The Mathematicization of Economics

If one thing has changed in the last one hundred years in economics it has been the huge outgrowth in the usage of mathematics:

This is largely a bad development, for a number of reasons.

First of all layers of mathematics acts as a barrier to public understanding. While mathematics is a useful language for communicating complex ideas, those without training in mathematics will struggle to grasp what an author is trying to communicate if a paper consists mostly of equations untranslated into English. This is bad practice; it is easier to baffle with bullshit in an unfamiliar language than it is in plain English.

Second, mathematical models are always simplifications. Human action and economic behaviour is complex and unpredictable. While mathematical models can sometimes approximate a pattern quite well and so have some limited uses as toys, the complexity of human behaviour means that there are always unmodelled variables that can throw off a model’s output. Over-reliance upon or excessive faith in mathematical models can lead to bad forecasting and bad policy decisions. The grand theoretical-mathematical approach to economics is fundamentally flawed.

Third, attempting to smudge the human reality of economics into cold mathematical shackles is degenerative. Economics is a human subject. Human behaviour is not mechanical, it is not mechanistic. Physicists can very accurately model the trajectories of rocks in space. But economists cannot accurately model the trajectories of prices, employment and interest rates down on the rocky ground.

Economics would benefit from self-restraint in regard to the usage of mathematics. Alfred Marshall made some useful suggestions:

  1.  Use mathematics as shorthand language, rather than as an engine of inquiry.
  2.  Keep to them till you have done.
  3. Translate into English.
  4. Then illustrate by examples that are important in real life
  5. Burn the mathematics.
  6. If you can’t succeed in 4, burn 3. This I do often.

I hope the blowout growth in mathematics in economics is a bubble that soon bursts.

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91 thoughts on “The Mathematicization of Economics

  1. Someone once said: “Like all sciences, economics should be driven by data. For if we are not driven by data than we are just daydreaming.”
    Is mathematics a good source of data?

        • Depends on whether you use mathematics simply to observe data or you are building a mathematical model to guide future decisions. A lot of mathematical models have been built to guide future decisions, which are very dense, hard to understand. If the future events do not pan out as thought, the model is rubbish. Does economics toss out pathetic models as much as say, physics?

        • Nonlinear Dynamics sums this up very well. The output of a mathematical model is not data; it’s forecasting and interpretation. The data are the inputs, in other words the real world observations.

          I think where we were in the early 1900s — with a few well-placed mathematical expressions and equations where necessary is a much more sensible place to be than where we are now where the norm consists mostly of playing around with algebra to create complex hyper-fragile hyper-specialised models that begin by assuming away reality.

          I admit that I am not naturally gifted with mathematics, and I also admit that studying mathematics (primarily so I can understand other’s quantitative work, and do some of my own) has been very beneficial. So I am a little biased here, of course.

  2. You have posited previously that gold is valuable because it is scarce, have you not? I would presume from this you think the Pound is, or is not, valuable due to its scarcity, or lack of it? These are quantity arguments.

    Mathematics is the language of quantity, Mr Aziz, how do you reconcile your argument above with this fact?

    And If you don’t believe that math is the language of quantity, look up Lancelot Hogben, a man with a superior knowledge of mathematics than most.

    • Gold is valuable because humans value it. Value is subjective.”Scarcity” is an objective characteristic, but not everything that is scarce is valuable, and not everything that is valuable is scarce.

      If you think I am suggesting that economics should contain no mathematics, that is not the case. Mathematics is useful, but it should not be a substitute for English. If something can be said in English, it is better to express it in English, not least because translation clarifies the thought process. To misquote Einstein, mathematics should be used as little as possible, but no littler.

      • “Gold is valuable because humans value it. Value is subjective”

        So why do humans value gold? You haven’t given an answer to that except to say, in a previous article, “gold is naturally scarce”, which is a quantity argument. Because “value is subjective” is not an answer.

        I was suggesting to you that your position on mathematics in economics is inconsistent with your position on what determines value. What is economics if not the study of value? If quantity determines value then mathematics, the language of quantity, can describe it, no matter how complex the equation.

        On the other hand, if quantity doesn’t describe value, then your argument has a sound basis. For instance, gold, that humans value, has a certain QUALITY that no other element possesses, at least not in this universe.

        • People value gold for different and individual perceptions and reasons, quality and quantity. Value is in the eye of the beholder.

          I was suggesting to you that your position on mathematics in economics is inconsistent with your position on what determines value. What is economics if not the study of value? If quantity determines value then mathematics, the language of quantity, can describe it, no matter how complex the equation.

          Economics is the study of behaviour. Individual preferences determine value, and the contrast between individuals’ values determine prices. Quantity and quality influence these determinations, but they are not the determinations themselves.

