Pseudo-scientists, pseudo-shamans and mass delusion: contemporary US culture
[ opinion - december 10 ]
Time is not something separate from the Self... not an enemy of the Self. The human brain is so fond of labeling that which it does not understand or that which 'causes' loss or suffering as an illusion. What about studying how harmonies and symmetries and geometries are generated, created or birthed in time rather than relegating it to the 'illusion of the mind' bin?
- Lori Tompkins, comment on Huffington Post
Next, economics as true science. Theories are tested and, unless backed by evidence, are disregarded.
- Charles P McQuaid, "Squirrel Chatter II: The School that Changed the World" (in first quarter 2008 Columbia Acorn Family of Funds Report)
The two statements above are examples of nonsense. The first is an example of a string of syntactically correct words without semantic content. The second is an attempt to define science so that the academic discipline called Economics as pursued at the University of Chicago can be considered as such. Both are excellent examples of contemporary empty-speak. The goal of the second statement is clear, being a preamble to an attempt to promote a world view in accord with a political sentiment. The goal of the first statement is not easy to see, but needs to be taken in accord with the pseudo-scientific, pseudo-shamanic article in Huffington Post by one Robert Lanza, MD (Is Death the End? Experiments Suggest You Create Time). It is amazing what gibberish can pass for profound by tossing around the word quantum.
To be fair, in the second quote McQuaid is discussing the five characteristics that Johan Van Overtveldt in his book The Chicago School considers the underpinnings of the success of the Chicago School of Economics. We will address the underpinnings of nonsense in McQuaid's statement shortly when we discuss why it is that he is wrong about economics adhering to some kind of scientific discipline (but fair to say that only those who hanker to be scientists from disciplines like Economics impute a scientific method; scientists who build theories, to which term an operational meaning will be attached shortly, tend not to worry about some magic method called scientific). But one ought to get a creepy feeling from the oxymoron "true science."
Reality is that contemporary US society is afflicted with mass delusion. A goodly bit of it is illustrated by the above statements: ceremonial certification in lieu of active education whereby verbiage for verbiage sake passes for accomplishment. As an example of active education the author challenges the reader to give an argument that the square root of two is not a fraction (and for those who are not educated, a fraction can be taken as the ratio of two non-negative integers, assumed without common divisors, and a square root of a number is another number which when multiplied by itself equals said number). This is a simple exercise, but it does require two important items missing from both statements quoted above: operational definition and reasoning. Without them, words are wasted except for emotive purposes.
Science versus engineering
Most people have no idea of the difference between science and engineering, not that this is surprising, given the level of education of a society in which everyone is ceremonially certified but no one can translate simple questions into algebraic form (a joint failure of ability to read with comprehension and to abstract at even the simplest level), let alone perform the algebra. Test yourself; put into algebraic form the statement: If a number has the property that its square equals itself minus one, what is that number raised to the 99th power? If you can read comprehensively and think abstractly enough to accomplish that translation, solve the equation without resorting to brute computation, though brute computation might not work in any case). Succinctly said, the difference between science and engineering is in goals. Engineering aims to make things that accomplish tasks, whether it be bridges or circuits or clones or cures for cancers. The goal of science is to produce theories that explain how things work. To be a theory means that the explanation must provide a means to falsify itself.
Forget scientific method. Like the axiomatic method as a basis for mathematics, it is an illusion (see for example the discussion in chapter seven of Bruno Poizat's A Course in Model Theory, 2nd Edition, which proves and explains the famously misunderstood and misstated incompleteness theorem of G÷del in terms of recursive function theory and also explains why said theorem shows that an axiomatic foundation for mathematical reasoning is illusory; the reason is probably not what you believe or might have read. And be aware that Poizat is a diehard Platonist). There is no scientific method except for the necessity of anything that purports to be a scientific theory to provide the ability to make predictions that can be objectively observed as correct or not, thereby serving to falsify the theory if the predictions are incorrect (for example, Newton's gravitational theory incorrectly predicting the orbit of Mercury) but not to prove the theory if they are correct (Einstein's general relativity correctly predicting said orbit). There is no proof of a scientific theory, at least not in the sense of a proof in mathematics, though mathematics has no relationship to physical reality (which is why mathematics is not a science). Scientific theories are never true, only in search of disproof.
Science is a form of philosophy. That is why the claim by the physician Robert Lanza mentioned above to be theoretician and scientist is more nonsense: scientists are theoreticians, nothing more nor less, even those who are the experimentalists who figure out how to extract from theory a method of falsification. The mechanism of falsification is called experiment. For a good example of this consider the work of John Bell in deriving Bell's inequality that became the basis for Alain Aspect's experiments to settle the spooky action at a distance issue raised in argument against the standard approach to quantum physics by Einstein.
Science is the sort of philosophy that used to be called cosmology. That it has grown to invade a lot more territory than the cosmos does not obviate that fact. Its invasion of areas once considered the domain of metaphysicians has made it quite unpopular, particularly given its success at explaining how things happen without a need for why, something decried by those who live in the supernatural like the religious, certain philosophers, mystics and other superstitious people who cling to a need for something more than how. This debate is not worth taking up, however. In fact, it is pointless to take up since it cannot be settled given that no one in the debate can operationally define what it means to explain to the others satisfaction.
Lanza as a medical doctor is an engineer. Physicians are not scientists unless they engage in the building of theories to explain how things work, with the above proviso that a theory must be testable through experiments to verify predictions that can be duplicated by others. That he is engaged in cloning does not necessarily make him a scientist unless he is cloning as a means of testing theories, which would be experimentation. I am allowing that this might be the case; however, he calls himself a theoretician and a scientist, and to distinguish theoretician from scientist is either evidence of a misunderstanding or else a form of hype. Perhaps what he means to say is he is an engineer and a scientist, or a scientist and some kind of speculative philosopher. It is easy to confuse science and the philosophy of science, though they can run together (the work of Bell cited above). The article by Lanza linked to above is not science or theory, but might be considered philosophy of some other sort, though it struck me as mystical nonsense, perhaps hucksterism of the Fritjof Capra or John Cunningham Lilly ilk (however Lilly's Programming and Metaprogramming in the Human Biocomputer is still quite entertaining).
