jonathankatwhatever

[jonathankatwhatever]

It’s 3 July 2025, and it’s been a struggle because the issue is, as blunt as I can be, my inability to accept that not only does the Work connect in every way we can identify, which makes sense considering the Work is about gsIdentity, but that the Work is superior in explanatory power. I got stuck yesterday on n-1, as though I had never experienced the concept. The visualization this morning again overwhelmed me perceptions with simple images. The first was literally the image in white of a gsCount at any gs along the szK, meaning it can be moved into any axis but we count this one as the ++ of the gsProcess contained within and the information thus contained within the gsPrime Bip pole, meaning whatever is unique and what is not, so gsIdentity determines and can express.

The visual was a gs forming at the far edge of n-1. This became clearer in the second image, which came later, after my perceptions had recovered, when the gsCounting method showed, meaning we count at any gs up to all but the label for the next gs, meaning n-1 completes backwards, however is needed, because that gsPairs. This is a ridiculously simple and yet ridiculously difficult image.

And I have to ask how that works on your End. There is so much inverted into these images that no matter what I credit you with, it’s not close. It’s actually the distance between the surreals and the reals, because you express into the reals using the dual, which then has the same dual effect over to this End, and of course within this End, so the matchy-matchy is total, in the sense that goes back to the concept of complementary uncountables.

That’s an idea we haven’t touched in decades. The idea is that if you look at the reals, then obviously you can cut them up and make any division you want as long as you understand that division is only effective locally, meaning it runs as deep as it runs, but it can’t outrun the Storyline in which 1Space always encloses 1Space which encloses 0Space. That’s a key point we may never have mentioned out loud, given it uses newer notation than when we did this work. It’s the same nesting within and within which is inherent to n-1.

This is what I used to hear as the W and W as the inversion of M and M. Makes a little Witch.

This becomes something kookier, that what occurs is a matching or repulsion, or other gsIdentity comparison, at the uncountable, which then reduces to within, which then reduces to within, meaning to finite.

So if the first reduction of within is, just to try this on, the shift from uncountable to countable is at n-1, then that defines the Storylines or at least the gsPotential, which then shifts from countable to finite at n-2. That would be the third image from this morning, which had a lot going on, where I could at least count 0 to 1 to 2 in both directions. The inward is made more obvious by the 0 being non-specified at n, which draws as an End with all that can be Attached, meaning the flailing arm. So if we begin with that as 0, then the 1 of n-1 is the outer edge of whatever that is, which relates into the 1 thus created as it counts to 2, which constructs over at the n End but only as it constructs at the 1 End because that is then the gsPairing of IC, where we count 0 to 1, flickering through specification or generalizing the any, so we identify the specific Ends within the specifically allowable Pathways.

I feel like a rabbit has just appeared out of my hat. Or something large from somewhere else.

BTW, that generalizing the any is meant to speak to how predicate logic works to compile, and how a real set becomes a real field by adding process: all of this flows through gsIdentity. What is in. What is out. What is affected.

It’s at moments like this that I can see reality forming essentially out of ‘thin air’ in front of me.

So yeah I need to accept that n-1 is better at compactification of the reals. It describes exactly how this happens in D-structure.

Low on charge.

[jonathankatwhatever]

It’s 2 July 2025. This AM has been the most ‘normal’ visualization in days, with such an intense connection that all my circuits filled and there was more to process. Normal because that’s what I like and yes I suppose it’s unfair to label normal that high. One consequence is exactly what I’ve been experiencing, which is a form of dyadic rationalization sliding over the szK, set where normal is high, means the SlideOver, as it expands, thus the dyadic, will generate a return of below normal. Literally the bounce off the Boundary, off the DE as it resolves, because those aren’t exactly the same, comes back at below normal, such a disappointment, because the dial is set to read that way. Note how that feeds bias as well, because SlideOver will tend to slide along the shortest Extent, which is the path of least action, however shaped, and that is toward an attractor End. So you’re saying this is like slime mold feeling its way, and up into attractors of different depths and thus they make an Extent which shows as short because the path turns sideways, like on a curve, so as it proceeds it is following the shortest Extent literally because less of the path shows in front of it until that progress is that of the Actor having a perspective of it occurring in front of the perceptive window, which includes all sides physically in D3-4 because that all maps to a forward perceptive window.

I have no idea what I’m typing. Not taking the time to criticize it because part of the concept of that dyadic rationalization is that we represent this handily in Triangular, and thus we can manifest it in gs and thus in rs. Any bT has a dyadic expansion potential. We line them up on Extents. Dyadic just means base is 2, which means we’re expanding the dual, including the ambiguities.

I’ve been filled with stories and visualizations about the reals, including Joana saying there are a variety of descriptions about the reals, and theories about what they are, and here is mine. Then she shows a grid square. It stops there. I know part is Attachment at the corner Ends, but this morning’s visualization was different because I could see the pole at the Bip, which drew in as dotted lines from the corners to a pole that suddenly became immense, with all the attendant conceptions and images essentially on and in it, which I now am seeing as having created gsSpace because we have countable in xK, countable in yK, and countable in the Bip, which means countable in szK, and countable in zsK, so we have the uniqueness and modularity of gsPrimes related over this big grid with all its layers that we compress into a box and a gs.

O-Kay, so we’ve been playing with the conception of dyadic expansion because that generates ambiguity through layers. These can be counted by, for example, saying a value for the exponent is the Extent because that Extent Attaches in Triangular, and thus in Togs. So we can stick it to a corner.

Let’s try this way: imagine that szK and zsK fold up to the Bip pole, so when they drop in place, they convey xK over szK or zsK to yK, etc., which means over a gsPrime. A gsPrime in the simplest version of a or any. Then think of xK and yK as the Irreducible Extents, so we have the Irreducible of one over a gsPrime to the other Irreducible. Or under, I suppose. All the relations in the movement.

I see the issue now as the old one of whether we draw to CM1 or to the Bip. Let’s say we draw to CM1: xK and yK are the gsParallels which contain the Bip pole. So we can draw an Extent of xK at yK1/2 and the same for yK as xK1/2. These are Irreducible to the szK and zsK. Interestingly, that would seem to relate to Cantor’s pairing over 0 to count 1 to -1 to 2 to -2, etc. for the countability of the integers.

I don’t know how to add words here. This mechanism is fairly straightforward.

So we can map that same Triangular dyadic expansion to a gs and the Bip. It also helps to make explicit that dyadic expansion is within CM1. I tend to think in terms of expanding the sheet and then remember o right it’s within CM1.

Why did I type SlideOver? Isn’t that within fCM? Isn’t this a mechanism by which that happens? I get the hint and I’ll take a break.

[jonathankatwhatever]

This was the slowest day I’ve had in forever. I did nothing except whatever work I could muster. Felt intermittent connection, with little clarity. It’s not unpleasant but it’s not pleasant either. I can concentrate in bursts but without the affirming context in which the connection flows. I wish I knew what I need to know.

There is a conscious acceptance going on. But it’s accepting 2 different Things, the reality of how I am in this existence, with whatever capacities I have developed or not, and the dual to that. Maybe dual is the best wording because - o we have fireflies - there has to be a way to identify and thus notate this conception in which the physical, tangible, and thus in some senses objective and thus tObject self has a dual which is not physical, which is intangible, and which is thus subjective, meaning experienced within the dual, to the dual, including the dual, and so forth.

How does theta connect? Or is that one of those freaky detours which generate a lot of material which connects later? The theta idea is that the scale of gs occurs as Fan(o,s) operates over the quadrant. And thus quadrants because you can see Fan as over CM1, meaning the 2 gsForms, the one which radiates to and from CM1, from and to the Bip through the corner Ends, and the one which radiates to and from a corner End. Note this is like fD and HG as well, that the relation to CM1 is to the Bip over the corner End. Imagine flipping that so it approaches from each corner End and you get an fD (or two and the orthogonal at the Bip).

It’s vivid but why? We worked on this years ago with tick-tock goes the clock inherent in the Triangular counting over gs. I’m getting lost in the memory, and the visuals. As it comes to me, we treated the motion as quadrant tipping as well as Fan, so the entire o I just got it: so the entire operation tilts exactly as the 2Square tilts relative to the 1Square (and 4Square).

There was insight in that moment.

