God and Nature 2025 #4
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By Doug Phillippy
In his book entitled Prayer: Does It Make Any Difference?, Phil Yancey notes that C. S. Lewis decided that it is altogether reasonable to pray at noon for a medical consultation that had taken place two hours earlier. Lewis comments that such a belief would be less shocking to scientists than non-scientists. This essay will explore the reasonableness of Lewis’s claim from a mathematical perspective. In particular, by investigating three-dimensional objects from within the bounds of two-dimensional space (a plane), we seek to provide a visual framework for discussing potential limitations of a theology that is confined to the bounds of the time-space continuum. A theology that moves beyond the bounds of time and space can not only make sense of Lewis’s claim but also open doors to think about theological concepts like predestination and free-will in new ways.
While there has been considerable conversation regarding the universe and higher dimensions, this essay will focus on the familiar time-space continuum that humanity experiences on a daily basis. To begin, consider the following question: Can an object simultaneously be a circle and a rectangle? The answer to this question may seem rather obvious: an object is either a rectangle or a circle or neither, but it is not simultaneously a circle and a rectangle. Suppose we change the question and ask instead: Can an object, depending on an observer’s perspective, have the characteristics of a circle in some instances, and at other times appear to have the properties of a rectangle? The answer to this question may still seem obvious—but suppose the observer’s perspective is limited in some way; say, by the “space” in which the observer experiences the object. Could this limitation be the reason for the different ways an object is perceived?
In his book entitled Prayer: Does It Make Any Difference?, Phil Yancey notes that C. S. Lewis decided that it is altogether reasonable to pray at noon for a medical consultation that had taken place two hours earlier. Lewis comments that such a belief would be less shocking to scientists than non-scientists. This essay will explore the reasonableness of Lewis’s claim from a mathematical perspective. In particular, by investigating three-dimensional objects from within the bounds of two-dimensional space (a plane), we seek to provide a visual framework for discussing potential limitations of a theology that is confined to the bounds of the time-space continuum. A theology that moves beyond the bounds of time and space can not only make sense of Lewis’s claim but also open doors to think about theological concepts like predestination and free-will in new ways.
While there has been considerable conversation regarding the universe and higher dimensions, this essay will focus on the familiar time-space continuum that humanity experiences on a daily basis. To begin, consider the following question: Can an object simultaneously be a circle and a rectangle? The answer to this question may seem rather obvious: an object is either a rectangle or a circle or neither, but it is not simultaneously a circle and a rectangle. Suppose we change the question and ask instead: Can an object, depending on an observer’s perspective, have the characteristics of a circle in some instances, and at other times appear to have the properties of a rectangle? The answer to this question may still seem obvious—but suppose the observer’s perspective is limited in some way; say, by the “space” in which the observer experiences the object. Could this limitation be the reason for the different ways an object is perceived?
Scripture implies that, unlike humanity, God is not limited by time and space. |
To see this, consider a three-dimensional cylinder intersecting a two-dimensional plane. The region that is formed by the intersection of the cylinder with the plane is dependent on the orientation of the cylinder relative to the plane. For example, imagine that the cylinder is moving through the two-dimensional plane in such a way that the axis of the cylinder is perpendicular to that plane (see figure 1). The intersection of the cylinder with the plane will be a circle (or the empty set if the cylinder does not intersect with the plane).
Now suppose the cylinder is turned on its side with its axis parallel to the two-dimensional plane (figure 2). As the cylinder moves through the plane, the intersection of the cylinder with the plane results initially in a line and then in rectangles of increasing width. Eventually, the rectangles begin to decrease in width and finally become just a line again. Thus, depending on its orientation, the three-dimensional cylinder is projected onto the two-dimensional world as a variety of different shapes.
Now, imagine two different observers, one living in a three-dimensional world, capable of seeing in all three dimensions; the other restricted to the two-dimensional world of the plane, capable of seeing only things as they intersect with that two-dimensional plane. The observer in the three-dimensional world is capable of seeing not only the cylinder in its entirety, but also the distinct shadows (lines, circles, rectangles) that the cylinder casts onto the two-dimensional plane. The observer trapped in the plane sees that cylinder as well, but in a very different way. Depending on the orientation of the cylinder relative to the plane, the observer might see a “rectangle,” or a “circle,” or something else as described above, but the observer cannot see the whole cylinder.
