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Flamebait: “Mathiness” in economics and political science

Political scientist Brian Silver points me to his post by economist Paul Romer, who writes:

The style that I [Romer] am calling mathiness lets academic politics masquerade as science. Like mathematical theory, mathiness uses a mixture of words and symbols, but instead of making tight links, it leaves ample room for slippage between statements in natural versus formal language and between statements with theoretical as opposed to empirical content.

Also some thoughtful discussion by Leopoldo Fergusson, who writes:

In empirical work there are phenomena akin to mathiness, and similar risks. Mathiness stems from certain obsession, healthy to some extent, with formal economic analysis. Similarly, in empirical work many risks arise from a healthy concern about being more rigorous when analyzing data . . .

Economists (social scientists in general) obsessed with identifying the causal effect (yes, it is redundant and yet we love it) can fall into the trap of studying comparatively minor problems . . .

In his (otherwise great) article on writing advice for PhD students, John Cochrane asks: “What are the three most important things for empirical work?” His response: “Identification, Identification, Identification”.

Wrong. The most important thing, always, is that we tackle an interesting question. . . .

Regarding the general problem of “mathiness” serving as a deterrent to research communication in economics, this is an interesting point, especially in that in many ways political science has gone in the opposite direction. Back when I was getting my Ph.D., there were not many “political methodologists,” and there was a large overlap with the formal theorists. Game theory ruled, and the people who were considered the top methodologists were aping econometricians. But the field was young and malleable enough that things opened up: “formal theory” became a bit of a backwater (at least from my perspective) and statistical modeling and graphics became more popular. So, sure, math is cool, but it’s a rare work of political science that uses math to exclude dissenters.

Also I was amused by Romer’s earlier post, “Ed Prescott is No Robert Solow, No Gary Becker.” As far as I can tell, Gary Becker was no Gary Becker. As for Solow, I only saw him once, in a talk at MIT 30 years ago where he anti-impressed me by making an offhand swipe at how he would cut funding for Amtrak—I guess he thought all those highways were just free.

Silver replied with some background of his own:

I entered grad school in 1965 and started out as a “Russian area specialist.” That my dissertation was largely a quantitative study of ethnic assimilation using census data was very different from the norm that was established at the major Russian area centers at Harvard and Columbia as well as the significant ones elsewhere. When I applied for a Foreign Area Fellowship as well as a year of study abroad through IREX, the interview committee asked me about my thesis. I told them I was studying ethnic assimilation by minority nationalities in the Soviet Union. The immediate question: “WHICH nationality?” My answer: “all of them.” It shocked them that anybody could try to do that! (I got the fellowships.)

Only when the Soviet system began to fall apart did this subfield begin to draw a lot of young scholars into it who applied a wide array of methods, including quantitative, to study the post-Soviet transition. About a third of my research was essentially “demographic,” and not obviously political. Today there’s practically nobody in US doing this work concerning the post-Soviet region. There is, however, something of a normal demographic science now within Russia — but one that treads very carefully and doesn’t deal with some of the issues that were among the foci of my research (language and ethnic identity change, bilingual education policy, etc.).

For the most part the “comparativists” at Wisconsin—the faculty—were qualitatively oriented. But back in 1965 we got to cut our data analysis teeth in the introductory mass political behavior course by analyzing the Almond-Verba data, which had just been released. So some of us comparativists learned to do quantitative data analysis—and multi-country research. Nobody taught formal theory there at the time. When I asked one of the comparative faculty why this was so, he quickly responded, “We don’t believe in it.” But they did believe in data analysis, and so some of us comparativists got decent training even in political science, and a few (e.g., Doug Hibbs, who was in my UW cohort) took econometrics from Goldberger.


  1. hjk says:

    I’m not sure to what extent this discussion captures what Romer means by ‘mathiness’. Does this align with
    > but instead of making tight links, it leaves ample room for slippage between statements in natural versus formal language and between statements with theoretical as opposed to empirical content

    What is your interpretation of what Romer means by the term mathiness? What does and doesn’t count?

  2. Anonymous says:

    Hmmm …. lets review the Ultimate List of Credibility Destroying comments:

    (1) Excel graphics are the best and I use nothing else.
    (2) Amtrak is worth every penny taxpayers spend to subsidize it.
    (3) Chairman Mao was a true humanitarian, but not as much as Stalin.
    (4) Socks and sandals are a must for any gentlemen.
    (5) Frequentism fails because it hasn’t been taught right yet.