        • You’ve still missed my point. If quantity determines value, then mathematics can describe it, invalidating your argument.

        • Value is only relevant when it is compared to another item. its not simply the quantity of x. It is the quantity of X for the quantity of y. It is not the quantity that determines value. This ratio is what we view as value. And this ratio is different for every product in the world and currently, there is no human understanding of mathematics that can decipher this ratio.

          Gold has value because it is a commodity coveted by humans just like grain, oil, etc. The ratio in which gold is converted into other commodities depends on how human beings desire, need, etc versus that other commodity.

        • ASDF — if the money is kept in a vault and out of the public hands, technically, yes you can print as much as you want without hyperinflation. If the money ends up in public hands, that is when the quantity starts to matter. So it is availability, more than quantity per se, that tends to affect perceptions of value.

  3. Couldn’t agree more. This is like an accountant projecting figures for a small business based on the assumption the owner is a machine who will never get sick or have a messy divorce. The maths looks good for next year, but the human element, if omitted from the maths, will sabotage the expected outcome more often than not. The increased use also of gearing in the economy, combined with relying on the expected maths, is a recipe for big surprises. I bet the Greek people just love the results of mathematical modelling of their economy by their politicians as advised by Goldman Sachs for example.

  4. @ Aziz ” This is bad practice; it is easier to baffle with bullshit in an unfamiliar language than it is in plain English”

    You took the words out of my mouth!

    I have studied economics for 20 years. Without the internet I would not have been presented with alternative views and theories. How do you expect the general public to understand!

    The reality is the Politicians spend imaginary money, and use their economic bureaucrats to justify to the public.

    It is theft and destruction of the economy with added layers of red tape and meddling and mal-investment in the economy. I can see that global capital wrecks individual countries then moves onto the next nation. Britain declined. USA is declining. The world is becoming more bureaucratic. Choices and freedoms are reducing. Taxes higher. The bureaucrat class is living better than the rest.

    Frankly politicians are criminals or worse incompetent. They should be forced out either way. We don’t need new legislation or spending programs. Common Law and Free Trade. Class actions can bankrupt companies that don’t trade ethically.

  5. Very well put. I am not an economist, but in engineering we have an expression for warning against missuse of models, “Garbage in, Garbage out.” This is usually meant to warn against junk data being fed into the front end, but I think it applies equally well to models based on insufficent data, data of the wrong type and flawed or grossly misunderstood models. These mistakes happen daily in science and engineering but in economics they have the power to impoverish nations.

    Thanks for your insight.

  6. To be fair, I don’t think all math in economics is a bad thing. We just have to understand its limitations. Don’t get me wrong, MATH SHOULD NOT BE USED FOR FORECASTING!!! It should be used to understand a system. In economics, I think math should be used to get an idea about how a system behaves based on certain assumptions–much in the way that Steve Keen uses it. Steve Keen’s models were very effective and understanding that a period of “stability” could end in a violent blowup.

    I will also say that the real world (and certainly economics) is highly nonlinear, which means that small errors lead to large deviations–we must understand that. In economics, the mathematics should be used to develop a qualitative understanding of what’s going on and how to deal with it; not to forecast, to a certain amount of decimal places, what employment and GDP will be next year.

    • Keen’s models work great. At the same time, there are probably plenty of eventualities under which they break down. We’ll see.

      Philosophically, I think that sometimes what we think of as nonlinear is linear. The problem is that we do not understand the lines because we are looking at the wrong variables.

      • I agree completely. We have to understand that a model is not, should never be, and will never be the end-all-be-all. The whole point of a model is to understand a system with certain assumptions better. We make assumptions, we model those assumptions in order to understand what the behavior of the system could be like.

        A model is a tool to understand the world–that’s all it is. Models are not necessary and don’t need to be used. They can be beneficial if used in the right way. However, if used in the wrong way, they are not only useless, but destructive.

        I view a model as a part of a toolbox. It’s like observing actual behavior or like doing an (economic) psychology experiment in a controlled setting. You can’t use any one of those as an end-all-be-all, but you can use them to help you understand what’s going on from a qualitative perspective.

  7. Excellent article, as usual Aziz! :D “Human behaviour is not mechanical” Even the human body, though biologically similar in terms of each person, still moves according to its own unique rhythm. No two bodies are identical!

  8. With apologies to Dr. Einstein, et al, math does not exist. Proof?

    It would seem that in order for math to hold up, you must assume that their are numbers. This is the fallacy. Every object in the Universe is unique. Therefore, there is no such thing as, two [2] or three [3] of anything.

    But, let’s say that you ignore the above. Math completely breaks down at each end, that is, approaching 0 and approaching infinity. How can that be?

