The Age of Imagination

This is not only the Age of Information, this is also the Age of Imagination. Information, at any point in time, is bounded, while imagination is always unbounded. We are overwhelmed more by the potential for new ideas than by the admittedly vast existing knowledge. We are drunk with the excitement of the unknown. Drunks are sometimes not a pretty sight; Isaiah (28:8) is very graphic.

It is true that topical specialization occurs, in part, due to what we proudly call the explosion of knowledge. There is so much to know that one must ignore huge tracts of knowledge. But that is only half the story. The other half is that we have begun to discover the unknown, and its lure is irresistible. Like the scientific and global explorers of the early modern period - The Discoverers as Boorstin calls them - we are intoxicated by the potential "out there", beyond the horizon, beyond the known. That intoxication can distort our vision and judgment.

Consider Reuven's comment, from long experience, that "Engineers use formulas and various equations without being aware of the theories behind them." A pithier version was said to me by an acquisitions editor at Oxford University Press: "Engineers don't read books." She should know.

Engineers are imaginative and curious. They are seekers, and they find wonderful things. But they are too engrossed in inventing and building The New, to be much engaged with The Old. "Scholarship", wrote Thorstein Veblen is "an intimate and systematic familiarity with past cultural achievements." Engineers - even research engineers and professors of engineering - spend very little time with past masters. How many computer scientists scour the works of Charles Babbage? How often do thermal engineers study the writings of Lord Kelvin? A distinguished professor of engineering, himself a member of the US National Academy of Engineering, once told me that there is little use for journal articles more than a few years old.

Fragmentation of knowledge results from the endless potential for new knowledge. Seekers - engineers and the scientists of nature, society and humanity - move inexorably apart from one another. But nonetheless it's all connected; consilient. Technology alters how we live. Science alters what we think. How can we keep track of it all? How can we have some at least vague and preliminary sense of where we are heading and whether we value the prospect?

The first prescription is to be aware of the problem, and I greatly fear that many movers and shakers of the modern age are unaware. The second prescription is to identify who should take the lead in nurturing this awareness. That's easy: teachers, scholars, novelists, intellectuals of all sorts.

Isaiah struggled with this long ago. "Priest and prophet erred with liquor, were swallowed by wine."(Isaiah, 28:7) We are drunk with the excitement of the unknown. Who can show the way?

Mind or Stomach? Imagination or Necessity?

"An army marches on its stomach" said Napoleon, who is also credited with saying "Imagination rules the world". Is history driven by raw necessity and elementary needs? Or is history hewn by people from their imagination, dreams and ideas?

The answer is simple: 'Both'. The challenge is to untangle imagination from necessity. Consider these examples:

An ancient Jewish saying is "Without flour, there is no Torah. Without Torah there is no flour." (Avot 3:17) Scholars don't eat much, but they do need to eat. And if you feed them, they produce wonders.

Give a typewriter to a monkey and he might eventually tap out Shakespeare's sonnets, but it's not very likely. Give that monkey an inventive mind and he will produce poetry, a vaccine against polio, and the atom bomb. Why the bomb? He needed it.

Necessity is the mother of invention, they say, but it's actually a two-way street. For instance, human inventiveness includes dreams of cosmic domination, leading to war. Hence the need for that bomb. Satisfying a need, like the need for flour, induces inventiveness. And this inventiveness, like the discovery of genetically modified organisms, creates new needs. Necessity induces inventiveness, and inventiveness creates new dangers, challenges and needs. This cycle is endless because the realm of imagination is boundless, far greater than prosaic reality, as we discussed elsewhere.

Imagination and necessity are intertwined, but still are quite different. Necessity focusses primarily on what we know, while imagination focusses on the unknown.

We know from experience that we need food, shelter, warmth, love, and so on. These requirements force themselves on our awareness. Even the need for protection against surprise is known, though the surprise is not.

Imagination operates in the realm of the unknown. We seek the new, the interesting, or the frightful. Imagination feeds our fears of the unknown and nurtures our hopes for the unimaginable. We explore the bounds of the possible and try breaking through to the impossible.

