Big Science

The only statistics you can trust are those you falsified yourself.— Winston Churchill, British Prime Minister


Econometrics, the application of statistics to social science questions, is without a doubt the biggest and most respected of all the Pseudo-sciences. It is a tool remarkable for its ability to demonstrate whatever a researcher wants it to demonstrate. As a political tool it is unsurpassed for its predictive powers; competing only with astrology in this regard, but having the benefit of sounding far, far more credible (it has lots of numbers and graphs in it).


Econometrics is particularly popular with economists from the World Bank, The International Monetary Fund and United Nations development agencies.
The same tool can be used to conclusively demonstrate that foreign aid “works” and will solve all the worlds’ problems as propagated by Jeffrey Sachs. It is just as effective to demonstrate that foreign aid is a waste of time and even counter-productive as William Easterly wants us to believe.
Fortunately David Roodman, a researcher at CGD, provides some excellent papers to help ordinary mortal make sense of all of this:
Through the Looking-Glass, and What OLS Found There: On Growth, Foreign Aid, and Reverse Causality - Working Paper 137, Macro Aid Effectiveness Research: A Guide for the Perplexed - Working Paper 134, Aid Project Proliferation and Absorptive Capacity - Working Paper 75.
The Center for Global Development (CGD) is a very informative and competent organisation “that works to reduce global poverty and inequality through rigorous research and active engagement with the policy community.”


In one of the Abstracts from these papers David Roodman explains the nature of the problem:

“Like many public policy debates, that over whether foreign aid works carries on in two worlds. Within the research world, it plays out in the form of papers full of technical language, formulas, and numbers. Outside, the arguments are plainer and the audience broader, but those academic studies remain a touchstone. While avoiding jargon, this paper reviews recent, contending studies of how much foreign aid affects country-level outcomes such as economic growth and school attendance rates. This particular kind of study is ambitious: it is far easier to evaluate a school-building project, say, on whether the school was built and children filled its seats than to determine whether all aid, or large subcomponents of it, made the economy grow faster. Because of its ambition, this literature has attracted attention from those hoping for clear answers on whether aid “works.” On balance, the quantitative approach to exploring grand questions about aid effectiveness, which began 40 years ago, was worth trying and is probably worth pursuing somewhat further. But the literature will probably continue to disappoint as often as it offers hope. Perhaps the biggest challenge is going beyond documenting correlations to demonstrating causation—not just that aid went hand-in-hand with economic growth, but caused it. Aid has eradicated diseases, prevented famines, and done many other good things. But given the limited and noisy data available, its effects on growth in particular probably cannot be detected.”


These are ambitious aims, and although the papers go some way in providing clarity, the author himself contributes, in his own small way, to noisy and limited data, through the all-too-common gymnastics of garnering authority through references to scientific principles. The problem with these principles is that they belong somewhere else and explain other things. The principles of physics and mathematics - as a rule - have no place in justifying social arguments.


By far the most irritating of all is the butterfly story that goes something like this; “the probability that it will rain in London is determined whether a butterfly flaps its wings in the Amazon forest.” One finds this statement all over the place, to justify and “explain” a surprising number of things, usually completely unrelated to either butterflies or rain. Or London and the Amazon forest.
However much I would like to rant against this stupid habit in more detail, David Roodman does not sink so low as to use it. He does nevertheless make some other statements in a similar vain, and just as insidious:


“in the intellectual revolution triggered by the twentieth century’s encounter with hard limits to human knowledge. Werner Heisenberg discovered that an observer cannot simultaneously measure the position and velocity of a particle with perfect accuracy. Kurt Gödel showed that there are true mathematical statements that are unprovable and false ones that are irrefutable.”

There is absolutely no statement, in science, or in any of the other knowledge generating systems, that unambiguously demonstrate that there are any hard limits to human knowledge (knowledge is the concern of Epistemology, by the way).
Practical considerations aside – lack of information, too much data, too much work, no funding, not particularly important or interesting – the only limit to human knowledge (if there is one) is human intelligence.


