# A Single Mathematical System that Unifies Liturgy and Physics – and Removes Wave Particle Duality

by on May 31, 2013

Are there any mathematicians out there who can tell me if this is nonesense? It might turn the whole of science upside down.

I recently did a posting about how the passage through sacred time might be viewed as a helical progression based upon the significance of the numbers 7 and 8 in the liturgy as commented on by St Thomas Aquinas. In the comments at the bottom of the article a regular reader called Alexey suggested that if this is so we can conclude that time exists in three dimensions. Here is his comment: Time then is more than one dimension. Just like, when traveling through space, it is not enough to say “I am at 40 degrees latitude”, — the longitude must be specified as well, so it is not enough to say “40 days passed”, one has to add “it is Thursday”.

What I fascinating idea. I have heard of multi-dimensional space (although really claim to understand the idea), but not three-dimensional time.

This immediately reminded me of someone I met years ago in Mountain View, California called Irwin Wunderman. His son was a friend of mine from my time studying engineering at Michigan Tech. Irwin was a brilliant man (he was in his seventies, I think, when I met him and he has since died). He was a PhD from Stamford, where he told me, his thesis was so advanced that even in awarding it his advisor told him that they weren’t sure that they fully understood it. He had invented a pocket calculator in the 1960s in his garage, which had patented and then marketed (you can read about this here). He was also an entertaining character who loved to give tours of his house which had been a speakeasy and bordello in the 1920s and had even been raided by the Untouchables.

When I met him he had just written a book in which he described a number system he had developed in which he suggested that numbers do not progress linearly (as we normally imagine them) but in fact counting from one to two is a vector operation (even in the absract world of mathematics). In moving from one to two, the vector of the transition is almost linear, but not quite. It moves slight off in two other dimensions as well. This means that the process of counting follows not a linear scale but a helical path.

At the beginning of the conversation he had immediately launched into a complicated description of how his theories worked. I have a degree in materials science (which is the physics of solids) from Oxford University and a Masters in engineering.  I was never a star student, but it does mean I have more than the average grasp of maths and science. Nevertheless, Irwin lost me in about three sentences. I was hopelessly out of my depth. So I stopped him and said: ‘Don’t tell me how this works. Tell me instead what the important consequences of this are.’

Then he told me that if you used his number system, rather than the conventional one, there were no irrational numbers and you could, for example, calculate precisely the area of a circle without having to use an approximate value for ‘pi’ (ratio of the length of the circumference of the circle to its diameter). Also, he said, through this he had come up with his own unified wave theory in which there was no wave-particle duality in the behaviour of photons, for example. I thought that this was staggering. If he really had done this then it could turn science upside down. However, Irwin couldn’t find anyone to take any notice of him because he was not associated with any university. He was a complete amateur who had developed this at home. It wasn’t just this (from what he was saying). It was so complicated that even most university mathematicians wouldn’t understand him. Eventually he had managed to find someone to read and understand it who had some authority and his book was published. But even then, its publication passed largely unnoticed. You can find it on Amazon here.

I tried to show his book any scientists I knew, but I couldn’t get anyone to take me seriously and as soon as anyone started to push me with further questions I couldn’t answer them; and again, because Irwin was an amateur they were inclined not believe that it could possibly be true.

At the time I had not thought about the comparison with the progression of time and the liturgy in a helix, but it is a striking parallel. Perhaps it means that anything that has magnitude (and not just space and time) is three dimensional; because that magnitude is counted by numbers and the number system is three dimensional? Woh, I’m getting out my depth again…I this needs a real mathematician! Perhaps someone who reads this might be motivated to read Irwin’s book and see whether there is anything to it. I would love to think there might be. Maybe this is unifying even more than waves and particles? We might have a bridge between the physical and the metaphysical. Readers help please!

Above: Irwin in his Mountain View house; below the garage in which he invented his desk calculator; and his invention as produced.

Lisa Andrews June 3, 2013 at 4:25 pm

David, I applaud your ability to bring disparate subjects into an artistic discussion of the sacred (economics, particle physics???). My mathematical training was in the field of economics and finance, so I am not qualified to comment on the question you raise. But I do remember a lovely book by Stratford Caldecott called “Beauty for Truth’s Sake” that succinctly laid out the splendid imperfection of mathematics and how faith is the component that allows us to see the perfection of the divine. I loved how Caldecott tied this awareness into the poetic language of the liturgy, especially the part of the Preparation of the Gifts: “By the mystery of this water and wine may we come to share in the divinity of Christ who humbled himself to share in our humanity”. The addition of the drop of water into the wine symbolizes the numerical discrepancies that are found throughout the created cosmos, which was understood by the Scholastics as the catalyst for our own “leap of faith” with Christ as the bridge between the material and divine. Maybe this ties in with Mr. Wunderman’s proposition that “the vector of the transition is almost linear, but not quite. It moves slight off in two other dimensions as well. This means that the process of counting follows not a linear scale but a helical path.” Sounds very Catholic to me.

