What computation rests on

Part of the series: Getting it organized properly. Notes from a field still finding its shape.

The strict way

A capability can be held loosely or strictly. Held loosely it names whatever a thing does well and asks nothing of the one who uses it. Held strictly it asks a great deal and in return it cuts: it divides what holds a capability up from what only held it over. A field that maps capabilities is forced to hold it that way.

This article holds it strictly and turns it on one subject: computation, what nearly everything now runs on, traced down layer by layer to ask what it rests on. The strict reading earns something the loose one never reaches: it distinguishes what a capability rests on from what only kept it in being.

Capabilities

The word capability carries more than its share of meanings. In ordinary speech it means little more than being able to do something. In the military it names a force or a system fit to carry out a mission. In business strategy it points at whatever a firm does well enough to compete on. Each sense is fair. None is the one meant here.

Here the word is used as Enterprise Architecture uses it, where it is narrower and more exact.

A capability is an ability that some organization, person or system possesses, named in its own right and held apart from the work that performs it. The function or process that carries it out can be reorganized or restaffed. The ability itself does not change. A capability, in this sense, is what is meant to stay while the work beneath it is rebuilt.

The term is Enterprise Architecture's; what it names is not. An ability held apart from the work that performs it can belong to a person, a craft or a civilization as readily as a firm. The definition fixes a shape, not a setting. The shape holds wherever an ability outlasts the work beneath it, long before there were enterprises to map.

Computation is taken as given. It is not defined here, only pointed at, the thing nearly everything else now runs on. What it is exactly is not the question here. The question is narrower: does it fit the definition just set out?

Set computation against that definition and it fits. It is an ability: to carry out calculation by rule. It is held apart from the work that performs it. The machines that compute are replaced one generation after another. The ability outlasts every one of them. By the Enterprise Architecture definition then, computation is a capability. That is the one thing established here.

Computation is recent. Built within reach of memory and record, it did not always exist. A thing that did not always exist was built on what was already there when it came. Whatever computation is, it rests on something earlier.

So the question turns around. Not what computation makes possible but what made it possible. When computation was built, what was already in place that it leaned on? And is any such thing a capability in the same sense?

If it is, the same question can be put to it. What is it composed of? Is any of it a capability in turn? The question repeats. Each capability is decomposed into its elements. Where an element itself is a capability the descent steps down to it. What the inquiry is after is a composition, capability within capability, read from the present backward as far as it reaches. Beyond the composition, it explains what keeps a capability when the building stops.

How the capabilities are found

Before trusting that the capabilities are there to find, ask how anyone finds one in history. The obvious methods all fail the same way.

1. Decompose from the top and the grain is free, cut to suit the answer.
2. List every ability ever held and there is no such list to build.
3. Name the turning points and the list is drawn by knowing the ending.

Each leaves the author at the end, choosing what points toward where they already stand.

So leave the choosing alone. History already did it. The capabilities still standing are the ones it kept. Which ones those are is not the author's to decide. Writing was kept and Greek fire was lost.

Humanity has always done capability selection, long before anyone drew a capability map. What served its time was carried and taught. What none of that reached was lost. Writing was taught to everyone and kept; the Byzantines' Greek fire, a weapon that burned on water, was guarded so closely that it died with the few who knew it. It kept and dropped not by plan but by use. The deliberate selection an architect performs is the small, conscious version of it. This descent does not select. It reads a selection already made.

History settles which capabilities survived. It does not settle which of those belong to a composition. In three specific ways.

The first is grain. History does not say whether to count writing as one capability or three. That choice is the author's, under one rule: cut where the survivors were named and taught, not at a convenient layer shared across the branches. A reader can check it.

A formal model might have fixed the grain from outside. TOGAF's capability mapping fixes one by authority. Reference models like APQC and BIAN do the same. All are built for an enterprise. None reaches back to a mark in clay.

The second is route. History does not say which thread runs down through the survivors. The descent follows the one that carries the subject's name and notes where the others branch off. This is not history read as aimed at the present. Survival already fixed which capabilities stand. The descent only chooses which thread to walk and where the others lead. A reader can check that too.

The third is hindsight. The survivors point nowhere forward. They cannot show what was once built on them and then lost, since only what was kept leaves a trace. The descent traces what was kept, not what was made and dropped.

