Sandra Murphy33 said:Is it just nerves...? 🙄
I can't recall exactly where I read this—it was ages ago—but there was a theory that the entire process of development and evolution actually serves one purpose: to strengthen and refine the nervous system.
It's almost as if the nerve is the core essence, the fundamental conductor, the sensory organ through which we receive the divine or the soul.
On a side note: I read Steiner a long time ago, and back then, he was a balm for my naive soul; I loved every sentence, the rhythm, the flow, the gentleness, and the ideas that felt like medicine and a breath of fresh air at the time...
I went back to read him today after several decades of silence, and honestly, it feels like I'm just spinning in circles ;( He repeats the same thing from the start to the end of the text, circling around the title as if it were an absolute claim, but he doesn't actually support that claim with any arguments. He just restates it in different ways... it's like a lullaby... or as if he's trying to hypnotize me into a state of mild resentment toward whatever his claim is. He puts me into a trance when what I am actually doing is waiting, hunting for something to feed my mind—something to give me information, actual substance I can chew on... instead, he just tosses me a bone to gnaw on, ensuring at least my teeth 😎 stay safe, and my jaw doesn't have to work too hard... there isn't much thinking involved... (you've probably heard Plečkov's assertion that a clenched jaw goes hand-in-hand with so-called "brain activity": deliberately relax your jaw and you'll shatter your usual grueling stream of thought... you break the elements 🙂
The body is a marvel.
Sorry for the tangent.
Why do we love "small integer ratios"?
(Does anyone else immediately think of the Fibonacci sequence and the golden ratio when they hear that?)
Addressing this requires a lengthy explanation. I will provide one detailed response.
Broadly speaking, ratios of small numbers distribute impacts across a wide frequency spectrum, ensuring they don't mask specific frequency ranges. Masking—or shadowing—is dangerous in nature because it renders us deaf to certain noises that could signal an attacker. Something along those lines; beyond that, it’s simply training our neural networks to fundamentally dislike being struck.
To touch upon one aspect of the impact: wave propagation, including sound, is described by differential equations. A harmonic oscillator—which is the basis for all musical instruments—is described by a simple second-order differential equation (the so-called harmonic oscillator equation).
With linear differential equations, it holds true that the sum of solutions is also a solution, as is the difference of solutions.
If we have two tones, we will hear both their sums and their differences. In reality, we won't hear the sums, as they would likely end up extremely high, even in the ultrasonic range, but we certainly hear the differences.
If two tones are very close together, that difference is small. And it is this difference that we perceive as an impact.
An impact can completely destroy the sonic image of everything else, effectively making us insensitive to things occurring around us.
I won't go further there... that leads into logarithms, and then why we possess logarithmic senses...
But let's look at the Fibonacci sequence.
As we know, it looks like this: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
In truth, however, it is a discrete analog to the exponential function. It possesses similar properties. What constitutes a difference in discrete terms is what constitutes a derivative (the ratio of differentials) in continuous ones. Thus, if we differentiate an exponential function, we arrive back at an exponential function.
If we create gnomons (the first differences, the differences of neighbors) of the Fibonacci sequence, we simply get the Fibonacci sequence again.
Our senses are logarithmic—or rather, inverse-exponential—waveguides. Sound travels best when impedance differences are adjusted via an exponential horn. This is why trumpets, vintage gramophone needles, and even modern high end audio systems utilize exponential horns.
This is why Fibonacci appears here. Naturally, his golden ratio is represented everywhere in nature, and the reason is the avoidance of crowding. When something grows—for instance, sunflower seeds expanding from the center outward—they expand, but so do the ones surrounding them. It cannot happen that they bunch up in one spot in space. It is optimal for them to expand such that each new one arrives at the so-called golden angle. You derive this angle by taking the golden ratio of 360°: 360/phi = 222.49°. However, that leans too far to one side, so we take the smaller angle from the other side, which is 360 - 222.49 = 137.5°. That is the golden angle.
When seeds grow such that each new one appears at the center at 137.5° relative to the previous one, they will, as they grow, experience minimal crowding.
The result: patterns known as Phyllotaxis spirals. We see them everywhere—in flowers, on pinecones, and so on.
If you count the spirals moving right versus those moving left, you'll find that those numbers are simply two consecutive terms in the Fibonacci sequence.
Essentially, the Fibonacci sequence itself serves as a template for what we might call asymmetrical growth. For instance:
Imagine splitting something down the middle. You start with 1 on the left and 1 on the right.
Now, suppose you continue dividing, but with a delay—an asymmetry.
You divide the left side, while the right side lags behind, remaining undivided for a moment.
Now you have 2 on the left and 1 on the right.
Next, you split one part of the left side while the other part waits; meanwhile, the right side finally catches up because its turn to be divided has arrived. Now you're looking at 3 on the left and 2 on the right.
Continuing this pattern of staggered division, you’ll reach 5 on the left and 3 on the right.
Then 8 on the left and 5 on the right. It's quite clear that the right side is always playing catch-up.
If you follow this logic far enough, you realize you are constructing the Fibonacci sequences.
Furthermore, the ratios—2:1, 3:2, 5:3, 8:5, 13:8, and so on—all converge toward the Golden Ratio.
The Golden Ratio is derived from the formula (1+sqrt(5))/2, which yields approximately 1.618033989.
Deriving this formula isn't particularly difficult:
when you divide something such that the ratio of the larger part to the smaller part is the same as the ratio of the whole to the larger part—that is, b:a = (a+b):b—it becomes easy to demonstrate that this leads to a quadratic equation whose solutions are the Golden Ratio and its inverse.
That is to say, 1.618 and 0.618.
The value 1.618 is roughly 1.666, which corresponds to a 4:3 ratio, while 0.618 is close to 2:3.
We are essentially dealing with thirds here. This explains why the "rule of thirds" is so vital in American fine arts, as the Golden Ratio can be approximated using these thirds.
It goes without saying that in music, a 4:3 ratio produces a perfect fourth, which sounds harmonious. A 3:2 ratio produces a fifth, which is equally consonant.
Historically, the Greeks developed a vast array of intervals based on these small integer ratios, turning it into a legitimate spiritual science. This brings to mind what Ghika once remarked: "The harmony of the sirens is like a planetary broadcast of the harmony of the spheres."
I am quoting this from a forum, though it is also found in Matila Ghika's book, *Philosophy and Mysticism of Number*:
Actually, within those harmonic analyses provided two pages ago, he is describing the Pythagorean concept of the TETRACHORD LYRE. The Tetrachord Lyre wasn't a practical musical instrument meant for daily performance, but rather a conceptual one. It was an instrument with equally tensioned strings of lengths 6, 8, 9, and 12, through which it was possible to derive all proportions and most musical intervals. To the Pythagoreans, the concept of the tetractys held divine significance (which is why, in prayer, they would say: "You who created both Gods and men").
The tetractys is typically visualized as ten spheres arranged in a "pyramid" or triangle configuration, consisting of 4, 3, 2, and 1 spheres (with 4 in the base row, followed by 3, then 2, and finally 1 at the apex).