Writing is my artistic expression. My keyboard is my brush. Words are my medium. My blog is my canvas. And committing to writing daily makes me feel like an artist.
I recognize this video is for a small audience, and I’m hoping to get some help. Joe and I are viewing the world as geometers, not physicists or mathematicians. If you know of someone smarter than us in these fields, we encourage dialogue and perspectives that challenge our thinking, please share.
Thank you!
But something is missing… and that’s the origin of this unique shape.
Not anymore. Joe Truss discovered, or rather uncovered, the following unique origin story of the Enneagram. Perhaps the Sufis of the past knew, but this knowledge was lost: The 2-Dimensional Enneagram has 3-Dimensional roots. Enjoy this short video to learn more: Secret Origins of the Enneagram.
“The Enneagram is a 3-Dimensional structure which manifests through the vertices of the icosahedron.” ~ Joseph Truss
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And if you think this is interesting, Joe has also uncovered the tetrahedral structure of our universe… if you know a physicist who can challenge these ideas, both Joe and I invite them to break this theory apart: We Live in a Tetraverse.
Please share with people whom you think might be interested.
Thank you.
After a 4 year hiatus, I’ve just published another podcast. Unfortunately, my link isn’t updating to my podcast hosting app or to Apple iTunes right now, and so the best place to listen is on my podcasting blog.
Description:
Join me on a trip in to Haliburton, Ontario, where Joseph Truss and I discuss the building blocks of the universe. This conversation assumes the conjecture that “We Live in a Tetraverse,” (the first video in a series called, “Book of Codes”). Watch this video first, to appreciate the premise of our conversation.
A conjecture is defined as: “an opinion or conclusion formed on the basis of incomplete information.” Joe is challenging the way Mathematicians and Physicists look at the universe today. Most perspectives put us in a three dimensional world based on three axis: X, Y, and Z. Joe says these are “necessary but not sufficient“, and that while we can do calculations based on this model of the universe, it will always require us to work with irrational numbers and rounding errors… but it’s all a question of resolution. Go deeper than the perspective of X,Y, Z and you encounter a universe built on triangles, or more specifically tetrahedrons. In a way, his premise is that working in a cube-based, X, Y, Z, universe is conjecture… it is working ‘on the basis of incomplete information.’
If we recognize that the smallest possible object in the universe (at the Planck length) is a tetrahedron and not a cube, (again see We Live in a Tetraverse to gain this insight), this doesn’t dismiss any calculations done in a cube universe, it simply allows greater resolution… and maybe eliminates the need to work with irrational numbers and rounding of decimals.
A simple metaphor for this would be moving from the imperial system of measurement to the metric system… measuring in millimetres instead of 16th’s of an inch.
Admittedly, this is a bit of a challenging conversation to follow, first because we start talking about waves as seen drawn in 2 dimensions on paper, and so the conversation is lacking some visual descriptions we discuss. Secondly because we have discussed these ideas at length previously, we are quite comfortable describing shapes and making connections that are not so easy to visualize when you haven’t had the same background conversations we’ve had. And yet, I felt the need to share this conversation, to bring to light some of the brilliant insights of Joseph Truss. One specific topic we discuss, that I haven’t seen anywhere else, is the idea that infinity is a fractal. The infinity conversation begins at 21:08 of the podcast and if you only listen to one segment, that’s the one to listen to. If you want to follow the full conversation, I’d suggest watching the video first.
Joe and I had walked down to a slow-moving river that adjoins his back yard. Joe, a musician as well as geometer, brought a drum with him and after playing a bit we started this conversation. I realized that this was worth recording and so I went back to to the house to get my phone. The podcast starts and ends with Joe playing the drums, and there is a drum interlude in the middle as well. So, pull up a seat next to us and enjoy this riverside conversation.
Whenever you see a movie like the Matrix, data sets, information, and all storage are shown in cubes.
Even beyond the movies, it is clear that we represent the world on three axis: X, Y, and Z.
In the words of Joe Truss, these 3 axis are ‘necessary but not sufficient‘ to really understand the world we live in. We Live in a Tetraverse:
This is the first video in a series called ‘Book of Codes’, which over time you will help you discover for yourself the power you inherently have as a natural geometer. Join Joe and Dave Truss as they discuss the building blocks of a tetraverse… where the foundations of life, and everything in our universe is built around the unique geometric shapes that are comprised in the geometry of stacked and interlocking triangles.
The Book of Codes will awaken the natural geometer within you.
Some people spend their weekends watching sports… while the Super Bowl was on, I was putting the finishing touches on this video. That’s not a slag on anyone who enjoys watching sports, it’s just not my thing. What I do enjoy is nerding out and thinking about how I can use geometry to make sense of challenging ideas in mathematics and physics that are actually way beyond my capabilities to calculate and understand without the geometry. Thanks to Joe, I have almost weekly meetings on Sunday mornings to learn from him and to think deeply about the hidden geometry behind our universe and all life within it.
We record most of our meetings. This is hopefully the first of many we will share. While there are more videos to come, don’t expect them too soon… I only really get a chance to work on them on the weekends and editing video takes a lot of time. Still, I hope you enjoy this video, and as always, feedback is appreciated.
Well today I did a whole lot of nothing. I came down to the basement do a workout 3 hours ago, and I have successfully completed a 10 minute row, less than 10 minutes of stretching, and an abdominal workout that lasted the length of a 2 minute and 40 second song. Hey, this might not be a typical workout… but I didn’t skip the day. Not every workout needs to be at 100%.
I listened to a part of a podcast, watched a few TikToks, and I’m writing this lying on my back next to a magnetic toy where I successfully made a couple DNA strands out of triangles. 
