# Proportion: Science, Philosophy, Architecture

By Richard Padovan | Go to book overview

Chapter three

UNIT AND MULTIPLIER

For measuring and counting, two things are indispensable: a unit and a system. That is to say, one needs both a static principle and a dynamic multiplication-system.1

3.1ORDER AND COMPLEXITY

Before we explore further the historical relation between science, philosophy and systems of architectural proportion, we must first try to get a clear idea of what these systems are. I shall define them as methods of ordering the relations between the measures of a building, and thereby also between the two- and three-dimensional shapes to which these measures give rise. However, it is not just a matter of reducing the number of sizes and shapes to a minimum, but of achieving unity within a multiplicity of different elements.

In his book Aesthetic Measure2 the American mathematician George D. Birkhoff (1884-1944) treats order and complexity as contraries. The gist of his theory is contained in the formula M=O/C: that is, (aesthetic) Measure equals Order divided by Complexity. The aesthetic value of an object increases, therefore, in direct proportion to its degree of order, and in inverse proportion to its complexity. And since he holds that the order and complexity of a two-dimensional figure can be exactly calculated—its order, by determining the degree of vertical or rotational symmetry, perpendicularity, etc., its complexity by counting the number of straight lines needed to delineate it—it is possible to quantify the aesthetic merit of any geometrically definable object. At the top of Birkhoff’s order of merit are the square and the square grid.

Against this, I would argue that the elimination of complexity tends towards disorder, or rather non-order. Uniformity—the repetition of a single element, for instance an uninflected grid of square panels of standard size—is, paradoxically, the antithesis of order. Where uniformity is absolute and complexity approaches zero, as happens with a

1. H.van der Laan, Het plastische getal, E.J. Brill, 1967, p. 3.

2. G.D. Birkhoff, Aesthetic Measure, Harvard University Press, 1933.

-40-

If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items
Notes

#### Cited page

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

#### Cited page

Proportion: Science, Philosophy, Architecture

Settings

#### Settings

Typeface
Text size Reset View mode
Search within

Look up

#### Look up a word

• Dictionary
• Thesaurus
Please submit a word or phrase above.

Why can't I print more than one page at a time?

Help
Full screen
Items saved from this book
• Bookmarks
• Highlights & Notes
• Citations
/ 388

### How to highlight and cite specific passages

1. Click or tap the first word you want to select.
2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

## Cited passage

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA 8, MLA 7, APA and Chicago citation styles.

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

"Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

## Thanks for trying Questia!

Please continue trying out our research tools, but please note, full functionality is available only to our active members.

Your work will be lost once you leave this Web page.