Sunday, 1 November 2020
Picture Post #59 Proscenium
Sunday, 13 September 2020
Poetry: The Non-linear Mathematics of History
Posted by Chengde Chen *
Things are so obvious, why can’t we see them?
We are still obsessed with developing technology
as if we wished to hasten our extinction
This is because history is deceptive
We have no understanding of the mathematics of history
hence are immersed in a linear perception of ‘progress’:
history has proved that man controls technology
so technology must do more good than harm
This has been our experience of thousands of years
thus our unshakable faith and confidence
We, of course, need to rely on history
which seems to be the only thing we have
Yet, history is not a piece of repeatable music
but more of non-linear mathematics
Some histories may be mirrors of futures
while some futures have no reflection of history at all
It is hard to establish such a non-linear understanding
as it’s so different from our intuition
Thanks to the difficulty, as a famous tale relates
Dahir, an Indian wise-man of 3000 years ago
almost made the King bankrupt his Kingdom!
One day, the chess-loving King challenged Dahir
by asking him to play the final phase of a losing battle
As it seemed impossible for anyone to turn the table
the King promised Dahir smugly:
‘If you can win, I’ll meet you a request of any kind!’
Dahir, with his superior intelligence, did win
but he only made a very small request:
‘I would like to have some grain
placed on the chessboard in the following way:
one for the first square
two for the second square
four for the third square
and so on and so forth
so that each square is twice that of the previous one
until all sixty four squares of the chessboard are placed’
What an insignificant request, the King thought
and approved it immediately
He ordered his soldiers to bring in a sack of grain
and to place them in the way requested
When one sack was finished, another was served
Then another, and another…
until they exhausted all the grain in the Kingdom
it was still far from completing the 64 squares
The grains required are such astronomical quantity that
even the amount of grain in today’s world
does not come near it (over 1000 billion tonnes)!
It was the modest figures of the early counting
as well as the linear intuition about ‘history’
that made the King miscalculate the matter completely
He is still in debt to Dahir to this day!
Technological progress is the kind of exponential curve
but it is even more deceptive
It had crawled very slowly for very long in ancient times
but rose quicker and quicker in recent centuries
People, however, have considered the change linearly
assuming the rate of growth the same as the past
Hence a common-sense conviction:
we have always progressed through technology
so through it we can always progress into the future
technology has always become more and more advanced
so with it we can always be more and more powerful
Oh, the linear thinking of progress!
History is not optics
nor is the future a mirror image of the past
In the past man was a small member of the club of nature
while today, we have changed the weather, raised oceans
and created new species, as well as new forms of energy
If we cannot see such a world of difference
we are as miscalculating as the old King was!
We cannot, however, afford to miscalculate
as we would have no time even to be surprised
The surface value of history is its usefulness
The deeper value of history is to prove itself useless
The history in which we controlled technology
was only history, no matter how brilliant it was
The future may mean a ruthless breaking away from it!
Editor's note. The amount required is 2 raised to the power of 64 minus one. Wikipedia offers that the total number of grains is eighteen quintillion, four hundred and forty-six quadrillion seven hundred and forty-four trillion seventy-three billion seven hundred and nine million five hundred and fifty-one thousand six hundred and fifteen (18,446,744,073,709,551,615) and that this is “about 2,000 times annual world production”.
Sunday, 14 January 2018
What Are ‘Facts’?
And yet surely it is the total anthology of facts — meaning things (their properties), concepts, and their interrelationships — that composes reality. Facts have multiple dimensions, including what one knows (epistemological aspects), how one semantically describes what’s known (linguistic aspects), and what meaning and purpose one attributes to what’s known (metaphysical aspects).
In short, the complete anthology of facts relates to all possible forms of reality, ranging the breadth of possibilities, from figments to suppositions to the verifiable phenomenal world.