Mind or stomach? Imagination or necessity? Every 'known' has an 'unknown' lurking behind it, and every 'unknown' may some day be discovered or dreamed into existence. Every mind has a stomach, and a stomach with no mind is not human.

Jabberwocky. Or: Grand Unified Theory of Uncertainty???

Jabberwocky, Lewis Carroll's whimsical nonsense poem, uses made-up words to create an atmosphere and to tell a story. "Billig", "frumious", "vorpal" and "uffish" have no lexical meaning, but they could have. The poem demonstrates that the realm of imagination exceeds the bounds of reality just as the set of possible words and meanings exceeds its real lexical counterpart.

Uncertainty thrives in the realm of imagination, incongruity, and contradiction. Uncertainty falls in the realm of science fiction as much as in the realm of science. People have struggled with uncertainty for ages and many theories of uncertainty have appeared over time. How many uncertainty theories do we need? Lots, and forever. Would we say that of physics? No, at least not forever.

Can you think inconsistent, incoherent, or erroneous thoughts? I can. (I do it quite often, usually without noticing.) For those unaccustomed to thinking incongruous thoughts, and who need a bit of help to get started, I can recommend thinking of "two meanings packed into one word like a portmanteau," like 'fuming' and 'furious' to get 'frumious' or 'snake' and 'shark' to get 'snark'.

Portmanteau words are a start. Our task now is portmanteau thoughts. Take for instance the idea of a 'thingk':

When I think a thing I've thought,
I have often felt I ought
To call this thing I think a "Thingk",
Which ought to save a lot of ink.

The participle is written "thingking",
(Which is where we save on inking,)
Because "thingking" says in just one word:
"Thinking of a thought thing." Absurd!

All this shows high-power abstraction.
(That highly touted human contraption.)
Using symbols with subtle feint,
To stand for something which they ain't.

Now that wasn't difficult: two thoughts at once. Now let those thoughts be contradictory. To use a prosaic example: thinking the unthinkable, which I suppose is 'unthingkable'. There! You did it. You are on your way to a rich and full life of thinking incongruities, fallacies and contradictions. We can hold in our minds thoughts of 4-sided triangles, parallel lines that intersect, and endless other seeming impossibilities from super-girls like Pippi Longstockings to life on Mars (some of which may actually be true, or at least possible).

Scientists, logicians, and saints are in the business of dispelling all such incongruities, errors and contradictions. Banishing inconsistency is possible in science because (or if) there is only one coherent world. Belief in one coherent world and one grand unified theory is the modern secular version of the ancient monotheistic intuition of one universal God (in which saints tend to believe). Uncertainty thrives in the realm in which scientists and saints have not yet completed their tasks (perhaps because they are incompletable). For instance, we must entertain a wide range of conflicting conceptions when we do not yet know how (or whether) quantum mechanics can be reconciled with general relativity, or Pippi's strength reconciled with the limitations of physiology. As Henry Adams wrote:

"Images are not arguments, rarely even lead to proof, but the mind craves them, and, of late more than ever, the keenest experimenters find twenty images better than one, especially if contradictory; since the human mind has already learned to deal in contradictions."

The very idea of a rigorously logical theory of uncertainty is startling and implausible because the realm of the uncertain is inherently incoherent and contradictory. Indeed, the first uncertainty theory - probability - emerged many centuries after the invention of the axiomatic method in mathematics. Today we have many theories of uncertainty: probability, imprecise probability, information theory, generalized information theory, fuzzy logic, Dempster-Shafer theory, info-gap theory, and more (the list is a bit uncertain). Why such a long and diverse list? It seems that in constructing a logically consistent theory of the logically inconsistent domain of uncertainty, one cannot capture the whole beast all at once (though I'm uncertain about this).

A theory, in order to be scientific, must exclude something. A scientific theory makes statements such as "This happens; that doesn't happen." Karl Popper explained that a scientific theory must contain statements that are at risk of being wrong, statements that could be falsified. Deborah Mayo demonstrated how science grows by discovering and recovering from error.

