Concordia University’s Enduring Questions & Ideas (Q&I) curriculum looks at the big questions of life through the context of the liberal arts and in the foundation of a Christian understanding of the world. The questions of “What is good?”, “What is true?”, and “What is beautiful?” are at the heart of the first year Q&I courses that students take in Core Biology, Core Theology, Core Philosophy, and, my subject area, Core Mathematics.
Of those three questions, the one that seems to be the most difficult for students to grasp (and for faculty to teach towards) is the question of goodness.Because of our culture and its generic use of this term, there seems to be a lack of understanding regarding goodness and what we mean when we talk about it. There are even those who say there is no real goodness anyway; it is just a socially created idea that is subjective at its very nature (see Amelie Rorty’s 2011 essay, “The Goodness of Searching,” for arguments against the existence of goodness from Aristotle, Spinosa, and others).
Using great works, rigorous thinking, investigation, and careful writing, the Core Mathematics curriculum seeks attributes of goodness as seen in the world and especially in mathematical concepts. In his book Awakening Wonder: A Classical Guide to Truth, Goodness & Beauty, Stephen Turley identifies one way that students can learn about goodness is through representation. He says, “By looking at our subjects through the lens of aesthetic representation, our subject matter transforms into a new set of eyes through which our students can begin to see the meaning inherent in the created order.” In Core Mathematics, we look at representations of goodness and analyze their attributes to uncover what goodness can mean.
One of the attributes that most people can decipher about goodness is that it is useful or beneficial. Unfortunately, this perception is one that is perpetuated in mathematics quite a bit. “When will I ever use this?” is a common question from students studying mathematics. While the application of mathematical concepts gives a great value to civilization, finding other attributes of goodness and where they exist around us can help us have a more complete picture. If something is only good if it is used, or only if it is beneficial to me, there seem to be many things in our world that would fail based on this criterion (family and faith to name two).
The ability for people to see goodness beyond just their personal benefit is a first step towards breaking this limited understanding. The collective or societal good is a concept that can move people past the self-centeredness we possess as humans and begin the process of empathy or caring for others. Even just the mental stimulation of working through a concept that is a societal good can change the perspective of that person into seeing a bigger and broader understanding of the world around them and where goodness resides.
Some scholars have traced the roots of the concept of goodness to something unchanging, foundational, and unifying that people can rely on. Saint Augustine identified that a happy life is found in holding fast to the unchangeable:
“Thus when the will, which is an intermediate good, holds fast to the unchangeable good as something common rather than private–like the truth, which we have discussed at length without saying anything adequate–a person grasps the happy life. And the happy life, i.e. the attachment of the mind holding fast to the unchangeable good, is the proper and fundamental good for a human being.” (On The Free Choice of the Will)
This gives a different perspective of goodness than just being useful or beneficial. Unchangeable attributes in life that are foundational and unifying can be seen in many mathematical concepts that are not normally studied by undergraduates in a general education course. The straightforward Fibonacci sequence (1, 1, 2, 3, 5, 8…) is quite attainable for the typical college undergraduate. Requiring only addition and division skills to see the various patterns involved within it, the Fibonacci sequence and its partner, the Golden Ratio, are seen as foundational aspects of optimal plant growth, architecture, art, animal reproduction, galaxy shapes, and the formation of sea shells. This wide variety of areas where this concept is observed is a foundational aspect and points us towards what is good.
Another topic we cover to investigate this attribute is the mathematics related to the infinite. Through the use of a foundational concept of “one-to-one correspondence,” we are able to see that the infinite has multiple sizes and that common notions in our world (the whole is greater than its parts) don’t apply to the infinite. But without the infinite there are major gaps and holes in the world of mathematics and many areas of our world would be left void (students especially appreciate that video gaming is often built on concepts stemming from the infinite such as fractals). This is a unifying concept in mathematics and again points us to where to look for goodness around us.
But students still have difficulty finding or observing goodness in the world around us. As a Lutheran Christian institution whose mission is grounded on “the Great Commission of Jesus Christ and the Lutheran Confessions,” we understand that our sinful conditions and the corrupting effects of sin in the world makes the vision of goodness (and truth and beauty) hidden from us in the fullest perspective. But through the Holy Scriptures, we can see goodness personified in the person and work of Jesus Christ, who is the image of God, redeems us, and who founds and unifies all things in himself.
“[God] has delivered us from the domain of darkness and transferred us to the kingdom of his beloved Son, in whom we have redemption, the forgiveness of sins. He is the image of the invisible God, the firstborn of all creation. For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him. And he is before all things, and in him all things hold together.” (Colossians 1:13-17)
Identifying goodness is an important aspect of helping young people see their role in society, enabling them to reach towards empathy with others, and knowing what (or whom) to hold onto and trust as good in life. Seeking attributes of goodness, even in topics involving mathematics, encourages students to think more deeply about this ancient, yet significant, question of life.
Bret Taylor is Professor of Mathematics at Concordia University Irvine