Elven
What I understand here by beauty ... is not what the common man generally understands by this term as, for example the beauty of living things and their representation. On the contrary, it is sometimes rectilinear ... and circular, with the surfaces of solid bodies composed by means of the compasses, the chord, and the set square. For these forms are not, like the others, beautiful under certain conditions; they are always beautiful in themselves.
Plato on architecture and mathematics.
I was looking at Roseannes thread about the Tower and found it very interesting, and wondered is there a thread or discussion about the Tower of the Tower Card?
Not so much looking at the surroundings of the tower card, the sky nor the people, but the actual shapes and designs of the building and the mathematics and theory of creating the building itself?
Do they say something about the type of Tower which is being destroyed? Does the card not also include the Tower depicted in certain meaings and symbology. Does the Tower not say 'What is being destroyed' as much as the lightning or the comets, or the hail etc show 'what/why it is being destroyed' ?
I am also interested as to why some Towers on the cards, are square, and some are round - some are tall and some are squat - why some have different shaped tops on them - some have windows and doors and others without.
Does the building shape chosen reflect the time of the cards making or the Tower constructions in the region at the time?
Were certain shapes of Towers used for certain purposes?
Were the Towers drawn and constructed symbolically? By this I mean, architecture at the time (Towers and Temlples) was based and calculated and constructed by mathematicians - and within some of the mathematical calculations of design was meaning - a very important factor was the calculations and relationships between symmetry and proportion.
I wonder if the Towers (some) were constructed with some form of meaning - and if any of these are used on the Tower Card/s for their meaning and not just their 'beauty'?
I was reading this article on architecture and noticed some names I have become familiar with through the history forum and doing some readings about the Visconti Sforza deck ...
The Tower reminds me of the probability Theory:
so, I wonder about the Towers themselves on the cards ... are they a mathematical, spiritual theory or calculation interpreted in pictures?
has anyone else wondered this?
Sorry my question resembles a dog breakfast - I am no scholar
Cheers
Elven x
Plato on architecture and mathematics.
I was looking at Roseannes thread about the Tower and found it very interesting, and wondered is there a thread or discussion about the Tower of the Tower Card?
Not so much looking at the surroundings of the tower card, the sky nor the people, but the actual shapes and designs of the building and the mathematics and theory of creating the building itself?
Do they say something about the type of Tower which is being destroyed? Does the card not also include the Tower depicted in certain meaings and symbology. Does the Tower not say 'What is being destroyed' as much as the lightning or the comets, or the hail etc show 'what/why it is being destroyed' ?
I am also interested as to why some Towers on the cards, are square, and some are round - some are tall and some are squat - why some have different shaped tops on them - some have windows and doors and others without.
Does the building shape chosen reflect the time of the cards making or the Tower constructions in the region at the time?
Were certain shapes of Towers used for certain purposes?
Were the Towers drawn and constructed symbolically? By this I mean, architecture at the time (Towers and Temlples) was based and calculated and constructed by mathematicians - and within some of the mathematical calculations of design was meaning - a very important factor was the calculations and relationships between symmetry and proportion.
I wonder if the Towers (some) were constructed with some form of meaning - and if any of these are used on the Tower Card/s for their meaning and not just their 'beauty'?
I was reading this article on architecture and noticed some names I have become familiar with through the history forum and doing some readings about the Visconti Sforza deck ...
In Europe there was little progress in mathematics and architecture until the 14th and 15th Centuries. Architecture was modelled on the teachings of Vitruvius and on the classical architecture which was still plentiful, particularly in Greece and Italy. The next person we want to mention is Brunelleschi who was trained as a goldsmith. There were really no professional architects at this time and Brunelleschi learnt his skills in architecture by visiting Rome:-
He made drawings of a great many ancient buildings, including baths, basilicas, amphitheatres, and temples, particularly studying the construction of architectural elements, such as vaults and cupolas. The object of his architectural researches, however, was not to learn to reproduce Roman architecture, but to enrich the architecture of his own time and to perfect his engineering skills.
Brunelleschi made one of the most important advances with his discovery of the principles of linear perspective. Classical scholars had understood some of the principles of perspective but no text seems to have been written on the topic.
We think of an understanding of perspective as being essential for a realistic two dimensional representation of a three dimensional scene when painting on a canvass. However Brunelleschi's understanding of perspective was used in his design of buildings as he created his designs to ensure that the visual effect he wanted was visible from all positions of the observer. Following the rules of proportion and symmetry of the ancients was important to Brunelleschi but he wanted these mathematical principles of beauty to be those seen by all observers.
In some sense he was trying to achieve a certain invariance of proportion, independent of the angle of view, and to ensure that it was the apparent proportion which was right rather than the actual proportion. Argan writes [1]:-
Perspective neither uncovers, creates, nor invents space. Rather, it is an essentially critical method or process that can be applied to the spacial data of architecture, reducing it to proportion or to reason. The Platonic influence predominates over Aristotelianism, in the synthesis of longitudinal and central diagrams into a perspective of contemplation, a perspective that leads theoretically to a single point.
Many of the famous mathematicians from the time of Brunelleschi made contributions to architecture. Alberti wrote a text on the topic, as well being the author of an important text on perspective in which he wrote down Brunelleschi's brilliant discoveries for the first time. He was one of a number of mathematicians to develop a general theory of proportion which, of course, was motivated by his architectural studies.
Although the name of Leonardo da Vinci makes one think of his stunning paintings rather than mathematics, in fact he was fascinated by mathematics. Architecture was another of his specialities and he learnt about it, in particular the mathematical principles behind it, from studying Alberti's texts. He was a man of wide ranging abilities and interests and, at one stage in his career, earned his living advising the Duke of Milan on architecture, fortifications and military matters. He was also considered as a hydraulic and mechanical engineer. He also worked for Cesare Borgia as a military architect and general engineer. Later the French King Francis I appointed him first painter, architect, and mechanic to the King.
Another mathematician from Renaissance times was Bombelli who was taught by Pier Francesco Clementi, himself an engineer and architect. With this training Bombelli was soon working himself as both engineer and architect employing his mathematical skills both in his work and in his deep investigation of complex numbers. Another to combine his skills in both mathematics and architecture was Bramer who was employed directing constructions of fortifications and castles. He published a work on the calculation of sines, prompted by the practical work in which he was involved. He followed Alberti (1435), Dürer (1525) and Bürgi (1604) when in 1630 he constructed a mechanical device that enabled one to draw accurate geometric perspective.
The Tower reminds me of the probability Theory:
Is the Tower then not unlike a representation of the chance and a 'wager' we bet in life, and the wager we lose?Probability theory studies the possible outcomes of given events together with their relative likelihoods and distributions.
Another curious argument of Pascal's is that which is known as the argument of the wager. God exists or He does not exist, and we must of necessity lay odds for or against Him.
If I wager for and God is -- infinite gain;
If I wager for and God is not -- no loss.
If I wager against and God is -- infinite loss;
If I wager against and God is not -- neither loss nor gain.
In the second case there is an hypothesis wherein I am exposed to the loss of everything. Wisdom, therefore, counsels me to make the wager which insures my winning all or, at worst losing nothing.
so, I wonder about the Towers themselves on the cards ... are they a mathematical, spiritual theory or calculation interpreted in pictures?
has anyone else wondered this?
Sorry my question resembles a dog breakfast - I am no scholar
Cheers
Elven x