A short code can open a very long explanation. That does not mean the code contains every word of the explanation.
Imagine that two people have memorised the same eight procedures. They agree that 000 names the first procedure, 001 the second, and so on. A three-bit message can now tell the receiver which procedure to use. The receiver might expand the instruction into two hundred words, but those words were already available through shared knowledge.
Now change the task. The sender wants to communicate an entirely new two-hundred-word procedure, one the receiver has never encountered. The same three bits cannot specify every possible new instruction. Something else must carry the missing distinctions: more writing, a shared rule, a known template or additional context.
This simple contrast sits underneath an important Voynich question. If the manuscript’s visible forms are unusually constrained, how much underlying information can they preserve? Can a short label encode a name? Can a compact group stand for a whole instruction? Does an expansive translation demand more information than the proposed writing system could supply?
The Channel-Capacity Problem is not a search for a magical number of meanings hidden inside each glyph. It is an accounting problem: which distinctions come from the manuscript, which come from the decoding convention, and which are supplied by the reader?
This article belongs to the Voynich Research Library. It is distinct from the entropy article, which examines predictability, and from The Representation Has a Material Ceiling, which concerns what a scan or transcription preserves.
The direct answer: no defensible single capacity figure is available from the surface alone
We cannot turn an observed Voynich entropy statistic directly into a measured amount of hidden meaning. A capacity calculation requires an explicit model of the available signs, legal combinations, message alternatives, decoding rules and relevant sources of uncertainty. Different models can give different bounds without any contradiction.
Yale still describes the script as unidentified and the text as undeciphered. Consequently, the underlying message system is not known well enough here to report its actual communication rate. Every numerical example in this article is hypothetical and labelled as such; none is presented as a new measurement of Voynichese. [1]
That does not make calculation useless. A proposed mechanism can be checked for internal consistency. If it allows too few distinguishable outputs to recover the messages it claims to encode, something is missing. The calculation can expose that problem without selecting a language or pretending to decipher a page.
Read through counting distinguishable choices, entropy versus capacity, the noisy-channel definition, shared knowledge and keys, cipher variation, the manuscript-level questions, and a worked claim audit.
Begin with choices, not with ink
A message selects among alternatives
Suppose a sender can choose between two distinguishable marks. One choice can identify one of two alternatives. Two independent positions can identify one of four alternatives. Three can identify one of eight. The growth comes from combinations, not from the visual complexity of the marks.
If there are N equally possible alternatives, the binary information associated with selecting one is log₂N bits. This is a measure of distinguishable choice under the stated model. It is not a measure of importance, truth, emotional impact or the number of English words used to explain the choice.
Shannon’s communication theory makes this separation foundational: the engineering problem concerns the reproduction of a selected message from a set of possibilities, not the evaluation of its semantic significance. The distinction allows precise calculations without pretending that every human meaning has been reduced to a simple count. [2]
A nominal alphabet gives a ceiling, not an observed rate
For an invented system with q distinguishable symbols and exactly n positions, there are at most qⁿ different strings. If every combination is allowed and the receiver can distinguish them, the maximum choice count corresponds to n log₂q bits.
Take sixteen symbols and six positions. There are 16⁶ possible strings, or 16,777,216 combinations. The corresponding ceiling is 6 × log₂16 = 24 bits. These numbers describe the invented system, not the Voynich alphabet.
The assumptions do much of the work. They require fixed length, known boundaries, a specified inventory and unrestricted combinations. If a writing system forbids most combinations, the nominal alphabet calculation overstates the number of messages distinguishable through those positions.
A structured token may offer far fewer choices
Consider another invented system. Each record contains three fields. The first field has eight legal values, the second sixteen and the third four. Every combination of those field values is permitted. The record therefore distinguishes 8 × 16 × 4 = 512 alternatives, corresponding to nine bits.
The fields could be drawn with elaborate shapes or written through several strokes each. That would not create additional message choices unless those visual differences were themselves available to the sender and distinguishable by the reader as part of the system.