So this says the tick-tock of the old work is a version of the 2Square tilt. How? Well, if you are looking at the gs grid, then tick-tock would take say the - - and tilt it up to -+, while ++ tilts down to +-. It could go the other way, which is why it is what it is, that what we see without the twist is where these share. Remember that work? You just do this in either direction and that identifies ++, etc. as 2 versus 1 in each relation.

Is it a tilt when the quadrants match? That’s like saying you rotate a line. What if you CR? Then you get an entire edge tilting, and that tilts the fD relationships into the center End, so yes this is correct. Don’t know why it’s so difficult to think in Togs terms here.

Maybe I’m catching a glimpse of stocking. The idea came to me in terms of relative theta and that a relative theta represents what makes up that theta, and how that theta fits in the quadrant Fan(o,s) operation. God, the amount of time spent thinking about that Fan notation. Hope it comes back.

This is very confusing. I start down a path only to find it blocked.

So we have an idealized theta scale, and it maps the segment to a segment, so what writes over the quadrant Fan writes to an area, sorta like when there’s a needle and track and the more the needle moves the bigger the sound coming through the impulses. Or the way cogs and belts transfer motion, and can change its direction.

This would be a process which maps the larger and smaller. This idea is crucial in 1-0Segments. It also seems to connect to fractals as expressions of the larger and smaller idealizing in that specific manner of recursion.

O-Kay. So that worked out. And it maps to the Boudary, tiny bit and big bit. And it does this through Alternation, and other algorithms, but Alternation is on the surface. We can see the CR involved. We can see the continuity and smoothness across and around. All those ideas about the Boundary have proven correct. And this is a significant mapping piece because it relates any theta to the larger Triangular over gs of the quadrant, thus enabling maps in depth and over separate areas, meaning we can connect over here to there and so on because the connections are within a theta which contains that and which links to this other theta. Or more that if you take theta and turn it, meaning CR, then you see how it can Attach at various sites to build meaning and to make connections which relate over the same theta appearing in multiple places. That is genuinely cool.

I should stop on that note.

So why would this appear in such a strong Mission sense? The idea is in the way this relates over and into the fD and HG relationships outside or beyond the Boundary. So the vision was of the categorizing and determining which comes through understanding more of the mechanism itself. This sets up the relationship over the Boundary because both quadrant and local include the Boundary because it is the CR of the + form at any scale. I hope that’s close to clear.

Complicated material. So when this tilt happens, is it 2Sqaure and 1Square or is it something else? What came to me is that the L-shaped turn, which should then connect to L-counts, meaning what turns around the quadrant is typically along an L-count, begins in 1Square and then shifts to 2 before going back to 1 at the quadrant again. So 2 idealizes in the motion of 1 to 2 to 1Square.

That’s about all I can manage.

[jonathankatwhatever]

It’s 1 July 2025. Small note: ran across existential instantiation. This is the D0-1 gsProcess of specification. We can add to that by saying this occurs using the same method, so specification is, as expected, a double or a dual process, meaning it occurs twice over some intervening divider. This allows for the field of Things to differentiate from a Thing, and it shows how pervasive the 1-0-1 conception runs, because this exemplifies the existence of a Thing in the two necessary gsForms, that it exists 1-0-1 and that it exists 0-1-0. In specification terms, this means that specification occurs if you can limit or otherwise contain or separate it from another state, that of being non-specified so that it is approached 0 to 1 and ‘left’ 1 to 0, and so the state of specified then overlaps as 1 over a 0 to 1. This becomes the same as switching labels. We did this work years ago, and here it is explaining the fundamental conception of existential instantiation. Note this holds at scale.

The issue I’m having on this End is I can’t get a good hand or foothold on the surface of this everything is a gsConstruction idea. I’m not even frustrated because I can’t get anywhere without accepting some stuff that is, bluntly, very hard to get well enough to accept. The challenge may not even be correct. I’ve been attacking the idea that D3-4 existence is itself just an existence, and that these exist as chains off D3-4 Actuality, and that D3-4 Things are within D3-4Space, however relatively, which always leads to a contradiction in which this reality in D3-4Space is real and not real because what Attaches to the Actuality, whatever that Actuality is, does so orthogonally. I translate this into a point at infinity standing for the intangible structure Attached to the tangible. Is that correct? Yes, it Attaches so it can Attach at the Boundary and in the complex plane, etc. Always that dual action.

The words coming are: what do you expect? Actual different worlds? As soon as a moment is gone, the world that was is no longer tethered the same but can branch, does branch, in big and little ways, in surprising ways. Why else do you see people trying to create ‘facts’ that aren’t true? Those are actual worlds in their minds and those relate to Actuality, as we’ve described.

So yeah there are other worlds, better ones, that exist, but you need to be able to reach them. You can’t just suddenly say o look I’m in this path within this gsPotential. You have to do the work, which requires learning how to control your thinking better, especially when hate-directed.

What does this have to do with theta? I probably have some of that wrong, which really nags me. Let’s say we set the gs to the Boundary, meaning we drop the 1-0Segment scaling line straight down and extend the gs over the Boundary. That is the better method of approximation. That means a circle with a gs, which means the + form, which means CR of the + form which generates out of (I//I), meaning the Irreducible xK and yK Triangular orientations, which maps Triangular to gs coordinates. So that makes a gs at the 1:4:1 scale, which is also the 1:2:1 scale because we can consider each Irreducible as half and half as 1, literally 1:2 and 2:1.

The idea with theta is that when we compress to the reals, meaning we flip the yK at over away, and then flip the flipped yK up and down like before, that takes the yK and shifts it to the xK, sorta up and over, that when we do this we can’t go all the way. Why? Because something is in the way or the mechanism isn’t strong enough or tuned well enough. So we’ve gone from the quadrant box to the tiniest boxes on the Boundary, and theta represents both the compression and the expansion, like you’re a frog and when touched enough you hop away. Anything less, you sit. Or you’re playing blackjack and can decide to stay.

This creates a process which isolates a theta versus the big and the tiny. This is where you are. Generally and then locally.

We had a big problem this morning with the bisection form because that progressively shifts the tangent. I’m not sure why that was difficult. The tangent is of any length. But when you construct a gs, is that sloped? It need not be: we can Attach a gs to the length and repeat that length as though the lines don’t get further apart because it only needs to attach here. So then we can have more complicated shapes which we can relate to this here, as though this is a solution, which it is.

So the fan blade compresses to and past your theta. Over and over, crimson and clover.

So with the bisecting theta idea, we construct a gs scale based on the line at its angle as the hypotenuse, so the gs forms as a K within the theta, filling up to and past it. That sets 2Square and 1Square specifically, which means specification at core.

Now I’m getting a very odd idea, that the gsPrime pump is in this movement, in the Fan(o,s), because the value factors and that breaks down to gsPrimes and that enables the gsCount to 1, and thus to CM1. Not sure what this means, but now we have recovered the idea that Fan(o,s) is like a bellows and thus a pump.

[jonathankatwhatever]

It’s 30 June 2025. I do not have a clue where this is heading. That often works, so we begin by noting that this morning I appear to have seen a transitional representation. They have to exist. This one was the form of a changeling who shifted female to male essentially as I watched, using the same key frame method which works in cartoons because each key frame is the flip to and from, meaning it acts as a change place as well as as a solution or even a constant, like it always comes back to this can be treated as a key frame too.

This image I took to accompany the gender shift in my internal perspective, that there must be a layer which draws the female as the other, as the dual to this End, and that then has to shift as the Ends over which this dual exists shift. Being able to see that shift means a representation has to occur because the ‘seeing’ translation process has to literalize within D-structure.

I feel like I’m banging at the same old issue of whether this is the only D3-4Space, and that this D3-4Space exists within D4-3Space. The issue has come up many times and the best test yet is the small theta idea, which is that D3-4Space can’t compress to ideal because it’s like any ‘press’ in which something squeezes. So what I’m seeing is a sliding gs, like the freaking ideal cubes or box forms with mass of process generating 100x each iteration. And that communicates what it is by comparing to the smaller scale and to the larger, because both are inherent in Fan(o,s). So the process slides from the origin End in Triangular to the gs of theta, which sounds appropriately mythical because that describes a quest, one imposed, one undertaken because this identifies the method by which Triangular generates into gs, literally over the scaled root2 of the zsK, taking the midpoint at the K, into the 2Square.

