The Economist on 100 years of Einstein

An important aspect for economics and its methodology is the relation between its definitions and the reality that those definitions (should) reflect. Creative minds coin definitions that maximize explanatory power. An example that highlights this phenomenon can be found in physics and notably by the article in The Economist January 1 2005 on 100 years of Einstein. Physics with its methodology has had more impact on economics than the other way round. Physics seems to have become an arcane science and one wonders whether economics goes the same road. Both sciences are in danger of losing touch with reality and either blow up the world or destroy the world’s economy if they don’t spend close attention to their definitions and their transparancy. While it is most likely that the author simply doesn’t understand physics, the exposition may still be beneficial for students of economics and its methodology.
 

Introduction

The Economist January 1 2005 features the article “100 years of Einstein. Miraculous visions” (p55-57). The reader gets the impression that this article is a marvelous piece of science journalism since the discussion seems to be crystally clear while the reader is left with the feeling of better understanding Einsteins theories, his genius (at simplicity) and their importance for both physics and our understanding of the natural world.

It may also be idiocy restated for nitwits again.

I mean, I am not a physicist, and after studying economics now for some 30 years I am close to understanding a tiny fraction of that field, so, who am I to judge ?

As a reader of The Economist I enjoy much of what they commonly write, so I might take the article on Einstein at face value and leave it at that. But, after flipping the coin (as seems proper for quantum physics), my decision is to reconsider this article and wonder: What does The Economist actually say ?

The following discussion should help economics students to better understand economics.
 

Some general points on the relation between economics and physics.

There are some general points that set the stage.

It is said of some physicist, I think it was Pauli, who confessed first to be interested in economics, but then, seeing how complex its subject of the economy was, turned his attention to the simplicity of physics. It is a good anecdote but this view isn’t necessarily correct. Jan Tinbergen was trained as a physicist and applied Hamiltonians in his Ph. D. thesis with Ehrenfest. He switched to economics since he couldn’t stand the poverty in some streets in Leiden. So it all depends upon personal conviction and biography, and such personal decisions can be respected as they are. Note also that discoveries in physics have been key to alleviate much poverty.

I recall that when I was a student at the gymnasium, back around 1971 when I was 17, that we had a surprise test to deduce E = m c^2. I passed - though I can’t reproduce all of that now - while many of my friends didn’t pass but only so since they were caught by surprise. We didn’t get around to quantum theory. Incidentlly, my interest was more in archeology, but, I couldn’t stand the scenes of Biafra and switched to econometrics.

For the discussion below it is also useful to mention the following from my personal biography. Around 1980, issues in methodology caused me to study some logic and the foundations of mathematics as well. Authors in these subjects you might want to read are Frege, Reichenbach, Suppes - where I regret that I had hardly time for them. This subject seems like a departure from economics, but there is some logic to it, also when you read the discussion below. I still have a draft book on a shelf with the title “A critical introduction into logic and the methodology of science” in Dutch that I can hopefully rewrite some day and then in English. There is still stuff that needs articulation, amongst others a ‘logic of exceptions’ (my approach to the liar paradox and ‘Gödel’). Critical observers will already find a discussion of propositional logic in my Economics Pack (1999, 2001). Anyway, after finishing that draft in 1980 I returned to economics, thinking of Biafra again, as newspaper reports on “The Global 2000 Report to the President” reminded us that the world population would rise from 4 billion in 1975 to 6.4 billion in 2000 - see Barney (1981). Studying all this philosophy also caused me to come across Keynes’s obituary of Frank Ramsey, and I could only agree with it:
 

“If he had followed the easier path of mere inclination, I am not sure that he would not have exchanged the tormenting exercises of the foundations of thought, where the mind tries to catch its own tail, for the delightful paths of our own most agreeable branch of the moral sciences, in which theory and fact, intuitive imagination and practical judgement, are blended in a manner comfortable to the human intellect.” (J.M. Keynes, obituary notice of F.P. Ramsey, The Economic Journal 40, March 1930; also quoted in Hao Wang (1974) and by D. H. Mellor, see the advised internet link below)

A key issue in the theory of science is the issue of measurement. Phycics before Newton suffered huge losses in intelligence, time and energy to discussions on unobservables and metaphysics. This in fact lasted partly into the 19th century with discussions on the ‘ether’. Their solution was to put a stop to fruitless discussion and concentrate on what can be measured. You don’t know what it is, but it moves this way, at that speed, and if you hit it here, then it moves there. This technical approach worked wonders, though it still seems that some theorists assume some ‘whats’ to derive their theories on the ‘hows’ (like Bohr for his model of the atom).