This is relevant to any token-template hypothesis. A string’s apparent length does not tell us how many independent choices produced it. A long-looking form might be assembled from a small menu of legal parts. Conversely, a compact sign could distinguish many alternatives if its meaningful features were reliably read.
Dependencies reduce the choice count further
Return to the three-field example. Suppose the third field is completely determined by the first two. It may still occupy space on the page, but it introduces no new choice once the earlier fields are known. There are then at most 8 × 16 = 128 distinct records, corresponding to seven bits, not nine.
The determined field could serve another purpose. It might make a pattern easier to recognise, reinforce a relationship or help expose an error. The loss of independent choice does not make it useless. It means that its contribution is not additional message variety.
This distinction connects capacity with redundancy. Extra marks can protect information or support usability while carrying little new information conditional on the rest. Counting every written position as a fresh independent choice would double-count what the system already determines.
Observed vocabulary is not the complete menu of possible forms
Suppose an analyst finds two hundred distinct tokens in a sample. It does not follow that the writing system permits only two hundred tokens. The sample may omit rare but legal forms. The difference between an observed inventory and an admissible inventory is essential.
As a counting statement, the observed distinct forms provide evidence that at least those forms occur under the chosen representation. They do not establish the total size of the system’s vocabulary. A capacity argument based on a closed list needs independent support that the list is actually closed.
The same caution applies to labels. A set of labels on one diagram might be exhaustive for that diagram while only sampling the manuscript’s broader notation. One cannot silently move from a local inventory to a whole-system ceiling.
Why entropy and capacity are not interchangeable
Maximum possibility differs from actual use
Imagine a system that permits four symbols. If they are used equally often and independently, each occurrence carries two bits of uncertainty. If one symbol is used almost all the time, the uncertainty is lower even though the nominal inventory remains four.
The general expression H(X) = −Σ p(x) log₂p(x) describes the average uncertainty of a random variable X under its specified probability distribution. The maximum is reached by a uniform distribution over its finite possibilities. A measured distribution is therefore not automatically a maximum-capacity distribution.
This distinction is part of the standard information-theoretic framework. In the manuscript setting, the interpretive consequence is simple: the way a source happens to use a system can be more restricted than everything the system could, in principle, express. [2]
Knowing the previous mark changes the question
A sequence can use many different symbols while allowing only a few after each particular predecessor. The uncertainty about a symbol in isolation then differs from the uncertainty after its context is known.
Conditional entropy makes the context explicit. For example, H(X₂ | X₁) asks how much uncertainty remains about the second symbol when the first is supplied. That is not the same quantity as H(X₂), and neither automatically measures the information in the underlying message.
A hypothetical code could create strongly predictable internal groups while allowing many choices between groups. A compound sign split into several transcription characters could also create an artificial-looking dependency. The interpretation depends on what the units represent.
A short-context estimate is not a complete entropy rate
For a stationary symbolic source, longer context can reveal dependencies that a one-step model misses. Its entropy rate is not established merely by calculating the uncertainty of the next mark given the immediately preceding mark.
Under the appropriate stationary assumptions, the full entropy rate is no greater than the corresponding one-step conditional entropy. But a finite manuscript may also mix regions with different distributions. The assumptions required to interpret an estimate must therefore be stated, rather than hidden inside one convenient average.
For practical Voynich discussion, the warning is enough: do not multiply a local entropy estimate by a glyph count and present the result as the manuscript’s measured stock of semantic knowledge. That operation combines assumptions about units, stationarity, model fit and source meaning that have not been established by the number alone.
The empirical Voynich result remains important within its scope
Lindemann and Bowern found unusually constrained character placement in their Voynich comparisons and investigated the effects of representation and writing conventions. That supplies a real constraint on explanatory models. It does not directly estimate how many instructions, concepts or source-language propositions the manuscript contains. [3]
The distinction does not weaken the research. It tells us what the measurement is good for. A proposed encoding should explain why its output has the observed kind of predictability. A claim about hidden message content requires additional information about how that output relates to a source.
The analytical task is to connect these levels, not to rename them all information. Alphabet size, token grammar, entropy, communication rate and semantic interpretation describe related but different objects.
