Propositional Knowledge and Tacit Knowledge: The Case of Tennis

Jonah Lehrer's Grantland piece on the physics of the tennis court is well worth your time if you're a tennis fan.  There's this, for example:

Although there still are no rules regarding the performance of tennis court surfaces — the game can be played on anything — in January 2008 the ITF began regulating the speed of courts used in Davis Cup tournaments. Because the host country gets to choose the tournament location, the new rules prevent the use of extremely slow or fast surfaces. So far, only one court — a clay surface in Croatia, used in a 2008 match against Brazil — has violated the regulations.

But Lehrer - a committed enthusiast of neuroscience - goes too far in reinforcing the distinction between propositional and tacit knowledge.  He points out - correctly - that that laws of tennis are ultimately the laws of physics but the speed of the game means that no player actually computes the trajectory of the ball using Newtonian mechanics while playing.  Instead the knowledge is displayed tacitly, in the way their bodies move, in the way they adjust their footwork and their racket motion, etc.  In Michael Polanyi's terms, this is tacit knowledge - knowledge that is expressed in action but is hard to express propositionally.  Lehrer chooses to illustrate this with the following example, which I found a little silly:

I met with the Caltech tennis team, arguably the smartest collegiate athletes in the country. (The average grade point average on the men's team is 3.73, which is one of the highest team GPAs in the NCAA. And these players are taking Caltech classes.) Despite this intellectual pedigree, the Caltech tennis players have struggled to win games: Last season, the men's tennis team went 1-16. Although many of the players can rattle off abstruse physics equations with ease, they all insisted that their textbook knowledge was not an advantage. "To be honest, it doesn't help at all," says Devashish Joshi, a freshman on the team. "I never think about science while playing."

Well, okay, if you say so.  But: 

"The top-ranked guys are all intuitive physicists," Hofmann says. "They know how the ball will bounce even if they can't explain why. This is what allows them to change their strategy based on the surface."

I don't want to de-emphasize how talented the top tennis players are.  But this makes it seem as though that that the only way of bringing propositional knowledge of physics into the game is if the players start calculating in their heads.  If you look at the role of knowledge in tennis, as simply something that gets displayed on courts, then, sure, there's only tacit knowledge.  But if you look at the world of tennis as a network (channeling Edwin Hutchins and Bruno Latour), then the propositional knowledge of physics comes into it at a number of different points:

Racket technology: There are actual physicists and material scientists who work on rackets.  They design rackets that are designed for different types of playing styles and different types of surfaces.  This is propositional knowledge as encoded into artifacts (in this case, the tennis racket), which then the players use. 

Coaching: Coaches help to get a lot of propositional knowledge on to the courts.  What's a "good" service action?  How much back-swing should you have while playing a stroke?  Is a long back-swing bad for grass?  A lot of this is backed up by actually thinking about physics and it gets incorporated into a player's game.  Novak Djokovic recently improved his service by making a "minor" adjustment - but this may have been key to his recent success because he is able to get some free points on his serve (69 more aces, according to the article). 

Playing strategy:  Recordings of previous matches are now easily available and allows players and their coaches to construct what is called a game-plan.  Game-plans are products of conscious reasoning and pattern recognition about an opponent's weaknesses and strengths - propositional knowledge and judgement at its best.  Of course, this is, in Lucy Suchman's famous formulation, like planning how to take your canoe into the rapids: useful only as a resource once you start playing.  But it is propositional knowledge, nevertheless, and is often the product of a whole network of people thinking: coaches, practice partners, managers, consultants, etc. as well as technologies like statistics, video recordings and such.


My point is that the propositional/tacit knowledge distinction is very useful.  But there are ways in which the two interact that is only visible at the level of networks.  In other words, knowledge, both propositional and tacit, is distributed - and while the best tennis players are definitely intuitive physicists, they are also beneficiaries of a lot of thinking that is careful and propositional - which is encoded into the artifacts they  use and the practices of coaching and training in their day-to-day life.