    The conclusion that must be drawn is that math is simply another construct that has no basis in reality or Reality. It’s [mis] use in all things certainly supports this notion.

    • These are valid points, particularly in economics although how far you can take uniqueness is debatable. In things like physics and chemistry, things are more quantifiable because they are measurable in more uniform ways (e.g. strength of a force, weight, size, etc), and obviously math in itself is a purely abstract logical system, not a thing per se.

      • John, they are no more valid in physics or chemistry than economics. If they were the Truth, then science would be static. All knowledge [especially science :] is transient.

        Physics and chemistry seem to work until the next theory mysteriously replaces the former. The way this works is that you start with the conclusion and work your way back. Although math seems to work in some cases, for example, two [2] dollars are two dollars, right? It only works in the system of math, that is, if you buy into the fact that two can exist.

        If you didn’t buy into this, then it wouldn’t make much sense. It sort of like a theistic religion. You have to buy into the fact that God exists. If you do not, then the rest holds little water.

        • Well what wouldn’t be debatable is a Planck-quantity of energy, because it would be indivisible and uniform. Whether such a thing is identifiable is another story, and up ’til then we have to make do with various forms of quantitative relativism/nihilism.

        • John, no need to go there. If you agree that knowledge is in constant flux, then there must be something that isn’t, no?. Nihilism is where people go when they reach the point where the intellectual no longer works, but they have not yet accepted the alternative.

          Really “smart” people are those who simply understand the current take on [fill in the blank]. Should they fall behind or sell-out [e.g., Paul Krugman], then they change from smart to total dufus.

          People who are actually smart aren’t necessarily smart at all, they are simply people who can see the transient nature of all things in real time [which, of course, doesn’t exist either :].

      • Personally, I don’t think there is a way to quantify the behavior of one individual, let alone a billion.

        Although, I wouldn’t throw math completely out of the window when it comes to economics. I see economics as more of a philosophical discipline rather than a science, it’s those damn ivory tower economists who use applied mathematics in a philosophical field and call it gospel.

        Aziz is right, value is subjective and humans act, those two facts alone can destroy any model, no matter how complex it is.

  9. Allow me to offer a slight criticsm.

    It is not the math that is wrong, It is the translation of math to the New Jersey Shore crowd (most of the devolped world) that is the problem.

    What if we made the attempt to explain the role and impact of the world’s cental banks to Snookie, what would we say?

    “Ahhh, like, yoo fat ass can’t handle any moo mai tai coctails, cause like the Bernanke is printin’ money and that printed money goes into goods and services that have inelastic properties. Alcohol is one of the goods that, throughout history, exhibits the most inelastic demand properties. The more he prints, the more expensive your booze is! Get it!”

    “That top looks great on you! OMG!”

    For me, Mr. Nobody, its not the math, its the analysis of the math, that is the problem.

    The Marginal Productivity of Debt in the Western World is negative. Adding more debt to the Western Economies only pulls forward the collapse. The math is straight forward, the analysis, must be ignored by the TPTB. They still think they’re getting out with their loot!

    “I’ll get rid of my herpes before the TPTB get away with their scam!” said Jay-Woo!

    Something like that!

  10. this is so uninformed I’m really shocked to read it on such high quality blog like this. I think our generation, John, should overcome neo-austrian limitiations rather than reinforce them. the great austrian economists, while delivering very sound theories on such complex topic as economics is, seem to suffer some kind of severe math-complex, rooted not only in poor math skills but also general misunderstanding what math is about in the first place:

    mathematics is the best tool for discourse ever known to our civilization

    unfortunately, most humans think math is about “finding x” and academic non-mathematicians think math is about equations (particularily differential equations over continous domains as if there were no other math tools out there to use). this is a devastating misconception.

    math is a methodology about reasoning: consistent definitions, clear assumptions and valid inference. genuine math at its heart consists of proofs: sequential record of logic deduction. equations are just a concise form of that record. ironically, it is austrians who claim economics should be based on deduction and who reject these wonderful tools at the same time. conversely, other economic schools understate fair deduction and immidiatelly proceed to deus ex machina equations – forms taken out of their original context, from some Equation Catalog and arbitrairly patched together to mimic a consistent proof. what they do is not math. this all comes from ignorance.

    there is absolutely nothing preventing austrians to express their valid ideas in a concise, reusable, clear mathematical form and reach exactly the same valid conclusions but with more confidence and in a way that engourages further exploration. nothing apart from ignorance, unwillingness, excuses and self-delusion, that is. (Rothbard excelled at these)

    there are different areas of math: continous, discrete, algebras, logic systems. there is even meta-mathematics which is essentialy reasoning about different flavours of reasoning systems. computability theory highlited limitations of math itself: halting problem concept says that some stuff cannot be calculated or simulated by any computer ever (even given infinite time!). Godel’s theorem says there are theories that one cannot ever prove or disprove to be sound. how clueless austrians look thinking they are beyond limitations of reasoning by merely refusing to admit their resoning follows these laws. but math can be used not only to taunt neo-austrians – it is far more fun to devastate monetarists with non-computability (by showing their models cannot apply even to machines) and computational economics does just that already!

