J Barkley Rosser - Collected Quotes

"And finally we wish to note that critical economies are associated with bifurcation values of the exogenous parameters of the economy. Critical economies are states at which an economy discontinuously undergoes a structural transformation in the pattern of its equilibria in response to slow changes in parameters. In short, general equilibria are susceptible to catastrophes in the general sense." (J Barkley Rosser Jr., "From Catastrophe to Chaos: A General Theory of Economic Discontinuities", 1991)

"At the large scale where many processes and structures appear continuous and stable much of the time, important changes may occur discontinuously. When only a few variables are involved, as well as an optimizing process, the event may be analyzed using catastrophe theory. As the number of variables in- creases the bifurcations can become more complex to the point where chaos theory becomes the relevant approach. That chaos theory as well as the fundamentally discontinuous quantum processes may be viewed through fractal eyeglasses can also be admitted. We can even argue that a cascade of bifurcations to chaos contains two essentially structural catastrophe points, namely the initial bifurcation point at which the cascade commences and the accumulation point at which the transition to chaos is finally achieved." (J Barkley Rosser Jr., "From Catastrophe to Chaos: A General Theory of Economic Discontinuities", 1991)

"It would seem that there may be a possible synthesis that can de-bifurcate bifurcation theory and give a semblance of order to the House of Discontinuity. Reasonable continuity and stability can exist for many processes and structures at certain scales of perception and analysis while at other scales quantum chaotic discontinuity reigns. It may be God or it may be the Law of Large Numbers which accounts for this seemingly paradoxical coexistence." (J Barkley Rosser Jr., "From Catastrophe to Chaos: A General Theory of Economic Discontinuities", 1991)

"Mathematically there are clearly degrees of continuity. Thus a function may be kinked, itself continuous but possessing discontinuous first derivatives. Or a discontinuity may occur in a higher, more remote derivative, but not in lower order ones." (J Barkley Rosser Jr., "From Catastrophe to Chaos: A General Theory of Economic Discontinuities", 1991)

"The major strength of catastrophe theory is to provide a qualitative topology of the general structure of discontinuities. Its major weakness is that it frequently is not associated with specific models allowing precise quantitative prediction, although such are possible in principle." (J Barkley Rosser Jr., "From Catastrophe to Chaos: A General Theory of Economic Discontinuities", 1991)

"Turbulence, or chaos, is not universal but comes and goes. Chaos may emerge from order, but order may also emerge from chaos." (J Barkley Rosser Jr., "From Catastrophe to Chaos: A General Theory of Economic Discontinuities", 1991)

"We must recognize here that continuity and discontinuity may not always be clearly distinguishable. Ultimately what may matter is the precision of the perspective applied to the question at hand. Thus, if quantum mechanics is true, then reality is fundamentally discrete at a microscopic level. Nevertheless it may be useful to view it as continuous when the analysis is less precise, much as we perceive a movie to be continuous even though it actually consists of a sequence of discrete and discontinuous still photographs. Our mind draws an in-visible line between the stills creating the illusion of continuity."  (J Barkley Rosser Jr., "From Catastrophe to Chaos: A General Theory of Economic Discontinuities", 1991)