On "The CFRCE Theoretical and Mathematical Minimum Forum"

Every era of human progress brings forth both opportunities and challenges with it. In a deep sense, these opportunities and challenges may be seen as twin aspects of an underlying complexity. One would perhaps like to interpret the opportunities as an affirmation of some desirable order and the challenges as a negation of that same order. So is it that often, the human mind seems baffled by its own inability to deal with the world order. Essentially, this could be felt as nothing but the mismatch between the complexity of the individual human mind and that resulting from the collective mind of humanity. The issue, therefore, is one of harmonizing the two complexities - the inner, cognitive complexity and the outer, environmental complexity.

As is well established in Cognitive Neuroscience, the human brain is a complex adaptive, bio-physiological and bio-psychological, active processing system. Any infiltration of information from the environment immediately stimulates it to learn and soon, match its own complexity with its appraisal of the outer. But there is a catch. It is possible for the environment to so condition the brain that it becomes subject to what the Nobel Prize winning economist Daniel Kahneman calls, "severe and systematic errors."

In a perfectly rational world, one has the choice to grasp the probability and utility of all possible outcomes and then take our stand. But one rarely has all the facts. One can't possibly know all the outcomes. Even if one did, one has neither the temporal flexibility nor the neurological capacity to analyze all the data. So one ends up making decisions based on limited, often unreliable, information and also limited by the brain's processing power and the environmental time constraints. One usually tries to overcome this barrier by a well-known subconscious strategy: heuristics. As Peter Diamandis and Steven Kotler write in their book, Abundance, "Heuristics are cognitive shortcuts: time-saving, energy-saving rules of thumb that allow us to simplify the decision-making process." Severe and Systematic errors compromise the brain's intrinsic processing capability.

The task of education is to hone the brain to optimize these errors. But there is here, a challenge. The brain learns spontaneously and naturally, from anything and everything the environment impacts it with. But provided, it does so subconsciously. Because, the subconscious processing speeds are enormous compared to the conscious. Conventional education developed in an era where the environmental complexity increased linearly and locally. In the 20th century all this has changed. The environmental complexity is increasing exponentially and globally. An education adapted to linearity is simply inadequate to deal with exponential growth. Fortunately, the brain also is essentially non-linear, exponential in its learning. It is forced to remain linear and local by educational conditioning. So all one has to do to come to grips with the environmental complexity is to liberate the brain from its linear conditioning. Here's where the cultural appreciation of a domain comes in. Cultural appreciation requires one to embrace the non-linear and global nature of the domain.

Consider, for instance, an illustration. In the mathematical domain of Lie Algebras and Lie Groups, there is the concept known as exponential mapping. The key idea of this is to simply connect the linear, local with the exponential, global aspects of a certain manifold (a manifold is something that looks like a space locally). Herein is a profound implication. If the culture of Lie Algebras and Lie Groups had been presented to young minds in the formative stage, they would have been better adapted, subconsciously, to the challenge of the environment. One would argue that "Lie Algebras and Lie Groups" cannot trickle into a culture. They are far too esoteric. But so is the concept of credit and currency, banking and finance and so may things one deals with in everyday life. They are all abstract. Yet, children come to have easy facility with them. So also, exponential mapping is something undergraduates can learn culturally as a more sophisticated version of the series expansion of a function, the relation between first-order linear approximation and the full series. And there are far simpler examples than this. And far simpler ways to convey them as a culture.

Therefore, the central message of this forum is that our inner cognitive complexity is more than a match to the outer environmental complexity and learning to appreciate domains as a part of culture facilitates this immensely. Theoretical Physics and Mathematics form twin domains that do this powerfully and evocatively. The Theoretical and Mathematical Minimum Forum espouses the corresponding domains as a part of culture.