Applied science is engineering named so to specify that it pursues engineering techniques based on scientific theory and to sound more prestigious. That scientific theory can be useful results from the fact that it makes predictions, and those predictions, besides potentially falsifying the theory, produce results from time to time that allow things to be engineered (for example, quantum physics and the atomic bomb). Note that even falsified theory is useful: orbital engineers working with satellites in near earth orbit rely on Newton's theory of gravity, not Einstein's. In the 20th century, science became more useful as a source of engineering technology than in any previous time, but even now significant engineering is not necessarily based on scientific predictions. In fact, considerable science has come from building theory to explain how engineering, unguided by theory, worked.
The first quote in the header above is more useful here because it illustrates a common abuse of language by displaying words that sound technical without actually meaning anything. For example, the word geometry. What kind of geometry? When a mathematician, or a physicist, says this it is informal but within the context of a given structure. For example, a mathematician might mean it as shorthand for determining the geometry underlying some analytical or topological phenomenon, as in the famous theorem of Atiyah-Singer or that which it generalizes, such as the Riemann-Roch theorem or the Chern-Simons theorem or that which Chern-Simon generalizes, the Gauss-Bonnet theorem. Note that a lot of this comes out of analysis, most especially the extensions of work by Elie Cartan and the Hodge-de Rham theory that deals with cohomology and integration or the Laplacian, and is defined within the specific structure of differential geometry, most especially Riemann geometry. (An excellent example that does not take much mathematics beyond calculus is the geometry underlying surface integrals via de Rham theory (initiated by Henri Poincaré), though it quickly becomes deep through the generalization of surfaces to differential manifolds, integrals to differential forms, and the tie to algebraic topology via cohomology. The interested reader is invited to delve into Ib Madsen and J°rgen Tornehave's From Calculus to Cohomology.) There is also a geometrical approach to partial differential equations due to mathematicians like Peter Olver and Alexandre M Vinogradov that dates back to the 19th century geometer Sophus Lie. In all these cases, geometry has a specific, operational meaning. It is not a general word that sounds technical to be tossed around without specifying what it signifies.
Operational meaning. What is it? It is the heart of mathematics and of science. Without it, it is not possible to determine how to bring diverse theorists into the discussion because without it there is no guarantee that everyone understands the same thing (specifically and in detail), or to put it more loosely (non-operationally), that everyone is on the same page. It is one of the reasons (which includes a hatred for abstract thinking) students mostly avoid classes in mathematics and science: It is possible to ask questions and determine if the answers are right or wrong.
An operational definition describes how one knows when one encounters the thing being defined. A simple example is square root: the square root of a number is another number that when multiplied by itself gives the said number of which it is the square root. Note that as simple as this sounds, there are numbers with square roots that cannot be seen, though they can be approximated as closely as one likes with tedious but specific arithmetic steps. One example is the square root of two, which is not something that can be written down as an expansion in an integral number base. That is because it is not a fraction. On the other hand, there are numbers which have quite simple square roots, like 4. (The concept of square root can be extended to stuff beyond numbers, by the way.) Given a number, one can determine what it is a square root of by multiplying it by itself. And if someone tells you they have a square root of some number, you can check by painstakingly multiplying it by itself the hard way (using a computer might mislead you into thinking some decimal is a square root of two since computers are digit-limited).
So the question is, what is the operational definition of the word geometry used in the quote? Is it Euclidean geometry, spherical geometry, hyperbolic geometry? Is it differential geometry, and if so, is it Riemannian geometry, or like general relativity, pseudo-Riemannian geometry? In what dimension? Or is it not referring to any fixed dimension? The geometry of general relativity is four dimensional: it is realized on a smooth (differential) four-dimensional manifold in which all the tangent spaces are isomorphic to four dimensional Minkowski spaces, which words signify well-defined objects. Operationally defined, to be sure. One of the important geometric characteristics of (pseudo)-Riemannian manifolds is curvature, another operationally defined concept that is at the heart of gravitation in general relativity. Mathematicians, by the way, are not bound to any dimension, finite or infinite.
My guess is that Ms Tompkins has no operational meaning for her invocation of the word geometry. One reason for guessing this is her reference to symmetry, because Felix Klein (in his so-called Erlanger Programm) in the 19th century studied symmetry and geometry, demonstrating that symmetry determines types of geometry; these results led to work by Elie Cartan in differential geometry, extending Klein's results to Riemannian geometry, completing Klein's program.
What is the operational definition of symmetry? Without going too far afield, it is a group of transformations acting on a space. If the reader wishes to understand what that means, there are references galore but they are not completely trivial (perhaps Willard Miller's Symmetry Groups and their Applications is a good place to get one's feet wet).
Different transformation groups determine different geometries. They also play an important part in physics, as demonstrated by the difference between relativity and Newtonian physics. In essence, Newton's field equations are invariant under a different transformation group than are the relativistic field equations. This means that the underlying geometries are different: Newton's is Euclidean. It became a critical point when people realized that Newton's equations were invariant under a different group of transformations than Maxwell's equations, which are invariant with respect to the same transformation group as is relativity. Critical because they could not both exist in the same universe, defining different geometries. In fact, this was a guide to formulating special relativity. (I recommend reading Freedman Dyson's lecture "Missed Opportunities" which can be found in the Bulletin of the American Mathematical Society, Volume 78, number 5, September 1972, pages 635-653 and can be obtained free online from the AMS. It also appears as an appendix in the book Second Year Calculus by David M Bressoud, which I also recommend; in fact, any person who wants to consider him- or herself educated ought to know this material, which is quite elementary but gets at the basics of modern calculus by motivating it with physical application, starting with Newton's geometric argument for his theory of gravity and ending with a derivation of E=mc2 via Maxwell's equations.)