Sunday, 22 October 2017
The Search For True History
We are all familiar, on a personal level, with the problems of history. In fact we continually revise the small histories which we ourselves create, with words such as ‘I misjudged him,’ ‘If only I had known,’ or ‘I can't remember it for the life of me.’ Our own practice of history, therefore, is contin-ually subject to review and correction.Much the same is true of history on a grander scale: revisionist history in the United States, postcolonial history in former colonies, the paradigm shift in Islamic Studies, and so on. Everywhere, history is being reinterpreted and overturned. Where then do we find true history? A brief exploration of the problems of history promises to help us further.
There are various problems in the field of history which are fairly unique to itself. History is unrepeatable. We cannot retrieve the facts if we missed them the first time. History, too, will always represent a loss of information—a reduction of the events themselves. No written or oral history can truly encompass all that happened in the past. Even if we should select a small and (seemingly) manageable part of history—say, regional history, period history, or military history—this is not isolated from the whole. Any history, no matter how big or small, is ultimately an open system, and will always run up against the limits of completeness.
Worse, we find such limits to completeness within our very selves. As we step back to survey the world as a whole, we observe that the facts in this world are infinite—yet we ourselves are finite. And not only are the facts infinite, but they criss-cross each other in infinite ways. There is a mismatch, therefore—between the number of facts we find in this world, and the number of facts we can combine in our minds. It is certainly impossible to combine an infinity of facts in the mind. Our combination of facts is always incomplete and partial—and full of holes which need to be patched with hopeful, and believing, guesses.
An infinity of facts, then, leads us to another realisation. While we cannot obtain a complete combination of facts, we do have a kind of completeness—a finite completeness—in every one of us. We call it our world-view—and it is within such world-views that histories exist as a kind of sub-set, being knitted into their fabric. In short, history is as subjective as we are. We may not recognise this in our present, but we see it in our past:
Historical perspectives which in the past were highly rated may now be so unfashionable as to raise eyebrows if one merely mentions them: that history serves the purposes of the state, for instance, that it is about great men, or that it has a goal. We also see the past reflect on the present. In our common life, we have been plagued by massive oversight. Among other things, we have championed ideologies without foreseeing their ruin, and announced progress without recognising its devastation. In the same way, history may be written with or without crucial considerations, and no one may notice at all.
This should not be misunderstood. The historical record deals with crucial events: the discovery of new continents, for instance, crimes against humanity, or international treaties. All are able to teach us. Facts do exist—and facts should not be fabricated where they do not exist. Yet wherever we combine facts, we are selective, and in the process de-selective. The facts, wrote the historian Charles Beard, ‘do not select themselves, or force themselves automatically into any fixed scheme of arrangement in the mind of the historian.’ We need to combine the facts in our minds, by acts of choice, conviction, and interpretation regarding values.
For all of its problems, history will be written, and history will be read. The question then remains: on what basis may the truth of our histories be assessed? Did Caesar cross the Rubicon? Was Jesus Christ crucified? Did Marie-Antoinette really tell them to eat cake? What shall we write about colonialism? Has racism been on the rise? That is, when we have done our best to appreciate the ‘facts’, how shall we judge their adequacy as history?
We know it from the movies—and from books. We say, ‘That didn't ring true,’ or ‘That was far-fetched’—or, on the other hand, ‘That was true to life.’ Similarly we may judge history on its truth claims—namely, whether we think it represents a credible and faithful interpretation of our world, or whether it does not. That is, history needs to be credible not merely from the point of view of its factual content, but from the point of view of what is credible in itself. In fact there is no other basis on which we may judge history, unless the facts should definitely show us otherwise.
At first glance, this might seem to be a negative finding—a defeat in our quest for a valid or objective history. But far rather, it suggests to us positively that every history must be a questioning, a discerning, a reading between the lines, which at its best sets us free from presuppositions. History cannot properly be taught. History is intelligent judgement, and truth requires independent, impartial, robust thinking to discern those arrangements of facts which are sound and those which are less than satisfactory, which press in on us every day.
Sunday, 16 October 2016
Does History Shape Future Wars?
