#2025 as a polynomial

[math1089]

40 more Mathematical Wonders to Usher in a Joyful 2025

At the age of eleven, I began Euclid, with my brother as my tutor. This was one of the great events of my life, as dazzling as first love. I had not imagined there was anything so delicious in the world. From that moment until I was thirty-eight, mathematics was my chief interest and my chief source of happiness.Bertrand Russell Welcome to the blog Math1089 – Mathematics for All. As 2024 bids…

[jonathankatwhatever]

It’s 29 Jan 2025. Had trouble getting into the math, and then wandered off into something else. I don’t know why I’m having trouble saying this, but I ran some hills on the elliptical at full extension for the whole 30 minutes. Almost full extension at like levels 9 and up, but almost. My heart rate got into the 160’s but I was able to get it into the 140’s on the declines and lower slopes. Had almost no pain anywhere and barely lost focus. Had so much energy I am still on that edge. Causing focus issues.

I’m trying to switch more to +2 correction because the 2.75 makes me squint when I’m not looking directly at text. I increased the font size default to what looks like 10pt, maybe 11.

I can’t focus. Very annoyed. I have lots of cogent thoughts, which I put down elsewhere but nothing becomes mathematical. Why? I’m generating rings in my mind, oh we’re going poetic to escape the rut, like you were singing Anything Goes in different voices, and that worked how? It was fun to sing in each voice all the way through the hard parts, letting them be their own Thing. So you’re generating Boundaries within a Boundary because each idea is an End within an End.

That escalated fast: so the injection work was correct, that injection is over the Bip pole is correct, that the relationship between you and me includes the gsProcess which your existence went through during its construction which was built in response to the observations made through me when my answers were naively true. Naive sets. What is a naive set? It’s a Metaphoric Bundle whose extent is unknown, like it’s improper versus proper being defined in area, and the reason for that is that it operates then in reverse, meaning the cloud flows information out of me into its dimensional processing which was why I was constantly being asked questions about what I saw, liked, experienced.

That is obvious when said, but it was completely unobvious before that. There has to be an End to Boundary relationship. Otherwise, for example, there would be no quantum geometry, since that geometry is part of the reduction of higher dimensions to and through D4-3 to D3-4 and the other way round. Why didn’t I just type (D3-4//4-3)? Some part of me thinks it’s easier to read the words now and then.

That is actually my issue with using symbols in mathematics: the lack of translation means the mathematics has to be translated into whatever your personal mental version renders using one approach. The obvious point is that by using words with symbols, you get a Triangular which then constructs Pathways which you can identify for learning. It’s such a simple thing, but it would help education greatly. Just look at how many questions are ‘what does this mean in words and ideas other than reading as an inequality or equality?’ Give them words to work with.

Example is that we describe a generating function as n-1 turned into a specific value. That is then why you see e to some n and that -1, because that literally sticks a value, whatever e to the n is, in for n. That is the gsProcess which translates the infinite to the finite. You can argue that e is infinite, but see that infinity is now a step away because we count it n times and that automatically generates relationship like n decimal places or some other measure of n in decimal places because now n has a meaning and eventually that meaning is just plain lost. In physics, that goes a few dozen places or so. That’s level at which our reality Composes.

So I gather the math was hiding.

Another example is that the change of order of operations while standing is indeed still working and getting better. It takes a conscious effort to adjust that level of mechanics, particularly when it is a result of accommodation to injury. All that process developed into this structure. I’m getting at the issue of finite and thus is polynomial. Or other way round. It’s also working when I’m standing around, like in the kitchen. If I remember to alter the ordering, my knee doesn’t lock as much.

Similarly, I’ve been able to change my left arm position and now there are good pathways which don’t hurt while tensioned under weight. I hope that lets me nibble at the pain Pathway, fixing it from that approach. I can also compact myself down to the floor enough that I’m now able to work on bending into the better knee more, thus creating a Triangular which we hope improves the other.