    those without training in mathematics will struggle to grasp what an author is trying to communicate if a paper consists mostly of equations untranslated into English

    papers aren’t for wide public, they are for researchers – people who need to communicate complex ideas to each other and need a sound methodology to verify their reasoning. mathematization of physics doesn’t force people to struggle to understand it alone – there are a lot of popular science books that reiterate complex theories in form accessible to average readers, even kids.

    it is easier to baffle with bullshit in an unfamiliar language than it is in plain English

    Lord Keynes once admitted he didn’t understand works of Mises he had read because his German was bad. to me it always looked as a pathetic excuse for ignorance and lock-up. Keynes wasn’t a researcher, he was a propagandist delivering fairy tales to those who needed them most. austrians aren’t researchers either anymore: they discard math, they discard empirical verification, they happily expose themselves to cognitive biases (not to mention intentional distraction, manipulation and definition-juggling) and claim it is the right way of doing economic research.

    I hope the blowout growth in mathematics in economics is a bubble that soon bursts.

    on the contrary, it’s high time the bubble of misconception is burst and math is employed the way it should have been long ago.

    attempting to smudge the human reality of economics into cold mathematical shackles is degenerative

    “cold mathematical shackles” – now this is exactly one of these manipulations that plain-English discourse is exposed to: tampering emotions. as if it were neccessary that research is nice and smiled. the problem with this kind of bias is one cannot see clearly when he commits it. with math, you have the tools to perform self-checks.

    Economics is a human subject. Human behaviour is not mechanical, it is not mechanistic

    this is a long established lame excuse that austrian economists have used for years to avoid math they did not manage to learn and certainly never approched to use to express their ideas. and what is so humanistic in bare industrial supply chains starting from mines to end at Foxconn sweetshops after all?

    Physicists can very accurately model the trajectories of rocks in space

    actually, they don’t :) you can’t know both location and velocity, you can’t measure stuff without destroying its state – these results came exactly thanks to math before they were empirically confirmed.

    economists cannot accurately model the trajectories of prices, employment and interest rates down on the rocky ground

    so why they don’t state that in the best available form our civilization has came up with?

    don’t take me wrong – I praise austrians for their achievements. but their stubborn reluctance against math, willingful ignorance and excuses are substantial reason of their marginalization and research stagnation. I also think a new generation of fresh minds could leverage these achievements to lead masses out of centrally planed misery.

    • Wow, good post.

      But, I actually think that “math” proves that Austrian economics, is, atleast on the right road.

      Too much debt as a % of GDP = Depression.

      The only way Debt as a % of GDP gets large enough to cause a depression is through government intervention.

      Why? Because free functioning markets would never let debt as a % of GDP get large enough to cause a depression.

      This is a the crux of Austrian economics and the math proves this point.

      Without the FED, BOE, ECB and the BOJ, the pain we are going through doesn’t exist. The bubbles would not have been blown, the bubble blowers would not have been bailed out and the markets would have sorted out the truth from the lies.

      • “The only way Debt as a % of GDP gets large enough to cause a depression is through government intervention.

        Why? Because free functioning markets would never let debt as a % of GDP get large enough to cause a depression.”

        This is completely circular reasoning. The first and second sentence are saying the same thing, but you have not proved either of them.

    • Mantrid —

      This is an interesting response, but the main point you didn’t address is the problem of nonlinearity and unmodelled variables. And from my discussions with Taleb, I am not sure that they can be addressed.

      I am not against mathematics. Unlike most Austrians (if you can call me an Austrian, many would say I am not) I have no problem with the use of some mathematics (so long as it is as simple and specific and explicable as possible). In fact as you know I sometimes use math in my posts — and I sometimes even try to construct predictive mathematical models for fun. I don’t want the number of equations-per-paper to fall to zero.

      What I am against is the misuse of mathematics — the substitution of mathematics for ordinary language when no thing is necessary and to baffle with bullshit and exclude non-mathematicians, as well as the lack of critical thinking/absurd assumptions involved in some branches of mathematical/econometric economics.

      Also, I’d argue mathematics is not a tool for discourse, as it requires non-mathematical language to define nouns. I’d say mathematics is a means for illustrating quantitative ideas.