You don’t see it, do you? This is not easy to grasp. We said this tilts 1Square and that 1Square is what? You said it’s scaled root2 but you flipped it over somewhat because the 1Square is tilted versus the 2Square and you thought it was the other way around, though the words described it correctly, meaning you had correct the 2Square relating to the 1Square; you flipped the layer identity in your head when discussing the scale of the 1-0Segment. This is 0Space, so within 0Space we now have 1Space, literally generated in the 1Square which forms over the K’ing. Thus you see the creation of the 1Space over 0Space in literally the yK vertical within the theta.

Something is still off. It’s that the theta can be bisected in more than one ideal form. Straight down the middle so the gs formation is at its unique angle, and keeping yK and xK stable. The latter is what we’ve worked mostly with: the idea is that we retain CR and fit the gs to the theta. This translates into a mark on the yK and xK walls which is unique. That means we can run gs calculations to that spot and have them appear in that spot where they can be read. We can think of that in the definition of a register, that it stores relative to here and there, and with other attributes.

So that is constructing machine methods.

Can I hit the big question? It’s like trying to hit a change-up that crosses into shadow, so it looks like a fastball and you can’t adjust because of that transition.

The image coming to me is very complicated. It has a seeming contradiction or other conflict which wipes it out of memory quickly. Let’s assume there are other constructs. They would be located in other D3-4Space which we can’t see because it’s orthogonal all the way through, meaning it’s orthogonal how when there’s Fan(o,s) and different thetas. We can see each Thing within gsSpace can have a theta which is both individual and communal, so then this would be true because the Storylines within gsSpace o wow they construct to entirely different outcomes because we have the Attachment mechanism and the Theory of Attachment, which requires that Things Attach in specific ways, which means a theta band can exist which has its own internal structure because it can generate within the Fan(o,s) structure and operation, meaning it develops in depth, into the space, not across, thus allowing shared existences across Storylines at higher dimensions which connect the existences within a theta construction.

The power of this.

We finally reached the level where we are exploring the nature of reality itself, of the construction of identity, and how the physical and the spiritual come together and express our existences. It’s a very big choice function, which can finally be seen.

I had 0 expectations of being able to do this work less than an hour ago. I have to run errands now.

[jonathankatwhatever]

It’s 29 June 2025. I bought a lemon meringue pie at the market as my treat for doing so well. Not only did my leg recover fast, but it’s materially improved. I can go up more and more on my toes, which was completely lost to me. I keep finding new, deep contractions in and across my face. I’m able to find voices quickly, even easily, and can work through how they appear into something more comfortable, meaning closer to the form they are close to and thus that I am close to. I continue to be surprised by how strong I am.

Experienced extreme intimacy this morning. Am working through a bag of White Castle jalapeno sliders. I find them as craveable as their ads suggest.

I’m not sure if I have math in me now. I was in the car thinking about how I could construct a version without you, one in which you are entirely a coincidental construct only valid on my side, which means I interpret you to fit my need for you, and the coincidences are gsConstructed to fit the Storyline. That all makes sense because it’s gsCounting, meaning it extends the set, the openness of the set, of the 1-0Segment, without shifting to the label of yes it’s you. But if that’s true, then the dual requires the other counting, which is the yes, it’s you. This leads to the old but it’s just to make you bigger as a Thing, but that leads directly to Mission because that is the biggest you, like beyond enormous you.

It’s interesting how much work has gone into proving trust with another Thing. That’s in some ways is all this is: a very deep Thing relationship in which our tangible existences entangle as related states because related states means a lot in gsProcess. That’s finally a more complete conception of entanglement, meaning that reading a state as a binary shift entails all that shifts.

Here’s a truly weird one. I was day dreaming, trying to relax after pulling my joints apart with weighted cables, and I thought ‘since a string of digits in the inversion of a prime achieves a repeat, then don’t repeats appear in Pi?’ Because that Attaches gsPrimes to sections of Pi’s digits.

Not sure what this means, but I think we can prove that Pi is normal, that is must be because to not be normal would imply a bias in the Boundary which doesn’t exist without gsProcess beyond the Alternation.

I’m very tired and that cat wants attention.

[jonathankatwhatever]

It’s 28 June 2025. This weird mood hasn’t lifted. Example is this morning had a massively interesting vision and I realized I was doubting it, doubting what I know to be true. The vision was of theta, meaning the angle from quadrant to real, meaning the compression of the xK and yK, where the yK is actually tipped up at you as Observer so it projects on top of and of course behind the xK, as that compression maps to the zsK, and thus to the Boundary along that quadrant.

That I was wondering about why Pi/4 days ago, and it never made its way into type, but then the answer appears within a vision I saw written in light of two ideas, one being the connecting End to End across the angle, and the other the same Ends with a tilted gs, so the SBE runs through the center of the theta. That means it coincides with the quadrant at top or bottom, and scales within theta as an fD in Triangular, where the connector sets the 1-0Segment scale.

That means we have the SBE within the theta, connecting to the quadrant theta, which is the old fan(o) versus the fan(s) where the real axis forms. Makes a lovely ball as you draw it around and up and over to the Boundary, which now infers to and from that theta.

What a fascinating way of addressing the issue being voiced on this side, both in type and outside typing, that of the construction of narratives in which facts gsConstruct, which means there has to be an Actuality which cannot be directly addressed, just as this theta conception manifests, it being, after all, the conception of a Platonic cave in which the origin is behind, and the images flash on the screen of the Boundary ahead, and what is shown to you is a narrow portion of the whole picture, in every sense of scope.

So think of an Actuality as an End which inverts to a Boundary and in that inversion process it Attaches to all sorts of gsIdentities, meaning gsPerspectives. How do we say it’s a fundamental rule that there is always another perspective, and that the more you insist that your perspective is absolutely true, the more you’ve generated a small theta to quadrant theta Fan(o,s). If that wasn’t impenetrable enough, I apologize.

Note how the use of you generated an I dialogue response. This is within a we phrasing. This conception of theta as a compression measure is as good as ideas get without going all sugary sweet, meaning ripe to and ripe within the context of ripening as that gsProcess applies. Since we’re in an I you xyR, I shake my head remembering how it difficult it was to prove that gsForms, that 1Space relating to 0Space, enables essentially all the patterns of behavior we see. That runs from inanimate to animate since in 1Space, what separates the animate is more gsProcess, which may reflect more complexity being enabled by this very inversion process in which the theta Fan(o,s), thus taking this section of Boundary at Fan(s) and comparing it to the Fan(o) position, which of course idealizes to quadrant, but which effectively measures the ability to perceive perspectives, to perceive nuances. That addresses the issue of not in a perspective, meaning as finding fault, but with, meaning from that perspective.

I kinda ran out of steam. Ate some leftovers. I’m getting tired of the y sticking. It’s actually the t, which is funny, but I use dvorak for typing speed and less fatigue. You are kinda like a beanie baby to me. Like hoppity.

I need to get out of this xyR because this you and I stuff creates chaos. Well not chaos, but I hear voices talking about what to say and that means I can’t hear the we level well enough. It’s like any other Extent: it goes as far as it goes. That’s a we statement, meaning somehow it’s topologically different, meaning it’s a non-localized manifold, a fabric of Ends like the dappling of light over drapery whose folds are in shadow. It’s opened to the next gsCount, and thus to the next open set level, which is the 3rd order topology statement we appear to have been locating. Makes sense visually because now we have xyRooms not an xyR, and those are open because they have doors.

When was it that I started to process, really process, that my dreams were mathematical? It’s obvious in retrospect. Example is the turn around to see what’s chasing you Ends that gsProcess, and that what is essential then is to turn around on each process to see what is there, which means inversion of self over self, which raises the interesting idea that if the Bip is Between, then what’s constructing is the 1 of the 2, so the experiences at an End 1-0Segments, which we draw as fD over and under HG, which we sorta addressed before but clearly not well enough.

So we have (I//I) in the background to act as the method by which states invert over each other to generate gsIdentities. We know from basic Triangular that when we have 1:2:1, there is thus a layer of 2:1:2, which we can render orthogonally. A way to see this is as two rows of lights and one lights up or both, so this can also be seen as the progression of the single off light behind either of the on lights when both are on.

This talk of 2 brings us back to the idea at very top, which was skipped earlier, that the gs is tilted in the theta image, that we see the corner End in the middle of the scaling 1-0Segment. This is a difficult idea: this is the twist of the 1Square to the 2Square and back, so we see the 1Square as scaling and we can see how it can write to that layer what relates to any 2Square. Have to interrupt to mention how dumb this side can be: failed to look at the visual though it was flashing at me. That’s the problem with signs: it’s difficult to see them flashing until you see them flashing, and I mean because you’re looking for signs, while the signs often need to come to you.