What channel capacity means in the strict mathematical sense
A channel needs an input, an output and a relation between them
In a standard discrete memoryless channel model, X represents the transmitted symbol and Y the received symbol. The channel is specified by probabilities for receiving each Y when a particular X was sent. Its capacity is C = max I(X;Y), with the maximum taken over allowed input distributions. This is the framework presented in MIT’s information-theory teaching material. [4]
The formula is precise because the model is precise. It states what can be sent, what can be received and how noise connects them. An unread manuscript does not arrive with those ingredients already identified.
For Voynich, one might model the historical encoding from source content into writing, or the later passage from writing into a damaged observation. Those are different channels. A calculation about one should not be presented as a measurement of the other.
A numerical example belongs to its assumptions
Consider a hypothetical binary symmetric channel. Each transmitted bit is independently flipped with probability p. Its capacity is 1 − H₂(p) bits per use, where H₂ is the binary entropy function. For p = 0.1, H₂(p) is approximately 0.469, giving a capacity of approximately 0.531 bits per use. [4]
This number is not a property of old parchment, medieval handwriting or Voynich. It is a consequence of the specified binary noise model. Change the alphabet, the error dependencies, the costs or the available observations, and the problem changes.
The example also should not be read as a promise of perfect recovery from a short message. Capacity concerns achievable reliable rates under a mathematical coding framework, with limiting behaviour as suitable code lengths grow. A finite historical artefact still presents a finite inference problem.
A damaged mark and an uncertain meaning are different uncertainties
We may be uncertain whether a visible mark is one sign or another. Separately, we may be certain of the sign’s appearance but uncertain about what it means. These uncertainties belong to different stages of the analysis.
Better imaging might help with the first while leaving the second untouched. A proposed key might address the second while assuming a transcription that remains uncertain. Calling both noise can obscure where the missing information actually lies.
A useful account identifies the stage being discussed: acquisition, segmentation, encoding, lexical interpretation or contextual meaning. Otherwise a reduction in one uncertainty can be mistaken for progress on all of them.
A finite object does not define every message it could have carried
We possess one surviving object, not a sample of every manuscript its makers might have produced. The physical text constrains possible explanations, but it does not by itself specify the full distribution of possible source messages.
That matters because capacity is about alternatives. To say that a system can distinguish a certain number of instructions, we need a model of which instructions are possible and how they are represented. A single elaborate-looking page cannot supply that model merely by being elaborate.
The responsible approach is conditional: under mechanism A, with these units and these external conventions, this bound follows. A competing mechanism may imply another bound. The calculations become tools for comparing explanations rather than unsupported pronouncements about the whole manuscript.
The missing term in many arguments: what the reader already knows
A short index can retrieve a long known text
Return to the eight memorised procedures. A fixed three-bit identifier is enough to select one of them. The receiver can then recite its full wording. No information-theoretic rule has been broken because the message only needed to distinguish eight alternatives.
Now suppose the sender modifies the selected procedure by adding an unprecedented amount, ingredient or action. The identifier alone no longer communicates the modification unless the shared convention already specifies how such changes are conveyed.
This gives us a clean way to assess claims that short Voynich tokens encode long instructions. They might select known entries from a shared repertoire. That is different from encoding arbitrary new instructions in full. The proposed repertoire and retrieval convention would then become part of the explanation.
Length of expansion is not the same as information transmitted
A familiar abbreviation can expand into many letters. A catalogue identifier can retrieve a long record. A mathematical expression can generate an extended calculation. The output can be much longer than the input because a shared rule contributes structure.
Conversely, a long string of random choices can carry substantial uncertainty without providing a meaningful instruction to a reader. Word count therefore cannot serve as a simple measure of message information.
For a proposed Voynich translation, the question is not whether the English is longer. It is whether the extra detail is licensed by a stable decoding convention, source grammar and context, or whether it has been supplied by an analyst who could equally have supplied something else.
A conditional information bound makes the accounting explicit
Let M be a message chosen from a specified set of alternatives. Let Y be the visible representation available to the reader, K a shared key or decoding convention, and Z other shared context. These symbols describe an illustrative mathematical model, not recovered Voynich variables.
