This is a huge subject and I can only summarise my understanding here and it’s by no means complete.
I. Kant, On Critique of Judgement Book 1, 1790
Nature approaches infinity using Phi scaling, (the Golden Ratio in Art and mathematics), to create Fibonacci spirals that reflect the dynamics of the curling of spacetime toward singularity… In metaphysical circles, the singularity is seen as the Big Other, God, the sublime.
What is form, what is matter when applied to the ideal of beauty?
In Kant’s view, the sublime has to do with grandeur rather than loftiness. The feeling of the sublime, like the feeling of the beautiful, pleases ….
Natural beauty reveals the principle of purposiveness in nature
It provides an aesthetic maximum (apprehension) without losing itself in a mathematical formula
Judgments about the beautiful and the sublime share several fundamental characteristics:
– they are both pure aesthetic judgments
– they are both reflective judgments
– they are both subjective judgments
– they are both singular judgments
– they refer to indeterminate concepts.
– they raise claim to universal agreement?
Similarities are very important but Kant shows that the differences are even more decisive. He says they are “striking”.
BEAUTIFUL is connected with the form of objects with definite boundaries.MSUBLIME is found in formless objects so far as with them a representation of boundlessness occurs to mind.
BEAUTY is the presentation of an indefinite concept of understanding. SUBLIME is the presentation of an indefinite concept of reason.
Satisfaction in BEAUTY is bound up with the representation of quality. (Form) Satisfaction in SUBLIME is bound up with the representation of quantity. (Size)
Purposiveness without purpose; Purposiveness, the lack of limit in the objects deemed to be sublime destroys not only any concept that could be applied to the sublime but any purposiveness in the object. The principle of purposiveness that we assume in regarding nature as a kind of big artist (what Kant calls the technique of nature) is not applicable to our judgments about the sublime. On the contrary we deem objects as sublime when they conform to our inability to apprehend the purposiveness of natural objects.
The purposiveness in the beautiful is not conceived either – it is not supplied by the understanding, it is only felt apart from the representation of any purpose.
But the “sublime a priori” eliminates any purposiveness except for the one that defines the possible use of our intuitions of it. This purposiveness pertains only to the workings of the representations of imagination. Therefore it does not display anything purposive in nature. However, it indicates a higher purposiveness in us – moral.
The ideal of beauty in Kant is an ideal we can try to measure almost like an horizon; how beautiful some thing is is like a concept of a maximum in mathematics, in the sense that for any specific number I can always imagine something greater.
As a quantity of measure, the judgement about beauty must give universal satisfaction.
Harry Shearer narrates an animation about The Golden Ratio
http://www.bbc.co.uk/programmes/p02bllqm
discordion {Artist Ian Pritchard} 