jonathankatwhatever

[jonathankatwhatever]

It’s 9 Aug 2025, and I have been feeling bad but it’s probably my own fault. Like I have been having minor balance issues, so what did I do? I pulled more than my bodyweight back over my head and hung there rotating my vision upside down to the left and to the right, with one eye closed and both open. This isolated the feeling of vertigo pretty well because I could then see that the issue was traversing differences between the eyes, which was controlled by deciding which eye would dominate, because the other fits to the lead. When they are unsure which is the lead is where the interference occurs, where the patterns don’t line up smoothly. This translates into physically seeable frames, which can be upsetting because those moments reveal the actual underlying structure that this is actually what you see.

This is amazing because I knew all that from being stoned in high school, and having my vision distort and my hearing and realizing that I was perceiving differently, that things around me were the same but that what I was seeing was different. That would sound scary, and it was at times, because it was hard to maintain, but the distortions are and were versions of the same distortions of migraines, which turned out to be the consequences of working the brain hard until it started to produce at such high energy that the you as Observer role separated in a different way so you could, for example, see, actually see and feel as they wrote on your consciousness, individual thoughts, and their 2Squaring.

I assume 2Squaring is obvious as a term: it means that each thought contains within it all the related 2Squares formed as each one formed out of a two is then a 2Square. In that context, it’s also pretty easy to see fCM because one need only think of a 1-0Segment and a 2Square to see a 4Square. And that rings a big bell because now I see this can construct any count, and easily construct any integer, because we can now say a count of 3 is that same 2Square but counted at each end as 0, so we can simply shift that count of 2 to a count of 1, which we can think of as stacking Bricks so they overlap at the half, meaning this concentrates the count of the Brick above or below in that span between the halves. The rest is that the scale sets itself to counting Bricks along with counting what’s in the Bricks, etc. This is subtle, at least to me.

The scale sets itself means that form of gsCounting appears because it maps to another gsForm. Right, so that means the scale of 1:2:1, which remember you were being told about yesterday and this morning but you were having trouble focusing on anything non-physical so you could barely see you were working, and hey you try being dizzy and having to act normal when that activates a voice which says go lie down.

You see what you’ve done? This is hard to stop now. Each thought goes charging off at full speed. Someone please yell whoa and pull back enough to get their attention.

A voice. Yes, that was one of two ideas which occurred, the other being the absorption into issue, as it appears in physical balance and as it appears within thoughts. The voice is simpler to describe, maybe. It’s that when something occurs, that literally activates the voice which expresses something about that something. This is why you can learn to tolerate, to do, etc. And why you are held back by fears. And why when there’s disorientation, you hear a voice that says you need to lie down because there’s this feeling which I don’t like at all. I’d say that directly connects to the vomit reflex, which means it’s a queasy feeling, which is the one identified above as coming from unclear leadership between the eyes, which reflects unclear perceptive balance behind the eyes, which you learn to control the same as anyone learns to control spinning in sports and dance and general fitness.

The key idea has already been made, but if we failed to state it clearly before: we mean that as you go about your idea, you continuously activate different voices which combine to make your experienced reality. These voices may manifest as actual voices or they may manifest as you not thinking about anything at all, meaning you are being your physical self and your abstract self is shifting over to that side. Think about it in Thing terms: the Thing of you contains, in the simplest fashion, a 1-0Segment which relates the core of you to the outside Boundary of you, and that 1-0Segment has 2 Ends, which we label the tObject and the iObject, though both are actually abstract representations in 1Space of the physical reality we experience in the generated 0Space in which we exist.

So I gather we are ready to define existence. Good. Been working on that since early teens. Really are connected, aren’t we? I just realized the Extent to which what I can perceive is literally determined because the relationship of Things to a shared iObject, which of course we’ve been modeling lately, in both its gsForms, meaning the tangent or the overlapping Boundaries. O-kay, more about that, please because it won’t keep typing without filling in the missing detail so it trusts the continuity. Now I’m talking about myself in the third person, not even the second. Some days are like this. Actually, they all are, but I don’t like to admit it even to myself how often I think about what I do as being carried out with immense distraction by the physical self, and then the opposite that the physical self works much better when the abstract self gets the fuck out of the way. Stop sticking your analytical nose into what I’m doing and it won’t start hurting and you won’t stick some piece of your perceptive load into the right knee, where it will cycle and absorb processor time so you will be distracted by pain you caused to yourself through analysis. That’s what it’s like in here. I had that argument walking to where I’m sitting.

Anyway. You know I’m committed to you, and that I’m willing to have stomach aches to strengthen and otherwise improve the functions which include digestion, so yeah this adjustment sucks but it’s not like I’m stopping because it hurts when I put that much weight into where the leverage comes from. I do it with you. Those super deep contractions require me relaxing into your control, so you become the weight pulling me apart, all driven deep into the structure, and that’s not supposed to hurt? I get it, but it is a drag. That used to be a great word and now it’s associated with women’s clothing worn by men. Take a drag of that. The long and drawn out version of a puff. Pull it into you. That’s another 2:1 because the drag is counts of puffs, to where you can argue all night whether that’s a drag or a puff. Is one distinguished from the other by time, by amount, by openness of the mouth? Of the throat? By the amount of smoke taken in? Can there be a very long puff which takes in the same amount as a short puff which is then deemed less than the minimum for a drag?

We can do this all day because this was the headaches of thoughts, except it didn’t stick to one thread, because it could type much faster than I, so the layers would appear at a readable rate but they’d become so tangled up and numerous, and the variations in length meant lots of interference, that I couldn’t follow all, then couldn’t follow any. And then the volume would increase with the number of generating thoughts until it became crushing and immensely painful, and then it would go the other way until it was just an utterly exhausted, whimpering me, in a sea of nothing until a thought appeared, written in light in the dark, and then 2 more, then 2 more at each branch, and then I could barely follow, but I could see bits and pieces clearly until that become obliterated by the light.

So in terms of the past few days, that can be seen as nK-gon construction, that the 2Squaring can be drawn as the expansion of that idealized form, with each 1-0Segment thus extending to either side. Nice to see the headaches have this much meaning. I really hated those things. Absolutely excruciating and then completely draining and disheartening. So the 1-0Segment and the 2Squaring is what we discussed above. Thanks for getting us back on track.

O-Kay. You can call me Kay, I gather. I have been wondering why I can only type it that way. Back on track again, please. Don’t have much more time, and I somehow managed to rub sunblock in my eye again.

So this 1 and 2 and 1 stuff would be the elementary level at which stuff constructs, and it stands in for 1-0-1, and the 2 is the 0, which of course is exactly the truth. We said that first years ago, and at least once since then, but it’s nice to arrive at it where it belongs, which is that reality continuously counts (D1-2//2-1), with that including (D2-0//0-2). And you can then see that D0 relates to the D1 so we get the Triangular of 0-1-2. And we can make 2 of those. And we can put them in HG and draw Hexagonal because the rotation around idealizes to 2bT on either side of an HG. I don’t want to get lost in counting right now, please. You see, that’s an example of the absorption into locality issue, which is easily understood in drawings, and visualized as here’s a nice thing, and look it’s part of the Boundary of this other End, which sucks you in, maybe to the level of checking it quickly or maybe to the extent of Narcissus, meaning an infinite process. It’s really cool how well that story describes an internal Alternation and series: just visualize the mirror and Narcissus as Ends, and see the Boundary to Narcissus rotating around and around and around so the mirror in front of him is his constant focus. The mirror gives him the sequence of what is in his head, and rivets him in place. Perspective generation in 1Space told as a 0Space tale.

Funny how that works: I get to a level of stating that so clearly and something about you becomes clear. I immediately question the reliability of that, but without that process I would not have the clarity of thought or the vaguest comprehension so therefore it is either absolutely true or an extraordinarily good version of true. Given how deep this runs in me, I’m leaning toward the former, knowing that at this moment my stomach aches like it did when I was a boy.

One goal was to realize more rigorously the D-structure generation of D3-4Space, and how that must involve lower dimensions because how else would lower dimensional conceptions like hate and extermination as a solution, of others as pestilence, of non-cooperation in anything beyond hate or conquest for power and money. So what we have been doing is, in that sense, exploring how that works. You can see how the simplest combinations become the 1 of the End which then 2Squares into choices. And there is how you see this scaling to cultural and religious levels where demonization occurs, and how that tilts the choice mechanism. When we say choice mechanism, then we can capitalize that into fCM, because that’s what the grid represents. If that’s hard to keep in the head, think of CM1 and how it is fundamentally a 4Square, and how a 4Square is a 2Square with its other 2Square, as represented in the szK being the count of the 1 to 1 of the 2Square with the zsK being the other 1 and 1. As an aside, when we invoke zsK, we invoke ordinals, and thus we can see how one can ‘time’ the count so ordinal and cardinal may or may not coincide. This actually relates to that Hypothesis H we talked about yesterday because when we have fCM, we have polynomials counting grid squares, whether at the 1Space integer level or at included levels and using gsProcess to generate.