But does this observer actually see a rectangle or a circle? To answer this question, imagine looking down at a coin on a desk. Now suppose that you begin to drop your eye level to the top of the desk. As you look across the desk, your vision is limited to the edge of the coin, giving the appearance of a line. In the same way, a circle lying in a plane has the appearance of a line to an observer restricted to two-dimensional sight. In some sense, then, points and lines are all that can be seen by an observer in a two-dimensional world. The idea of distance may help the observer to distinguish between the points of a rectangle lying in the plane and the points of a circle lying in that same plane, but both the “rectangle” and the “circle” will have a similar appearance to the observer confined to the plane. All this suggests that it is not easy for the two-dimensional observer to fully comprehend the higher-dimensional cylinder.
For visual purposes, the above discussion was limited to spatial dimensions. Suppose we consider a fourth dimension—namely, time—as well. From within the confines of time and space (the human perspective), it may not make sense to pray for an event after it has already happened, especially if the outcome of that event is known, but to an observer living outside the time-space continuum, prayer is witnessed independent of when that prayer is offered. In the same way that the two-dimensional observer’s understanding of the cylinder is limited by that observer’s environment, the human perception of prayer is limited by a confinement to the time-space continuum.
This discussion may also shed light on the seemingly contradictory ideas of free-will and predestination that are presented in Scripture. Passages like John 6:44, where Jesus says, “No one can come to me unless the Father who sent me draws him, and I will raise him up at the last day,” seem to downplay the idea of freedom of choice; while others like Joshua 24:15, where Joshua says, “then choose for yourselves this day whom you will serve…But as for me and my household, we will serve the LORD,” seem to highlight it. Many Christians consider themselves to be Calvinists, emphasizing the sovereignty of God and his calling of an individual to himself, while others consider themselves to be of Arminian persuasion, focusing on the free-will of humanity to choose or not to choose God. How do we reconcile these two seemingly contradictory viewpoints?
In his book Faith and Learning on the Edge, David Claerbaut (1) notes a tradition within Judaism that encourages an individual, when facing what seems to be a paradox, to embrace both extremes of the faith rather than trying to reconcile them. This seems wise, especially when there is evidence of both extremes in Scripture. But when paradox is a result of a limited human perspective and can be overcome by stepping outside of that perspective into a broader view of reality, effort should be made to do so.
Scripture implies that, unlike humanity, God is not limited by time and space. The model of dimension considered in this essay suggests that the paradox regarding free-will and predestination may stem from trying to understand these ideas from within the confines of the time-space continuum. A Christian who holds to the belief that God is not bound by time or space recognizes that God does not experience time the way humanity experiences time. While this recognition may not produce answers to questions surrounding free-will and predestination, it does provide motivation to think about these ideas from a different perspective, one that is independent of time.
For example, human beings understand that choices have consequences. But the very notion of consequence is bound up in time. Decisions made today have consequences in the future, not the past. However, present decisions are often made in light of consequences from past decisions. In short, the human understanding of choice is strongly rooted within the context of time. But what does the idea of choice look like from God’s perspective, a perspective that is outside of time? Could it be that from a human perspective the freedom to choose exists only because that perspective is bound up in time and space, and that this explanation and understanding of choice is completely meaningless from God’s perspective (outside of time)?
Much like the observer of three-dimensional objects confined to a two-dimensional plane, humanity is left pondering questions like these based on the shadows and images cast from a reality that extends beyond what we can observe in our time-bound existence. While the study of higher dimensions in mathematics may not help us answer these questions, it certainly motivates the importance of considering and even developing a theology that extends beyond the boundaries of time and space.
Douglas Phillippy Ph.D. in applied mathematics, is a Professor of Mathematics at Messiah College located in Grantham, Pennsylvania. Since coming to Messiah College, his research interests have shifted to include the integration of faith and mathematics and developing mathematical maturity at the undergraduate level. On a personal note, Dr. Phillippy is a runner and enjoys participating in a variety of other sports. He is married to Deb and has four children.
Now suppose the cylinder is turned on its side with its axis parallel to the two-dimensional plane (figure 2). As the cylinder moves through the plane, the intersection of the cylinder with the plane results initially in a line and then in rectangles of increasing width. Eventually, the rectangles begin to decrease in width and finally become just a line again. Thus, depending on its orientation, the three-dimensional cylinder is projected onto the two-dimensional world as a variety of different shapes.