If exact decoding is possible, then H(M | Y,K,Z) = 0. The remaining uncertainty about the message disappears when the representation, convention and context are supplied. By the definition of conditional mutual information, this gives H(M | K,Z) = I(M;Y | K,Z) ≤ H(Y | K,Z).
The conclusion is straightforward: the representation must distinguish whatever about the message is not already supplied by the key and context. It cannot reliably specify more independent message choice than it carries under the model. This is an application of the entropy identities underlying the standard channel framework. [4]
Putting the whole answer in the key changes what the claim means
Suppose a modern analyst creates a lookup table containing a desired translation for every observed token or line. The written string can then retrieve the translation perfectly. But the success says little about whether the historical manuscript encoded that translation.
The table itself contains the chosen answer. If a different table could retrieve a different coherent story, perfect lookup does not distinguish between the stories. A claim of historical decoding needs independent support for the table, not merely successful retrieval from it.
This is why the Key-Recovery Problem remains separate from capacity. A system may have enough distinguishable forms for many possible keys, while the surviving evidence fails to identify which key, if any, was historically used.
Shared context is not unlimited free storage
An intended reader may know the subject, the procedure library or a technical convention. Those are legitimate possibilities. But they cannot be invoked without limit whenever the visible text fails to support a detailed interpretation.
A responsible model names the assumed knowledge and explains how the reader obtains it. The model might require a separate codebook, oral training or an earlier passage. Each requirement narrows the historical audience and creates further questions.
The more content a theory places outside the manuscript, the less it should describe that content as recovered from the manuscript alone. There is nothing wrong with a distributed information system. There is something wrong with concealing where its information has been placed.
The original reader and the modern analyst have different knowledge
A system can be easy for a trained insider and difficult for an outsider without being poorly designed. The insider may know a key, a vocabulary or a set of conventions the outsider lacks.
That possibility means our failure to decode does not prove that the original channel was low-capacity or useless. It may instead reflect the loss of shared information. Equally, a modern model’s ability to produce plausible prose does not prove that it has recovered the insider’s convention.
The question is historical identification. Which assumptions about the reader are supported? Which are merely possible? A capacity argument should keep those categories separate instead of turning imagined expertise into evidence.
Why a varied ciphertext can carry less message information than it appears to
A worked example with four messages and sixteen written forms
Invent a system with four equally likely messages: A, B, C and D. Give each message four distinct written alternatives. The writer chooses among its alternatives independently and uniformly. There are sixteen equally likely outputs altogether, so the written output has four bits of entropy.
The message itself has only two bits of entropy because it selects among four possibilities. Once the message is known, two bits of output uncertainty remain: which of its four written alternatives the writer chose. Those additional choices do not communicate another message distinction in this model.
In notation, H(Y) = 4, H(Y | M) = 2, and I(M;Y) = H(Y) − H(Y | M) = 2 bits. The example is exact under its stated assumptions. It shows why output variety and source-message information cannot simply be equated.
The alternatives may still reveal something else
Now modify the example. Suppose different writers prefer different alternatives. The choice may convey information about the writer while remaining redundant about the message. A visible distinction can therefore be informative about one variable and uninformative about another.
This is especially useful when discussing manuscript evidence. Variation might concern lexical content, writing habit, production state or a deliberate encoding choice. An information calculation must specify which variable it targets.
Calling every observable distinction semantic content would erase that distinction. Calling every nonsemantic choice meaningless would be equally unhelpful, because the choice could still matter for understanding production history or the operation of the system.
Verbose encoding changes the denominator
Suppose one source unit is represented by a pair of visible signs. A calculation per visible sign and a calculation per source unit will then use different denominators. Comparing their numerical values without accounting for the expansion can produce a false impression of lost or gained information.
If every source symbol expands through a fixed reversible rule, the source can remain recoverable even though the visible sequence becomes longer and more locally predictable. The additional written positions may be components of the encoding rather than independent source choices.