Tinbergen copied this more technical approach of measurement to economics, creating with Frisch and others the approach of ‘econometrics’.

A key notion below will be that physics might ‘overshoot’ by concentrating on measurement and by neglecting definitions and logic. Econometrics is open to that same risk.

Mirowski (1989) discusses in more detail how (earlier) economists were influenced by physics. His book has been discussed critically in the journals and I apologize for not providing a summary conclusion of that debate. For now, it suffices to indicate the existence of that part of the literature.
It can be mentioned that economics benefitted from the concept of ‘entropy’. Theil (1971) provides an excellent introduction while Kapur & Kesavan (1992) extend the issue. I haven’t fully digested the latter yet but have my own application Colignatus (1997).The entropy based Theil inequality index has also found its application in Galbraith (1998). All these are additional reasons to thank physics of their contribution to economics.

A final point to understand about modern physics is that their math may not be that developed. There is a 1963 quote of Patrick Suppes that receives support in 1998 by Richard Gill, professor of mathematical statistics in Utrecht:

“There appears to exist a strange miscommunication between physics and mathematics. Gill quotes Suppes: “For those familiar with the applications of probability and mathematical statistics in mathematical psychology or mathematical economics, it is surprising indeed to read the treatements of probability even in the most respected texts of quantum mechanics. ... What is surprising is that the level of treatment in both terms of mathematical clarity and mathematical depth is surprisingly low. Probability concepts have a strange and awkward appearance in quantum mechanics, as if they had been brought within the framework of the theory only as an afterthought and with apology for their inclusion.” (P. Suppes, 1963). Gill suggests that this is still the case in 1998.” (Quoted again in Colignatus (2005:81) footnoot 64.)

A key ‘problem’ in physics is that their models assume time (e.g. on the horizontal axis) but seem uncapable of determining whether is goes forward or backward. This ‘problem’ is thought to have contributed to Boltzmann’s nervous-breakdown and eventual suicide. Perhaps. In 2003, in a lecture in Leiden for a general audience, Gerard ‘t Hooft, one of the developers of ‘the standard model’ in physics, suggested that Time’s Arrow originates in the order of calculations that nature has to do. At least, if I understand him correctly. This is a complex thought since ‘1 and adding 1 gives 2’ has an order of calculation while the reverse ‘2 minus 1 gives 1’ also has an order of calculation while it might be considered, though not necessarily is, an opposite. My impression basically is that such an approach could be a petitio principii, a begging of the question, since one might define the order of the calculation precisely by their occurrence in time. It is more sensible to consider Time’s Arrow a ‘conceptual primitive’. As time flows in one direction, it creates a natural environment in which creatures develop that try to cognate that reality. The mind can develop a model of time that flows in a same manner, and, that might also be the best for a mind, if reality is to make sense. This ‘problem’ of Time’s Arrow might be a good example of how definitions that mimic reality guide our thinking.

One will understand that I have been thinking like this when I wrote Colignatus (2002), “Without time, no morality”. Note that a better version of that article has been included in Colignatus (2005), “Definition & Reality in the General Theory of Political Economy”, 2nd edition.

With these thoughts in the back of our mind, let us now reconsider the “miraculous visions” as discussed by The Economist. Again, it seems a very clear article, much better than other discussions one can find in the Einsteinalia. Yet, it causes questions.
 

Miracles apparently happen - No. 1

The Economist states: “(...) according to Newton, gravity travels instantaneously - which, according to Einstein, is an impossibility.”

Is this a theoretical or an empirical impossibility ? Let us suppose that the Big Bang exploded in three or four dimensions, but not in a fifth - so that all matter and energy are still connected in that fifth dimension, and basically all located at point 0 along that axis. Let us call this direct connection, and its effect shown to us, ‘gravity’. What, then, is wrong with instantaneity ?

From what I have read in popular discussions about physics, they still haven’t fully solved the question of ‘local effect’ or ‘effect at a distance’, so, it would seem proper that they explain why they wouldn’t use Occam’s razor and adopt this simplest model. 
 

Miracles apparently happen - No. 2

The Economist reports: “(...) Maxwell showed that it [light] consists of oscillating electric and magnetic fields. This immediately raised the question of what the fields were oscillating in. At that time, no one could conceive of waves which were not vibrating in some medium. The ocean has waves in water, and sound waves travel through air; it seemed nonsense to imagine that waves could just “be”. (...) Lorentz (... derived ...) that there was a contraction in the direction of the Earth’s movement (...) Einstein realised (...) that there was no seem about it. Space was really contracting, and time was slowing down.”