Moreover, the difference goes to the heart of relativity and the idea that time is coupled with space, unlike the independence of time from space in Newtonian space-time. Another way to view it is that Newtonian space is a place to put things, whereas in relativity it is instead relationships between events. The absolute character of Newtonian place is lost, as is the absolute character of time and its passage, which occurs at different rates for different reference frames. Distance in relativity is not between things but between events, with the only absolute being the global pseudo-distance between space-time events. This is an issue not discussed by Lanza in his article, but Lanza is pushing an agenda that promotes somehow reducing physics to biology, more like a territorial dispute than a scientific pursuit. This issue of coupled space-time goes to the heart of the nonsense in Lanza's article, since he must explain how it is that biology determines the curvature of space-time and the physical difference in the passage of time within different reference frames that are functions of purely physical conditions. It is also at the heart of the difference between the metaphysics of Leibniz, who considered space a series of relationships, and Descartes who believed, as codified in Newton's system, in space as a place for things. (Bertrand Russell gave a nice discussion of this in his book A History of Western Philosophy.)
To be sure, it was eventually noticed by astronomers and physicists that Newton's gravitational field equations do not accurately predict the orbit of Mercury, a defect cured by the relativistic field equations. Besides providing a method for falsifying Newton's theory and giving a reason to consider general relativity as a superior alternative, it also makes it difficult to explain how this orbit and its anomaly might be reduced to biology. But that is more of another story hinted at above.
Notice that none of this work could have been carried on through generations of different mathematicians and physicists if not for operational meaning. They were able to understand what the others meant with complete precision, allowing generalizations of theories and identification of errors.
So the next time you use some sloppy term with a scientific sound, like geometry or trajectory or quantum, think about what you are doing. Chances are you are trying to frame some nonsense in a way that sounds scientific. Try to formulate your language with operational meanings that specify to the listener or reader an operation that will allow them to know if they indeed are confronted with what you are talking about or if it is just bullshit.
Societies have short memory. Even traumatic events like the Korean and Vietnam police interventions are barely a blip except for those who participated, whether in-country, as protestors, or through the loss of family, friends and lovers. However, it is clearly enough of a memory to keep citizens of the US from wanting a democratic form of spreading the suffering of war by some means such as conscription. Whether that is good for democracy is a question almost never debated and not to be addressed here, either. Instead the interest here is with mass delusion and how quickly it is forgotten.
If you go to the link on the Huffington Post, the article by Lanza, you will find a plethora of delusional comments besides Tompkin's. My favorite is the commentator who brings up Jehovah as the source of his reality. This is the same Jehovah or Yahweh, I assume, Which as a genocidal maniac in the Old Testament not only condones mass murder, ethnic cleansing and genocide, but orders it under pain of death to those who don't follow the order. Mercy from this Merciful One is to allow girls who are still virgins to remain as slaves instead of being slaughtered like their parents and brothers (never mind the age of the victims). The same Jehovah which in Its inspired word has the number pi as three. Which is jealous like an infant. Which sends a couple she-bears to kill 42 children for teasing Elijsha for being bald. It is amazing that someone could hold to such malarkey. I personally want to call these Jehovah-intoxicated clowns out in the same way that Elijah supposedly called out the Baal worshipers to a duel between Baal and Jehovah, taunting them by saying perhaps their god didn't answer because it was in the toilet, then killing them all when they lost the contest. I would like to see these Jehovah-intoxicated pray a satellite into orbit. Would Jehovah be too busy at the toilet to answer their prayers? Would a rocket put a satellite into orbit first? An even easier test for their all-powerful Thing would be something simple like making the square root of two into a fraction. That ought to be a snap for an all-powerful god, if such exists. Once they convince the God to perform this miracle, they can write down an integral-based expansion of this fraction which could be expressed with a finite number of terms or in an expansion that repeated a pattern ad infinitum. Surely a digitary revelation would not be too much more to ask of such a creature. In any case, since we have an operational definition of square root, whether Jehovah got it right or not could be tested. Probably Jehovah is as afraid of mathematics as are most humans.
Of course, that a majority of the nation believes in such a demonic creature as a model of righteousness is a form of mass delusion. But it is not necessary to attack delusion at this level. It is more enlightening to consider recent national history.
To wit: the 1980s. It was a flashback to the Salem witch trials made famous in colonial history as a local form of moral panic writ large. The nation was in the grip of a moral panic regarding devil worshipers molesting and eventually murdering millions of children. People went to prison and parents lost custody of their children in this mass delusion carried out in courtrooms across the US and relentlessly reported in the national media. Eventually the insanity was exported to other nations before it was finally halted. The crimes were in most cases physically impossible. They involved magic. Children claimed they were flushed down toilets into secret rooms and raped. They were flown through the air to magic caverns. The stories on which people were imprisoned were totally outrageous, unbelievable stories defying logic. I remember yards being dug up in the coastal area north of Santa Barbara to find thousands of purportedly buried dead infants. They came up empty and the accusers (social workers, mental health professionals and prosecutors who practiced leading interview techniques with the children) claimed this as proof of their accusations, since it showed that the devil worshipers used magic to make the children remember the wrong locations.
No evidence was found for any of these crimes, which itself became a form of evidence for the accusers. As far as I know, all the victims of this mass delusion have finally been freed from prison. But when the FBI pointed out that it was unbelievable so many infants could be slaughtered in ritual sacrifices every year and no one reported them missing or found traces of them, the panicked said that high governmental officials were involved, perhaps the President of the US, and the FBI was part of the conspiracy. Eventually most citizens came to their senses and the panic ended, though there remain believers even now lying dormant like a cancer in remission. Worse, there are mental health professionals who continue to push this agenda, some of them using the discredited technique called recovered memories.
