Most continuations are possible. Few continuations are stable.
There is a clean way to make sense of the phrase "an infinite canvas." Treat it as a possibility space, the space of all symbol sequences that could be written, and treat writing, or thinking in language, as a trajectory through that space. This is not an aesthetic metaphor. It is a way to separate three things that are otherwise constantly mixed, syntax, probability, and meaning.
Start with syntax. Fix a finite alphabet, the set of symbols the system is allowed to use. A text is a finite prefix over that alphabet. A continuation is another prefix that extends it. The infinite canvas is the set of all infinite continuations, which can be viewed as the limit of all finite prefixes. A prefix matters because it carves a cylinder, the set of all sequences that begin with that prefix. Two texts are close in the only natural geometry this space has if they share a long prefix, because then they still agree on many next-step constraints.
Now add probability. A "next token" process is a rule that assigns, at each prefix, a distribution over allowable next symbols. This rule induces a measure over the space of infinite continuations. The measure is not the canvas. It is the way an entity moves through it. Blind typing corresponds to a measure that is close to uniform over symbols, high step uncertainty, high branching. A more directed process concentrates probability mass on a much smaller set of continuations. It does not eliminate the canvas, it changes the measure.
Now add structure. Most sequences are structurally empty, and this is the first point that matters. They are not empty because they lack characters, but because they lack compressive constraint. If a prefix does not bind anything, then almost any continuation is admissible. The next line can vary wildly without "breaking" anything, because nothing has been committed. This is the ocean.
Islands begin when commitments appear. A commitment is any condition that rules out otherwise possible continuations. Definitions rule out meanings. Boundaries rule out cases. Mechanisms rule out causal stories that do not fit. Tests rule out claims that do not survive contact with evidence. Tradeoff statements rule out ambiguous optimization. Internal consistency rules out contradictions. Each commitment reduces degrees of freedom. This is what "structure" is in operational terms, a reduction in the space of admissible futures induced by what has already been fixed.
This is where the intuitive use of "entropy" becomes honest without importing thermodynamics. Entropy here is simply the width of the next acceptable move given the commitments already made. High entropy means many next steps remain admissible. Low entropy means few remain admissible. Low entropy is not boredom. It is grip. A text has grip when the next step becomes hard to vary without changing what the text has already committed to. Grip is how islands feel from the inside.
The difference between the monkey and an intelligent entity is therefore not that one prints fewer tokens. It is that one cannot preserve grip. A blind process can stumble into an island, but it cannot stay, because it does not know which constraints are doing the work. It cannot maintain coherence over time. An intelligent process does not only sample. It navigates by preserving constraints. It spends computation not to produce more words, but to keep the trajectory inside regions where commitments accumulate without contradiction, where meaning becomes stable, where the continuation becomes increasingly forced by what has already been fixed.
This produces a second clean distinction, surface detail versus depth. A text can be long and still be shallow if it keeps leaving important degrees of freedom unresolved. It can add examples, context, ornament, and still require the reader to guess the missing condition that makes the sentence usable. Depth is different. Depth is what happens when a text keeps moving required structure from the reader into the artifact. Whenever a sentence still permits two incompatible readings that change what it commits you to, the text is not yet determinate at that point. The missing piece is not "nice to have." It changes truth conditions, action conditions, or constraint force. The text depends on it. A deepening step is therefore not "say more." It is "write the exact missing condition that removes the ambiguity."
This is why questions are not decoration in this model. Questions are the natural probes that detect unresolved degrees of freedom. A serious why question is asking for grounds, the condition that makes the claim hold rather than float. A serious how question is asking for mechanism, the missing step that makes "therefore" more than a gesture. A serious when or where question is asking for boundary, which cases the claim governs and which it does not. A serious what would count as failure question is asking for falsification, what would force revision. In the ocean these questions have no stable target because nothing was fixed. On an island they do, and they tend to expose what was still left implicit.
This leads to the closure signature. Early in a good explication, questions generate new necessary writing. The text grows because it is still missing pieces it depends on. Each time a good question forces the introduction of a condition without which the claim cannot be used, the text moves deeper into the island. Closure is reached when this stops. Questions can still be asked, but they stop forcing new necessary structure. They stop uncovering hidden dependence. They only point to where the relevant condition is already stated. Questions become navigation.
The infinite canvas frame therefore does not assert that everything will be printed. It asserts something more useful. The space of possible sequences is enormous. The measure induced by blind sampling spreads mass over the ocean. The measure induced by intelligent constraint-preserving search concentrates mass on islands. The island property is grip, meaning the progressive reduction of admissible continuations as commitments accumulate. Depth is the systematic removal of degrees of freedom by making dependencies explicit. Closure is the regime change where questioning ceases to force new necessary structure and becomes address selection inside what is already explicit.
This also clarifies a common confusion. Unlimited compute does not collapse the canvas to a single path. It increases the ability to search and to stay on islands. It makes it easier to find high-grip continuations and to maintain them. It does not guarantee a unique global optimum across the entire canvas, because the canvas is not itself an objective. It is a space. Objectives live on top of it. Compute amplifies the capacity to satisfy an objective. It does not create an objective where none is well-defined.
In this frame, an "ASI on the canvas" is not defined as a magic writer. It is defined by two observable behaviors. First, its trajectories concentrate on islands of high grip across domains, not by accident but by method. Second, it can convert local grip into global structure, meaning it can build long continuations whose constraints remain consistent, whose meanings remain stable, and whose questions collapse into navigation rather than continuing to reveal missing necessities. That is the clean content of the infinite canvas theory.
A huge space plus a concentrating measure is the difference between noise everywhere and meaning somewhere.