Quantitative Geometry
excerpt from sacred geometry: philosophy & worldview (pages 12-13)
Benjamin Franklin
(1706-1790)
"As to the usefulness of geometry, it is as certain that no curious art or mechanic work can either be invented, improved, or performed without its assisting principles."
However, I can tell you that in the process we also lost something essential—the visceral linkage between hand, paper, and world that drawing with the human body used to bring to the table.
Consider for a moment that people experienced this natural connection from the origin of civilization until the early 1990s. Those whose careers started later are probably intellectually aware of the tectonic shift in technology, but fewer still are viscerally aware of the sensibility of stylus, ruler, and compass and what that natural immediacy meant to countless generations.
Understanding how to use geometry quantitatively can help you get a job or improve your professional skills. Most of my career focused on learning, using, and teaching AutoCAD (and other design software) to members of the Architecture—Engineering—Construction industry.
The quantitative use of geometry can fulfill the core human desire to learn, build skills, work, achieve, and succeed in many industries."
It might be illuminating for you to learn how I used quantitative geometry in my career. It's one example to give you a taste.
My Quantitative Uses:
Quantitative Geometry Courses

3ds max, Autodesk VIZ, Lightscape, Autodesk AutoCAD & AutoCAD LT, Autodesk Architectural Desktop, Revit, SketchUp, Twilight Render, Adobe Photoshop, Illustrator, Premiere Pro, After Effects, Audition, Fresco, Shapr3D, Procreate, Sketchbook, Euclidea Sketches, Unity, Wordpress, plus AutoLisp, JavaScript & C# programming.

I was a decade too early for the word 'Grok' to be understood by the mainstream; today, as we approach AGI, 'Grokking'—the ability to understand something intuitively and fully—is the most vital skill a human can possess.

More recently, I continue to offer qualitative geometry courses through Udemy, Skillshare, Learndesk, Eduonix, LinkedIn Learning, and SourceCAD.com in India. Of all these, here is complete listing of my 28 LinkedIn Learning video courses, to give you a sense of my areas of focus within Architecture | Engineering | Construction:

Engage in a Sacred Anachronism: DRAW GEOMETRY.
Stop consuming the digital world and start constructing an analog one. By returning to the primary language of
shape and proportion, you bypass the noise of the standard worldview and rediscover the qualia
of your own consciousness.

Technical Books I Wrote

Technical Books I Edited

My Education and Tech Evolution So Far
For math homework, where corrections were constant, I relied on 0.5mm mechanical pencils and Staedtler Mars Plastic eraser holders—the only way to maintain precision through the endless reworking of algebra and geometry. Things were a bit different then: my teachers all wrote on blackboards rather than whiteboards, and my geometry teacher famously took swigs from his flask during class. He was a functioning alcoholic who taught so poorly, and I was so bored that I eventually decided to learn geometry by reading the entire textbook on my own. It was just natural for Gen-X: figure it out yourself, what is the problem? I was used to it, having to always adapt, being born without my legs below the knee and without my right hand (as I detail in my book, The Unlikely Cartographer). That experience of self-directed study, and a lifetime of adaptation, taught me the foundations of a discipline and an attitude that would ultimately define my career.
When I started university in 1988, my parents gifted me a prestigious and expensive tool: the second Macintosh model—the "Fat Mac." Originally retailing for $3,300 in 1984 (roughly $10,000 in today's money), it featured a 9" grayscale screen, an 8 MHz processor, and an upgraded 512 KB of RAM (the "fat" over the original 128 KB). It had no hard drive, only a single 3.5-inch floppy diskette drive. The workflow was an exercise in great patience: I had to load the operating system from one diskette first, eject it to load the software (like Microsoft Word) from a stack of others, and finally save my work onto a separate hard-shelled diskette.
I spent two years studying mechanical engineering before pivoting to architecture, eventually earning my degree in 1992.

The transition to the digital age was happening right in front of me. My college friend, Tiffany Shlain—who would go on to found the Webbys—even appeared on Good Morning America as their "on-air Internet expert" to explain to the nation what "the Web" actually was. I was struck by her moxie in landing that gig, but it was telling that the media turned to a 24-year-old to explain the future to a nation. A generation or two later, that dynamic remains unchanged; technology is changing faster than the generations can assimilate.
Looking back, the technological leap is staggering. My current PC has 64 GB of RAM—131,072 times more memory, or five orders of magnitude, than my university Mac. My 16 TB backup hard drive offers seven orders of magnitude more storage than a 1.4 MB floppy disk once did, and my four-year-old Ryzen processor runs five orders of magnitude faster than that 8 MHz Fat Mac. Instead of a 9" screen that could display 256 shades of gray, I now sit in front of an array of three 27-inch 4K monitors with wide color-gamut support with (millions of calibrated HDR colors) made for designers.
I ran this through an LLM to help refine my draft, and it used an ungodly amount of compute to do so. To put it in perspective, while my local workstation is a beast, the datacenter that processed these words operates at a scale six orders of magnitude beyond my own—roughly a million times the raw processing power, fueled by enough electricity to power a small city. If my PC is a single candle, the LLM cluster is a stadium floodlight. This is absolutely freaking crazy.
Yes, the jump from my current PC's processor and RAM to the cloud LLM's processing and RAM is actually larger than the jump from my 1984 Fat Mac to my current PC. Friends, we are now inside the event horizon of the singularity. No one gets out of here alive, but maybe we'll live a heck of a lot longer enjoying universal high income poolside, with robots serving our every need and beverage? I doubt it, but still I hope for a Jetsons future!

