Tradition becomes our security, and when the mind is secure it is in decay.
― Jiddu Krishnamurti
Over the past couple of posts I’ve opined that the essence of value in computing should be best found in the real world. This is true for scientific computing as it is for the broader world. The ability of computers to impact reality more completely has powered an incredible rise in the value of computing and transformed the World. Despite this seemingly obvious proposition, in recent years and with current plans, the scientific community has focused its efforts on the part of computing most distant from reality, the computing hardware. The bridge from the real world to the artificial reality of the simulation are our models of reality.
Tradition is a fragile thing in a culture built entirely on the memories of the elders.
― Alice Albinia
In science these models are often cast in the esoteric form of differential equations tobe solved by exotic methods and algorithms. Ultimately, these methods and algorithms must be expressed as computer code before the computers can be turned loose on their approximate solution. These models are relics. The whole enterprise of describing the real world through these models arose from the efforts of intellectual giants starting with Newton and continuing with Leibnitz, Euler, and a host of brilliant 17th, 18th and 19th Century scientists. Eventually, if not almost immediately, models became virtually impossible to solve via available (analytical) methods except for a handful of special cases.
There is no creation without tradition; the ‘new’ is an inflection on a preceding form; novelty is always a variation on the past.
― Carlos Fuentes
When computing came into use in the middle of the 20th Century some of these limitations could be lifted. As computing matured fewer and fewer limitations remained, and the models of the past 300 years became accessible to solution albeit through approximate means. The success has been stunning as the combination of intellectual labor on methods and algorithms along with computer code, and massive gains in hardware capability have transformed our view of these models. Along the way new phenomena have been recognized including dynamical systems or chaos opening doors to understanding the World. Despite the progress I believe we have much more to achieve.
What might be holding us back? The models are not evolving and advancing in reaction to the access to solution via computing.
The difficulty lies not so much in developing new ideas as in escaping from old ones.
― John Maynard Keynes
Today we are largely holding to the models of reality developed prior to the advent of computing as a means of solution. The availability of solution has not yielded the balanced examination of the models themselves. These models are
artifacts of an age where the nature of solution was radically different. One might wonder what sorts of modifications of the existing paradigm would be in order should the means of solution be factored in. For example the notion of deterministic unique solutions to the governing equations is pervasive, yet reality clearly shows this to be wrong. Solutions to reality are always a little bit, to very different even given nearly identical initial conditions.
The assumption of an absolute determinism is the essential foundation of every scientific enquiry.
― Max Planck
Originally the models focused on the average or mean tendency of reality. This is reasonable for much of science and engineering, but as the point-of-view becomes refined other issues begin to crowd this out. These variations in outcome can dominate the utility of these models. For many cases the consequence of reality is driven by the uncommon or unusual outcomes (i.e., the tails of the distributiuon). Most of our current modeling approach and philosophy is utterly incapable of studying this problemeffectively. This gets to the core of studying uncertainty in physical systems. We need to overhaul our approach of reality to really come to grips with this. Computers, code and algorithms are probably at or beyond the point where this can be tackled.
It is impossible to trap modern physics into predicting anything with perfect determinism because it deals with probabilities from the outset.
― Arthur Stanley Eddington
Here is the problem. Despite the need for this sort of modeling, the efforts in computing are focused at the opposite end of the spectrum. Current funding and focus is aimed at the computing hardware, and code with little effort being applied to algorithms, methods and models. The entire enterprise needs a serious injection of intellectual energy in the proper side of the value proposition.
Cynics are – beneath it all – only idealists with awkwardly high standards.
― Alain de Botton