Wednesday, July 19, 2017

Jason Smith — What mathematical theory is for


Cuts to the chase on the use of math in science, including economics.

Information Transfer Economics
What mathematical theory is for
Jason Smith

27 comments:

Matt Franko said...

This is over 99.9999 % of people's heads....

Let's get back to more useless discussions of concepts and constructs using as many figures of speech as possible....

Neil Wilson said...

You can't derive a framework based upon 'empirical success', because the empirics are affected by the framework. The empirics are collected in the context of policy choices.

That's the basis of the Lucas Critique. The arrogance of mainstream economics is to believe they have the power to divine the 'deep parameters', by which they mean the universal truths that are unaffected by choices.

They don't. They are just curve fitting to a biased data set the same has those before them.

The solution is to look the other way. You have to construct a simulation that mirrors reality according to actual people that have experience of both.

We need a flight simulator.

Tom Hickey said...

The problem is assuming that there is constant measurable data using the same standard in a historical discipline based on policy choices and changes.

There is only limited "hard" data in economic history and it is over various countries that have shifted policy often, and in a global system that has also shifted in major ways.

The result is that there is very little actual hard data without doing some hard work to deconstruct it from official reports, accounting statements, etc.


This is a big reason that conventional economists agree on a some a priori framework and work in terms of it. It is also shy there is little correlation between the model and what is purportedly being modeled.

The proper approach is a case approach. There is no general case in economics to speak of over any significant historical period, let alone in principle.

Matt Franko said...

"The problem is assuming that there is constant measurable data using the same standard in a historical discipline based on policy choices and changes."

Tom, you are aware I assume that you yourself bring up Marx all the time?

Jason Smith said...

Neil,

You can't derive a framework based upon 'empirical success', because the empirics are affected by the framework.

How did one come up with this framework that affects data without at least looking at data in the first place?

Are you telling us there is some framework that came down from, say, aliens that affects our view of data that never started with data some human observed?

In reality there are different levels of "framework". Galileo started with the general rationalist one where God made the universe comprehensible to humans. Modern physicists have quantum field theory. Between those points, there was a great deal of back and forth between framework and empirical data. Sure, the framework dictates the data to some extent, but not completely. And the data challenges the framework. That makes a convergent process.

If it doesn't appear to converge, then perhaps you're in a regressive research program.

...

Also, Lucas critique is more like Lucas advice: a macro empirical regularity might fade away if used for policy. Key is might. Not will. Lucas thought writing models in terms of rational agents would help prevent this, so he definitely thought that macro empirical regularities existed. If you stumbled upon one of these without a microfounded model, it would be an empirical regularity that didn't fall victim to the Lucas advice.

Tom Hickey said...

Tom, you are aware I assume that you yourself bring up Marx all the time?

Because Marx got it right that there is no "natural economy" based on "human nature, with "natural laws" comparable to the laws of nature in the physical sciences, but rather complex historical and geographical processes that are iterative and incremental.

Marx held that the foundation for this historical dynamic was economic. But that claim would have to be established scientifically.

My view is that while the economic infrastructure of a society is integral to its development and expression of its cultural and institutional superstructure and therefore a chief factor in the historical dialectic, there is no compelling argument based on evidence that it is either the foundational factor, or even the chief one among other factors.

Marx called it his guiding principle. He seems to have been generalizing on his knowledge of history. He was working prior to the development of the social sciences — anthropology, sociology and political science. He was also working before economics was recognized as a discipline.

Marx the philosopher was an innovator in what became the social sciences, including economics.

Marx is not the only one who came up with the insights he did but he was generally the first to do so, and he deserves credit for historical priority. Many of those insights have been incorporated into sociology and economic sociology.

But most anything that appears "Marxian" is excluded from conventional economics.

I think we need to break the spell of contemporary ideology, not be substituting another ideology like Marxism but recognizing useful ideas that break mold.

Matt Franko said...

"Marx the philosopher was an innovator in what became the social sciences, including economics"

You're making my point....

AXEC / E.K-H said...