    You come it at #2 Andrew.

    • Andrew says:


      I did not say #2. I should perhaps clarify that Solow seemed to be recommending that the subsidy be cut to zero, not based on any specific issues on Amtrak (you can search this blog for Amtrak to hear what I think of them) but under some general principle of economics under which public funding for railroads is bad but public funding for asphalt roads is to be unquestioned.

      As for the others:

      1. Solow’s speech predated Excel. I suspect he’s too old to be making his own graphs.
      3. I don’t know where Solow stands on Mao or Stalin. I suspect they’re a bit too far to the left for him.
      4. I don’t remember but I’m pretty sure Solow was wearing socks and dress shoes.
      5. I have no idea where Solow stands on frequentism but I’d guess he had a classical statistical education and hasn’t thought much about statistics since.

  3. Fernando says:


    It seems to me Romer’s critique is not against math but against mathiness passing off as math.

    Just like fake jewelry to pretend one is rich, so mathiness to pretend something is rigorous and scientific.

    PS not clear in your reaction whether you are criticising math in general.

  4. Richard McElreath says:

    There’s something to this critique, but we’re always negotiating a line between mathiness and the sloppy “nuance” that goes on in other social sciences. There are risks on both sides. So perhaps a good antipode to Romer is Kieran Healy’s recent “Fuck Nuance” (PDF):

  5. Rahul says:


    What do you mean by “using math to exclude dissenters”? Any examples?

    e.g. If my study concludes that “Homeopathy is bogus” & say there are dissenters, isn’t using math to prove them wrong A Good Thing?

    • Dale says:

      I can’t speak for Andrew, but I wholeheartedly believe that economists use math to exclude dissenters – often without even knowing they are doing it. Much of the edifice of economic theory – efficiency, for example – is built upon mathematics. There is nothing wrong with the math itself, and it does further understanding of how markets do (and don’t) work. But when the math (which can be quite intense) ends up showing things like “health insurance is inefficient” it does exclude most dissenters who don’t have the math background to understand the argument. In this particular case, the argument boils down to people receiving medical care that costs more than they are willing to pay for it (yes, it’s more complicated than that, but this is the essence of the inefficiency argument). Much of the public (potential dissenters) will be lost in the math and never understand the essential argument. I would call this “mathiness.”

      • Rahul says:



        So, are you saying that the “mathy” argument itself is sound? Or not even that? i.e. Is it a sound argument that’s hard to communicate? Or is the argument itself flawed?

        Or are you saying that the argument is sound but the math is a distraction in the sense that the same conclusions could have been reached without recourse to math or at least not as complicated as the math that gets used?

        • Dale says:

          The argument is not based on evidence. It is based on the assumption that the proper way to value health care is the same as the way markets value other goods – based on willingness to pay. Rather than argue for that particular measure (which many people might not accept), economists generally assume that is the correct measure and then, via considerable mathematics, prove various things (such as the inefficiency of government provided health care, and perhaps even the inefficiency of health insurance itself). The mathiness ensures that much of the public has no idea what is being assumed. And, I believe, many economists are not even aware there is a problem or that their assumption might be questioned.

          • Ming says:

            Tangental to the main discussion at hand, perhaps your views stem from the literature you have read or the economists you have conversed with. However, the entire field of health economics does not consider the welfare economic framework to be infallible, or the only way to analyze health related issues. Arguably, health economics is its own subfield, and one that is fairly interdisciplinary in my opinion, precisely because economists recognized (e.g., Kenneth Arrow’s 1963 paper: that health and health care may be different from other goods, in addition to the failure of assumptions that weakens the conclusions one may draw from standard welfare economic analysis. If you are interested, Hurley (2000) ( offers an excellent survey of the frameworks that health economists use to analyze health related issues such as medical care insurance and it is framed in a way to highlight the differences between the welfarist (i.e., standard economics) and extra-welfarist approaches.

            • Dale says:

              To be sure, there are exceptions. Virtually every field of economics has some alternative views. But let’s not kid ourselves about the prevailing paradigm used in economics. In health economics it is the welfarist approach – I’d guess that over 90% of the published work uses that approach and most of that is characterized by “mathiness.”