The realm of uncertainty contains contradictions (ostensible or real) such as the pair of statements: "Nine year old girls can lift horses" and "Muscle fiber generates tension through the action of actin and myosin cross-bridge cycling". A logically consistent theory of uncertainty can handle improbabilities, as can scientific theories like quantum mechanics. But a logical theory cannot encompass outright contradictions. Science investigates a domain: the natural and physical worlds. Those worlds, by virtue of their existence, are perhaps coherent in a way that can be reflected in a unified logical theory. Theories of uncertainty are directed at a larger domain: the natural and physical worlds and all imaginable (and unimaginable) other worlds. That larger domain is definitely not coherent, and a unified logical theory would seem to be unattainable. Hence many theories of uncertainty are needed.

Scientific theories are good to have, and we do well to encourage the scientists. But it is a mistake to think that the scientific paradigm is suitable to all domains, in particular, to the study of uncertainty. Logic is a powerful tool and the axiomatic method assures the logical consistency of a theory. For instance, Leonard Savage argued that personal probability is a "code of consistency" for choosing one's behavior. Jim March compares the rigorous logic of mathematical theories of decision to strict religious morality. Consistency between values and actions is commendable says March, but he notes that one sometimes needs to deviate from perfect morality. While "[s]tandard notions of intelligent choice are theories of strict morality ... saints are a luxury to be encouraged only in small numbers." Logical consistency is a merit of any single theory, including a theory of uncertainty. However, insisting that the same logical consistency apply over the entire domain of uncertainty is like asking reality and saintliness to make peace.

Picking a Theory is Like Building a Boat at Sea

"We are like sailors who on the open sea must reconstruct their ship

 but are never able to start afresh from the bottom." 

Otto Neurath's analogy in the words of Willard V. Quine

Engineers, economists, social planners, security strategists, and others base their plans and decisions on theories. They often argue long and hard over which theory to use. Is it ever right to use a theory that we know is empirically wrong, especially if a true (or truer) theory is available? Why is it so difficult to pick a theory?

Let's consider two introductory examples.

You are an engineer designing a robot. You must calculate the forces needed to achieve specified motions of the robotic arms. You can base these calculations on either of two theories. One theory assumes that an object comes to rest unless a force acts upon it. Let's call this axiom A. The other theory assumes that an object moves at constant speed unless a force acts upon it. Let's call this axiom G. Axiom A agrees with observation: Nothing moves continuously without the exertion of force; an object will come to rest unless you keep pushing it. Axiom G contradicts all observation; no experiment illustrates the perpetual motion postulated by the axiom. If all else is the same, which theory should you choose?

Axiom A is Aristotle's law of inertia, which contributed little to the development of mechanical dynamics. Axiom G is Galileo's law of inertia: one of the most fruitful scientific ideas of all time. Why is an undemonstrable assertion - axiom G - a good starting point for a theory?

Consider another example.

You are an economist designing a market-based policy to induce firms to reduce pollution. You will use an economic theory to choose between policies. One theory assumes that firms face pure competition, meaning that no single firm can influence market prices. Another theory provides agent-based game-theoretic characterization of how firms interact (without colluding) by observing and responding to price behavior of other firms and of consumers.

Pure competition is a stylized idealization (like axiom G). Game theory is much more realistic (like axiom A), but may obscure essential patterns in its massive detail. Which theory should you use?

We will not address the question of how to choose a theory upon which to base a decision. We will focus on the question: why is theory selection so difficult? We will discuss four trade offs.

"Thanks to the negation sign, there are as many truths as falsehoods;

we just can't always be sure which are which." Willard V. Quine

The tension between right and right. The number of possible theories is infinite, and sometimes it's hard to separate the wheat from the chaff, as suggested by the quote from Quine. As an example, I have a book called A Modern Guide to Macroeconomics: An Introduction to Competing Schools of Thought by Snowdon, Vane and Wynarczyk. It's a wonderful overview of about a dozen theories developed by leading economic scholars, many of them Nobel Prize Laureates. The theories are all fundamentally different. They use different axioms and concepts and they compete for adoption by economists. These theories have been studied and tested upside down and backwards. However, economic processes are very complex and variable, and the various theories succeed in different ways or in different situations, so the jury is still out. The choice of a theory is no simple matter because many different theories can all seem right in one way or another.