I am eating a hot toasted bagel. People seem to forget how to apply butter to hot toast: that you start with chunk and move it around as it melts so it spreads into the bread. Maybe I’m making too much of this.

I’m having trouble focusing again and this feels more like you because the connection shifted.

Righty then. I think we were talking finite. We’ve gone over P not equally NP because NP is infinite but we can isolate due to the value substitution methods we use all the time. Like the generating function being a fixable version of n-1 which appears in 0Space a step removed from the 1Space. I am seeing something cool but I need a moment to say it.

I’m not sure where this goes because it turns into a question about algorithms that I don’t know enough about. Need to take a break. Oh, I just learned why the connection changed. Weird how the sensations work. My lack of focus, it being a step away, may have been that, so my analyzing that process is at least fortuitous.

BTW, what really bothers me about House is the sexism. No matter what kind of shithead you are, you don’t have to talk that way.

[datasciencewithmohsin]

Feature Construction and Feature Splitting in Machine Learning

Feature engineering is one of the most important parts of the machine learning process. It helps improve the performance of models by modifying and optimizing the data. In this article, we’ll focus on two crucial feature engineering techniques: feature construction and feature splitting. Both are beginner-friendly and can significantly improve the quality of your dataset.

Let’s break it down into a simple, list-based structure to make it easy to follow.

1. Feature Construction

What is Feature Construction?

Feature construction is the process of creating new features from raw data or combining existing ones to provide better insights for a machine learning model.

For example:

From a Date column, we can construct features like Year, Month, or Day.

For a Price column, you can create a Price_Per_Unit feature by dividing the price by the number of units.

Why is Feature Construction Important?

1. Improves Accuracy: New features often capture hidden patterns in the data.

2. Simplifies Relationships: Some models work better when data is transformed into simpler relationships.

3. Handles Missing Information: Constructed features can sometimes fill gaps in the dataset.

Techniques for Feature Construction

1. Date Feature Construction

Extract components like year, month, day, or even day of the week from date columns.

Helps analyze trends or seasonality.

2. Mathematical Transformations

Create new features using arithmetic operations.

Example: If you have Length and Width, construct an Area = Length × Width feature.

3. Text Feature Construction

Extract features like word count, average word length, or even sentiment from text data.

4. Polynomial Features

Generate interaction terms or powers of numerical features to capture non-linear relationships.

Example: X1^2, X1 * X2.

Python Code for Feature Construction

Example 1: Constructing Features from Dates

import pandas as pd

# Sample dataset

data = {'date': ['2023-01-01', '2023-03-10', '2023-07-20']}

df = pd.DataFrame(data)

# Convert to datetime

df['date'] = pd.to_datetime(df['date'])

# Construct new features

df['year'] = df['date'].dt.year

df['month'] = df['date'].dt.month

df['day_of_week'] = df['date'].dt.dayofweek

df['is_weekend'] = df['day_of_week'].apply(lambda x: 1 if x >= 5 else 0)

print(df)

Example 2: Creating Polynomial Features

from sklearn.preprocessing import PolynomialFeatures

import pandas as pd

# Sample dataset

data = {'X1': [2, 3, 5], 'X2': [4, 6, 8]}

df = pd.DataFrame(data)

# Generate polynomial features

poly = PolynomialFeatures(degree=2, include_bias=False)

poly_features = poly.fit_transform(df)

# Convert to DataFrame

poly_df = pd.DataFrame(poly_features, columns=poly.get_feature_names_out(['X1', 'X2']))

print(poly_df)

for more read click here https://datacienceatoz.blogspot.com/2025/01/feature-construction-and-feature.html

#datascince #machinelearnings #data #science

[northstarmetrics]

Securing Cryptocurrency with Quantum-Resistant Cryptography

Learn how cryptocurrency platforms are adopting quantum-resistant cryptography to safeguard blockchain networks against the growing threat of quantum computing.