Heisenberg’s Uncertainty Principle, which is what is referred to above, belongs in physics, more specifically in Quantum Theory.
It goes something like this: “The probability with which we can know the velocity of a particle is inversely proportional to the probability with which we can know where it is.”
A more accurate, but more obscure, explanation is that the uncertainty in the velocity of a particle x the uncertainty in its position x its mass cannot be less than Planck’s constant.
There is a number of other more accurate but also more obscure explanations of the same phenomenon.


This phenomenon applies to moving particles only and is an inherent feature of reality rather than simply a quirk of Quantum Theory. Niels Bohr and Albert Einstein argued about this for decades. Niels Bohr won the argument.
The ability to know the exact position as well as the exact velocity of a particle would provide us with information at best, not knowledge. It does not affect our ability to know.
Who would want to know such a strange and irrelevant a thing as the exact position and exact velocity of any given particle? Why?


The same sort of argument applies to the theorems of Kurt Gödel. These are, if anything, even more abused than any other mathematical statement, probably because they sound so compelling.


Kurt Gödel made some rather important contributions to the Theory of Relativity but is best remembered, and abused, for his two Theorems in Number Theory. These are the Completeness Theorem and the Consistency Theorem.
Their very names suggest that they must be very compelling.


They are very boring. They consist largely of very long lists of numbers.
They have none of the elegance of the many other mathematical theorems that caused David Deutch, for example, to consider the power of mathematics as miraculous.
Gödel’s Theorems have no application in the real world.
There is no aspect of reality that is a bit fussy because it is incomplete, or places where we are told not to go because it is a bit inconsistent.


Reality likes to live on the edge, it is often the case that our explanations of it must skirt the very edges of completeness and contradiction, but reality itself is always both complete and consistent.


What is more Gödel’s Theorems apply only to axiomatic systems. Axiomatic systems are systems that postulate things that are so simple that they are considered to be self-evident and then build up a number of theorems from those axioms.
The two main axiomatic systems are Number Theory and Geometry.
Number Theory has several hundred axioms, but has no practical application as far as I know. Physics rely on axioms only very weakly, and mostly in that interface where it justifies using mathematics to explain physical phenomena.

Geometry has only five axioms, and a lot of practical applications. It only becomes incomplete and contradictory under very strange circumstances, such as the behaviour of space and time in or near singularities. To fully explain what happens there we can cheat and use algebra. Or something else.

The quirks of mathematics and physics should not be considered to have correlation in all of reality.


Werner Heisenberg and Kurt Gödel cannot be blamed for the weakness of Econometrics.
Econometrics itself is responsible for this. I will cop out at this point in trying to explain it in detail, there is too much of a risk of boring both myself and everybody else.
David Roodman admits to the major weakness when he claims that “Theories are merely nice stories describing reality.”


A nice story about reality is simply that – nice story.


Even the most simpleminded view is that a theory is a model of the universe, or a restricted part of it, and a set of rules that relate quantities in the model to observations that we make. A theory is only any good if it satisfies two requirements. It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations.


Invoking the limitations of one knowledge generating system to explain weaknesses in another or, worse, invoking a fundamental, inescapable property of unrelated real things (particles for example) to explain systemic limitations, is quite simply making excuses.
One cannot systemically determine what is knowable and unknowable in any particular system if there is no coherent underlying system to do it with and Econometrics is notable, if anything, for its incoherence. It is notable for the way that equations are arbitrarily invented and imposed on haphazardly collected data, its obsession with smoothing out inconvenient little details and its ability to see straight lines and “Ordinary Least Square” graphs when the most logical explanation is the fact that the data is scattered all over the place.


The power of mathematics may be miraculous but it does not and cannot explain everything.


It is impossible to imagine doing Biology without mathematics and without assuming at least the truth of evolution. The results of Biology in fact support evolution and confirm its truth, but the Theory of Evolution itself contains no mathematics. There is no place for it there. There may even be no place for it in Economic growth on large scales and over long periods of time. A purely descriptive explanation may do perfectly well.