A technologist’s reluctant journey into numeric mysticism (that wasn’t)
Let me level with you.
I didn’t set out to discover a recursive harmonic engine. Or a musical number grid that expands fractally. Or to revisit the Lo Shu magic square with a python interpreter in one hand and a raised eyebrow in the other.
No, I was irritated.
Irritated by the vague but persistent buzz of spiritual mathisms floating around the web—angel numbers, Solfeggio frequencies, vortex math, and the infamous “3-6-9 secret.”
They were just interesting enough to feel like they should mean something—and just hollow enough to feel like they probably didn’t.
They were woo.
Woo vs. Work: A Tale of Two Domains
By day, I’m a software engineer. Data analytics, machine learning, web APIs, server stacks, databases. It’s all satisfying in a puzzle-piece way, but I wouldn’t exactly call it romantic.
It has its elegance, but it doesn’t hum.
So when I ran face-first into Solfeggio frequencies for the eighth time in my online wanderings, I decided to do what any spiritually-jaded technologist might:
I wrote code. Lots and lots of code.
As we go on, I’ll share it in segments like this:
Python code coming in the next post — stay tuned!
Sure, you can run it here in most browsers…
Interactions, anyone?
Specifically, I created a directional path-walking algorithm on a standard 3×3 number pad grid. I called it the Preston Toroidal Scale (PTS).
From this simple procedure, I generated 81 unique three-digit numbers using consistent movement vectors.
What I didn’t expect was that all of them would be:
- Multiples of 3, 6, or 9
- Reproducible using only 8 directional rules and a stand-still state
- Internally consistent under digit reduction (always resolving to 3, 6, or 9)
And yes—they included both the angel numbers and Solfeggio frequencies that had annoyed me in the first place.
Was I onto something? Or just getting good at pareidolia with integers?
The Lo Shu Returns
Curious to test the PTS structure, I decided to substitute my values into a classic 9×9 magic square, where each row, column, and diagonal should sum to the same constant.
To my surprise, the column and diagonal totals remained intact using the PTS values.
The new magic constant? 4995—a tidy harmonic scale-up from the Lo Shu’s original.
And then, as a lark, I tried generating higher-order magic squares—not randomly, but by recursively expanding the Lo Shu itself.
By subtracting 1 from each cell of the Lo Shu (forming what I call the “proto-Lo Shu”), multiplying it, and embedding the result back into itself across scales of 3×3, 9×9, 27×27…
I generated Lo Shu rank-n matrices, including a rank-8 square of size 6561×6561, that still obeyed all the classical magic square rules.
Just one cell at a time. Deterministic. Reversible.
This was partially inspired by a video from mathematician and educator Presh Talwalkar, whose construction of a 9×9 matrix based on the Lo Shu pattern (as shown in this video) offered a visually striking approach. While his method of rotating and compacting 3×3 sub-squares is more aesthetic than algorithmic, it was enough to spark the next phase of exploration. Credit where it’s due.
Interestingly, the constant sum in Talwalkar’s original 9×9 matrix is 369, derived from its integer sequence design—not 495. The 495 magic constant only emerges once the 3-digit PTS values are substituted into the structure. More on that in an upcoming article.
Digit Roots, Fractal Math, and Maybe Music
The real mind-bender? Every value in the 3-digit PTS reduces to 3, 6, or 9 under Pythagorean summing. Every. Single. One.
This doesn’t hold for 1-digit, 2-digit, or 4-digit extensions—only the original 3-digit PTS set, generated from that 3×3 keypad walk.
That seemed odd. Resonant. Maybe even tonal.
So I plotted the values against a standard 12-tone equal temperament (12TET) frequency mapping. The PTS data didn’t align perfectly, but the curve was similar—almost logarithmic.
Enough to raise the question:
What if some of this ancient number woo is actually compressed memory?
That is—the hand-me-down echo of symbolic systems designed by people whose intuition was sensitive to patterns, but whose tools weren’t equipped to fully explain them?
That maybe all this woo we love to dunk on is humanity’s first attempt at building a vibe-based physics engine?
What This Blog Is (and Isn’t)
This won’t be a place to push pseudoscience. It will be a place to:
- Run ancient numeric systems through modern code
- Visualize harmonic structures interactively
- Respectfully analyze mystical math for meaning
- Build tools, charts, and visual models
- Treat woo with skepticism—but also curiosity
Each post in this series will include:
- A core concept
- A narrative walkthrough
- Code tabs (Python & JavaScript)
- A live interactive demo
Up next: How the Preston Toroidal Scale is generated, and what makes it so weirdly harmonic.
Until Then
I leave you with this:
The person who knows they know not everything… possesses the capacity for discovery.
And perhaps, even a fondness for a little well-structured woo.