Economics: math-adorned incoherent blather
Comment on Jason Smith on ‘What mathematical theory is for’

Jason Smith asserts: “The primary purpose of mathematical theory is to provide equations that illustrate relationships between sets of numerical data.”

This is a bit shallow and falls below the level of Wikipedia: “Mathematics is the study of topics such as quantity (numbers), structure, space, and change. … Rigorous arguments first appeared in Greek mathematics, most notably in Euclid’s Elements. Since the pioneering work of Giuseppe Peano, David Hilbert, and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous deduction from appropriately chosen axioms and definitions.”#1

Why mathematics is so admirably appropriate to the objects of reality is not fully understood: “I find it quite amazing that it is possible to predict what will happen by mathematics, which is simply following rules which really have nothing to do with what is going on in the original thing.” (Feynman) see also (Wigner) and (Velupillai)

How does this relate to economics? Walrasian economics, too, is axiomatized, the hard core premises are verbally given as follows: “HC1 economic agents have preferences over outcomes; HC2 agents individually optimize subject to constraints; HC3 agent choice is manifest in interrelated markets; HC4 agents have full relevant knowledge; HC5 observable outcomes are coordinated, and must be discussed with reference to equilibrium states.” (Weintraub)

It should be pretty obvious that the Walrasian axiom set contains THREE NONENTITIES: (i) constrained optimization (HC2), (ii) rational expectations (HC4), (iii) equilibrium (HC5). Every model that contains a nonentity is A PRIORI false. And this is why mathematics does not work in economics and why economics is a failed science or what Feynman famously called a cargo cult science.

In practical terms, it follows immediately: as soon as the word equilibrium/disequilibrium appears in an economic paper or textbook it can be thrown into the waste basket. The same holds for all other nonentities. Note well that this holds also for Jason Smith’s information equilibrium.

The decisive insight for the role of mathematics in economics is: “If it isn’t macro-axiomatized, it isn’t economics.”

The natural math of economics is the elementary math of accounting. This is the formalism to start with and NOT SS-function-DD-function-solution.#2 The problem with economists is that they grab a piece of math from the math department and apply it without deeper understanding.

The cargo cultic methodologist Jason Smith asserts: “A big step in using math to understand the world is when you’ve collected several different empirically successful models into a single paradigm or framework. That’s what Newton did in the seventeenth century. He collected Kepler’s, Galileo’s, and others’ empirical successes into a framework we call Newtonian mechanics.”

And how does Newtonian mechanics start? Yes, with the axioms of motion, see Axiomata Sive Leges Motus at the very beginning of Principia.

Physicists got the axioms right and this is why math works, economists messed up the axioms (first and foremost with HC5, i.e. equilibrium), and this is why the representative economist became a scientific laughing stock. The economist-turned-physicist Jason Smith is no exception.#4

Egmont Kakarot-Handtke

#1 Wikipedia Mathematics
https://en.wikipedia.org/wiki/Mathematics

#2 Macro for dummies
https://axecorg.blogspot.de/2017/07/macro-for-dummies.html

#3 Wikipedia Newton’s laws of motion
https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion

#4 You are fired!
https://axecorg.blogspot.de/2017/07/you-are-fired.html

Matt Franko said...

A not insignificant amount the blame could also be put on the mathematics department itself in my opinion

Calgacus said...

Matt Franko:Let's get back to more useless discussions of concepts and constructs using as many figures of speech as possible....

That is a pretty good description of what "pure" mathematicians do most of the time. Though I don't think it was intended as such. Equations and suchlike that look mathy to hoi polloi are for the mathematically immature or for suspicious characters like me who sometimes feel compelled to check things out when their "little man" tells them there's something wrong.

EKH:Why mathematics is so admirably appropriate to the objects of reality is not fully understood:

But it is not particularly badly understood. The traditional name for tight logical arguments using standardized concepts and constructs that are appropriate to reality and these concepts and constructs is "mathematics". So it is not much more mysterious than the fact that most people wear shoes that fit them and even match most of the time.

Matt Franko said...