To be sure, lessons can be gleaned from the study of past wars, as did Thucydides, answering some of the ‘who’, ‘what’, ‘how’, ‘why’, and ‘so-what’ questions. These putative takeaways may be constructively exploited—albeit within distinct limits.Exploited, as the military historian Trevor Dupuy said, to “determine patterns of conduct [and] performance . . . that will provide basic insights into the nature of armed conflict.” The stuff of grand strategies and humble tactics. But here’s the rub: What’s unlikely is that those historical takeaways will lead to higher-probability outcomes in future war.
The reason for this conclusion is that the inherent instability of war makes it impossible to pave the way to victory with assurance, regardless of lessons gleaned from history. There are too many variables, which rapidly pile up like grains of sand and get jostled around as events advance and recede. Some philosophers of history, such as Arthur Danto, have shed light on the whys and wherefores of all this. That is, history captures not just isolated events but rather intersections and segues between events—like synapses. These intersections result in large changes in events, making it numbingly hard to figure out what will emerge at the other end of all that bewildering change. It’s even more complicated to sort out how history’s lessons from past wars might translate to reliable prescriptions for managing future wars.
But the grounds for flawed historical prescription go beyond the fact that war’s recipe mixes both ‘art’ and ‘science’. Even in the context of blended art and science, a little historical information is not always better than none; in the case of war, a tipping point must be reached before information is good enough and plentiful enough to matter. The fact is that war is both nonlinear and dynamic. Reliable predictions—and thus prescriptions—are elusive. Certainly, war obeys physical laws; the problem is just that we can’t always get a handle on the how and why that happens, in face of all the rapidly moving, morphing parts. Hence in the eyes of those caught up in war’s mangle, events often appear to play out as if random, at times lapsing into a level of chaos that planners cannot compensate for.
This randomness is more familiarly known as the ‘fog of war’. The fog stems from the perception of confusion in the mind’s eye. Absent a full understanding of prevailing initial conditions and their intersections, this perception drives decisions and actions during war. But it does so unreliably. Complexity thus ensures that orderliness eludes the grasp of historians, policymakers, military leaders, and pundits alike. Hindsight doesn’t always help. Unforeseeable incidents, which Carl von Clausewitz dubbed friction, govern every aspect of war. This friction appears as unmanageable ‘noise’, magnified manifold when war’s tempo quickly picks up or acute danger is at hand.
The sheer multiplicity of, and interactions among, initial conditions make it impossible to predict every possible outcome or to calculate their probabilities. Such unpredictability in war provides a stark challenge to C.G. Hempel’s comfortable expectations:
“Historical explanation . . . [being] aimed at showing that some event in question was not a ‘matter of chance’, but was rather to be expected in view of certain antecedent or simultaneous conditions.”To the contrary, it is the very unpredictability of war that makes it impossible to avoid or at least contain. The pioneering of chaos theory, by Henri PoincarĂ©, Edward Lorenz, and others, has shown that events associated with dynamic, nonlinear systems—war among them—are extraordinarily sensitive to their initial conditions. And as Aristotle observed, “the least deviation . . . is multiplied later a thousandfold.”
Wars evolve as events—branching out in fern-like patterns—play out their consequences. The thread linking the lessons from history to future wars is thin and tenuous. ‘Wisdom’ gleaned from the past inevitably bumps up against the realities of wars’ disorder. We might learn much from past wars, including descriptive reconstructions of causes, circumstances, and happenings, but our ability to take prescriptive lessons’ forward is strictly limited. In describing the events of the Peloponnesian War,
Thucydides wrote:
“If [my history] be judged by those inquirers who desire an exact knowledge of the past as an aid to the interpretation of the future . . . I shall be content.”Yet is our knowledge of history really so exact? The answer is surely 'no' – whatever the comfortable assurances of Thucydides.
Can History Shape Future War?
Posted by Keith Tidman
In describing the events of the Peloponnesian War, Thucydides wrote, “If [my history] be judged by those inquirers who desire an exact knowledge of the past as an aid to the interpretation of the future ... I shall be content.”Yet is our knowledge of history really that ‘exact’? And can we apply what is learned, to shape wars still to be fought? Is there a prescriptive use of military history? That is, does the historical study of past wars increase the probability of victory in the next?
