I. Representing abstraction
Where can we draw the line between representation and abstraction?
Strictly speaking, the word abstract means to separate or remove something from something else. It refers to what exists as an idea, but has no concrete existence.
While figurative art has traditionally derived from the representation of real objects, abstract art does not attempt to represent an accurate depiction of a visual reality, and it is free from figurative constraints.
Albeit an artist may have a real subject in mind when creating an artwork, shapes, textures, material, and proportions may be used to convey an underlying feeling, sensation, or idea, rather than produce a realistic replica.
In a similar way, abstraction in mathematics is the process of extracting the underlying structures, patterns, or properties of mathematical concepts, removing any dependence on the physical world.
We find abstract art attractive because it stimulates our neural activity as our brains try to identify familiar shapes, thus making it particularly powerful. Yet, for many this abstraction is perceived as a barrier when it comes to mathematics.
Didactics and philosophy provide us with ways to overcome these cognitive obstacles, such as shifting from concrete examples to abstract thinking or diversifying the modes of representation we use.
Semiotic representation and transmediation are keys in mathematics education. Semiotic representation is a way of talking, thinking, and interpreting sign systems – language, images, objects – standing for meaning through any of our senses. Transmediation refers to the ability to move from one mode of representation to another.
The roles of representation and transmediation apply to both artistic expression and mathematics. The first chapter of this exhibition highlights the relationship between art and mathematics, between representation and abstraction.