Ambiguity, Duality, God, & Christ

I’ve been reading this book called “How Mathematicians Think” by William Byers which is real fascinating and a produced much thought and mediation which I love! So I thought I share some of my musings. It's long. It's a 4 page document.

Byers maintains that mathematics is not just logic but a lot of ambiguity. What a mathematician does is a creative art in the midst of ambiguity. These are some things he had to say.

• “Logic abhors the ambiguous, the paradoxical, and especially the contradictory, but the create mathematician welcomes such problematic situations because they raise the question, “What is going on here? Thus the problematic is a potential source of new mathematics. How a person responds to the problematic tells you a great deal about them. Does the problematic pose a challenge or is it a threat to be avoided.” p.6
• “In our response to reason, w are the true descendants of the Greek mathematicians and philosophers. For us, as for them, rational thought stands in contrast to a world that is all too often beset with chaos, confusion, and superstition. The ‘dream of reason’ is the dream of order and predictability and, therefore, which we attempt to implement that dream are mathematics, science, and technology. The desired end is the emergence of clarity and reason as organization principles of the entire cosmos.” P.12
• He defines ambiguity as “Ambiguity involves a single situation or idea that is perceived in two self-consistent but mutually incompatible frames of reference.” P.28
• “A joke is an example of ambiguity and creativity – you have to get a joke.
• “E= mc^2 sys that matter is energy. It says that these two mutually exclusive ways of describing reality are in fact one – that there is one reality that can be seen as energy when we look at it in one context and as matter when we look at it in another. Thus, the equation is something that could be called a scientific metaphor…. ‘Getting’ a metaphor requires an insight: it requires an looking at the world in a new way.” P.33
• Byers goes on to show many examples which one including that 1 is the same as 0.999…..(ie goes on forever). He says the following about it. “That is understanding involves the realization that there is ‘one single idea’ that can be expressed as 1 or as 0.999…, that can be understood as the process of summing an infinite series or and endless process of successive approximation as well as a concrete object, a number.” P.41
• There is much in math that we take as being true though there is no proof of it, just a lot of evidences. Could you say that even math which runs so much of our society exists on faith? “Goldbach’s conjecture can be stated simply: Every even number greater than two can be written as the sum of two prime numbers…. A conjecture is a ‘proposition that has no been prove, but is favored by some serious evidence.’ … There is great deal of evidence in favor of the validity of Goldbach and most mathematicians believe it to be true. For small values on n (small for a number theorist), n = or < 6*10^17, the conjecture has been verified by computer.” P.54
• “Many people regarded the existence of complementary properties like wave/particle duality as paradoxical…. After all, one might ask, what is it really, a wave or a particle? We feel that it cannot be both. Yet there is one thing of which we can be sure – there is one electron. When we look at is in one way (in one frame of reference) we observe particle-like properties. When we look in another way we get wave-like properties. The electron is precisely the singular entity that emerges out of this fundamental ambiguity.” pp.60-61
• “Ambiguity also involves dual concepts, but each context stands on its own, each context describes the entire situation, so to speak.” p.61
• “Physicists use the term duality to describe theoretical models that appear to be different but nevertheless can be shown to describe exactly the same physics.” P.63
• “The problem lies not in the mathematical activity but in the way that activity is described and therefore misinterpreted by people who teach mathematics, who use mathematics in their work, or who find it comforting to hold to a vision of the world that is logically coherent and devoid of ambiguity. Mathematics is mistakenly used as justification for such a simplistic point of view. The resulting damage to students, to teacher and to society at large, is considerable.” P66
• “Metaphors are not purely ‘logical’ entities… Grasping a metaphor requires a discontinues leap” p.70
• Consider the Old lady/young women picture that most people know about… “The picture has two perfectly consistent interpretations, the young woman and the old lady. These are the two self-consistent frames of reference … the entire picture is really a field of black and white dots…. Second, each interpretation is an adequate description of the entire field of black and white dots. It is not as though some of the black and white dots are interpreted as the young women and some as the old lady. The entire field is subject to the given interpretation.” pp.72-73

So here’s the musing: What if this is so much of our problem, the way we view things? There is something true in one context and another true in another context such as energy and matter. We can look at an object and it is energy and it is matter. However we try to look it only from the perspective of matter, how could it be energy then?