This is a reason to describe a proposed cipher operationally. The model should state its units, how boundaries are represented, and what choices are legal at each stage. Without that description, bits per glyph and bits per word can be impressive-looking numbers attached to incompatible objects.
Shorthand can omit distinctions when context supplies them
Consider an invented shorthand that omits predictable material. Its visible form can be shorter than the full expression because a trained reader supplies the rest. When the context is sufficient, the intended source can still be recovered.
When the context is insufficient, several expansions may remain possible. The system has not necessarily failed; it may have been designed for settings in which the missing context was normally available. But a modern decipherment cannot assume the intended expansion merely because one plausible expansion exists.
The accounting remains the same: what is preserved in the shorthand, what is supplied by the convention, and what uncertainty remains? Compression is not a licence to place arbitrary information into a short mark.
A codebook changes the unit of the message
If one code selects a whole known word, name or procedure, the source unit is larger than a letter. This can make a short label sufficient for a long conventional expression.
Yet the size of the required selection still matters. A code selecting among thirty known entries needs fewer alternatives than a code selecting among every possible sentence. The first task is compatible with a small inventory; the second requires a much richer system.
A codebook hypothesis should therefore specify the domain of possible entries. Otherwise, it can expand silently from a closed set of names into an unlimited dictionary of arbitrary instructions whenever the interpretation needs more expressive power.
What these distinctions change when reading Voynich
A glyph inventory must be independently justified
A capacity calculation depends on which distinctions the reader could use. If two shapes are variants of one functional sign, counting them as separate message symbols inflates the inventory. If two meaningful distinctions have been merged, the inventory is understated.
Similarly, a compound represented by several transcription characters can make the observed string longer without adding the corresponding number of independent choices. The counting system must remain connected to the historical writing system being proposed.
This is not an argument that any particular Voynich alphabet has been proved. It is a requirement for a conditional calculation: state the inventory and explain why it is appropriate before using its size as an evidential ceiling.
Recent unit research makes that requirement more explicit
Rozanova and Temerev’s August 2026 preprint challenges automatic equations between glyphs and letters, tokens and words, or all blanks and equivalent word boundaries. Its relevance here is the need to justify units before assigning information rates; it is not adopted as a recovered Voynich code. [5]
A unit model that later changes can change the denominator, the legal combinations and the apparent dependencies. A robust interpretation should explain what remains invariant through reasonable alternatives instead of treating one convenient transcription as a complete statement of the historical channel.
Positions can contribute information, but must not be counted twice
Suppose a hypothetical diagram contains four labelled sectors. A short mark inside a sector can be interpreted together with the sector’s position. The full observable representation is then not just the mark; it includes its placement.
If position already determines a category, the text may need to communicate only the remaining distinction. But an analyst should not count the category once as information in the position and again as independent information in a label that merely repeats it.
The existing Label Problem: When Short Text Is Part of the Diagram owns the spatial-function question. Here its implication is informational: define the complete observable message and the shared context before calculating what the text alone contributes.
A label’s length cannot identify its semantic type
A short label might be an abbreviation, a name, a number, an identifier or one field of a larger diagram. Length can constrain particular encoding proposals, but it does not tell us which of those categories is correct.
For example, a two-position code over twenty-six symbols permits 26² = 676 combinations if every pair is available. It can distinguish at most that many entries through those positions alone. A fixed lookup table could attach a long name to each entry. That does not make the pair a literal spelling of the name.
The number in this example is not a Voynich label measurement. It illustrates how a legitimate capacity argument can restrict a model while leaving the semantic identity of the code unresolved.
Thirty alternatives illustrate entropy and fixed-length coding
Imagine an independently established list of thirty equally likely names. The uncertainty in selecting a name is log₂30, approximately 4.907 bits. A fixed-length binary identifier needs five positions because four positions provide only sixteen patterns, while five provide thirty-two.
The fractional entropy does not mean a physical five-bit label is somehow inconsistent. Entropy and a particular finite code length describe different aspects of the problem. The extra available patterns can remain unused or serve other agreed purposes.
This example matters because claims about compact inventories often slide between theoretical average information and actual written representation. A rigorous account should say which is being calculated, rather than treating a rounded number as a recovered historical design.
