A tool's name tells its user what to expect of it. Call something a model of influence and people will ask it what to do next; call it a calculus and they will expect it to calculate. A formal system for political work has to pick its name with that in mind, because the reader most likely to take the name literally is the technically trained one, and the reader most likely to be misled by it is the executive who is not.
The Lam System for Political Interaction is called a system because that is what it is: a vocabulary with a grammar, a record, and rules that move the state of a maneuver forward one entry at a time, with the actor's judgments as an input. It was first described as an algebra, then in the terms of a calculus, and both names were dropped. What the System Is tells the history in a paragraph. The reasons are worth having in full, because each one says something about political work, and so is the line where the mathematical words still apply.
What an algebra would have promised
An algebra is a way of combining things. Its operators take two objects and produce a third whose behavior follows from the two and from the way they were joined. If maneuvers formed an algebra, an executive could write two of them side by side, join them, and read off what the joint maneuver does from what each part does.
Illustrative. The people and the company are invented. Emilio Sandoval runs engineering at a payments company. He wants the chief financial officer, Kofi Odhiambo, to fund a rebuild of the settlement platform, and he wants the chief executive, Annika Sorel, to approve two senior hires for it. That is two maneuvers, with two targets and two decisions. An algebra of maneuvers would let Emilio write the funding and the hires as one maneuver and derive how it behaves from its halves.
The work does not behave that way. Whether Annika approves the hires depends partly on whether the rebuild is funded, and the standing Emilio spends persuading Kofi may be standing he needed for Annika. The two maneuvers interact through Annika's reading of the situation and through what Emilio holds, and neither is an operator anyone could write down. No rule about the parts gives the behavior of the whole, since the parts are two other people's decisions.
The system writes Emilio's pursuits as two cycles under his agenda, numbered in the order they began, and the second opens only once nothing in the first is waiting. Whatever the first returns, such as the funding, joins what Emilio holds, and the second cycle's gates can find it there. The two are connected through his holdings and through the order of the cycles, and the record shows both exactly.
Emilio's two pursuits, as the record keeps them
Illustrative. The people and the company are invented. Each row is one entry in the record, in the order it was written. The two pursuits are two cycles under Emilio's agenda, the second opened only once the first had closed, and no entry joins them: the funding commitment the first cycle returns is among what he holds when the second cycle's gate looks for it.
Cycle: Emilio and Kofi: the rebuild
- OpenThe cycleThe first pursuit opens under Emilio's agenda, numbered one.
- InterestActorEmilio wants a commitment to fund a rebuild of the settlement platform.
- DetectionActorKofi will fund the rebuild this year, or keep patching the old platform.
- ObjectiveActorKofi funds the rebuild.
- IntentionActorShow Kofi what settlement failures on the old platform cost last year.
- Required resourcesActorThe settlement failure costs and Emilio's standing with Kofi.
- Gate passesThe cycleEmilio holds both.
- ExecutionActorThe cost case goes to Kofi.Spent: the settlement failure costsSpent: his standing with Kofi
- PerceptionTargetKofi reads the rebuild as cheaper than another year of failures.
- SelectionTargetKofi commits the funding.
- OutcomeThe cycleThe rebuild is funded.
- Obtained utilityTargetKofi gains a platform that stops losing money on failed settlements.
- CloseThe cycleThe first pursuit closes, with nothing in it left waiting.
- Flow backActorEmilio holds the commitment.Returned: Kofi's funding commitment
Cycle: Emilio and Annika: the hires
- OpenThe cycleOnly now does the second pursuit open, numbered two.
- InterestActorEmilio wants approval for two senior hires for the rebuild.
- DetectionActorAnnika will approve the hires, or have the rebuild staffed from the current teams.
- ObjectiveActorAnnika approves the hires.
- IntentionActorShow Annika that the rebuild is funded and that the current teams cannot staff it.
- Required resourcesActorKofi's funding commitment and Emilio's standing with Annika.
- Gate passesThe cycleThe commitment came back from the first pursuit, so Emilio holds both.
- ExecutionActorThe staffing case goes to Annika.Spent: Kofi's funding commitmentSpent: his standing with Annika
- PerceptionTargetAnnika reads the hires as what a funded rebuild needs.
- SelectionTargetAnnika approves the two hires.
- OutcomeThe cycleThe hires are approved.
- Obtained utilityTargetAnnika gains a rebuild with the people to finish it.
- CloseThe cycleThe second pursuit closes.
- Flow backActorEmilio holds what he opened the second cycle for.Returned: approval for the two hires
Early on, much of the notation looked like composition. A sub-cycle sits inside the lever that opened it; an address grows longer as one constituent is placed under another; a cycle's levers are gathered into a set. Each of these turned out to be containment, one thing placed inside another at an address that says where. Containment gives every constituent one place in a tree, which is what makes the record exact, and it joins nothing to anything. Once that was clear the algebra had nothing left to describe, and the framing was dropped whole.
The nearest the system comes to combining is two levers in one cycle that can be played in either order. What the System Guarantees shows that the order of two such levers never changes where the maneuver ends. That result concerns two steps taken in turn on one record, each touching its own resources, and the levers remain two steps in one state.
What a calculus would have promised
The second framing borrowed from the calculi that computer scientists use to describe programs, including programs running side by side. A calculus of that kind has two parts: an account of when two expressions are the same, and a set of steps that rewrite an expression into another, usually smaller, until no step applies. What remains at the end is the result, and the original expression has been used up on the way.