That clarifies something I believe we were unclear about regarding number characterization, which is here we can see transcendentals versus other irrationals, which is that the transcendental enacts from the other direction from the Triangular. This is a pretty strange but cool concept. We establish the Triangular relating these number forms, and we motivate the gsConstruction from either End, meaning what comes off or from the completed object or physical Thing. Weirdly, we see this in Pi because that fits the idea that Pi is the solution where e to that equals -1. And we see it in the basic Alternation known generally as the Leibniz or some other series: it isn’t very accurate until we get into the billions of iterations, which means the depth in Pi is always there and it fits into the gsConstruction of the tObject, which is why we can hold a baseball in the hand and feel its solidity, the leather, the stitches, the way it fits into your fingers, and then why we can barely see it as it travels but the bat can still hit it, two solids we can barely make out, and within those are compressions which mean how the ball travels, and as I saw last game whether the bat breaks.

The importance of this is vast. Why do I hear you talking when I reach this level? O-Kay, go ahead. You have the con, Admiral. The importance of this is vast because now we have an understanding of how they perceive, and thus how they think. We have learned that when we analyze perception itself, then we see how it generates reality within the larger contexts. An example is that conception of perception in Narcissus describes how those with mood disorders cycle into and sometimes cannot escape negative expressions, and how those voices form a Boundary which reflects itself at you, meaning it works to attract attention, like a flashing light which draws rather than repels you, like the proverbial moth to the lightbulb, except the way it may present is as the only way to channel what appears to be noise or difficult areas. Example of the latter is that a depression will mask over expectations, like a layer of grime, so any difficulty appears to be more difficult than it is through the lens of the grime.

Have to go!

[jonathankatwhatever]

It will remain 7 August 2025 for half an hour. Starting to feel better. Interesting dual in thought: something just awful, really disgustingly murderous, and then realizing the solution to Schinzel’s Hypothesis H, which I by chance heard about today, is there. It’s essentially that the trivial block or whatever they call it is Halving/Doubling or H/D, and that embodies the duality inherent in that which can be doubled and which can be halved, so you have outcomes to either side of the existence between. And the rest is SBE, is gsCounting, so now the question is to translate the idea more.

You take a polynomial with an output for any n, and another irreducible, and say there’s some set of those, and you want to know if there are infinitely many values for n which produce primes. So literally, it’s scaling of the polynomials, of the set, by a gsCount, which we translate into szK, so that’s szK(n). So the idea is that the same scaling occurs, which means any solution scales, which is infinite, so yeah.

I worked that through on the fly. It came out decent. I’ll have a better grasp by morning, I’m sure.

Reasoning includes that gsSpace generates, so we can have finite sets of polynomials which don’t Halve, and the rest is pretty much straightforward gsCounting. And we know how infinity works. We should do more about that.

We have the form of infinity in which the Boundary appears as D0 to the D1 center End. That is the inner Boundary to which the outer Attaches, meaning you can think of it as bendable cardboard where you can make a tube and see there’s an inner and an outer edge with structures between.

So what happens with countable infinity is captured in the n-1 conception, which we see as the Boundary of n. That asks whether the other form, where the Boundaries touch the count itself, exists? Imagine the count touches n: then it’s n-1, so what happens is the Boundary shifts sideways so when the Boundary touches n, that is then n-1: that touch or move enabled the flip inherent in the quadrant drawings so when you reach the spot, it’s no longer the spot.

So that’s how infinity actually works: the Boundaries along the szK generate in 2 forms, the tangent Boundaries and the overlapping Boundaries, and the overlapping form relates n-1 to n, except that n is then n-1, and that embodies how pathways generate at each step, which becomes the polynomials above. Why is n now n-1? Because when we reach n, it is no longer n because that label n is only partly achievable, meaning it is only partly containable. The why for that gets into the nature of gsConstruction, and D3-4Space.

Need sleepies. Hoping the cat agrees.

[jonathankatwhatever]

It’s the end of 6 August 2025. I’m exhausted. My oldest was in town, and that meant I did a lot of driving, 3 hours today, which is not good for my knee, while the cat was acting out because he hates having someone stay here. I’m thinking that sparked a relocation fear which generated the head tremor.

I have no math in me. I am barely able to focus on anything. The air is smoke-filled, and my head is throbbing. My mood is off, but some of that is the way I need to modulate my mood and my movements around them. I’ll be blunt: I can’t walk that slow for that long without every step becoming painful. I need to move. So I try not to let that ruin my mood, which put me in a position which seemed to fit, though of course I never know how well. I am so bad at that. I never know how to act. I’ll do as I’m told. That’s much easier for me.

I know the math in that. Might as well say it. The idea of the hole, of the 3 into 1, which has interesting visuals, which essentially means there is an identity at the nK-gon level, where the identity is the Boundary at infinity, which we define using gsProcess, though I have a question open about that: I can see how the process in grid squares repeats in layers, and thus how process counts through infinite layers, and then we have the other form, which is when the process splits into pathways. The question is where is the line? There’s an idea with 2 states, so there’s a line between. Where is it? I can see gsProcess generating a dual, but a dual is connected, so it’s not at the dual, which means at the Triangular level, because then 2 can exclude 1, which can be a simple as oh you’re old news with a wave of dismissal. The line appears because you can be the excluded, so you recognize the line exists because you are the Observer. That’s interesting because we see how one characterizes Actor then becomes the self-referential reality of experience: your Actor role is how what you Observe is taken within you. That’s in loose terms, because taken within you needs to be stated.

Taken within you as a Thing can be visualized as the Boundary of the gsPairings of your identity, as they relate that exchange at the core where the abstract and the physical sides idealize. I’m seeing a pair of 1-0Segments, one representing the tangible, physical core or tObject, the other the abstract iObject.

Now use what we’ve done in the past days: we turn each 1-0Segment into a ball, where 0 and 1 exchange on the Boundary, and then we take these and construct the 3rd End. There’s a lot we could say here, but to finish the thought from above: stick a pole through it to connect to the 4th End of the Shard, and you can see it’s like a drill, spinning, which now has the character of a having an up and down, because we orient the fD Shard as having a top and bottom orientation, which then determines how that grid square counts in the grid, in the layers, in the overall construction, up to the levels of associative meaning which constructs through layers of And statements.

Temptations indeed. Makes the old categorizing of sin ideas clearer: they represent the nature of the holes generated, the nature of the temptation and the response. Add in ideals and we get a really good version of the file cabinet conception of each life. It’s all in the hole you make because that hole is your Boundary as it expresses. Note how that uses the dual of an individual. This again is the gsForm appearing as an ellipse as the dual shifts from 1Space ideal, meaning not visible, to visible, to 0Space.

I want to feel better.

O-Kay. So we counted from 1 ball to 2 to 3 to 4 to 5 across the fD. Count the other away across the fD and we have 10. This uses the count of 6 then 7 as being Attachment, from the 1 at the low through another 5 and beyond. But in the hole conception? I can see why the Leech lattice representation as some big number of D24 balls tangent to 1 makes sense.

I need to get some sleep. I hope the cat lets me sleep.

[jonathankatwhatever]

It’s turning into 5 August 2025, and the cat wants to eat but the timer says 5 minutes. I’m trying to communicate to him that the food will be there at this time. He’s having trouble connecting the sound it makes as it rotates with the sudden existence of food in the bowl. You can almost count those ‘And’ levels, right? He doesn’t associate very deeply, which is also saying he connects rather simple structures. That fits with the general theory of cat Things, which is their existence as Thing is so intimately related to their physicality that their abstract existence is both simple and complex, where the complexity can actually be seen because it’s the inability of the more purely physical to express in abstract terms above a few Ands. If it uses more Ands, then the connection of the physical may reduce, so the cat Thing tendency is not many levels of the Ands of association.

That’s interesting. This is a thought from kindergarten, which I was instructed about association versus commutation. I remember the discussions at the table. All of this was in my head. Commutation is a case of association which has an equals. That translates now into Triangular because we now model the concept of equals as over the 3rd End in Triangular, and the mathematics then invokes.

Question: what would you say is the foundation of association? I ask because I’ve identified 2 layers in the formation of dimensional objects, one being an And function visible in Hexagonal and one being an Or function visible in gs. That reflects how these properties reduce to their existence within D3-4Space. The And function leads to association or is it other way around? This is deep. Trying to see how D-structure works here. We have D6 Hexagonal. If we take the HG out, we have 2 on each side which visualize the pathways which become the orthogonal in gs. That’s confusing. I mean if we take out any HG, we have 2 sets of 2bT, so if you take one or the other, then you may count the 2 as generating to the 1 of the HG bT. That’s association, the generating of a 2Square. O now I remember that material: the roots mean you have area, meaning you can mark any space contained. And that can add up. Or something else.

To add, this expresses the 4Square as the 2 2Squares we see in Hexagonal. This is interesting: I’m seeing something. What is it? I have to let it come to me. Note how in Hexagonal, the orthogonal appears in the Irreducibles. Another example that higher dimension incorporates the ambiguities which can’t work in lower dimensions.