The Republican War on Science and David Bloor's Symmetry Principle

In Knowledge and Social Imagery, his manifesto for the Strong Program in the sociology of science, David Bloor lays out his four principles for the discipline of Science Studies.  One of these is the Symmetry principle which he expresses as follows:

[The Strong Program] would be symmetrical in its style of explanation.  The same types of cause would explain, say, true and false beliefs.

There is a certain aesthetic reasonableness to this principle that I like very much: after all why should there be different explanations of true and false beliefs?  And the principle itself is intended to oppose the traditional conception of scientific knowledge: that true beliefs need no explanation, but false beliefs do.  The explanation of false beliefs is usually distorting factors like personal beliefs, commitments and ideology.

But I've always found it hard to explain the utility of the symmetry principle to others.  What's the use of it? is usually the question.  And I must admit it was always hard to explain its utility outside the field.  As a principle in understanding any kind of knowledge (including scientific knowledge), the symmetry principle has always seemed to me an indispensable tool.  What it could be used for -- outside of the sociology of knowledge --  I couldn't really say. 

Well, until today, that is.

I've been reading Merchants of Doubt: How a Handful of Scientists Obscured the Truth on Issues from Tobacco Smoke to Global Warming by Naomi Oreskes and Erik M. Conway.  The book is a meticulously researched piece of political journalism.  The story is galvanizing, if a little wearying in its repetitiveness: how a handful of scientists, financed by corporations, helped to create doubt about the scientific consensus on topics like the risks of smoking and acid rain to the ozone hole and global warming, leading to considerable delay in the enactment of regulatory policies (and for global warming, no policies at all).  It's astonishing how the same names of the same scientists keep popping up in every debate: these guys really were deep-pocketed merchants of doubt.  They had a clear objective which they shared with the rest of the American conservative movement: to oppose any possible Government regulations on corporations as well as dismantle the already existing ones. 

So far so good.  Unfortunately, despite all the wonderful data that the authors have combed through, the story the authors tell is frustratingly traditional and asymmetric.  It's true that the road to the regulation of tobacco (and now it seems global warming) was long and arduous and disturbing.  But the road to regulation for acid rain and the ozone hole was arguably much shorter.  We were able to regulate the emissions of sulfur and CFCs despite the doubts created by the right-wing machine using both straight-forward bans and cap-and-trade mechanisms.  Why were regulators quick to respond in these cases but not in the others despite the right-wing noise machine?  The authors, it seems to me, don't think it is especially relevant.  For instance on page 124, they say:

The combined results of the Ozone Trends Panel and the field expeditions caused the Montreal Protocol to be renegotiated. The results also convinced the industry that their products really were doing harm, and opposition began to fade. CFCs would now be regulated based on what had already happened, not on what might happen in the future. Because the chemicals had lifetimes measured in decades, there was no longer any doubt that more damage would happen.  [My emphasis]

But didn't they spend the previous three chapters describing how industry leaders almost never accept scientific findings when they go against their own interests (e.g. Big Tobacco on the risks of smoking)?   So why should the industry be convinced in this case?  It seems to me that the authors don't really care.  When scientific findings lead to the appropriate regulations, it's because they were true.  When they don't, it's because of the right-wing doubting machine and its near-fanatical free market ideology.

This is where the symmetry principle would have been useful.  If we assume that there is one process that leads from scientific findings to the appropriate regulations, then the same process holds irrespective of whether said regulation was enacted or not.  (It's not as if the doubting thomases didn't start beating their drums during the ozone hole controversy, it's just that they were not successful in blocking regulation.)  So knowing what we did right in the ozone hole and acid rain case will arguably be important for us if we want to enact global warming regulation.

I don't mean to suggest that if the authors did treat these cases symmetrically, we would know what to do to enact emissions reductions in the US.  No.  And it's possible that the difference is just that the right-wing machine threw less money at these problems where we were able to enact regulation.  Or maybe because of the consequences of acid rain or ozone depletion were so close to home (skin cancer, etc.) whereas the consequences of global warming are strikingly diffuse (what exactly does it mean for average temperatures to rise by 2 degrees?), the American public was just more supportive of regulation in these cases.  But whatever it is, it would be useful to treat the cases of successful regulation and delayed (or impossible) regulation symmetrically.