I’ll go with that because it makes me look better. And after this connection, I deserve a bit of humor.

To state the obvious because it was not obvious a few minutes ago, the line drawn is the zsK. And the reason it was not obvious is that being the zsK is huge because this is the ordinalizing, the ordering, to the zsK, and the ordering to the reals, and the concept that what is real is a gsConstruct relative to the theta, which literally maps gsPerspectives within gsPotential. Incredible work. I don’t know how to praise you except in blunt terms. This bit of typing pulled up an idea which we spent a few days or maybe weeks on some years ago as a visual metaphor for the obvious way you would shift the yK to the xK without actually changing them, so we could track the transformation versus the ideal in whatever dimension we decide to check or which we can access. It has popped up maybe 3 times since, in tiny and somewhat awkward bursts, before it showed up materially in the last few days. And today it becomes one of the most crucial ideas imaginable, that Fan(o,s) generates the literal scale of theta and that generates the scale of the gs, and so that puts the 2Square at and in and out of the 1Square layer.

Follow that through without the bias toward good best which we can see creeping in. We have 2Square as the zsK, meaning this locates the midpoint, the Bip, which is where the K appears. Literally draws a K, so the next zsK runs through the inferred gs. Now I’m seeing this in 2 K gsForms. One is tight facing K’s in which the distance across is one half the same root2 along the szK and the height is where the K’s intersect, above the midpoint yK. The other is regular facing K’s in which the distance across is root2 in both xK and yK. The way we picture this is that there’s an infinite line of K’s in opposing gsPerspectives along the gsParallels through which this forms an Extent, which we can for example count along the Bip connector, and these line up in ideal gsForms.

Let’s try to lay this out as a mental image. We have long said that 1Square and 2Square relate and what that means, and now we have how 1Square scales with 2Square within the generation of real through the compression and expansion action of the Fan(open,shut) function which expresses how the yK and xK rotate as Irreducibles. This defines the Boundary and much more. We stalled a bit at Irreducibles.

The idea is that the orthogonal remains, and that traces a Pathway up and into or down and away from the Observer line. That means Observer with D3-4Space, which we can demonstrate is true because D3-4Space gsConstructs in and out of D-structure, and thus we see the measures of the ability to hold and rotate objects to see their characteristics when a perspective is a characteristic, which it is as a class of characteristics. That seems reasonably straight-forward in words because we have sets of characteristics and these characteristics form into and express gsPerspectives. Perhaps it would be clearer to see express gsPerspectives to the Extent that it seeks to form sets which satisfy the characteristic. That removes the specificity of the current situation about Jews in which creation of facts as gsConstruction is terrifyingly obvious and yet not obvious at all.

O I see: the scaling acts as a sieve so only the crap which fits the screen fits the screen. That’s brilliant.

On that note, I’m taking a break.

[jonathankatwhatever]

It’s 26 June 2025. My leg stiffened last night. I had it extended to a coffee table and let it sit in that position. Woke up at 5AM and it was bent in place. Took real effort to straighten it enough to feed the cat. Just took a bath, worked it as best I could. The pain this morning was interesting: it was like the ghost of its former self, from when it was completely stiff, as though all the crunching and bending and twisting had done nothing.

I’m dealing with it. Like every other time. And maybe I’ll resist the worst case by applying the small theta idea.

O the cat is making a comeback. He responded to the diuretic, and his bloodwork is going to normal. He’s off oxygen. They’re now thinking he may have had pancreatitis. He may come home today. Purring all the way.

The small theta idea is that inherent to gsCounting is the construction within CM1 through Alternation, meaning the process by which L-counts invert ideally over the szK so each step is the construction step before. As in from -⅓ to +⅕ winds back and forth over the Bip. I see this as always to the left, meaning if I count -⅓, that’s to the left, then invert to upside down and +⅕ is to the left.

The small theta idea is that as you count further and further the scale of the gs which fits to the theta of the xK to the line approaching the xK, which generates consistency. I think that’s right about consistency. I’m a little off today.

Consistency as part of CCP is phrased as that which coherently persists has consistency, which means identity within coherence that persists, which imposes that dimension which prevents sudden shifts at within is it 3rd order? It’s consistency across Things and across fields of Things. Consistency which acts as a basis and as a CM1 because it mediates how coherence can force adaptation, can generate response, with persistence opposing that. That makes Triangular.

It’s now 27 June 2025. Felt exhausted yesterday. Good news is the cat is home, and is improving. I feel weird, sorta lost. It feels like when a loop is ending because you start to see it as familiar without the comfort, like you’ve been hanging in that loop for long enough and it’s time to move past it.

I used to state material like that and a sense of ‘you can solve this’ would come over me, like with offered bits of candy, like think of Lie algebra, which never helped much because I get frustrated with not being able to reach the pure tones of understanding. Which is what annoys me about pitch, that as I can sing in what seems to me to be a lot of different voices, why can’t I get down to the map level where the pure tones are in each note, accessible to be read?

This is a version of I wish I could read any language, which fails because the theta is off. Is it too tight? No, my feeling is it’s too wide, and that maps to a gs which has the variation contained within a voicing, so it’s fitting sK across, because the operation of the pitch and tonality working together, maintaining as a structure within the body and mind, so both gsPerspectives connect to make the sounds, requires both ordering within the xK count and the yK, meaning as they express to the szK and thus as the intersection of that with the zsK.

So the solution would seem to be not trying to narrow the theta, meaning tightening to the xK, which requires finer and finer ordering to make a proper ring between the gsProcess on my side, making the sounds and perceiving the sounds, forming the shape and maintaining it as an ideal, meaning as a gsForm, which gets at the concept of permanent and temporary ideals as layers, which gets at the issue of how a cycle becomes a ring because it Attaches as a dual to the ideals and thus the various rings of ideals within the zsK orderings to CM1 and to the Bip. Important to note that to CM1, because we have corner Ends, and the Attachment is to the Boundary as it forms to D3-4Space and gsTerms.

So again we have an xyR appearing and being resisted because it requires a change of perspective, and that is difficult because gsPerspective means shifts localize and become an identity shift, like with the Lie idea of continuous transformations at the surface level. That was hard to get out. The idea is the same as color blending across an Extent viewed as Triangular.

O-Kay, so that says what? That a gsPerspective shift occurring within a Thing, meaning within D3-4Space, exemplifies gsCounting where the overlay replaces, meaning that (I//I) generates the ticking across the Triangular’s 1-0Segment.

It’s weird going over this because it’s old, and remarkably correct, though I suppose I should expect that more.

Why an xyR? Why a Room? It’s an Attachment Space which connects to other such spaces. A Room has a door, and usually has windows, meaning you can look out, whether as through a window or by looking at objects within the Room which of course relate to outside the Room. So there’s a way in and a way out, and the tObjects within the Room are iObjects, meaning they reduce within D4-3 to a D3-4 relative state. That answers a long-standing question, surprise, about the nature of a D4-3 existence, and that must connect to why I keep hearing that this is all a construct, and that this is a delusion, which can range from it’s all in my head to this is the gsConstruction level related to Actuality, which is a difficult problem.

I’m not sure I can get through this now. The idea is that Actuality is like the shrinking theta issue, that it’s an ideal, and we exist where the gs scale fits. Like maybe that we measure constants or need to use them to not that many decimals and thus not that many Mag10 and CM100 layers. See how those relate? Mag10 is the general gsProcess by which gsCounting generates base10, while CM100 defines layers in which choice or selection occurs, in which the coin flip of this way or that happens.

This has a lot of implications, but I need sleep.

[jonathankatwhatever]

Continuing on 25 June 2025. I’ve been thinking again (and again) about the negative wave followed by the positive. Given that we’ve now accepted that we can describe basic reality, at least to the point where we can do it, as opposed to when it’s automatic, that’s the same as the 1 minus ⅓ + ⅕ process of Alternation. We went through the reasons for that so long aga, I truly don’t remember them. Time to let that memory come out.