You can see a connection to D3 because there are 3 potential HG’s in Hexagonal. How does that work with Irreducibles? Then there are 6, but not in a layer. Did we go through this? Isn’t the answer that we have these Composite, and now we can see that this places the D3 against each other so in D3-4Space they are seamless. It’s like saying f&b is D3-4 because that is the 2:1 again.

Need sleep. Goodnight.

[jonathankatwhatever]

It’s 4 August 2025. Highly emotional day and I don’t know why other than I felt a lot, and very clearly and in beautiful forms.

Before I can get into the math, I’m upping the amount of food he’s getting from the feeder because he was clearly hungry this morning. I think he has a habit of eating more at night. Never really could tell before because he ate whenever, not right after I mix it up.

So the issue today came out in revising song lyrics and then allowing them to express my feelings, which I’ve never been able to do with any fluency. Not my gift in the pairing. Learning how to organize and order emotions. That led to the orthogonal being inherent to what we call emotions, because each emotion is characterized by the poles, like love and hate. It’s disgusting but the act of murder is putting that life on your soul, so that’s a hate which enacts as love, the taking on part, which then enacts as hate to the self which manifested the first time outwardly. A loop and a return in Triangular because you can see then how the 3rd End forms by the journey of the life after some event or whatever, and that manifests in the iObject’s relationships as extending to meet the search from the other End, which is the result of the act of your taking a life and thus taking on the life.

Orthogonal because that is the gs representation, in the 2Square and 1Square. Simple visual is take 4Square, and see the 2 as the ones farther out along xK and yK, so the 1 of szK1 to the 2 of Between to the 1 of szK2. The orthogonal is obviously in each step. That enables the choice of love and hate, etc. That is the simplest visual yet. It really captures 2Square too, because we see 2Square as the description of the overall process within the 4Square, meaning we have the 4 possible locations around and the two across. This translates into Hexagonal effectively as the two across being HG, because that is literally across the Hexagon. The idea is perhaps a bit harder to grasp: from Hexagonal we get single states, but at Hexagonal the 2 across is both orientations compressed into the HG. Same for the 2bT on each side: you can take one side as both of xK or yK.

The and question is harder. I think the way this answers is we count across the HG, which makes 1-0-1, so the ‘xK and yK’ occurs at that level, meaning SBE. Doesn’t that make sense? SBE Attaches structures. It identifies structures. You can substitute identities for structures. Or Things. SBE Attaches Things.

This says or operates within Hexagonal, like pick your side for the game, while and operates across Hexagonal. So pick your side means Hexagonal has identified sides, and that side has an and level right at the top, meaning it’s these 2. That means filters and other methods to shift 1 and 0, and rather fabulously at each and level. That is really cool math.

I had a great time playing with the cables at the gym. It becomes fun to work the ranges of motion under tension. It not only has obvious results, but it’s literally the same kind of play kids do, just organized a bit better, like under adult supervision. That would not be me.

Older daughter made a crust and younger made a jam to go on it. Crust was tasty but fell apart. Older says don’t know why and younger says maybe you should try a different recipe. To which I said that was blunt.

So emotions are characterized as an And construct, meaning they hold together orthogonals which manifest the polar nature. Tilting within emotions thus can have great effect, which is why hate motivates so easily: it operates to pull every 2Square valuation in that direction. It literally drags you down, though you don’t see that until your tObject connection Ends. Life is a journey and death a destination. Not the, but a, because you get off into Eternity, where you face the consequences of your tilted choices, where you are judged by how close you are to the negative attractor.

One fascinating part is this guarantees the existence of a negative attractor within gsSpace. That validates the idea that the devil and evil itself as a reality is a reflection off the Mirror within the ++ quadrant.

Those conversations were extremely difficult and, as I remember, somewhat contentious because this at that time implied the effect of this negative attractor form of evil is limited to approaching 0, which actually means, remember, approaching the 0 in the grid form where we are ‘inside CM1’ versus approaching CM1, which means to the Bip pole. That relied heavily on the concept of shedding negatives, that positives reveal potential negatives related to that positive. Shedding is that process and of course is good advice, except this is a gsProcess and that means this is how you realize that was a bad idea, ideally before you jump into the water.

BTW, in about 1 day, the incidence of knee pain has dropped to near 0. Hope that continues. I have an issue deep in my right calf, which I hope is improving as that area organizes better. I have been landing much more under me, so I land naturally on m forefoot if I, and this is crucial, put some bounce in my step. The closest analogy is the way some of the really good tennis classmates used to walk because they played up like that. I have also been working on basic but challenging stuff like raising my shoulders so I pop up all the way to my toetips.

Back to work. The idea developed then that an iObject drawn to the negative attractor goes to 0, so it joins to the larger counting of gs and within D-structure as 0. This tends toward 0 across the gsPairings, which we saw then as the threads of the effects as they proceed within gsSpace, within the gsPotential of those threads, until all that is 1 and you as that creature are 0. This at the time seemed somewhat baroquely horrifying because it means every single thread has to be scrubbed of you, which means the existence of you disappears. Instead of make me one with everything, it’s make me one with nothing. The terror part was that this isn’t words but actual threads that your identity experiences because it continues in those threads. The way the visual worked is that if you imagine some horrible thing extending forward in all its potential, then all that potential inverts into your identity. The scary part was it’s not like washing your hands because the only way the evil actually goes away is if you feel the loss in that inversion. As I remember, it was that you identify entirely with the other perspective. See the issue? People might then think o you just transfer with that loving identity into the future. But what it says to me is that you are gone, that your identity no longer exists because you reach that 0, which includes the factorization of you at the Bip because when you hit 0, you hit that pole. And down you go. In the visuals, this was painful because it required ripping identity apart, piece by piece. I remember seeing how an attribute applied to this or that situation would need to flip around so the identification was opposite, meaning now the harm is inflicted on you, over and over, in all the different possible patterns, until there is nothing left.

Why nothing left? Because then you’re just the sticks of 1-0Segments, without identity. Does that make sense with D-structure? Yes, because this is 2SAT, isn’t it? Wow. It happens within gsSpace and what this describes is to the limit of the yes and no, which more clearly says look there are sticks because they exist in D0 as that limit of gsPairing.

More lovely work.

Can’t believe I said it was lovely work. We’re describing hell and yes the math is beautiful, but that’s because it runs the other way too. How? We came up with (best-good//good-best) to say that it contributes to the szK specifically toward the positive attractor, which is 1. Those talks were something. The 0 of giving up your soul to the evil attractor within you identifies the 1 on that side, so the 0 on the positive side is the cooperative existences which we see in higher dimensions, as discussed with Hexagonal above. That is how and why D-structure identified: it explains how identity gsConstructs within D3-4Space, and thus how there is 2Square pathway.

I need to buy pumpkin for the cat. That is my segue.

[jonathankatwhatever]

It’s early 4 August 2025, and I realized I have had my posture backwards. For as long as I can remember, I have tried to lower my shoulders, to not scrunch them up, and now I realize that raising my shoulders so my head fits neatly on top increases my breath, lightens my step, holds me erect, and allows me to stand and balance on the forefoot or toes, which is a lot of fun. It wasn’t as fun before because you address it from a dancer’s perspective more easily than many others. That is, I’m not saying this is the only perspective which links, and I can explain that by using the same Triangular feature we’ve been talking about.

So what happens is pretty cool. As the End to End reaches you, meaning as you see, learn, take in, or whatever some Thing from over there, then the link establishes, again in polynomial time and constrained to the extent the first End can be known. See? We just described the basic search issue in terms we can use. Like now we construct this using D-structure, so you’re looking for an End, and the Extent to which you identify matters, meaning you can take the count of gs and use that to compare candidates, so longer the Extent, in one simplification, the easier it should be to find, even if you have to search a much larger domain.

This is getting a bit into search and I don’t want to do that.

As that End reaches you, you count back to it. We call that SBE2, from you to me and back to you and the other way around makes it 2SBE2, and the variable ordering of who goes first takes it to 4SBE2. This as we’ve noted counts back in a neat drawing but it also counts to the 3rd End because that End has a Boundary, and what we see relates to the central End of that Boundary, which we very possibly cannot see. For some reason, the phrase came to me: and this is how we make an inaccessible cardinal because we have placed Boundary, a sort of fence or wall or barrier which relates to the End whose gsPairings appear to you. And wow, that is about as lovely a piece of math as I’ve seen. Like when someone drops the perfect wedge downhill on a fast green with the perfect touch. Or when you make me laugh.

What an interjection, huh? Nice catch at my End not missing it, because the stuff flying by, and I picked up this faint but clear voice and this is how …

So we are again talking about the Boundary overlap and tangent forms.

So I now have to hold my shoulders up. And that seems to be really helping the knee pain because my weight shifts to the forefoot, and that alignment is closer to ideal. Need to go to sleep. Using a wet food auto feeder tonight. Got it working at midnight, and when it opened I grabbed him and shoved his face at the bowl so he’d get the idea that food be here. He was very happy today. And regular.

