inherited relationship of a historically confused attribution, as the formulaic object for one vacuum or another, has never been so much fun.
Stefaan Vossen ⊙
Five-dimensional chess played between ideas, not personas.
