Thursday, April 7, 2016

Jason Smith — The mathematics is not the issue here, Dude


Some interesting reflections by Jason Smith.

Instead of talking about math and "mathiness," perhaps we should speak about formalization of informal arguments and conceptual models in the interest of rigor. 

Humans think and communicate using ordinary language, which is product of evolution and consists of many alleys and byways as well as highways. As Ludwig Wittgenstein sought to show, ordinary language can be something of a minefield. Meaning is context-dependent. Failure to appreciate the use of signs in context leads to misunderstanding signs as symbols.

Wittgenstein explored rigorous expression before turning to ordinary language. The Tractatus was a response to Russell and Whitehead's Principia and also to Frege. Russell was so impressed he invited Wittgenstein to Cambridge.

The Tractatus as an exposition of the logic of description can be seen as a work not only about logic but also the philosophy of science. Wittgenstein was an engineer by training. His Tractatus was developed out of the introduction to Hertz's Principles of Mechanics.

Wittgenstein's work turned the focus of Anglo-American philosophy in the direction of analysis. There are arguably three periods in the history of Western philosophy. Ancient and medieval philosophy were chiefly absorbed in the question, What is there? In founding modern philosophy, Descartes pointed out that prior to answering this question, it is necessary to answer the question, What can we know about what is? Wittgenstein shifted the focus from thought to language, asking the question, What can we say meaningfully?

Formalization of language is an attempt to increase rigor in expression. However, it is not the only way, since logic is broader than formal logic and mathematics. Clear and precise expression is a challenge because the ordinary language that grounds our thinking process contains a lot of noise, and it is a temptation to confuse some of that noise with a signal.

The history of Western thought is generally traced to Socrates as his student Plato set forth the dialectical method in the Dialogues. It is clear that the method that Socrates employed was intended to clarify expression by introducing rigor through debate. This was the beginning of the scientific method, as it were. If one insisted instead in talking about gods, they were sent to the temple.

Science is usually thought as a being chiefly empirical, so Aristotle is credited with founding the scientific approach. But prior to observation is expression, and expression involves the use of signs as symbols. Getting clear on how language works is a prerequisite to gaining knowledge as the confluence of experience and understanding. Aristotle agreed. His works begin with the logical investigations, Prior and Posterior Analytics. Aristotle's logic can be viewed as a proto-formalization of logic implicit in the Dialogues.

Tradition has it that the lintel of Plato's Academy was inscribed with, "Let no one ignorant of geometry enter." The term "geometry" may have meant "mathematically literate" in context. Aristotle wrote in the Analytics that one should not talk "geometry" with those who are not geometrical, that is, not so inclined. This could be extended to mean that one should not attempt to be rigorous with those who are non-rigorous and who cannot deal with abstraction.

Descartes initiated the second great step in formalization in his Discourse on Method, the full title of which is Discourse on the Method of Rightly Conducting one’s Reason and Seeking Truth in the Sciences. "Clear and distinct ideas" are fundamental to correct method. 

Descartes was a mathematician as well as a philosopher. Descartes developed analytic geometry and Leibniz initially developed calculus, although it was Newton that usually credited. Formalization begins to incorporate mathematics, and mathematics is developed to support greater formalization.

Since then, the overwhelming view is that formalization in science is chiefly mathematical. This quite obviously followed since science is about measurement of quantity and changes in quantity. But basic logic still applies. You can't add apples and oranges, and the meaning of terms cannot shift within the same context. 

Occam's razor also applies: Let expression be as simple as possible for the task. This is where over-formalization and "mathiness" can come in. Is the exposition as simple as it could be to get the job done? Or is it being complicated as a matter of jargon that protects the trade?

I don't think any of this is controversial. Say what you mean as simply as possible and as rigorously as need be, and don't get pedantic. To the degree that a subject is amenable to quantification, the preferred method is to use math appropriately. Is there any argument about this?