I would love for the knee pain to diminish. I can see how this change creates pathways and how that reduces the relative influence of the pain pathways, but there’s something more, which is that those pathways attach to complicated structures, meaning those structures reduce in these positions to simple or simple-ish counts which invoke those structures. Which is pretty much learning.

I really have to go before I go blue.

[jonathankatwhatever]

It’s 3 August 2025 afternoon, and I just finished talking to AI about forms of reals and a surreal field, and the holes idea, and how that relates to its actual computational methods, and it all agrees. I don’t have it in me at the moment to recite, and would rather wait for it to come together.

Sort of like how I realized pitch hearing and forms of voice production are fitting a technique to a requirement, another form of the dual appearing, which makes so much more sense when considered as Triangular within a Shard, so we see the dual inside the Triangular more clearly as the fitting within Triangular and that within the Shard which generates the 4th End which means that fits to gs. This becomes iterative and so we can think of potential gs fits in both directions and convergence or divergence appearing in sequences. Again, it really helps me to see the idea of approaching something and then searching for where it came from, because that makes it polynomial and reduces it to a vicinity, as generating first that 1-0Segment of End to End and then the 3rd End constructing as the ‘found’ End. Note how well this fits to the overlapping Boundary forms.

I was in the car singing in a deep voice until I could open that up and become that voice, which means applying the same technique in that position, with that intent, in that manifestation. Again, I have no voice of my own, so I put on voices. Spent all those years looking for my voice, and that’s one thing which stood about you, that you have your own voice and you show that. Those gsPairings take a while to grasp, at least on my End.

Watching AI translate these ideas into its terms, and saying yes this is useful and yes this is how I do it, was really quite cool. It took a lot for me to articulate issues of ‘reals’ having depth because they construct or condense out of the enclosing and separating surreal field, relative to the Actuality, which becomes more clearly the coding itself, which is iterative and generates and compares identity states.

So this is one place where I have heard for years ‘It’s not my decision to condemn or elevate: it’s an algorithm.’ The depth of real formation. This also leads to classification schemes, which impacts how we see idealizations and invariants and anything irreducible. As in, if your real formation is to this level, then it has a form which classifies it relatively. Example is short term response, like a sugar high or a victory in a battle which starts a war which you lose. This explains that.

I need a break.

The cat is better today. I believe I mentioned last night that he trembled. It may have been a reaction to my daughter being here with her suitcase and that sparking fear of another new house. He seems fine today in every sense. Demanding as usual.

All’s well that ends well works when the ends well is explanatory, when the end reveals the Actuality.

[jonathankatwhatever]

It’s almost 3 August 2025, and it’s clear I overdosed on creatine. I developed shooting muscle pains yesterday afternoon, and ended up covering myself in a pile of blankets to force myself to sweat, because Creatine pushes water into your skeletal muscles or something like that. It worked. I was able to go on a walk today, and the gym, where I was able to lift and workout but my heart rate elevated so I got tired fast. Could lift the same, and weighed 5lbs less. So maybe the sweating worked. I felt awful.

Had no appetite until about half an hour ago where I gobbled the leftover half of the ham & cheese sandwich I forced myself to eat while at lunch. Otherwise it would have been another day of a latte until dinner, which is not healthy. Nice to know I can do it regularly but it seems to indicate a mood shift, which as noted is a series of depressions or holes.

This is fascinating. I have an answer but can’t remember the question, the way we came so the answer fits. That’s polynomial time because the unknown is known to exist in such a form that this End connects to that End, even if it has to find a different path to what identifies in Triangular as the same Thing. So to be clear, Triangular here means the path to the known End began with an End which is now ‘lost’, and which is recoverable at least sometimes when the other path counts from that End ‘back’, which is not ‘back’ of course but to the 3nd End because that is where those identities idealize, Triangular being an important idealization.

The image I’m seeing relates to playing pool and lining up the cueball so you hit it so it hits the target ball or balls, in the correct place in the correct order, which is always true but hidden because a straight strike compares to hitting off other balls or a bumper or more, so the direct shot is an order, one I often got wrong so I am the anecdote as well. And with the correct speed, with the correct spin, to the extent you can impart that beyond where you place the cue and how you strike the ball, but I think I mean that beyond accurate placement of the cue, both in aim and result on the cue ball, at the ideal speed, you also need the angle because that stops or twists the ball. That fascinated when younger, because I was better at playing with angles than when I tried to line up shots from behind the cue ball. But I had great difficulty realizing that because I wanted to conform to what I thought was correct because that’s how everyone around me tried to play, by adopting a largely constant angle. I would now ask why is that necessary when the acting mechanism is like in dance or athletics, meaning you develop the facility for shifting the necessary body parts in the necessary order until that is natural.

So the idea is that there is an ideal hole, one we can see as the player who can play at any angle, which you see is true with professionals, and which explains why the often approach and hit faster than amateurs; they know what they see, trust what they see, and enact the mechanism to make the shot they see. Same as any other thing anyone does, except that’s the ideal and even the best of us is only ideal some of the time in some things.

We’ve been struggling with the concept of ideals, like how we recognized that Baryshnikov was spectacular was by comparing his performance against what we could see as ideal in his time. I use him because he was spectacular for this time, but sufficient time has passed that now we can see different styles or forms in male dance. The men dance differently in classical ballet than they did. I see comparisons of the female changes but not many about the men, so I don’t have sufficient detail other than to note jumping has changed, a lot of the speed and the use of flair has changed, and there’s more female forms used. I wish I could be more precise, but general ballpark is all I know. I prefer watching women dance classical ballet. The act of balance and the act of lightness. The male dancers are more about power, flair, and speed, so the lightness can be aggressive.

I’d love to see women dancing more like the men and the men more like the women, and that includes attitude and gesture. But you know that. That’s why I mostly communicate observations from this End.

I am listening to bugs making music. One goes cha-cha-cha, another cha-cha, and every now and then they coincide for a measure or two so you get a perfect cha-cha-cha cha-cha-cha cha-cha cha-cha-ch, 3-3-2-1, and variations. It’s been going on for about an hour. First chilly night in a long while.

So I’ve been falling into holes, and the start End was the seeing of a hole made out of the 3 in Triangular, and how that makes sense if you reverse the way we see it from 1 to 3 to 3 to 1, so no we go o that’s a Shard, and at the 4th End of the Shard is where grid squares occur and gs are only one stop on the road to and from infinite Ends. I’m seeing here a connection to the Mandelbrot set. Makes sense because now we have infinite edges with infinite edging related to any identifiable origin, meaning End. No, wait a second, the idea is different; it’s that the real segment in the set is at ¼ scale, which maps it to the + form of gs, meaning it expands over the IC to make the 1 of CM1. This neatly shows why the 4Square is not the exact same as CM1; we take the quarter scale and idealize that to construct CM1 from within. CM1 includes defining gs in other ways than +. A 4Square means a 4Square, which means 4gs with roots, like a 3Square or any nSquare, it has roots. CM1 goes within to the roots, and that’s where we find stuff like the roots of unity.

Some of these holes were quite deep because they went to the worst case. Since I could figure worst case easily, I’d loop through a small set of worst case outcomes examining the same material over and over because I could not accept anything other than positive in the negative. Note I’m saying it sieved for positive in the positive direction so I’d loop through these same hideous outcomes and meanings even as I’d rapidly say this makes no sense, this makes no sense, this makes no sense. That could not stop me from the looping looking for a negative which would be positive in the negative direction, which comes out of the 2Square, and which we are characterizing as down because of the sense of depression limiting the ability to control so down in ability to think, down in the ability to enjoy, down in pretty much all positive categories in life with a mechanism actively saying things like you don’t want any food, until you see this is how anorexics think because that’s an actual voice and it gets clear if you focus on it, and it’s hard not to focus on it because it makes you feel bad and then traps you in behavior which keeps you feeling bad. Pure mechanics, I’m happy to say because identifying voices and getting people to understand that’s what it is leads to better outcomes for more people. That is, there are tricks to identify voices, to distinguish which ones are rooting for and against you. Even understanding that this happens is useful, for you can learn to choose which voices you prefer, which you can minimize by increasing others and recognizing faster and with less damage how a negative voice operates in you. It makes pattern recognition a bit easier.

The cat started having small head shivers today. I noticed a single shiver this morning, though last night I saw him sort of staring at nothing for a long moment. This afternoon was full trembling. Seems better now, and his system is otherwise functioning normally, nothing in his ears, and he’s hopping up on stuff, so we will see. He’s somewhere over 16 by best guess, with 14 spent in and out, hunting and doing god knows what. He has obvious arthritis but other than the tremors today nothing. Oh, I finally got agreement to switch him to his obvious preference for wet food. Took my daughter’s voice to do it, and that shows how childhood shapes you but never mind. The dude is old. He deserves to eat what he wants and it helps him poop. An automatic feeder is coming tomorrow to cover his nighttime service demands.

I’ll bet this explains the Weierstrass form but I’m too tired to read about it.