A long procedural translation needs an information path
Suppose a short written sequence is rendered as an elaborate instruction containing an object, quantity, action, duration and warning. The translation may be legitimate if the system supplies those details through shared conventions or other text. But each detail needs a path back to evidence.
Which signs distinguish the quantity? Which convention provides the action? Does the warning come from the text, a standard procedure or the translator’s domain knowledge? These questions do not assume a letter-by-letter code. They ask where the independent distinctions originate.
A capacity argument becomes useful when a proposal claims more independent specification than its own mechanism permits. It becomes misleading when it rejects any long expansion simply because the visible input is short.
Some information may be carried across a passage, not inside each token
A document can establish a subject once and then omit it from subsequent entries. A page heading can define a category for everything beneath it. A diagram can supply the object while text supplies changing properties.
These arrangements mean that a token’s apparent information burden depends on context. Requiring every token to restate the whole situation would overestimate what it needs to encode. But assuming that every missing detail was established elsewhere would be equally unjustified.
The proposed information path must be explicit. A reference should point somewhere. A shared state should have a supported boundary. A contextual assumption should be distinguished from an observed mark.
Variable length and boundaries are part of the system
If strings have varying lengths, the receiver needs some way to determine where one ends. A visible separator, a self-delimiting code, a fixed field structure or a page boundary can supply that information.
A calculation that counts only the interior signs but assumes free, perfectly known boundaries may understate the resources needed for decoding. Conversely, a code whose structure already determines its boundary should not be charged for a separate delimiter it does not use.
This is another reason the writing mechanism matters. Length distributions and spacing cannot be treated as cosmetic details when the proposed inverse mapping depends on them.
A readable output and a historically identified output are different successes
A decoder may produce grammatical text from a compact input because it has strong language expectations. That capability can be useful, but it does not by itself show that the output is the historical message.
Many coherent expansions can share the same broad structure. If the visible evidence does not distinguish among them, fluency cannot supply the missing historical choice. The uncertainty has been resolved by the model’s preference rather than by new evidence.
This connects capacity with semantic grounding. A meaningful-looking expansion must still establish why those meanings, rather than other plausible ones, belong to the manuscript.
A worked audit: can one code represent a whole instruction?
Consider a hypothetical proposal for an invented manuscript. It says each entry consists of a six-position code drawn from a sixteen-symbol alphabet. The code is claimed to recover one of a large family of instructions. We are not evaluating Voynich data here; we are checking the proposal’s own logic.
If all six positions are freely variable and distinct, the output can identify at most 16⁶ alternatives. That is the twenty-four-bit nominal ceiling established earlier. If structural restrictions permit fewer strings, the ceiling decreases.
Now ask what the proposed instruction family contains. If it has only eight predefined procedures, the nominal space is more than sufficient. If it contains arbitrarily many independent choices of ingredients, quantities, actions and order, the claim needs a much more detailed account.
Case A: a shared library
Suppose the writer and reader share a library of one thousand fixed instructions. A unique identifier can select an entry. Since 2¹⁰ = 1,024, ten binary positions would be sufficient for a straightforward fixed-length catalogue code, and the invented six-position alphabet has ample nominal variety.
The capacity objection therefore disappears. But the historical questions remain. Did the library exist? How was it organised? Why should the proposed identifier map to this instruction rather than another? Where did the reader obtain the list?
Capacity has established possibility under an assumption, not evidence for the assumption. A system with enough room for a thousand instructions does not tell us which thousand were used.
Case B: compositional fields
Suppose instead that the instruction is assembled from fields: one of eight objects, one of sixteen actions and one of four states. The 512 combinations can be represented with nine bits of choice if every combination is legal and uniquely recoverable.
This is a different mechanism from the library. It can generalise to combinations not previously written, provided the component meanings and composition rules are shared. A correct analysis should therefore find reusable contributions rather than treat each whole entry as an arbitrary lookup.
The mechanism also creates constraints. It cannot suddenly specify a seventeenth action or a fifth state without an extension, escape convention or change in its inventory. A proposal must describe such changes instead of making them whenever a translation needs more freedom.
