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.