The Symmetry principle is often derided for its relativism towards science.  Here is one case where it could be used (although in a political economic analysis) for science, and not against it.

[I don't mean to hit on the book, I think it's rich and very detailed and a rich source of data for anyone who wants to understand the political economy of scientific findings and their relation to regulation.  I highly recommend it.]

Defending Thomas Kuhn from Errol Morris

Errol Morris' series on Thomas Kuhn started amusingly: it was fun to hear that Morris -- the director of great documentary The Fog of War -- was actually a first-year graduate student in the History of Science program at Princeton (and rejected by Harvard's History of Science department!).  (I don't know, that gave me quite a kick.)  And it was funny to hear that he and Thomas Kuhn hadn't gotten along, that Kuhn had thrown an ash-tray at him because he refused to give up his Whiggish ways of doing the history of science.  (There's probably some poetic license here, but it's still funny!)

But as the story progressed (parts two, three, four, five), my enjoyment started to wane.  It wasn't the flowing, free-associative style, which was still fun, although I really didn't see what the digressions into the Pythogorean society had to do with the concept of incommensurability.  No, it was the intellectual portrayal of Thomas Kuhn.  If one reads Morris without reading Kuhn, then Kuhn comes across as an idiot.  And all of us who found The Structure of Scientific Revolutions useful come across as either idiots or fashionable post-modernists who like Structure because it fits in with the relativistic fashions of the day.

What is Morris' problem with Kuhn (other than that he clearly didn't like him)?  Two things.  First, he argues that the concept of incommensurability is incoherent.  And second, that it opens the doors to all sorts of relativism.  The second point is old hat.  Much ink has been shed on how if we give up the idea of Truth, of an unmediated reality out there that we are accountable to, then we are on a slippery slope to ethical relativism.  That it leaves us without a reply to totalitarian dictatorships, that it leaves the door open to the O'Briens of the world who want us to believe that 2+2=5.  Etc.  The first point is old hat too.  As John Holbo points out, incommensurability was criticized in just this way even when Structure was published.  The idea here is that if two paradigms are incommensurable, then we have no way of doing the history of science; so the fact that Kuhn himself could understand the older paradigms proves that paradigms are not really incommensurable.  

As fields, the history of science, and Science and Technology Studies (STS) have moved on: the idea of a linguistic conceptual framework that under-girds scientific theories has been replaced by a search for material practices that constitute science.  Kuhn is studied less as someone who offered fresh new insights but as one of  the oldies: routinely grouped together with Popper, Feyerabend and Lakatos.  (I also think that while Kuhn makes several missteps in Structure -- he tries to define incommensurability linguistically, he starts to talk about using computer programs to understand incommensurability -- the idea of science as being constituted by material practice is there in the book.  As are other things that we now look for as STS scholars: the practices of pedagogy and training in science, the incentive structure, etc.) 


Still.  I'd like to offer a defense of Kuhn and of Structure and why the criticisms that Morris offers are mistaken.  Reading Structure was a transforming experience for me -- and I'd like to bring out why. 

So without any further ado, here goes.

Kuhn's book is more heard about and talked about than read.  For example, I knew (or thought I knew) the fundamentals of its argument long before I read it.  That argument goes something like this:

• That scientific advances happen not cumulatively, but in bursts -- conceptual revolutions alternating with periods of "normal" science
• That  underlying all scientific theories is something called a "paradigm" (think of it as some kind of underlying conceptual scheme) and that one paradigm gets replaced by another during a scientific revolution.  
• And finally, when paradigms change, when a new paradigm replaces the old one, the two are incommensurable, so that when scientists argue for the merits of either paradigm, they are essentially talking past each other.  The paradigm that wins out wins not because it is true.  