C,

I'm sarcastically referring to Jason here :

"The primary purpose of mathematical theory is to provide equations that illustrate relationships between sets of numerical data. That what Galileo was doing when he was rolling balls down inclined planes (comparing distance rolled and time measured with water flowing), discovering distance was proportional to the square of the water volume (i.e. time).

(Skipping the Darwin part can't have everything...). And while there exist many cases where economics studies unquantifiable behavior of humans, a large portion of the field is dedicated to understanding numerical quantities like prices, interest rates, and GDP growth.

Once you validate the math with empirical data and observations, you've established "trust" in your equations. Like a scientist's academic credibility letting her make claims about the structure of nature or simplify science to teach it, this trust lets the math itself become a source for new research and pedagogy."



I think this is pretty good... egmont is being unfair here...

Neil Wilson said...

"Modern physicists have quantum field theory"

Physics envy again. You're suffering from precisely the same problem as the mainstream economists.

Changing the framework in physics doesn't fundamentally alter the behaviour of the elements studied - even in quantum physics.

It does in social sciences and economics - because they involve people with brains and emotions that change their mind. That's the bit the soulless mathematicians can't get their head around. They want to treat people like ants or particles in a Brownian motion soup.

It doesn't work Jason. It hasn't worked. It can't work. It's the Black/Scholes disaster and lipid hypothesis disaster all over again in a different field. The curve fit stops working once people switch into a different mode of thinking.

Change the policies and you change the aggregation function, which makes your 'micro founded' model useless - even assuming the 'micro foundations' have any validity in the first place.

You cannot talk about what a free man can do by studying the actions of a man in a straitjacket. You have to take the straitjacket of and see.


AXEC / E.K-H said...

Neil Wilson

You say: “Physics envy again. … Changing the framework in physics doesn’t fundamentally alter the behaviour of the elements studied ― even in quantum physics. It does in social sciences and economics ― because they involve people with brains and emotions that change their mind.”

This is not a case of physics envy but of social science delusion. Economics is a system science, i.e. about the structure/behavior of the economy, and NOT a social science, i.e. about Human Nature/motives/behavior action. This is the subject matter of psychology, sociology, political science, etcetera.

Economists are simply on the wrong party and have not realized it since the founding fathers.

Standard economics is based on behavioral axioms (constrained optimization, rational expectations, equilibrium) and mathematics simply does NOT work with nonentities. The calculation that when three angels and four angels dance on a pinpoint then the total is seven angels is not applied arithmetic but brain-dead crap.

It is well-known among mathematicians, but not among economists, that not all mathematical structures incorporate ‘certain aspect of empirical reality’, which means, that there is a “... whole crop of monster-structures, entirely without application.” (Bourbaki)

Standard economics is such a monster-structure, entirely without application. This is NOT the fault of mathematics but of abysmally incompetent economists. Count Jason Smith and yourself among them.*

Egmont Kakarot-Handtke

* Incompetence — the original sin in economics
https://axecorg.blogspot.de/2016/02/incompetence-original-sin-in-economics.html

Matt Franko said...

"Economics is a system science, i.e. about the structure/behavior of the economy, and NOT a social science, i.e. about Human Nature/motives/behavior action. This is the subject matter of psychology, sociology, political science, etcetera."

This is pretty good...

Matt Franko said...

These things: " Human Nature/motives/behavior action." have no place in the discussion...



Tom Hickey said...

These things: " Human Nature/motives/behavior action." have no place in the discussion...

This kind of attitude is why STEM plays little or no part in politics and governance, and STEM people don't get involved in it.

Result: no technical expertise in political life and governance = failure.

If STEM people want to play a part in political life then they need to get a grip on what is important to people that vote and learn to how persuade them in terms that they can relate to.

Otherwise, STEM people should stop whining about what's happening lacking tech expertise.

Kudos to Mike, Warren and Stephanie for being involved politically.

Neil Wilson said...

