Sharp thinking

Sharp Thresholds

The Kolmogorov Zero-One law states that for tail events on infinite-dimensional probability spaces, the probability must be either zero or one. Behavior analogous in a natural sense to this exists on finite-dimensional spaces as well. Events exhibiting this behavior are said to have a sharp threshold. Let Qn = {0, 1}n be the discrete hypercube with the probability measure Pp defined by Pp(ω1, ω...

Dimensions for Thinking About Thinking

We start by making a distinction between mind and cognition, and by positing that cognition is an aspect of mind. We propose as a working hypothesis a Separability Hypothesis which posits that we can factor off an architecture for cognition from a more general architecture for mind, thus avoiding a number of philosophical objections that have been raised about the "Strong AI" hypothesis. We the...

Critical Thinking about 'critical Thinking'

Goods-thinking vs. tree-thinking

While it has become increasingly clear that the Tree of Life hypothesis has limitations in its ability to describe the evolution of all evolving entities on the planet, there has been a marked reluctance to move away from the tree-based language. Ironically, while modifying the idea of the Tree of Life to the extent that it is only very distantly related to its original descriptions, there has ...

Thinking slow about thinking fast

In his book, Thinking, Fast and Slow, Daniel Kahneman attributes experientially-learned real-world coping skills to an " associative machine " acting on declarative memories of facts and events. While this attribution is probably correct for the unfamiliar types of situations that are the subject of his famous experiments conducted with Amos Tversky, we argue that experientially-learned real-wo...