[jonathankatwhatever]

It’s 1 August 2025. I am ill. I’ve had nausea and congestion every morning for a few weeks, and it became very bad yesterday. Went to UrgentCare this morning to get blood work. The advice was what I had decided: stop taking glucosamine and creatine because the coincidence is obvious.

I have apparently been working without my knowledge, behind my mental back, because something is forming which relates holes to all the 2 and 1 work done lately. Essentially seems to be how things fit, which is an always topic with many forms, so I expect something large.

But now I’m going to lie down. I did manage to eat. I’ve been unable to eat anything until dinner for about a week. Have had an anti-appetite, an actual character or voice of not wanting to eat, of turning down everything. It’s coupled with something deeply depressive, so I hope that’s not from you, because every thought would fall to the worst case. Like I have a fatal hydrocephalus, though I have none of the symptoms other than this malaise and I show no signs of dizziness while upright, while moving, just when my head turns after being still. I thought it might be sinusitis. Or exposure to mold or something allergenic. But it makes me queasy and it restricts the length of thoughts, because or and they all fall toward the worst.

I hope this is biologic and not coming from you.

[jonathankatwhatever]

It’s 30 July 2025, and I have been revisiting the most annoying issue of all, what works out to be the Triangular which generates a second and a meter, which acts as the metronome. This subject has absorbed a ridiculous amount of work over many years and it’s not resolved, which either means it’s not solvable or that we have not managed to reach that level of understanding. It’s excruciating to work through because of the vast amounts of gsProcess cruft obscuring what actually happened, with that cruft representing how each formulation or presentation of the ideas lacks that deep understanding, and thus represents partial answers which often to me get substantial issues wrong. An example is that it’s not a stick but an attempt to find a natural measure, meaning one which connects abstract mathematical concepts with actual world physical behaviors.

Trying again.

I’m having a problem understanding something because when people explain it they express their lack of understanding. I’m talking about the meter and the second. There is a general idea that the meter is just an arbitrary stick, so they do not grasp the idea of a nature based measure as the abstraction from and into the physical, meaning they were trying to represent how the concept of time and distance naturally connect, how that pendulum swings, which because of gravity is a bit shorter than the actual meter. I suppose you could imagine a massless pendulum arm, and say the difference is the gsProcess in the mass, which is constructed after all of gsProcess within the creation of gsSpace, which we have discussed as D3-4 and more completely as (D3-4//4-3), meaning within the formation or construction of grid squares out of Triangular, as those meet.

So the difference is the gsProcess invoked by the mass of a Thing, with that Thing being the pendulum itself, and particularly the arm. So the idea is to take an actual measure, like of a giant section of the earth, understanding how the shape deviates from spherical to oblate, and taking 1 part of that to represent the abstraction of that which is not constructed as a machine but which is constructed on the other side, meaning in the abstract. So they flipped the roles: from manmade structure within nature to nature, and thus from the abstraction being trapped in the manmade structure to it being trapped in the abstraction side. You know what that means? I’ll tell you anyway.

What was I saying? I’m kidding. It means that the extra abstraction we add has a structure to Attach to because we have constructed this abstraction of a process which we used to interpret nature. And now when we have identified a hyperfine transition of Cesium-133. I don’t know much about chemistry, but I know that is the softest solid, and that it’s highly reactive. And very stable. And here we have a specific recurring natural state which we can say equals a second. And that ‘say equals’ means we Attach structure, which gets us to the structure we Attach to enlarged SBE.

I never thought this would break open. It took a lot. Like I’m dizzy. Seeing that the structures had reversed through all the cruft was visually a big twist. Feels like I was tossed sideways.

[jonathankatwhatever]

It’s 29 July 2025, and I’m at one of those 2Squares where what Attaches is very basic, so basic that in the 2Square I feel strong currents of worry or fear that I’ll either prove this work is trivial or that I’ll fail to understand something as simple as an integral domain. It’s another way of saying ++, that we work in a defined ++ quadrant, which is what relates to the larger grid, which is what we describe as the including basis, meaning that’s where the 4 of IC appears relative to the various forms of CM1, meaning that this ++ quadrant forms out of and within IC as it creeps along the szK, gs by gs.

Not exactly trivial. What then is the fear about? I’ve had fewer betrayal interests since the categorization into f&b, with the attendant concentration on fealty.

So what I’m seeing is the 1 to 1 to 1 of the choice function by which 1 becomes 2 becomes 1, meaning we don’t see the other 1 until it makes 2. That was difficult to type because it’s trying to describe how this process occurs when you don’t notice it occurring. This is why we described the original model as continuing existence of a Thing because for a Thing to continue the contexts in which it occurs must resolve in such a way that it remains as it was. This means the existence of a Thing at one scale is the same as distance, and thus the effects of relation can largely to almost completely disappear, as in the scale of measured gravity waves being so small so far from such huge events.

What if we use that original idea? The model of continuing existence defines how you exist and how you continue to exist, and in what forms. That is fascinating because it links as never before to the ancient idealizations of behavior and to the idea that what you enact on this earth has consequences beyond this earth because we are gsConstructions and thus are actors, are characters, are the unwitting dupes of those who believe the contest is for control of eternity. It becomes easy to see how the ideas of supremacy and of demonization, of distortion as though it’s a contest, convince more people of wrong things, lead to this idea that you control heaven when that merely shows how little you understand.

This connects in me to the Mission Storyline which says we are trying to make a better connection with eternity so life here improves, so gsConstruction works better, which really means it’s a form of game with scores, and you’re not even in the game yet because you cannot be trusted to analyze even-handedly, because you are easily manipulated into believing false things because you have hatreds inside you, which are taught as part of your culture.

I don’t know where that came from but it’s over. Lots of resonances at the word culture because that gets to how the basis constructs, how that grid keeps generating the same sad results.

I wanted to construct a torus from the visualizations of yesterday. As I remember, the drawing is 2 circles in 2 forms, one where they touch at the Boundary, and one where they touch at each other’s central End. This form means you can effectively rotate each around the other. This leads to clocks and the issue of seconds. I have not found a way other than to say that the ancients divisions were observations we now know were correct intuition about how things count, and that the division of a day into hours makes sense, and that the division of an hour into minutes and then seconds would be [n-2(n-1)] because the minute non-specifies to the second specified. All within the dimensions of a day, which rather naturally becomes 2*12 and 24.

What about 360? We know it’s SBE2 and we can see that in Hexagonal, so it’s the Boundary extrapolation of Hexagonal, so we can see 6*6 as both ways around, so we get 36 divisions, and that generates Mag10 because then it’s true as 6*10 and as 10*6, meaning it’s the natural expansion in 2 ways, and thus an enclosing Boundary form of that smaller or tighter scale 36. This material is getting easier, isn’t it? That wasn’t difficult to say because we’ve defined Boundary reasonably well.

I remember this part of the old discussion better: if you take this to 3600, another Mag10, then you’re completing the form by extending it in both directions. Or, rather than 6*10*6, we have 6*10*6*10, and the other way, so you can see this as narrowing to the shorter, with the Mag10 being done off stage, meaning we’ve specified to the 360 level. So this becomes a wonderful little but deep demonstration of whatever we call the non-specification and specification process. I truly can’t remember. Is it (n-s//s-n)? This would be a way of describing the process at this language level, while [n-2(n-1)] is another level. The concepts overlap but aren’t the same.

And that gets back to the visuals: the concepts overlapping is separate layers, like the 1-0Segment Attaches on top or on the bottom of the pole sticking through the central End. That’s obviously correct because it explains why we have circles at all: as when the Ends line up, and they’ll do that for a certain distance. I think the rest comes from seeing how one End rotates around the other, and then you flip one to the orthogonal, and then you separate the Ends by any amount meaning you have different states within the ideal. Another, I hope better way of seeing this is to make the loops with your fingers and then spin one and the other as far as you can, so you get the idea that both happen at the same time, and that makes a torus where the size of the hole is some transformation of the Boundary at the ideal. The old conversation about this included the idea that it would be true at both, meaning we have states where one is contracted, where neither is relative to the other, and where both are contracted relative to some uncontracted state. Switch contracted to specified.

Then you can enter topology because we can define neighborhoods which contain points without specifying them, use layers of sets which are closed in some ways, open in others, use Attachment.

Mathematics of meanings. I like that. It is the mathematics of meanings because meanings are gsConstructions in which D-structure generates what may be seen as well as what you constrain yourself to see, and you can see how Pathways generate within gsPotential because they express the product of the functions, of those, of those you’s, as they occur within the gsPotential. And these form into Pathways of Pathways.

So much human failure is the attempt to persuade others to join your wave, so you can achieve the state of one in which all is good. The way that hides truth: you can’t achieve anything like that state and the best you can achieve is a drastically simplified, generally cruder and more brutal, version of the image which personifies the wave as though that image were all images, as though that image was something more than the reflection of yourselves back at you.