"The fox knows many things, but the hedgehog knows one big thing." Archilochus

The fox-hedgehog tension. This aphorism by Archilochus metaphorically describes two types of theories (and two types of people). Fox-like theories are comprehensive and include all relevant aspects of the problem. Hedgehog-like theories, in contrast, skip the details and focus on essentials. Axiom A is fox-like because the complications of friction are acknowledged from the start. Axiom G is hedgehog-like because inertial resistance to change is acknowledged but the complications of friction are left for later. It is difficult to choose between these types of theories because it is difficult to balance comprehensiveness against essentialism. On the one hand, all relevant aspects of the problem should be considered. On the other hand, don't get bogged down in endless details. This fox-hedgehog tension can be managed by weighing the context, goals and implications of the decision. We won't expand on this idea since we're not considering how to choose a theory; we're only examining why it's a difficult choice. However, the idea of resolving this tension by goal-directed choice motivates the third tension.

"Beyond this island of meanings which in their own nature are true or false

lies the ocean of meanings to which truth and falsity are irrelevant." John Dewey

The truth-meaning tension. Theories are collections of statements like axioms A and G in our first example. Statements carry meaning, and statements can be either true or false. Truth and meaning are different. For instance, "Archilochus was a Japanese belly dancer" has meaning, but is not true. The quote from Dewey expresses the idea that "meaning" is a broader description of statements than "truth". All true statements mean something, but not all meaningful statements are true. That does not imply, however, that all untrue meaningful statements are false, as we will see.

We know the meanings of words and sentences from experience with language and life. A child learns the meanings of words - chair, mom, love, good, bad - by experience. Meanings are learned by pointing - this is a chair - and also by experiencing what it means to love or to be good or bad.

Truth is a different concept. John Dewey wrote that

"truths are but one class of meanings, namely, those in which a claim to verifiability by their consequences is an intrinsic part of their meaning. Beyond this island of meanings which in their own nature are true or false lies the ocean of meanings to which truth and falsity are irrelevant. We do not inquire whether Greek civilization was true or false, but we are immensely concerned to penetrate its meaning."

A true statement, in Dewey's sense, is one that can be confirmed by experience. Many statements are meaningful, even important and useful, but neither true nor false in this experimental sense. Axiom G is an example.

Our quest is to understand why the selection of a theory is difficult. Part of the challenge derives from the tension between meaning and truth. We select a theory for use in formulating and evaluating a plan or decision. The decision has implications: what would it mean to do this rather than that? Hence it is important that the meaning of the theory fit the context of the decision. Indeed, hedgehogs would say that getting the meaning and implication right is the essence of good decision making.

But what if a relevantly meaningful theory is unprovable or even false? Should we use a theory that is meaningful but not verifiable by experience? Should we use a meaningful theory that is even wrong? This quandary is related to the fox-hedgehog tension because the fox's theory is so full of true statements that its meaning may be obscured, while the hedgehog's bare-bones theory has clear relevance to the decision to be made, but may be either false or too idealized to be tested.

Galileo's axiom of inertia is an idealization that is unsupported by experience because friction can never be avoided. Axiom G assumes conditions that cannot be realized so the axiom can never be tested. Likewise, pure competition is an idealization that is rarely if ever encountered in practice. But these theories capture the essence of many situations. In practical terms, what it means to get the robotic arm from here to there is to apply net forces that overcome Galilean inertia. But actually designing a robot requires considering details of dissipative forces like friction. What it means to be a small business is that the market price of your product is beyond your control. But actually running a business requires following and reacting to prices in the store next door.

It is difficult to choose between a relevantly meaningful but unverifiable theory, and a true theory that is perhaps not quite what we mean.