Stepping down is then simple. Decompose a capability into the capabilities composing it. Most recur at every layer and distinguish none: power, materials, manufacturing. What distinguishes the layer is its own contribution, the new thing it adds; set that aside and the step below is what remains. Where more than one capability remains, the descent walks those that lead on toward the floor and notes those that lead elsewhere. One path down the composition, not the only one.

That last phrase is meant plainly. The same survivors could be cut at another grain and joined in another order; more than one composition can be drawn from them and more than one is sound. What the descent claims is not that its path is the only one but that the path is real: each step a capability history named and kept, each resting on the one below. Below means the nearest survivor, not that nothing lay between. To prefer a different decomposition is to choose a different grain and route, not to find an error here.

Ubiquitous Computation (1950s onward)

The descent starts where the reader stands. Computation is everywhere. It runs in the office and the factory, in the pocket and the car, in devices that do not look like computers at all. It is no longer a thing one goes to. It is a thing already there. This is Ubiquitous Computation, the steady presence of computation across every kind of human work.

Decompose it and the two words come apart (Figure 1). Computation is General-Purpose Computation, one machine that carries out any task by holding its instructions as data. Ubiquitous is Solid-State Switching, a switch made so small and so cheap that millions sit on a single chip. Put that many switches everywhere and computation is everywhere with them.

Solid-State Switching is the making of the switch, hardware rather than logic. Its dependencies run toward shaped matter, off the path the descent follows.

Both are capabilities, abilities held apart from the work that performs them. But the new capability here is not a new kind of computing. General-Purpose Computation already did everything Ubiquitous Computation does. What was added is reach, an old capability arriving everywhere at once. Reach is what cheap and abundant switching supplied.

The descent follows General-Purpose Computation, the capability reach was added to. Solid-State Switching, which supplied the reach, it sets aside, off to the right of the figure.

General-Purpose Computation (1945-1948)

General-Purpose Computation is the capability of one machine to carry out any task by holding its instructions as data. Its distinguishing contribution is not more machinery but an arrangement: the instructions live in the same memory as the numbers they work on, so the program is read and followed like any other data. The arrangement was set down in the 1945 report that bears von Neumann's name. To change what the machine does is then to change what is in memory and leave the wiring as it stands.

In June 1948 a small machine at Manchester ran the first program held as data. With the program in memory, one instrument takes on new work by reading a new program, so the work spreads faster than machines can be built.

That arrangement is a join. Set it aside and what it held together comes apart on the layer below (Figure 2): Machine Computation, a machine that computes, and Defined Computation, the idea that one machine, given a description of any task, can carry it out. General-Purpose Computation takes them as given and supplies only the join, which lifts a single limit, the need for a new machine to do a new task.

The descent follows Machine Computation first and returns to Defined Computation after.

Machine Computation (1941-1945)

Machine Computation is the capability to carry out computation by machine, in quantity and at a speed no hand could match. Its distinguishing contribution is not an idea about logic at all but the realization: a design in switches actually built, wired by the thousand and made to carry a real calculation through to its end.

The proof was what the period supplied, because until then the thing was in doubt. A machine that did arithmetic was old. A machine that carried a logical procedure of any length through to its end, reliably, without a person steering each step, had not been shown to be possible. Several were built within a few years of one another, in places that did not know of each other's work: Zuse's relay machine in Berlin by 1941, Flowers' Colossus at Bletchley by 1944, ENIAC's eighteen thousand tubes at Pennsylvania by 1945.

Set the building aside and what it rested on comes apart on the layer below (Figure 3): Buildable Logic and Reliable Components. Buildable Logic is the principle that such a machine can be built at all, that logic and switching are one thing in two forms.

Reliable Components are more hardware running the same way: the switch made dependable and in quantity, tubes that stay lit.

Reliable Components the descent sets aside; in the figure it falls under Solid-State Switching, the second capability to gather in the right-hand column. Buildable Logic, the principle the machine realized, lies one layer further down. But the descent picks up Defined Computation first.

Defined Computation (1936)

Defined Computation is not a machine but the idea of one, the idea that a single machine could be enough for every task. It is the capability to say exactly what computing is: what counts as a finite mechanical procedure, what one machine can do when handed a description of any other and what no procedure can reach at all.