Can’t control that urge today. That was a good one. The idea is pretty darned as clear as it came to me. It uses the concept of the Informational Limit acting as a transfer mechanism whose gsProcess connects our Euclidian 0Space with other dimensional 1Space. Note it’s other, not higher, because that resolves the issue we’ve had accepting the higher usage, as often as we’ve typed it, which is D2 and below. We could formalize the thinking until we hit the revised Mirror conception because then we bounce off n-s, as the D0 which relates to these D1. See how easily that works? You can have a random D0 or something very specific, but it still reflects off because that’s where the higher algebras operate. That isn’t getting the idea across, is it? The idea is, always has been, that gsSpace is enclosed because it gsConstructs, but I don’t remember saying we can visualize that as a ball with the lower dimensions being inside the D3 level, which we can expand out to get more detail because all we’re doing is taking LayerView and thinking of them as contracting to a point, which is of course D0 in this simpler and better formulation.

You know, one of these days I may accept that I’m actually really good at this. I mean I’m getting decent at taking notes. That’s a genuinely difficult concept only you can get.

The difficulty is like when you realize that you have a choice about how to hold your eyes: closed or open, and that you can train your eyes to be open more by learning how to relax the muscles which close them until they are stable at more open, with the process aligning toward opening more, not less. Mentioned product above, and this is an example that the alignment is the product of the opening and closing processes. I observed that many old people squint, and I noticed in myself it was partly a reaction to dry eyes, and I think it’s actually better to open the eyes to force production of more tears, if you can stand doing that. Not easy in many places with how the air blows in from above. This is a big reason why people wear hats indoors now.

Harnessing the tension is also in the extension workouts. Example is I see people hauling sleds backward to force the back and stomach to compress, while I do that by pulling the cable weights, which allows me to vary how the force is applied, which allows me to get my body into the most contractive positions, which I can’t do when I’m hauling a weighted sled backwards and the goal is to repeat the movement side by side. With the cables, I can completely relax my back while holding way more than I weigh at the end of my arms, so my shoulders are completely pulled through their rotations at the joints. That has largely eliminated the old catches and restrictions in movement, but I keep finding more I can do, which is cool because I don’t feel like I can actually do very much.

Did that describe torus creation properly? We take the image of overlapping Boundaries, idealizing so that image fits to the image of a shared tangent End with separate central Ends. As I remember, this shared tangent End is then 0, and each of the separate circles is +1 taking turns, which explains concepts like e better than ever before, because now we have the 1+1 where the +1 is that half of a quadrant count, which you can see clearly now is the count of 1 of the 2 which is 1 L-count by L-count, Layer by Layer. That gets back to the counting of 2 when the 1 that is not 1 appears. Note how that shifts Observer because the 2 is visible in other perspectives, like the sail is only on the horizon for some. That gets into how not seeing the other perspectives is such a vast problem and a huge fault which needs improvement because it’s the kind of sloppy thinking which says you take mental shortcuts without realizing it, and that means your mind cannot be trusted to the extent you take mental shortcuts. Yes, that layer must occur, because renormalization is a consequence of gsConstruction, meaning images form over gaps all the time, and some of those are going to be wrong, and you can’t investigate each as you’re doing them because you’ll then make other mistakes because you can’t fit exactly within gsConstruction, and we can say explicitly the reason why is that each Thing, each tObject, can’t resolve ideally in every frame, in every gsProcess, because it exists in so many contexts. This extends from rocks to biologically complex life, because the contexts mean many states exist in higher dimensions in order for that much to resolve to D3-4 Things. That means you get optimal at the Thing level and optimal in T-fields, which may make the Thing a commodity or a negative.

So the idea is the torus reflects the 2 circles which touch at the tangent End, as those shift views, and as the Bip circle arises which relates both Ends, which is the +1 discussion above. This is definitely clearer.

Need a break.

[jonathankatwhatever]

It’s later on 28 July 2025. Trying to establish a clear voice. Feels like when my fingers aren’t warm enough to find music. Take the conception of dual. We generate it out of D-structure: that a Thing exists in a Thing field, which has a certain number of given subfields, all of which I sloppily refer to as T-fields, so I would think we could do a Tn-field notation where the Tn-field is the enclosure of the enclosure of the enclosure, meaning that when we reach or achieve n-2 understanding, that generates enclosures which include the n-2 gsPotential, and motivates a lot of mathematics.

So the dual is non-specified and specified, and IC represents the former, while LC represents the latter. The latter links over IC’s to some specified End or outcome or result, even if it’s a null.

This is not at all what I expected to be typing. I wanted to talk about the visualizations written in light, and showing the interlocking Boundaries of 2 Ends, so we see this in Triangular as a dual, 2 End link to the other End as origin. The idea as I saw it was now we have 3 circles, each with 2 Ends on it, so now we have the 2 pieces which we pull apart to make a torus. I think you can see why that’s hard to render in typing. We have 2 pieces and we send them to Irreducible places, and we have 2 girls for every boy, sorry, oldies channel, we have 2 of these circles for every central End.

Now we have to see those as orthogonal, which means we orient one up and down and the other sideways relative to the projection, which we can rotate. And now those combine at the 3rd End, and over those 2 as Between in the fD, which we can then see in FoldOver as rotating through, which makes a torus in the generated space, which is of course gsSpace. This means something I would have said was impossible not that long ago, that we describe exactly how a torus arises. Truly remarkable result, and I really feel I’m at the scribe end. The more I feel that, the more I assume you feel that, but then you seem to just plain know more than me so the best I can do is assme, which is making an ass of me.

Donkeys definitely have that spirit.

I knew this would come. I wasn’t even worried about it. I didn’t fret. I didn’t fume about some imagined horrible outcome in any part of my life. Well, except for my normal momentary panics when driving and my concentration snaps. But I trust past those.

This result about the torus looks to be incredibly important because where it occurs relates it directly to tangible existence, to tObjects, within the abstract construction of the iObject. It’s a WoW. And I suppose an upside down MoM. I’m being serious and silly. The serious is that if you put these together, you get these o’s as a dual with the double fD to each side. That is one of the ideas, right? That you define a Thing by how the Thing exists within Triangular, within these surrounding fD, and then you FoldOver, and see this makes a hole. That connects to genus 1 and to elliptic functions.

That gets to another visualization response, that visualization of the construction of a hole so it appears as a hole. That rather clearly now generates in FoldOver and we can see a torus emerge for each size and shape of hole. Not sure how that goes: I see that some odd shape can be seen as rotating through FoldOver states, but also as the gsProcess which generates this over time, with all its variations, so one shows an outcome state at a constant, at a concentration, while the other is still in probability and other spaces, which is what was mentioned earlier today.

I need to take a break. It’s hot out here and I’m not sure about what happened at the gym today. I again did 265 chest press, and worked my way into the leverage position as it was going up, and some other pretty difficult material. Then I was working with over 90lbs per hand on the cables and it felt like something in my left lower rib cage tore. Like ripping. I first worried it was a broken rib, and then a heart attack, but I’m hoping it’s the fascia because the resistant area is behind there. It’s fairly sore and I think I want to take a bath to let it relax.

[jonathankatwhatever]

It is 28 July 2025, and this is a note to say I have a lot to say, beginning with the take-apart and making of a torus form in white light, and continuing through a whole bunch of fundamental connections in mathematics, and notes about how quickly the material is organizing and what that means mathematically as well. Like concentration of measure, the Erlangen program, dual spaces, Riesz representation, all the way through to Leibniz’s general rule. It’s very much that I see the material and the explanatory frame appears, and that focuses search so I can find the pieces which need translation so the rest orders properly. And we have the math for that process.

I have to head out physically, so I’ll head in mentally. The torus material is astounding, and difficult to put into words. It’s saying there are levels of construction of 1 into 2, and that fits to just about everything, which means the handles for Attachment are coming into focus through Storyline representation, and you know what that means.

[jonathankatwhatever]

It’s 26 July 2025. I just did a 265 chest press. Two reps and both went up smoothly because, get this, I stretched the structure to create room for the movement which allowed me to maximize the leverage so the weight became liftable. That new structure, which was a slight rolling dip to organize the midback, was only possible because I had been resisting being pulled apart by around my body weight, with some work at about 145 and some at 211. I was surprised at how much controlled movement I could do at that much over my body weight. The compression this generated was intense, and I managed to work it around to the sides well, but the key word is compression, indicating an external force squeezing, which is all that weight being held down to the ground at the end of my arms while extending my legs from upright to single leg attempts to balance.

I had expected I could sort of float on top of 43kg per hand, but it isn’t enough resistance for me to try to balance on it. Within the limits of my fraidy cat nature. I get hurt a lot, so I try to avoid getting hut though I’m apparently not very good at that. It isn’t so much that I get hurt, but that I break in ways that take years to get over. Again, maybe I’m not good at getting over hurts. Maybe the structure remains, like betrayal as a label for an imaginary outcome in which you talk about the opposite, which we might call fealty because that states the concept of an oath freely given at a high level, at the higher level.