The knowledge-ignorance tension. Recall that we are discussing theories in the service of decision-making by engineers, social scientists and others. A theory should facilitate the use of our knowledge and understanding. However, in some situations our ignorance is vast and our knowledge will grow. Hence a theory should also account for ignorance and be able to accommodate new knowledge.

Let's take an example from theories of decision. The independence axiom is fundamental in various decision theories, for instance in von Neumann-Morgenstern expected utility theory. It says that one's choices should be independent of irrelevant alternatives. Suppose you are offered the dinner choice between chicken and fish, and you choose chicken. The server returns a few minutes later saying that beef is also available. If you switch your choice from chicken to fish you are violating the independence axiom. You prefer beef less than both chicken and fish, so the beef option shouldn't alter the fish-chicken preference.

But let's suppose that when the server returned and mentioned beef, your physician advised you to reduce your cholesterol intake (so your preference for beef is lowest) which prompted your wife to say that you should eat fish at least twice a week because of vitamins in the oil. So you switch from chicken to fish. Beef is not chosen, but new information that resulted from introducing the irrelevant alternative has altered the chicken-fish preference.

One could argue for the independence axiom by saying that it applies only when all relevant information (like considerations of cholesterol and fish oil) are taken into account. On the other hand, one can argue against the independence axiom by saying that new relevant information quite often surfaces unexpectedly. The difficulty is to judge the extent to which ignorance and the emergence of new knowledge should be central in a decision theory.

Wrapping up. Theories express our knowledge and understanding about the unknown and confusing world. Knowledge begets knowledge. We use knowledge and understanding - that is, theory - in choosing a theory. The process is difficult because it's like building a boat on the open sea as Otto Neurath once said. 

Fog of War

"War is the realm of uncertainty;

three quarters of the factors on which action in war is based 

are wrapped in a fog of greater or lesser uncertainty."

Carl von Clausewitz, On War

What makes a great general?

Hannibal changed Carthaginian strategy from naval to land warfare, and beat the Romans in nearly every encounter. Julius Caesar commanded the undying loyalty of his officers and soldiers. Napoleon Bonaparte invented the modern concept of total war with a citizen army. Was their genius in strategy, or tactics, or logistics, or charisma? Or was it crude luck? Or was it the exploitation of uncertainty?

War is profoundly influenced by technology, social organization, human psychology and political goals. Success in war requires understanding and control of these factors. War consumes vast human and material resources and demands "genius, improvisation, and energy of mind" as Winston Churchill said. And yet, Clausewitz writes: "No other human activity is so continuously or universally bound up with chance."

Why? What does this imply about the successful military commander? What does it mean for human endeavor and history in general?

Clausewitz uses the terms "chance" and "uncertainty", sometimes interchangeably, to refer to two different concepts. An event occurs by chance if it is unexpected, or its origin is unknown, or its impact is surprising. Adverse chance events provoke "uncertainty, the psychological state of discomfort from confusion or lack of information" (Katherine Herbig, reference below).

Chance and uncertainty are dangerous because they subvert plans and diminish capabilities. Soldiers have been aware of both the dangers and the advantages of surprise since they first battered each other with sticks. Conventional military theorists aimed to avoid or ameliorate chance events by careful planning, military intelligence, training and discipline, communication, command and control. Clausewitz also recognized that steadfast faithfulness to mission and determination against adversity are essential in overcoming chance events and the debilitating effect of uncertainty. But "Clausewitz dismisses as worse than useless efforts to systematize warfare with rules and formulas. Such systems are falsely comforting, he says, because they reduce the imponderables of war to a few meagre certainties about minor matters" (Herbig). Clausewitz' most original contribution was in building a systematic theory of war in which the unavoidability of chance, and its opportunities, are central.

Why is uncertainty (in the sense of lack of knowledge) unavoidable and fundamental in war? Clausewitz' answer is expressed in his metaphor of friction. As Herbig explains:

"Friction is the decremental loss of effort and intention caused by human fallibility, compounded by danger and exhaustion. Like the mechanical phenomenon of friction that reduces the efficiency of machinery with moving parts, Clausewitz' friction reduces the efficiency of the war machine. It sums up all the little things that always go wrong to keep things from being done as easily and quickly as intended. ...