Case C: arbitrary narrative expansion
Now suppose the same code is claimed to specify any new paragraph the translator can imagine, with no fixed library, bounded fields or additional context. The proposal has removed the assumptions that made compact retrieval possible.
A finite set of distinguishable codes cannot uniquely identify an unlimited set of arbitrary messages through the code alone. Several messages would have to share an output, leaving the receiver unable to distinguish them without more information.
This is a genuine capacity problem. It does not prove that the invented manuscript is meaningless. It proves that the proposed explanation has not supplied enough distinctions for the task it claims to perform.
Case D: a reader completes a partially specified instruction
Finally, suppose the code provides only a general action and a material class. The trained reader supplies conventional amounts and technique. The complete action can be richer than the information explicitly written.
This may be a plausible working system, but it changes the claim. The manuscript does not independently specify every detail of the resulting performance. Some details belong to the reader’s prior practice.
A reconstruction should state that division honestly. It might recover a procedural cue rather than a verbatim instruction. The distinction protects useful partial understanding from being overstated as a complete translation.
What a capacity argument can rule out—and what it cannot
It can expose an impossible mapping under fixed assumptions
If a noiseless fixed code offers only sixteen distinguishable outputs, it cannot uniquely identify thirty equally permissible messages without another source of information. At least some messages must collide. The conclusion follows from counting, not from a preference for one historical theory.
That kind of argument is strong precisely because its assumptions are explicit. A proponent can respond by identifying an additional channel, a restricted message set or a different encoding. The revised account can then be assessed on its own terms.
What should not happen is an unnoticed change in the model. If a key, picture or contextual state is added to rescue capacity, it becomes part of the explanation and must be supported accordingly.
It cannot tell us whether a message is true
An accurately transmitted false statement is still accurately transmitted. A highly important warning may require only a small number of alternatives. A random string may be difficult to predict while having no agreed use.
These examples show why information quantity should not be confused with truth, value or interpretation. The mathematics measures a specified relation among alternatives. Historical meaning requires a connection between the representation and the world in which it was used.
A Voynich capacity calculation cannot certify a botanical identification, a medical procedure or an author. It can help evaluate whether a proposed representation could distinguish what the interpretation asks it to distinguish.
It cannot choose the historical key merely because enough keys exist
A system may have enough possible mappings to encode many different texts. That is an existence claim. Identifying the mapping used for one historical object is a different task.
Indeed, a large space of possible keys can make identification harder. Several keys may produce coherent-looking outcomes under flexible assumptions. The fact that an encoding is mathematically possible does not make it historically privileged.
This is why constructive models and decipherments deserve different descriptions. A constructive model demonstrates that a mechanism can produce relevant behaviour. A historical decipherment needs independent reasons to identify that mechanism and its values in the actual manuscript.
It cannot be replaced by a compression-file size
A compressor can exploit repeated substrings, formatting and other regularities. Its output size depends on its algorithm, implementation and the input representation. A smaller file can be evidence of exploitable structure without being a direct measurement of source-message capacity.
Even a careful compression comparison must specify whether headers, markup, tokenisation and character encoding are included. Otherwise, part of the apparent difference may arise from packaging rather than the historical writing.
Compression can be a useful analytical tool. It should not be promoted into a semantic meter that reveals how much the manuscript knows. The distinction between a model’s description length and the historical message remains necessary.
The questions a serious proposal should answer
What is the message? State whether the model is trying to recover letters, words, identifiers, procedures or contextual states. A rate has no stable meaning if the source unit changes during the argument.
What is one observable output? State whether the receiver uses a glyph, compound, token, line, diagram position or a combination. Include boundaries and distinguish genuinely independent choices from determined components.
What is shared in advance? Name the key, vocabulary, codebook, grammatical knowledge and document context. Do not hide a detailed translation inside a supposedly neutral lookup table.
What is being measured? Distinguish an observed entropy estimate, a nominal count of possible strings, an achievable rate under a channel model and a semantic interpretation. These quantities cannot be exchanged merely because all involve information.
