Although Christians believe in a transcendent God and the existence of a transcendent God is supported by the scientific evidence, I find that most people, both believers and unbelievers, have a very poor understanding of the characteristics of a transcendent being. Many of the questions I hear from atheists about God are framed in a context that completely ignore his transcendence. Many of the problems that people have about how God interacts or doesn't interact in our world arise apart from an acknowledgement or understanding of the ramifications of God's transcendence. As a scientist I may have some insight into some of the characteristics of a transcendent being and how that might affect our understanding of God's interaction with us finite beings.

For the sake of discussion, let's define God as simply a being who exists in dimensions outside of our three dimensions of space and one dimension of time. This is an insufficient minimum model of God but it will serve our purposes. Is it possible for me as a three dimensional being to fully understand the characteristics of a four dimensional being? I would say that a three dimensional being cannot fully understand a four dimensional being and so humans can never fully understand a trans-dimensional God. A tool to help illustrate some of the challenges of understanding a being that exists in more dimensions than I do is the book

*Flatland: A Romance of Many Dimensions*written by Edwin Abbott in 1884 (under the pseudonym "A Square"). The book describes a universe that is flat like a piece of paper and only has two dimensions, length and width. The Flatlanders are confined to live out their existence on this two dimensional plane.

In the novel, a three dimensional being like you and I who is from Spaceland tries to explain the third dimension, height, to the Flatlander. Let's consider a very simple three dimensional object: a sphere. In order to try to explain a sphere to a Flatlander, I must pass the three dimensional sphere through the two dimensional plane that the Flatlander lives on and is confined to. In the book, Abbott draws this scenario as shown in the figure below.

When the sphere first touches the plane of Flatland, it would appear as a single point. As the sphere passes through the plane the point becomes a circle which gradually grows in size. The circle is largest when the sphere is halfway through the plane and as the sphere continues to pass through the plane the circles become smaller and smaller, eventually becoming a single point that then disappears as shown in the figure. In order for the Flatlander to understand the sphere, I as the Spacelander simply ask the Flatlander to join all of those circles together into one continuous object and the Flatlander will understand a sphere. To you or me it seems trivial to connect the circles into one continuous object so surely the Flatlander can do that in his mind. Well maybe not.

Suppose a four dimensional being came to you and I and said he wanted to show us what a four dimensional sphere looks like. It would seem that should be simple enough to do. I can even write the equation for a four dimensional sphere.

^{1 }So the four dimensional being passes his four dimensional sphere through our three dimensional space. It starts as a point when it first crosses our space, it grows, not as a circle, but as a sphere that gets larger and larger until it reaches its maximum size, then gradually shrinks maintaining its spherical shape until it finally shrinks to a point then disappears. The four dimensional being then asks us to simply put all of those different sized three dimensional spheres into one continuous unbroken surface and that is a four dimensional sphere. At this point my mind is completely blown. I can't begin to picture those spheres in a single continuous object. The four dimensional being can easily do so, but I'm completely lost.

This Flatland illustration can help us try to appreciate various aspects of a being who can exist outside of our dimensions. First, as stated above, there is no way I can fully comprehend something (or someone) outside of my experience of three dimensions and one dimension of time. A four dimensional sphere is probably the simplest object that fits that description yet I can't even begin to comprehend that! It follows that full comprehension of a transcendent God is definitely not possible.

Another aspect of God's character that becomes clear from this illustration is that I can only know anything about him if he chooses to reveal himself to me. Note that the Spacelander does not have to intersect the plane of the Flatlander. The Spacelander could spend her whole life without ever crossing the plane of the Flatlander. If so, the Flatlander would have no way of knowing the Spacelander even exists. I know atheists who say they will only believe in God if God interacts with them on their terms. But the Flatlander is in no position to dictate the terms of communication to the Spacelander. The Spacelender must willfully choose to interact with the Flatlander and intersect with his plane in order to be known. Though the Flatlander cannot access the dimensions of the Spacelander, the Spacelander can access the dimensions of the Flatlander whenever and however she wishes. The Spacelander must initiate the contact and can show herself on her terms, how and when she chooses. In doing so, the Flatlander can only see a two dimensional representation of the three dimensional being. Of course, this is exactly the Christian doctrine of the incarnation of Jesus. God chose on his terms to show himself to humanity as a finite being who intersected our universe. That is the only way we could see a representation of a higher-dimensional being.