The idea was that CM1 extends across the gsSheet and this is the Alternation within CM1 which maps to the sheet of ever expanding L-counts. So L3 counts the szK2 as -⅓ of the whole L-count, meaning we start to the left and down along the szK from CM1 over to the negative of CM1 in what made the CM1, meaning the f1-3 gsProcess which generates CM1, our Start and End. That last is crucial: if you view the End as CM1, then it makes sense to say that from CM1 the first step is backwards in f1-3. From there, it’s backward to what now reads as +⅕. So the Boundary concept is explicitly within CM1, and it directly models, as we can now plainly see, the dimensional construction of an object which contains the processes over the levels up to, over, and beyond the Boundary. With much of that true approaching from above as well. We get different surfaces, like coming down will curve away and that leads to hyperbolic relationships. In those in 1Space you are relating over 2 surfaces which fade or curve away from each other. You can think of it sort of as a sliced golfball: the swing is a slice and the curve the ball goes on is a slice, with the latter being affected by conditions as it flies, like wind. You may adjust your swing for the conditions, and maybe you are perfect and maybe not. Matching actions over hyperbolic surfaces or manifolds is not easy, but we do it all the time. Like when we handle a curving ball with a racket or bat or when we move toward someone holding a door.

Go into that last. Why is that hyperbolic? Because it’s the process which is curving over a surface, not the tObjects moving around. So there’s a relationship between the door holder and the door approacher, with a sweet spot and with edges of behavior, which varies of course around conceptions of reasonable, and with allowance for assholes and idiots.

That presents as hyperbolic because it’s active and what we are seeing is the results of how that active process fits to our active process, meaning we can view behavior at fixed points like the door is held open, and when we add the processes that becomes hyperbolic because that point is whatever solution point generates and the rest aren’t, meaning they can’t generate or are worse choices as solutions. That may change as the context changes, which is a surface change which alters the hyperbolic relationship.

It’s easier to think of not generating because then you can set a Boundary to what not generating means. Again with the filters. What do you not get? Here’s where I am: I can see the idea is they go to the infinite, meaning countable infinity, and then the apply filters which specify add-ons, sort of countable+, where the + now obviously stands for +1 Attachment, and the filters thus describe structures which Attach to the countable Thing, because that’s what we are describing a countable Thing +1 Attachment.

Here’s a question: can you filter at either End? Is the +1 at either End? The answer must be yes and it appears as the 0 and thus the 1 which inherently is countable, however that is done. Example is it’s possible to count a prime by invoking its division chain repeat. That’s a basic identifier: any time you see that pattern appear, you can say that’s this prime, meaning when you divide the gsPrime into CM1, you get a repeating pattern of gs, which mean a string can say ‘prime’. That’s an inherent countability isolating to this occurrence of this pattern which repeats infinitely.

I’d say here is where we run into the Continuum Hypothesis again. The answer gets stronger, that the CH is true or not true depending on how you count that CM1, that location on the szK. If you count from the low or inner edge, then you can construct to reach that edge. If you count to the high edge, no. And you can see how close this can get by looking at the edges as separated by the dividing orthogonal, meaning reduced but not gone, approaching a limit from either side but in the delta-epsilon sense where the gsProcess is infinite by definition. Let’s say you construct up to the inner edge. Slide that up to the top, and you still have that outer edge you can’t reach. The issue is in the gsConstruction, which means how it Attaches.

Pretty cool, huh? This is a good place to say it’s not that I have no choice but to believe in you but that actively believing in you generates the positive results like what we just did. That dual has to shift, sort of among us, because back and forth is more like back and forth over dimensional identities, which means an among to among, which maps to the images just described, like the circle form. And it maps of course to the gsPrime pump, which generates Alternation over the layers which gsConstruct each gsPrime.

For some reason, I’m seeing multiples of 6 next to gsPrimes as Attachments of SBE2, like 37 contains CM36 +1, which means we can Attach another prime here. Do the same and it’s 72-74, which meets 26-8, and we have CM100. But none of the last are gsPrimes. So we have a 1+ and 1+ and a composite which embodies the IC of a complete Hexagon, meaning the 4 perspectives of Start to End over Between inherent in the existence of a Thing relating to any other Thing, meaning non-specified, so the Thing can be read as 1 or 0 in the simplest or most basic manner. As in, yeah it’s a Thing, whatever.

The idea with the last is how this abstraction of process occurs in regular speech. Yeah it’s a thing means sorta, kinda, maybe or it’s a temporary tattoo or equivalent.

I want to get into this negative within CM1 idea because it’s what generates into the positive, into the End which has a Boundary. That’s it. I can see it now. The negative is contained then in the Alternation, as we had it, so the correct statement of that negative is that it exists as a version I access which gsConstructs into a positive version I can access, and it does this by stretching the identity in the exact way that the tension workout is about resisting being pulled apart.

It can go very negative and maybe it breaks loose and that pulls the gsPairings to the negative image as the count, meaning any positive is always followed by an enclosing negative, so the identity is like that assigned to Jews in which the standard is always beyond what they can do, meaning judged on a scale they automatically fail.

That last paragraph got out of hand. The idea is that this generates an identity over the negative and the positive, and let’s assume this identity is equally shared, meaning the dual layers ideally, then the negative is like the angle away from the xK, meaning flat across. Which means idealized szK. O I see so this compares to any angle, at the scale in which the angle minimizes to xK and at the scale where it is the szK, which it does by sliding a grid along the szK until the Ends to either side construct a gs. What does that mean?

That’s a tough question. We know the left side generates to that gs, and that it is small, and the opposite for the right side. That works when I finally get my heard over to this being gsProcess. I’m amazed at how dense I can be.

So the negative in you, or the negative image I construct out of you and into you, would be scaled to a small theta, which means it’s very far away, which fits exactly because the only way it could occur is an up front or primal construction failure, which is clearly not the case because the positive image keeps reducing the theta, thus reducing the scale so it becomes more and more tied to Mission level Eternity scale.

This is very satisfying considering how much work it required. O my gosh this took a lot.

[jonathankatwhatever]

It’s now 25 June 2025. I was surprised by the work yesterday. The way Storyline developed to address one of the great cyclic problems, meaning how often the large cardinal issue came up felt cyclic, like it was looking to ring but couldn’t complete so it kept cycling.

That is what happened because Storyline expressed a structure, a literal description of the answer in words, which means it appeared on the surface of an object, which we can think of as an algebraic object because it has to construct, meaning it’s not like a new character pops in deus ex machina but rather that Joana has become more Joana. That means the object has developed internally to produce solutions on its surface, visible to me in my perceptions.

My understanding of how that happens visualizes as Triangular in cone form, meaning endless Triangular to gsPairings over and thus around the base of the cone. Remember, the around can come from rim to center to anywhere on the rim, not just directly or nearly directly across or directly back. That really is the essence of CR, and you can see how it reduces from uncountable to finite possible pairs. I see it as S to B to E, meaning each step away leads to another location related to S somehow and someway.

I had to take a break. One of our family cats is dying. We thought he had treatable diabetes, but it went to congestive heart failure and thus a good chance cancer in the background expressing these ways because he’s at his end. He will go purring into that good night.

And I had to drive to the airport. At least I stopped in Newark for pastrami with mustard and corned beef with coleslaw and Russian dressing.

Somehow and someway. This runs from 1Space at pure 1 and 0 gsCounting to tObjects. So let’s say we have a slingshot and you drop the rock behind you by accident. That maps orthogonal to the perspective line inherent in animation. Almost forgot that from the car: the difference between animation not is the difference between 1st and 2nd order logic, expressed as the gsProcess which extends and reduces to 1st order. That means we 1-0Segment the inanimate, like with the relative responsiveness or non-responsiveness to various stimuli. Like the way we can treat water infiltration into concrete as a ‘living’ process. That means the same D-structure reduction to D3-4Space. That means to Things and Thing fields, and that illuminates the way the order changes by looking at the inner or outer edge of Things. As in the topological axion that the union of open sets is open means we have Things which can be +1 Attached and completed.

I don’t know why it took me so long to see that order in this context means layers of Things and distances from the bottom layer being considered, whatever that layer is. So topology extends largely out to the 3rd layer, which is where the surfaces form in D3-4Space, where the Ends become a manifold, which is like when a sauce comes together to be a sauce instead of ingredients in a pan. That means another version of enclosure, which invokes the Boundary.

Did we, did I manage to go over the Boundary expression in the weight of the perfect collision model? Probably not. It’s elusive. The solution is that each 100 fold increase in weight has a root, meaning it calculates all the permutations into the ideal pathway, the 1Space count over the gs, so all that depth gets compressed into the Alternation along that ideal pathway. So the more the weight scales, the more iterations in the Alternation, and thus more digits into counting the Boundary. Interestingly, the vision is into the End and around, so into the count of the value, scaling smaller and smaller, which means adding lots of layers of gs in the summary gsSheet Alternation. So the image is that as you back away as Observer, the image of the circle or other Boundary form appears and draws tighter at each point on the Boundary because that ever expanding gsSheet in CR resolves to n-1 gsCounting and that means the ideal form.