I’ve spoken about playing with geometry before, this ‘playing’ was the most productive part of my day.
Tomorrow is Day 1 of the new school year and the pace for the next month will be anything but lazy. So, I look at my 3 hours of ‘wasted’ time as time very well wasted. Today was the calm before the storm. Batteries are charging, and I’m taking full advantage of my last lazy day, not even caring that I’m mixing my metaphors. 🤪
Now off to pick up pizza, ain’t no way my wife and I are cooking tonight! 😀
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To all the educators out there, I wish you a fabulous year of teaching and learning ahead!
I came across this Map of Mathematics in a TikTok where people working in the field of Mathematics were all sharing how their fields intersected different parts of the map. Here is the video:
I love how the concepts and fields of study connect and interconnect.
The the video starts with a ‘stitch’ of a Tiktok user asking, “Did everyone know that Mathematicians are, like, discovering new Math?”
This plays into a recent post in which I state that Math is ‘Discovered more than invented‘. There is so much more to discover, and I believe, thanks to my conversations with Joe Truss, that geometry is the foundation of Math. But math is a hard conceptual language with which to understand the geometry… and if we study the geometry we can understand the universe without having to do the hard math. Oh, and if Mathematicians better understood the geometry they could discover new Math a little faster.
Is Math invented or is it discovered? Is Math a human, or at least biological construct that helps mammals understand the world we live in? Or does it exist inherently in the universe and is it revealed to us through curiosity and scientific discovery?
I’ve shared my fascination in playing, learning, and discovering secrets held in Geometry (here and here) with Joe Truss.
Recently I watched a video that quoted Galileo Galilei:
“Mathematics is the language with which God has written the universe.”
With everything Joe and I have been playing with, I thought of an adaptation of this quote:
The universe is written in the language of geometry, and Mathematics allows us to measure it.
When I shared this with Joe, he tweaked it:
The universe is written in the language of geometry, and Mathematics allows us to take its measure.
I like this because it speaks to the idea of Math being discovered, of it being inherent because it is present in the geometry. It is Geometry that is the underlying language. Math is the alphabet, the universe is written in geometry. This is why Pi pops up where you don’t expect it; why the Fibonacci sequence is prevalent in nature; why we can land a ship on the moon and Mars; and even why our religious symbols come out of geometry.
The challenge we have is that we don’t fully understand the geometry, sometimes rather than discovering the true essence of the mathematics, we have to invent approximations that help us make sense of universe. Understand the geometry and maybe we can remove infinities and irrational numbers in our calculations… Understand the geometry, and the math becomes more accurate. Understand the geometry and maybe we can unify our theories that currently seem to contradict themselves.
Discover the geometry and we discover the math behind it, no longer needing to invent approximations of the math to translate the geometry into a world of calculations and numbers that don’t quite fit with they universe we are trying to describe. When we discover the geometry, we no longer needs to invent Math, the geometry allows us to take its measure… And in fact we can explain the universe with the geometry, and then we don’t have to be a physicist or mathematician to understand it.
I’ve already shared that I’m playing with geometry a lot with Joe Truss. We met on Zoom today and talked about living in a ‘Tetraverse’, a universe that is built on the structure of a tetrahedron.
Today we spoke about how this Tetraverse would (and does) affect gravity and wheels spinning on axis. Then I went back to my magnetic ball and rod 8-frequency tetrahedron that I built a few weeks back and played some more. It’s late and I’m not going to try to do a synopsis of the intricate patterns I saw. What I do want to say is that it’s fun to play in a space where I am constantly learning both by being taught and by discovery.
The image below is a blue cube octahedron with each triangular face forming a tetra-octa-tetra pattern coming out from the center.
This is a tetra-octa-tetra, with two yellow tetrahedrons on opposite sides of an octahedron:
I’m fascinated by these shapes thanks to my uncle, Joseph Truss, who has been playing with these shapes for decades, and who believes the fundamental building blocks of our universe is the tetrahedron. We live in a ‘Tetraverse’.
But the geometry he describes goes far beyond this. He intuitively understands the underlying structure of the universe through geometry in a way that mathematical physicists understand it through math.
Watch this 28 minute movie, Hacking Reality. It gets to some of the topics Joe and I discuss. I really think he’s on to something some of the smartest physicists in the world are still trying to figure out… but he’s done it purely by playing with geometry, and visually/intuitively making sense of how shapes are formed and come together.
Two of the smartest people I’ve ever met are my uncle and my dad. Last night I sat with my uncle until 4am, and he broke down the origins of the Enneagram… not the personality types attached to it later, the actual origins of the symbol.
Basically, there is a 3-dimensional geometric shape that the enneagram, traditionally shared as a flat, drawn image, is derived from. He basically shared a mind-blowing fact that has essentially been ‘lost knowledge’ since before George Gurdjieff (1866-1949), “a Armenian philosopher, mystic, spiritual teacher, and composer of Armenian and Greek descent, born in Alexandropol, Russian Empire (now Gyumri, Armenia)” (Wikipedia) introduced this symbol to western culture.
Seeing the 3-dimensional origins of the image ‘unlocks’ some sacred geometry that is lost, or rather not available to be seen, in the 2-dimensional enneagram. My uncle has shared this with me before, but I couldn’t conceptually ‘see’ what he saw, and understand the underlying geometry. Last night I made a video of him sharing this lost secret.
The video needs a bit of editing, and I want him to share it on his own YouTube channel, not mine, but look for it to be shared soon. It’s not often you get to see an answer to a question asked and unanswered for over 100 years, but my uncle has ‘discovered’ the 3-dimensional origins of the enneagram!