      • the problem of nonlinearity and unmodelled variables. And from my discussions with Taleb, I am not sure that they can be addressed

        then how about proving mathematically these cannot be addressed rather than just guessing. you do not always have to fully specify the model to reason about its capabilities: Reductio ad absurdum is commonly used tool in math. it is also used in natural language but unfortunatelly often it is misued.

        What I am against is the misuse of mathematics — the substitution of mathematics for ordinary language when no thing is necessary and to baffle with bullshit and exclude non-mathematicians, as well as the.

        it’s like saying that reserach paper published in Chineese excludes non-mandarin westerners. one either has to learn mandarin/math himself or seek a translation.

        lack of critical thinking/absurd assumptions involved in some branches of mathematical/econometric economics

        then it is not problem of mathematization particularily. it is general problem of departure from estabilished scientific methods. if fools are making absurd assumptions so they can easier use math, then they fitting theories to tools, which is absolutely against science. at this point it doesn’t matter if the tools are math or natural language – witch doctors do not follow valid research practices.

        Also, I’d argue mathematics is not a tool for discourse, as it requires non-mathematical language to define nouns.

        you mean axioms.. axioms and definitions come prior to discourse and are not part of itself. you can’t discuss anything before agreeing on definitions first. discourse only starts when you have that agreed.

        • then how about proving mathematically these cannot be addressed rather than just guessing.

          Coming. Going to do a mathematical takedown of neoclassical theory and assumptions, but before I can write it I need a lot of preparatory reading. But thanks for the tip — reductio ad absurdum seems like an appropriate angle.

          then it is not problem of mathematization particularily. it is general problem of departure from estabilished scientific methods. if fools are making absurd assumptions so they can easier use math, then they fitting theories to tools, which is absolutely against science. at this point it doesn’t matter if the tools are math or natural language – witch doctors do not follow valid research practices.

          Agreed.

    • I argued with my Finance Professor about why we needed to learn the Black Scholes Option Pricing model, when historical data can’t predict the future. He said because it is the best we have. I said that’s why i will never use Options, unless I know for certain an event will take place. I really hope the last 6 months strength of the US dollar gives me really cheap Put Options!

      • Options = gambling

        Only during secular turning points in the economy will options make sense.

        The good news? We may be close to a secular turning point.

        Kyle Bass likes Japan.

        I have no idea.

  11. “mathematics is the best tool for discourse ever known to our civilization”

    You know what, they used to swear by drilling holes in people skulls to allow the evil spirits to escape too [a Medicare covered procedure until 1968 :].

  12. It is true that mathematics may only exist insofar as one interprets things through it, though that is not to say that despite its somewhat illusory nature it cannot still prove useful, i.e. in the construction of bridges. We can interpret things that are but the whim of creative, human imagination to still have a particular, practical use in other words.

    Interestingly, some positivist types of philosophy — the most extreme forms of which (i.e overly mathematical econometrics) claim that obtaining and verifying data that can be received from the senses…titled empirical evidence — seek to suggest that “society operates according to laws like the physical world”. Indeed, positivism in extremis — ala the Utopian socialists Auguste Comte — has even been labelled “Catholicism minus Christianity” by Thomas Huxley …

    http://en.wikipedia.org/wiki/Religion_of_Humanity

  13. furthermore, the idea that an individual can “rise above” (any type of) cognitive biases is nutty as nutty gets. there mere use of mathematics, whether for productive, practical and productivity increasing purposes or not, itself evident a ‘cognitive bias’….otherwise known as a simple preference…. for mathematics …mantrid would be interested to know your thoughts on the following ideas:

  14. Another Great Artcle Aziz,
    Along with the comments & discussions…

    I personally believe that mathematics should be used as a tool only and measure social economics of the past. Use of this data as a forecast of what is to come but, not to make decisions solely on these mathematical models. As an engineer, I see mathematics as absolute and inflexible, which has its uses but it does not include tolerances. Tolerances can be equated into mathematical equations but these “tolerances” +/- of human actions and reactions, can not be calculated. Furthermore, if we use mathematics which is indeed absolute, who is to say the absolutivity of mathematics can be applied to human society without severe repercussions?

    Take for example the latest responses from the IMF, where they were surprised that the latest trade debt ratio figures, of Greece will be near 2% for 2012, while initially forecasting it to be around 7%. Achievements and failure of human society can not be measured accurately nor forecasted accurately, hence making decisions (austerity) based on such mathematical equations and forecasting tools, may lead society/ies down the wrong road.

    Ofcourse one must keep in mind that the mathematical tools used to observe and forecast economics of countries and the market, can be easily manipulated and or expressed solely on how the presentor views this data. The people that are presenting these economical figures are the people I personally distrust. Politicians, Financial institutions, experts, etc… So, who is to say that the IMF, is currently expressing a “fudged” opinion, as to help the Greek politicians trump through “the last” package of austerity measures?