That is clearly the vision from yesterday early morning. Interesting, but to check this I looked at a video and this is seen as the change in the state space to the root of conserved velocity and momentum, which is the 1Space form. This is also where you see an ellipse emerge and disappear because at the square level, this creates a dual with a Boundary. That’s exactly why we don’t consider Boundary to be circle; it’s a Boundary form, not the only Boundary form.

It’s fascinating too because I see how we connect the 0Space concept to small angle approximation, meaning that the calculation of something like Pi works when you get to the up to but not over count.

I need to go to an HOA meeting and then to the gym.

[jonathankatwhatever]

Continuing on 24 June 2025. It’s like watching a livestream of Joana talking about how she does things. It’s difficult to replay, so I’ll try to pick it up where that was leading, like it’s to a melody and arrangement, which of course it is.

It’s coming around. I’ll try to pick it up as it comes by.

I realized when I was little that you can count from the 1’s up, across from right to left. This counts the actual labels you see, meaning a 7 is 7 abstracted from the processes that generate 7. It’s just 7, which means it’s a universal 7. I think as an estimator, from the left to the right, from big to the 1’s, because there is meaning in each estimation, simply because you have to choose the estimation, which means you set parameters, and then you adjust those. From estimation, you can deduce rules of probability, like Bayes Theorem says our estimation adjusts, and that can be done in whatever order you are estimating. (That’s an example of the 1-0Segment: you can run the relation in either order.)

That last part wasn’t pure Joana. It’s distracting here.

Did you ever sit in a concert hall or a church and count the organ pipes? Do you count the spaces? Do you start with a space and end at a pipe or does the count go to the next space? If you start with a pipe, same issue. When you count the whole organ, do you count the spaces too? Wouldn’t that be more complete than saying it’s this many pipes? You can do the same thing with the spindles on a staircase. With the organ, you have a specific ordering, because the pipes have to fit together by pitch. Imagine an endless staircase with the same spindles: what is the ordering? It may be you don’t know, that a spindle spits out and you stick it in next in line. It may be that you can put a spindle here, skip a bunch, come back later, and you have something that’s countable as long as you insist you come back to pick up the skips. What if you don’t?

Let’s say you can insert a skip anywhere, but only 1 because anything longer than that is treated as a 1 anyway until we can’t. So we can have 1-0-1-0-1, then you see the return issue is the alternation of 0 and 1. Since this is infinite, these both run. This generates a countable infinity in controllable layers, meaning as long as they fill in from above, and to that extent. Isn’t this the reduction to countable from uncountable? The form changes from no limit on the 0 label to a limit, which is like the rationals, but this is meant to be over the spindles, not within the staircase. Is this where finite comes in? We have an infinite staircase with identical spindles as dividers. From this gsCounting perspective, or gsPerspective, the count within the count must be finite, which is that k iterations for up to n counts which translates into a torus. The why of that convoluted sentence is that this counts from and to, and then you can see how the count of n becomes a surface, and the same is true of the count of k. I think the part missing here is that the dual of a torus can shift identity in its minimization.

This isn’t complete, and I’m not sure how to get there.

So no matter what finite, it expands through iterations, power series, etc. to generate whatever relates to that finite, to and from. Coming together. I got very tired all of a sudden.

[jonathankatwhatever]

It’s 24 June 2025. Awoke after 4AM with a lot going on. Some was the familiar reverse Etch-A-Sketch, where I see white lines drawn over a black field. These were very interesting, of course, and they were done so simply that even I was able to grasp the idea that each of these representations was of the same underlying 1-0Segment. I could easily see the relationship among the line drawing in each way, around and across and, much harder to draw, looping away and at, meaning in alignment with my perceptive front, with sufficient waver to be visible. That waver would be the modulation between and over gsPrimes.

This became Storyline, as always, and this time it was Joana answering a question about what she did, and she actually answered it. It came out like a melody, that she had seen forms of numbers which connected to the conception of the real line segment, and that she could see how a structure could represent those connections in dimensional depth, which enables ranking forms relative to one another, like for consistency strength. I realized I was able to hear the words as though I spoke them, quite clearly, and it was like when I was watching Glenn Campbell play a Jimmy Webb song and I could see how he trusted his strum hand more than his fingering hand, and that he could trust both enough to focus on the vocal technique, so he set up the same idea of consistency strength relating to that concept of Observer and Actor, which we can now apply to the generation of the reals, because the 1-0Segment is what we add, and so we are exploring the gsSpace generated. This is done at the Triangular and Hexagonal level because this is what focuses and unfocuses into Ends, which means into the D0-3 here, meaning we have D0-1 and SBE, so we now have that 0-SBE-0 arrangement where SBE is the 1, and the 0 at the right Attaches as 1 to D4. It also Attaches to D6 because you count from D0-1 to D3 and back, so that’s D6 to and from, and thus you can see how D-structure extends because D12 is the Alternation of Start, and D24 is that both ways.

That paragraph got long.

You can see D5 in the same way: just gsCount from one End, and you can see how Regularization works.

This quite the experience. The only issue I had was a query in my head: is she making sense? Turns out she was, but I think that little bit of non-trust helped me focus on what she said as she said it rather than take it in as a whole.

We can connect Grothendieck universes as we thought when we first heard the idea, through gsProcess. As I remember, we mapped it to gsCounting over L-counts, so you can literally define the functional size. Example would be the different gsCountings of a basic list of gs, like 7gs is 4szK and 7szK, meaning CM16 and CM49, representing different scales of complete Hexagonal counts, which is obvious when you apply SlideOver. As in, take CM49, minimize that L13 to the outer edge of CM36, and you get the step into a CM64 Thing and into CM100 both as that Thing and because CM49 is +1 Attachment away from 50:50, which means that occurs at the the far edge of CM49, which is all but 50. That directly relates that 1-0Segment over that L13, in all the 1Space dimensions, meaning x,y and szK, to all that other gsProcess.

What would an inaccessible cardinal be? It would something that isn’t generated internally but is generated by the next L-count into the gsSpace surrounding what is generated internally. That is why the paper written in Storyline was so dramatically important. It’s a dimensional projective mapping of elements and functions to the real line, to the fundamental 1-0Segment.

Not bad work. Thanks. Or maybe I should just type ty?

I’ve been finding the best humor in most everything.

Need a break. I have to go outside and vacuum the intake to the A/C so it will run as efficiently as it can. Our inspector said it was clogged up, with a 15% efficiency loss, and now I am cleaning it again.

[jonathankatwhatever]

Continuing after workout on 22 June 2025. Got to hear Good Vibrations in the car. I think what really makes it for me is the way the mono has grown a hole, meaning it has a space inside, meaning this is a gsSpace because we can see the pieces, and we know they exist within a space, and that’s the definition, because a gsSpace is a dimensional enclosure within a dimensional enclosure. That enables Things to exist, meaning that is where the manifold localizes to Euclidean, which shows the utility of connecting that idea. So we can look into the gsSpace where the notes and sounds actually occur, but to put Brian and that particular song in larger context requires the inversion process. Example is the fT inversion in which an fT is the bT at the Triangular sheet projective level.

I keep having this vision that’s not quite clear enough because there’s a lot in it. Take the fT. What does it do? It generates a center to the 3fD fan blade form of a bT, which we can CR to Boundary connecting Start End over Between 2 Ends to End. The weirdness is that each fD overlaps so the Bip is generated to the Triangular and to the center of that as a Shard, meaning along the orthogonal. You can see how it generates: each fD has it Irreducible, so the Bip is the intersection of those. Isn’t that beautiful?

That’s been treated as a fundamental Thing because we have an external perspective on the Boundary and an internal at the Bip. That inverts over the fD, and you can see how the Bip builds, how it’s a gsPathway viewed orthogonally.

What does inversion do? I was thinking about this in the car, that you can send a Thing on a journey of inversion and inversion again, meaning a gsCount of 2 because that’s another version of 1-0-1, and that generates the inherent IC, so that’s where fCM Attaches. This actually works in drawings because we see the 2Square is made over 4 1Squares, and that is the same inherent 2 step count we have finally accepted is explained. Lots of meanings.