To any rational person, this was a mass delusion. However, it has been forgotten by society. Perhaps that was because of the national mood swing from moral panic to mass euphoric mania with the internet bubble. Though that is remembered, it is not remembered in its gory details of venture capitalists praising the genius of children pushing juvenile ideas, of financiers hailing the coming of the New Economy, of companies listed on the NASDAQ stock exchange with not only no profits but no revenues at all. I remember Austin, Texas, in the grip of this mass delusion. Sitting on a flight from Los Angeles in first class behind some children talking about how they could save DrKoop.com by keeping everyone's medical records online as a parade of younger people came up from coach to beg the kids in charge for their jobs. It was hilarious; my seat partner and I laughed out loud. What was funnier was hearing the news tout the youngster taking over the moribund company as an experienced turn-around expert. And it got worse, with Austin entrepreneurs headed for bankruptcy praising Bush Jr. at his inauguration as leading the way in this New Economy. Names like garden.com and Steve Papermaster and that of some woman I have forgotten who started a stupid company that went bust following which she started a sperm bank in California are all forgotten now, though they were the toast of the bubble at the time. Papermaster and the nameless woman both spoke at Bush's shindig.
It isn't over, either. The latest mood swing has been in the opposite direction, with people bemoaning the crash of equity and commodity markets (with the exception of gold) and buying Treasury bonds in a sort of inverse bubble, again paying hundreds of times more than the value of their investments but now certain of impending financial doom. Others of us have done quite well in the current bull market for equities and commodities, but it is easy to find harbingers of doom claiming it is impossible to make money in the current equity and commodity markets even as they continue to go up. Turn on the tube or go on the internet. The Casssandras wail everywhere and lose money, many for clients.
The question is, why are waves of mass delusion sweeping across the US? Granted, US citizens are as superstitious as any residents of Haiti, of any so-called third-world nations in Africa or Latin America. And there are occasions of mass hysteria in those places. For example, there have recently been localized delusions regarding witches in parts of Africa and New Guinea. But the operative word is localized. In the US it is national.
Consider that the Salem witch trials were localized, though likely influenced by earlier European witch frenzies. The Salem trials, like their European counterparts that were less localized, were amplified by religion, most especially of the uniform variety. The Church of the Middle Ages amplified and spread these sorts of moral panics.
The insanity of the 1980s in the US was also religious in nature, but the amplification was more a function of media. Local insanity was reported on and gained supporters in new locales who began to look for devil worshipers near home. Other factors also played a role. For example, the pseudo-scientific, pseudo-medical practice of psychology became a factor, with "mental-health professionals" spreading the delusion via conferences, particularly the method for extracting "repressed memories." This became the means of spreading the panic outside the US. Media personalities like Geraldo Rivera jumped on the bandwagon when it seemed that this was going to be a hot topic, ratings and stardom always incentive for idiocy.
Since the eighties, the media has fragmented into newsgroups that cater to their own brand of listeners who follow only their favorite media and refuse to hear any other side. They are open to what are often bald-faced lies spread as news, along with opinions that are at best childish and most often uninformed, without substance or understanding and like the examples touted above, full of emotive language with no operational content. The words socialism and communism and fascism are bandied about by people without a hint of operational meaning. Or a smidgen of conventional or historical context.
The internet has amplified this. Now all groups from right-wing militias and anarchists and white supremacists and racists and anti-bankers and anti-Muslims and anti-Semites and accusers of those who do not agree with Israeli policy of anti-Semitism to left-wing anti-bankers and anti-businessers and Marxists and aging new-agers and anti-Semites and accusers of those who do not agree with Israeli policy of anti-Semitism to Christian fundamentalists of all persuasion and terrorists of all persuasion and believers in Icke's contention that the rulers of the world are alien bipedal lizards who eat children and conspiracy theorists of all shape from believers that Obama is not a US citizen and is an agent of Muslim domination to believers that the US staged the 911 attacks to the likes of Alex Jones who believe everything is a conspiracy to pedophiles and zoophiles and people who are sexually aroused by scat, all have their own personal links to like-minded individuals and clot into feedback reservoirs oblivious of the world around them.
In essence, there is no longer any center. It is akin to the social dissolution common in times of crisis as documented and discussed by W H McNeill in his classic history The Rise of the West. These periods are characterized by the intellectual splintering and destruction of all the authority of classical knowledge and belief.
But why does it seem centered within the US? That is perhaps more easily answered by considering that the US has become an empire, especially since WWII, and contrary to certain political commercials and blather by irrational politicians, the major internally destructive force in empire is the burden of military. The US is becoming like the Soviet Union and Britain and Rome, among other former empires, cannibalizing its citizenry in pursuit of military solutions to all problems. This myopia is characteristic of empire.
To expand on this, a recent Republican fear-mongering television ad in the mid-term elections of 2010 showed a Chinese professor telling a class that what brought down the US brings down all great nations (he didn't use the word empire), namely spending on social services for citizens like health care or pensions. For examples he gave Rome and Britain, but avoided the Soviet Union. The professor in the ad is not cognizant of history (or maybe it was the script writers), because Britain and Rome (and the Soviet Union) did not provide these kinds of services. What brought them down financially was spending all their resources on a military, or as in the Soviet case, a military-industrial establishment running the government. That coupled with too much concentration of wealth (and hence power) in too few hands (a result of printing money to fund a bloated military bureaucracy). Any student of history will find this to be the case.
Economics as superstition
The recent turmoil in financial markets has been partly caused by insufficient attention to rigorous financial modeling. Among the causes of this failing is the relative shortage of mathematically well trained professionals in the financial services industry.
- Darrell Duffie, reviewing Stochastic calculus for finance, by Steven E Shreve, Bulletin (New Series) of the American Mathematical Society, volume 46, Number 1, January 2009.
Darrell Duffie's quote above is an example of how it is possible for humans with great expertise to become so immersed in nonsense that they are unable to see reality. Realty is that the major cause of the failing to which he refers (the banking crisis of 2008 due to derivatives) was not poor modeling but implementation of a "theory" that has as much application to finance as Ptolemaic physics has to orbit determination. That the American Mathematical Society would lend itself to such blatant propagandizing is astonishing to me, a member for many years.