The key thing to understand here is that most people would be fine with this argument if it wasn't for the incommensurability part.  Here, for instance, is Thomas Nagel, reviewing Alan Sokal's Fashionable Nonsense:

Much of what Kuhn says about great theoretical shifts, and the inertial role of long-established scientific paradigms and their cultural entrenchment in resisting recalcitrant evidence until it becomes overwhelming, is entirely reasonable, but it is also entirely compatible with the conception of science as seeking, and sometimes finding, objective truth about the world. What has made him a relativist hero is the addition of provocative remarks to the effect that Newton and Einstein, or Ptolemy and Galileo, live in "different worlds," that the paradigms of different scientific periods are "incommensurable," and that it is a mistake to think of the progress of science over time as bringing us closer to the truth about how the world really is.

Before I read Structure, I pretty much agreed with this.  (How could I not?)

When I did read Structure, however, I realized that while this summary was not wrong, the book said a great many other things.  I realized that: 

That Kuhn is not doing philosophy of science, despite the fact that he's almost universally known as a philosopher of science.  It's true that Structure makes a series of bold, philosophical claims.  But it also tries to back them up with historical evidence -- not by using anecdotes but with the kind of concrete, archival research that historians do.  Analytic philosophy, on the other hand, is not an empirical field.  The subject it resembles the most is pure mathematics: you solve "problems" (the problem of knowledge, of skepticism), you use symbolic logic, you use paper and pencil, you construct proofs and thought experiments.  But you do NOT collect data of any sort, you do not make hypotheses that you then hope to confirm by looking at the data.  Kuhn was grounded in the history of science, the theory of scientific change that he propounded came from his close study of early modern science. (Although, as Ian Hacking points out, very few historians of science mix history and philosophy in quite the way Kuhn did -- which is probably why he is more known as a philosopher than as a historian.)

That the biggest claim in Structure -- one that usually flies under the radar -- is not the concept of scientific paradigms, even though much space is spent talking about paradigm changes.  No.  Rather, the central aspect of science, according to Structure, is that the activity that doing science most resembles is solving puzzles.   Kuhn calls this puzzle-solving activity "normal science."  We need to understand the claim here: the point is not to denigrate scientific activity.  The point is that puzzle-solving is not usually understood as a search for knowledge.  So even if science, understood as a collective activity, is engaged in a search for knowledge, in actual concrete terms, this search for knowledge gets done by building and solving puzzles.  Now, to an extent, constructing and solving puzzles is part of all knowledge fields.  Kuhn's point though is that nowhere is this reduction of knowledge into puzzles as prevalent or as polished as in the sciences.  (This is related to how a scientific community is structured as well as its pedagogical practices.)

Finally, the paradigm is not just a linguistic conceptual scheme.  This is the mistake that interlocutors like Morris make.  They think that a paradigm and incommensurability are philosophical concepts.  They are not.  They are not even linguistic (although Kuhn sometimes talks about them that way).  They are -- and this is more important than anything else -- about practice.  My key to Structure, the moment when it all came together for me -- what a paradigm was and how it functioned.  I'm going to reproduce the full paragraph from Kuhn:

A phenomenon familiar to both students of science and historians of science provides a clue.  The former regularly report that they have read through a chapter of their text, understood it perfectly, but nonetheless had difficulty solving a number of the problems at the chapter's end.  Ordinarily, also, those difficulties dissolve in the same way.  The student dicovers, with or without the assistance of his instructor, a way to see a problem as like a problem he has already encountered.  Having seen the resemblance, grasped the analogy between two or more distinct problems, he can interrelate symbols and attach them to nature in the ways that have proved effective before.  The law-sketch, say f = ma, has functioned as a tool, informing the student what similarities to look for, signaling the gestalt in which the situation is to be seen.  The resultant ability to see a variety of situations as like each other, as subjects for f = ma or some other symbolic generalization, is, I think, the main thing a student acquires by doing exemplary problems, whether with a pencil and paper or in a well-designed laboratory.  After he has completed a certain number, which may vary widely from one individual to the next, he views the situations that confront him as a scientist in the same gestalt as other members of his specialists' group.  For him they are no longer the same situations he had encountered when his training began.  He has meanwhile assimilated a time-tested and group-licensed way of learning. (Structure, pg 189) [emphasis mine]