Great quote here:


"Emanuel Derman, who was among the first physicists to work on Wall Street, doubts that biologists possess secret sauce for investing. Derman rose to lead the quant risk strategies group in his 17 years at Goldman Sachs Group Inc. He found that as physicists applied their expertise of the laws of motion, atoms and mathematics to investing, their models didn’t work nearly as well as they did in a lab.

Newton’s law of gravity hasn’t changed for eons, Derman said, but human behavior in markets changes all the time, wreaking havoc on even the best models made by scientists.

“I’ve developed a lot of skepticism about anyone bringing their expertise from one field to another,” said Derman, author of the book “Models.Behaving.Badly” and a Columbia University professor of financial engineering. “They say stocks are like atoms, or like genes. But stocks are not atoms or genes. There is a resemblance, but ultimately they are very different.”"

We should require these economists to make a load of money in the market before they start pontificating to the rest of us.

Somewhat like Warren has.

Matt Franko said...

All you have to do is first get the concepts settled, then maybe write a legal construct, THEN just bring in competent STEM people to implement it ...

3 step process...

Matt Franko said...

You don't want stem people in law, or in philosophy ... let those people do those things.. nor do you want those people in stem which is the current problem...

AXEC / E.K-H said...

Neil Wilson

You quote: “Newton’s law of gravity hasn’t changed for eons, Derman said, but human behavior in markets changes all the time, wreaking havoc on even the best models made by scientists.”

WOW, what a revelation! Guess what, this has been known to scientists of all ages except, of course, to retarded economists: “The bifurcation of motion into two fundamentally different types, one for natural motions of non-living objects and another for acts of human volition … is obviously related to the issue of free will, and demonstrates the strong tendency of scientists in all ages to exempt human behavior from the natural laws of physics, and to regard motions resulting from human actions as original, in the sense that they need not be attributed to other motions.” (Brown)#1

Economists, in their ignorance, built economics on a set of BEHAVIORAL axioms with utility maximization at the core. This was 140+ years ago and neither has Orthodoxy abandoned this proto-scientific rubbish nor has Heterodoxy come forward with something better. Economics has never risen above the level of folk psychology and folk sociology and second-guessing other people’s expectations.

Of course, there is NO such thing as a behavioral law or regularity or stable functional relationship, never was, never will be. Being axiomatically false, economics has to be abandonment and fully replaced.

There is no use to criticize Walrasianism, Keynesianism, Marxianism, Austrianism. It is ALL proto-scientific sitcom blather. The only question is how to replace these failed approaches as fast as possible.

The first step to a paradigm shift is to understand that economics is not a so-called social science like psychology/sociology and not a natural science like physics but a system science. The economist’s proper task is to look out for objective systemic laws and to empirically verify/falsify them. Science is about the invariants beneath changes on the surface and not a commonsensical description of what happens here and now. There are NO BEHAVIORAL laws but there are SYSTEMIC laws, and they are as objective, certain, mathematically exact, and eternal like physical laws.#2

Egmont Kakarot-Handtke

#1 The existence of economic laws and the nonexistence of behavioral laws
https://axecorg.blogspot.de/2015/12/the-existence-of-economic-laws-and.html

#2 New Economic Thinking: the 10 crucial points
https://axecorg.blogspot.de/2017/07/new-economic-thinking-10-crucial-points.html

Matt Franko said...

"economics has to be abandonment and fully replaced."

They could redo the curriculum...

Tom Hickey said...

All you have to do is first get the concepts settled, then maybe write a legal construct, THEN just bring in competent STEM people to implement it ...

You don't want stem people in law, or in philosophy ... let those people do those things.. nor do you want those people in stem which is the current problem...


It would be nice is that were the sequence but experience shows it is not. So we have to ask why not and what can be done about it.

Everyone needs to be educated in "philosophy" broadly speaking because voters need to understand issues and this requires both method (logic and critical thinking and also familiarity with the frame in which issues are set. Otherwise, politics is just a game of persuasion that boils down to sophistry and propaganda.

One of the problems is that there are not enough STEM people participating in the debate from the outset at the ground level, so STEM thinking is absent until the end, when is apparently too late, given the history. Qualified people are not put in place at the end so the problems don't get solved and its' wash, rinse and repeat with a new crew failing each time.

