Home > Uncategorized > The pseudo-scientific use of small-world models in a large world

The pseudo-scientific use of small-world models in a large world

from Lars Syll

Radical uncertainty arises when we know something, but not enough to enable us to act with confidence. And that is a situation we all too frequently encounter …

aaLLWORLD_largeThe language and mathematics of probability is a compelling way of analysing games of chance. And similar models have proved useful in some branches of physics. Probabilities can also be used to describe overall mortality risk just as they also form the basis of short-term weather forecasting and expectations about the likely incidence of motor accidents. But these uses of probability are possible because they are in the domain of stationary processes. The determinants of the motion of particles in liquids, or overall (as distinct from pandemic-driven) human mortality, do not change over time, or do so only slowly.

But most of the problems we face in politics, business (including finance) and society are not like that. We do not have, and never will have, the kind of understanding of human behaviour which emulates the understanding of physical behaviour which yields equations of planetary motion. Worse, human behaviour changes over time in a way that the equations of planetary motion do not …

Discourse about uncertainty has fallen victim to a pseudo-science. When no meaningful quantification is possible, algebra can provide only spurious precision, while at the same time the language becomes casual and sloppy. The terms risk, uncertainty and volatility are treated as equivalent; the words likelihood, confidence and probability are also used as if they had the same meaning. But risk is not the same as uncertainty, although it arises from it, and the confidence with which a statement is made is at best weakly related to the probability that it is true.

The mistake that Viniar of Goldman Sachs exemplified as the credit crunch bit was to believe that a number derived from a “small world” model—a simplification based on a historic data set—is directly applicable to the “large world,” complex and constantly evolving, in which we live. We are both strongly committed to the construction and use of models—we have spent much of our careers in academia and in the financial and business world doing exactly those things. But that has left us aware of the limitations of models as well as their uses.

John Kay & Mervyn King

Since yours truly thinks this is a great article — as is the authors’ book Radical Uncertainty (The Bridge Street Press, 2020) — it merits a couple of comments.

To understand real world ”non-routine” decisions and unforeseeable changes in behaviour, ergodic probability distributions are of no avail. In a world full of genuine uncertainty – where real historical time rules the roost – the probabilities that ruled the past are not those that will rule the future.

Time is what prevents everything from happening at once. To simply assume that economic processes are ergodic and concentrate on ensemble averages – and a fortiori in any relevant sense timeless – is not a sensible way for dealing with the kind of genuine uncertainty that permeates open systems such as economies.

When you assume the economic processes to be ergodic, ensemble and time averages are identical. Let me give an example: Assume we have a market with an asset priced at 100 €. Then imagine the price first goes up by 50% and then later falls by 50%. The ensemble average for this asset would be 100 €- because we here envision two parallel universes (markets) where the asset-price falls in one universe (market) with 50% to 50 €, and in another universe (market) it goes up with 50% to 150 €, giving an average of 100 € ((150+50)/2). The time average for this asset would be 75 € – because we here envision one universe (market) where the asset-price first rises by 50% to 150 €, and then falls by 50% to 75 € (0.5*150).

From the ensemble perspective nothing really, on average, happens. From the time perspective lots of things really, on average, happen.

Assuming ergodicity there would have been no difference at all. What is important with the fact that real social and economic processes are nonergodic is the fact that uncertainty – not risk – rules the roost. That was something both Keynes and Knight basically said in their 1921 books. Thinking about uncertainty in terms of “rational expectations” and “ensemble averages” has had seriously bad repercussions on the financial system.

Knight’s uncertainty concept has an epistemological founding and Keynes’ definitely an ontological founding. Of course, this also has repercussions on the issue of ergodicity in a strict methodological and mathematical-statistical sense. I think Keynes’ view is the most warranted of the two.

The most interesting and far-reaching difference between the epistemological and the ontological view is that if one subscribes to the former, Knightian view –- as I would argue Kay and King have a tendency to do –- you open up for the mistaken belief that with better information and greater computer-power we somehow should always be able to calculate probabilities and describe the world as an ergodic universe. As Keynes convincingly argued, that is ontologically just not possible.

If probability distributions do not exist for certain phenomena, those distributions are not only not knowable, but the whole question regarding whether they can or cannot be known is beside the point. Keynes essentially says this when he asserts that sometimes they are simply unknowable.

John Davis

To Keynes, the source of uncertainty was in the nature of the real — nonergodic — world. It had to do, not only — or primarily — with the epistemological fact of us not knowing the things that today are unknown, but rather with the much deeper and far-reaching ontological fact that there often is no firm basis on which we can form quantifiable probabilities and expectations at all.

Sometimes we do not know because we cannot know.

  1. September 7, 2020 at 4:42 am

    I would have liked to have seen this distinction you make between epistemological and ontological views unpacked a lot more.

