How the myth of Arachne tells us an important lesson about epistemology and how this lesson connects to modern financial theory, theories of nationalism, and evolutionary biology
And why spider webs should not be confused for flies
And why spider webs should not be confused for flies
This one's a doozy. Pretty big topic I've been thinking about recently so It's pretty much certain I won't be able to do it any justice. Here we go:
Claim 1: The world/universe is very large and complex relative to the individual or even to humanity as a whole.
Claim 2: Human beings are bounded in terms of time and cognitive capacity.
Claims 1 and 2 form Problem 1: Individuals and groups don't have the time or capability to process all this information about the world. Not a big problem so far, demands for perfect information have always been a delusion reserved for only the most ardent of rational-choice theorists. Given that our memory retention isn't great e.g. our ability to retain a short string of numbers is naturally quite limited (takes ages for me to learn a phone number by heart) and that there's so much information out there- what is a dedicated seeker of knowledge to do?
Solution: Heuristic devices
Thankfully evolutionary logic has eased many of these processes for us. Human beings use (consciously and subconsciously) a variety of different heuristics (mental short cuts) which allow us to use impressions of large amounts of information and reach a conclusion without exhaustively examining every bit and piece of it. This would be the sort of 'fast thinking' talked about in Kahneman's monster hit of a book, Thinking Fast and Slow. Sometimes we consciously use these sort of short cuts to make sense of otherwise complex phenomena in the form of creating dichotomies, defining terms, or creating conceptual boundaries. By compartmentalising ideas into discrete groups we simplify it enough not to be overwhelmed by it all. This has arguably been quite successful and the same sort of abstraction and simplification has led to the creation of the scientific and social(read 'pseudo')-scientific models of the world around us. We eliminate the extraneous information and focus in on the causal relationships which we deem significant in relation to the phenomena we are investigating.
The problem which arises here (Problem 2! ) is that our decisions about what boundaries to create is often fairly arbitrary and at worst reflects deep cognitive biases or even political considerations. What I plan on writing about in the post is the various difficulties which arise from all these conceptual short cuts we create on our pursuit of practical understanding and usable knowledge. It's a problem that any university student or academic ought to relate to whenever they are confronted with a analytical definition or conceptual model that is collectively known to be demonstrably false yet remains part of an overarching paradigm of understanding. I argue that due to the cognitive ease (and functional requirement perhaps) of using these epistemological tools, social scientists have built an intricate and entrenched web of definitions, theories of cause and effect, and conceptual boundaries which entangle us. This conceptual web can end up trapping us (the spider) rather allowing us to feast on some delicious flies (which would be usable knowledge I guess?). Hence the title of the post: unweaving the conceptual web.
Picture above is an illustration for Dante's Purgatorio 12 by Gustave Doré, showing the meeting of Dante and Arachne.
Claim 1: The world/universe is very large and complex relative to the individual or even to humanity as a whole.
Claim 2: Human beings are bounded in terms of time and cognitive capacity.
Claims 1 and 2 form Problem 1: Individuals and groups don't have the time or capability to process all this information about the world. Not a big problem so far, demands for perfect information have always been a delusion reserved for only the most ardent of rational-choice theorists. Given that our memory retention isn't great e.g. our ability to retain a short string of numbers is naturally quite limited (takes ages for me to learn a phone number by heart) and that there's so much information out there- what is a dedicated seeker of knowledge to do?
Solution: Heuristic devices
Thankfully evolutionary logic has eased many of these processes for us. Human beings use (consciously and subconsciously) a variety of different heuristics (mental short cuts) which allow us to use impressions of large amounts of information and reach a conclusion without exhaustively examining every bit and piece of it. This would be the sort of 'fast thinking' talked about in Kahneman's monster hit of a book, Thinking Fast and Slow. Sometimes we consciously use these sort of short cuts to make sense of otherwise complex phenomena in the form of creating dichotomies, defining terms, or creating conceptual boundaries. By compartmentalising ideas into discrete groups we simplify it enough not to be overwhelmed by it all. This has arguably been quite successful and the same sort of abstraction and simplification has led to the creation of the scientific and social(read 'pseudo')-scientific models of the world around us. We eliminate the extraneous information and focus in on the causal relationships which we deem significant in relation to the phenomena we are investigating.
