Poetry, much more than prose, requires the reader to apply reason and interpretation to the words on the page - much as a mathematical proof requires the reader to apply known rules to interpret the often cryptic notation of the mathematics…
The Mathematics | The poetry | The prose |
---|---|---|
The modern mathematical model of cognition. The neural net - statistics without ambition. |
The neural net classifies by computing a simple function and deciding if the result is less than or greater than 0. By using layer of computation, it is possible to build complex regions. | |
As f(x) serves to partition , (into f(x) > 0 and f(x) 0), So does behavior divide the space of man (into good and evil). |
A single valued function divides space by the simple process of evaluation - every point results in a value that is either less than or equal to 0 (on the "non-positive side" of the function, or greater than 0 (on the "positive side" of the function.) | |
But f(x), the heart of neural cognition, partitions without Reason. And the French structuralists argue, mind is a dichotomizing machine. |
The exact functions we use may have no obvious or intuitive interpretation. The coefficients may have no physical meaning. For simplicity, these are often constrained to be conics (quadratic). | |
A biological implementation of f(x) would lead to a dichotomizing system, giving light v. dark, ying v. yang, male v. female, a two-color binary world. |
The biology of the neural net is known, the sensitivity of the neurons is mimicked by the mathematics of training the neural cells. In biology, the cells grow closer to make the response easier. In the mathematics, the coefficients of the weights change. | |
Yet the action of nearly uncountable f(x)'s would appear complex, complex as imagination could divine, harsh boundaries made fuzzy. |
By adding breadth (see Figure 1) it is possible to build arbitrarily complex spaces. To obtain more breadth - which occurs on the surface, the brain becomes convoluted - getting the most surface out of the fixed volume. | |
A chaotic system - stochastic at the surface - driven by tiny ( 0) variances At the lowest levels, quantum mechanically uncertain (sorry Al, God does play at dice). |
The quantum mechanics that drive the deepest processes are governed by probability - stochastic processes - that ensure that the future is only predictable from the present to within a tolerance that is part measurement error but in truth represents a fundamental unknowability of the world at the smallest level. This unknowability behaves similarly to the macro-unknowability we experience in a simple dice-based board game. | |
The current world a conditional (Pr[f(x|X)]) The future a posterior (Pr[f(X|x)] |
The Reverend Bayes' provided a formula that combined the three forms of knowledge - knowledge of the present (the prior probability); knowledge of the causal (the conditional probability); and knowledge of the future (the posterior probability). | |
Identity now the presentation of this chaos. Freewill the prior (Pr[f(X)]) that modifies the dice. |
"Cogito ergo sum." Rene Descartes, Discourse on Method |