Duffie is a kind of engineer, a financial engineer with a PhD from Stanford in Engineering Economic Systems, a department founded by David Luenberger, an electrical engineer specializing in optimization. Duffie is now a professor in Stanford's Graduate School of Business. (Duffie and I worked for the same company in Palo Alto though at different times a few years apart; one of the engineers I worked with there had an office full of crystals to improve his vibrations.)
Shreve's book that Duffie reviews is centered on the application of stochastic processes, in particular the theory of stochastic integrals begun by Norbert Wiener for integration of non-random functions with respect to Brownian motion in the sense of Stieltjes integrals, to finance. (For those with incomplete education, look at the construction of the Riemann-Stieltjes integral in chapter six of the elementary text by Walter Rudin, Principals of Mathematical Analysis, this being material anyone with a college education meant to be beyond ceremonial certification ought to know in any case.) Wiener's integral is linear in the sense that the integrand does not depend on the sample paths of the Brownian motion; Kyioshi Ito extended this to integrals in which the integrand depends explicitly on the Brownian sample paths. His famous theorem, usually referred to as Ito's lemma, gives a chain rule or variant of the fundamental theorem of calculus for these processes. Succinctly put, the sample paths for the Brownian motion process have no derivatives. They are, in fact, of unbounded variation in every interval which sort of means that if you took one of these paths and straightened it out over a time interval, no matter how short, it would be arbitrarily long. (See Rudin cited above for an operational definition of the elementary concept of variation of a real-valued function over an interval.) Because of this unbounded variation, the chain rule or change of variable formula or fundamental theorem of calculus for these Ito integral-defined processes, however the reader cares to look at it, includes second order terms that do not occur in the bounded variation case (this can be used as motivation: the reader ought to find it enlightening to consider this in terms of the fundamental theorem of calculus and apply Taylor's theorem to a Riemann-Stieltjes integral with respect a process of unbounded variation and watch the second order terms pop right out).
The punch line of this technical stuff comes from Duffie. He writes in his text Dynamic Asset Pricing Theory (page 80), "More than any other result, Ito's lemma is the basis for explicit solutions to asset pricing problems in a continuous-time setting" (italics his). Duffie is discussing what are called derivatives. The tool he is working towards with the use of Ito's lemma is the Black-Scholes (B-S) options pricing formula, which earned a Nobel prize for Myron Scholes and Robert Merton. It is sort of the cornerstone of financial engineering and derivative pricing and is generalized to other derivative products well beyond plain vanilla options. In fact, these generalizations are an industry in their own right now, both the generalization of B-S and the numerical solution of associated partial differential equations. (For the reader interested in a more elementary introduction to this sort of mathematical finance or economics, I suggest Duffie's Security Markets: Stochastic Models or even Ioannis Karatzas and Steven E Shreve, Methods of Mathematical Finance for the reader already hip to stochastic integrals. Karatzas and Shreve also wrote a gentle textbook introducing stochastic calculus, Brownian Motion and Stochastic Calculus, unfortunately too late for the poor author who as a graduate student was forced to trudge through the short but terrifying Stochastic Integrals by H P McKean, Jr.)
The important point is that if economics were science, Black-Scholes would be gone. Duffie's review of Shreve's Stochastic calculus for finance shows precisely why economics is not science. Moreover, it highlights the dogmatic ideology of modern economic "theory." Duffie's quote at the head of the section is the analogue of a practitioner of Ptolemaic physics explaining how to remedy the repeated failures of his "theory" to put satellites into earth orbit. Reality is that B-S has failed every empirical test it has encountered, beginning with the spectacular failure of Long-Term Capital Management (LTCM) in 1998, when it lost over four billion dollars in a scant four months and caused a major crisis in the financial industry leading to a bailout to save the system (nearly everyone on Wall Street was into this outfit with significant capital). And it is not possible to claim that the people running LTCM were na´ve and untrained, since they included both Merton and Scholes (who lost their own money in the venture). (Roger Lowenstein has written a book on this fiasco entitled When Genius Failed: The Rise and Fall of Long-Term Capital Management, but I cannot recommend it since I have not read it and fear it might not get the details right.)
Of course, the more spectacular failure of B-S was that referred to above by Duffie, namely the recent near-failure of the financial system due to mortgage derivative products. More sophisticated modeling is not a way to fix a theory that produces wrong predictions. No matter how sophisticated the models, if the underlying theory and its assumptions are wrong, they need not work.
Nor can one fault Duffie for not appreciating and understanding the underlying beautiful mathematics (though it is not clear that all users of the Ito theory are aware of the assumptions regarding the Brownian motion process, or Wiener process as it is often called, in terms of physical reality). But if sophisticated mathematical theory is the standard for a science, then Ptolemaic physics passes that test (as does modern astrology). In fact, just like Duffie suggests above as a fix for the financial theory, the Ptolemaic models became ever more complex to account for failure of prediction. It took the genius of Newton to see that what made planets remain in orbit was the same thing that made objects fall near the surface of the earth. And this gets to the quote in the beginning regarding the University of Chicago economists practicing science by examining evidence. In science, the evidence is almost always simple, but requires something economists seem unable to bring to their work: objective observation. The data Newton required was the planetary orbits as constructed from painstaking observations by men like Brahe and Kepler. The requisite test of his theory was to determine if the theory correctly predicted the observed orbits. Either it did or it didn't. The failure of Newton's theory to predict the orbit of Mercury was not noted until much later and it falsified that theory of gravity. One of the first tests passed by general relativity was the correct prediction of the orbit of Mercury, accompanied by explanation of how it worked in that case (Mercury's near approach to the Sun make higher order terms in the gravitational field equations apparent).
The problem is that mathematical beauty and rigor are not sufficient for physical viability. To quote RK Sachs and H Wu ("General Relativity and Cosmology," Bulletin of the American Mathematical Society, Volume 83, Number 6, November 1977, page 1163) and substituting in your imagination the term economics or finance for it, "As with other current physical theories, trying to regard it as pure mathematics results at best in piecewise clumsy and ill-motivated pure mathematics." And it is worse when regarded as a scientific theory with predictive power.