David Clayton June 5, 2013 at 7:37 am

Hi Lisa
I know the book you mention. In fact his chapter on numbers was based on an article I wrote for his journal Second Spring (he mentions this in the book) also other sections of the book about the connection between the cosmos and the liturgy drew inspiration from another article I wrote for him at Second Spring, both before he wrote his book, called The Cosmic Liturgy and the Mind of God. He mentions this in the acknowledgements of the book. So its not surprising you noticed some parallels
David

Anabel June 6, 2013 at 3:50 am

Hmmm. Interesting. I am a historian and know very little about particle physics, except for the many documenaries I like to watch (and they are a lot). From my humble prespective I have always found the duality particle-wave totally senseless. In fact I remember having heard in one of the episodes of Morgan Freeman’s “Through the Wormhole” of some scientists that consider that is a particle guided by a wave. Of one of them I remember the name: Phillippe Coudé (well that is how I remember it, and it could be misspelled), and he was working in Paris.
David, Do you think someone with a general interest in physics but just that could follow (and notice that I don’t say understand) Irvin’s book?
Thanks,
Ana

Alexey June 6, 2013 at 7:50 am

“Perhaps someone who reads this might be motivated to read Irwin’s book and see whether there is anything to it.”

David, I second your call; it is now incumbent on me to read it, or at least try, but I have another book to finish first and I am a slow reader.

What I am suggesting is similar to how Einstein defines time: imagine an observer (with a fully equipped laboratory) making note of a repeating event; the observer counts the events and thus creates a measure of time. To which I add: well enough, but note that since there is more than one event to observe, he must attach a quality to some events: his repeating event T1, T2, T3, … all of the quality T; and also various P, Q, X, Y singular events. Now is a significant logical step: a time measuring event may be such that it has both repeatability and quality: A1, B1 – A2, B2, – A3, B3 – … This is two-dimensional time where one dimension is finite of ordinal 2: {A, B} and the other is infinite natural number set {1, 2, 3, …}. Our practical time system, of course, is a collection of finite-ordinal cycles such as several 60-cycles, 4-season climate cycle, 7-day weekday cycle. The 60-cycles do not have each a quality; the climate cycle has an intrinsic quality as seasons are recognizable to observer by quality; the days of the week cycle have quality that religion creates.

Next we notice that the observer with his einsteinian unidimensional time can count time intervals only subjectively: to speak of universal time he must synchronize his choice of event and his starting point with other observers. Whereas if events have recognizable quality, within the set of events observers can refer to each event without synchronization: “it happens in the summer” or “it happened on Sunday” are self-sufficient values of season-time and week-time and can be communicated to others as they are, within the given year or given week.

So perhaps philosophically we should not think of time as unidimensional but rather as a combination of distinct-quality events, and the time has as many dimensions as we have cycled distinct-quality events available: seasons, governorships of Judea, earthquakes, etc. We may, however, attach our own quality to a cycled event provided it is finite set, as quality must be of finite ordinal number. We do so to the days of the week. Time therefore has as many dimensions as there are suitable cycles: “In the third watch on 14 of Nisan as Pilate was governor of Judea.”

The fascinating thought here is that to an observer of a particular cycle the events coincidental to the same quality event in that cycle are contemporary events: one Sunday, for example, cannot be distinguished from another if all you observe are week cycles.

David Clayton June 6, 2013 at 8:14 am

Can’t wait to see you in Kansas. Reading what you have written I think this is where the traditional idea of number has something to add to modern mathematics. Modern maths, as I understand it tends to think of it as quantifying, but traditional maths thinks of it also as qualifying ie denoting a quality of something as much as a quantity. This is reflected in the symbolic number language. It is in the quantifying aspect of number that huge strides have been made since ihe middle ages, but the qualifying aspect has been neglected These two should not be seen in opposition, but complementary to each other. I suggest that a scientist or mathematician who is aware of both of these properties of number would be more creative and imaginative in his field as a result because he would have greater insight into the patterns and rhythms of the natural order and so would see solutions to problems – the natural way things ought to be – much more easily.

Dr. Donald P. Richmond, Obl.OSB, CCS June 6, 2013 at 1:34 pm

David

This stuff, quite frankly, is well beyond my pay grade. With Lisa, however, I DEEPLY appreciate your ability to bring great and erudite diversity to the table! I will say this, however, from Thomas a Kempis: “He to whom all things are one, he who reduces all things to one, and sees all things in one; may enjoy a quiet mind, and remain peaceable in God.” If God is One, all things hold together in Him and are ordered by His purposes. Thanks for making me think, David.

Teófilo de Jesús June 12, 2013 at 6:49 am

A recent episode of “Through the Wormhole” with Morgan Freeman addressed the issue of multi-dimensional time. The episode’s name was “What is time.” the relevant segment suggested that quantum events that seem random to us in reality aren’t because the events are connected in a multi-dimensional time coordinate grid. The issue is difficult to address mathematically because adding multi-dimensional time to current equations tends to make heads explode.

+JMJ,
~Theo

Wil Roese June 12, 2013 at 9:44 am

I often thought it is very interesting that Jesus Christ, the light of the world, is fully human and fully God and light is both a wave and a particle.

David Clayton June 13, 2013 at 7:54 pm

Very interesting thought!

Brendan June 13, 2013 at 12:02 pm

Ever think of bouncing the idea off of Fr. Robert Spitzer or someone in his Magis Institute for Faith and Reason? I think they’re a pretty science-heavy bunch. Thanks for the article – it was great!