Its distinguishing contribution is the model. In 1936 Turing described what a person does when following fixed rules with paper and pencil, then pared it to the barest steps: read a symbol, write a symbol, move, change state. A machine made to that model could take the description of any such procedure and carry it out as if it were that procedure. That is the universal machine, the idea of one machine for any task in exact form. The same year Church reached the same boundary by another road. The two accounts agreed.

The same work drew the limit. If one machine can carry out any procedure, questions about what procedures do can be handed to it. Some of them, Turing showed, no procedure can answer. The capability that says what computing is says in the same breath what it cannot do: not a step toward anything but the shape of the thing seen whole, at the moment it was first set down.

Set the model aside and what remains is not a pair but a single capability: reasoning already reduced to the following of fixed rules on symbols. That capability, Calculable Reasoning, is the layer below (Figure 4). Defined Computation is no join. It is a model laid over one capability, the wholly abstract step in the descent, with no second thread turning off toward shaped matter and so nothing to set aside. Where the figures above forked, this one runs straight down.

Defined Computation rests on Calculable Reasoning, the algebra of logic. The descent returns to Buildable Logic first, which rests on the same capability; the two threads meet there, at the layer below.

Buildable Logic (1937)

Buildable Logic is the capability to build logic out of switches, so that a logical operation becomes a circuit and a circuit carries out a logical operation. Its distinguishing contribution is a recognition: that two things from fields with no dealings with each other were one and the same.

In 1937, in a master's thesis, Claude Shannon showed that the algebra written ninety years earlier for logic described the make and break of switching circuits exactly. A network of switches could be read as a logical expression. A logical expression could be built as a network of switches. From there a designer could work logic in symbols and hand it over to be built in hardware.

That recognition is a join. Set it aside and the two things it found to be one come apart on the layer below (Figure 5), and because they differ in kind they lead toward different floors. One is Calculable Reasoning, logic already written as calculation, an algebra worked by rule. The other is Signal Control, a switch that a signal can throw, so that switches can be set to act on one another.

The descent follows Calculable Reasoning down toward the floor. Signal Control it sets down here, the third capability in the right-hand column and the last of the three set aside.

Signal Control's dependencies are short and end on different ground. It rests on devices that hold and pass an electric force, made of worked metal and glass; those rest on older crafts of shaping matter, the forge and the furnace, down toward metalworking and the controlled use of fire. The floor there is not a recorded mark but worked material. So computation stands on two floors, one of recorded reasoning and one of shaped matter. The three capabilities set aside above all belong to this second floor: Solid-State Switching, Reliable Components and Signal Control. Each was set aside where its thread turned toward that floor.

Calculable Reasoning (1847-1879)

Calculable Reasoning is the capability to write reasoning as calculation, so that an inference can be carried out by working symbols according to fixed rules, the way sums are worked. Its distinguishing contribution is the writing: in symbols it sets down not quantity but argument, its joinings, denials and alternatives.

In 1847 George Boole set down an algebra in which conjunction, disjunction and negation became operations a person could calculate with, so that an argument's validity could be checked by the manipulation of signs rather than by a judgment of meaning. Others widened the system over the following decades, Frege among them giving it a fuller reach by 1879. Reasoning, long held to be the work of a trained mind, was shown to run partly on rules a clerk could follow.

Set the writing aside and what remains is the older capability it works on: reasoning already understood to have a form, a shape that holds apart from whatever it is about. That capability, Formal Reasoning, is the layer below (Figure 6).

The general-purpose machine, high in this composition, was built once before, here in the same century. Charles Babbage designed the Analytical Engine, a single machine to carry out any calculation, its operations directed by instructions on punched cards. Ada Lovelace, in notes of 1843, worked out how it would be directed and saw that it could act on more than numbers. That is General-Purpose Computation, reached a century before the one this descent traces. What differs is everything beneath it. The engine was composed of gears and precision metalwork resting straight on the shaping of matter, without the algebra or the switch the later composition was built from. The same upper capability. A wholly different composition below. It was never finished. To trace that other composition would be a descent of its own.

The form that Calculable Reasoning works on is far older than Boole. It had only to outlast the centuries between. What that form is comes next. How it lasted comes after.