If the same kind of theories as one finds in Economics and Finance were applied to building bridges, people would stop driving across them because they would collapse. And if the bridge builders were like economists and financial engineers, they would blame reality for the problem because that is what is done in economics. B-S and its modern extensions have as much applicability to finance as does Ptolemaic theory of planetary orbits to space exploration. Experimental results show repeatedly that neither theory fits the empirical universe. But Economics and Finance are unlike science; if an Economic "theory" is shown to not fit reality, a scapegoat is found. Usually it is a temporary aberration in reality itself; in this case it is "untrained professionals." Hogwash. The entire edifice of modern economics has become little more than religious (or superstitious) dogma.
There is plenty of economic nonsense that has been falsified as thoroughly as B-S. For example, the counter-intuitive notion that cutting taxes increases revenue (so-called supply side economics). Guess what? It doesn't. People like to say Reagan's tax cuts increased revenue, but they overlook that it increased the budget deficits so much that the national debt tripled. In essence, borrowing to pay for big government (unless one does not consider a huge military establishment as government) increased revenues and the government got a small percentage of that increase. (And in reality, the "borrowing" included printing money in the same fashion as done now, that is by the Federal Reserve, a branch of government, buying Treasury debt by crediting new money (high powered money) to the Treasury accounts. It was clandestine, though, because instead of doing it openly, the Fed bought the debt from the primary dealers, paying them a commission to make it appear that government was borrowing from the public. Does anyone see the irony of government borrowing from itself? And how does one account for freshly printed "electronic high powered money" on a balance sheet? This clandestine method of printing money is discussed in Milton Friedman's little book Money Mischief, still a good read.) Bush Jr. gave this nonsensical "theory" another test, resulting in even more massive budget deficits while actually pretending that he fought two wars on foreign soil without cost. The deficits falsify this notion.
One would do better to study Thorstein Veblen's The Theory of the Leisure Class (ignoring the notion of social Darwinism to which Veblen subscribed for some reason it is difficult to fathom) in order to understand and perhaps construct a theory for "economics" (finance) if such be possible. (Part of the problem for "economics" is that the same actions can precipitate different outcomes, unexpected outcomes, when used at different times and in different societies, like the Japanese with financial stimulus since they save the money. That is, the results of economic actions are unpredictable, something science cannot deal with. This unpredictability is pointed out and exemplified further by Friedman in the little book cited above.) Veblen captured the basic primate behavior that is the real root of what is called "the economy" (call it economic behavior). But more importantly Veblen showed why the edifice upon which modern mathematical methods in economics rest are wrongheaded. First and foremost, the attempt to isolate and extract "the economy" from society makes no sense and leads to a lot of bad assumptions. Secondly, the idea of humans as rational in their choices, even within the framework of their primate behavior (such as conspicuous consumption, conspicuous leisure, pecuniary culture and the conservation of archaic traits, among a host of primate behaviors that include a variety of ritualistic posturing like ceremonial certification as necessarily implying (and in lieu of) education), is nonsense since they are no more aware of the basis of their behavior than is a chimp. And third, the falsification of the very idea of what is called a utility function. Utility does not exist as a function, and is in essence a fictional notion without predictive value. It's major function is to allow meaningless mathematical optimization, application of the theory of games, and to attack theories outside the conventional dogma. The best methods for making financial decisions like investing are based on "economic behavior" and not on mathematical models (apply Veblen. One can argue that the method called charting is an attempt to capture group behavioral trends; clearly charting is at odds with the model of Brownian motion as noise source, since Brownian motion in discrete time is the random walk of the random walk down Wall Street).
The "economic" assumptions that underlie Black-Scholes are not valid in any case. And if one desires to play Mathematical Economics, consider the theorem of microeconomics that in perfect competition it is impossible to make a profit (this is, or ought to be, part of any standard course in microeconomics, but really should be part of any class in elementary Economics; see Ralph W Pfouts, Elementary Economics: A Mathematical Approach for a concise, elementary discussion or David M Kreps, A Course in Microeconomic Theory for a more detailed derivation and discussion in a more up to date and more available text. Pfouts' book is worth finding if one wants to learn basic Economics without pleonasm.) If one considers competition to be essential to free markets and free markets to capitalism, then one can argue that massive profits are a sign there is no free market (hence no capitalism): simply take the contrapositive. If the existence of perfect competition implies there can be no profit, then if there is profit there is no perfect competition. (I once had an economist tell me that the contraposition was illogical; not a surprise that someone who studied Economics would have no grasp of even the most rudimentary principles of propositional logic.) By relaxing requirements and fudging a bit, one could work this into a "theorem" that the more profit made by enterprises, the less competition and that in a corporate run economy, competition and hence capitalism is impossible. But of course, that would be heresy, never mind it is as viable as any other argument resting as it does on a well-respected theorem in the formal discipline of Economics. Such a game is pointless since no one really believes the Economics' bullshit they spout; instead it is the bullshit they feed one another and their constituents in the games of politics or finance they play for control.
Most especially, the "Capitalist" dogmas of Economics and Finance play well to "conservative" political groups and to their benefactors, big business. For that reason, we will likely see the nonsense continue until there is a large enough collapse that everything will be forced to reset. Until then, most citizens need to prepare themselves for a rich diet of bullshit. (Or as e e cummings put it,
"(if you can't dentham
Empire and delusion
It is amusing (in that terrifying sort of way like riding a roller coaster off the tracks) that when something is not understood among the human primate, the natural (instinctual?) reaction is similar to that of the physician Lanza: drag in some magic words or phrases as evidence from some theory of which few in the audience will have the vaguest conceptual grasp. Never mind their use be without basis in that the magic words neither point to anything specific in a body of knowledge or themselves offer support for the position. Currently every crank pushing hooey uses quantum physics (might it be the result of the ridiculous movie What the bleep do we know? or is that a symptom?); it seems to be the current snake oil applied by those who want to push amphigouri that might be called mystical while appearing scientific. Of course, it is not science. It is not theory. It is not even loose speculation. It is the purest of galimatias, almost worthy of Dr Erwin Corey: syntactically correct strings of symbols without semantic content. Nowhere in it does one find operational definitions or testable hypotheses; but in contemporary society, technical-sounding jargon applied without signification predominates.
