"Algebra as confused music... Stevin, too easily impressed by algebraic technique, falsely took this equal semitones and the whole tones to be the true foundation of harmony. Modern musical treatment of music generally began from the assumption of equal tones and semitones. This incorporated the cumulative error of five hundred years of theory." (Jeffery Kalb, Music and Measurement: On the Eidetic Principles of Harmony, Pages 34-35) Notes: Google AI Overview: Building directly on Klein's work, author and tutor Jeffrey C. Kalb wrote a book titled Music and Measurement: On the Eidetic Principles of Harmony . Kalb takes Klein’s critique a step further: [ 1 ] He claims that the philosophical presuppositions of modern algebra and calculus are conceptually incoherent . He argues that modern mathematics has deeply confused abstract symbols with real physical quantities and measurements . Instead of validating algebra as a standalone absolute truth, Kalb posits that algebra is a...
Does math expert Jacob Klein think Algebra created an artificial lens that distances humans from the actual understanding of real things & nature?
“Our rationalism is a symbolic one. It is the true result of the Cartesian distinction between „mind“ and „external world“. It is the true expression of the paradox of which we have spoken, that the mind, which is supposed to be sufficient to understand the world, is preconveived as a mind alienated from this same world. We approach the world not directly but by means of concepts which are abstractions of abstractions and which at the same time we interpret as being in direct contact with the world.” ― Jacob Klein, Lectures and Essays [https://www.goodreads.com/author/quotes/80050.Jacob_Klein] Notes: Google AI Overview: The Core Argument Behind the Quote In his research, Klein outlines how the shift from ancient Greek mathematics to modern symbolic algebra altered the human relationship with nature: [ 1 , 2 ] Ancient Greek Intuition ( Arithmos ): For the Greeks, a number was always a concrete "number of things" (e.g., four apples, three triangles). Mathematical thought rem...