It was early found out that mathematical exactness and beauty were not the same. By making its two sides geometrically equal, the living expression of the most beautiful marble statue is destroyed, and it becomes simply a piece of architecture. It is well known that the two sides of the human face are not precisely the same; the irregularity of the one modifies the irregularity of the other, and thus a higher symmetry and harmony is the result. The two sides of the leaf of the begonia are unequal, and if folded together will not correspond. The same is true of the leaf of the elm and the lime. But when the mass of the foliage is seen together, this irregularity gives an added charm to the whole. Every object in nature has some imperfection, which indicates that it has a relation to some other object, and is but a part of a greater whole. The intentional irregularity of the windows in the Doge's Palace at Venice enhances the effect of the marvellous facade. By comparing the Parthenon at Athens, with its curves and inclinations, with the Madeleine at Paris, we see how far short the copy comes of the original in beauty and expressiveness, because of the exact formality of its right angles. The ancient Egyptians understood this well; and in their architecture they sought to rise to a higher symmetry through irregularity; and we can see in their frequent departure from upright and parallel lines in the construction of their temples, an effort to escape from formal exactness, and a longing for the nobler unity which is realised to the full in the rich variety of the Gothic. We may be sure that "every attempt in art that seeks a theoretical completeness, in so doing sinks from the natural into the artificial, from the living and the divine into the mechanical and commonplace." The Egyptian obelisk is thus but a type of a great law of nature. In this simplest and most primitive specimen of architecture we have an illustration of the principle which gives its expressiveness to the human face, beauty to the flowers of the field, and grandeur to the highest triumphs of human art.