In the quadrivium of the liberal arts - the 'four ways' of arithmetic, geometry, music and astronomy - students learn not only the language of mathematics in which number is a sign of a truth (much as a word is a 'sign' that reveals a truth another way), but learn to relate those mathematical signs to each other in a pattern of relationships that reflects beauty of God. This order is common to the abstract worlds of mathematics and geometry, the cosmos, the beauty of musical harmony and the moral order and it governs also the rhythms and patterns of our worship in the Mass and the Liturgy of the Hours as we progress through sacred time; ultimately all point to the Word, the Logos, in whom, as Pope Benedict XVI put it, 'the archetypes of the world's order are contained'.
When understood in this way, the study of these disciplines provides the student with a set of principles by which all human work can be governed so that it is intimately linked to the liturgy. Furthermore through its beauty all human work can potentially give 'praise to the Lord', just as the cosmos doe,s as described in the Canticle of Daniel, for example.
Architecture is the field which comes to mind first when thinking about how to make use of the traditional harmony and proportion, but as I have indicated, we can incorporate this order into any aspect of time and space and then potentially any human creation or activity can participate in this divine order and bear witness to Him through its beauty. When human culture once again reflects the divine beauty, in ways that are not in-your-face statements of the creed, but are built upon the foundation of an assumed faith, then we will have something very powerful that will draw people into the Church. This is the via puchritudinis and it is the beauty that will 'save the world', to use the famous phrase of Dostoevsky. It is preparing the hearts of men to receive the Word and respond with love when presented with it in more direct ways; and it is most powerfully and directly presented to them in beautiful sacred liturgy. This is why cultural reform and liturgical reform are so closely tied together and why there is an article about furniture design on a blog about liturgy.
This little book By Hand and Eye, was sent to me by one of the authors when he read an articles in my blog about proportion and harmony in architecture. Walker and Tolpin are working carpenters who have done their research on the design and proportions of fine furniture of the 18th century such as we might see for example, in the work of Chippendale and Adam. They demonstrate first how the visual features of furniture are closely linked to the architecture of the buildings they are made to sit it. For example you can link the look of the columns of the building to the design of the legs of chairs and tables. Second, and of most interest to me, is their work in the examination of the proportions of the furniture. Their research, based upon examinations of original drawings and measurements indicates that the simple Pythagorean harmonious proportions, based upon ratios of whole numbers such as 1:2, 2:3 and 3:4 govern the design of furniture. This matches my conclusion relating to the proportions of architecture and like me, they do not see the Golden Section, which many assume to be fundamental to systems of proportion. Their presentation is a good balance of the theory - going right back to Plato and Pythagoras and the practicalities, with several case studies of how you might build a piece of furniture using these principles.
It is their personal knowledge of how carpenters actually make furniture which contributes to their conclusions. The designers of the past did not generate drawings from CAD software but, just like the gothic mason designing a cathedral, multiples of a single, arbitrarily assigned first dimension. So, in furniture, they maintain, all dimensions were constructed relative to a single unit governed by a pair of dividers. The furniture maker very likely never knew during the process what the dimension of his work were in any absolute measure of, for example, inches or feet.
I should say that I am not against CAD in principle, but designers should be aware that such software is as likely to make one design badly as well!
Below, design by Robert Adam
 Pope Benedict XVI, The Spirit of the Liturgy, pub Ignatius 2000, p76