Alfred Marshall advised economists to use math intelligently to clarify their thought and make their point.
I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypothesis was very well unlikely to be good economics: and I went more and more on the rules - (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 last I do often. — Letter to A.L. Bowley, 27 February 1906, cited in: David L. Sills, Robert King Merton, Social Science Quotations: Who Said What, When, and Where Transaction Publishers, 2000. p. 151.
Keynes said of Marshall:
The study of economics does not seem to require any specialized gifts of an unusually high order. Is it not, intellectually regarded, a very easy subject compared with the higher branches of philosophy and pure science? Yet good, or even competent, economists are the rarest of birds. An easy subject, at which very few excel! The paradox finds its explanation, perhaps, in that the master-economist must possess a rare combination of gifts. He must reach a high standard in several different directions and must combine talents not often found together. He must be mathematician, historian, statesman, philosopher – in some degree. He must understand symbols and speak in words. He must contemplate the particular in terms of the general, and touch abstract and concrete in the same flight of thought. He must study the present in the light of the past for the purposes of the future. No part of man's nature or his institutions must lie entirely outside his regard. He must be purposeful and disinterested in a simultaneous mood; as aloof and incorruptible as an artist, yet sometimes as near the earth as a politician. Much, but not all, of this many-sidedness Marshall possessed. But chiefly his mixed training and divided nature furnished him with the most essential and fundamental of the economist's necessary gifts – he was conspicuously historian and mathematician, a dealer in the particular and the general, the temporal and the eternal, at the same time. John Maynard Keynes, Essays In Biography (1933), p. 170.
Keynes thought of economists as wearing many hats. This accords with the ancient conception of the philosopher as lover of wisdom. A philosopher studies the whole, regarding nothing as alien. Robert Heilbroner called the great economists "worldly philosophers." They are not only social and political scientists but also social and political philosophers.

I would say that the placing math on a pedestal in economics may tempt some economists to forget that that they are doing something other than natural science, which the conception of "market forces" is apt to convey if not designed to do so. Math is not a end in itself other than for those doing pure mathematics. Those who use math for other than pure mathematics are doing applied math. What they are doing may involve much more than math and even more than is quantitive, since human life is qualitative as well.

There is also pure science and applied science. Theoretician are dong pure science, while engineers are going applied science or technology. Engineering uses science as theoretical knowledge to make stuff. So it is an art. Some theoretical physicists are exploring the boundary of science and philosophy.

Economics also has theoretical and applied aspects. Theoretical economists explore model space. Applied economists attempt to make economics useful in explaining the world. Some applied economists also use economic to affect the affairs, e.g., through policy formulation.

Conflating pure and applied results in confusion. What holds in a model does not necessarily hold in reality. Exploring model space is interesting and important, but it is not the whole of the field.

Moreover, and most importantly, theoreticians may not be well qualified in areas of application, such as policy formulation. A noble prize in theory doesn't necessarily quality a person as a policy adviser.

It is also useful to remember that Ronald Coase received The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel for "the Coase theorem," which is not expressed mathematically.

There is also a place for people like John Kenneth Galbraith that translated economics and politics economy into a level of expression that non-economists could understand and use in approaching policy.

Generally speaking, math cannot be used to sell an idea politically without appealing to argument from authority since most of the audience won't understand the math. Voters need to understand the rationale for policy and have criteria for evaluating it. Otherwise it is a matter of proliferating post hoc ergo propter hoc (before therefore because) fallacies.

There's a difference between buying a piece of technology that depends on complicated math and intricate science that very few have the capacity to understand and buying into to policy prescriptions based on "experts."

In summary, there is a need for rigor in expression. Math is one tool in the toolbox for achieving rigor. But just as tools can be applied to uses for which they are not fitted, so too can logic and math.

When this is unintentional, it is called ignorance. When it is intentional, it is called sophistry. So while rigor is a plus, user beware. Rigor is a only prerequisite — a necessary condition but not a sufficient one.

Information Transfer Economics
Jason Smith

33 comments:

Bob said...

Convince me that economics is apolitical, that it isn't about making up elaborate excuses to direct more resources towards an elite. The issue is that economics is a con job.

Tom Hickey said...

Economics is not necessarily either political or a con job. Some aspects of economic are political though, and economics as whole can be politicized through assumptions.

The degree to which that economics is political needs to be established.

If this is shown to be the case, the questions arise, to what degree is this the result of manipulation or unintentional bias. If manipulation, how does the manipulation work and who is doing the manipulating.

It's not like these are new issues either. The early economists were aware of it, and it is a chief focus of Marx and Engels, for example. Now it is studied mostly by heterodox economists and economic sociologists and economic anthropologists.

Bob said...

Cui bono? The wealthy are benefiting from current economic policies. I can imagine alternative policies where the wealthy are taxed and income is redistributed to those most in need. It is redistributed to individuals who will spend a high proportion of the income, which will increase economic activity. Those policies have economic merit, yet they are not favored.