Formal Reasoning (4th century BC)

Formal Reasoning is the capability to treat an argument as having a form apart from what it is about, so that its soundness turns on its shape and not its subject. Its distinguishing contribution is that abstraction: form lifted clear of content, so a piece of reasoning has a shape that can be set down and judged on its own.

It is Aristotle's, the fourth century BC. In his hands it was worked daily, taught and argued, as fully exercised as it would be in the two thousand years that followed. By any measure of the thing itself it was complete.

Set that abstraction aside and what remains is a way to hold a piece of reasoning still outside the mind, set down where its shape can be examined. That is the Durable Record, the floor. Formal Reasoning rests straight on it, a single step down (Figure 7).

But a puzzle sits between this layer and the one above. Calculable Reasoning, which rested on Formal Reasoning, is Boole's, in 1847. More than two thousand years separate the two. Logic did not stand still in that time. The Stoics carried it on. The medievals took it further along lines of their own that branch off the thread this descent follows. None of that secured it.

Completeness is not survival. A capability finished in the fourth century BC was not thereby safe across the centuries. It could not carry itself across them. A thing can be in full motion and be lost all the same, if nothing keeps it.

Under this sits an old distinction. Enterprise Architecture holds an ability apart from the work that performs it; Aristotle had drawn a kindred distinction long before as dunamis and energeia, the power held apart from the power in action. Formal Reasoning, worked and taught daily, was energeia: fully in action, not a dormant potential.

Until this layer the keeping mostly looked after itself. Each capability in this descent is held alive by the one built upon it: read downward, a layer is made of the one below; read upward, the lower layer is kept in use by the higher. As long as the building goes on, nothing beneath it is let go. The building pauses. Ninety years separate Boole from Shannon, more in places. In each pause the layer below waited, held not by the composition but by use, worked in its own right until the next layer came. Use can hold a capability. But it is local and it lapses. The short gaps were short enough that it never had to hold for long.

Formal Reasoning is where that ran out. For two thousand years nothing was raised on it. Across a span that long use could not be counted on. The layer was whole and the floor lay a single step below it. It could have been lost all the same. What was missing was not an element but the keeping itself. What supplied it was carriage: being copied and being wanted, from one place to the next.

Carriage is not something the capability rests on. The figure draws it apart from the descent for that reason. It is what kept Formal Reasoning alive across the gap, a branch of two capabilities running down beside the descent to the same floor.

The descent follows this branch down, Reproduction Without Loss first and Portable Knowledge below it.

Reproduction Without Loss (1450)

Reproduction Without Loss is the capability to copy a record exactly and in quantity, so that what is written no longer depends on any single copy surviving. Its distinguishing contribution is exactness and quantity. Copying was old. Copying without drift and in numbers was not.

Movable type supplied it in Europe around 1450, though it was not the only thing that could have supplied it and not the first place it appeared. What the press changed was the arithmetic of survival. A hand-copied text lived or died with its few copies, each a little different from the last, each loss permanent. A printed text existed in hundreds of identical copies at once. A work held in hundreds of identical copies is hard to lose. Knowledge stopped thinning as it traveled.

Set exactness and quantity aside and what remains is the older capability of carrying knowledge by copying it at all, one hand at a time. That is Portable Knowledge, the layer below (Figure 8).

The press added nothing to what an argument was. It added to how surely the argument would still be there to be read. Portable Knowledge is the older and frailer carriage it improved on. The descent follows it down.

Portable Knowledge (750-1200)

Portable Knowledge is the capability to keep knowledge alive by carrying and copying it, so that it survives beyond the place and the lifetime where it was set down. Its distinguishing contribution is movement. A record fixed in one place and never copied lasts only as long as its one object. A record copied and carried outlives any single copy and travels to where it is wanted.

The capability did its heaviest work in the centuries when Formal Reasoning might otherwise have been lost. Greek texts were copied in Byzantium, translated and studied across the Islamic world, then carried into Latin Europe and copied again. Aristotle's logic came down by this route, hand to hand and tongue to tongue, kept current by being wanted in each place it passed.