The problem is that the first step is with a view to passing legislation which gets the lawyers and lobbyists involved at the outset and all the way through.

The selection process is broken and needs to be fixed.

Six said...

Economics is a social science. Social science is "a major category of academic disciplines, concerned with society and the relationships among individuals within a society." The numbers part of economics is accounting of one sort or another. An awful lot of economists are confused about the numbers part of economics, as are an awful lot of non-economists.

Matt Franko said...

"Everyone needs to be educated in "philosophy" broadly speaking". Agree...

AXEC / E.K-H said...

Matt Franko, Six, Tom Hickey

Everybody can climb on a soap box and make an economic proposal ― except an economist. In the political realm, anything goes and no qualification is needed, only an emotionally backed opinion and some rhetorical talent. An economist, on the other hand, is supposed to be a scientist and to know what he is speaking about, that is, to know how the economy works.

Economists who have no scientific knowledge are at the same level with political cranks and these morons thrive when the economy is sluggish or worse: “A sure sign of a crisis is the prevalence of cranks. It is characteristic of a crisis in theory that cranks get a hearing from the public which orthodoxy is failing to satisfy. In the thirties we had Major Douglas, and social credit — it can all be done with a fountain pen — and Warren and Pearson who convinced President Roosevelt that raising the dollar price of gold would raise the price of everything else and bring the slump to an end. The cranks are to be preferred to the orthodox because they see that there is a problem. Nowadays we have plenty of cranks taking up the problems that the economists overlook.” (Joan Robinson)

The difference between a crank and an economist is NOT in the political orientation but in the necessity that the proposal of the economist must have a sound theoretical foundation. That is, the economist must be in the possession of the true theory: “In order to tell the politicians and practitioners something about causes and best means, the economist needs the true theory or else he has not much more to offer than educated common sense or his personal opinion.” (Stigum)

Now, scientific truth is defined by material and formal consistency and the problem of economics is that we know for sure that economics is false: the four main approaches — Walrasianism, Keynesianism, Marxianism, Austrianism — are materially and logically inconsistent.

So, people like Krugman have to be opposed NOT because they are liberal or conservative but because they are scientific fraudsters: they speak in the name of economic science but there is NO such thing as economic science.

How is scientific knowledge established? “Research is in fact a continuous discussion of the consistency of theories: formal consistency insofar as the discussion relates to the logical cohesion of what is asserted in joint theories; material consistency insofar as the agreement of observations with theories is concerned.” (Klant)

And this is the point where math comes in. Math is simply the best available means to establish logical cohesion. And here, in turn, is where the problem of economists with math comes in: as natural born muddle heads and cranks they abhor nothing more than logic. Fact is that economists do not even get the elementary mathematics of accounting right.* Where things become comical is when these folks cover their stupidity by posing as philosophers.

Egmont Kakarot-Handtke

* Macro for dummies
https://axecorg.blogspot.de/2017/07/macro-for-dummies.html

Neil Wilson said...

"Everyone needs to be educated in "philosophy" broadly speaking"

I'd argue we should all be educated in the art of rhetoric, because that is what allows you to spot when it is being used.

Rhetoric classes were always part of the English public school system (which confusingly are the private schools with the highest fees used by the rich and powerful).

Which shows you that the purpose of mass education is all about training individuals to be efficient robots in the workplace, and little to do with broadening the mind.

AXEC / E.K-H said...

Neil Wilson

The curriculum at British schools is the business of the British people. Likewise for the US. No economist has to tell these or other countries how to organize their education and what to teach. The business of economists is to figure out how the economy = world economy works. Fact is that economists are failed/fake scientists. They do not even know the elementary mathematics of accounting, which, if anything, is the minimum condition of doing economics.*

Economists are a nuisance because they have an opinion on everything but knowledge of nothing.

Egmont Kakarot-Handtke

* See also ‘A new curriculum for swampies?’
https://axecorg.blogspot.de/2016/11/a-new-curriculum-for-swampies.html