Recent political efforts to broaden the scope of science education and bring science into the mainstream have generated a great deal of controversy. One of the things that has been sorely missing is the relationship between mathematics and religion. Here we attempt to inject a greater mathematical essence into religion as well as explore one immediate implication, the Immaculate Induction Hypothesis.
1. INTRODUCTION: We focus on the injection of a greater mathematical sensibility within the religious community and examine the resulting implications. In doing so we agree that intelligent design is a valid viewpoint, but ask what this implies. We find that this implies a countable sequence of all-powerful and all-knowing entities going back through all time. The basic argument is that the complexity of the known universe implies the existence of a creator. The union of the creator and creation is a set that is more complex than just the universe and thus implies a creator of the larger set. An induction hypothesis follows readily from this approach.
The motivation for this work comes from recent efforts to inject the ideas of intelligent design into the science curriculum which have generated enormous attention of the main stream media. Unfortunately, both sides accuse the other of being close minded. In a game of “tug of war” both sides must be recalcitrant in order for the game to continue.
The current situation comes as little surprise to those of us in the mathematics community. We have been well aware of the proclivities of both sides. We have been long time observers of both sides and have noted these tendencies for many millennia. The mathematics community itself is also composed of people who share most of the traits of both sides, dogmatic, religious fervor combined with supreme arrogance, and we watch this terrible conflict with an awful understanding of the pain felt on both sides.
It is for this very reason that the mathematics community can no longer sit on the sideline. In particular we address the need of a greater mathematical ethic within the religious community through a preliminary investigation of intelligent design. This may seem one sided, but the close relationship that has developed between the mathematics and science communities (with the exceptions of chemistry, biology, geology, and psychology) is already well documented and subject to intense scrutiny.
2. THE GENESIS STORY: There have always been some tension between science and religion. Ironically, this tension has been focused on seemingly minor issues. The trial over Galileo’s assertion that the earth revolves around the sun relies on a single, ambiguous statement within the Hebrew bible. Men of great intellect and passion clashed over a trivial statement that has since been all but forgotten.
We now find ourselves with a similar clash. We are focused on the story of our origin. Again the clash centers on a relatively minor aspect of a broad tale. This time it is the Genesis story that is at the center of the conflict. One might think that the Genesis story is really about the gift given to us by the Creator. This is the gift of creation but more importantly the gift of free will. We were given creation and allowed the freedom to experience it on our own terms with all of the associated responsibilities.
It is easy to think that the story of Genesis comes down to the simple message that it is immoral to force particular beliefs onto others. Such a simple interpretation ignores the powerful draw of the story of our origin. It is the story of our origin that has become the focal point of conflict. The primordial draw of the question of our origin drives us in a way that is beyond reason or explanation.
The sacred texts of Christianity, Judaism, Islam and all other religions provide numerous examples about the relationships between the weak and powerful, the rich and poor, and provide explicit guidance on how we should treat one another. Rather than focus on such simple ideals which are already clearly articulated within each of the sacred texts we instead focus on the much more difficult and important story of our origin.
3. THE MATHEMATICS OF THE CREATOR: Our only way of studying the creator is to examine creation. The universe is a collection of simple objects that when brought together represent a staggering set of interactions. We are capable of studying and generating a basic understanding of small parts but are incapable of understanding the whole. For example, while sitting within this goldfish bowl we call “earth,” light seemingly strikes us that appears to have been generated millions of years ago from events taking place on spatial scales beyond our understanding. At the same time the molecular kinetics of proteins within our own cells exhibit nonlinear, chaotic oscillations that taken together create the reliable, stable clockwork that makes life possible. This complexity implies the existence of a creator.
All things around us has been created, and we denote creation as the “universe” or more formally as U0. That which initiated the creation of U0 has the full power and understanding of all that is within U0. All that is within us and beyond us is contained in U0 and thus is a part of the understanding and abilities of the creator. At the same time the creator, denoted C0 is an integral part of creation. The two do not stand apart rather are part of the unity of the “Grand Design.” Taken together we denote the union of C0 and U0 as G0.
From where did G0 arise? The subtle interactions found within U0 imply the existence of C0. The cardinality of G0 is greater than or equal to the cardinality of U0, since:
We find that a creator, denoted C1, must exist that can explain the intricacies of G0. From the existence of C1 we find that G0 must be contained within another universe composed of all that created by C1 which we denote U1.
It is possible that U1 be equal to G0 but it is not necessary. Hence we have that:
We now have the basis for our induction hypothesis: C1 initiated U1. We denote the union of these two sets,
Since the cardinality of G1 is greater than or equal to the cardinality of U1 which was created by C1 there must exist a C2 that can explain the intricacies and complexities of G1.
Proceeding in this way we must conclude in the existence of G2. Applying the same reasoning implies the existence of a countable set, Gi, where
We leave the formal statement and proof of the Immaculate Induction Hypothesis as an exercise for the reader.
Finally, this construction of Gi leads to a fascinating array of corollaries such as
which we do not explore here. We leave these as work to be completed with hopes that they will provide an enormous draw to this new and fascinating field of study.
4. CONCLUSION: In this paper we examine the mathematics of creation and uncover just one implication, the Immaculate Induction Hypothesis. The availability of the power of mathematical analysis helps make clear the connections between the sacred and the profane. In this one example we examine the implication of just one simple religious truth, the complexity and beauty of the world around us imply the existence of a creator, C0.
Through this one example we readily see that the power of mathematical analysis is a necessary component of any complete religious education and makes the case that greater mathematical content be added to the religion curriculum. This is necessary because the practice of religious study requires the communication of complex ideals with intricate interactions. Religious dialogue requires that we discuss and share the nature of infinite love and the infinite universe. In doing so it simply is not possible to share the full spectrum of the sacred without the language of mathematics.
Put simply, it is self-evident that the nature of religious dialogue has all the hallmarks of a hidden grand design. The intense and complicated interactions of nearly all human thought hide an underlying intelligence that can only be explained by the presence of an intrinsic, hidden mathematical structure.