“I never learned maths, so I had to think”
from Lars Syll
Professors may find themselves ill-prepared for the macro classroom. To become academics they had to answer erudite questions posed by more senior members of the discipline. To become good teachers of introductory macro, they have to give clear answers to muddled students. That requires an intuitive feel for the subject. It is not enough to crank through the equations.
Indeed, Mr Rowe attributes part of his success as a teacher to his shortcomings as a mathematician. He quotes Joan Robinson, another clear expositor of macroeconomics: “I never learned maths, so I had to think.” Because the answers did not leap out at him from the equations, he had to dwell on the economic behaviour underneath the algebra.
Macroeconomics is difficult to teach partly because its theorists (classical, Keynesian, monetarist, New Classical and New Keynesian, among others) disagree about so much. It is difficult also because the textbooks disagree about so little.
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Real-World Economics Review Blog 
Thank you. My advisor in 1968 advised me to go practice in corporations, agriculture and construction. Earlier math history with chemistry and physics had shielded me but were about to need updating. Economics was toughing up with math.
Cosmic powered biology began at the beginning, when the first two quarks mated.. How is artificial intelligence superior to 13.7 billion year evolving cosmic powered biology manifest as human?
Futile maths cannot program geometrically accelerating human evolution.
Yes, the assumptions made in virtually all economic analysis lead to a collection of results which are not in accord with empirical reality and are therefore futile. However valid mathematical analysis is not futile.
Conventional analysis rationalises (Duhem-Quine etc) and fails to discard hypotheses which are not in accord with the empirical evidence. If it did, it would become clear that it has NO valid theory what so ever!
Math is fine, thinking/theorizing is fine….especially if they are also accompanied by an awareness of the nature and signatures of paradigms and paradigm changes.
Here are the primary reasons why economists cannot seem to get beyond math and theorizing and do not/cannot see the new paradigm.
Macro-economics is only a recent discipline unconsciously designed to obscure and prevent solutions rather than solve them because:
1) The financialization of capitalism has been continual for its entire history and its coalescence was well under way before macro-economics came into being.
2) Private Banking/Finance enables the virtual monopolization of the means of survival for individuals and enterprise, and also enforces upon them its paradigm of Debt Only for the form and vehicle for the distribution of money.
3) As retail sale is the terminal end of the legitimate economic/actually productive process and Finance/money creation is increasingly post retail sale it is a parasite upon the rest of the legitimate economy.
4) Economists attempting to be dutiful scientists tend to ignore and/or reject concepts that even remotely reflect spirituality even though philosophically such concepts can be stripped of any supernatural or religious bias, and so they lack a clear and relevant philosophical concept of grace as in gifting/the free gift which, being in logical/conceptual opposition to the current paradigm of Debt/Burden Only, tends to obscure the new paradigm of Monetary Gifting.
5) Finally economic thought still adheres to a prejudice for employment even though technology has reduced the need for human effort and AI is more and more intrusively destroying both aggregate demand and the need for the input of human employment. There is nothing inherently wrong with employment as an economic factor of course and it still has a long way to go, though an ever decreasingly operant one, but positively acculturating leisure as in self chosen attentive purposeful activity is the healthy and intelligent route forward for economic systems and for humanity.
Paradigm perception and paradigm changes are deep and transformative events both mentally-conceptually and temporally, and thus require such fundamental openness and deep and incisive examination.
“To become good teachers of introductory macro, [academics] have to give clear answers to muddled students.” Good try, Craig, but where you say “unconsciously designed” you look to me like one of the “muddled students”. It seems to me Gareth hit the ‘time’ nail on the head when he refused the pre-progamming of what emerges from evolution. Frank misses it, not seeing that “empirical reality” refers to what one can see NOW. Craig’s grace – the motivation for giving – cannot be seen, of course, but the gifts can, and Providence recognised from the history of them – or as Keynes saw, the build-up of unemployment for lack of them. Though I don’t agree with Craig’s (5) it is at (3) I seem him going wrong: still stuck in the same emprical paradigm as Frank, stil seeing exchange at moments in time as the be-all and end-all of economics. That surely is ‘micro’ rather than ‘macro’ economics.
Please excuse that scene setting. We are discussing students having to think because they have not yet acquired the necessary math students. Within the ‘micro’ economic paradigm the Economist article illustrated that imaginatively with its mango-ised exchange of apples and bananas. Delightful.
The way I was taught the mathematics of flow systems was with a similar model consisting of a battery connected with wires to an old-fashioned filament lamp, and a circuit diagram iconically representing that, with its iconic battery symbol labelled V (for volts). The current through the lamp icon (symbolised by a directional arrow) was labelled i (why I don’t know, unless to suggest the current has to be imagined). The mathematics for this was derived with the aid of a voltmeter and an ammeter (the unit for current being amps). The lamp “resisted” the flow of current, so it was labelled r. It was found that Ohm’s Law prevailed: the resistance was always given by the voltmeter reading divided by the current meter reading so r could be defined as V/i or (multiplying both of these by i) V = ir. The questions then arose naturally: what happens of you have two lamps one after the other (in series) or fed directly by the same battery (in parallel)? What happens of one has two batteries, the same or the opposite way round? A whole series of different possibilities came into view as we 16-year-olds were talked through the mathematics of increasingly complex battery circuits, then the same circuits with alternating currents derived from a dynamo rather than a battery.
