Thursday, June 16, 2022

Common Problems

arithmetic - from medieval latin, ars+metrica = art+counting

"The history of mathematics exhibits the generalization of special notions observed in particular instances. In any branches of mathematics, the notions [organically] presuppose each other. It is a remarkable characteristic of the history of thought that branches of mathematics, developed under the pure imaginative impulse, thus controlled, finally receive their important application. Time may be wanted. Conic sections had to wait for eighteen hundred years. ... But the accurate expression of the final generalities is the goal of discussion and not its origin. Philosophy has been misled by the example of mathematics; and even in mathematics the statement of the ultimate logical principles is beset with difficulties, as yet insuperable." AN Whitehead, Process and Reality, 1929

Continuing a tradition ... or blindly following a futile quest ?

From Euclid to Einstein and from basic arithmetic to pure mathematics [which Whitehead identifies as principles merely waiting-to-be-applied], we find thinkers who cannot resist enticing thoughts suggesting that the universe can somehow be reduced to numerical functions and algorithms which, via scientific technological applications, are capable of accurately explaining the past and predicting the future ... of eliminating the messy morals of free-will and reducing creativity to deterministic, quantitative analysis.
NEVER in human history has this been as true as it is today ... when a global, centrally banked technocracy [HQ'd in Davos by math-ignorami] disingenuously assures us it can manage human actions and planetary conditions by reducing them to continuously surveilled, quant-data calculations and AI prescriptions in its cloud computers.

But over and over again, the demigods come up short ... and discover that math is as indeterminate as any of the amorphous liberal arts they despise and disclaim as irrelevant to modern life. Psalm 2 comes to mind:
"Why do the heathen rage, and the people imagine a vain thing? ... He that sitteth in the heavens shall laugh: the Lord shall have them in derision."
And we forget that the truly great mathematicians never permanently lost sight of the limits of their understanding of action at a distance ... even if a little pride in their accomplishments blinded them for a time:
"It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro' a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers." — Isaac Newton, Letters to Bentley, 1692/3

Blindly following a futile tradition ... or continuing a quest ?

On the other hand, there are those who dismiss mathematics as mechanistic and thus incapable of assisting us in approaching and articulating eternal verities in any morally meaningful way:

"Mathematics is a game played according to certain rules with meaningless marks on paper." — David Hilbert

And so they shun the demanding study of mathematics, engineering, science and technology as a colossal waste of a very precious and limited resource ... TIME ... time that could and should be spent on the study of other things.

Going organic ... and erasing the dividing line

But there is a third group which believes that math is a path to the liberal arts and that one without the other is impoverished and incomplete, because in nature they are simply facets [or viewpoints] of the single fundamental, organic truth which holds all things in the universe together at a distance ... both quantitatively and qualitatively ... measurably and morally.

Here's an initial mission ... what are we waiting for?

It was in this spirit that a small group met for lunch at McAlister's Deli in west Wichita in June 2022 to discuss ways to bring together local resources and people
  • to promote a more coherent and durable understanding of the roles and limits of mathematics [STEM as its broadest extension] in a liberal education and
  • to enable and strengthen liberal educators seeking to identify, amend, enhance and reintegrate currently failing pedogogical and curricular attempts to conduct and integrate STEM instruction in the distinctive primary, secondary and post-secondary learning environments.

MATH PATH to the liberal arts

Initial "math path" meeting members included:
  • Bob Love, Northfield School Trustee
  • Joseph Myers, Friends University Professor
  • Finn Lanning, Northfield School Math Teacher
  • Dan Snyder, Concordia Academy Headmaster
... but there is room for many, many more ... before we even begin to approach infinity !!! So why not join us at our next meeting ... the educator energy is palpable.