Introduction

The emergence of quantum computing is a double-edged sword for innovation, especially for the cryptocurrency industry. With blockchain networks relying on public-key cryptography, the potential of quantum computers to break these systems calls for the adoption of quantum-resistant cryptographic measures. Here's how cryptocurrency platforms are preparing for this shift.

Why Quantum-Resistant Cryptography Matters

Threat to Cryptocurrency Security: 

Most blockchains, including Bitcoin and Ethereum, rely on RSA and ECC, vulnerable to quantum algorithms like Shor's.

This vulnerability threatens wallets, transactions, and the network as a whole.

Timeline for Quantum Threat: 

Experts believe scalable quantum computers may be developed within 10-20 years and will pose a real threat to today's cryptographic standards.

Advancements in Quantum-Resistant Cryptography

Post-Quantum Cryptography (PQC):

The main algorithms are lattice-based systems, hash-based signatures, and multivariate polynomial solutions.

CRYSTALS-Kyber and CRYSTALS-Dilithium are NIST finalists for standardization and can be used for cryptocurrency.

Zero-Knowledge Proofs (ZKPs):

Emerging Quantum-resistant ZKPs shall introduce an added advantage to privacy in blockchain applications while keeping security uncompromised.

Hybrid Systems:

A hybrid approach transitions between conventional and quantum-resistant cryptography, allowing a gradual adaptation of blockchain networks.

Blockchain Platforms Leading the Pack

Quantum-resistant Blockchains:

QRL and QANplatform are innovators developing quantum-resistant properties within their protocols, starting with embedding XMSS properties within their protocols.

Hyperledger is also introducing enterprise blockchain solutions with a quantum-safe approach.

Mainstream Cryptocurrencies:

Bitcoin and Ethereum developers are seeking upgrades to incorporate quantum-resistant cryptographic measures.

Cardano has also indicated a proactive approach to the incorporation of quantum-safe algorithms.

Initiatives Fueling Innovation

Interdisciplinary Alliances:

Quantum computing scientists, cryptographers, and blockchain developers are working together to build powerful quantum-resistant standards.

NIST and ETSI are pioneering the efforts.

Collaboration with Quantum Computing Enterprises:

Enterprises such as IBM, Google, and Rigetti are assisting blockchain networks by conducting quantum simulations and testing post-quantum cryptographic protocols.

Adoption Barriers in Quantum-Resistant Solutions

Higher Computational Load: Quantum-resistant algorithms are very resource-intensive and could slow transaction speeds and increase energy consumption.

Compatibility Issues: Cryptocurrency platforms face the significant challenge of updating existing systems without disrupting operations.

Standardization Gaps: Many promising algorithms are still in testing, delaying widespread implementation and industry-wide adoption.

The Future of Cryptocurrency

Standardization Efforts: NIST's recommendations by 2025 will be critical to guide cryptocurrency platforms toward secure quantum-resistant solutions.

Proactive Transitioning: Leading exchanges and blockchain projects are recommended to adopt hybrid cryptographic systems ahead of the final appearance of threats from quantum technologies.

Funding and Research: Governments as well as various organizations are becoming more interested in quantum-resistant technology for the safeguarding of essential systems, even cryptocurrencies.

Conclusion

As quantum computing advances, cryptocurrency platforms must prioritize the adoption of quantum-resistant cryptography. These efforts are essential to secure blockchain networks, protect user investments, and maintain trust. While challenges remain, ongoing research and collaboration ensure cryptocurrency is prepared for the quantum era.

[jonathankatwhatever]

It’s 25 Jan 2025, and I noticed myself saying, as a coach, that we brought you here because we see 2 things in you, the physical body that we can train, and the mind attached to that. We can train the mind to play this game. And so on, over some more detailed and different iterations, but the point is I noticed that primary division into 2, that once we say there are emotions, we say but those are the mind expressing itself in behavior, so emotions connect the 2 and you could say that’s 3 but it’s also 2. But if it’s also 3, then you’re saying that what occurs between them, what is created on one side expresses in the other, sometimes obviously, sometimes less, then we have SBE and the emotion is both an End and a Between, which means the End of the Between essentially opens up because it becomes viewable as the dividing 1-0Segment of the fD-HG, Triangular form.