This, you will note, is a non-sequitur. It doesn’t make logical sense. What Einsteins model does is to stop imagining what those waves oscillate in. Instead he focusses on the measurement results and makes these the absolute source of wisdom. This is not necessarily the best answer to the question what those waves oscillate in, since you might also develop a theory and deduce testable hypotheses. Einstein does deduce testable hypotheses but without a theory about what those waves "be". How can they exist without being something ?

Einsteins model subsequently seems to confuse the definition of space, given by the definitions of Euclid, and empirical space as measured by the instruments of physicists. 

Modern physicists shy away from the possibility that space and time have independent definitions within the mathematical modelling of the world. They regard space and time as what they measure. However, they don’t seem to see that they can be hopelessly confused when they measure speed in meters / second while those meters and seconds change under measurement. My impression is that is better to accept measurement error and try to explain that error.

When physicists get weird readings, then there can be measurement errors and something may happen in interaction of their instruments with what they try to measure. If all instruments, and all the best of them, show the same measurement error, then there can still be such an interaction. Physicists, apparently within their philosophy of measurement, tend to conclude that reality is weird, with “space contracting and time slowing down”. The proper approach would rather be to stick to the Euclidean definition of space (and time) as independent concepts that likely form part of the mind and the ability to think itself, and subsequently judge observations in those terms. 

While Euclid’s definition of space creates emptiness, it may well be that empirical space is filled with ‘something’ that allows oscillations. Presumably, electro-magnetism is the proof that such ‘something’ exists. There are reports that the ‘void’ would be able to produce particles. Also, there can be phenomena in that ‘void’ that appear to us as ‘contracting’ or whatever. All that is OK. But if you want to understand what space is, you would rather turn to Euclid where contracting is out of the question by definition.

It may also be that I simply don’t understand what Einstein did. But then this article of The Economist really hasn’t been clear enough.
 

Miracles apparently happen - No. 3

The Economist reports: 

(1) “(...) the world is ‘non-local’. That is to say, quantum interactions occur instantaneously over arbitrarily long distances.”  Here they refer to the Alain Aspect experiment in 1982.

(2) “This shows that light is actually neither just a particle nor just a wave, but rather both simultaneously.”

(3) “Physics, up to that point in history, had been “deterministic”. (...) But uncertainty is at the core of quantum mechanics.”

(ad 1) You will note that there is now non-locality while with gravity it was considered ‘impossible’. Can we please have some consistency ?

(ad 2) The same goes with the wave-particle opposition. This is like saying that two sides of a coin are the same side. OK, this might be true if the coin is a sphere, but, generally the definition of a coin is understood to be a flat circular object with two sides. We can only conclude that this discussion of waves and particles is gibberish. 

The crux of the problem seems to be that physicists first tell us that atom are particles, and then they do an experiment and conclude ‘Hey, it is a wave !’. One can agree that it is important to generate curiosity, but the proper conclusion is that the definitions aren’t right yet, instead of saying that something is a wave and a particle. Would you enjoy economists explaining to you that inflation is up and down at the same time ?

You also remember the story that masses that move at the speed of light get infinite weight ? Well, light moves at the speed of light - does it have infinite weight ? Well, light would have no mass, correction, it would have some weight since it apparently is deflected by the sun ... Please, ever heard about consistency ? 

Yes, Little Red Riding Hood was eaten by the wolf and later jumped out of the belly alive. Let us move away from that level of explanation.

(ad 3) One should distinguish physics from morality.

The true opposition to determinism is the free will (volition). This is a discussion within the theory of morals and it has little to do with physics. Colignatus (2005) clarifies that the two opposing views of determinism and volition are each consistent and that there is no way to determine which is true. The mind has to consider both angles and cannot avoid the moral weight of choice even though the scientific method assumes determinism by definition. Some moralists hold that ‘freedom is recognition of the necessary’ and that is fine as long as there still is moral responsibility. For example, we still need a judiciary system and cannot absolve criminals for their crimes by accepting that they had a bad upbringing.

The other opposition within physics is between certainty and uncertainty. Richard Gill, referred to above, holds that quantum mechanics provides a true model for probability:
 

“We should be collectively ashamed not to know anything about quantum mechanics. I would like to see all introductory texts in probability theory going a little into the physical (quantum) theory behind the geiger counter before using some data of alpha particle counts as an illustration of the Poisson process; I would like a discussion of the Bell inequalities together with a modicum of quantum mechanical background to show how elegant probabilistic reasoning shows that the quantum world is truly random (unless you would like to go for an even more weird non-local deterministic theory).” (Gill, 1997, quoted in Colignatus (2005:80).)