The problem which arises here (Problem 2! ) is that our decisions about what boundaries to create is often fairly arbitrary and at worst reflects deep cognitive biases or even political considerations. What I plan on writing about in the post is the various difficulties which arise from all these conceptual short cuts we create on our pursuit of practical understanding and usable knowledge. It's a problem that any university student or academic ought to relate to whenever they are confronted with a analytical definition or conceptual model that is collectively known to be demonstrably false yet remains part of an overarching paradigm of understanding. I argue that due to the cognitive ease (and functional requirement perhaps) of using these epistemological tools, social scientists have built an intricate and entrenched web of definitions, theories of cause and effect, and conceptual boundaries which entangle us. This conceptual web can end up trapping us (the spider) rather allowing us to feast on some delicious flies (which would be usable knowledge I guess?). Hence the title of the post: unweaving the conceptual web.
Picture above is an illustration for Dante's Purgatorio 12 by Gustave Doré, showing the meeting of Dante and Arachne.
Before I start examining some cases of this that I've found in the social sciences, I'd like to visit the ancient Greek myth of Arachne, a great weaver, who boasted that her skill was greater than even that of Minerva, the goddess of wisdom, strategy and weaving among other things. Here's a brief summary of one variant of the myth I lifted form the Wikipedia page on Arachne: When Arachne refuses to acknowledge that her skill comes, in part at least, from the goddess, Athena takes offence and sets up a contest between the two. Both are very skilled with a loom, but clearly Athena is better and swifter. Athena's weaving represents the gifts that Olympians have granted humans and showed four separate contests between mortals and the gods in which the gods punish mortals for setting themselves as equals. Arachne's weaving depicts ways that the gods have misled and abused mortals, particularly Zeus' tricking and sexually abusing of many women. Athena sees that Arachne has insulted the gods and rips Arachne's work into shreds. Arachne hangs herself. Moved to mercy, Athena bids Arachne life...turning her into a spider and cursing her and her descendants to weave for all time.
Some quotes below are shown (adapted from a translation of Book VI of Ovid's Metamorphoses which includes this tale)
Minerva wove a portrait of herself, bearing a shield, and in her hand a lance, sharp-pointed, and a helmet on her head—her breast well-guarded by her Aegis: there she struck her spear into the fertile earth, from which a branch of olive seemed to sprout, pale with new clustered fruits.—And those twelve Gods, appeared to judge, that olive as a gift surpassed the horse which Neptune gave to man
Arachne, of Maeonia, wove, at first the story of Europa, as the bull deceived her, and so perfect was her art, it seemed a real bull in real waves. Europa seemed to look back towards the land which she had left; and call in her alarm to her companions—and as if she feared the touch of dashing waters, to draw up her timid feet, while she was sitting on the bull's back.
While Ovid's version of the has Arachne's tapestry being clearly superior, others emphasised Athena's rage at this mortal girl depicting the Gods as cruel and wicked. What seems clear from the story is that there was a strong difference of opinion between these two ladies on the relation between gods and humans. What also seems obvious is that neither tapestry seemed to fully depict the full relationship between mortals and the Olympians given that their shared history was full of both magnanimity and maliciousness. The gods were known to be both cruel and kind. The message communicated by both pieces was therefore an incomplete one, it abstracted some details in order to communicate a image of Gods being glorious and generous or wicked and petty. Similarly, in the social sciences, we use conceptual models of the world to weave a tapestry as well, one which communicates an intended message about the nature of the world. While this message can be elegant and convincing it often by the very fact there it is merely a representation of the world, not entirely honest about what it depicts. 'The map is not the territory' as they say. While Arachne's story and many other ancient tales seem to have outdated moralities, I'd argue that there is still a nugget of wisdom left in this myth. If we take Arachne's story as a metaphor for the hubris of man in striving to attain universal truths, we should remember that there is a cost for assuming that a particular model is representative of the world. A beautiful tapestry may still very well lead to ruin when it is brought to bear against the external world.
