Closer to Truth: Is Mathematics Eternal?

What is Math?

Dan Falk

Given that these questions about the nature of mathematics have been the subject of often heated debate for some 2,300 years, it’s unlikely they’ll go away anytime soon. No surprise, then, that high school students like Cunningham might pause to consider them as well, as they ponder Pythagorean theorem, the geometry of triangles, and the equations that describe lines and curves. The questions she posed in her video were not silly at all, but quite astute: mathematicians and philosophers have been asking the same imponderables for thousands of years.

[Laird]

Team Platonist here.

For some time, it's appeared to me that the mathematical relationships we use to describe our physical observations, are really a description of some architecture from which those physical observations emerge.

In this presentation of the Science of Consciousness conference, 2021, Prof. dr. Erik Verlinde, well-known for his ground-breaking theory of entropic gravity, talks about emergence in mind and nature, as well as the Platonic realm physicists tap into to describe the world.

The concepts of mathematics themselves arose from consciousness in the first place ~ mathematics makes no sense when it comes to the unmeasurable, however, like emotions, ethics, painting, music, meditating, thoughts, etc, etc. Majority of the time, we don't even think mathematically.

I half agree, but if all you had was a computer and you wanted to re-create western music, you would quickly find yourself doing some maths involving the twelfth root of two.

I half agree, but if all you had was a computer and you wanted to re-create western music, you would quickly find yourself doing some maths involving the twelfth root of two.

Yes and no. I'm familiar with the idea of 2^(1/12) in computer music. I've also used it in calculating the positions of the frets on a stringed instrument. But that's only one approach.

Music is based on a number of things, which can be described mathematically, but there is more than one way to describe things this way, and they give differing results.

https://www.britannica.com/science/Pytha...m/Geometry

At an early date they discovered empirically that the basic intervals of Greek music include the elements of the tetraktys, since they have the proportions 1:2 (octave), 3:2 (fifth), and 4:3 (fourth). The discovery could have been made, for instance, in pipes or flutes or stringed instruments: the tone of a plucked string held at its middle is an octave higher than that of the whole string; the tone of a string held at the 2/3 point is a fifth higher; and that of one held at the 3/4 point is a fourth higher. Moreover, they noticed that the subtraction of intervals is accomplished by dividing these ratios by one another. In the course of the 5th century they calculated the intervals for the usual diatonic scale, the tone being represented by 9:8 (fifth minus fourth); i.e., 3/2 ÷ 4/3, and the semitone by 256:243 (fourth minus two tones); i.e., 4/3 ÷ (9/8 × 9/8). Archytas made some modification to this doctrine and also worked out the relationships of the notes in the chromatic (12-tone) scale and the enharmonic scale (involving such minute differences as that between A flat and G sharp, which on a piano are played by the same key).

No mention of the 12th root of 2 there. Everything is based around simple ratios. Some of them are indeed fundamental, chords (different notes sounded together) which sound beautiful and harmonious to us are dependent upon the simplest of these ratios.

But @Valmar makes a vital point. The emotional content of music and other arts is something which is not present in the computerised music. I see music as a form of mind-to-mind communication, an expression of emotion in one person transmitted to others via this medium. Some of the important characteristics such as variations in pitch, volume, timbre and timing in a singer's rendition are not simply random fluctuations, but are felt deep inside.

Yes and no. I'm familiar with the idea of 2^(1/12) in computer music. I've also used it in calculating the positions of the frets on a stringed instrument. But that's only one approach.

Music is based on a number of things, which can be described mathematically, but there is more than one way to describe things this way, and they give differing results.

https://www.britannica.com/science/Pytha...m/Geometry
No mention of the 12th root of 2 there. Everything is based around simple ratios. Some of them are indeed fundamental, chords (different notes sounded together) which sound beautiful and harmonious to us are dependent upon the simplest of these ratios.

But @Valmar makes a vital point. The emotional content of music and other arts is something which is not present in the computerised music. I see music as a form of mind-to-mind communication, an expression of emotion in one person transmitted to others via this medium. Some of the important characteristics such as variations in pitch, volume, timbre and timing in a singer's rendition are not simply random fluctuations, but are felt deep inside.

Well ratios are themselves mathematical concepts. Then the scale was 'tempered' this ended up with successive notes (regardless of key colour - black or white) with frequencies f1 and f2 having the relationship f2=f1*k where k= twelfth root of 2. This in turn means that an octave, with twelve successive multiplications by k is obtained b a doubling of frequency.

Remember that pianists play on a tempered scale (their pianos are tuned that way), so they all depend on that twelth root of two ultimately.

Is Mathematics Eternal?

I think Aaronson is a new addition to the original interviewees, or at least there has been a new highlighting of his answer:




Aeon Magazine also highlighted this excerpt with this description ->

In this video interview from the long-running interview series Closer to Truth, the US presenter Robert Lawrence Kuhn asks Scott Aaronson, a professor of computer science at the University of Texas at Austin, a single question – ‘What can you say about the nature of truth?’ From that starting point, Aaronson makes a case for what he calls the ‘autonomy of mathematical truth’, arguing that, whether agreed upon by humans across cultures, advanced species across planets, or even with no one to contemplate them at all, the truths of arithmetic are universal.

Unpacking the Mystery of Ramanujan's Dreams

Kristin Posehn

Hardy famously stated that if you were to score mathematical ability on a scale of 100, with 100 being the most capacity possible—then Hardy would rate a 25, Littlewood 30, Hilbert 80, and Ramanujan 100...

...Ramanujan had no conventional qualifications. He was about as far from the inner sanctum of math society as you could get. While Hardy and the Royal Society at Cambridge rightly recognized his genius, they perceived him through their own biased conceptual framework, and in both subtle and not-so-subtle ways omitted, suppressed, or just plain ignored facets of his character that didn’t fit their worldview.

In their remarks, English mathematicians were careful to stress that Ramanujan was rational and rigorous—characteristics that were worthy, in their eyes, of conventional respect, while Ramanujan’s devout practice as a Hindu was glossed over, as if this were merely a set of odd behavioral codes he happened to scrupulously observe. His first biographer received complaints about having included in the biography various remarks from Ramanujan’s childhood friends which detailed his great passion for occult and religious subjects, because any association with such matters apparently contaminated his mathly reputation. And these distortions persist to this day: His most popular biographer avoids the topic of his dreams, merely including a few as incidental, offhand notes. Personally, I think if you’re a 25, or sub-5, or even an 80 on the mathalete scale, it would be prudent to cultivate a healthy, open-minded curiosity about someone operating at a 100. What did Ramanujan know about mathematics that we don’t?

Gödel’s Incompleteness and the Realm of Wildlife

Yaakov Lichter

Humans relate to nature through the intermediation of abstract linguistic concepts that aren’t themselves part of nature. Animals, on the other hand, relate to nature through actions—gestures, secretions, sounds, etc.—that evoke meaning in a manner directly grounded in the elements of nature. The potential power of this more direct approach has been illustrated by Kurt Gödel, who used elements of mathematics—natural numbers and arithmetic operations—to model mathematics itself and investigate its nature, thereby unlocking great insight. This is analogous to how animals relate to their world. Could Gödel’s insight help us transcend the artificial boundaries created by our abstract concepts and, thereby, better understand reality?