Quantum physics is a well-developed theory with operationally defined terms and the absurd promotion of bulwa by invoking the word quantum is not any sort of application of the theory except propaganda or nostrum. (For the handful who are able to read and with a mite of ambition, I suggest chapter one of the first volume of Quantum Mechanics by Albert Messiah (it is now available from Dover), "The Origins of the Quantum Theory," which describes the foundational experiments. For the more ambitious reader, try something after this little elementary assignment like reading the more up to date Quantum Mechanics for Mathematicians by Leon A Takhtajan. And for those overawed by Heisenberg's uncertainty principle, take note of the fact that it is an artifact of the Fourier transform as used in quantum physics and in signal processing (occurring in both). In particular, it is not mysterious (position and momentum are Fourier transform pairs in quantum mechanics). Take a look for example at Patrick Flandrin's Time-Frequency/Time-Scale Analysis (translated from the French by Joachim St÷ckler) for an elementary discussion (he calls it the Heisenberg-Gabor uncertainty principle for Dennis Gabor who studied it in the context of communication theory). Flandrin discusses the work of David Slepian's explaining how it is possible for a signal (in electrical engineering) to be both band-limited and of finite temporal duration, a feat more mysterious than the uncertainty principle since this is mathematically impossible. But read Slepian's two charming little expository papers, "Some Comments on Fourier Analysis, Uncertainty and Modeling," in The July 1983 issue of Siam Review (volume 25, pages 379-393) and "On Bandwidth" in the March 1976 Proceedings of the IEEE (volume 64, number 3, pages 292-300). And if you cannot grasp this elementary material (or do not know what is the wave function), then you probably ought to avoid raising the specter of quantum physics to ceremonially validate any of the bullshit you are likely spouting. But if you like cool sounding words, Slepian brings in prolate spheroidal wave functions! Think how much magic is contained within the words "prolate spheroids.")
What does this have to do with mass delusion? Again, it may be more symptom than anything, though it is worrisome to have people without an inkling of an idea of what quantum physics is suddenly claiming it as a sort of divine revelation that validates any nonsense, akin to a Quantum Revelation to John for end-time visionary New-Agers. With media feedback loops and the coalescing of like-mindless bozos, one finds that feedback (and feed forward) amplifies ridiculous signals. Media feedback has made mass delusion more contagious over wider spatial areas and faster spreading than ever. Time has entered, despite the notion of Lanza of time as being a purely mental phenomenon (which brings to mind the California cult of a couple decades back of devotees convinced that not believing in time and aging would prevent aging and death; those who died simply did not have faith. It seems more people need to learn the reality of the Marine Corps proverb the author experienced in Vietnam: Shit in one hand, wish in the other, weigh which is heavier).
Mass delusion seems to be a symptom of social crisis. The US has, since WWII for certain, grown into a military state as a means of building an empire. Not to say it did not have empire as goal prior to WWII, given the Manifest Destiny push of 1848 into Mexico, for example, among a host of other aggressions leading into the 20th century. But prior to WWII the US did not maintain a standing military at such unreal cost. Nor did it maintain what can only be called one of the most effective police forces in the world, a police force pushed under Bush the Younger to unimaginable extremes to spy on its own citizens. The society seems willing to sacrifice its citizens to military domination, much as did the Soviet Union (and Rome). Many of the current financial crises are due in good part to localized inflation in specific markets, like local real estate hyperinflation resulting from massive government spending on programs like "defense" that are not uniformly distributed spatially (and have nothing to do with either defense or war-fighting). Moreover, the US is on constant war-footing now in terms of spending, but without any real ability to fight war since fighting war diverts the funds from creating jobs within a handful of corporations to spending it abroad on troops.
In order to convince the population at large that this sort of expenditure is justified, it must be kept in constant fear. The government has been quite good at this, as those of us who did duck and cover drills in case of Soviet nuclear attack remember. This plays a part in building a crisis scenario. It is intentional, but it has unintended consequences like mass delusion.
Not everyone in politics is convinced that an empire is necessary. For example, the original tea party politician (long before the infinite-mouth-to-brain-ratio clown Santelli on CNBC), the libertarian Ron Paul, has worked with the socialistic Barney Frank to attempt to close US bases abroad. Does anyone believe it will succeed?
There is no real debate on government spending doled out to big defense corporations who contribute little to nothing to defending the US. But they are part of the government bureaucracy, both DOD and the corporations, and indeed part of the foreign policy apparatus, working with DOD to guide foreign policy. Or perhaps to create foreign policy. Cutting those defense contracts to Lockheed-Martin and Raytheon, two among a host of government subsidized administrators of public works programs (pork), is out of the question.
Politicians and pundits talk about the center, about moving to the center, but the problem is that the term center has no operational definition. There is no center except when someone declares they are there and someone else is not. And John Boehner's center is not Ron Paul's center or Barack Obama's center. So far as I can see, the center has moved to a place where no social programs are allowed. The only sanctioned government spending in the now forming center will be for "defense" which means jobs programs through big corporations to provide little to nothing necessary for defending against, or invading, anyone. And for police. And for security programs that spy on citizens and non-citizens alike. The center wants to cannibalize the middle class, the citizenry, for big government as military-defense conglomeration and police-security apparatus. All other services are unnecessary in the new center and will be provided by corporations for their own profit while enslaving the citizens. Obama attempted to move this Bush-center to what is termed the left (which means providing some social services) and people say that is away from the center. (Though I have not yet heard proposals for getting rid of the FAA. Few citizens who fly would appreciate the "free market" solution: the airlines that crash too frequently would go out of business when people stopped flying them.)
