1. I recommend reading and analyzing The Soul of a Horse by Joe Camp for its structure, for the thinking skills and logic implicit in it, for the role independent thought plays in living a good life, and for the importance of science and logic to being true to what we love so we can help it flourish. Logic is not some book or abstract thing only, it is a tool of survival and a tool to help us love. Sometimes, just as we should move slow, we should read slow. Process. Feel and think it out. Relish. Take time to experience.
2. Getting a concept and induction right
To figure out where an idea logically comes from, so you can do a hierarchy diagram, ask:
- 1. what did I have to learn (or should I have learned) from when I was a baby till now to know this idea?
- 2. what did scientists have to learn through history to discover this idea?
3. Understanding means:-you know the essence of something (its nature; what makes it what it is)-you relate the idea back to the evidence of the senses (step by step)-you connect it to other, causally relevant ideas
4. You said you use triangles to help you better move and better think about movement. Thales did some thing similar, as you can read about in this nice article: http://dbanach.com/homepage/thales.htm
One thing I think is key there is not just “shape,” but also essentialization. (And, as we said, concretization and integration.)
5. Some great books on reasoning and epistemology. Highly, highly recommended. Nothing has been so useful in my life, I think. This epistemology has underlied and made possible most of what I have done and most of the progress I’ve made in overcoming errors I’ve made in the past. Still have more work to do, of course! 🙂
i. Introduction to Objectivist Epistemology by Ayn Randhttps://www.amazon.com/Introduction-Objectivist-Epistemology-Expanded-Second/dp/0452010306/
ii. The Logical Leap: Induction in Physics by David Harrimanhttps://www.amazon.com/The-Logical-Leap-David-Harriman-audiobook/dp/B003VXLRSW/
iii. And the chapters on epistemology in Objectivism: The Philosophy of Ayn Rand by Dr. Leonard Peikoffhttps://www.amazon.com/Objectivism-Leonard-Peikoff-audiobook/dp/B0006IU47K/
iv. To really get induction, we need to learn from practice, not experience. We need to induce things about induction by learning where it went right and how some thought wrong. So I recommend Introductory Physics by Dr. Herbert Priestley. It’s rare you’ll find one for sale, but I have several copies. 🙂 I can send you one, if you want. But it would take some disciplined, targeted time to go through and get anything out of.
6. Edward Tufte: The DaVinci of Data
His site: https://www.edwardtufte.com
NY Times article (behind pay shield): https://www.nytimes.com/1998/03/30/business/the-da-vinci-of-data.html
Blog post about him: https://sites.psu.edu/julieludeman/2016/02/22/edward-tufte-the-da-vinci-of-data/
6. I’d say consciousness involves something mathematical (as opposed to math proper) more fundamentally than geometry. We use, as Aristotle discussed in studying animals (hence he thought of this as an external thing, not an aspect of consciousness, as I do), the-more-and-the-less in identifying things: ranges of shapes of bird beaks, ranges of lengths of bird beaks, ranges of intelligence in humans, ranges of eye color in people, ranges of jumping distance in humans, ranges of wisdom in humans, ranges of surface areas on tables, ranges of size of circles, etc. I got that from Ayn Rand.
Remember consciousness has to be ready to adapt to and to identify all sorts of things, not just shape.
It’s more appropriate, I think, to call consciousness a “difference detector,” as I have heard some say, than as a “shape detector,” shape being one of many differences we need to identify to survive and thrive.
7. Words are symbols, but more: they concretize concepts. They can be spoken as well as written. More fundamental than shape, I think, is that we think in terms of concretes, hence we need words to retain abstractions.
Rand’s thoughts on “words:” http://aynrandlexicon.com/lexicon/words.html
8. While we know some physics and geometry of sound, think back to youth and think of what animals do: sound is an experience that marks some thing moving or doing something. Shape has nothing to do with sound for them. They don’t get, and don’t need to get, that higher level of discovery and abstraction. Humans did not even know sound was a wave until the 1600s/1700s, though they had some idea a few thousand years ago.
Info about Chladini and the scientific history of sound, at the end of this email. Chladini did some fundamental work in the science of sound and music.
- i. Watch “Chladni Plate Demonstration from the National Museum of American History” (1 min 39 sec) https://www.youtube.com/watch?v=KEttRmu2kGkii.
- ii. Watch “Demonstrating Resonance with Chladni Figures – Christmas Lectures with Charles Taylor” (9 min 40 sec) https://www.youtube.com/watch?v=OLNFrxgMJ6Eiii.
- iii. Look at the diagrams on pp. 611-633 (key on p. 594) “On the figures obtained by strewing sand on vibrating surfaces, commonly called acoustic figures” by Charles Wheatstone https://royalsocietypublishing.org/doi/10.1098/rstl.1833.0027iv.