The popular image puts this carriage in the monastery, the monk at his desk copying by candlelight. That image is true to a part of it. Latin monasteries kept the old logic, Aristotle's Categories and On Interpretation in Boethius's translations from around 500, copied and recopied through the early medieval centuries. But the fuller logic came by another route. Greek into Arabic in the translation movement of the Abbasid centuries, then Arabic into Latin in twelfth-century Toledo and elsewhere. The monk carried one part. The translator carried the rest.

None of that copying was done to reach 1847. It was done because the knowledge was useful where it stood.

Set the moving aside and what remains is the bare mark, durable but stationary. That is the Durable Record, the floor (Figure 9).

Portable Knowledge made copies at all and made them move, where Reproduction Without Loss made them exact and many. It rests on one thing only, a mark durable enough to be copied from. Below it lies the floor this composition stands on. One step remains.

Durable Record (3400-3000 BC)

The Durable Record is the capability to set knowledge down in a mark that outlasts the moment, so that it holds outside any single mind. Its distinguishing contribution is endurance, a mark that stays when the hand that made it is gone and can be read by another mind in another place.

The first durable records were pressed into clay in Mesopotamia, around 3400 BC. They were not philosophy. They were counts: measures of grain, heads of cattle, who owed what to whom. Writing began as accounting, a way to hold a number still when memory and trust would not stretch far enough. The mark that outlasts the mind started as a tally.

Figure 10 shows nothing below it. Something does lie beneath, though nothing of its kind. A mark that stands for a count rests on capabilities older than any record: symbolic representation, to let one thing stand for another; numeracy and categorization, to have a count and a kind worth marking; the shared language and habit of abstraction that let a sign be read the same by another hand.

These are real and prior. But they are carried in minds and in shared practice, not in any durable thing. A method that follows kept records cannot trace them by the same light. So the descent floors here, not at the bottom of everything but at the bottom of what a kept mark can show.

The descent kept Durable Record, Portable Knowledge and Reproduction Without Loss apart. One capability of keeping a record would have joined them and drawn a shorter path to the same floor. But each of the three was a craft taught in its own right: the scribe's mark, the copyist's carriage, the printer's press. The grain cuts where the survivors stand. The descent chose three, not the only grain it could have cut.

The composition traced here comes to rest on a count pressed in clay. Computation, calculation by rule, stands at the top of it. Far below, at the floor of what a kept mark can show, the oldest mark it rests on is itself a number set down to be kept. The descent set out from the thing everything now runs on and ends at the first enduring mark, a stylus pressed into soft clay.

Organizing this is harder than naming it. The work is collective and slow. The field gets organized by many people writing carefully about what they can see clearly. This article is one small contribution to that work.

Sources cited

• The formal capability models named in the selection section are TOGAF, with the reference frameworks of APQC and BIAN.
• The stored program rests on von Neumann's 1945 report on the EDVAC, the Manchester machine of 1948 and Turing's parallel design, with Babbage's unbuilt engine and Lovelace's 1843 notes beside them.
• The wartime machines are those of Zuse, of Flowers at Bletchley Park and of Eckert and Mauchly at Pennsylvania.
• Defined Computation rests on Turing's 1936 paper and its universal machine and on Church reaching the same boundary by another route.
• Buildable Logic is credited to Shannon's 1937 thesis.
• The engineering capabilities set aside here, the switch and its making, run through the valve and the transistor down to the older crafts of metal and glass.
• Calculable Reasoning runs through Boole and Frege.
• Formal Reasoning is Aristotle's. The pairing of a power held apart from the same power in action is his dunamis and energeia, a kindred distinction to Enterprise Architecture's holding of an ability apart from the work that performs it.
• The survival of that reasoning across the centuries rests on histories of the Abbasid translation movement and on al-Khwarizmi, whose name gives the word algorithm and whose al-jabr gives algebra.
• Reproduction Without Loss draws on Elizabeth Eisenstein for the tie between identical copies and a critical culture. It rests too on the earlier movable type of Bi Sheng in China and the metal type of Korea, where the Jikji was printed in 1377, so the press was neither the first nor the only thing that could have supplied the capability.
• The account of writing growing out of clay tokens used for accounting follows Denise Schmandt-Besserat, the leading reconstruction rather than a closed one.

Where a date is given it marks when an idea first appears in the record, not the whole of its making.