  2. Gerald Holtham
    September 7, 2020 at 4:07 pm

    Indeed. I agree with Kay and King of course. But I have always supposed that uncertainty was an epistemological phenomenon. Ontological uncertainty implies that God indeed does play dice. We know about quantum uncertainty but is there any evidence that it leads to random effects at the level of sensible phenomena? That we do not have the knowledge to predict the future path of a chaotic or complex system does not imply that it is not determinate. Perhaps the question is of purely philosophical interest. If we don’t know, we don’t know and it is of less consequence in the immediate future whether something is ultimately unknowable or not. My preference is to assume not much is unknowable given a few centuries to work at it. Lars, on the other hand seems to take pleasure in our invincible ignorance.

    • Yoshinori Shiozawa
      September 9, 2020 at 2:16 pm

      I stand by the side of Gerald Holtham. Lars Syll is too romantic and not realistic in his idea of economics and scientific research.

      I hope readers would not fall in the fallacy of Romanticism. Romanticists often imagine that they can get to the essence of the reality by rejecting formalism and mathematics. They are wrong as Yoshio Inoue points it in his book review of our book “A Review of on Yoshinori Shiozawa, Masashi Morioka, and Kazuhisa Taniguchi, Microfoundations of Evolutionary Economics, Springer, 2019” in EIER 2020:

      This reviewer [Inoue] once discussed that evolutionary economics has some elements in common with Romanticism in their way of thinking (Inoue (1999), chp.8). If there is something related to this book [Microfoundations of Evolutionary Economics], it is the significance of having a formal theory of evolutionary economics. Romanticism tends to regard rational or formal thinking as being shallow and inessential. As a result, Romanticism is often critical of building formal theories, and tends to have a pessimistic view on how well a formal theory works before any testing. Some Romantic thinkers have been very skeptical about theoretical understanding; The most remarkable case was probably the English historical school; W. J. Ashley, who appears to be the central figure of that school, was inclined to oppose the economic theory in general, and declared that what we can or should grasp is the uniqueness of economic phenomena in each specific place and period. Then, he created the new field of economic research, Economic History, to pursue his own style of economics, which he called “evolutionary economics” (Collini et al. (1983), chp.8).  Two [ ]s are added by the citer.

      Today, evolutionary economists are usually not as hostile to such a general understanding. On the contrary, they often try to get a general vision so as to elicit a strong feeling of “this is the Economy!” in the readers. That is the very reason we need a formative theory of evolutionary economics. If we only reject the formal theory when we try to get a general understanding of the economy, our whole economic understanding could be swallowed up by an “unstoppable torrent of imagination”(as a Romantic poet once said), which is almost the heart of Romanticism. We should not forget that the original role of formalized theories is not to profess its (so called) scientific nature, but to restrict our images from taking on a life of their own by pushing them into some kind of pattern. Having too much imagination free from any pattern risks making us believe that we have realized an economy with our unrestrained imagination which includes hopeful expectations.

      • Meta Capitalism
        September 10, 2020 at 10:43 am

        This entire effort to argue Lars is engaging in Romanticism is nothing more than a pseudo intellectual argument hiding debased ad hominem and the utter inability of Shiozawa to respond to the substance of Lars arguments. It shows his utter lack of philosophical depth and intellectual honesty. It is frankly, pathetic.
        Perhaps this is acceptable in his circle of Japanese pseudo intellectuals who confuse emotion for substance, but it lacks substance in that first it ignores the critical arguments and it does not address the logic and substance of Lars arguments. This goes to show that Shiozawa has a poor grasp of even basic logic and the use of logic in analysing arguments and only pays lip service to logic.
        That is also essentially what Holtham does when he writes, “Lars, on the other hand seems to take pleasure in our invincible ignorance.” He neither address the substance or issues raised, but simply makes an emotional appeal to I like apples you like oranges. How silly and shallow in my view.
        I think that they (Holtham and Shiozawa) are unable to discern the difference between causality and determinism and their naïve mechanistic determinism wedded to causal determinism has enslaved their imaginations.
        No surprise there as Shiozawa is attempting to model economics along the lines of 19th century physics (econophysics) when 20th century physics has moved on to more advanced experimental and philosophical understanding of causality that breaks the bond between causality and determinism (Lars knows what I am talking about).
        How sad to see such low and debased ad hominem being passed off as erudite intellectual argument. It most certainly is not.

      • Yoshinori Shiozawa
        September 10, 2020 at 2:52 pm

        Those who want to read whole text of Inoue’s review, please send me an e-mail at y@shiozawa.net .

      • Yoshinori Shiozawa
        September 10, 2020 at 4:12 pm

        There were ardent discussions in the past on the strategy that we must take in order to break down “neoclassical economics” dominance. This is one of then:

        Discussion inspired by Lars Syll’s article What is (wrong with) neoclassical economics?