So be it. The US is not a free enterprise system based on competition in the sense of capitalism. It is structurally a monopsony with single buyer government supporting a plethora of large "defense" corporations that pump money into a public that is forced to buy from an oligopoly of providers of commodities, services and goods. The government to which the monopsony feeding tubes are attached prints money to fund its "defense" programs and police and security forces and military (which is more a funding mechanism for the parasitic "defense" contractors than an army for fighting wars). Moreover, the corporations are a part of the government, making policy regarding how to divvy up services. Defense corporations and the military establishment are a major part of determining foreign policy and constructing programs for the "military." The health care industry makes policy regarding health care in the US. The same is true of security and police, and also education which itself might soon disappear (perhaps no loss, given its real goal is to teach conformity and mythology and ceremonially certify an educated class). Citizens are not relevant except as serfs to the corporations.
To be honest, the government of the US has much in common with the Holy Roman Empire of the 14th century, the time of predatory prelates and knights and robber barons. And perhaps 16th century Poland-Lithuania, a democracy in which king and diet were elected by noble elites for fixed terms, with a Pacta Conventa at coronation enforcing that the king was hired on contract to manage the state. In the models of state governments during the so-called "age of absolutism" there were far fewer absolute monarchies than is commonly taught; the political structures ranged from the decentralized and constitutionally governed republics to constitutional monarchies and hired kings to Papal states to the absolutist monarchies like France. (See Norman Davies' Europe, Chapter VI, Chapter VII, and Chapter VIII.)
The word capitalism as it is used seems to have nothing to do with competition or free markets, and there are libertarian definitions of free market that do not necessitate competition. Worse, what people seem to not understand, especially the libertarians, is that laissez-faire is not synonymous with or equivalent to or sufficient for or guarantee of free enterprise or competition. This is particularly true in oligopolies which is what control by large corporations entails (though there are plenty of other examples). To repeat past points, the US is more than a form of oligopoly. It is, in fact, corporate government. Recent Supreme Court rulings have given corporations more control than ever before over government. Ron Paul called it corporatism. A better term might be corporacracy: democracy with the political choices made by corporate elites. In effect, it is a purely American manifestation of fascism, which with the examples given above from Davies' history can be seen as not particularly new, incorporating older ideas (not implied as deliberate), which could also be said of Mussolini who to be sure was emulating what he thought to be the Holy Roman Empire as a model.
(This is not to defend Ron Paul, who really doesn't seem to get the "economy" (more or less meaning financial system of the society of the US or of the world) based on what he says and writes. Paul ought to stick to what he does well: delivering babies. He has his own private mythos of "Capitalism and Free Markets" and his own personal revelation of the Constitution, a highly overrated document as mired in mythology, ambiguity and private interpretation as the Bible. He says he is a fundamentalist Christian, a form of delusion that borders on lunacy. It is not clear that he believes in the god often referred to as The Market, usually brought up by emotive Republicans who sound like Old Testament prophets crying out to Jehovah, but he does seem to worship gold as a magical substance he believes the writers of the Constitution intended to be the basis for the monetary system of the US. At least he doesn't seem to confuse capitalism with the stock markets or commodity markets (though he may confuse it with profit), which is the case with most of the nitwits on CNBC, particularly their lot of homely women who cry the word Capitalism as a purely emotive term.)
As noted above, when crises occur societies lose traditional values and fragment. McNeill's book cited above gives a wide variety of examples. Of course, it is usually impossible to ascertain if there were mass delusions as these cultures disintegrated and transformed, but judging from Europe from the middle ages to the present and from the experience in the US and in certain native cultures that faced extinction (the ghost dance among US native peoples facing invading Europeans), it is likely. Human primates have not changed that much in the last short period of six thousand years or so. But consider Rome, in which there were competing cults to replace the traditional forms of religion. Eventually one particular cult emerged triumphant, becoming the mass superstition of organizations today called Christianity that seem to have in common only the name of the mythical creature that most (but not all) of them worship. One of the major threats of modern culture is science which through its form of philosophy has allowed the growth of technology by engineering based on the predictions of its theories (for example, even Newton's discredited gravity provides the tools for orbit determination that allows the launch and orbit maintenance of man-made satellites, an idea unimaginable before Newton overthrew Ptolemaic physics). If not for this success of technology, the competition between science and Christianity would not be an issue except for an educated (not just ceremonially certified) few. Yet even though only a small segment of the population of the US has even an inkling of any scientific theory in detail, they do not doubt certain precepts (the Sun as center of the solar system) that were deemed heresy not so long ago, heretical enough to get a believer (i.e., in a heliocentric solar system) burned at the stake. This is a crisis in itself, since there is no way that prayer will get your satellite launched into orbit. Scientific theory, even a discredited one, can help an engineer to do so. And most of the other mechanisms used for the launch are products of scientific theory or have been improved by scientific theory.
That religious (organized superstition) beliefs continue to fall to theories that provide seemingly magical mechanisms outside the superstitious' ability to create or control pushes them into a corner and takes away their small claim to utility. And the jealous superstitions that are formal disciplines like Economics and Psychology and Sociology and their ilk want to share in the glory of science, but continue to fail miserably in their ability to produce any viable results. Worse, when given credence and allowed free hand to manipulate society, they create debacles like LTCM and the banking crisis or recovered memories and the quest for devil worshipers abusing millions of children.
There is no doubt there will be more mass delusions, perhaps increasingly fragmented, within the population, and with them more crises of government and financial systems. They feed off each other. Fear and angst drive the increasing cries of the leaders to whatever supernatural entities they find useful in controlling the superstitious masses, whether it be Jehovah, quantum physics or The Market. Papalist pederast-saints, Pentecostal glossolaliacs, Mormon's baptized and married beyond the grave, quantum mechanical shamans, the variety is impressive. To watch how these social phenomena play out together will be interesting, but I prefer to do it from afar.
However, there is one thing for certain. The new political center will form so that any social safety net is ripped away in order that those who were once considered to be middle class can teach themselves to do what the actress Veronica Moser taught herself to do to make a living: Eat shit. Literally. That ought to bring up the mass hallucinations.