Preference orderings are either (locally) convex or concave. Risk aversion is just that, a preference ordering over mean/variance bundles.
There was an econ textbook that gave a memorable example of a (qualified) exception to convexity: ice-cream and olives. Usually I'll want to have ice cream and olives in my fridge, but I don't want them at once! - so pure ice-cream would be prefered to a mix of them at my plate, right now.
Risk aversion does not imply, on its own, that you don't want risk at all. It implies that you want some mix of risky and non-risky assets; while concavity towards risk would imply you want either one or the other.
The problem with making risk aversion/convexity work with lotteries and such is that the price you're supposed to pay for lotteries is off your utility surface. But: since lottery tickets and small bets are relatively small in the context of your budget, one can figure that the mispricing in your overall mean/variance bundle is small, and that the emotion of betting may be the case of not wanting to optimize for a grey wall, an optimal mixture.
Finally, re: universal formulae, I think you'd profit from reading Elie Ayache's _The Blank Swan_.
This is just so ignorant and backward that I have a hard time taking the author of this article seriously. There is no "postmodernist movement". The term refers to a hopelessly large field of practices. Most great so-called "postmodernist" theorists typically have not referred to themselves as such.
If you want to discredit theorists who have been critical of scientific practices, you need to put down the Sokal and actually engage with specific works. You might be surprised to find that many of these "postmodernists" are either trained scientists or actually know what they're talking about. Just a few suggestions if you want to dip your toes in the water:
– Gilles Deleuze wrote powerfully on metaphysics, integrating many incites from mathematics in the 60's and 70's: http://en.wikipedia.org/wiki/Deleuze#Metaphysics Check out "Difference and Repetition".
– Alain Badiou uses set theory in his ontology: http://en.wikipedia.org/wiki/Alain_Badiou#Mathematics_as_ont... – I find his ontology lacking though; he should learn something from the failings of set theory in the early 20th century.
– Bruno Latour in a the domain of Science and Technology Studies has written voluminously about scientific and technological practices from a more anthropological point of view: http://en.wikipedia.org/wiki/Bruno_Latour#Biography
– Isabelle Stengers has written something more along the lines of what's critiqued in this article, a critique of the authority of science in society: http://www.amazon.com/Cosmopolitics-I-Posthumanities-Isabell... – works like this question whether the privileging of science over all other forms of knowledge is good for society. This particular work argues that it is not.
– Mike Cooley argues powerfully that the deskilling of the engineering industry caused by computer-aided design and manufacturing is a travesty: http://www.amazon.com/Architect-Bee-Human-Technology-Relatio...
A general note about so-called "postmodernism". The Wikipedia definition includes the following:
"Postmodernism is largely a reaction to the assumed certainty of scientific or objective efforts to explain reality. In essence, it is based on the position that reality is not mirrored in human understanding of it, but is rather constructed as the mind tries to understand its own personal reality."
It's important to understand that "postmodernism" isn't critiquing the effectiveness of science. It is merely claiming that, as it says, reality is not mirrored in human understanding. The models we create to explain observed phenomena are not direct reflections of reality, they are simply characteristically human, linguistic models that correspond to our observations. As Niels Bohr wrote:
"There is no quantum world. There is only an abstract physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature..."
The question is whether our habit of elevating scientific explanation to the 'one true truth' is (1) right and (2) a good thing. Most "postmodernists" argue that other forms of knowledge are perfectly legitimate (for instance, indigenous people who still live tribally lead perfectly happy lives without science) and that the privileging of science over other forms of knowledge is not a unilaterally good thing (for instance, it is reasonable to say there's a decent change that we will extinguish ourselves as a species in the next hundred years thanks to the exploits of scientifically advanced societies).
You may notice that both of those examples are anthropological. This hints at something very important about "postmodernism". When people talk about "postmodernism", they're often talking about "post-structuralism", which is another hopelessly broad category referring to theory that in some way extends "structuralism", which is in turn closely connected to the theories of Claude Lévi-Strauss, the "father of modern anthropology". "Postmodernism" can be seen in this sense to be a kind of anthropologically informed philosophy. Rather than creating theoretically sound abstract models, they look at how those models actually play out "in the field" and draw conclusions. Hence the critique of science: despite the power of scientific explanation, it may not necessarily result in a better society and indeed the evidence shows that it does not.
And one final point, the author is totally wrong to claim that scientists have not been concerned with the philosophy of science. Many early twentieth century scientists – the ones who create the theory of relatively and quantum physics especially – even wrote books on the philosophy of science as well as its role in society. Some examples:
– Schrödinger - "What is Life": http://www.amazon.com/What-Is-Life-Autobiographical-Sketches...
– Herman Weyl ("His overall approach in physics was based on the phenomenological philosophy of Edmund Husserl, specifically Husserl's 1913 Ideen zu einer reinen Phänomenologie und phänomenologischen Philosophie. Erstes Buch: Allgemeine Einführung in die reine Phänomenologie"): http://en.wikipedia.org/wiki/Hermann_Weyl
– Heisenberg - "Physics and Philosophy": http://www.amazon.com/Physics-Philosophy-Revolution-Modern-S...
– David Bohm - "Wholeness and the Implicate Order": http://www.amazon.com/Wholeness-Implicate-Order-David-Bohm/d...
Here's a more modern book from an economist that references Deleuze and other "post-structuralists":
– "The Blank Swan": http://www.amazon.com/The-Blank-Swan-End-Probability/dp/0470...
If you know Zizek as the media clown he presents himself as, Graham Harman’s “Tool-being” (a book about something else entirely that briefly surveys other philosophers and gives a very positive appraisal of Zizek even though they’re polar opposites) makes the best case for Zizek.
I guess the best case for Graham Harman is the edition of the journal “Collapse” on speculative realism.
I guess the best case for that journal is Quentin Meillassoux.
And the best case for Meillassoux is Ayache’s “The Blank Swan”
And Taleb wrote a cool review of the Blank Swan somewhere that gets a pull quote in the book’s cover.
I guess the best case for Taleb is made by Paul Wilmott. Ayache also wrote for Wilmott.
And presumably Wilmott made money in the financial markets.