What happens on material not used to formulate the account? A stable system should reuse its conventions rather than expand its dictionary of exceptions indefinitely. That question concerns historical identification and generalisation, beyond the counting bound itself.
A reader workshop: make the information visible
For younger readers: eight cards and three choices
Prepare eight cards with different instructions and number them using three binary positions. Give two learners the same set. One can send a three-position code and the other can read out the full instruction.
Then replace one instruction with a new sentence unknown to the receiver. Sending the old code will not communicate the change. The learner can see exactly where the missing information lies: not in the short identifier, but in the card the receiver no longer shares.
This is a concrete way to explain why a short signal can retrieve a long text without containing an arbitrary long text. The shared library is doing part of the work.
For secondary readers: count legal records
Invent records with an object field, an action field and a state field. First allow all combinations. Then introduce a rule making the state fully determined by the object and action.
Count the possibilities before and after the rule. The written record may occupy the same space in both systems, yet the number of independently distinguishable choices changes. That is the difference between visible length and informational freedom.
Next, ask whether the determined state field could help detect an error. The class can see the connection between reduced independent choice and possible redundancy without assuming that every constrained system was designed for error protection.
For advanced readers: separate message entropy from output entropy
Use the four-message, sixteen-output example. Each message has four legal encodings. Calculate the uncertainty of the message, the uncertainty of the output and the remaining output uncertainty once the message is known.
The three quantities make the distinction visible: two bits choose the message, two more choose its written disguise, and the output has four bits in total under uniform selection. Only the first two concern which source message was selected.
Then change the selection probabilities or introduce writer preferences. The exercise shows why an empirical distribution needs an explicit model before its entropy can be interpreted as information about a particular hidden variable.
For teachers and independent readers: audit the expansion
Take a compact instruction and expand it into a paragraph. Mark which details were explicit in the original, which followed from a shared convention and which were newly supplied for explanation.
The expanded paragraph may be helpful and accurate, yet it should not be mistaken for a verbatim decoding of the short instruction. This is an ordinary writing exercise with a direct lesson for manuscript interpretation.
A clear explanation can add context for a modern audience. A historical claim must keep that added context distinguishable from what the original representation independently specifies.
Sources, calculations and scope
[1] Yale Beinecke Library: The Beinecke Cipher (Voynich) Manuscript. Institutional status and access information; not a measurement of the manuscript’s source-message capacity.
[2] Claude E. Shannon: A Mathematical Theory of Communication (1948). Foundational definitions of information, entropy and communication. The invented inventories and numerical examples above are applications, not Voynich observations.
[3] Luke Lindemann and Claire Bowern: Character Entropy in Modern and Historical Texts: Comparison Metrics for an Undeciphered Manuscript, revised 2021. Comparative character predictability and representational assumptions, not a count of hidden semantic propositions.
[4] MIT OpenCourseWare: 6.441 Information Theory, Lecture 8 (2010). Discrete memoryless channels, mutual information and the binary symmetric channel. Its model assumptions are not asserted as properties of Voynich.
[5] Liudmila Rozanova and Alexander Temerev: A Glyph Is Not a Letter, a Token Is Not a Word, a Space Is Not a Space (2026 preprint). A recent argument about unit definitions, not an established historical decoding system. Sources checked on 5 September 2026.
The final idea: every recovered distinction needs somewhere to come from
Voynich may encode much more than an isolated token suggests, because a trained reader could have used shared knowledge, page context and a structured convention. It may also encode less independent content than a fluent modern translation makes it appear to contain.
Neither possibility can be settled by counting English words. The useful question is where each distinction comes from. A sign can select a known procedure. A diagram can supply a category. A key can define a correspondence. A reader can contribute prior knowledge. The explanation becomes trustworthy when those contributions are made visible.
A sound capacity argument will not announce how many secrets the manuscript contains. It will show whether a particular proposed system has enough distinguishable evidence to recover what it claims—and where any additional information has entered.
Continue with Why Voynichese Is So Predictable, The Key-Recovery Problem, and The Mnemonic Problem, or return to the Voynich Research Library.