              • Ming says:

                Certainly, health economists are still economists by training, for the most part. Again, perhaps the differences in our views are coloured by our own experiences: the economics department where I am currently studying at is comprised of faculty members that are likely more sympathetic to extra-welfarist views in health economics.

                Nevertheless, I disagree with your statement that economists who investigate health related issues base their analysis solely “on the assumption that the proper way to value health care is the same as the way markets value other goods – based on willingness to pay.” Assuming that the standard curriculum in health economics does not vary significantly, both undergraduate and graduate, the distinction between health and other standard economic goods is the very first topic one would be exposed to. If health economists are not socialized to strongly consider this caveat, they are at least aware that, absent a plausible justification, such an assumption will be heavily scrutinized and questioned by some of their peers and academics in related fields, the public notwithstanding.

                Even then, recent economic research on health insurance and its (in)efficiency with regards to utilization (e.g., the Oregon Health Insurance Experiment) is more empirical in nature where the welfarist/extra-welfarist distinction does not affect the statistical analysis, but may colour the subsequent discussion of results. However, a layperson with the appropriate statistical background can interpret the results and come to their own conclusion.

                Back to the post, I agree that economics as a field has a communication problem with the public, but my impression after reading Romer’s article is that his grievance is with the academic field rather. Specifically, my understanding is that it has to do with the disconnect between the written/verbal claim and its mathematical representation that should corroborate the claim but does not either because of mistakes, a lack of understanding with regards to the math employed in the first place, or a deliberate attempt to obfuscate from even other academics in the pessimistic scenario. That would be a different issue than, say, the average layperson not understanding the technical details of certain economic research due to a lack of field-specific knowledge.

        • David Tate says:

          I’d say that the argument is formally sound, but either relies on assumptions that would be quite controversial if stated in non-mathy terms, or expresses conclusions that don’t quite mean what they seem to if you translate them back into non-mathy terms.

          In the example given, it is formally true but unimportant that health insurance is inefficient. “Inefficient” is being used in a technical sense. Nobody who favors universal health insurance as a matter of public policy is bothered by this kind of inefficiency, because they perceive the long-term societal benefits to be worth the (admitted) costs — but phrasing the argument and conclusion in mathy terms preempts counterarguments of that kind by those who can’t follow the math.

          • Rahul says:

            Thanks for clarifying.

            But that means that the models in question here are plain bad. i.e. A model with poor assumptions is a bad model, period. The issue goes beyond social sciences. I cannot set up a reasonable aircraft aerodynamics model assuming in-viscid flow.

            The key question is: Why do other economists let them get away with it? Surely there’s other people who understand the math enough to see the bad assumptions?

            • cheese_d says:

              This is fairly close to a technical minefield here… There’s a very popular, in econ circles, quote from Milton Friedman that says almost the opposite.

              ‘The relevant question to ask about the “assumptions” of a theory is not whether they are descriptively “realistic,” for they never are, but whether they are sufficiently good approximations for the purpose in hand. And this question can be answered only by seeing whether the theory works, which means whether it yields sufficiently accurate predictions. The two supposedly independent tests thus reduce to one test.’)

              Economists have frequently invoked this to justify bad models. (I’d suggest a Bayesian framework to solve the riddle of the quote, whereby the realism of the assumptions influences your prior, and then you update the prior over time as more and more predictions are made and their results come in.)

              Bigger points are that much of economics, and social ‘sciences’ more generally, have seemed to focus on explanatory analysis and not clearly testable predictions (the core of science, as I thought it).

              As for welfare and efficiency analysis in econ… the theoretical underpinnings of using $ metrics and talking about deadweight losses, etc., as I recall, rely on either Pareto efficiency, or Hicks Kaldor criteria. Both of which rely on magical thinking as they don’t actually work, which is troubling for pretty much any comparative statics analysis that is normative in nature.

              To the extent economists use math to make useful predictions, great. But that seems to be a small slice of their craft these days.

            • Hasdrubal says:

              Part of the problem is that, fundamentally, the decision of what is “important” cannot be determined by an economic model. The economic model can tell you that 3rd party payer insurance leads to higher consumption and thus higher prices; higher training and licensing requirements lead to a lower supply of doctors, higher prices, but suffers from diminishing marginal returns on quality; more stringent drug testing requirements lead to fewer Type II but more Type I errors; high deductible insurance policies and price advertising leads to consumers assessing whether it’s worth it or not to get a treatment and lower prices.