Now, imagine two different observers, one living in a three-dimensional world, capable of seeing in all three dimensions; the other restricted to the two-dimensional world of the plane, capable of seeing only things as they intersect with that two-dimensional plane. The observer in the three-dimensional world is capable of seeing not only the cylinder in its entirety, but also the distinct shadows (lines, circles, rectangles) that the cylinder casts onto the two-dimensional plane. The observer trapped in the plane sees that cylinder as well, but in a very different way. Depending on the orientation of the cylinder relative to the plane, the observer might see a “rectangle,” or a “circle,” or something else as described above, but the observer cannot see the whole cylinder.
But does this observer actually see a rectangle or a circle? To answer this question, imagine looking down at a coin on a desk. Now suppose that you begin to drop your eye level to the top of the desk. As you look across the desk, your vision is limited to the edge of the coin, giving the appearance of a line. In the same way, a circle lying in a plane has the appearance of a line to an observer restricted to two-dimensional sight. In some sense, then, points and lines are all that can be seen by an observer in a two-dimensional world. The idea of distance may help the observer to distinguish between the points of a rectangle lying in the plane and the points of a circle lying in that same plane, but both the “rectangle” and the “circle” will have a similar appearance to the observer confined to the plane. All this suggests that it is not easy for the two-dimensional observer to fully comprehend the higher-dimensional cylinder.
For visual purposes, the above discussion was limited to spatial dimensions. Suppose we consider a fourth dimension—namely, time—as well. From within the confines of time and space (the human perspective), it may not make sense to pray for an event after it has already happened, especially if the outcome of that event is known, but to an observer living outside the time-space continuum, prayer is witnessed independent of when that prayer is offered. In the same way that the two-dimensional observer’s understanding of the cylinder is limited by that observer’s environment, the human perception of prayer is limited by a confinement to the time-space continuum.
This discussion may also shed light on the seemingly contradictory ideas of free-will and predestination that are presented in Scripture. Passages like John 6:44, where Jesus says, “No one can come to me unless the Father who sent me draws him, and I will raise him up at the last day,” seem to downplay the idea of freedom of choice; while others like Joshua 24:15, where Joshua says, “then choose for yourselves this day whom you will serve…But as for me and my household, we will serve the LORD,” seem to highlight it. Many Christians consider themselves to be Calvinists, emphasizing the sovereignty of God and his calling of an individual to himself, while others consider themselves to be of Arminian persuasion, focusing on the free-will of humanity to choose or not to choose God. How do we reconcile these two seemingly contradictory viewpoints?
In his book Faith and Learning on the Edge, David Claerbaut (1) notes a tradition within Judaism that encourages an individual, when facing what seems to be a paradox, to embrace both extremes of the faith rather than trying to reconcile them. This seems wise, especially when there is evidence of both extremes in Scripture. But when paradox is a result of a limited human perspective and can be overcome by stepping outside of that perspective into a broader view of reality, effort should be made to do so.
Scripture implies that, unlike humanity, God is not limited by time and space. The model of dimension considered in this essay suggests that the paradox regarding free-will and predestination may stem from trying to understand these ideas from within the confines of the time-space continuum. A Christian who holds to the belief that God is not bound by time or space recognizes that God does not experience time the way humanity experiences time. While this recognition may not produce answers to questions surrounding free-will and predestination, it does provide motivation to think about these ideas from a different perspective, one that is independent of time.
For example, human beings understand that choices have consequences. But the very notion of consequence is bound up in time. Decisions made today have consequences in the future, not the past. However, present decisions are often made in light of consequences from past decisions. In short, the human understanding of choice is strongly rooted within the context of time. But what does the idea of choice look like from God’s perspective, a perspective that is outside of time? Could it be that from a human perspective the freedom to choose exists only because that perspective is bound up in time and space, and that this explanation and understanding of choice is completely meaningless from God’s perspective (outside of time)?
Much like the observer of three-dimensional objects confined to a two-dimensional plane, humanity is left pondering questions like these based on the shadows and images cast from a reality that extends beyond what we can observe in our time-bound existence. While the study of higher dimensions in mathematics may not help us answer these questions, it certainly motivates the importance of considering and even developing a theology that extends beyond the boundaries of time and space.
- David Claerbaut. Faith and Learning on the Edge: A Bold New Look at Religion in Higher Education. Zondervan, 2004.
Douglas Phillippy Ph.D. in applied mathematics, is a Professor of Mathematics at Messiah College located in Grantham, Pennsylvania. Since coming to Messiah College, his research interests have shifted to include the integration of faith and mathematics and developing mathematical maturity at the undergraduate level. On a personal note, Dr. Phillippy is a runner and enjoys participating in a variety of other sports. He is married to Deb and has four children.