    It is nice that there are many views of mathematics here in the comments from both sides, but my base concern is not whether or not these models are applicable or not to society but the “puppeteers” whom are using mathematics to guide society.

    My forefathers stated that life should be, “Pan Metron Ariston.” Which badly translates into English as “balance in everything, is briliance.” Society and how we/they are running it is anything but balanced. So the absolutivity of mathematics only worsens the problems of society rather than help it.

    • I agree. Economic houses sell their research to Politicians and their political parties for a fee. Numbers can be massaged to tell a story, and this story is used to baffle the masses.

  15. I’m studying a Masters in economics at the moment. At the beginning of every model or theory that we study, we essentially just assume away all natural human behaviour and then start playing with the numbers, drawing so-called conclusions from the results.

    In the same way that people who are not mathematically inclined tend to shy away from the numbers, I’m finding that the people who are mathematically inclined tend to shy away from accepting that reality isn’t necessarily represented by their maths equation, which I find concerning.

    • My advice. Listen to your Professor. Make him feel like God. He’ll be marking your Papers!

      To get any job, you need to impress your Manager that you have the qualifications to save his arse if you stuff. He can say: “But he had a Masters in Economics! How was I to know!”

      Then you can read what you like and argue with us to your hearts content.

      • Thanks, I’ll be taking that advice on board! I’ve been biting my tongue for the last few weeks – fighting the urge to blurt out “is it just me or does anyone else think this is a complete pile of boll***s?” :-)

        • It is a pile of bollocks! When I was your age, I did not realise that Finance Professors usually can’t operate in the real world, and have no idea how things actually work. It was not until my final year that we had a lecturer who was a self made millionaire property investor, and he ridiculed the financial model for determining the ratio of optimal equity to debt in a company. He said when bankers are giving money away and assets are rising, borrow as much as you can and sell out at a profit, before the other fools. I will never forget that advice!

    • Excellent comment, Nigel.

      As someone who is not mathematically inclined, I have gained a lot through studying some models and equations. I think the math-heads would gain just as much from working on epistemology.

  16. This issue goes deeper than just economics, and affects all of science. Too much emphasis on quantity especially with regards to human action is deeply flawed. Humans cannot be represented by numbers…when individuals make decisions some very complex things are going on, simplifying it to numbers only and gathering mathematical data serves to further hide the truth instead of making it clearer. The truth is human behaviour cannot be quantified and attempts to do so are based on unscientific meta assumptions.

    In the realm of quantum physics we are told that the human observer affects the behaviour of the sub atomic particles. How can the human observer be represented mathematically in their theories?

  17. Aziz, you nailed this with mathematical precision! ;-)
    The way I see it mathematics is nothing but another language, even if a very special one.
    ‘Natural languages’ allow for two kinds of imprecision/lying. The speaker either doesn’t have all the information or he chooses to withhold/alter it, in whole or in part. Most listeners/readers have the ability to sense when the information might be incomplete and/or altered and, as such, are able to take the necessary precautions.
    When reading information written in ‘mathematics’ almost nobody does this because apparently you cannot lie when writing an equation. Since in reality the writer can always chose how much to disclose of the information he controls the ‘no lies’ assumption almost everybody makes is false.
    The problem is even more dangerous because a lot of us considers that a mathematical proposition is not only true but also complete, that it incorporates not all the information that is available to the writer but all the information that is to be known about a particular subject,
    And, as robc just mentioned, this is utterly impossible.

  18. Lots of great posts! The bottom-line is that math, akin to all intellection, can approach reality, but it can not get there. This is one of the reasons why math breaks down all over the place. Each step of the intellectual journey, gets one further and further from the Truth.

    If your perception is not so accurate due to time-lag, medium difference and other physical variability, etc., and your interpretation of your perception is not so accurate either [do to previous errors compounded by bias/inaccuracies of all sorts], then plugging these values into a formula [which can never really describe the actual process, in any case], leaves you with what?

    The problem isn’t that you can not understand [appreciate] Reality through the intellect, but instead, what this means, vis a vis, the self. This is where people can not go, and that idea which keeps them chasing after reality on the intellectual treadmill.

  19. Great piece. Just don’t forget: The time value of money is the most fundamental concept in finance. A dollar today is worth more than a dollar in the future. We divide a future cash flow by a discount factor to determine the present value. This is a totally indispensable mathematical procedure in economics.

    Ludwig von Mises, the harshest critic of mathematical economics, stressed the importance of economic calculation. Entrepreneurs must calculate profit and loss. Entrepreneurs must calculate the present value and net present value of potential investment projects.