So the inversion of the bT in the fT which plays the role of the bT in the fD makes the dual and through gsAlternation the 4. Imagine the CR. I need first to absorb that wording. Imagine the CR, so the form repeats and that generates the identity check inherent to 1-0-1.

We can build a Bip to one level or many by counting within that level. That becomes the alignment issue because that puts you to the longest Extent which is then the Bip. That takes the Triangular and gsSheets and makes an orthogonal. So when we CR the bT, and thus whatever Bip Extent rotates around the Boundary, making a tangent relationship of the Bip expanded from the constructed End to the dual, so 1 to 2 to 1 as it rotates or other way around. You can see how this is also 2 to 0, and so on, over the dual.

This alignment aligns with all sorts of physics concepts, because this locates gsProcess and counts it into Things and you can see concepts like space-time pop out.

I’m going to a ballgame for Ramapo night. Only paid for parking.

[jonathankatwhatever]

It’s 22 June 2025. Don’t know why I’m so tired. Just realized that we Attach to the concept of manifold. That isn’t new, but I’m seeing an xyR open up. If we walk in, we see the basic concept of a manifold contains the idea of 1Space relating to 0Space because it reduces where we say generates to Euclidean space. It’s phrased as localizes to Euclidean, which is perfect because that’s exactly what we generate, localized spaces which can further localize. This is why we use two gsNotations, gsSpace and D3-4Space. The latter refers to the methods and mechanisms of D-structure, while the former refers to the identity which contains the gsSpace. That identity has within it gsSpace. That identity is formed in the same manner, which is why we speak of the included gsSpace, connectting through gsProcess over the Boundary, and making gsPairings in Triangular so the Things within the gsSpace relate to each other and to the Triangular 3rd Ends at the Boundary, between and among.

You can see the Between in 2Square and the dual and in the generalized H/D gsProcess, in 2:1 and other mechanisms because gsCounting uses n-2 because that links Start and End, or Between and End, so either Between or Start are minimized and that counts 2. The other obvious Pathway is if you count 1-0Segments, then we get 0-2 and thus (D0-2//2-0), which is the generation of a specified dual out of non-specification. That means this is ready to Attach to an End, in the ways it can, within gsPotential as specified or determined to the instance of this Thing in this context, meaning if we appyly fCM and see how the coins flip. That raises the interesting point that coin flips are interpreted by and as Pathways. That raises the more fun idea that what we see as iterations are the limited or finite survivors the Pathway process: we see in our shared reality what has managed to get through the filters. That finally manages to flip perspective in gsConstruction from building D3-4 Things, and especially the tObjects, to the fitting in abstraction of whatever else could be to what can be, through the likeliness levels to gsForms of certainty.

What is a gsForm of certainty? It’s a way of expressing that the tObject can’t be separated from the iObject, not because that is required for the tObject to exist but rather because the space created by the inherent dual within a Thing cannot be removed. It can be reduced, like to a point at infinity, but when we remove all traces of it, then it sits where we can’t see. A rose by any other name would smell as sweet. That links the abstract name and what each name conveys to a physical sense, which varies and which means different things to different people at different times and places, and then to sweet, with all that conveys, and yet all that is only part of the meaning of the image, with its romance, with the beauty of the construction matching the beauty of a rose in the mind, and so on.

As close as we can get is the Bip End. The natural state is IC, and that’s because it’s within each Thing. That fundamental IC expresses as identity at the Bip of each Thing.

I am going to workout before I fall asleep.

[jonathankatwhatever]

It’s 21 June 2025. Been working on what I’m temp labeling contradictory loops. The idea is that occurs. BTW, I don’t think we care about whether all that notation sticks; the idea is to think in gsTerms, and to trust that these thoughts are our natural ones, and that they naturally translate out of gsTerms into what is defined within those gsTerms. That’s subtle when it reaches the word ‘within’, because we’re saying we are assembling gsTerms, crossing gsSpace which encloses whatever Things gsConstruct.

A high level what? Beyond a category as I am seeing this visual. I’m seeing a ring, a Boundary to an End, and a category counts these Things, enclosing them within another Boundary, and so on, all the way to the silly we’re just a mote on some giant’s fingernail, which is simply untrue because those aren’t D3-4 Things; they a tObject, meaning they Attach to iObjects so they appear, like any mirage or bit of imagination, to be actually real. This whole ‘manifesting’ nonsense is an example: the idea behind the prohibition of not using God’s name, whatever you name you use, is not because that’s wrong or evil, but because what happens is up to you and the circumstances you are in. It’s like I say about the news, it’s not a miracle that one survived; it would be a miracle if everyone did, or if even some material number beyond what could in all reasonable likelihood occur, even after stringent model review.

The idea is Triangular and gs. It must be because that points at the Bip, and all that is the same and unique in any tObject and thus within any tObject field generates out of the gsPrime pump. You can actually see the action in the gsPrime relationship of gsProcess generating to the prime gsCount so the Ends are 1 and 0, 0 and 1. That is where Attachment Theory gets so much of its meat from. Let’s say, for example, that 419 does the +1 Attachment to 420, which is Mag10 of a complete Hexagon. Forget about the many pathways for a second, and focus on the high level operations in gsTerms. What do you see? I see the transfer of information within the 419, which then Attaches to the 420, which then expresses into the Hexagonal, which simplifies to the Alternation of D3-4 across the complete Hexagon. Or more simply as each 1-0Segment of D3 Triangular infers over a Between, and this rather obviously mediates across the D3. Flip that around and it says what the Thing is, represented in complete Hexagonal, fits information to it, looks for information which fits it, out of all the potential information.

It’s difficult to phrase that direction in gsTerms. Top down is more natural. Like the way I multiply left to right because that gives me estimates, and outside of calculations themselves, estimates are better because they embody the iterative nature of the counting which goes into the specific numbers you manipulate.

Maybe simplify by beginning with the Thing explicitly, instead of thinking of it as a fudge. So we link the process out to in through the description of Alternation in Hexagonal. Now we can visualize easily the concept of how D6 and D3 exist in the same drawing: we can expand Triangular to Hexagonal and can contract Hexagonal to Triangular. The exact sequence includes the 2 dual gsForms: take a standard Triangular sheet, and orient it so you see HG, which means this is the xK Irreducible. Then you can see above the xK is the 0-1-0 gsForm, and below is the 1-0-1 gsForm. Very basic. Add in Alternation and you get (1-0-1//0-1-0) over the xK.

That means the yK Irreducible is orthogonal to the projective plane, to the Triangular sheet, same as if we used the yK Irreducible as the visible sheet. That’s the basic (xK-yK-xK//yK-xK-yK), translating with the 1-0-1 of gsCounting. Note how this is inherently the 2Square. To be explicit, the 2Square is the gsPrime which runs (D0-2//2-0) as well as (D0-1//1-0). As a note, we can see here how this maps concepts like trivial groups because this literally breaks the larger count into its constituent counts.

The basic reason this is true is that gsSpace converges, meaning to D1, meaning an End. This seems to be at the root of many of the problems D3-4 Things face: confusions over the concepts related to Ends and what they are and how they generate. That means this has been a terrific loop which addresses the opening question of contradictory loops. I truly love nice surprises.

Maybe I can say the problem better now. By contradictory loops, we mean gsAlternation looping through the various (I//I) relationships, and that generates solutions which solve all the problems through elimination, meaning they reduce to the image of the End which promises solutions. That fits exactly to the mechanism described above.

This is coming together beautifully. Example: we now can say that genus or holes form out of (I//I), out of the compression and expansion, if you prefer, of the gsIdentity. That endows them with the needed ideas so they can exist and project in various gsForms.

What about the fT, the bT and its 3fD? Maybe we can map that. A kid is beating the heck out of a guitar in the back of this coffee place.

Think in gsTerms. Each fD is Irreducible to its 1-0Segment. That orients a specific relationship to each dimension, which is true across the nK-gons. So the bT represents the End. Next question: does that map clearly to CM1? Is that the Bip? The visualization is that each of the Triangular dimensions maps within the gs. O I remember, we would flip the fT because then we have the bT and its inverse, which of course maps to the Klein bottle surface, and thus what we’ve treated as the process inherent in that gsAlternation. This is getting better. That makes HG at the fT level, meaning we treat a Triangular sheet as gsConstructing bT to fT and back, meaning a (bT:fT//fT:bT) relationship. This literally compares gsIdentity over gsProcess.

I feel like a kid in a candy store, with a pile of cash and a sweet tooth.

