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The 32 Dimensions to the Shortest Distance Between Two Points
Last edited Mon Mar 3, 2025, 02:42 PM - Edit history (1)
I posted information on the Pythagorean Curvature Correction Theorem previously but I'm now attempting to expand the solutions from 4 to 32. By doing so, I can echo certain quantum effects. I wrote an entirely new blog post to support my new position.
What if the shortest distance between two points isn’t just a straight line? What if that concept collapses when you step beyond three dimensions, revealing hidden pathways that warp, fold, and bypass conventional space? In The 32 Dimensions to the Shortest Distance Between Two Points, I explore how dimensionality itself dictates the nature of movement, connection, and efficiency—whether in geometry, physics, or computation.
This isn’t just an abstract mathematical journey. We’ll break apart rigid definitions of space and time, uncovering how curvature, entanglement, and hidden structures create shortcuts nature itself exploits. From quantum mechanics to topological spaces, from energy flow to information compression, we’ll redefine what it means to "connect" two points—not just physically, but conceptually.
By the end, you'll see why a straight line is just one answer among many—and not always the most efficient one. Whether you're a physicist, mathematician, or just someone who enjoys breaking the rules of conventional thinking, this idea will challenge everything you thought you knew about distance.
The 32 Dimensions to the Shortest Distance Between Two Points
Imagine you know the basic rule for right triangles: the square of the longest side (the hypotenuse) equals the sum of the squares of the other two sides. This is one of the most fundamental rules in geometry, something you might remember from school. It works perfectly in a flat world, where space behaves just as you expect. But what if space isn’t perfectly flat?
Now, imagine you’re standing on the surface of the Earth. If you walk in a straight line and then turn at a right angle, then walk again, the distance between your starting point and where you end up isn’t exactly what the simple triangle rule would predict. That’s because the Earth’s surface is curved. And this doesn’t just apply to planets—it applies to space itself. Space can be curved too, affected by things like gravity, and that means our classic triangle rule needs a small tweak.
To adjust for this, I modified the equation to include an extra term that accounts for how much space is curved. This new term contains two parts: one that describes the amount of curvature (think of it as the radius of a giant sphere or saddle-shaped space) and another that determines the direction of the curvature—whether it bends outward, like a saddle, or inward, like a sphere. In traditional geometry, you’d pick one of these options and stick with it. If space is curved one way, the equation follows one rule; if it’s curved the other way, the equation follows a different rule.
But here’s where things get interesting. Instead of picking just one, I allow both possibilities to exist at the same time. I don’t force space to be curved in only one direction—I let it be either, treating it as a set of possibilities rather than a single fixed answer.
Now, here’s the mind-bending part. In math, when you square a number, you lose information about whether it was originally positive or negative. For example, whether you start with +3 or -3, squaring it always gives you 9. That means when we look at squared values—like the sides of the triangle, the curvature term, and even the radius of curvature—we don’t actually know whether each number started as a positive or a negative value. This uncertainty is built into the equation itself.
If we allow every squared value in the equation to have both a positive and a negative possibility, the entire equation starts branching out into different outcomes. Each individual number in the equation can be thought of as a switch that can flip between two states: positive or negative. So, if you count all the places where this happens—each side of the triangle, the curvature term, the radius of curvature, and the handedness of space—you get five switches that can each flip two ways.
When you multiply all these possibilities together, you find that instead of just one outcome, there are actually 32 different possible outcomes hidden inside the equation. In everyday life, we only see one of these outcomes, because we typically assume that lengths are always positive and that curvature follows a single fixed rule. But mathematically, all 32 possibilities exist at once.
This is where the connection to quantum mechanics comes in. In the quantum world, particles don’t just exist in a single, well-defined state. Instead, they exist in a superposition—many states at the same time—until they’re measured. A particle could be spinning in two directions at once, or it could be in multiple places at the same time, and only when we observe it does it settle into a single state.
By allowing all 32 outcomes to coexist in my equation, I’m suggesting that the way space is curved might actually behave in a similar way. Maybe space itself isn’t fixed in just one form but exists in multiple possible configurations at once. Maybe the way particles move through space—the way they behave, the way they interact—depends on this hidden structure that we usually don’t see.
Why should you care? Because this could be a clue to something much bigger. Right now, physics has two great but separate explanations for how the universe works: one that describes big things, like gravity and space-time (Einstein’s theory of relativity), and another that describes tiny things, like particles and quantum uncertainty (quantum mechanics). These two theories work incredibly well in their own domains but don’t fully agree with each other when you try to put them together.
What I’m doing here is uncovering a possible link between the two. If space itself naturally contains multiple possibilities—like quantum systems do—then this could be a key to bridging the gap between geometry and quantum mechanics. It could mean that the structure of the universe isn’t just a passive stage where physics plays out, but an active, dynamic system that influences everything in ways we haven’t yet fully understood.
Understanding this better could lead to breakthroughs in physics—helping us move toward a true theory of everything, a deeper understanding of the universe, and possibly even new kinds of technology based on the hidden nature of space itself.
Disclaimer: Please note that this idea represents a conceptual exploration that combines established theories with speculative and original ideas. Some aspects of the discussion, particularly those linking curvature corrections to quantum phenomena, are creative interpretations and have not been directly sourced from existing literature. This work is intended as a theoretical exploration and should be viewed as a thought-provoking invitation to further inquiry rather than a definitive account.
https://qmichaellewis.blogspot.com/2025/03/32-dimensions-of-shortest-distance.html
My blog post goes into precisely how to use the equation and how to derive the 32 possible answers. The only variable that is not (+) and (-) by its nature is h. 'h' is the Chirality variable and I force a definition of chirality as requiring both a left and a right.
This blog post discusses a new arrangement for a quantum circuit...
https://qmichaellewis.blogspot.com/2025/03/measuring-distance-like-quantum.html
https://qmichaellewis.blogspot.com/
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