        Almost all arguments were around the dictum “it take a theory to beat a theory”.

        I posted many “replies”. The following was my final “reply” to the arguments.

        February 5, 2018 at 8:58 am Reply
        I have no time to argue in detail. A paradigm change requires a new vision backed by a new theory. Please read my post February 3, 2018 at 3:41 am in a Reply to Rob Reno.

        Methodological arguments such as criticisms on methodological individualism, reductionism, emphasis on uncertainty, and lack of realism have no enough power to change the economics itself. Those criticizers must present a theory or set of theories that are free from those defects they criticize and equipped with a new vision. Lars Syll should contribute by his criticisms and orienting new generation to construct such theories.

      • Craig
        September 10, 2020 at 7:28 pm

        It DOES take another model/paradigm to replace an old model/paradigm. The current model of trying to maintain a statistical equilibrium which is both a temporal impossibility and prone to austerity for most economic agents needs to be replaced by an abundant monetary state in perpetuity that matches the interactive, integrative flowing process known as the flowing moment in the temporal universe; and that has policies implemented at strategic points in the economic/productive process that absolutely eliminate any possibility of inflation (the 50% discount/rebate policies at retail sale and at note signing). And finally also has regulations and sanctions that keep the less than rational and/or ethical agents from trying to game and de-stabilize the new model/paradigm despite its universal benefits.

      • Yoshinori Shiozawa
        September 11, 2020 at 5:35 am

        The following is some paragraphs of Yoshio Inoue (Read i.no.u.e)’s review. Although I have some reservations on what is written here, I reproduce it without my comment.

        However, for the moment, let us put that aside. What we would like to reconsider now is that the idea of rational economic man emerged in the late 18th century or the early 19th century, and from the beginning, it was self-evident that such a being did not exist in the real world. A rational man was an ideal image that a real human being should aim to be. A rational economic man was not an average positive image of real person, but a normative image of a human in modern Enlightenment thinking.

        Moreover, the central idea of that norm was an independent and autonomous individual who was free from the feudal status system. The more sophisticated and formalized claims of homo-economicus in the 20th century was just an ideal construction developed by pursuing independency and autonomy to an extreme. In that sense, we should also understand that homo-economicus was a historical being. In fact, in the modern age, the ways to make a society that is consistent with such an image of humans began to be explored. An ideal society was supposed to primarily consist of rational humans, and in turn make its members more rational. People in a modern society were not just satisfied with their given rational ability and they began to understand that they could live a much better life by developing their rationality on their own. It was a basic condition for the modern society that such individual experiences would not be denied in their real lives; there, we can find the origin of the micro–macro loop.

        The market economy was considered to be the most suitable system to satisfy these claims of modern society. It should be managed by rational humans and also could be evolved by its members becoming more rational that is, desiring more information and more intelligence, deciding their behaviors not by tradition or custom but by demand–supply calculation, conducting with a wider and longer sighted view, and so on. The market economy was a system where people could hope to improve their social positions by acquiring those rules of behavior and strengthening their competence. In short, the market economy was expected to be a system that would both presuppose and develop rationality. It can be said that a variety of theories of market economy, including the general equilibrium theory, directly and almost naïvely followed this idea of the modern age.

        Therefore, unless modern society abandons that idea of modern age, however much homo-economicus is criticized by the new trend of positive economics like behavioral economics, among others, the market economy will never be completely abandoned. Market theory has been pursued not because it has a positive ability to explain the market mechanism, but because it is suitable for the norm of modern society. Furthermore, if it really captures the true essence of market economies, we could already have grown to be more rational and more intelligent beings by simply submitting ourselves to the fow of the market economy.

  3. Yoshinori Shiozawa
    September 10, 2020 at 4:42 am

    As for making economics more relevant to large economies, see my “Reply” posted on September 9, 2020 at 10:20 am on Lars Syll’s article Do ‘small-world’ models help us understand ‘large-world’ problems?. Readers will see that an approach, more realistic than romantic, is possible.

  4. September 10, 2020 at 5:40 pm

    Lars ends at “the mistaken belief that with better information and greater computer-power we somehow should always be able to calculate probabilities and describe the world as an ergodic universe”.

    He is here falling into the epistemological trap himself. As Shannon showed and I’ve repeatedly argued, the aim of the game is not to “describe” the economy, it is to learn how to steer it. Which involves recognising real errors in the better information resulting from knowing where to look for them in the data received, and greater computer power enabling the errors to be corrected quickly, before they can do any damage. If economics wants to be a real science, therefore, it should become an information science, enabling us to pursue our aims reliably by showing us where to look for errors and how to correct them. Edward Fullbrook’s use of decimal fractions as a small-scale inverse Copernican model of decimal numbering reminds us that today’s economy takes up only a tiny bit of the space in an initially empty but adaptively evolving universe.