Case study 1: Modern Portfolio Theory
The above is a tapestry of sorts showing what's known in finance as a efficiency frontier. This graph is derived from a Nobel-Prize winning theory of finance known as Modern Portfolio Theory (MPT). It attempts to maximise the expected return for a portfolio for a given amount of risk by choosing a proportion of various assets. The theory is behind why GZA from the Wu-Tang clan in the famous Chappelle Show sketch yells, 'You need to diversify your bonds, nigga!'. Unfortunately while the theory is elegant and internally consistent, it is problematic for holding a few serious assumptions about the nature of risk and behaviour of investors. Firstly it assumes volatility=risk which is only true if your time horizon is short. Furthermore even if this were true, as Taleb mentions in his book, the mathematics involved rely on accurate estimations of expectation and volatility which in practice is unlikely:
'Take for now that anything estimating a parameter and then putting it into an equation is different from estimating the equation across parameters (same story as the health ,of the grandmother, the average temperature, here “estimated” is irrelevant, what we need is average health across temperatures). And Markowitz showed his incoherence by starting his “seminal” paper with “Assume you know E and V” (that is, the expectation and the variance). At the end of the paper he accepts that they need to be estimated, and what is worse, with a combination of statistical techniques and the “judgment of practical men.” Well, if these parameters need to be estimated, with an error, then the derivations need to be written differently and, of course, we would have no paper— and no Markowitz paper, no blowups, no modern finance, no fragilistas teaching junk to students. . .'
This sort of understanding of risk and the strategy of managing risk facilitated by this model of the world pushes people to take more open positions without a consideration of extreme risks. By only modelling risk in Gaussian terms (as a statistical bell curve) it only expresses risk in terms of 'average risk' which is highly problematic if a market is defined by high degrees of uncertainty. When an extreme event like the 2008 financial crisis happened, a lot of investors lost a great amount of wealth, partly because they were depending on a view of risk which didn't reflect reality. Their epistemological hubris led to a punishment doled out by the market (although perhaps not as bad as being turned into a spider).
The above is a tapestry of sorts showing what's known in finance as a efficiency frontier. This graph is derived from a Nobel-Prize winning theory of finance known as Modern Portfolio Theory (MPT). It attempts to maximise the expected return for a portfolio for a given amount of risk by choosing a proportion of various assets. The theory is behind why GZA from the Wu-Tang clan in the famous Chappelle Show sketch yells, 'You need to diversify your bonds, nigga!'. Unfortunately while the theory is elegant and internally consistent, it is problematic for holding a few serious assumptions about the nature of risk and behaviour of investors. Firstly it assumes volatility=risk which is only true if your time horizon is short. Furthermore even if this were true, as Taleb mentions in his book, the mathematics involved rely on accurate estimations of expectation and volatility which in practice is unlikely:
'Take for now that anything estimating a parameter and then putting it into an equation is different from estimating the equation across parameters (same story as the health ,of the grandmother, the average temperature, here “estimated” is irrelevant, what we need is average health across temperatures). And Markowitz showed his incoherence by starting his “seminal” paper with “Assume you know E and V” (that is, the expectation and the variance). At the end of the paper he accepts that they need to be estimated, and what is worse, with a combination of statistical techniques and the “judgment of practical men.” Well, if these parameters need to be estimated, with an error, then the derivations need to be written differently and, of course, we would have no paper— and no Markowitz paper, no blowups, no modern finance, no fragilistas teaching junk to students. . .'
This sort of understanding of risk and the strategy of managing risk facilitated by this model of the world pushes people to take more open positions without a consideration of extreme risks. By only modelling risk in Gaussian terms (as a statistical bell curve) it only expresses risk in terms of 'average risk' which is highly problematic if a market is defined by high degrees of uncertainty. When an extreme event like the 2008 financial crisis happened, a lot of investors lost a great amount of wealth, partly because they were depending on a view of risk which didn't reflect reality. Their epistemological hubris led to a punishment doled out by the market (although perhaps not as bad as being turned into a spider).
Cast Study 2: Modernity and the Origins of the Nation-State
As the old cliché goes, you can't know where you are going until you know where you have been. Like most aphorisms it isn't actually true in all circumstances and shouldn't be taken to an extreme (aphorisms are a classic heuristic). Knowing the origin of something can shed light on the nature of a thing or an idea, but at some level of specificity it begins have increasingly diminishing returns. When social scientists look through the past to identify the movements of history: the rise and fall of civilisations or the origins of such complex social phenomena like modernity or the nation-state, they have a tendency to spend an inordinate amount of effort and time on neatly setting a conceptual boundary between one part of human history and another. The reasoning behind this is fairly reasonable, it is difficult to treat history as a whole. The very basis behind analysis is that we break down something into parts in order to facilitate a greater understanding of each part and eventually the whole entity. Thus we create demarcations in time, dividing classical from medieval, industrial from agricultural.
