Years ago I was impressed by the power of Law to transform me. I was impressed because I was sincerely changing my nature and behaviors due to the way I had encountered Law and Order (the justice side of it), and wanted to ensure that I did not encounter Law in that way before. I began a long series […]
Mathy Stuff and Ternary Logic
This "Mathy Stuff and Ternary Logic" category covers mostly mathematical essays, with occasional forays right into ternary logic, which underpins my inquiry into mathematics.
Upon glimpsing the unicorn of Riemann's missing one half while awakening
I just now, minutes ago, was drifting between awake and asleep. slowly becoming aware of the lightly falling rain outside, while also in a half-dream state, contemplating random mathematical ideas, when I caught a glimpse of the 1/2 which completes the sphere of infinity. I have glimpsed it […]
In which I realize my life now is a fractal of a beautiful idea from 24 years ago
The following quote brings a compelling moment of perception into clear view. Dinah is keen that I not misquote her by writing something as sentimental and clichéd as "being at one with the universe." So she describes a process in which there was a "dissolution of the self" and a […]
How many fragments of infinity does it take to make one complete infinity?
A fragment of infinity happens when we count "one, two, three, four," or any sequential series of numbers, and conclude it by saying "and so forth, unto infinity." Note, this not infinity, it is only a fragment of it, which represents it. We symbolize this repeated iteration with […]
Insight into Time and its relationship to Good and Evil
In a series of meditations on the nature of infinity while in the process of developing a larger concept of a new kind of mathematical infinity -- a super-infinity which contains all possible infinities in an intuitively-coherent way -- I have been bumping into the relationship between time and […]
In the "Sense of an Ending" is a sense of equilibrium
Reading D.G. Leahy's writing is to me an experience that feels like reading Isaiah. It is obviously densely packed with meaning, but so inscrutable, it's like reading hieroglyphs must have been before the Rosetta Stone was found -- glimpses of meaning percolate up through the text in iridiscent […]
The origin of synarché and why it is an infinity greater than all infinities
The word infinity is from the Latin roots for "un-limited" or "without-end." Structurally, this word is similar to Greek aperion, Hebrew ein sof, Chinese tai-ji, and many others, all referring to the same underlying concept: that which is so great it is beyond ability to measure, […]
The Point of Grace
I subscribe to a number of techy innovation-rich groups via social media, and every now and then a real gem of the genre comes scrolling past on my newsfeed. A few days ago, social media linked me to a curious article recently posted on Vice Motherboard. I have no interest in astral travel, but the […]
Mathematical infinity at the beginning instead of at the ends
The following is a "thinking-out-loud" kind of thought experiment which sort of went off the rails... and then got righted again. The simplicity of emptiness We accept the simplicity of emptiness as a reliable foundation upon which to establish all of mathematics without question. The […]
Imagining the Riemann Sphere rotated for new insights
This article is related, and a little similar, to another recent article. While researching, I was simultaneously reading through both a Wikipedia entry and a Better Explained discussion on a subject I know fairly well (Imaginary Numbers). The articles were saying the same things from different […]
If i² = -1, what's happening inside i² to get it to -1?
A confusing thing about imaginary numbers happens when they are accidentally conflated with reals as if they are somehow on the same line. As we know, if we imagine imaginary numbers the same way we imagine reals, there is only a single point where the imaginary line and the real line coincide -- […]
Yes, hyperbolic geometry does describe the inside of a sphere
I tried for years to get a clear intuitive image for the inside of a sphere, as clear as I already have for the outside of a sphere. It's really hard! I've even been inside a large spherical room (there's a church in Boston with one), and of course, as we all do, I can easily imagine being inside of […]
Local sovereignty ontologically precedes infinities of counting
Before you can understand the physics of mathematical infinity properly you will need to understand the role of local sovereignty in the act of counting. The fundamental structure of infinity is not defined by layers and layers of division-of-divisions which grow larger in quantity but smaller in […]
An "infinite number of infinitely transparent absolute actualities"
I was going to call this "Monotonic monads of infinitely superimposed zeros: Inquiries into categorical atomism at the foundation of mathematics" but I think I'll wait a moment before giving this a public title, and go with this working draft, which auto-save calls it "draft […]
Initial Meditation on the Point of Humility Required to Envision D. G. Leahy's Cube Like No Other
At the time this is written, the mathematics and logic of D. G. Leahy are less well known than his philosophical and theological work. Yet it may be the mathematics for which he is remembered longest. For Leahy has discovered a mathematical structure of primordial dimension, a layer of math beneath […]
On learning the quasicrystalline nature of prime numbers
It is wholly hilarious that I got to this point in studying prime numbers before I learned of the quasicrystalline nature of prime numbers, which was discovered by Freeman Dyson while in idle conversation with Hugh Montgomery over lunch one day in the early 1970s. I knew of the legendary […]
The Greek subject lives in the excluded middle of binary logic
Well, well, well. I am delighted to find yet another piece of private intuition has a respectable home already existing in the public domain. I've been working on this insight for years, but not able to put it into words well enough to relay it to others coherently. Much to my delight, I find that […]
Ternary logic and a coin toss
Discovered a quick way to illustrate the value of ternary over binary logic. Think of a coin toss. Although it might take millions of times, there is a tiny possibility that the coin could land on its edge. What do you call this result, in the binary world of heads or tails? This is a crude example […]
Unitarity and locality are linked to time and space
Just figured out that unitarity and locality are linked to time and space, respectively. I've known for a while now that time is a purely mental thing which has no physical existence outside of the present moment. (This is empirically proven, for those new to the idea). As a consequence, I've been […]
Binary logic is actually ternary in structure
This is one of those things which thoroughly surprises me, because it seems so obvious, yet it has taken me more than a couple decades to learn how to see. I've written about the idea being revealed here from a number of directions, but never before have I seen it with the clarity that I now see. […]