Believe it or not, this is exactly how it happened for me.  I studied how to draw free-body diagrams on my own, just after 10th grade.  So I had no teacher to take me step-by-step through a few solved examples, which is generally the case.  Instead, I had to read the solved examples in my textbook -- many of which struck me as incomprehensible.  I remember staring at diagrams of bodies moving on inclined planes in frustration, almost ready to cry because I didn't know what to do.  My frustration was accentuated, I think, because we had moved to a new town and I was just starting to adapt to it.

And then one day -- I am not sure how --  it went away, .  All I remember is that one fine day I found I could do free-body diagrams just fine, that in fact, I even enjoyed doing them.  Gestalt switch is probably a really good way of describing the change.  A diagram of a body on an inclined plane now means something to me that it did not before.  To use some of Kuhn's own expressions, it was as if, for me, the world had changed and while I could recall recall my frustration with how the world had looked before, I could never recapture my previous world-view; it was irretrievably lost.  Kuhn's description of paradigm shifts as gestalt switches and his talk of scientists with differnet paradigms living in "different worlds" often leads people like Morris and Nagel to call him an idealist and a relativist but I know exactly what he is talking about.

Personal remininsces aside, it's worth unpacking the paragraph in detail and making explicit all the points that Kuhn is making in it:

• A paradigm is not a set of rules.  It's more like practice, a skill, like knowing how to apply the equation f=ma to different types of scenarios (a body moving on an inclined plane, an oscillating pendulum, a body attached to a spring, etc.)   There is no way to describe in the form of rules what it means to solve problems using f=ma, you just have to learn to do it.  It's tacit knowledge, sort of like riding a bicycle.  At the same time, being able to solve problems is the only way to become a scientist.
• One has to literally go through hell to be initiated into a paradigm.  And as a matter of pedagogy, scientists have it down pat what it takes to create a competent member of their community: you teach him or her the concepts, and then you make them solve a bunch of problems.  Somewhere along the way, the student gains competence.  This authoritarian way of doing things turns away many people from doing science, but it works wonderfully well for those who like it. 
• Finally, it provides an explanation of incommensurability, of what Kuhn means when he asserts that when scientists argue over competing paradigms, they are essentially talking past each other.  Yes, if they wanted to, if they took time and effort, they could possibly understand each other.  Philosophically, incommensurability can be refuted (as Morris tries to do).  But practically, in practice, it exists.  Because learning a paradigm is a long back-breaking process, and is done usually when one is a student, established, practicing scientists have neither the time, nor the inclination, to imbibe and learn a new paradigm.   So they keep on arguing without truly understanding each other.

"But doesn't that open the door to relativism?" Morris might say.  Kuhn's answer is that the paradigm that wins out is one that the community perceives as more productive. The key word here is productive.  Scientists should feel that a certain paradigm allows them to create a rich set of problems (puzzles) that they can then solve -- which makes them prefer that paradigm.  So there is some sort of progress.  But what about the role of nature, you might ask.  Does nature play a role in the choice of a paradigm during a revolution?  The answer is yes.  And again, it goes back to the learning.  Paradigms need to be learned: by solving problems and by practicing doing experiments; nature plays a role in both of these. 

All in all, Structure taught me three things.  First, to pay attention to material practices and craft-work that are often the building blocks of any kind of scientific or engineering work.  And second, contrary to rhetoric, to pay attention to the values that often underlie scientific work.  By values, I mean things like what counts as a "good" problem, what counts as an "elegant" solution etc.  To be able to use these words successfully is to have mastered scientific practice.  Scientific knowledge can't be studied without a close understanding of the practices and values that produce it.  And finally, pedagogy is incredibly important.  Pedagogy is how a community licenses its practitioners.  How scientific practitioners are made is important if we want to understand scientific knowledge. 