If someone wants to investigate whether or not God exists, that person can try to dictate the terms of God's engagement, but that is likely a flawed strategy since the higher dimensional being always ultimately chooses the time, place, and method of the interaction. Of course, I do believe God often responds to someone who is truly seeking and shows himself to that person. But it may be a more effective strategy for someone who wants to know if God exists to instead look for evidence of where God has previously intersected with our world. Such evidence is found with the resurrection of Jesus. Humans do not rise from the dead but a resurrection is trivial for a higher dimensional being. The resurrection is evidence that God has intersected with our plane of existence.

There are other aspects of God's character that are illuminated through the Flatland illustration including God's presence, his ability to perform miracles, and whether or not he can be examined using the scientific method. We'll explore those subjects and more in the next post: A Transcendent God: Part 2.

^{1}The equation for a circle is x

^{2}+ y

^{2}= r

^{2}. The equation for a sphere is x

^{2}+ y

^{2}+ z

^{2}= r

^{2}and the equation for a four dimensional sphere is x

^{2}+ y

^{2}+ z

^{2}+ w

^{2}= r

^{2}

Dr. Strauss, It might interest you to know that we ourselves are 4-dimensional beings in a 3-dimensional world. Or as I like to say, spiritual beings in a material world:

ReplyDeletePost-Darwinist - Denyse O'Leary - Dec. 2010

Excerpt: They quote West et al. (1999),

“Although living things occupy a three-dimensional space, their internal physiology and anatomy operate as if they were four-dimensional. Quarter-power scaling laws are perhaps as universal and as uniquely biological as the biochemical pathways of metabolism, the structure and function of the genetic code and the process of natural selection."

They comment,

"In the words of these authors, natural selection has exploited variations on this fractal theme to produce the incredible variety of biological form and function', but there were severe geometric and physical constraints on metabolic processes."

"The conclusion here is inescapable, that the driving force for these invariant scaling laws cannot have been natural selection. It's inconceivable that so many different organisms, spanning different kingdoms and phyla, may have blindly 'tried' all sorts of power laws and that only those that have by chance 'discovered' the one-quarter power law reproduced and thrived."

Quotations from Jerry Fodor and Massimo Piatelli-Palmarini, What Darwin Got Wrong (London: Profile Books, 2010), p. 78-79.

http://post-darwinist.blogspot.com/2010/12/how-much-of-body-plans-of-organisms-can.html#links

The predominance of quarter-power (4-D) scaling in biology

Excerpt: Many fundamental characteristics of organisms scale

with body size as power laws of the form:

Y = Yo M^b,

where Y is some characteristic such as metabolic rate, stride length or life span, Yo is a normalization constant, M is body mass and b is the allometric scaling exponent.

A longstanding puzzle in biology is why the exponent b is usually some simple multiple of 1/4 (4-Dimensional scaling) rather than a multiple of 1/3, as would be expected from Euclidean (3-Dimensional) scaling.

http://www.nceas.ucsb.edu/~drewa/pubs/savage_v_2004_f18_257.pdf

The second part of this following video, at the 10:08 minute mark, also covers quarter power scaling

The abject failure of Natural Selection on two levels of physical reality – video (2016) (princess and the pea paradox & quarter power scaling)

https://youtu.be/ISu-09yq2Gc?t=609

This following recent video is also of related interest to 'higher dimensions':

ReplyDeleteQuantum Mechanics, Special Relativity, General Relativity and Christianity - video

https://www.youtube.com/watch?v=gKggH8jO0pk

Paper:

https://docs.google.com/document/d/1nRZECqs8Iqeqv0GzP5lV6et_K9_rYrz06Tchoa4U0Rw/edit

notes from preceding video and paper:

The Unreasonable Effectiveness of Mathematics in the Natural Sciences – Eugene Wigner – 1960

