Philosophy Discussion Forums | A Humans-Only Club for Open-Minded Discussion & Debate

[Jellymeat]

Recently I have been doing some research into the classical "Quadrivium", which for those who don't know is the final four of the seven "liberal arts" - number, geometry, music and spherics or cosmology.

The contention is that sacred number and sacred geometry govern the laws of harmony which is most easily studied in music. The next logical leap is that these laws somehow relate to everything in nature both macrocosmic and microcosmic. A school of thought going right back to Plato and Pythagoras. For anyone who has read 'Timaeus' you will know what I'm talking about.

Perhaps erroneously, this school of thought dominated the minds of early astronomers right up until the last few centuries. My favourite being Johannes Kepler who's models and depictions of the solar system made of interlocking platonic solids are fascinating.

During the quest to establish a definitive periodic table of elements, the English chemist John Newlands classified the then 56 known elements into 11 groups with similar physical properties. Newlands noted that many pairs of similar elements differed by an atomic weight of eight which he likened to the musical scale.

My question to you is whether or not you think there is any validity to this view of the arts and sciences?

[Belinda]

Sacred geometry, which is a fact about harmony between music,geometry of e.g. seashells, number, and perhaps also visible beauty of form and line, is perhaps caused by the brain's selection of items that please it, that make it feel more comfortable. Is the brain and its limitations the linking cause of those apparent harmonics?

[Jellymeat]

Is the brain and its limitations the linking cause of those apparent harmonics?

I don't think it can be written off as simply the brains interpretation. I think we find things beautiful because they are in harmony and proportion and not the other way around. Nature itself seems to find them beautiful. The fact that the golden scission is the only way to bisect a line with parts in proportion to it's whole is not subject to interpretation.

[Belinda]

Jellymeat, What you are saying about harmony being a fact that is external to man's perspective, is a strong statement of Platonism, with a slant towards Pythagoras, of course.

It's not for me, I am a relativist, but I do respect the Platonic point of view, and Pythagorean sacred geometry is fascinating in its many applications. I am not good at geometry but the very little that I have understood of sacred geometry particularly as it applies to numerology in the Bible,and to the architecture of old churches, interests me.

I wonder if you know about the connections with the Essenes, and the Druids of Gaul.

The fact that the golden scission is the only way to bisect a line with parts in proportion to it's whole is not subject to interpretation.

I think that if anything stopped me being a relativist it wouod be this!

[Jellymeat]

Jellymeat, What you are saying about harmony being a fact that is external to man's perspective, is a strong statement of Platonism, with a slant towards Pythagoras, of course.

I understand that concepts like beauty can be more subjective, but harmony itself is mathematically universal. My Platonist bias makes me tend to think that beauty is related though.

The Lambdoma is a diagram of the relation between the series of 2nd and 3rd powers.

1
2 3
4 6 9
8 12 18 27

(If this doesn't post in the correct format, it's supposed to form an equilateral triangle)

The ratios between the numbers also perfectly describe the series of musical intervals. It's basic music theory, but it has much wider implications as was the contention of Plato and Pythagoras. Also of interest is that all the intervals converge on a mysterious Zero which is off the top of the diagram.

If you have ever played with a harmonograph you would notice pendulums swinging at these intervals produce beautiful spiral pictures with perfect symmetry, while those at dissonance produce random scribbles. Again, this is not something terribly subjective, but a fact about mathematics and nature.

the very little that I have understood of sacred geometry particularly as it applies to numerology in the Bible,and to the architecture of old churches, interests me.

It interests me too. There's a great documentary that you can watch on youtube about Chartres cathedral featuring Keith Critchlow, a professor of architecture and author of several books on sacred geometry. Cathedrals like Chartres were used as mystery schools where topics like the trivium and quadrivium were taught and displayed.

I wonder if you know about the connections with the Essenes, and the Druids of Gaul.

I can't say I've heard this one before.