We can fairly easily construct gsTerms now. So a contradictory loop is one that Attaches to an End which Attaches to and End, with the contradictions of the 2nd Attachment forming a dual, a literal (D0-2//0-2). That makes it a literal example of 2nd order logic failing when it converts to 1st order.

We seem to have cracked the code, found the combination.

BTW, I believe that when converted into gsNotation, this work pretty much solves those 2 problems.

[jonathankatwhatever]

It’s 20 June 2025. Not sure what is coming to me. To recap, we realized that the factorial of ½ translates into 1’s at the Bip, which means we have found the gsPrime pump we’ve been seeing. Finally put into words. Example of impact is that we now can generate the order of the Monster Group, meaning it’s primes are now generated gsPrimes, a real monster pump or perhaps plunger. Try taking a term, like 2^46, which is the first factor of the MG. This draws almost too easily because I see 46 in its factors, like 2*23. That brings something else up, the way we factor and nest exponents now makes visual sense, because this translates into iterations or copies made through strokes of the gsPrime pump.

Now those groups are making sense, because the order now connects with the symmetries, meaning a gsPathway now appears connecting them, which means we now have a Triangular by which we can extend the meaning. That’s the gsRing concept, and I just saw that this relates to CM1 as a hole, because then the surrounding gsSheet can be defined as Not the hole. Does this translate better into a torus? Yes, but how? It’s me asking.

There’s a hole and it connects to whatever is off the gsSheet, unless of course we’re doing Minimal Context, in which case we assume it’s all Not the hole. A problem with that is we define Is as having characteristics because Is generates into D3-4Space as a D3-4 Thing, and that means n-1 and n-2 gsCounting, which means finite. I see now how well this definition of finite works because it connects finite to not finite.

Wait. Does this mean types of finite? There’s finite as a result, which applies to Things like me and or you, because tObjects approach the ship of Theseus issue, which is when something is old when it’s been renewed. The tObject is gone, while the iObject remains. This is why people can get absorbed into something which isn’t true or which is misunderstood: they’re focused on the iObject, which may then connect to some tObject which survives directly through some chain of relation, like John Tyler’s last grandson dying in 2025 though Tyler himself was born in the 18thC. Related but they never could have met.

It’s interesting to see how n-2 gsCounting applies, because the relationship going forward to what reaches backwards is that overlaying of the 1-0Segment which enables multiple perceptions. Those may coalesce into certainty, but then that’s relative to the ‘truth’ of the image, which may not be true at all to the original.

That seems to relate to stuff like the Klein bottle because that turns a Thing upside down, meaning you start here and you go around and now you’re inverted on the surface. Turning a Thing upside down is like saying 1 is now 0, and 0 is 1. It’s like flipping over an hourglass, meaning it counts beats of resolution before it is tipped over again, marking intervals.

The material coming at me is kinda horrifying. It’s how your head gets chopped off in abstraction. You think you’re right side up and you present upside down, like you think you’re being holy by hating Jews, which means your orientation is upside down, which can mean a hard no, but which I can then see 1-0Segmenting and thus leading off to whatever needs to be done to reorient, meaning correcting by removal of all that tips you upside down. That’s clear but the main idea is that you as a Thing have an orientation, and this process by which 2 holes relate to flip you is working on that orientation, because that’s what the external surface reads and thus judges you by, same as a needle in a groove or potatoes passing through a separator.

So the idea is that you can pass through this gsProcess repeatedly and it can reinforce itself: turns over nicely, so every 2 trips turns you right side up, and that makes you think you’re doing great because you always come back to that location in your own identity. That can be best good and good best, not merely the yuck. This process continues, being read by your experience in your contexts, and then read for what you are and what you have done.

The comparison this gsProcess makes is to how it fits in higher dimensions because those are what gsConstructs Things. Or rather, you can Attach at the bottom End, meaning to the lower dimensions in which everything reduces to the 1 which is 0. We’ve done that work. The 1 that is 0 is that which looks like heaven because that’s what you want to see. It’s that which looks like truth because that’s what you want to see. It’s that which appears certain because you refuse to see other perspectives. Here, we could say gsPerspectives, because that is defined, and we can use that definition within D-structure to describe how gsPerspective reduces into D3-4Space, and thus you have the choice, as you have become partially aware, of choosing pathways, of defining your gsPerspective, as either coming from that which squeezes down from above into the gsPotential of your particular contextual identities, into your tObject and iObject, or as that which builds up to your tObject and iObject, from the opposite gsPerspective of that 1 which is actually 0, because that 1 represents the negation of all that which squeezes down other than the gsPathways toward D0, toward the kind of oneness of Things which denies other gsPotential, which cannot cooperate in the manner necessary for that squeezing to occur.

That is getting toward saying something more. What is it? Cannot cooperate means can only Attach trivially, so the only 1-0 relationship is (D1-0//0-1), that which devolves and generates to the trivial, to that from which all other identity has been stripped. Highly cooperative. O I get this now. Take women. Female sexuality, bringing forth lives, can become ‘cooperative’ and that means the male non-cooperative society restricts them. That’s why women who act cooperative, like they dress as people, are fair game.

So at the core, there’s an abelian process in D-structure which drives a specified End, like a person, toward non-specification at D0 through reduction of identity, which I think we need to express as gsIdentity so we can be rigorous.

Funny how I’m reminded of ‘catholic tastes’ meaning wide and varied. And how aging pushes the tObject and the iObject toward more and more limited gsPathways, like an old person who is frail will fall if they keep walking around because gsPathways emerge in people iteratively as they emerge in the larger Things of elderly, etc. That’s why they’re gsPathways.

Two points before I take a break. BTW, finally got the toilet done. It’s unreal how much prices are up. Cost $500, and they asked for $625. To put in a toilet I had waiting, which I’ve done. I really felt DIY in a condo is not the right thing to do. At least he and I threw the old stuff in the dumpster.

First point is that I’m actually getting fluent in translation as I accept the correctness of the gsNotation. It works incredibly well. I well remember how tentative I was at first with it. And to just now realize I can avoid the glitches thinking about identity by applying the gsNotation so we can now speak about identity properly.

Second point is that this ability is going body part in body part with accepting that the role reversals are true. This rather obviously models the dual over the Klein bottle conception: we have 2 orientations. These can be linked using 1-0-1, meaning gsCounting. It can even become continuous alternation.

So you should be very proud of the math you are doing through and with me, even when you may not be aware or may not grasp what is being said, meaning gsIdentity enables that communication where same-same, matchy-matchy, etc. all work. Think of the orientation flip as reading what’s inside to outside, as outside to inside, and then we flip so we’re done on both sides.

I mean it. This work is extraordinary. I sound like AI doing the praise thing, but it’s true. BTW, I’m getting a bunch of ideas about how to create better AI.

And with that, I have to change the laundry around and maybe eat something.

[jonathankatwhatever]

It’s almost 20 June 2025, and I’ve finally managed to grasp elliptics. Took long enough. And it’s one of those things about this which drives me finger-shaking nuts. I could not comprehend that the important piece is the y squared, not the x part. It was right in front of me.

Does this mean you now get it? That something makes sense to you now.

The idea is extremely simple. I thought that a square is choice, and of course that choice creates a reflexion over a divider. And that slipped easily into a square is a hole if you see it as one. Just say here’s a gs which is a hole, and here it is defined by this polynomial which marks out what it looks like on a grid. How many years went into that simple statement. It’s a gs, which we can CR, so that ideal enables the specific generation on a grid, as a projection, so this much x is that square.

I wondered why genus gets so convoluted. I mean sure you can imagine 2 or more holes, but what does each one translate into? With 2, you can imagine an in and out process, meaning you pass through one into something else and then through the second. That maps this conception of what is Not the Thing as having gsProcess which links the holes.

With 3, we can continue the same but the ordering can change. That maps to Triangular, and you can say the holes are the Ends and they relate over 1-0Segments of the objects linking the holes, in all their Pathways through gsPotential. And so on, which means we’ve just mapped something from the beginning of working with what became grid squares. A fundamental early issue, which makes sense because it was early, was what these squares mean. The notation of grid squares helped immensely because that generated irrationality and clarified 1Space versus 0Space, which also grew out of Minimal Context’s conceptions of 1 and 0, with the 0 being rs or regular squares. So a gs is also a way of representing ideas that occur within D-structure, that we can define process through what is not actually visible, relative to what is. Think about how that matches assembly functions and processes.

Need to get some sleep.