So how is the resistance to the flow of money defined in an economic system, and do not the solar seasons and geographical distribution of resources introduce an element of flow
and the solar seasons an alternating current into the economic system? What are barns and foodbanks and warehouses and banks for if not for managing this?
Take your eye off the supermarket tills for a bit, Craig, and see what you can make of this ‘not-so-new’ but surely ‘new-to-economics’ paradigm.
At Craig’s (5), I suggest as an alternative paradigm to the excuses of the idle rich the behaviour of athletes, who know that constant practice is necessary to perfect oneself.
Yet another typo, despite my deliberately taking time to proof read this. One does begin to wonder about the site and/or system as well as oneself. In the second para “math students” should (of course?) have simply read “maths”. In the fifth para there is another hiccup, which definitely wasn’t obvious in the text submitted.
Please explain:
“Frank misses it, not seeing that “empirical reality” refers to what one can see NOW.”
and
“…still stuck in the same empirical paradigm as Frank, still seeing exchange at moments in time as the be-all and end-all of economics.
You have clearly misunderstood my analysis completely. The mathematical analysis encompasses extended periods of time. I never mention anything which I can translate as any form of exchange.
You ignore the facts. Empirical evidence does not falsify my analysis. That it predicts previously unknown relationships which are present in the empirical evidence, you ignore! You say you are an information scientist, so get your facts straight.
Frank, I did ask you to excuse the inadequacies in my cryptic scene setting! Apologies anyway for upsetting you, and I accept that your mapping the limits of production possibilities or whatever is not about exchange. What I am seeing in it is mathematical models plotting dynamic relationships as continuous series of fixed points on Cartesian graphs, and empirical observations at whatever points in time being related to the graph rather than causality. The graphs don’t enable the as yet numerically illiterate to visualise flows and interactions between them, whereas my circuit diagrams do.
I was not actually criticising the micro approach to economics, which may produce useful approximations in limited contexts. My target was macro models using quantitative micro methods involving the fallacy of composition. Even when (as in Samuelson) the equations for these are set up using a circuit diagram, the circuit envisaged is a simple series one, thereby excluding the effects of parallel circuits like short-circuits and control feedbacks. The way I was taught started with an understanding of these, allowing the mathematical methods to develop as questions arose or more practical details were added. My point was to suggest that economics teaching should follow suit.
To Dave Taylor:
I asked you to get your facts right, My analysis contains no model and yet you talk about mathematical models. My analysis describes, in abstract terms, the production-space in the real world. Your statement about causality is simply wrong. The cause of the output differences is clear. Different choices of the proportions of effort applied to tool making and maintenance or to production is what produces the different outputs.
Unless physically valid rigorous mathematics is applied, there is no way you can predict outcomes. Econometrics is curve fitting of concrete data, simply that. It describes one slice of past reality and is immutable.
You prescribe the forlorn hope, that keeping on doing what has been done for some 300 years will produce a different result. Einstein has been attributed as describing that as madness.
Only through first principles analysis, which provides descriptions of the warp and weft of reality will any progress be made. Really look at the hard sciences which demonstrate the truth of that assertion. First principles analysis is paramount in developing abstract descriptions of reality.
I’m the one advocating the natural philosophical concept of grace….and also stuck in an empirical paradigm? No, I’m for the thorough integration of both empiricism and philosophy…and the thirdness greater oneness that such thorough integration of truths, workbilities, applicabilities and highest ethical considerations would create.
When one refers to the duality of TOTAL costs/prices in ratio to TOTAL actually available individual incomes they are talking about aggregates which is what macro-economics is about.
Economics is stuck in the figure-figure of gathering data and formalizing theory. It isn’t “into” perceiving paradigms old or new and hence by definition is shallow analysis. Even guys like Steve Keen whose brilliant de-bunking of DSGE and unconscious re-affirmation of Douglas’s monetary insight talks about paradigm change….but he doesn’t study historical paradigm changes to derive their signatures so as to recognize what a new one would be characterized by. Let’s talk about and study paradigms and paradigm changes here. It would be extremely enlightening.
Neither capitalism nor socialism is the true integrative combination of the two perspectives. Consult the integrated duality within an integrative trinity-unity-oneness of the dialectic
[ (thesis x antithesis) —> synthesis ]
[ (capitalism x socialism) —> The profit making system and new paradigm of Direct and Reciprocal Monetary Distributism ]
A paradigm change is the ultimate radical human change, mentally and temporally. As our mental state and the temporal universe are opposites it is by definition an ultimate integrative event. Such a radical change is by definition temporally deep and mentally extraordinary. How much more radical a monetary change can you get than one from scarcity to abundance and from the monopolistic power of private finance to identification as an illegitimate economic business model?
To think paradigmatic-ally you have to dare to think in terms of opposites and inversions. Otherwise you’re only doing the legitimate but less integrative actions of gathering data or theorizing.