              But I have to decide which I think is more important: The fundamental fairness that anyone who sprains an ankle can go to a world class emergency room to have it treated by a doctor with 18 years of schooling and training without having to consider the expense. Or the fundamental efficiency of anyone who sprains an ankle deciding whether it’s worth it to them to go to the emergency room immediately, go to a doc in a box and be treated by an LPN, just walk it off and reassess it in a couple days, or something in between.

              Economics can tell us the tradeoffs (but not with perfect accuracy, just more or less), so we can make an informed decision. But we have to decide which is most important and actually make that decision.

              This is where mathiness (and scientism) comes in, imo: Attempts to use economics; to dress up theory in the trappings of math and science; attempts to get overly precise results in an attempt to make that final decision seem like the only right decision. Mathiness and scientism try to make economic research portray economic models like fluid flow models: That wing will either create enough lift or it won’t. But economic models really more like weather forecasts: It’s likely (but not guaranteed) to be between 58 and 62 and dry today, but it’s up to you to decide if you should wear a jacket.

          • Ming says:

            I am going to assume the statement under discussion is that “government provided health care is inefficient,” where government provided health care is deemed to mean some form of government-provided health insurance and inefficiency is deemed to mean utilization above what is deemed appropriate based on relevant medical evidence.

            Certainly, the simplest argument from a welfare economic standpoint (first put forth by Mark Pauly (1968) in response to Arrow’s paper above) is that health insurance does induce inefficient consumption, and therefore leads to welfare loss. However, because the standard assumptions of welfare economics break down when it comes to analyzing health and health care, there is much disagreement as to how large those losses are (or whether there are benefits that are not captured in the standard model, such as Nyman (2003)’s access motive).

            More importantly, to analyze publicly provided health insurance on its own does not capture the whole picture, as such a design inevitably brings in considerations of health care financing including allocative efficiency (should parallel private insurance be allowed), access (wait times being a hot topic, for example), system-wide technological investment, etc. Without empirical evidence, it is a priori fairly difficult to definitively conclude whether a specific alternative health insurance system is a net positive to a particular society compared to some other alternative/status quo (e.g., cultural differences between the U.S. and another country could mean favouring different aspects of health care to be of a greater priority).

        • Kyle C says:


          Another example of mathiness that came up in discussions of the Romer paper are models that purport to show that “technology” drives long-term economic growth rates. It turns out that this “result”(which seems to suggest that countries should invest in “technology”) is essentially tautological, because the math term for “technology” in the models doesn’t mean anything, it’s just a named residual, the part of the growth that other variables in the models don’t explain.

  6. Dale says:

    I got timed out, but the short version is I agree with David.

  7. AJG says:

    As an econ student, I think it’s important to draw a distinction at least between microeconomics and macroeconomics. I find macroeconomics less empirically convincing because I think it does have a tendency to get caught up in, maybe not exactly mathiness, but unproductive math. It’s harder for me to see the connection between the terms and concepts in macro and real-life economic experience than it is for micro.
    There’s a lot of concern in micro for identification, and I think it’s the right direction for the field. It’s just way too easy to wind up with regressions that look good at first, but everything turns insignificant once you get good identification. So we’re very aware of the risks of false positives when measuring, say, policy effects. I think that’s productive math- it is useful at helping us learn about why our models fall short of reality and how well our empirical techniques can bridge the gap. There are some areas within micro where identification is harder to get than others, and it might be true that some papers go overboard on robustness checks and things like that, but you don’t have to read those parts.
    It’s two different questions to think about mathiness in the sense of being overzealous about proofs that are mostly just theoretical goofing off, and mathiness about trying to get causal interpretations of empirical work. The first might often be a waste of time, but I think the second one is usually worth doing.
    I’m also a little unclear on this health insurance and efficiency argument. I thought the big question was moral hazard, not efficiency? Those aren’t really the same thing, and a lot of the recent lit I have seen has been related to pricing and market power anyway.

    • Ming says:

      The conclusion from a standard economic analysis of the (ex post) moral hazard problem in health insurance is that a high level of insurance induces over-consumption of health care (i.e., marginal social benefit < marginal social cost), and consumption over the optimum (in the theoretical framework) can be characterized as inefficient in the lay sense. Of course, the extent of the actual associated welfare loss is still a hotly debated issue and how you perceive the issue likely depends on how severe you believe the violations of the standard assumptions are.

