That’s from George Polya, who was Professor Emeritus at Stanford and a mathematician who wrote the 1968 book I’m reading on math; ‘Mathematics and Plausible Reasoning, Volume II – Patterns of Plausible Inference’. The father of problem solving. I like the way he thinks.
Interesting stuff, opposite to Aristotle’s suggestion two thousand years ago that all reasoning conforms to certain patterns. Polya argues that there are practical limits to impersonal, universal and self sufficient reasoning.
The basis for difference: your own background, judgement and intuition affects any outcome. ‘It cannot escape being provisional…. The direction is impersonal, the strength may be personal.’
Inferred = forgeddabout the genes already (which jibes with the new science of genetically identical bacteria wildly diverging and mutating). The relevancy of life and how one is formed by it, determines reasoning and style.
Polya: “…Demonstrative reasoning appears as ‘machinelike’, definite, final, while plausible reasoning appears as vague, provisional, specifically ‘human’. ….the ‘strength’ or the ‘weight’ of the conclusion may depend not only on clarified grounds such as those expressed in the premises, but also on unclarified, unexpressed grounds somewhere in the background of the person who draws the conclusion. A person has a background, a machine has not. Indeed, you can build a machine to draw demonstrative conclusions for you, but I think you can never build a machine that will draw plausible inferences.”
So maybe I’ll crack the math codes after all.
“My method to overcome a difficulty is to go around it.” G Polya
UCTV is my current favorite TV channel. I always find interesting programming there, and last night on Conversations with History, Stanford Professor Lucy Shapiro, spoke about having come from an artist’s and musician’s sensibilities into the world of microbiology. It’s fascinating to listen to her trajectory. She found herself confident enough to try anything after having studied the fine arts. ‘Thinking differently is critical’.