"What makes friction more than a minor annoyance in war is its confounding with chance, which multiplies friction in random, unpredictable ways."

War, like history, runs on the cumulative effect of myriad micro-events. Small failures are compounded because war is a coordinated effort of countless local but inter-dependent occurrences. Generals, like symphony conductors, choose the score and set the pace, but the orchestra plays the notes. A mis-tuned violin, or a drummer who mis-counts his entry, can ruin the show. Moses led the children of Israel out of Egypt, but he'd have looked pretty funny if they had scattered to the four winds. Moses' genius as a leader wasn't plied against Pharaoh (Moses had help there), but rather against endless bickering and revolt once they reached the desert.

Uncertainty originates at the tactical rather than the strategic level. The general can't know countless local occurrences: a lost supply plane, failed equipment here, over-reaction there, or complacency someplace else. As an example, the New York Times reported on 27 November 2011:

"The NATO air attack that killed at least two dozen Pakistani soldiers over the weekend reflected a fundamental truth about American-Pakistani relations when it comes to securing the unruly border with Afghanistan: the tactics of war can easily undercut the broader strategy that leaders of both countries say they share.

"The murky details complicated matters even more, with Pakistani officials saying the attack on two Pakistani border posts was unprovoked and Afghan officials asserting that Afghan and American commandos called in airstrikes after coming under fire from Pakistani territory."

Central control is critical, but also profoundly limited by the micro-event texture of history.

Conversely, uncertainty can be exploited at the tactical level by flexible and creative response to random opportunities. The field commander has local knowledge that enables decisive initiative: the sleeping sentinel, the bridge not destroyed, the deserted town. The general's brilliance is in forging a war machine whose components both exploit uncertainty and are resilient to surprise.

Uncertainty is central in history at large, like in war, because they both emerge from the churning of individual events. In democratic societies, legislatures pass laws and executive branches formulate and implement policies. But only active participation of the citizenry brings life and reality to laws and policies. Conversely, citizen resistance or even apathy dooms the best policies to failure. This explains the failure of democratic institutions that are imported precipitously to countries with incompatible social and political traditions. Governments formulate policy, but implementation occurs in the context of social attitudes and historical memory. You can elect legislatures and presidents but you can't elect the public. Non-centralized beliefs and actions also dominate the behavior of industrial economies. The actions of countless households, firms and investors can vitiate the best laid plans of monetary and fiscal authorities. All this adds up to Clausewitz' concept of friction: global uncertainty accumulating from countless local deviations.

In peace, like in war, the successful response to uncertainty is to face it, grapple with it, exploit it, restrain it, but never hope to abolish it. Uncertainty is inevitable, and sometimes even propitious. The propensity for war is the ugliest attribute of our species. Nonetheless, what we learn about uncertainty from the study of war applies to all our endeavors: in business, in politics and beyond. Waging peace demands the same staunchness, determination and inventive flexibility in the face of the unknown, as the successful pursuit of war.

Main source:

Katherine L. Herbig, 1989, Chance and Uncertainty in On War, in Michael Handel, ed., Clausewitz and Modern Strategy, Frank Cass, London, pp.95-116.

See also:

Peter Paret, 1976, Clausewitz and the State: The Man, His Theories, and His Times, re-issued 2007, Princeton University Press. 

Can We Replay History?

After the kids' party games and the birthday cake came the action-packed Steve McQueen movie. My friend's parents had rented a movie projector. They hooked up the reel and let it roll. But the high point came later when they ran the movie backwards. Bullets streamed back into guns, blows were retracted and fallen protagonists recoiled into action. The mechanism that pulls the celluloid film forward for normal showing, can pull the film in the reverse direction, rolling it back onto the feeder reel and showing the movie in reverse.

If you chuck a round pebble off a cliff it will fall in a graceful parabolic arch, gradually increasing its speed until it hits the ground. The same pebble, if shot from the point of impact, at the terminating angle and speed, will gracefully and obligingly retrace its path. (I'm ignoring wind and air friction that make things a bit more complicated.)

