Why Mathematics Points Beyond Numbers to Design September 14, 2011 With Dr. David Berlinski
Mathematician and author David Berlinski, in his new book, One, Two, Three, explores the exciting, satisfying story of numbers, their history in human culture and their implications for modern man. In an informal Discovery Institute luncheon in Seattle on September 14 (Wednesday), Dr. Berlinski – a Senior Fellow of Discovery Institute – will describe how far one can go in saying that mathematics, as a body of thought derived from nature, points to design.
The event will be held at Discovery Institute, located at 208 Columbia Street in downtown Seattle on Wednesday, September 14, from 12:00 p.m. to 1:30 p.m.
Therefore no one is to act as your judge in regard to food or drink or in respect to a festival or a new moon or a Sabbath day– things which are a mere shadow of what is to come; but the substance (literally body) belongs to Christ.
For the Law, since it has only a shadow of the good things to come and not the very form (literally image) of things, can never, by the same sacrifices which they offer continually year by year, make perfect those who draw near.
I love the Biblical imagery of a “shadow.” The Greek word translated as “shadow” (σκιά, pronounced skia) shows up three times in the New Testament in a metaphorical sense. Two of the three verses are listed above and we will get to the third (and perhaps most interesting use for the purposes of this blog) shortly. The word σκιά can be translated as “shadow” or “foreshadow” or even “reflection.” There are several examples outside of the Bible of the word being used to refer to an image as seen in water – in which case the translation of “reflection” might be more apt. In all metaphorical cases, including the three instances in the New Testament, σκιά can generally be taken to mean: “a mere representation of something real” (BDAG).
One thing about shadows, they need a body to make them (Col. 2:17). Reflections need an original, or true, image (Heb. 10:1). In both passages listed above, Paul and the author of Hebrews are not claiming that the Mosaic Law was bad. The Law was in fact very good, but incomplete. In as much as a person’s shadow is not a complete description of who they are since it only provides an outline of their form, the Law was not a perfect description of how humanity is to relate to God, but it did give an outline, an idea. The Law was meant to point toward Christ. It provided only a boundary of holiness in which Israel was to operate in order to be a distinct and set-apart people of God. The Law was the shadow. Christ is the body. The Scriptures above demonstrate that since Christ has been revealed we no longer live in a shadow of unreachable standards, but instead we are to be intimately related with God in person: Jesus Christ.
So what does this have to do with math?
This brings me to the third passage in which σκιά is used metaphorically:
For every high priest is appointed to offer both gifts and sacrifices; so it is necessary that this high priest (Christ) also have something to offer. Now if He were on earth, He would not be a priest at all, since there are those who offer the gifts according to the Law; who serve a copy and shadow of the heavenly things, just as Moses was warned by God when he was about to erect the tabernacle; for, “See,” He says, “that you make all things according to the pattern which was shown you on the mountain.”
This passage references Exodus 25 – an entire chapter (plus) devoted to instructions for constructing the Tabernacle. Whereas the two passages we began with seemed to describe the Law as a shadow of Christ, Hebrews 8:5 seems to take that imagery a step further and claim that the physical Tabernacle is a shadow of the heavenly place of worship in the presence of God. What I find interesting is that the construction of Tabernacle is at its root a mathematical process. Exodus 25 is filled with detailed dimensions and lists for construction. When God wanted to teach Israel what He was like and How He was to be worshiped, the language of mathematics played a vital role in communicating that message.
Maybe there is something in this imagery of “shadow” that can help us understand the place of mathematics in this world – both its importance and its limitations. Is the language of mathematics simply a “shadow” of our divine understanding to come? While my thoughts are just beginning on this issue, initially my answer would be yes.
In pursuing this further, it is comforting to know that I am not the only one who believes mathematics can be best understood with this “shadow” imagery. The following is taken from the book Thinking About Mathematics, by Stewart Shapiro:
“At the end of Book 6 of the Republic Plato gives a metaphor of a divided line (see Fig. 3.1). The world of Becoming is on the bottom and the world of Being on the top (with the Form of Good on top of everything). Each part of the line is again divided. The world of becoming is divided into the realm of physical objects on top and reflections of those (e.g. in water) on the bottom. The world of Being is divided into the Forms on top and the objects of mathematics on the bottom. This suggests that physical objects are ‘reflections’ of mathematical objects which, in turn, are ‘reflections’ of Forms” (p. 53-54).
In some sense Plato saw mathematics as reflecting the Forms, or the true world of knowledge.
Plato described Forms such as the Good, the Beautiful, the True, the Just. Today we as Christians can understand these Forms as being attributes and expressions of the divine nature. God’s nature defines goodness, beauty, truth, justice. As we pursue study of the divine nature, in some way mathematics provides a “shadow” (an outline) that guides us.
What exactly that means, I’m not yet certain. I just found this imagery very interesting in light of Scripture and I will be pursuing this line of thinking further in the future. For now I leave it to you to do with this what you will. I would love to hear your comments. As we wrestle with this topic we can be comforted that while we may not understand the shadow completely, there is a true body to whom we relate and who we will one day see.
For now we see (a reflection) in a mirror dimly, but then face to face; now I know in part, but then I will know fully…
1 Corinthians 13:12 (object added)
And Lord, haste the day when my faith shall be sight,
The clouds be rolled back as a scroll;
The trump shall resound, and the Lord shall descend,
Even so, it is well with my soul.
Why is mathematics different (in a good way) from every other subject you learned in school?
Two words: Pythagorean Theorem.
Let me explain. The Pythagorean Theorem in itself isn’t really the reason math is unique; it is merely an example I wish to use to illustrate my point. I chose this Theorem for an example because it has been my experience that it is one of the few things everyone remembers from math class, regardless of how much they enjoyed math or how well they did in the course. But just in case the P.T. slipped your mind, here is a recap:
For any right triangle, the square of the hypotenuse (side opposite the right (90 degree) angle), is equal to the sum of the square of the other two sides.
This result is attributed to the Greek mathematician and philosopher Pythagoras (hence the creative name for the theorem). Pythagoras lived between the 5th and 6th century B.C. and while he is ultimately the one credited with proving the theorem, there is evidence that the result of the theorem was known to the Babylonians 1000 years before Pythagoras was born. Notice this old tablet:
My point is that in what other class are you performing the same operations as people were performing 3000 years ago? Certainly in history class you learn about earlier civilizations, but you are not being taught how to do history in the same manner as those civilizations. The precision that modern history requires was largely unknown to those ancient people. Perhaps in literature you read Homer’s Iliad and Odyssey, but again, you aren’t being taught to write in the same style of epic poetry.
So then why is it that in math class, while advancements have been made and technology certainly has come a long way, we still find it beneficial to perform calculations the way they were performed thousands of years ago?
My answer: there is nothing to perfect, nothing ot improve upon, when you come across truth. Real truth.
To all of us who hold the Christian belief that God is truth, anything that is true is a fact about God, and mathematics is a branch of theology.