What is Reification?
The dictionary gives the definition for the word "Reification": as "to convert into or regard as a concrete thing." I love the definition and what it captures of the human capacity to bring an imaginary thing into something concrete. The artist imagines a picture and then sets about bringing that picture into the realm of the visible. Architect envisions a building and uses his craft to make plans for the making that building part of the landscape of a city. The poet has thoughts and feelings and renders these fleeting senses into words and phrases that communicate to others. The social engineer dreams of justice for all and develops programs that will make it possible in society.
In the beginning, God thought of the multitude of stars, planets, living creatures and then made them into visible reality. God spoke and it was fashioned. Man was just one of those things fashioned by His skill, but man was made in the image of God with the ability to convert imaginary things into concrete substances.
The word for this process of bring the imaginary into a concrete thing is reification. At the heart of every mathematician is the desire to make the imaginary into the visible. Sometimes the mathematician is just part of the process for someone else's reification, but every person needs the skill of the mathematician to make the invisible concept, visible.
In the beginning, God thought of the multitude of stars, planets, living creatures and then made them into visible reality. God spoke and it was fashioned. Man was just one of those things fashioned by His skill, but man was made in the image of God with the ability to convert imaginary things into concrete substances.
The word for this process of bring the imaginary into a concrete thing is reification. At the heart of every mathematician is the desire to make the imaginary into the visible. Sometimes the mathematician is just part of the process for someone else's reification, but every person needs the skill of the mathematician to make the invisible concept, visible.
Should it become part of the school curriculum?
I know that many peoples' concept of mathematics would not include reification. My own background in mathematics involved wading through problem after problem that rehearse process after process. Now that I have left school, mathematics provides a vehicle for making concepts into real things. Perhaps we ought to change school mathematics, but I wonder whether I would have really appreciated this important application of mathematics then as I do now. Some things are best left for the seeker to discover, rather than be another thing that burdens the curriculum.
There are some educators who try to have their students create things and use the opportunity to expose the students to the mathematical processes involved. These are not legitimate examples of reification because the imaginary is not becoming concrete. The imaginary part for the students is a concrete problem posed by the teacher. This is a far cry from the imagination of the engineer or the inventor or the researcher. It may be a good substitute and inspire the student to try some for himself, but the curriculum looks so packed already, it is hard to see where this type of activity would be given the time.
A suitable analogy could be drawn with the learning of music. Composing music is very much a process of reification, but it will not teach the budding musician how to play with techniques and confidence. Composing will enhance one's understanding of the world of music, but the drill of practice and interpretation is for the classroom, while the composing is for the dreamers.
There are some educators who try to have their students create things and use the opportunity to expose the students to the mathematical processes involved. These are not legitimate examples of reification because the imaginary is not becoming concrete. The imaginary part for the students is a concrete problem posed by the teacher. This is a far cry from the imagination of the engineer or the inventor or the researcher. It may be a good substitute and inspire the student to try some for himself, but the curriculum looks so packed already, it is hard to see where this type of activity would be given the time.
A suitable analogy could be drawn with the learning of music. Composing music is very much a process of reification, but it will not teach the budding musician how to play with techniques and confidence. Composing will enhance one's understanding of the world of music, but the drill of practice and interpretation is for the classroom, while the composing is for the dreamers.