In mathematics, a function can be represented several different ways. Numerically, Graphically, Verbally, and Algebraically. Lets take a moment to look at each one.
Verbally
"y varies directly as the cube of the difference of x and 2."
Numerically
Graphically
Algebraically
Each of these expressions for the function have value to our students because they help them see and understand the relationships that exist in the function. It also increases their ability to communicate what a function is and exactly in what way the y value changes with the x value.
Levels 1 and 2
From another vantage point, each of these "Ways to Express A Function" is also a different window of knowledge about that function. The verbal is at the lowest level. We have some idea of how y varies with x, but we have no data points, only that some cubic relationship exists. At the numerical level we begin to see specific data points. We know exactly what the y value is for each x value given in the table, but not for other x values outside the table.
Levels 3 and 4
Once we begin to hit the graphical level, we begin to make connections between the data points we know, and values we don't have. This helps us make estimates for values that were not given to us. The algebraic expression is at the highest level, because once we have the equation, we now have the rule whereby we can know all solutions to the problem. Simply input a value of x that is in the domain of the problem, and get the corresponding y value. So what on earth does this have to do with the apostle John? I'm glad you asked.
Knowing God and Abiding in the Light
In 1 John, the apostle is concerned for the church; that it remains in the truth of the gospel and in the light of the truth. "God is light, and in Him is no darkness." 1 John 1:5.
The gospel comes to us first verbally, "faith comes by hearing..." Romans 10:17, but while we are Christians, we are brand new. We don't know much about God other than Jesus has paid the price for our sins, and by repentance and belief in the Son of God, we have eternal life.
As we grow, and if we continue to walk in the light, God brings new data points into our lives. We learn how to pray a little, God answers our prayers in different ways. We begin the process of reading our bibles and memorize certain scriptures. We also begin to gain understanding of what we now have in Christ Jesus.
Moving forward in our sanctification, God brings us to the place of greater dependence on Him in the midst of suffering and pain. We experience a world that is not only void of God but opposed to Him! Our prayer life deepens and God teaches us, to the level that we obey, how to walk in the light of the truth in a world full of darkness. We begin to learn how to connect the points in order to engage the bigger picture.
In 1 John 2:20 the apostle tells his readers, "But you have been anointed by the Holy One and have all knowledge." We have direct access to the truth because our fellowship is with the Father and the Son if we are abiding in the light. [1 John 1] God's desire is to lead His children to that place where they can truly say, "I have all knowledge because I know Thee." The ability to say with confidence, "He is my God." regardless of the circumstances is the current desire of my heart. I fall so short of it. Yet God remains true. "Ask and it shall be given to you, Seek and ye shall find, Knock and the door shall be opened." Matthew 7:7
Concluding remarks
I fully confess it can be easy to talk about a subject (or many subjects) one might not have fully experienced or immersed one's self into. In response I will close with a brief paragraph from the preface of J.I. Packer's book, "Knowing God."
"Stand at the crossroads and look; ask for the ancient paths, ask where the good way is and walk in it, and you will find rest for your souls. (Jeremiah 6:16). Such is the invitation which this book issues. It is not a critique of new paths, except indirectly, but rather a straightforward recall to old ones, on the ground that the "good way" is still what it use to be. I do not ask my readers to suppose that I know very well what I am talking about. "Those like myself," wrote C.S. Lewis, "whose imagination far exceeds their obedience are subject to a just penalty; we easily imagine conditions far higher than any we have really reached. If we describe what we have imagined we may make others, and make ourselves, believe that we have really been there" -- and so fool both them and ourselves. (The Four Loves, Fontana ed., p.128) All readers and writers of devotional literature do well to weigh Lewis' words. Yet "it is written: 'I believed; therefore I have spoken.' With that same spirit of faith we also believe and therefore speak." (2 Cor 4:13) -- and if what is written here helps anyone in the way that the meditations behind the writing helped me, the work will have abundantly been worthwhile.
J.I.P
Trinity College Bristol
July 1972
John Partridge
August 20th 2019
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