All art creates content
by Oscar van Dillen
Abstraction
Understanding abstraction requires developing imagination. Any abstraction that does not meet with an imaginative grasping is doomed to remain form without content. The process of going from form to content follows rigorously defined codes in the sciences; there are symbolic languages that allow for concise descriptions of very complex matters, like Algebra or Mendeleev's "Periodic Table of Chemical Elements"[1]. Such systems are always based on imaginations, and have often been developed over a longer period of time before becoming a more abstract "language"; knowledge of this development however is often forgotten. There are e.g. many far more elegant ways to perform a division in arithmetic by hand or mental calculation than the commonly taught long division.
Thus for example today we have Algebra at our disposal, but who still teaches or studies its history? The term comes from Arabic al-jabr, الجبر “restoration”[2]. Algebra was described and published at the time (indeed) in the works of Mohammed Ibn Musa al-Khwarizmi (ca 780-850), whose name is still preserved in our word "algorithm", but who built on Indian mathematicians. Following mathematics along the Silk Route further eastwards, we find older Chinese sources for the Indian mathematics, that share a concrete and direct approach that is practically lost today. Here there were methods for calculating the square root, based on simple multiplication and difference. Product (multiplication) and Difference (subtraction) are perceivable procedures, as is the Square (exponentiation), but less so the Root. All these Arabian, Chinese and Indian source were basically public knowledge (even though at the time this did not mean "immediately available") and, the more basic the knowledge, the more it could be and was in fact connected to visual experiments. Carl Sagan mentioned the very less public approach to knowledge in the Pythagorean schools[3], where, despite the fact that their mathematical contributions where mainly of a geometrical nature and often taken from ancient Egypt, deliberately the results of their research was withheld from the public as occult knowledge.
The closer one approaches the source of knowledge, the closer it remains to perception itself. Allow me to demonstrate this with the example above, and old visual proof of a²+b²=c² , better known as the "Pythagorean theorem". This visual proof from the Zhou dynasty dates from about 3000 years ago and is taken from the famous book Zhou Bi Suan Jing (周髀算经).[4] In this early visual representation we find whole numbers (3, 4 and 5) in the line segments, easily perceivable and imaginable quantities. If we now fitted the two upper bold triangles below, we see the proof of the theorem as Pythagoras would have delivered it, according to Jacob Bronowski: visually[5]. As long as the angles are right, the summation of surfaces checks out, which one can be test by cutting out the image and connecting the proper thinking to the perception oneself. There can be no science without perceivable experiments.
To understand an abstraction with thought, we thus use our imagination related to perception. The closer the imagination resembles the perception, the more concrete the imagined is, the more effort needed in imagining, the more abstract it is. Abstraction requires effort. We daily deal with many abstract matters, regrettably all too often without real knowledge and thus a proper imagination of the matters at hand. Excessive confrontation with such abstractions leads to a decrease of understanding, of language eventually. For instance, what do we imagine with the abstract concepts Black Hole, Global Warming, Freedom, Civilization, Culture, Art: indeed, what is our imagination of thinking itself? Only with apt knowledge can imaginations be tested for their accuracy. Abstraction without content is dangerous.
Perception
Content
See also
- Version as published December 2010 in De Cascade 14 by Stichting Cosmicus[6]
- Alle kunst schept inhoud Dutch version
- Google translate slightly confusing machine-translated version of this page
- The original title's tweet of 15 November 2010
Notes
- ↑ Article on Dmitri_Mendeleev on English Wikipedia
- ↑ History of Algebra on English Wikipedia
- ↑ Carl Sagan on Pythagoras and suppression of knowledge (from Cosmos: A Personal Voyage 1980) on YouTube
- ↑ Zhou Bi Suan Jing on English Wikipedia
- ↑ Jacob Bronowski's visual proof of Pythagoras' theorem (from The Ascent of Man BBC 1973) YouTube
- ↑ De Cascade