What matters is whether one really thinks or not. Mathematics help people to thinks deeper, but many economists are simply a slave of mathematics. They are not using mathematics. They are used by mathematics. Using mathematics imply that one uses them creatively. In some cases, it is necessary to create a new mathematics.
I had a chance to discover a new mathematics when I was exploring the logical structure of Ricardian trade theory in general situation (pure labor input economy) . It had the same structure as tropical algebra but basic operations used there were minimization and multiplication. I named it subtropical convex geometry. You can see how this exotic algebra works to elucidate the logic of Ricardian trade theory in the following papers and conference presentations:
https://www.researchgate.net/publication/280900871_Subtropical_Convex_Geometry_as_Ricardian_Theory_of_International_Trade
https://www.researchgate.net/publication/280646264_International_trade_theory_and_exotic_algebra
https://www.researchgate.net/publication/236020268_Subtropical_Convex_Geometry_as_the_Ricardian_Theory_of_International_Trade
As a trade theory, this discovery was a halfway to a more complete theory, because subtropical algebra cannot treat input trade. Even though, it helped me to advance in the theory of international trade.
From my humble experience, mathematics are sometimes a necessary tool to explore a new field or new theory of economics.
Dear Yoshinori Shiozawa August 2018
Congratulations on your;
“What matters most is whether one really thinks or not.”
To my simple mind learning how to think is the beginning of knowledge, then keeping an open mind is also important to evaluate alternative ideas. My point is as some economists have described much of the current education as teaching students of all ages how to regurgitate the misinformation indoctrinated into them as education. Thus when this attitude becomes entrenched in ones subconscious be they student or academic it becomes difficult for them to think outside their belief system. To me this lack of thinking with an open mind has to be addressed before any real progress can be made in reforming economics. Ted
Ted, after Frank’s hostile response to friendly fire, thank you for this.
Let me draw your and Yoshinori’s attention back to the brain having two sides, one specialised for sound and the other for sight, so we can differ in the way we think. We can relate words (including names for maths symbols) to what we see, but also conversely (i.e. translate what we see into words). However, some of us (especially academics) think almost entirely in words and symbols, while practical people often compare one thing with another.
This is not to say that one of these ways is better than another; it is rather a matter of “horses for courses”. Purely linguistic (or mathematical) thinking, however, is more efficient only if one already knows reliably what one is talking about. Frank’s first principles are perhaps best found by looking for them, not by relying on what other people say. Yoshinori’s interesting defence of mathematics suffers when even those with a mathematical dictionary have trouble understanding what he is saying mathematically. He might like to reflect on how a polytope transforms not into a tree but into a network capable of mapping not the limits of production (ignoring nature) but the directions and limits of flows, i.e. the actual distribution of selling.
The empirical evidence disproving Ricardian international trade theory is of course that accepting international trade is profitable for a country has licenced importers to profit from financially from importing rubbish and exporters from selling off local necessities (Macmillan’s “family silver”), thereby impoverishing local economies and that of other countries. Right now in the UK this matters, as despite being overwhelmed by unbuyable housing, intolerable commuting, transport fumes and land-fill overflowing with plastic, we seem about to be hoist by our own petard. Not that that prospect worried Ricardo, making money (at arms length from real trade) by gaming stock market prices, buying bankrupted property and thereby accumulating rents. His contemporary Cobbett didn’t find him a man worthy of the honour economists have bestowed on him: read “Rural Rides”.
Today economic thoughts are divided in many strands. This may be a good chance for education, because students can learn much from that state. They can learn that scientific truth is not easily obtained or determined. Decision making in everyday life (for example in business) is much more ambiguous and requires ingenuity. What a wonderful study environment!
Economics professors should take in account this opportunity and intentionally use it to enhance people to think independently and creatively.
Yes. As someone educated mainly as an algebraic geometer, almost everyone’s- except for yours – comments here about math often seem misguided to me. If things are understood well and naturally, there should be no difference between “the math” and “the economics”, with insight going back and forth as you say.
The most superficially mathematical economics is often the least mathematical in spirit as mathematicians understand mathematics. And vice versa, the most “verbal” seems quite mathematical to a mathematician. But your work connecting tropical algebra and geometry and economics sounds of the highest importance and to be both mathematical and economics in all senses.
Thank you, Calgacus. It is rare to find true mathematicians in this blog. There are so many unreasonable mathphobes who only judge that economics is wrong because it is full of mathematics whereas real economic life is no such things. It is like contending that physics is wrong because it is described in math and physical phenomena run without mathematics.
Sometimes, this unreasonable mathphobia is given a support from philosophers of economics. This does not help economics to redress itself in a more scientific discipline.
From experience we see that actions and things (including people) are processes of relationships. Mathematics is a tool Sapiens invented to depict and study these relationships. The objects of study don’t need mathematics. The observers (humans) of these objects don’t “need” mathematics either. The observers choose to use mathematics. Thus, mathematics in economics. Since humans are reflexive as well as active, they study their study. Thus, they consider the mathematics they invent and use in their actions, in scientific and nonscientific life. And reinvent is as they believe necessary.