A particularly fuzzy boundary is over the rise of modernity and the origin of the nation-state. Reliable old Wikipedia defines modernity referring to a historical period marked by a move from feudalism (agrarianism) towards capitalism, industrialisation, secularisation, rationalisation, the nation-state and its associated institutions. It's a big old mess of a concept as far as I'm concerned considering it's individual constituents are all fairly complex phenomena themselves. For example, at what point was the world a modern one by industrial standards? When the most of the world's production was a result of industrial processes? Such a change would have largely been contained to European nations considering the effects of industrialisation and its diffusion did not happen overnight. What about something like the modern state? Is there really a clear line in which we can say that a state took on modern characteristics? A professional bureaucracy doesn't appear overnight, it takes a variable amount of time to develop. These sorts of changes are considered by modernist scholars of nationalism to be prerequisites of nationalism and accordingly the nation-state. Given that these trends developed gradually over time, it seems difficult to assess a specific point in human history where the nation-state emerged. You'd be surprised to find that, despite this, many scholars have spent a good amount of time debating 'when is the nation?' and 'when is the nation-state?' as central questions in the study of nationalism. Answers usually revolve around England, Netherlands or France as being candidates for this distinction and for the most part these academics argue their case coherently and at time skilfully. The differences between their answers lies in two major difficulties:
The modern state system did not suddenly emerge out of the series of treaties grouped under the Peace of Westphalia in 1648, it would be ludicrous to think so. A regional system of political and cultural interaction does not alter itself at that sort of pace. This much should be obvious. Even if we take the argument that these treaties set a foundation for the emergence of the state system then that does not establish credible reason for it to be considered the starting point of IR studies. There are numerous things which provided the foundation of the state system, it's just a convenient but arbitrary marker which allows for academics to limit the scope of their studies to a discrete period of time. The same sort of heuristic is being used in studying the origins of nationalism. The only issue however is that while in IR, the Peace of Westphalia is generally not a major concern of most academics, in the study of nationalism the origin's of the nation are are a central concern. My view is that this probably shouldn't be the case, either we accept a certain date (or range of dates) as a marker for 'the beginning of the nation' or we acknowledge that it's an unnecessary conceptual boundary. Scholars would be free to investigate the idea of the nation in ancient Hebrew or medieval Europe while still acknowledging that the conditions which bring about the idea of nation are more prominent in a particular period of time (modernity).
A particularly fuzzy boundary is over the rise of modernity and the origin of the nation-state. Reliable old Wikipedia defines modernity referring to a historical period marked by a move from feudalism (agrarianism) towards capitalism, industrialisation, secularisation, rationalisation, the nation-state and its associated institutions. It's a big old mess of a concept as far as I'm concerned considering it's individual constituents are all fairly complex phenomena themselves. For example, at what point was the world a modern one by industrial standards? When the most of the world's production was a result of industrial processes? Such a change would have largely been contained to European nations considering the effects of industrialisation and its diffusion did not happen overnight. What about something like the modern state? Is there really a clear line in which we can say that a state took on modern characteristics? A professional bureaucracy doesn't appear overnight, it takes a variable amount of time to develop. These sorts of changes are considered by modernist scholars of nationalism to be prerequisites of nationalism and accordingly the nation-state. Given that these trends developed gradually over time, it seems difficult to assess a specific point in human history where the nation-state emerged. You'd be surprised to find that, despite this, many scholars have spent a good amount of time debating 'when is the nation?' and 'when is the nation-state?' as central questions in the study of nationalism. Answers usually revolve around England, Netherlands or France as being candidates for this distinction and for the most part these academics argue their case coherently and at time skilfully. The differences between their answers lies in two major difficulties:
- Definitional disagreements between what criteria is crucial to be considered a nation-state and to what degree does a polity need to possess these characteristics in order to qualify.
- Difficulty in assessing a mind-set or belief system of historical people en masses given that most primary sources are produced by learned people and elites.