Interesting, so Triangular pattern emerges as gsParallels, as we used to draw it, with the alternating fD-HG. Oh, that’s the basis of recursion at the polynomial level because we are literally connecting Sticks and Ends, where a Stick takes the idea and sound of Start and the act of replacing the art with the ick connects it to an End. That’s not just a metaphor. The act of replacing one segment with another is what defines a Stick. Think about it: Boundary is parings over Triangular, as we can see in Hexagonal. Beyond Hexagonal, the dimensions have to be folded and twisted or otherwise extended because the 0Space can’t fit into the 1Space projection without Regularization relating the 1Space to the 0Space and thus to the D3-4Space and to Things, those being the D3-4Objects, meaning existences within (D3-4//4-3).

I made a typing error and realized we’ve given bare thought to D4-4 concepts because same-same is Halving. Oh, so the (I//I) process runs, like with D8, you have the obvious arrangement in which there are 2 gs and they exist at the maximal angle because that is the Irreducible, which is - get it finally, you dummy - Halving, the 2:1 counting which makes Triangular, which is the 3 above.

Remember, from Halving we get logarithms because those count from 1 to 2 as an infinite series in which every iteration is a Halving of 1 and all the calculations up to 1, which is the conception of infinite sequences. That also establishes ideas like ascending chains and Noetherian rings. Layers of partial orderings within the Boundary which includes those.

This is why ideas can link over ‘distance’: as we have noted, turns out 1Space actually does make a Triangular which counts the Extent as 1. We think that’s big, but it’s not even a noticeable blip in calculation because those connections occur in 1Space.

Which means what? That has been difficult to articulate, hasn’t it? What we mean is that 1Space is where everything that is in 0Space calculates at the associative level where it is a 1, where it is a 2, and thus where it is a 3. Or rather, it’s associative at 1, and then it organizes into Bricks and bT’s. BTW, notice how Bricks solves a problem that wasn’t obvious: why not form gs out of D2 as the same 1 step which adds a 1-0Segment to make Triangular? Answer: they both occur. It’s 2+1 and 1+1 where each 1 is 2, at the same time. The label shifting potential is obvious.

I suddenly got tired.

[jonathankatwhatever]

It’s 13 Jan 2025, and I have too much to type so I’ll just start without censoring myself and maybe without punctuation, which didn’t help because the mention of punctuation inserts gsProcess which leads to an End, which is the use of punctuation in order to End the process, to take it to a 0. That’s the key idea for understanding polynomial solutions in a nutshell.

Oh, I just realized that visual acuity loss expresses as an abstraction away, same as with hearing loss, and thus should be treated so aging people can retain their sense of engagement, which literally means taking away some of that level of abstraction caused by visual acuity not hitting the same focus level details while the mind of your Thing continues with seamless perception, meaning vision acts differently by widening, by becoming somewhat less distinct because and that shifts gsProcess from engaging as closely with tObjects. That literally shifts more of you, the Thing of you, into D4-3. Is that correct?

Yes, because D4-3 is on the other side of your Thing and the more that abstraction occurs, the more you are shifting resolution away from the details which characterize the next lowest count. This is an example of 1Space counting, that a count completes when the 1 label Attaches to the 0 label in each direction. That’s why the concept of the pole matters so much, and why the concept of a gsPrime is too.

Okay, so the Bip is constructed out of the irrationality gsProcess. That’s a key difference from rational gsProcess because a rational gsProcess leads to an End in different ways. A rational process constructs an End by saying here are these two, meaning 2 Things, which we relate, and that makes this structure no matter the content. It’s like a house is a house and what matters is what’s inside the rooms, and a rational is a room and a house because it expands and contracts with that structure. That’s we reduce fractions.