I am not sure Morris will buy this defense of Kuhn.  He is an admirer of Saul Kripke, after all. 

Internal vs. External Incentives: The Case of Economics

[This is a random, off-the-cuff post, with some wild generalizations, so please let me know if you think any part of it is wrong.]

There's been an interesting debate in the blogosphere recently about what science is and whether economics is a science.  The debate is interesting not so much because it settles the issue but because it's a good data-point for looking at public understandings of what it means to do science. 

Tyler Cowen started it all off by saying:

Economics is most like a science when people do not care about the outcome of the argument.

To which Matthew Yglesias responded in agreement, adding:

In other words, social science is like science when it’s like science—disinterested. But when it’s like politics, then it’s like politics. I note that American economists are generally able to reach a much greater degree of consensus when they offer policy recommendations to foreign countries than when they offer recommendations to the US congress. That’s not because foreign countries have easier problems to solve. 

When Cowen talks about the "outcome" of the argument, he means the external outcome of the argument: in this case, specifically, the public policy that seems to be the logical consequence of a certain knowledge claim.  When a knowledge claim has no link to a public policy choice, he suggests, economics is most like a science -- a condition Yglesias calls being "disinterested."  In Ygelasias' view, when a economic knowledge claim has no obvious public policy consequences (especially for the country said economists live in), economists behave like scientists -- which is not to say that they agree, but rather, that they disagree, but in a disinterested way.

In STS, this is what I call the Internal vs. External debate on what drives science.  Do scientists accept theories because they are, in some sense, true?  Are they convinced of the validity of a certain knowledge claim because of "internal" reasons -- reasons deemed to be "proper" within the field?  Or are they influenced by what one might call "external" reasons, reasons deemed by the community to be properly out of bounds, such as the desire for money, support for a political program, etc.? 

But an interesting aspect of what it means to be a disinterested economist struck me (and correct me if I'm wrong).  As far as my reading goes, ideology doesn't count as an improper reason for being partial to a knowledge claim.  So economists will routinely proclaim that they are libertarians or progressives or egalitarians.  What they won't say is whether they are Democrats or Republicans -- and so this is often deployed in debunking someone's claim.  Thus one  is more likely to hear things like "X has nothing to say about this because he worked for a Republican president and so would rather not contradict said president's policies" rather than "So-and-so makes this claim because he is left-wing and is therefore biased"  One also hears things like (at least on blogs) "I am sympathetic to such-and-such claim because I believe in progressive causes" -- which means that ideology is arguably a more acceptable reason for being sympathetic/antagonistic to a knowledge claim, than, say, membership of a political party.

Which is, in a way, different from what counts as a proper reason for accepting a knowledge claim in the actual sciences, like physics or biology.  Here, I'd say, even ideology does not fly.  Membership of a political party, of course, is completely out of bounds.  (Note that this is an assertion about community standards and rhetoric rather than about the actual workings of the hard sciences.)

Which is to say economists should probably be comparing themselves to other social scientists rather than to the practitioners of the "hard" sciences.

Other links:

And here are two more posts about the "Is economics a science?" debate which bring out interesting rhetorical perspectives on what economists think being a science is: here and here.   Greg Mankiw's little paper on "The Macro-economist as a scientist and engineer" [PDF].  And finally, on Crooked Timber, Henry Farrell applied public choice theory to economics. 

Can we ever read articles of the opposite political persuasion? An alternative model

Sean A. Munson, & Paul Resnick (2010). Presenting diverse political opinions: how and how much Proceedings of the 28th international conference on Human factors in computing systems : http://doi.acm.org/10.1145/1753326.1753543



Can we ever be convinced by someone we usually disagree with completely? Can we even manage to read regularly people whose views are antithetical to our own? These are fascinating questions, I think. First, because they are political questions; conversations and debates matter very much for any kind of open, democratic society. But I find them fascinating because they also bring up questions about the nature of knowledge: is knowledge just a matter of true and false propositions? Or is it something different, a mangle of practices, propositions and institutions, and in some way inherently inarticulable?