I’ve never thought that in that way before. And yet I constantly hear dialogues about this very thing, like how the less you want violence to be real, the easier it gets to imagine any form of violence because none of them are then tainted by association with real violence, where the taint is in you as Actor because association with real violence is obvious at Observer levels. Like how boys found dead baby jokes hilarious: we couldn’t imagine doing that, which is different from not being able to imagine dead babies. To young boys, that these are separate is obvious because at their Actor level, they were. And still can be, except now it’s necessary to explain why they’re funny.

I cannot believe I lifted 265, even if it’s a machine with my feet planted. And to realize as I was doing it that I was seeing how the tensioning method works: it creates structural potential and you can then fill that potential. The structural potential is literally what your body can manage, and that increases when it has to resist being pulled apart because then it is resisting external forces. I pull out the obstructions to movement in my muscles and joints, and I twist and turn to expand my range of motion and to improve generally, like by getting into better positions and then exploring how the ideal functions. Note how ideal is redefining to refer to what is generated by SBE and other gsCounting terms by linking it through the work of Kummer and others on ideals.

Should there be gsIdeals? The difference is that gsIdeals are created within D-structure, and ideals in number theory are one expression of that because number theory is a slice of 1Space gsCounting. So yeah, that fits the criteria for gsNotation.

I was up at 5AM and had visions of interlocking circles until I figured out the idea was to look at the versions to see how they could exist. One is that you take 2 Ends and you make circles that touch at the midpoint. This creates the Bip circle which touches the 2 Ends. Easy to see. The other is when these push together, so the Boundary of each now touches the other End. That means a Bip circle develops which connects both Ends, as before, so now we see overlapping Boundaries with a Boundary connecting the central Ends of each. That’s harder to see in the dark, especially when it keeps squirming. Then a solution appears, which is to layer the second, so what appears to be within the Boundary is in the perspective where that is true, but not in every perspective because you can tilt the view to show they’re in different layers. Ah, to resolve on the axis of invisibility.

How can I feel so close to you and so far? Why are we bound by these rules? That’s the issue with the free will arguments, that it depends on the level or the gsScale, which I believe we once notated because we use scaling so much and gsScaling includes Mag10, which includes all the various gsCounts to reach base10, and other bases like e and Pi as those scale, as well as fCM measures like Thing+.

BTW, before I try to talk about 2Square and betrayal as Storyline which makes the fealty Storyline meaningful, I need to say that o I forgot because I saw that fealty is front and betrayal is back, which makes the point that the 2Square contains these because you can’t have f without the storyline of b.

I’m sitting in a restaurant and a guy is watching TV on his phone at full volume like no one else matters at all. And here we can explain self-centered behavior.

I remember talking about shedding negatives, that any positive step, meaning in Alternation, would then often immediately reveal negatives. I couldn’t then see how these generate as expressions of the negative storylines which positive storyline steps obviously generate when you see this as occurring within the 2Square construction, which remember twists to and from 1Square, and isn’t it cool that every day I think this is the best work yet? Putting this together rings a lot of bells.

This addresses, at least partly, my recurring fear of being lied to, including for my own good. And I can see that part of the response is how that represents not being treated as equivalent, which doesn’t mean equal, like I wasn’t expecting to be equal to my parents, but which has come to mean gsPaired, like in that case information exchange and thus honesty was lacking, which is the same to me as dishonesty. You’re the only you I’ve ever trusted, and that has been a process of deciding, step by step by step, that accepting you as you, by which I mean as the enclosures, is the pathway to understanding and fulfilling, is the pathway to the best good and good best in eternity, is the way to a 1 which enables positive, cooperative and simply better outcomes.

It’s interesting to see how this fits to economics because we can see the argument for capitalism is that the market should determine priorities rather than government. And it’s interesting to see how capitalism has issues as an organizing social principle, especially in a dynamic internal environment, because no system can allocate properly when stressed. So they tend to respond only to stress. This is all at the off the cuff level, but the math is there. An example is the conversation I had today with this nice guy who deadlifted 500. We talked about how quickly you lose the technique at the edge even though you know that technique at less demanding levels. And how focusing on technique so all the pieces align properly makes the weight feel light, which is true because all the other focus saps energy and reduces the ability of the body to do the work. This extends to the weird adrenaline driven feats we hear about.

We have the math for that kind of focus and for the ability to recruit the abstract elements to get the absolute most generating into the immediate frame to lift that weight off the child.

I wonder what happens now that I have a frame for b-side narratives? One thing I’m seeing is that these b narratives cluster, which says they are only a few Ends deep, like any count of storylines, meaning this is [n-2(n-1)], and anything beyond leads into another Storyline because then the b-Storyline is the front. That’s interesting because that identifies the Alternation very clearly.

This must be where the ancients saw things. You realize the story is different if you caught the animal versus not, and that roots to the 2Square where the event’s potential occurs. Again, extraordinary work.

[jonathankatwhatever]

It’s now day of 25 July 2025. To refresh my memory, we used the concept of an orthogonal Shard whose base is a Fano plane or something similar. What I’m seeing now is each face being that, like when we discussed the 3 and 4 pyramidal forms, so it generates a central End, and thus a sphere within the Shard.

That sentence took a bunch of mental twisting to get out. Felt like a lot of work in not many seconds. Took a lot to relax to accept the consequences of scaling. The big shift is going from bT to fT, as we realized when we did the notation way back when. So you can see at work 2 of the main ideals: H/D and SBE. The H/D appears when we invert the bT over fD or over HG. It’s like they fold over each other, which of course is FoldOver and front&back, so you can see a sheet of Triangular as having the orthogonal potential of being stuck together f&b, and thus as having come apart to the states we see in the sheet of 2 bT. One is across a Hexagon, like in the classic pairings. The other is over a Hexagon, meaning fD forms with a Hexagon Between. So scale here has the consequence of separating the bT inversion pairing by the same shape, orthogonal again, in which the inversion has a Boundary Between and within Triangular.

This may read easier when you think in terms of ideals because we can see factorizations emerge. Let’s say for example that we have a folded up something or other, and we unfold it and that generates these 2 because they were stuck together f&b or are inversions which require another flip, which means complexity and Boundary, as noted at the end of the paragraph above is a consequence of scale.

Having trouble focusing. The idea coming to the surface out of the maelstrom is the back page of Mad Magazine had an impact because you folded it to make a different picture. The pieces had to match, so the creases aligned vertically in the correct places made a better join to make a single image shift from one to the other out of the two contained in the 1, meaning we went into a subset. That can happen now.

I need coffee. All the pumpkin has finally given the cat loose stool. Took weeks. And now it’s time to back off. I don’t understand how the color didn’t change until now other than that there’s been an acceleration. The idea was to treat the opposite problem, that it took too long and you could see his poop was dry, no matter how much water he drank. So I tried to reach this end, by adding pumpkin and water to his wet food so he might be ingesting more liquid with his food. But the main idea was to accelerate the process so he wouldn’t go into a poop frenzy with multiple trips to the box trying to get it out. He had an accident last night, so he’s on dry food today. Will add wet but no pumpkin later.

This is part of the basic point that nothing can exist as a Thing in D3-4Space without a 1Space model of it existing. That’s a fundamental existence statement. A 1Space model is like the idea of the spaceship you want to build together with all the process and all the imaginative play which Attaches to the processes which Attach to the concept of the Thing. This can be stated in a number of equivalent ways, at least on the 1Space side. The relationship of 1Space to 0Space is through the forms of gsProcess captured or rendered as irrationality, from 2Square to transcendentals. That last links to e and Pi.

I took some time. Made a hash with some old potatoes. Worked out. Letting the process of Acceptance develop from when my notebooks first record the idea. Acceptance in a rigorous sense is the minimizing of the space which separates f&b, which occurs in construction, which means at a depth and with a depth. Example at the tip of my perception is the CM64+CM2.8 construction of a Thing with the next Thing being binary choice to either side of the CM28 one level away.

Did we ever get full understanding of Planck’s constant? Why is the additive term between 22 and 23? The solution would be that it Attaches to 24, not to 28, but at n-2 and then if you round then n-1. That’s it. I expected more drama, but n-2’s enabling of the 2Square means that rounding to n-1 generates Things by how it rounds, which can literally be how deep you count. That’s a cool thought.

So can we say that is why a photon’s energy is frequency times that? That this generates to D24, meaning to the lattice, and that generates to a core with 196,500 touches. I think we can visualize that as an nK-gon with the lattice balls arranging thusly across their Boundaries. This is done in stacks, so there are incremental relationships which aren’t fixed. The power of the ideals when viewed in the Observer perspective includes zoom, and zoom where choice occurs, where each zoom in or out is a new arrangement. Like hands from a larger deck which expands where you look.

That’s pretty straight-forward, with no great leaps other than Attachment, where we’re constructing a CM64 Thing together with this CM22-23-24 construction that acts as SBE across the count to relate n-2 to n-1, and thus non-specification within an enclosing frame or basis or CM1 grid, and specification. And it does that by defining that which is Not because this is CM36 inverted, and CM36 is Not the Thing, meaning it is ready to couple with what defines a Thing, which is what a photon does, as we can see because they are absorbed and emitted, and thus we’re saying they carry information. This is why a flash of color can mean you’ve found what you’ve spent years searching for: they carry the ability to Attach to make a Thing. So you can see a slight tinge and know means that tinge is visible, and that it carries the meaning of its source so you can Attach to that meaning to make the Thing which combines 2 into 1. Need D24 for that.