We observe the effects of austerity policies that have resulted in stagnation. The outcomes are contrary to what was predicted by austerity proponents. Yet austerity continues.

This suggest that economics, which informs policy, is not rigorous. Instead, it is designed to serve the interest of those who benefit most from it. The appeals to authority, as well as the modeling and mathematics, are intended to obfuscate this reality.

If it weren't a con, policy makers and academia would be doing everything they could to arrive at new approaches, or to rethink policies that worked in the past. An economy that only benefits the few is a failure, full stop.

Matt Franko said...

"An economy that only benefits the few "

Its survival of the fittest.... those "few" are aka "the fittest"... this is textbook Darwin 101 which has been taught in schools for decades... people are just believing what they have been taught...

"We observe the effects of austerity policies that have resulted in stagnation."

There has been no stagnation... GDP is up to 19T now having been at only 14T back in 2008 at the GFC...

Stock market near all time highs, unemployment down to 5% usual bottom... those 5% unemployed cant compete... they are the opposite of "the fittest"...

What's to complain about? Sounds like Biology 101 is working out just as taught....

Matt Franko said...

Bob here is Tom from the piece:

"Humans think and communicate using ordinary language, which is product of evolution"

This is how evolution works its "survival of the fittest".... why the outrage?

The 1% think better and are smarter more intelligent which is a "product of evolution"...

You have a 1% moving on and 5% who cant hack it... some in between.... sounds like normal evolution to me ....

Why do any of you people have a problem with this?

Matt Franko said...

" "Let no one ignorant of geometry enter." The term "geometry" may have meant "mathematically literate" in context."

Tom I think the word they used for these people was "mathetai" which imo means what we might call today a "creative learner"...

In the Greek Scriptures, this word is translated as "disciple".... as in "Jesus and His disciples...."

Then this is interesting:

" If one insisted instead in talking about gods, they were sent to the temple."

So in the academe, you had these mathetai or "creative learners" which is opposite 'rote' learning... which based on this statement, would mean the temple people were the 'rote learners'.... the temples somewhat 'deified' human tradition via rote methods passed down from human ancestors... the 'gods' or 'theos' or 'placers' were deified depictions of anonymous key human ancestors...

So the two approaches were "creative learners" vs. the "rote learners"...

imo WE are the 'creative learners' in this while the economists are the 'rote learners'...

So their approach mimics the old temple system in this way while in truth, we are the academy...

Christendumb are also 'creative learners' at this time so we can see them struggling and trying to learn the hard way ... Paul never called anybody he was talking to a 'disciple' aka 'mathetai'....

So it looks like it breaks down where you have a bunch of us who learn via the way of a 'creative learner' while the other half of us learn via 'rote'....

Matt Franko said...

Like economists learn "money printing causes inflation!" via rote and they just memorize this and believe it... via rote...

while someone like myself just scratches their head looking at these people as there is no credible mathematical derivation they are relying on in order to make this statement...

Auburn Parks said...

I cant believe that you are actually supporting the crazy libertarian view of just desserts Matt. Never thought I'd see the day.

Matt Franko said...

this also is why I look at you guys glorifying Minsky and scratch my head as there is nothing there with that guy ... the guy has nothing... ie 'Minsky doesnt matter...'

"stability creates instability" ?????? this is AT BEST some sort of statement out of a rote methodology.... or imo actual sophistry....

So the whole Minsky thing with you guys is hard for me to understand where that is coming from....

Matt Franko said...

Auburn I'm playing "Devil's advocate" there...

I dont see how the Darwin people can be outraged at current outcomes...

Matt Franko said...

iow if one believes evolution is true, then imo one logically cannot be outraged at current outcomes... I dont see how you guys square those two positions up...

Matt Franko said...

Auburn, eg. imo Romney's "47%" comment is straight out of Darwin...

Ignacio said...

Mayb we shall be teaching Biology 102 instead fs spouting the same stupid things over and over, Matt?

How is survival of the 'fittest' if the 'fittest' write the rules of what is allowed and isn't? If you are alone is the jungle, there are any laws that tell you what is and isn't allowed? It's an hoax! Fittest and biology my ass, is just an excuse to sustain the status quo. Why you keep ignoring this!? There are NO WRITTEN RULES which tell you what is allowed or not in 'nature'. You can't say we live under that paradigm unless that was the case for us in human societies.