- Reformed the Imperial Constitution to create non-violent processes for adjudicating religious disputes;
- Reduced the authority over religious matters accorded to German princes in the 1555 Peace of Augsburg; and
- Generally revitalized the Empire as a supranational political entity.
The modern state system did not suddenly emerge out of the series of treaties grouped under the Peace of Westphalia in 1648, it would be ludicrous to think so. A regional system of political and cultural interaction does not alter itself at that sort of pace. This much should be obvious. Even if we take the argument that these treaties set a foundation for the emergence of the state system then that does not establish credible reason for it to be considered the starting point of IR studies. There are numerous things which provided the foundation of the state system, it's just a convenient but arbitrary marker which allows for academics to limit the scope of their studies to a discrete period of time. The same sort of heuristic is being used in studying the origins of nationalism. The only issue however is that while in IR, the Peace of Westphalia is generally not a major concern of most academics, in the study of nationalism the origin's of the nation are are a central concern. My view is that this probably shouldn't be the case, either we accept a certain date (or range of dates) as a marker for 'the beginning of the nation' or we acknowledge that it's an unnecessary conceptual boundary. Scholars would be free to investigate the idea of the nation in ancient Hebrew or medieval Europe while still acknowledging that the conditions which bring about the idea of nation are more prominent in a particular period of time (modernity).
Case Study 3: Ring species
In biology, the idea of a speciation (the origin of new species) allows scientists to define at what points an organism becomes distinct from another similar organism in a way that is not linked to morphology but to genetics. It is an example of how academics create discrete categories as a heuristic. This definition generally relates to the ability of a population to interbreed. The existence of ring species however presents a challenge to this.
The diagram above (Self-published work by EnEdC) shows a number of natural populations along a cline (a gradual change in conditions which gives rise to slightly different characteristics predominating in the organisms that live along it). Such variation may occur in a straight line (for example, up a mountain slope) as is shown in A, or may bend right around (for example, around the shores of an ocean), as is shown in B.
In the case where the cline bends around, populations next to each other on the cline can interbreed, but at the point that the beginning meets the end again, as is shown in C, the differences that have accumulated along the cline are great enough to prevent interbreeding (represented by the gap between pink and green on the diagram). The interbreeding populations in this circular breeding group are then collectively referred to as a ring species. All that distinguishes ring species from two separate species is the existence of connecting populations - if enough the connecting populations within the ring die off to sever the breeding connection, the 'end's of the rings will be recognized as two distinct species.
The problem is whether to categorise the whole ring as a single species (despite the fact that not all individuals can interbreed) or classify each population as a distinct species (despite the fact that it can interbreed with its near neighbours. The idea of species does not actually exist in reality, it is simply as concept that we use in order to help understand a particular set of problems in a given context. The problem which arises is because species as a category of understanding serves two purposes:
In biology, the idea of a speciation (the origin of new species) allows scientists to define at what points an organism becomes distinct from another similar organism in a way that is not linked to morphology but to genetics. It is an example of how academics create discrete categories as a heuristic. This definition generally relates to the ability of a population to interbreed. The existence of ring species however presents a challenge to this.
The diagram above (Self-published work by EnEdC) shows a number of natural populations along a cline (a gradual change in conditions which gives rise to slightly different characteristics predominating in the organisms that live along it). Such variation may occur in a straight line (for example, up a mountain slope) as is shown in A, or may bend right around (for example, around the shores of an ocean), as is shown in B.
In the case where the cline bends around, populations next to each other on the cline can interbreed, but at the point that the beginning meets the end again, as is shown in C, the differences that have accumulated along the cline are great enough to prevent interbreeding (represented by the gap between pink and green on the diagram). The interbreeding populations in this circular breeding group are then collectively referred to as a ring species. All that distinguishes ring species from two separate species is the existence of connecting populations - if enough the connecting populations within the ring die off to sever the breeding connection, the 'end's of the rings will be recognized as two distinct species.
The problem is whether to categorise the whole ring as a single species (despite the fact that not all individuals can interbreed) or classify each population as a distinct species (despite the fact that it can interbreed with its near neighbours. The idea of species does not actually exist in reality, it is simply as concept that we use in order to help understand a particular set of problems in a given context. The problem which arises is because species as a category of understanding serves two purposes:
- To help categorise and identify organisms
- To help understand evolutionary processes