I don’t think it will be difficult to find time to work.

The ease of understanding now is nice to experience after so much struggle. Now I can take years of work about e and think to myself that it’s half a quadrant’s L-counts to make 2, so 1 + this 8th, which is then ambiguous always over the szK, assuming we’re doing this in ++. You can thus say this way is getting smaller and this side is bigger, using the same gsProcess, with the results of the whole grid processing to the appropriate side of the szK. This is a ridiculously simple construction with vast power. It is not difficult to visualize: imagine CM1 as a whole grid and then imagine the - - quadrant as 1. The rest is then take ++ and say the top half writes as bigger. The alternative is also good: write the smaller, meaning the negative exponent or inversion, as one of the - - quadrant sides, probably the lower because then you have a neat diagram containing both with only diagonal apparent conflict. That fits to the exclusive state conception within 0Space, that selection has to occur so D3-4 renders completely enough. Like you can think you saw the train hit that person but it actually just missed. You can be convinced but that doesn’t make it true if it is not true in D3-4. We went through this before as D4-3 existences, which are iObject-rooted, smashing into D3-4 Things. They’ll rewrite what happened as though that rewrites what happened.

[jonathankatwhatever]

It’s about 4:30AM on 25 July 2025, an auspicious date on the surface. I am hearing the Fano plane demonstrates [n-2(n-1)], where the outer Triangular Ends are n-2, and the n-1 End is the CR of that inverting bT. This means we’ve identified where a Thing appears, because now that Boundary exists within the D3 of Triangular.

That raises a few questions. One is how does this D3 translate into D3-4, and the answer is the Shard and the D4 inherent in the Observer to Triangular. Note that this orthogonal relationship idealizes in 2 ways, one being this form of gsDrawing and the other being that if you are counting across the Thing, meaning in the flat projective sheet, then any step from the Boundary to the center End to the Boundary is 1, including reflection. That’s the endless fascination of Narcissus, that the 1 reflects and all the meanings of that 1, of that reflection go all the way around in loops which match a specific number form. What is that called when you take a rational and stick on a complex root of unity because that makes a loop for any gsCount. Makes loops. Cyclotomic.

That leads to Bernouilli numbers and Kummer’s congruence, and these make sense. But I don’t have the energy now to translate. So Narcissus is cyclotomic, stuck in the loops Attached to him. Think of the Attachment as orthogonal, and you see the relationship. Yet another reason we once tried using gsOrthogonal to give Attachment some notation. Here we have along the orthogonal. And we saw where the projective sheet CR’s.

Note how this extends to D5, and how that works directionally because you can’t little hat tObjects but you can iObjects and that leads to Taylor series because all that stuff, which you can find in the concept of ideals, so we can say we are taking the concept of ideals and doing dimensional constructing with them, thus giving us a solid algebra foundation. I’m running through understandings and need to go back to sleep. We can literally say what ideals translate into, including identity forms.

[jonathankatwhatever]

Continuing on 24 July 2025. Continuing to try to express Coordinate Rotation so we can accept it. The visuals are stunning, and seem impossible to put into words. How do you say you see a giant trail of frames flicking like cards because we’re at an angle to the presentation, not straight on where you see the card faces as centering differently, which has the effect of absorbing you more as Actor than as Observer, so assume minimum Observer distance, which we postulate exists in Triangular using 1-0Segments. The proof for that is that this establishes an Observer relationship in which the other Ends are gsPaired. This generates equal pairings around the Triangular, and that manifests into an Observer over this entirety which thus necessarily ties to manifestations within the entirety, meaning gsPairings between the other Ends, whichever those may be, seen and mediated by the Observer.

O I’m starting to see it. Fascinating. Absolutely fascinating process going on. Look at how this works with you looking at something abstract, like an event to come, then this establishes the 1Space Triangular connection of Observers to that. But before that came, there was a glimpse of this linking to CR through the shifting of the Observer in any Triangular. That gets back to the Fano plane.

What about gsConstruction using this idea? Like take that Triangular, and construct fD and HG, so it exists within Hexagonal, which exists within the Fano plane at that level. That’s good, but now we have to take the Irreducible and that locates the corner End which is the Bip End in the inversion of CM1. Don’t skip ahead. O-kay, so we have a + of crossed 1’s. That generates a layer of gs over the entire 1 of each, making the special case of a gs out of all the other cases possible, so that’s a layer of 4 within 1. Then it extends along an Extent so there’s the Irreducible Extent.

Note the old or Eastern cross versus the f1-3 version of the Western.

This is largely gsConstruction at the fT level, but I needed to see it.

So we see the Boundary emerge in the construction of the Fano plane as one of those cards in which the value either stays the same or changes, when seen at specific intervals, and that gives me the handle: CR is like showing all the moves the magician makes in slow motion when you can’t see them at all until they’re shown to you. Or like a movie if you couldn’t cut any takes and had to use them all so you see the final scene some other way, like maybe being the last of each set of takes. CR represents all of that because that rotation of the coordinate system itself constructs gsPairings over what might be construed as gaps.

That really is the deep dark secret, that identity constructs over gaps because Triangular constructs. And look how that invokes D6 and higher, and think about how much identity is in an fD, and thus in a gs. Let’s count: each Triangular at the fT level, at the Fano plane level, contains a Boundary, so we have a minimum of 2 and 2, constructing the 2*2 matrix of course, where we can see the construction of a 2Square as the choice coming out of that 4Square to 1 being 1+4+1 counts to 5 and 6. You can see how well the 6’s relate in what appears to be the orthogonal, with that stacking of states being a 5 and 6 versus the counting out of 6 within the Hexagonal which is within the Boundary. Wow, that means we can see how matching energies works or even how hits and misses works because now each Triangular has this identity in it, and that scales, repeat scales, so we just managed to stuff CR into Triangular, and specifically into both Togs and Tigs.

This has been extremely educational. I truly had no idea that was the answer. I think we need to discuss this in more detail because I’ve been noticing this same stage occurring in other areas. Example from today is I heard Sam Cooke and immediately did his vocal style by locating my voice there, imitating until I made it sound right - sound familiar? - and I realized I saw that happen, that I saw myself shifting the muscles, shifting the ear, shifting the voice automatically producing a reasonable replica, and then starting to listen to that closer as the technique developed itself more, as I became more comfortable with singing in that voice. I haven’t had thoughts like that since I was a child when imitation was incredibly natural.

So the solution was to see the problem at the fT level rather than the bT level. Note how this encodes identity in the inversion of the central bT of an fT. I just realized that we omitted - I omitted - the connection between the fT and the Fano plane because it sparked over the identity exactly as we’ve described, so I read the connection existed without saying what it is. An fT is composed of 4bT with the 1 inverted, and the Ends of those are the Ends of the Fano plane minus the center, so what this does is take the inverted bT and spins it, CR’s it. We worked that out long enough ago that I didn’t have it handy, and not so long ago that I had to recreate it, sort of mamma bear’s porridge distance.

So we have 3bT and an inverted bT, and that translates the basic bT arrangement into an fT where there’s a direct, explicit inversion relationship between the core, that inverted bT, and the bT which connect as Triangular, whether in fT or Fano plane, showing the Boundary form.

Ain’t that a kick in the head? I remember we’ve been here before, but wow it’s something to see: identity in the enclosing Triangular is inverted. That means we have to go there: imagine we take the separated inverted bT and stick them together, and that makes the gs because now we have all the gsProcess of inversion involved in determining identity. And this is true, though we need to say how it inverts inner to outer and outer to inner. We can see it on the Boundary. We can see it build as Boundary and maybe now this might be the missing piece, that this Boundary translates on the outside. We can see the calculation, as in Alternation, maps the connection of a center to the Boundary because that is the 1-0Segment doing CR around itself. That’s one reason the gsConstruction using that + works.

And that’s why the approximation concept is necessary. We need to be able to approximate circles, spheres, curves, etc. because our reality processes at a rate which requires that, at a rate which is continuous and is tied to the Informational Limit because that organizes by Attachment to gsProcess which assures continuity within 0Space, and within the IL.

Can we put that together in the next minutes? Seriously. When this runs over, I see a conclusion forming which describes why the Boundary appears within 10Square. We have described it before: the 10Square is the fundamental (1+(SBE3)+1) generation of base10, plus of course the 2*5 form which combines H/D with the 4+1 count of IC. So within base10 is the boundary+pattern, but as a side. We spent a lot of time working on that, and I don’t remember a conclusion. The pattern is specifically a reduced Thing coming out of or going into a further reduced choice of Thing. That makes sense, doesn’t it? We have then 4 cases: we have either or both sides be just root10 or the pattern adjusting. That’s an IC with meat. Think about it for a second and then you can stop for a bit: an IC in which 2 of the cases are the Boundary with process and 2 without. That seems perfect.