Deterministic mechanisms, like the movie reel mechanism or the law of gravity, are reversible.

History is different. Peoples' behavior is influenced by what they know. You pack an umbrella on a trip to the UK. Google develops search algorithms not search parties because their knowledge base is information technology not mountain trekking. Knowledge is powerful because it enables rational behavior: matching actions to goals. Knowledge transforms futile fumbling into intelligent behavior.

Knowledge underlies intelligent behavior, but knowledge is continually expanding. We discover new facts and relationships. We discover that things have changed. Therefore tomorrow's knowledge-based behavior will, to some extent, be unpredictable today because tomorrow's discoveries cannot be known today. Human behavior has an inherent element of indeterminism. Intelligent learning behavior cannot be completely predicted.

Personal and collective history does not unfold like a pre-woven rug. Human history is fundamentally different from the trajectory of a pebble tossed from a cliff. History is the process of uncovering the unknown and responding to this new knowledge. The existence of the unknown creates the possibility of free will. The discovery of new knowledge introduces indeterminism and irreversibility into history, as explained by the philosophers G.L.S. Shackle and Karl Popper.

Nonetheless history is not erratic because each increment of new knowledge adds to the store of what was learned before. Memory is not perfect, either of individuals or groups, but it is powerful. History happens in historical context. For instance, one cannot understand the recent revolutions and upheavals in the Arab world from the perspective of 18th century European revolutions; the historical backgrounds are too different, and the outcomes in the Middle East will be different as well. Innovation, even revolution, is spurred by new knowledge laid over the old. A female municipal official slapped a Tunisian street vendor, Mohamed Bouazizi. That slap crystalized Mr Bouazizi's knowledge of his helpless social impotence and lit the match with which he immolated himself and initiated conflagrations around the Mideast. New knowledge acts like thruster engines on the inertial body of memory. What is emerging in the Mideast is Middle Eastern, not European. What is emerging is the result of new knowledge: of the power of networking, of the mortality of dictators, of the limits of coercion, of the power of new knowledge itself and the possibilities embedded in tomorrow's unknowns.

Mistakes are made, even with the best intentions and the best possible knowledge. Even if analysts knew and understood all the actions of all actors on the stage of history, they still cannot know what those people will learn tomorrow and how that new knowledge will alter their behavior. Mistakes are made because history does not unwind like a celluloid reel.

That's not to say that analysts are never ignorant, negligent, stupid or malicious. It's to say that all actions are, in a sense, mistakes. Or, the biggest mistake of all is to think that we can know the full import of our actions. We cannot, because actions are tossed, like pebbles, into the dark pit of unknown possible futures. One cannot know all possible echoes, or whether some echo might be glass-shatteringly cataclysmic.

Mistakes can sometimes be corrected, but never undone. History cannot be run backwards, and you never get a second chance. Conversely, every instant is a new opportunity because the future is always uncertain. Uncertainty is the freedom to err, and the opportunity to create and discover. 

The Language of Science and the Tower of Babel

And God said: Behold one people with one language for them all ... and now nothing that they venture will be kept from them. ... [And] there God mixed up the language of all the land. (Genesis, 11:6-9)

"Philosophy is written in this grand book the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and to read the alphabet in which it is composed. It is written in the language of mathematics." Galileo Galilei

Language is power over the unknown. 

Mathematics is the language of science, and computation is the modern voice in which this language is spoken. Scientists and engineers explore the book of nature with computer simulations of swirling galaxies and colliding atoms, crashing cars and wind-swept buildings. The wonders of nature and the powers of technological innovation are displayed on computer screens, "continually open to our gaze." The language of science empowers us to dispel confusion and uncertainty, but only with great effort do we change the babble of sounds and symbols into useful, meaningful and reliable communication. How we do that depends on the type of uncertainty against which the language struggles.