In spite of the optimism of Thucydides, the answer has to be no. And for an overarching reason: The complexity, indeterminacy, and dynamical nature of war. Conditions unfold in multiple directions; high-stakes choices are made to try pushing back against the specter of chaos; and overly idealised visions are applied to war’s unfolding—where ‘victory’ is writ large, to win both in battle and in the arena of political will. Of course, lessons of past wars may be useful within limits. Yet, in the words of military historian Trevor Dupuy, only to provide “basic insights”—tracing the contours of conduct and performance.
Variables pile up like grains of sand and are jostled as events advance and recede—unforeseeable incidents that the military theorist Carl von Clausewitz dubbed ‘friction’, which become magnified when war’s tempo spikes or acute danger looms. The instability of war makes it impossible to have confidence in victory, regardless of historical lessons. If the ultimate metric of war is wins, consider a few of America’s post-World War II crucibles: Korea, a stalemate; Vietnam, a loss; Iraq and Afghanistan (fifteen years later!) teetering precariously—constabulary skirmishes in Panama, Haiti, Somalia, Grenada, and Kosovo too minor to regard.
An example of failure has been counterinsurgencies. The last century has seen many efforts go awry. The history includes France in Algeria and Indochina, the Netherlands in Aceh, Britain in Malaya, the Soviet Union in Afghanistan, and the United States in Vietnam, Iraq, and Afghanistan. These were asymmetric conflicts—often fought, by insurgents’ intent, away from sweeping battlefields, and where insurgents at least instinctively understood military strategist Sun Tzu’s observation that “all warfare is based on deception”. Field manuals have provided military, political, informational, intelligence, and psychological tools by way of a counter—yet sustainable victory has often proven elusive.
Some philosophers of history, such as Arthur Danto, have shed light on the whys and wherefores for this disconnect. History does not merely deal with isolated events, but with great intersections—and how they play off one another. These intersections result in major changes, making it numbingly hard to figure out what will emerge. It is even more complicated with war, where one seeks to translate intersections that have played into past wars into reliable prescriptions for managing future wars.
Further, a blizzard of events does not yield dependable means to assess information about what was going on and to convert conclusions into sound, high-probability prescriptions for the next time. Even with hi-tech battlegrounds and mathematical simulations, a little historical information is not always better than none. A tipping point must be reached before information is good enough and plentiful enough. The reason is war’s nonlinear and dynamic nature. To this point, Arnold Toynbee was right to assert that history progresses in nonlinear fashion. In the eyes of those caught up in war’s mangle, therefore, events often play out as chaos, which military planners cannot compensate for. It has been called the ‘fog of war’.
Minor events, too, may lead to major events. Chaos theory has shown that events associated with dynamic, nonlinear systems—war among them—are extraordinarily sensitive to initial conditions. The sheer multiplicity of, and interactions among, the initial conditions make it impossible to predict most outcomes. Efforts by decision-makers run into head winds, as conditions degrade. Errors cascade. The many variables are just the starting point of war, subject to change dramatically as war persists. The ‘butterfly effect’, as dubbed by Edward Lorenz, where the metaphorical flapping of a butterfly’s wings (initial conditions) can cause extreme weather far elsewhere.
Too many to list here, the initial conditions of war include the prospect of third-party intervention, risk of battle fatigue, unexpected coupling of variables, cost-benefit bargains, resilience to setbacks, flexibility of tactics, match between force mix and mission, weaker party’s offsets to the other’s strengths, inspirational leadership, weight placed on presumed relative importance of factors—and numerous others. And as Aristotle observed, “the least deviation . . . is multiplied later a thousandfold.”
The thread linking the outcome of future wars to lessons from history is thin, and errors have come with high costs—in blood, treasure, and ethical norms. ‘Wisdom’ gleaned from the past bumps up against wars’ capacity to create disequilibrium. Much might be learned descriptively from past wars, but the prescriptive value of those lessons is tenuous.