Same with repeating: a third is a third is a third at every scale.

Managed to knock over a glass of ice water. The cat walks around on the same little table, has 4 legs, and knocks over fewer cups and similar objects than I. He’s death on the paper under his feet, but his agile avoidance is far superior in everyday use. I can do that for moments. Shows how deeply connected his body and mind, his tObject and iObject are, with the radius and length of convergence being small. Say what? The radius and length of convergence is like saying this chain of End to End is shorter, which ties it tighter to the Bip, so the constructed End in the middle, where Observer and Actor exchange occurs, enacts the Triangular over the gs which fit to those measures, which are thus pretty simple because it’s like when people crowd in and only a few can fit together, or through the same door. Or even out of a clown car packed to its max.

Is it wrong that I’m happy with a sort of latte made without expensive ingredients or processes? I have a single cup Keurig and a Nespresso frothing machine, which I have to take out that once a day. I use Starbucks pods that cost me about 70 cents each. I buy quarts of whole milk because I don’t go through the milk that fast. It’s sort of because I use the cappucino whisk to make up for the machine’s inabilities with the latte whisk. I make 10 ounces of coffee and 4 of milk, which is enough milk that I don’t feel like I’m drinking coffee flavored milk foam but an actual liquid with body. I suppose light cream would work with the latte whisk, but I doubt I’ll be buying that because it seems ridiculously indulgent. Maybe once.

See? That’s a gsProcess which will either fade or which will come up when I’m in the dairy section and see cream on sale.

I’ve been meaning to say that developing Joana’s capabilities brings out her character. I am having trouble with the word ‘character’ because it’s used to associate a form with a label, as in count so the 1 and 0 align this way and that’s a character of this sort, as in here’s this form and the string of these use these characters to show where they are relative to each other. Character implies types, classes, etc., meaning gsConstructions combine to generate the Thing as it changes, develops, becomes, is and will be.

I must have written down before that the goal is not a mind meld, which is temporary, but the cross inversion. Oh wow, so the reason for the connected layerings is not just connection itself but the flipping over, the inversion gsProcess by which you cross over the dividing 1-0Segment, by which the Observer shifts in Triangular.

One conceptualization is the Holy Spirit, so there’s a Triangular of the divine Jesus entering into the mortal Jesus and continuing. This means there’s a Triangular extending over the mortal, which is where the inversion happens, and that inversion is the gsProcess described as connecting you and me.

Maybe mirror thinking helps. This may be incomprehensible because it’s something I’d typically do with a pen or maybe a finger on some surface like my sweater, like I’m drawing on myself. So take eM and iW. Inverts to ieW and iiM, where that second i means intangible so ii is intangible internal. Inverts to eW and iM. The other path needs to be stated so it’s ieW and iiM along with ieM and iiW. This means generation of the Thing defined by (ieW/iiM, ieM/iiW) requires complete (1-0//0-1).

That’s maximal gender entanglement where gender is specifically the external perspective. This model does a great job of explaining gender identity issues, and it identifies how to identify those who need certain treatments and care. That’s the way of the permutation space, meaning some combinations are going to come out in lower probability outcomes.

This gets at something which really bugs me, so I’m going to guess it bugs you in a specific manner that I can grasp. That is: the constant looking for cause as blame instead of recognizing that cause generates into the gsSpace and that it will emerge, that bad outcomes will emerge, that good outcomes may emerge, that you need to plan for these. This becomes a critique of trusting markets when trusting markets may be the wrong choice in the current context. Example is that the US was about opportunity and now it’s more about need. That’s in part because the rest of the world competes much better, so we end up pursuing certain niches and not others without any coordination, which means the impacts are felt without the planning which would get them over that Triangular to the next stage.