Mathematical equations encode our understanding of nature, and Galileo exhorts us to learn this code. One challenge here is that a single equation represents an infinity of situations. For instance, the equation describing a flowing liquid captures water gushing from a pipe, blood coursing in our veins, and a droplet splashing from a puddle. Gazing at the equation is not at all like gazing at the droplet. Understanding grows by exposure to pictures and examples. Computations provide numerical examples of equations that can be realized as pictures. Computations can simulate nature, allowing us to explore at our leisure.

Two questions face the user of computations: Are we calculating the correct equations? Are we calculating the equations correctly? The first question expresses the scientist's ignorance - or at least uncertainty - about how the world works. The second question reflects the programmer's ignorance or uncertainty about the faithfulness of the computer program to the equations. Both questions deal with the fidelity between two entities. However, the entities involved are very different and the uncertainties are very different as well.

The scientist's uncertainty is reduced by the ingenuity of the experimenter. Equations make predictions that can be tested by experiment. For instance, Galileo predicted that small and large balls will fall at the same rate, as he is reported to have tested from the tower of Pisa. Equations are rejected or modified when their predictions don't match the experimenter's observation. The scientist's uncertainty and ignorance are whittled away by testing equations against observation of the real world. Experiments may be extraordinarily subtle or difficult or costly because nature's unknown is so endlessly rich in possibilities. Nonetheless, observation of nature remorselessly cuts false equations from the body of scientific doctrine. God speaks through nature, as it were, and "the Eternal of Israel does not deceive or console." (1 Samuel, 15:29). When this observational cutting and chopping is (temporarily) halted, the remaining equations are said to be "validated" (but they remain on the chopping block for further testing).

The programmer's life is, in one sense, more difficult than the experimenter's. Imagine a huge computer program containing millions of lines of code, the accumulated fruit of thousands of hours of effort by many people. How do we verify that this computation faithfully reflects the equations that have ostensibly been programmed? Of course they've been checked again and again for typos or logical faults or syntactic errors. Very clever methods are available for code verification. Nonetheless, programmers are only human, and some infidelity may slip through. What remorseless knife does the programmer have with which to verify that the equations are correctly calculated? Testing computation against observation does not allow us to distinguish between errors in the equations, errors in the program, and compensatory errors in both.

The experimenter compares an equation's prediction against an observation of nature. Like the experimenter, the programmer compares the computation against something. However, for the programmer, the sharp knife of nature is not available. In special cases the programmer can compare against a known answer. More frequently the programmer must compare against other computations which have already been verified (by some earlier comparison). The verification of a computation - as distinct from the validation of an equation - can only use other high-level human-made results. The programmer's comparisons can only be traced back to other comparisons. It is true that the experimenter's tests are intermediated by human artifacts like calipers or cyclotrons. Nonetheless, bedrock for the experimenter is the "reality out there". The experimenter's tests can be traced back to observations of elementary real events. The programmer does not have that recourse. One might say that God speaks to the experimenter through nature, but the programmer has no such Voice upon which to rely.

The tower built of old would have reached the heavens because of the power of language. That tower was never completed because God turned talk into babble and dispersed the people across the land. Scholars have argued whether the story prescribes a moral norm, or simply describes the way things are, but the power of language has never been disputed.

The tower was never completed, just as science, it seems, has a long way to go. Genius, said Edison, is 1 percent inspiration and 99 percent perspiration. A good part of the sweat comes from getting the language right, whether mathematical equations or computer programs.

Part of the challenge is finding order in nature's bubbling variety. Each equation captures a glimpse of that order, adding one block to the structure of science. Furthermore, equations must be validated, which is only a stop-gap. All blocks crumble eventually, and all equations are fallible and likely to be falsified.

Another challenge in science and engineering is grasping the myriad implications that are distilled into an equation. An equation compresses and summarizes, while computer simulations go the other way, restoring detail and specificity. The fidelity of a simulation to the equation is usually verified by comparing against other simulations. This is like the dictionary paradox: using words to define words.

It is by inventing and exploiting symbols that humans have constructed an orderly world out of the confusing tumult of experience. With symbols, like with blocks in the tower, the sky is the limit.