It would make sense if we had no society, civilization and rules, but guess what, humans have never operated that way. And yes, is because we have EVOLVED to not act like that (as have done other social species).

What we may have to do is become with procedures to identify the sociopaths and free riders amongst us to neuter them, then maybe we get somewhere and stop non-sense discussions like this.

Tom Hickey said...

According to the neoclassical economic frame that grounds economic liberalism on equilibrium as clearing of the all markets — goods, money and labor — in the long run, the way it works is that when a market doesn't clear then market forces prune inefficiency.

For example, the most inefficient firms go bankrupt and the less efficient workers lose their work. So the solution is pruning back the dead weight. This means that either the surplus workers have to either become destitute and die off, or else be supported socially.

According to economic liberalism social support amount to a subsidy and subsidies are inefficient, so the surplus workers should just be left destitute to die off. BTW, this is the situation that prevailed at the time of Marx and which he was confronting. Not only that working conditions were abysmal with no protections, let alone benefits, and the tendency was toward a subsistence wage to increase profits.

That is the meaning of "survival of the fittest" under Social Darwinism in a capitalist economy under a market regime. A welfare regime allows for subsidies to smooth out cyclical effects.

Tom Hickey said...

iow if one believes evolution is true, then imo one logically cannot be outraged at current outcomes... I dont see how you guys square those two positions up...

Because Social Darwinism is not implies by natural selection and other aspects of evolution showing the important role that cooperation played in addition to competition contradict it.

Again, it is the elite taking a germ of truth and distorting it for their own benefit, as they do with virtually all aspects of knowledge. A strong objective at present is to control of education from K to PhD. In fact the push to do so is on hard now.

Bob said...

Matt, I'm not a Social Darwinist.
I'm not Bob Roddis (not to suggest that he's a SD either).
I doubt that Kevin Williamson reads this blog.

jrbarch said...

Matt - 'playing Devil's advocate' - and maybe quietly stirring the pot cos you like to see the bees buzzing about :-) I don't think the 1% have any real Intelligence at all - depending upon how you define it. But anyway, evolution does lead to a fully rounded out personality, but that persona doesn't become conscious until it discovers the energy of the heart - imho. No much use for a candle unless it is lit.

Matt Franko said...

jr its not just to stir up controversy... coming at it from the other side on this imo people are relying on Darwin for guidance in establishing these policies... there is no doubt about it...

The other thing is I'm trying to point out that with 5% unemployment the complement of that is 95% employment so that is normally deemed a very good outcome... get 95% in university and you get a 4.0 GPA...

Yet you guys are not satisfied by this normally A+ outcome.... why?

Why is 95% not good enough for you guys? Where is that coming from?

I'd encourage you guys to look inward and reflect on that....

Tom Hickey said...

Why is 95% not good enough for you guys? Where is that coming from?

Because 5% unemployment on a large scale, national, regional and global, is a huge number of people either not working or underemployed, which is economically inefficient, politically explosive, and socially unnecessary where resources are available to employ them.

The reason for a reserve army of the destitute under capital is purely and simply to discipline labor and reduce labor power for the advantage of owners. It's imposed legally and institutionally even when MMT has shown that there is no economic necessity for it.

Creating a buffer stock of employed through public works removes the bulk of the issue, and further government policy can effectively end it. The alternative is a buffer stock of unemployed for the convenience of owners at the expense of the public at large and the unemployed and underemployed in particular.

How does that make sense socially, politically and economically. It's even possible to accomplish in managed capitalism, as MMT shows.

MRW said...

According to the Labor Dept, as of March 2016, there 252,577,000 in the civilian noninstitutional population over the age of 16 and not in the military. I’m assuming this means the "available work force."

"158,890,000 participated in the labor force by either holding a job or actively seeking one." That’s where you--or they--get the 5% figure. It’s not real. The 5% number is

According to the March report here http://cnsnews.com/news/article/susan-jones/labor-force-participation-improves-slightly-94m-americans-not-labor-force, 93,688,000 Americans were not in this labor force.

That’s not 5%, Matt. And it’s no fucking record of who’s fittest, or who’s qualified to have a job.

5% of the “available work force” is 12,628, 850, not 93.68 million. The number of people out of work is 7.5X more than 5%.

Besides, the Labor Dept has reported elsewhere in the past six weeks that real unemployment is 10%, but there are no jobs to measure it by.



MRW said...