The way a calculus presents its rules suited the system, and the system kept it. The claim to be a calculus failed first on what a step acts on. A calculus rewrites the thing it is computing. LSPI's steps advance a state, and the state has four parts: the cycle in control, the record, the cycles waiting for a sub-cycle to hand back, and what the actor holds, counted. A computer scientist would recognize them as a pointer to where execution stands, a log that only grows, a stack of suspended calls and a store. A step moves the pointer, adds to the log, suspends or resumes a cycle and adjusts the store. No expression lies underneath the state for the steps to work on, so the machine is the whole system.
The difference reaches the executive through the record. A rewriting system forgets as it goes, since each step replaces what came before with what is left of it. LSPI's central discipline runs the other way: nothing in the record is overwritten, a failed gate stays failed after the sub-cycle has fixed it, and a projection stays beside the realization that answered it. The Record explains what that buys. A system whose steps consumed their own history could never have kept that promise, so the persistence rule and the calculus identity were incompatible from the start.
The claim failed again on what decides a step. A calculus computes: each step is defined so that a machine can find it and take it, and a program can run any expression to the end with nobody supplying anything. LSPI's important steps wait on the actor, for whether the target's reading matched the projection, which irreversible election to make, and whether what the cycle rested on still holds. The Boundary of Computation argues this at length. The property a calculus is most prized for is that every way of running an expression reaches the same result, a theorem about steps a machine takes alone. LSPI has a property of the same shape, and it holds only once the actor's judgments are fixed. Claiming the calculus's version would mean claiming that a maneuver's end can be known without the actor.
What the system kept
Dropping the two identities left their tools in place. The system is set out the way calculi are set out, with an account of sameness first and then steps from one state to the next, each stated with what must already be true before it can be taken. It has a typed grammar, a vocabulary of twenty-one constituents specialized to political work, a mark that tells a projection from a realization, a record that only grows, and guarantees proved from the layers beneath them. Even its five layers, read in order from grammar to guarantees, follow the usual arrangement for systems of this family.
The tools are real and correctly used, and borrowing them leaves the system outside the family they came from. Of the ten statements in the figure below, five can honestly be made of LSPI. The other five claim what an algebra or a calculus would have, and the system makes none of them.
What can honestly be said of the system
Illustrative. Ten statements a technically trained reader might make about LSPI: guess which the system can stand behind and which claim what an algebra or a calculus would have, then select each to see why.
Select each item to see the verdict.
One of the three facts the sameness layer rests on. Inside that layer, axiom is the right word.
No operator joins maneuvers. Two pursuits sit under the agenda as two cycles, one after the other, connected only through what the actor holds.
Sameness holds inside every larger expression, which is what makes it an equivalence in the standard sense.
It is contained: it sits at an address under the lever that opened it, and its close hands back one resource.
The presentation is borrowed from calculi and correctly used, and borrowing it makes the system no calculus.
Each step advances a state: it moves control, adds to the record, suspends or resumes a cycle, or changes what the actor holds. Nothing is used up.
Any well-built system reads its data that way, and reading data well does not make a system an algebra. The steps act on the state, never on classes of expressions.
The steps that matter wait on the actor's readings and elections, which nothing in the record settles.
Each guarantee follows from the grammar, the types, sameness and the steps. None is a rule of its own.
Only once the actor's judgments are fixed. Then the order of independent steps never changes the end; without them, nobody can say how it ends.
- Statements the system can stand behind
- 5 of 10
Slash addressing, the way of writing paths with slashes, dots and numbers, is the most visible part of the notation, and it is easy to take it for the whole. It is one family of operators inside the system. The system's name covers everything: the grammar and types, the sameness rules, the steps, the guarantees, and the worked maneuvers they are tested against.
The question a skeptic asks
A technically trained reader will press on one point. The system has an account of when two expressions are the same. Do its steps act on classes of equivalent expressions, the way a calculus that rewrites up to sameness does? If they did, it would be a calculus whatever it called itself.
They do not. The steps act on the state. Where a step reads an expression held inside the state, such as a path inside an entry or the set of alternatives a detection names, it reads it up to the three facts the sameness layer rests on: grouping does not change where a path leads, the order of a set's members does not matter, and the Latin A and the Greek capital alpha are one letter. A program that compares two names after ignoring capital letters has not become a calculus by doing so. Rewriting expressions up to sameness is a different shape of thing, and LSPI has none of it, because it rewrites no expressions at all.
Where the words still apply
Inside that one layer the mathematical vocabulary is honest in full. Sameness in LSPI is an equivalence in the standard sense, and it holds inside every larger expression: replace a part with something the same and the whole stays the same. The three facts are genuine axioms. Reducing two expressions to one canonical form and comparing the results is the right way to decide whether they match, and the guarantee that sameness can always be decided rests on that procedure. Someone describing this layer may say axiom and congruence without apology.
The honesty stops at the layer's edge. Equational language describes how expressions relate to one another. The claim to be a calculus or an algebra concerns how steps, states and the actor's judgments relate, and the three reasons hold at that level whatever is true inside the sameness layer. Where the system uses a mathematical word, the word means what it means in mathematics, and where the word would promise more than the system delivers, the system leaves it out.
Why the history is published
The rejected framings could have been left out of the account. They stay in because they show the name was chosen by someone who knew what the other names meant and had a reason for declining each. A reader who knows what a calculus is can check those reasons and need not take the name on trust.
The same habit runs through the rest of the system. Where one part of the notation contradicted another, the contradiction was written down and settled in the open, with the choice and its reason logged. Where the system cannot yet represent something a maneuver might do, it says so, and What the System Cannot Yet Represent lists what is outstanding.