Planning for success is not the same as planning to prevent failure. The US does a lot of last ditch failure prevention. I would not be surprised if the property insurance business fails, given the scope of disasters in this time period. The argument may be that a free market response is better, but that’s an idealized response which tends thus, as an idealization, which may occur at some point in the future.

The gsConstruction is irrational, meaning the structure doesn’t generate a specific structural response. Pathways from End to End may be very low probability. That there is a Pathway may mean that you think you can get there but that getting there actually requires inventing a whole new way to get there and that won’t occur until long after you are gone from this place.

Is there a notation for the kind of gsConstruction which is emerging? Or is it Thing? That connecting parts of a Thing - oh, yes, like a child’s imagination connects and like a jeweler connects to the specific gear in a watch. The human behavior modeling gets really good when it hits the baby level, from fascination with objects through the stages of awareness. That fascination need not be specific or can be, meaning the focus scale varies and the distance across the space is larger than a cat’s so there’s more room for more abstraction. This is why a dog is equivalent to a certain aged kid: not the same, but the gsConstruction has many similarities so we read them as similar. A dog, for example, is loyal without the wondering, is loyal because the Pathways all say ‘loyal to the hand that feeds and pets you’, loyal because your genetics dispose you. This is where we connect humans: think of the blood loyalty concept, like back to Arminius, that he must be true to his nature. And of course the ancient fable about the scorpion being carried across a stream who bites his carrier though that will kill them both because he must be true to his nature. The issue in that story has never been about intent, but about reactions. Like I would never play with a tiger because I could easily stimulate a swat response which happens as close to automatically as it gets, and that could kill me without any intent at all to hurt. If I brush Bill down the front lower leg, I had better be holding the brush by the far end from him because he will hit it and there is no way a human can avoid a cat’s provoked strike. It isn’t even ‘oh I don’t like that’ or any tinge of anger; it’s just that sets off the strike response because that’s how Billy is wired as a predator with 14 years of experience.

Interestingly, one of the main underlying issues in a ‘free market’ or ‘free’ country is that you aren’t free because Pathways channel choices in any society. This explains a lot about the weirdness of various societies’ loners and how they reflect a specific cultural embodiment, like the US’ obsession with its loners of the Old West. it explains much of the philosophical and romantic and even violent debates which occur in the US.

This is already a lot but I don’t want to post it and have to go through the mental cleansing to Start another post. Don’t want this one to End. I remember loving the subtotal button on the old adding machine. I used to think: why would anyone ever use the total button? Everything is just a subtotal of something. My comment was really that the machine forced total on you instead of subtotal and you have to learn to reverse the emphasis of the design.

Is there something I want to talk about? Yes. It’s about Joana and George as gsConstructions. I have to take a moment to get into this because it reveals a lot.

I no longer have a piano. But I hear piano music all the time and that music is now often very clear, which means it translates into actual motions in my head where I can feel or otherwise perceive my fingers. We can explain in great detail stuff we haven’t directly discussed, meaning they’ve been discussed in the iObject sense of a Thing, and that appears in the iObject of my Thing, which means it’s paired over the inversion process to you, which means it’s reflective of what?

I’m not going to fight the distraction. While the water boils, I’m whistling Mancini’s pink panther theme, letting it become variations at the same cadence, within the same tonality, until it’s a new song and I drop the initial reference, maybe stick it in the middle. Yesterday I made explicit a variation on the weighted box squat machine in which I push my hips side to side as far as they can go, under weight, with my body lightly held against the support cushion. Now I’m tossing my body forward with a hip twist.

That happened whilst musing. I’m never sure if I’m musing off you or you off me because these tend to be Metaphoric Bundles, which I wanted to type out because MB is easily passed by. Flashes of deep insight and flashes of very large meaning which reveals how the deep insight, which is remarkably precise, down to specific body sensations in specific positions under weight or in movement or both, connects to a larger plan, to a more coherent version of you, one which inverts more completely.