Excerpt: We now have, in physics, two theories of great power and interest: the theory of quantum phenomena and the theory of relativity.,,, The two theories operate with different mathematical concepts: the four dimensional Riemann space and the infinite dimensional Hilbert space,

http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

Here is an interesting quote about the infinite dimensional Hilbert Spaces in quantum mechanics:

The Applicability of Mathematics as a Philosophical Problem - Mark Steiner - (page 44)

Excerpt: The role of Hilbert spaces in quantum mechanics.. is much more profound than the descriptive role of a single concept. An entire formalism-the Hilbert space formalism-is matched with nature. Information about nature is being "read off" the details of the formalism. (Imagine reading off details about elementary particles from the rules of chess-castling. en passant-a la Lewis Carro;; in Through the Looking Glass.) No physicist today understands why this is possible..

https://books.google.com/books?id=GKBwKCma1HsC&pg=PA44

And here is an interesting piece of trivia about Einstein's 4-dimensional space-time

Spacetime

Excerpt: In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zurich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the definition of a spacetime interval that combines distance and time. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded.

Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 general theory of relativity, wherein he showed that spacetime becomes curved in the presence of mass or energy.,,,

Einstein, for his part, was initially dismissive of Minkowski's geometric interpretation of special relativity, regarding it as überflüssige Gelehrsamkeit (superfluous learnedness). However, in order to complete his search for general relativity that started in 1907, the geometric interpretation of relativity proved to be vital, and in 1916, Einstein fully acknowledged his indebtedness to Minkowski, whose interpretation greatly facilitated the transition to general relativity.[10]:151–152 Since there are other types of spacetime, such as the curved spacetime of general relativity, the spacetime of special relativity is today known as Minkowski spacetime.

https://en.wikipedia.org/wiki/Spacetime

Wigner's text is a classic in the world of science and math.

DeleteYes, space and time are in some sense interchangeable and Minkowski space does describe our four-dimensional space-time universe. For practical purposes and purposes of understanding transcendence, it is much simpler to just consider the three dimensions of Euclidean space.

Thanks for your comments.

I should have read this before I commented on your last post. Still, if God set the universe in motion like a clock and it is so finely tuned (and I should say I follow you on that...it makes sense), why would it need to intervene? It sets the gears in motion then lets it go. Time means nothing to it or at least it experiences time differently. I'm not sure I understand why God would feel the need to show himself at all unless He was like a human. I totally agree that I cannot understand God and I follow you on the fourth demension thing I think. But it's like we have to attribute human characteristics to God to understand God on a personal level. So isnt that kind of a contradiction? Makes my brain cramp up ;-)

ReplyDeleteGod wants to have a relationship with people. Since we are confined to this universe he must step into the universe to have a relationship with us. In the Flatland analogy if the 3-d person wants a relationship with the 2-d person, she must try to show and describe herself in 2-d. God's intersection with our universe is not necessarily to keep it working since as you say a good clock can work on its own. His intersection is so he can have a relationship with us finite beings.

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DeleteThe lack of inderstanding of the concept of divine transcendence is why certain atheists think they're parodying religious belief by comparing God to a flying plate of spaghetti. Pastafarians amuse me because they fail to realize that they're actually parodying their own ignorance.

ReplyDeleteUm ... to paraphrase the sphere example using only some of your words, but the general idea of it in the flatland example, you say that as a sphere enters flatland, it first appears as a circle and then the circle becomes larger, then smaller, then a point, then disappears again. "First," "begins,"then," "disappears." All of those words suggest time. They suggest a being in a 2 dimensional space understands time and you try to explain three dimensions by describing how a sphere would pass through. No two dimensional being could understand the third dimension by way of the fourth dimension. In fact, a two dimensional "being" wouldn't understand anything as any sense of understanding an comprehension requires an appreciation of time passing and that demands a minimum of four dimensions or at least the appreciation of time as one of the dimensions you comprehend. Without time, there's no such thing as "comprehendING."

ReplyDeleteWhen I talk about 2 or 3 dimensions I mean 2 or 3 space dimensions. Both flatland and spaceland have the same concept and dimension of time.

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