Are you ready? Tongue-in-cheek: Maybe we should ask a Gen-Alpha to explain artificial intelligence (AI), artificial general intelligence (AGI), and an artificial super-intelligence (ASI) to us? Wait, no one is going to be up to that trans-human task.
We'll need an AI to understand an AGI and we'll need an AGI to understand ASI.
Not sure anyone really even understands current AI in the first place. How does that very large matrix of numbers feel? We can ask it, but isn't that a simulation of qualia? What is the nature of consciousness? Are we just biological computers? What about our inner lives, our souls? How is it that consciousness collapses the wave function but computation does not? What is the nature of reality? Do we live in a simulation ourselves? If any of these questions intrigues you at all, please enjoy my fiction which address all of these issues in differing ways.
When was the last time you actively read a whole book of fiction? It's one of those 'sacred anachronisms' that keep us human, wrestling with the ideas to help you decide what you think about it.
Then and Now
RAM: 5 Orders of Magnitude Increase
Processing: 5 Orders of Magnitude Faster
Storage: 7 Orders of Magnitude Increase
Display: Single 9" Grayscale CRT vs. Triple 4K Wide-Gamut HDR designer monitors
Cloud Compute (Local vs. AI): 6 Orders of Mag (1,000,000x) Further Increase!
Reclaiming the Visceral: Why I Built 'Q'
Master the Essence Before the Execution
I have found that the most effective way to master professional 3D/CAD/BIM is to first understand the "Qualia" of geometry—the inherent logic and feeling of proportion—without the distraction of command lines and complex coordinate systems.
Why Start with Q?
- Transferable Skills: Because Q shares the same DNA as QCAD, every tool you learn and every "muscle memory" action you develop translates directly to the professional version.
- Focus on Logic: By removing the quantitative "noise," you learn the underlying geometric construction methods that make you a faster, more intuitive drafter in any software.
- Professional Output: Q uses the ancient standard .DXF format. You can start a design in the contemplative space of Q and "graduate" that exact file into QCAD or AutoCAD or SketchUp when it’s time to add dimensions, layers, 3D geometry, and written technical specifications for construction.
Your Graduation Path
Master the universal language of geometry in its purest form, and you will find that the transition to high-end quantitative software becomes not just easier, but a natural extension of your creative wit and will.
- Q (The Essence) – No dimensions, no distractions. Just pure geometry and the logic of CAD.
- QCAD or AutoCAD (The Execution) – Add the math, the layers, and the technical specs.
- Building Information Modeling: AutoCAD toolset (such as Architecture, MEP, Mechanical) or Revit, etc.
- Product Design and Manufacturing CAD/CA: Inventor, Fusion, Navisworks, etc.
- AI-Tools - watch this space because it will probably make much of the above 'legacy' or obsolete.
Q - Sacred Geometry Drawing App & Course
- Concentrate: On the precision of the line.
- Contemplate: The meaning of the proportion.
- Meditate: On the feeling (Qualia) of the finished form.
Q is built on open-source foundations, ensuring it remains a free and accessible tool for the geometry community. I believe the "universal language" should be available to everyone; therefore, the Q software is free and available for download on the course page below.
While the tool is free, the Foundation Q Pathway below is a paid experience designed to save you many hours of trial and error. By enrolling, you gain access to:
- 5+ Hours of my Video Instruction: A step-by-step masterclass where I show you how to move from basic shapes to complex geometric analysis.
- The Sacred Geometry Library: A curated collection of royalty-free DXF files I’ve built over years, allowing you to hit the ground running with classic patterns and my own personal explorations.
Epistemological Navigation
Truth / Sat
TOP VERTEX:
Mathematical Geometry
Euclid's Elements | KhanAcademy.org

Illuminated Epistemology
Goodness / Chit
LEFT VERTEX:
Quantitative Geometry
Houses | Cars | Airplanes | Electronics | Rockets
Beauty / Ananda
RIGHT VERTEX:
Qualitative Geometry
Everything here on SacredGeometryAcademy.com





