I meant to write, “The 5% number is a figment of accounting choices."

MRW said...

Correction: It’s the Department of Labor U-6 number: 9.8%
http://www.gallup.com/poll/190343/trump-clinton-supporters-lead-enthusiasm.aspx

Bob said...

Mass unemployment is a systemic problem. Putting forth a mythical 5% rate does not change that.

Greg said...

Well at least Matt didn't call unemployment "just a figure of speech" ;-)

Bob said...

Maybe the 'recovery' is a figure of speech ;)

At least Matt gave it the 'old college try', who else wants to try their hand at playing devils advocate?

Simsalablunder said...

"Well at least Matt didn't call unemployment "just a figure of speech""

Unemployment numbers are _ex post_ so they should be ignored… Top spending is enough…

Greg said...

@Bob

I agree with you that unemployment is much more of a problem than the "reported" 5% but I don't like terms such as mythical or notions that the govt is trying to deceive/manipulate the numbers. The methodology of the measurement is transparent and if one looks at how it is made you can see that it is not trying to find "all people who would like a job but cant find one". It has a very specific definition of "employment" and of "unemployment" both of which may not comport with what the average guy thinks of when he hears unemployment rate. Trouble is many people reporting do not know what the intended measure is or what it misses.

Adding to the problem you have a very influential stream of economic thought that truly believes that unemployment is simply people choosing not to work, that there is, by and large, no such thing as involuntary unemployment..... smh

Greg said...

IOW.... they think "Involuntary unemployment" is just a figure of speech! (one more needling of Matt)

Tom Hickey said...

@ Greg

It's called "fixing the data." Goes with fixing the assumptions.

There no problem with using math in economic. It's not the math unless math is used to disguise loaded assumptions and selective data chosen to persuade rather than inform.

Tom Hickey said...

IOW.... they think "Involuntary unemployment" is just a figure of speech! (one more needling of Matt)

"Involuntary unemployment" has an operational meaning in a model. The problem is that this model is not representative of the real world. So "involuntary unemployment" becomes a rhetorical device to dupe the rubes. Then it becomes a figure of speech and is no longer defined operationally in the relevant context.

Greg said...

Agreed Tom

Its like all the revised metrics for poverty levels over the years. They were all done to simply justify cutting financial support to poverty programs. Were there some valid questions regarding how maybe our metrics might miss economic activity in some low income communities? Yes, certainly a lot of economic activity that keeps these communities "richer" than we can measure is happening but its kind of perverse that we spend so much time/effort and money splitting hairs about rather minuscule amounts of income support relative to our countries GDP and govt budgets. The amount we spend trying to determine if the poverty programs really are going to "necessary" recipients is probably close to the amount we spend on the supposed "un needy".

Looking for waste and fraud in those programs is a full time good paying job for quite a few people, and the fraud is costing us virtually nothing in the grand scheme.

Simsalablunder said...

"So "involuntary unemployment" becomes a rhetorical device to dupe the rubes."

Don't you mean voluntary unemployment is a device to dupe the rubes, where the assumption "voluntary" is mostly hidden or described as they won't take a job because they live better off on welfare, therefore they are said to be choosing to not work?

Sure involuntary unemployment also has an operational meaning in a model but it's based on the fact that a lot of people who lost their job struggle to find another paid one, hence they're involuntary unemployed.

Tom Hickey said...

Don't you mean voluntary unemployment is a device to dupe the rubes, where the assumption "voluntary" is mostly hidden or described as they won't take a job because they live better off on welfare, therefore they are said to be choosing to not work?


Yes, you are right. My bad. I should have said "voluntary unemployment."

The neoclassical argument that all unemployment is voluntary is based on the model of all markets clearing owing to price flexibility and substitution, so that employment results from workers refusing to be flexible. The argument is that if those out of work are subsidized for not working by social welfare, then there is reduced incentive for them to be flexible.

If some unemployment is involuntary (no jobs even with flexible wages), then the government needs to step in to purchase the available resources that would otherwise be idle. The neoclassical models argues against their actually being no jobs, since if wages fall low enough firms will hire workers, creating new jobs if need be. Opponents argue that this model is unrealistic and overlook how things actually are in real world owing to factors that the neoclassical model excludes from consideration.

Neo-Keynesianism attempts to explain unemployment based on wage "stickiness," that is, inelasticity.

Paleo-Keynesianism and Post Keynesianism look deeper.