      • Dale Lehman says:

        While this is a bit off the original topic, I have never found this argument convincing (Nyman is the only one I have seen similarly upset with it). Moral hazard does indeed imply that people will consume more health care if insured – but I don’t see how this is overconsumption or inefficient (speaking of privately provided care here). Insurers certainly take the moral hazard into account and voluntarily enter contracts with the insured. Given that the contracts are voluntary, I don’t see that the care is too large.

        If I decide to read 100 psychology articles each week if you will pay me $1000 (I’d need higher!) and you agree, how is it inefficient – and, recognize that I will read 0 articles without the payment?

        • Ming says:

          The welfare loss here is simply a result from a standard welfare economic framework. There is very little disagreement that ex post moral hazard (e.g., by virtue of being insured an individual would obtain more care than is necessary) exists among health economists, but because the original argument invokes the neoclassical assumptions the extent of its significance is still debated; Nyman is not the first or only person to challenge the welfarist conclusion, and I do sympathize with his argument which explicitly and correctly reminds us that health care is a derived demand (i.e., no one would voluntarily undergo heart surgery if there is no need). While the RAND Health Insurance Experiment (given its price tag, we will probably never see another one on its scale) did shed much light on this issue, some may certainly opine that the response of insurers and policymakers may be overzealous in some regard.

          Certainly, the moral hazard problem has a lesser impact on private insurers (though there is obviously a response to the issue together with providers, e.g., HMO’s in the US). However, you must consider the other stakeholders in the health care system. For individuals, over-consumption of health care is benign at best and may be detrimental to their health in the worst case (e.g., iatrogenic complications, given the inherent uncertainty of medical care treatments). In addition, pecuniary costs from what may be unnecessary care aside, providers also incur other opportunity costs as a result (e.g., physician time that may be better spent providing other necessary care, MRI wait times, etc.). Also, because all developed countries are looking to “bend the cost curve” in the long run, tackling the issue here is non-trivial.

          Since there are many in the U.S. that wish the national conversation would turn towards a single payer/universal design, the (demand side) moral hazard issue then comes to the forefront since a public insurer would essentially be on the hook to reimburse all health care provision under coverage, making the cost issue (pecuniary and time) all the more pertinent.

          • Dale says:

            I wish you would stop expanding the discussion. Let’s leave publicly provided care and/or insurance out of it. Certainly we agree that moral hazard is real – people with insurance seek more care than they would without insurance. Let’s leave care that might pose a danger to them out of it as well – there is a huge literature on whether people make decisions that are in their own interests or not. Let’s also leave out the issue of bending the cost curve – while extremely important in many respects it is somewhat off this issue here.

            You still appear to maintain that somehow there is an inefficiency in the moral hazard associated with private insurance. I simply do not see it. This is where mathematics can actually help the discussion. I don’t believe the math can support the argument that moral hazard is an inefficiency in privately provided voluntary health insurance – without invoking externalities, irrational behavior, or some other tangential topic. I believe the continued confusion on this is related to the issue of mathiness – excessive use of mathematics has obscured the argument to the point that it is difficult to parse. And, worst of all, it serves a particular ethical and political agenda to not be clear about the arguments. Most economists are happy to have any “analysis” that suggests that government provision of health care or health insurance is a “bad” thing.

            I don’t expect you to agree, but I am reluctant to let you have the last word here.

            • Ming says:

              The inefficiency from the standard model is fairly straightforward. As a motivating example, if a person consumes $1000 worth of health care to restore themselves to a healthy state absent any insurance, and consumes $2000 worth of health care to do the same under insurance, the extra consumption here is the result of ex post moral hazard in the standard model. It is inefficient and wasteful because $1000 worth of health care is what was necessary to restore the individual back to a healthy state, and the extra consumption (which does not have to be expressed in monetary terms; it could be number of specialist visits, for example) could have been reserved for other necessary care. Of course, in practice this is not so clear cut (lack of data regarding individual preferences, imperfect markets, etc.).

              On the contrary, it is precisely the case that because there are externalities, individuals may appear to act irrational (the more plausible explanation being that there is a huge degree of information asymmetry between the consumer and the provider of health care), etc., that invalidates the assumptions behind a standard economic analysis of health insurance and therefore renders the moral hazard issue a topic of debate in the first place. If those were not important considerations, then there would be a clear conclusion in favour of the welfarists: health insurance induces inefficient over-consumption and therefore leads to welfare loss. Fortunately, that is not the case.