    Math is the only way to calculate profit and loss. Any use of math beyond profit and loss calculations should be approached with skepticism.

  20. “Math is the only way to calculate profit and loss.”

    This is like saying that letters are the only way to spell words. This is true, but what if the words have no meaning?

    Math is a language. The basis of this language is fallacious, as are all things “knowable.” This does not mean that you can not use math, it simply means that you have to understand its limitations [relative nature].

    It’s like women…it’s not like you don’t know what to do once you get one, it’s just that you don’t know what to do once your done.

    • I think you nailed it with the word “limitations”. There are strict limits on the use of math in economics. I would argue the use of math in economics should be limited to calculating profit and loss.

  21. The fundamental paper that everyone should read about mathematics, data and economics:

    http://www.econlib.org/library/Essays/hykKnw1.html

    “What is the problem we wish to solve when we try to construct a rational economic order? On certain familiar assumptions the answer is simple enough. If we possess all the relevant information, if we can start out from a given system of preferences, and if we command complete knowledge of available means, the problem which remains is purely one of logic. That is, the answer to the question of what is the best use of the available means is implicit in our assumptions. The conditions which the solution of this optimum problem must satisfy have been fully worked out and can be stated best in mathematical form: put at their briefest, they are that the marginal rates of substitution between any two commodities or factors must be the same in all their different uses.

    This, however, is emphatically not the economic problem which society faces. And the economic calculus which we have developed to solve this logical problem, though an important step toward the solution of the economic problem of society, does not yet provide an answer to it. The reason for this is that the “data” from which the economic calculus starts are never for the whole society “given” to a single mind which could work out the implications and can never be so given.

  22. This is something I see everywhere – the mathematicization of everything. It’s as if Latin has returned and only a select few will decipher for the many. I noticed this while helping my child with her homework and I said, “It’s as if every single subject is being reduced to math.” Amazing!

    • I think you have nailed it: “It’s as if Latin has returned and only a select few will decipher for the many”

      The Priests had huge power over the masses in respect to this one, until the Prostestant revolution, the Bible was “magic”. As money is our new “God”, Economist have taken over where Priests left off.

      Hopefully blogs like Aziz’s will have the same effect on the masses as the Guggenheim press and the translation of the Bible into native languages. Economics is a simple discipline. Wonks complicate it to justify their positions.

  23. I just read your comment, Buddy! Funnily enough, that same Essay to which I above made mention and which I am still in the process of writing…actually has a line in it …titled…

    “Less State-centric, Max Weber even declared that a “bureaucratic organisation is well illustrated by the administrative role of the priesthood in the modern church” – tacitly comparing “Papal infallibility” to the more contemporary, legal mechanism of diplomatic immunity.”

  24. The solution to all of this entire miasma is to get back to basics, that economics is the base relationship between producer and consumer. Each factor added to this interdependency distorts this supply and demand equilibrium until you arrive at the colossal monstrosity aka the global economy.

    Each step towards increasing complexity are added inefficiencies to the point where people can sit around doing absolutely nothing and become billionaires. This is a great social crime.

    The entire purpose of constructing layers of complexity is in insuring [institutionalizing] the theft. It’s all about stealing other people’s labor-value, always has been and always will be.

    • PNG is the last wilderness. The mining boom has bought drugs, guns, crime to the local population. Elders are bashed by crazed youth. Unheard of 10 years ago. Travesty. How do you measure this economic cost? You can’t. PNG Tourism would make billions, because humanity can be reminded of its spiritual primitive past. For eternity. The NPV of the discounted future tourism dollars to PNG would outweigh the mineral boom!

      Some Elders traveled to London as part of a documentary and after seeing “Civilisation” had very wise words for mankind. Rerturn of the Tribe (2007) The Elders were outraged that the Queen (London’s head Chief) would not meet them. This was a Faux pas in the Insect Tribe!

      http://www.tvthrong.co.uk/tag/return-of-the-tribe/

  25. I’m shocked by how many comments you got for this article…something that would seem somewhat technical. I would add this: unlike in Physics or Chemistry we know something in Economics – namely, that humans act. We can assign no motive of action/purpose to a rock falling from a ledge, it simply falls. Since we cannot assign a motive, we acknowledge empirically that the rock fell and we can measure how fast it fell. From there we create theories (gravity) and formulas (Netwon’s mechanics) to describe what we observe empirically.

    However, studying economics in this way, purely using empiricism and mathematics unnecessarily narrows the amount of knowledge we can attain. For example, for someone using empiricism and mathematics without deductive reasoning (rationalism), they may be tempted to believe that the way to economic recovery is by providing easy money via low interest rates, and by providing inflation because in the past economic recoveries have been associated with rising inflation.