What if our problem is that we try to stay within one frame of reference and when something comes along to question this we throw it out without giving much consideration because it’s “illogical” or we throw it out because it’s problem, a threat to be avoided rather than a challenge an opportunity to discover what is going on here—what is true.

Think about how often we do this to each other! A person did or said something and from our perspective they meant xyz, another person interpreted it differently, and the one who said it really meant something that neither were getting. Then we go off and make assumptions from our perspective and often this arises in conflict because we don’t bother to seek the truth.
Think of the other areas we do this in? What about God being good and suffering in the world? So often we see evil and suffering in the world, in our family’s lives, and our own. If God allows suffering in my life, or this person’s life, then God must not be good. We are saying that “lack of suffering = good God.” So when suffering comes along we force it fit into that equation. What if there is another perspective.

Now, the examples I’ve been given assumes more that one perspective is wrong and another right. However the author Byers talks a lot about both perspectives being right. Let’s get to some more touchy subjects. Oh, like predestination and free will. (Okay, this does require you to consider that there is a God and God who has the power and ability to cause predestination to happen). It seems that most people see it through the lens predestination or free will. You could say that people view this as follows “predestination + free will = reality” where either predestination or free will is equal to 0. But what if this is one of the examples like Byers was talking about. They both are true, each it’s own context. It requires us grasping at the metaphor. Grasping at another perspective and world view that it is outside the one we are use too. Outside how this society now often defines “logic.”
Let’s take this another step. What about the duality of Christ. (I’m going to go off the assumption that Christ was a real living person and that the Bible is historically accurate. Now if you don’t believe that, then this hold no value. But maybe you could suspend that and consider “what if it is true?”

In the Bible, Christ makes many references that seem to say that he is God but also fully human. It seems that we often function on the question [(1-x)*God + x*Human] = 1 where x= or > 1. How can Christ be both man and God? Could he be half human and half God like so many other religions such as roman and Greek have. How could God become human? How can something so big be confined to a human form? These are questions this may cause us to grapple. Or we may not considered it at all because we on first glance considered illogical saying that of course x=1, Christ was just a human. How could it be any other way? But the Bible poses an ambiguity.
If the world is full of examples of ambiguity in nature (such as matter and energy and that an electron is both a wave and a particle), do you think it might reflect on the Creator who created nature to be that way? (Assuming you believe there is a creator which I will not cover here.) What if this ambiguity the author talks about is part of reality. The world cannot be reduce into logical, orderly, algorithmic functions.

The question is will we entertain the question “what if it is true?” What if there are two perspectives and context to view Jesus like the electron that is both a wave and a particle yet there is just one electron. There is just one Jesus of Nazareth? Will we simple dismiss this question or respond to this “problem” as a challenge to understand. Will we be the “logical” ones that see this as a threat (because if you decided that Jesus is God it has a lot of implications to on one’s life) because “Logic abhors the ambiguous, the paradoxical, and especially the contradictory.” p.6 Many of the Jews, Pharisees, and Sanhedrin viewed it that way? They knew that Jesus was claiming to be God and they could not reconcile this in their context, persecution, or frame of reference. Jesus was a threat to be killed.

How will I respond will “ambiguity” appears. When I have conflicting emotions? When things are bad and therefor God doesn’t love me, but the Bible says he does? Can suffering and love exists together? What will I conclude? What will you conclude? Christianity is full of ambiguity that should be searched out to mind its depth and treasures. Not only for those seeking to see if it’s true but also by those who blindly accept it being true without truly understanding. I don’t want to just “plug and chug” through a algorithmic equation- getting the right answer. I want to understand why the answer is right. I want to “get” it.
Or there could be an entirely different frame of reference than anything here!