I bring all this up because of a talk I attended at CHI 2010 -- a presentation of a paper by Sean Munson and Paul Resnick at the University of Michigan -- that explored their very preliminary results of getting people to read articles with opposite political persuasions. Here's the abstract:

Is a polarized society inevitable, where people choose to be exposed to only political news and commentary that reinforces their existing viewpoints? We examine the relationship between the numbers of supporting and challenging items in a collection of political opinion items and readers' satisfaction, and then evaluate whether simple presentation techniques such as highlighting agreeable items or showing them first can increase satisfaction when fewer agreeable items are present. We find individual differences: some people are diversity-seeking while others are challenge-averse. For challenge-averse readers, highlighting appears to make satisfaction with sets of mostly agreeable items more extreme, but does not increase satisfaction overall, and sorting agreeable content first appears to decrease satisfaction rather than increasing it. These findings have important implications for builders of websites that aggregate content reflecting different positions. [pdf]

Remember this was a CHI paper so there was a lot of emphasis on how to "present" diverse views so as to make people read them. The results were disappointing -- people don't really seem to want to read the opposite side -- but since not everything has been tried yet, and the web still has a lot to evolve, we shouldn't really lose hope.

I want to speculate on a different sort of model in this blog-post. I am going to take for granted that people of opposite political persuasions need to talk to each other in a liberal democracy*. But if it is important for Democratic-leaning and Republican-leaning (or as they are called in the US, liberal and conservative) voters to talk to each other, is it a good way to rank news articles and people on a sliding scale from liberal to conservative and then mix and match them up? Or do we need to classify people (and articles) on some other orthogonal parameter? I.e. a parameter that doesn't correlate with being Democratic or Republican-leaning.

In what follows, I am going to propose two such parameters. This is by no means a very systematic analysis, just some thoughts that I've been playing around with, based on my own personal experiences. Most important, I have absolutely no idea how I would go about implementing such a system computationally and frankly, it may be wrong and not even work in practice. With all those caveats in mind, here goes.

The first parameter maps the content of an article. The content of an article spans the spectrum from "uncertain" to "certain". An "uncertain" article sounds unsure of itself, has many caveats in it, has a respectful tone perhaps, even if it does have definite conclusions. A "certain" article is more sure of itself, perhaps more dogmatic, even snarky. One point though. If an article is uncertain, does that mean that its author is non-ideological? Not at all. All it means is that he chooses to express himself in a certain way that seems uncertain even though the article itself may end up endorsing a very specific ideological point.

The second parameter maps the disposition of the reader. The disposition of the reader spans from "prefers interesting" to "prefers true". This is not a straight-forward spectrum and its terms need some explanation.

The terms are based on the expression "I prefer saying something interesting to something true". E.g. most philosophers**, you see, would rather write something interesting and therefore be read by generations, than solve a problem definitively and thus not be discussed at all in a few decades. In the same vein, a reader who prefers something interesting likes intricate arguments even if sometimes they lead to conclusions he does not agree with. Note that this does NOT mean that this sort of reader does not have an ideology or that he is an "independent." Nothing of the sort is required, just that he likes to read clever things.

Since no ideology has a monopoly on clever things to say so this reader probably reads a lot of clever things that come out of his own camp. A reader who prefers "true" things is the opposite. He prefers "truth" to "play", has no use for "play" and would rather prefer to say it as it is. When I say truth, I don't really mean truth-as-it-exists. I mean things that the reader believes to be true. Note that most readers will fall somewhere in between these two positions.

If indeed, in an ideal world, these metrics i.e. the certainty of an article, and the disposition of the reader could be computed with some degree of accuracy, and if we also knew the ideology of the reader as well as the ideology of the article, this is what I would do in order to get people to read articles with opposite points of view:
The flowchart is clearly a little vague and is not meant to represent some definite algorithm. The heuristic that it depends on is that those readers with a taste for the interesting will find at least some of the uncertain articles that are however in the opposite ideological camp thought-provoking to read.