- iv. Look at the patterns made on circular plates in “Chladini Patterns”https://www.nhn.ou.edu/~johnson/Education/Juniorlab/Chladni/2002-Chladni_S2002.pdf
9. Aristotle on experience vs perception
“All men by nature desire to know – – this is indicated by the pleasure we take in our senses. This pleasure is independent of their utility: we delight in them for their own sake and particularly in the case of sight…. Sense represents the first stage. Next comes memory in the case of the animals which have it. In man memory leads up to experience; many memories of the same thing occurring come in the end to have the force of a single experience.” —Aristotle, first chapter of Book A of the Metaphysics, as quoted by Thomas Heath in his book Mathematics in Aristotle.
10. While I recommend The Greek Experience for the insight into Ancient Greece and the poetry of the writing (shows what history writing can ba and should be like!!!), the book I had in mind and from which I learned some deep insight into the Greeks was The Greek Way by Edith Hamilton. The things I discussed today you’ll find in the last two chapters: The Way of the Greeks and The Way of the Modern World. They are only 28 pages in my edition of the book; not much. I highly recommend you read them.
Rand on concepts: http://aynrandlexicon.com/lexicon/concepts.html
Rand on concept-formation: http://aynrandlexicon.com/lexicon/concept-formation.html
We form concepts when things in the world have differences that are too small to matter in comparison to other things in the world or in comparison to things in some context (except for “axiomatic concepts,” which are another story).
In “Good Vibrations,” Joyce R. McLaughlin wrote: “But why did the lines on Galileo’s plate appear only when it vibrated at the natural frequency? At any frequency an excitation produces waves that travel back and forth across the object. At resonance, these waves reinforce each other, producing a combined response called a standing ave. The standing wave divides the object into parts that oscillate up and down. The boundaries that separate the parts remain stationary and do not oscillate. In a one-dimensional object, such as a vibrating string, the boundaries are single points, called nodes. In a two-dimensional object. such as Galileo’s plate, the boundaries form nodal lines.
“When Galileo’s plate resonated, the filings made by the chisel accumulated in the places of minimum vibration, the nodal lines. They bounced away from the vibrating regions. When the plate was not resonating, the traveling waves did not reinforce each other, so all points on the plate vibrated and the grains did not get a chance to accumulate.
“This phenomenon attracted attention again around 1800. At that fume it was studied extensively by Ernst Chladni, a Hungarian who was first educated for a legal career and then later turned to music and finally to science. Chladni put rectangular, triangular and circular plates on pedestals and scattered sand on them. He stroked the edges of the plates at different frequencies with a bow, carefully and empirically choosing natural frequences. The resulting “Chladni figures” formed bv the sand made a sensation in Napoleon’s court, and led the French Institute to offer a prize in 1809 for an investigation of the tones of the vibrating plates. Six years later, in 1815, the prize was awarded to mathematician Sophie Germain for her theory of the vibraton of an elastic surface.” ((American Scientist, p. 342, Volume 86) https://www.jstor.org/stable/27857058)
Note that Robert Hooke had done some similar experiments:
1. “Chladni repeated the pioneering experiments of Robert Hooke who, on July 8, 1680, had observed the nodal patterns associated with the vibrations of glass plates. Hooke ran a violin bow along the edge of a plate covered with flour and saw the nodal patterns emerge.” — “Ernst Chladini-The Father of Acoustics” by Harald Sack (http://scihi.org/ernst-chladni/)
2. “On July 8, 1680, Robert Hooke was able to see the nodal patterns associated with the modes of vibration of glass plates. Hooke ran a bow along the edge of a glass plate covered with flour, and saw the nodal patterns emerge.
3. “The German musician and physicist Ernst Chladni noticed in the eighteenth century that the modes of vibration of a membrane or a plate can be observed by sprinkling the vibrating surface with a fine dust (e.g., lycopodium powder, flour or fine sand). The powder moves due to the vibration and accumulates progressively in points of the surface corresponding to the sound vibration. The points form a pattern of lines, known as ‘nodal lines of the vibration mode’. The normal modes of vibration, and the pattern of nodal lines associated with each of these, are completely determined, for a surface with homogeneous mechanical characteristics, from the geometric shape of the surface and by the way in which the surface is constrained.
“Experiments of this kind, similar to those carried out earlier by Galileo Galilei around 1630 and by Robert Hooke in 1680, were later perfected by Chladni, who introduced them systematically in 1787 in his book Entdeckungen über die Theorie des Klanges (Discoveries on the theory of sound). This provided an important contribution to the understanding of acoustic phenomena and the functioning of musical instruments. The figures thus obtained (with the aid of a violin bow that rubbed perpendicularly along the edge of smooth plates covered with fine sand) are still designated by the name of ‘Chladni figures’.” (https://en.wikipedia.org/wiki/Cymatics)
Scientists who studied sound:
- Galileo Gallilei: 1564-1642
- Robert Hooke: 1635-1703
- Isaac Newton: 1642-1726
- Ernst Chladni: 1756-1827
- Sophie Germain: 1776-1831
- Charles Wheatstone: 1802-1875