    However, economic empiricists have a difficult time connecting the boom that follows their easy money policies with a bust many years out – something that a theory using deductive reasoning in addition to empiricism may uncover. Using reason with our axiom that humans act, we can know that if humans act and money exists they will either save/invest or spend their money. If they save that money there will be more money available for entrepreneurs/businessmen to use in their business – more money on the capital markets to expand businesses (particularly those that take a long time before providing a return on investment – they need capital since they won’t have enough profit in the beginning to keep alive.) If they spend that money, less capital will be available for expanding business (business projects that could take awhile to produce a return would not be feasible.) Society has these sorts of preferences for saving or spending based on each individual’s choice. Thus, at a deeper level, the interest rate is a characteristic of society’s spending/saving preferences (less supply of money/more demand of money – the more interest will be charged to avoid shortages.) This must be true – even though I used no empiricism (unless you want to count “Humans Act” or the “Law of Supply and Demand” as empiricism – they both may be, but if they are they are extremely basic) and no mathematics in concluding it.

    If the Fed changes the interest rate, but society’s preferences have not changed, then there is a disconnect between society’s preferences and the Fed’s manipulated rate. This disconnect is likely to mislead (admittedly, strict deductive reasoning not used here since I use the word “likely”) businessmen into taking on psuedo-capital that cause projects to fail because they won’t have enough real capital to sustain themselves that will ultimately lead to a recession.

    Granted I didn’t go into a full explanation here, but my point is, there’s no way in economics you could reach the conclusion that manipulating interest rates would lead to recessions with the same sort of conviction as you can by using deductive reasoning. Sure, in a perfect world where you could conduct controlled experiments – you could – but our world does not allow for it. I’m not saying you never use empiricism in economics – I’m just saying that given that we cannot have laboratories/controlled experiments in most economics, empiricism is limited more so than it is in Physics. Rationalism, however, given that we have the axiom that humans act toward a certain end, even if it be to walk outside a room, can provide knowledge in economics where in Physics it could not. Thus, if I had to weigh Rationalism v. Empiricism I would definitely way empiricism more towards the natural sciences and rationalism more towards economics without giving either a knockout victory.

    I see the overuse of mathematics in economics pushing out the importance of deductive reasoning/using crude empiricism and that is why I would say macroeconomics has been going backwards/not progressing much since the 1930s.

    • I totally agree with you. I think Bernanke’s biggest mistake is underestimating the information flow on the internet. Does he read the multiple blogs out there that berate him? How many retail investors read these articles? The general “vibe” “gut feel” on the net blogs equates QE/low interest rates with desperation and thus humans withhold spending due to fear and uncertainty, causing a deflationary spiral despite zero interest rate policy. In fact deductive reasoning would suggest, raising interest rates would encourage people to buy now before interest rates go too high, and also the associated risk on/animal spirits released due to a air of comfort that the worst is past. There is no empirical evidence but intuitive logic suggest this could work.

      I for one am very risk averse due to ZIRP. How many others are risk averse too? How many businesses are withholding investment decisions before the election outcome and the fiscal cliff? Is this factored into Ben’s model?

      The reality is Ceteris Paribus (All other things remaining unchanged) is unreasonable and dangerous assumption in mathematical models.

  26. Funnily enough, I again see similar sentiments to that which are contained in the introduction of my essay above, namely:

    “Power’s centralised conception of human action is said to do a disservice to the complexity of everyday life and the empirically innumerable amount of constantly shifting motives therein, along with the concordant assortment of definitions we must still employ for the sake of practicality, despite their liability for boundless ambiguity given the number of persons concerned.”

    • How do they account for the decision making of the mentally ill or down right neurotic Fashion freaks. Price is not a factor. Brand substitution that is to say hedonics is not a factor in their minds. As the next generation becomes more brand conscious, the axioms of the past don’t hold true.

    • I mean, they use data to predict human action, which is generalised as the standard behaviour of the population to react to a given set of conditions. Their models predict behaviour based on historical empirical observations. But humans are not rational, and many irrational decisions drive spending patterns. Some people are just crazy and would buy more of a good because the price is higher and more “exclusive” i.e. neurotic types who need to be “cool”. As advertising twists the mind of the youth, no longer do they base spending patterns on old fashioned price increases quantity decreases like our forebears did, but they are “illogically” driven to make economic decisions.

      HOW DO YOU MODEL THIS?????

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  33. Reblogged this on The Nineth House and commented:
    This is a very good point. Unlike morphogenesis, climate, or chaos dynamics, economics and human behavior do not lend themselves well to mathematical modeling as we tend not to follow a set of predictable parameters. Humans are a chaotic phenomenon also known as a strange attractor, which run on feedback loops and amplification, we cannot make us into an equation we are too non-linear.

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