At this point, it also seems appropriate to explain the theory of knowledge that underwrites this model:

• I assume that a person's ideology gets fixed pretty early in life. A person has an ideology by the time he or she reaches the mid-twenties. Ideology however does not mean a voting preference. It means a way of looking at the world, a preference for certain types of people (who become your friends) and a certain set of issues that become important, and a certain stance towards them.
• Ideologies do not change because someone offers "rational" arguments for the opposite side. People only change their minds about certain things, and these things are small technical things. World-views do not change much. When they do, and this is rare, the comparable analogy for it is religious conversion.

This seems pretty bizarre at first sight. After all, if one believes that world-views don't change, why even bother recommending articles of the opposite ideology? The mistake here, I think, is that people assume that getting people to read more articles of the opposite ideology is just an instrument for something else, sometimes termed "bipartisianship." I think of it as an end on its own, irrespective of whether it makes people change their views (which I don't think it does anyhow).

Let me make one final point before I end this (pretty unsatisfactory) post. What makes me think that people don't change their minds all that much? Well, for one, it's my own interactions with people. Arguments about politics or policies are rarely closed, the way that arguments about the validity of a mathematical proof are, for instance. So there is no control on what counts as an argument. People usually have an infinite variety of arguments to choose from and many discussions are a circle of question-begging assertions.

In his book, Knowledge and Social Imagery, David Bloor provides a very good example of how world-views are woven together. In tribal Azande society, an oracle is usually asked to tell the people the witches residing in their midst. Being a witch is taken to be a hard physical fact and it is commonly believed that a male witch passes on this "substance" to his sons, a female witch to her daughters. One would therefore think that when the oracle says someone is a witch, the whole corresponding line of people will have been or will be witches. In practice, however, the Azande don't act this way, only the close paternal kinsmen of a known witch are considered witches.

At this point, one could simply say that the Azande are being illogical and irrational. But to counter this, Bloor gives another example, one that's closer to our own culture. We commonly believe that a murderer is one who deliberately kills people. But in that case, are pilots and soldiers also murderers? As citizens who rely on the armed forces to protect us, we will immediately resist this conclusion. But aren't we being illogical or irrational here? After all, if one takes the laws of logic seriously, they lead us inexorably to this conclusion: All murderers kill people deliberately. Soldiers kill people deliberately. So all soldiers are murderers.

But no, someone will say. It all depends on what you mean by "deliberately." Soldiers don't kill "deliberately," they kill to protect us, or they kill because one of us had been killed. Or it all depends on what you mean by "kill." And so on and on. The point here is that our ideologies are "informal knowledge", we believe them because they are common cultural practices. When we reason about them ("formal knowledge"), the laws of logic and reasoning are flexible enough that we can use them to justify what we only know informally (i.e. our ideologies). That's why rational argument never succeeded in converting someone to a different ideology. Arguments like that tend to go round and round in circles. But that doesn't mean that they are unimportant or that one shouldn't be having them. One should just remember what they can or can't accomplish.

*The discussion above is heavily US-centric. In India, for example, it is very hard to isolate "opposite" political persuasions, but that's a topic for another day.

** E.g. here is Daniel Dennett's variant of it:

In an informal survey, I have been asking philosophers a slightly different question recently, and will be pleased to field further answers in response to this review: Which would you choose, if Mephistopheles offered you the following options?

(1) simply solving an outstanding philosophical problem so definitively that after a few years, only historians ever mentioned it (or your work) again, or

(2) writing a book that was so tantalizingly equivocal and problematic that it would be required reading for philosophy students for centuries to come.

The history of science offers many instances of the first sort, and none, really, of the second, but I find that many of my philosophical colleagues admit to being at least torn by the choice. They would rather be read than right. Perhaps it is of the "essence" of philosophical problems to admit of no permanent solutions, though I doubt it, but in either case it is no wonder we make so little progress.