  5. Gerald Holtham
    September 10, 2020 at 7:51 pm

    “I think that they (Holtham and Shiozawa) are unable to discern the difference between causality and determinism and their naïve mechanistic determinism wedded to causal determinism has enslaved their imaginations.”

    I plead guilty. I do not understand the distinction being made between causality and determinism and “naive mechanistic determinism”. Determinism is determinism. I was unaware it had naive and non-naive varieties. Nobody mentioned “mechanistic”. A cause can be electrical, chemical or social depending on the category of phenomenon being studied.
    To talk of “ontological uncertainty” is either using big words carelessly or it is a denial of causality and determinism.

    I had better avoid gentle teasing in future if it is confused with low debased ad hominem argument. I had forgotten that not everyone has sense of humour.

    • Meta Capitalism
      September 10, 2020 at 11:16 pm

      It is not so much your gentle teasing as the caustic pile-on that is off-putting. If it was only gentle teasing Gerald you might consider the parroting pile-on posters who then make fallacious ad hominem arguments that Lars arguments are rooted in romanticism. Such specious arguments are for only one self-serving purpose; to hawk a book with a tissue thin veneer of pseudo-intellectualism. While not your fault, it is nevertheless used as such.
      I have not the time to untangle your assumptions — and they are naïve — about quantum physics, causation and determinism, etc., but only note you yourself often use “big words” without defining them in naïve ways (these fundamental concepts do have histories that are relevant to the discussion) in some of your more or less enlightening and insightful posts that have skirted around the meanings of causation, determinism, and the scope and limits of knowledge and uncertainty.

  6. Robert Locke
    September 11, 2020 at 8:09 am

    a product of the british empir in world of great power rivalry.

    • Robert Locke
      September 11, 2020 at 8:55 am

      Times Higher Education (THE) World International University Rankings 2020 had some damning news. Just two Japanese universities are currently in the world’s top 200, below the 2013 rankings, when there were five in that position.
      The University of Tokyo came in 36th place this year, tying with King’s College London and just behind the University of Hong Kong at No 35. Kyoto University ranked 65th, one place below South Korea’s Seoul National University. For Japan’s hundreds of public and private universities – there are a total of 604, according to a 2017 estimate – the low rankings have b’

      the tryanny of merit.

      • Robert Locke
        September 11, 2020 at 9:35 am

        What is the best school in Germany?
        Best universities in Germany 2021
        World University Rank 2021 Germany Rank 2021 University
        32 1 LMU Munich
        41 2 Technical University of Munich
        42 3 Heidelberg University
        =75 4 Charité – Universitätsmedizin Berlin
        44 more rows•Sep 2, 2020

        so best in germany only 32 world ranking.

      • Robert Locke
        September 11, 2020 at 9:54 am

        the higher the eduaional rqankings. the worse the economic performance.

  7. Ken Zimmerman
    September 26, 2020 at 5:44 pm

    Brief comments. First, placing radical in front of uncertainty is redundant. Uncertainty is uncertainty. It can only be what it is. Radical adds nothing to our understanding.

    Second, uncertainty arising from when we know something, but not enough to enable us to act with confidence is not a frequent state for humans. Rather, it is the usual state. Although humans can sometimes be quite convincing in feigning confidence, even certainty in acting. Witness the Republicans in the US Senate. Bunch of lost sociopaths holding on to “great ideals” they do not understand and cannot quite pull off.

    Third, you imply, strongly in my view that physical events and things are not uncertain. Quite the contrary. They are an example of your first premise, that uncertainty is endemic with humans. Physical events and interactions are chaotic. Our limited view does not allow us to glimpse this most of the time. One of the more interesting questions of deep space travel for humans is how will we deal with this when we encounter it? Or can we deal with it at all? Neither science nor science fiction provide much comfort here.

    Finally, economists are new to these debates. In the social sciences they have been going on for over 100 years. Anthropologists debate the role of culture in knowledge and being. In 2003, Eduardo Viveiros de Castro identified the cardinal value that, in his view, consistently guides anthropology: ‘working to create the conceptual, I mean ontological, self-determination of people[s]’ (2003: 4, 18). This was a big statement that has generated (and indeed should generate) both uneasiness and excitement. The ‘ontological turn’ in anthropology has since been strongly encouraged by some scholars who were directly inspired by de Castro (Henare et al., 2006). Henare et al. (2006), in ‘Thinking Through Things,’ argue that a genuinely ontological approach (one that does not privilege epistemology or the study of other people’s representations of what we know to be the real world, acknowledging rather the existence of multiple worlds) does not render ontology synonymous with culture. Culture, they argue, is equivalent to ‘representation:’ there is one world (reality) and many worldviews (cultures). An ontological approach on the other hand acknowledges multiple realities and worlds (beings). This distinction between ontology and culture is one of the issues at the center of the debate.

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