              If you are interested in the theory behind the standard economic analysis of insurance markets and the conversation within the field regarding the issue, feel free to peruse the following resources. Contingent on some economic background, the math involved is actually not at all difficult; college-level intermediate calculus (maybe less) is more than sufficient to tackle the content:

              Standard private insurance model with imperfect information: Rothschild and Stiglitz (1970)

              Arrow (1963)’s seminal paper that opened up the field essentially outlined reasons why health and health care are different:

              Pauly’s (1968) response that opened up the moral hazard debate:

              Section 3 of Cutler and Zeckhauser (2000) has a bit more on the theory:

              From there, you can simply go with a citation search (e.g., Google Scholar) and fall down the rabbit hole of responses. Since you are aware of Nyman’s recent perspective i will not repeat that here.

              One last thing: I neglected to address your point regarding the insurers voluntarily contracting with individuals, firms, etc. The problem with moral hazard is precisely that insurers cannot completely account for it, because they are unable to observe whether an individual’s behaviours/motivations changed after insuring (ex post moral hazard is synonymous with “hidden action” in the literature). Of course, if they had more individual information they would be better able to account for this, but then we run into selection issues with insurers themselves (e.g., cream-skimming and choosing those that have the lowest risk profiles to include in the risk pool). This was an issue that the PPACA in the US attempted to tackle with its community rating rules and in general such rules should attempt to strike a balance between positive selection (cream-skimming) and adverse selection (unsustainable risk pools).

              • Dale Lehman says:

                Your result hinges on the assumption that the demand for health care is unaffected by insurance – the price (at the point of service) is reduced and more care is demanded. However, income effects can destroy this result and income effects could be quite large, particularly for catastrophic health care. Then the issue is ambiguous. If you really believe that moral hazard makes insurance inefficient, then perhaps we should outlaw insurance.

                Note that this is different than the issue of whether moral hazard is welfare-decreasing. Undoubtedly, the world would be more efficient if there were no moral hazard. It would also be more efficient if there was no disease. Given that both exist, the only issue is whether insurance (I’m speaking of private insurance here) increases or decreases that inefficiency.

                Back to Andrew’s original point – I think this literature is a perfect illustration of mathiness. The articles you cite are not particularly complex (for economics articles) but are more complex than necessary and more inaccessible to the many people that have a significant interest in this subject.

  8. Mark Hadfield says:

    “Remember, Isaac Newton believed in leprechauns!”

    Glorious! I’d always thought that when marshalling facts in support of an argument, one should strive above all for correctness. I was wrong.

    Isaac Newton did devote a lot of effort to studying alchemy. But that wouldn’t have sounded nearly as good.

    • Andrew says:


      That’s just humorless and rude of you. For the benefit of any readers here in the comments, here’s the actual quote from my linked blog entry:

      Remember, Isaac Newton believed in leprechauns! Well, not really, but you get my point.

      And, by the way, I’m neither a lawyer preparing a case nor a high school student writing a position paper. I don’t “marshal facts in support of an argument”; I look at facts and make arguments without regard to trying to prove a point, I let reality guide my reasoning. Isaac Newton was undoubtedly brilliant and Isaac Newton believed some goofy things, hence “the smart people fallacy” which I discussed in that linked post.

      And regarding “that wouldn’t have sounded nearly as good,” which you seem to regard as some sort of criticism: Damn straight I want my writing to sound good. It’s a little something called readability. Entertaining the readers is no sin.

      • Rahul says:

        Tangential to the point, but wasn’t there some social science meme / theory / paper that said Humans very often already have made a decision sub-consciously and most of what we think (fool ourselves?) of as following a process of “facts + reasoning guided decisions” is only post-hoc rationalization? Perhaps to make us feel better that we actually take decisions rationally and not merely on a hunch.

        Again, nothing to do with Mark Hadfield’s comment at all. Just was a thought that came to mind. Perhaps we ain’t as rational as we like to think?

      • Mark Hadfield says:

        Hi Andrew

        I think the meaning you have taken from my comment is the opposite of what I intended. The humour of the Newton-leprechauns assertion was not lost on me–quite the opposite–and any rudeness on my part was not intended.


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