But Gill’s argument does not convince me. Note that our uncertainty is essentially an uncertainty in our knowledge and predictive capability, not necessarily a fundamental uncertainty in physics. The point is: you may pose that nature would be a probability machine, but you don’t know for sure. You are still using only a model. The scientific challenge remains to develop a model that increases accuracy - and eliminates uncertainty by developing proper definitions. 

Some years ago, I started out trying to understand that Aspect experiment. I gave up since the definitions and terms where hopeless. I am quite willing to follow Gill’s advice that we revise introduction courses into statistics by including quantum mechanics, Bell inequalities and then also that Aspect experiment, but let us first require some clarity on what these are. 
 

Caveat (precaution)

I have been using terms like ‘matter’ and ‘energy’ without properly defining them. I hope that I am excused and that the reader concentrates on the issues of logic and economy of mind raised here. 

I wonder about some experiments of modern physics: do they really know what they are doing, and isn’t there the slightest possibility that they create a black hole on Earth ? I don’t think that I like that risk anymore. My suggestion is that those experiments are banned to the Asteriod Belt.

Physics with its methodology has had more impact on economics than the other way around. Should this continue, so that, so to speak, economists develop gibberish that can destroy the Earth’s economy ? It is a fun question to ask, with the obvious answer that both sciences should enhance transparancy. It is a bit slow, after 100 years, to discover that physics with Einstein’s approach has been turned into an arcane science. Yet, it is never too late to come to one’s senses. One way to enhance transparancy is to tell science journalists that they write gibberish instead of thinking ‘it is only for the lay public’.

There is a caveat for both sciences with respect to mathematics. There is a danger with mathematicians that they lose track of reality and the very aim of their research. Paradoxes like the liar paradox, the Russell set theory paradox, Gödel on his epi-phenomenon on the liar paradox, and the like generate confusion, but some solutions proposed by mathematicians are no deep mathematical results though many think so. Kenneth Arrow with his theorem on voting caused much havoc, since, though the math is right, his interpretation wasn’t. Thus, it is difficult to strike a balance between mathematics and reality, and more awareness of this problem would help research. It might be wise to include more statistics in your programme of research.
 

Conclusion 

I can't avoid the conclusion that I simply don’t understand modern physics. 

Hopefully things will be clearer when The Economist writes about “200 years of Einstein”, if and when the world survives the gibberish of physics.

Yet, it seems that the considerations in this short discussion can at least be of use to students who wish to understand more of economics.
 
 

References

Barney, G. O.  (1981), “The global 2000 Report to the President”, Blue Angel Inc. 

Colignatus (1997), “An estimator for the road freight handling factor”, ewp-urb/9703001, also available at http://thomascool.eu/Papers/Freight/HandlingFactor.html

Colignatus (1999, 2001), “The Economics Pack, Applications for Mathematica”, Scheveningen, JEL-99-0820, ISBN 90-804774-1-9

Colignatus (2005), “Definition & Reality in the General Theory of Political Economy”, 2nd edition, Dutch University Press (non-printable pdf on my website)

Galbraith, James K. (1998), “Created Unequal. The crisis in American pay”, The Free Press

Gill, R. (1997), “Roundtable discussion on education of physicists” www.math.uu.nl/people/gill/

Hao Wang (1974), “From mathematics to philosophy”, Routledge & Kegan Paul

Kapur, J.N. & H.K. Kesavan (1992), “Entropy optimization principles with applications”, Academic Press

Mirowski, Ph. (1989), “More heat than light”, Cambridge 

Theil, H. (1971), “Principles of econometrics”, John Wiley & Sons
 
 

Websites

http://www.economist.com

http://www.math.uu.nl/people/gill/  (Also relevant for survival analysis and the position of statistics as decision science.)

http://www.utm.edu/research/iep/r/reichenb.htm (PM.1. This states “Another example is the definition of straight line which is co-ordinated with a physical process, namely the path of a light ray.” Note that a straight line is axiomized by Euclid so that it is quite another matter whether light follows such a path. Light wouldn’t go straight if it is deflected by gravity. PM 2. This states “that the reality of space and time is an unquestionable result of the epistemological analysis of the theory of relativity.” Note that, instead, reality is defined by your sense-experiences. You can never arrive at reality by analysing a theory. PM 3. Reichenbach is apt at such phrases, but there are sensible statements too, so he seems to be up to something.)

http://www.stanford.edu/~psuppes/

http://www.dspace.cam.ac.uk/bitstream/1810/3484/1/Ramsey.html (highly advised, especially when you want to know how philosophers determine whether the pub where they want to go to truly exists)

http://www-groups.dcs.st-and.ac.uk/~history/Societies/Times__obits.html