I found myself yesterday, as on prior days, going down a dark road, expecting a story there only to find it renormalized fast, that it hit known points which sparked over the gap with a solution, that being since you’ve been developing this as a conception of what is real, from all the forms of the numbers to physical reality to theology and other abstractions, including love and honor and duty and how identity works and how this material could only be revealed to me if it were not together with you, not as partner but as 1 becoming 1, meaning the generation of 2 from 1 and the generation of 1 from 2, then with all that having been accomplished using this model which has proven material which has resisted all human efforts to prove, proving D-structure, proving gsProcess, and bluntly I used to hope I could prove one thing and I’ve lost count of how many known questions, huge questions, we’ve solved. Together.

That’s how I take this imbuing of Joana and George with attributes that come from both of us because we are that entangled. I hear music now that used to be more a sensation or a melodic flow but not in a specific key and not with the fingering visually accessible in the same way it is when music actually comes out of the fingers.

Just made eggs in a stainless pan. I usually like my eggs fluffy with little color, but this cooks differently and I can make browner eggs which aren’t dry, which means higher heat that retains the non-stick qualities of the pores in the metal closing with thermal expansion of the surface because the coating added, the oil or butter sits on that non-stick surface at a heat which enables the fat to be as non-stick as it can be, like oil becomes thinner, as in a car’s engine. So the issue is less the non-stick surface than how the object, typically the fat acts when it hits this thermally expanded non-stick surface. That’s a very cool understanding which can be useful.

We answer each other’s questions because we are attuned to each other so the construction between us reflects those entangled identities. I’m trying to say that the distance Between is distance Between, the 2, meaning separated as 2 tObjects, united at one End, united at the other End by the processes which unite at each End (1-0//0-1).

So when Joana can play what she hears, that’s an End I perceive which generates a picture out of both of us, meaning I’ve been picking up capabilities through you and other way round because each of these has a ring which we also think of as a radius of a power series.

That power series idea kind of threw me because my inclination is to think: a power series for one Thing versus a power series for many Things, then I realize that many is counted in a Thing, that if you take cubing or any other action, like duodecahedroning, then each value you reach can be squared, cubed, etc. And that means we treat each End as a Thing: it has this power series, which becomes these power series at each calculation, at each n, and it’s part of this power series. And whatever else. Another proof of gsConstruction. I like that because it simplifies saying gsProcess constructing or generating; I can say gsConstructs and that references the entire set of gsProcesses involved.

Like irrationality - just crashed the app with the backspace bug. Like irrationality. I mean that 2 is 1+1 so square root of 2 connects to the gsProcess inherent to that definition of 2, where it fits to a gs, so it can be measured in rs, so we can invoke layers of precision through layers of gsProcess.

The difference from a rational is that the values, like 2 are used at that level, as notation, but that 2 also connects to the irrationality of its roots. So when we have 2 of something or 2 is in a number in some way, like it may be a cube with sides of 2, then the root of that 2 is irrational, which means it is a gsConstruction of a different character. I guess you could say there’s a function which outputs a value for rational and one for irrational. And within irrational for algebraic and transcendental. Let’s say rational is 0, and algebraic is 1, then -1 would be transcendental because that translates a gsProcess which is about counting 1Space and not the counting of 0Space. As in, put rational coefficients in a power series, like n as integers, and that invokes 0 because the gsProcess abstraction is in that context. Put in algebraic, and there’s a clear connection to the prior level, so that becomes 0Space too. And the -1 is transcendental because that calculates the abstraction, that gsProcess, into a count in 0Space, which shows the translation from that abstraction into ++.

I think that’s sensible. We can identify the differences and the labels make sense. That means we can now use similar forms that output -1, 0, and 1. This sounds correct. I’m not 100% sold I have it though because this is new to me. But it answers a lot of questions.

I need to take a break. I’m sorry if this is a lot, but I wanted to be productive for us.

Did I finish the thought? Maybe. I was saying that given this work, a solution pops up which 0’s the thread of something bad happens because the character changes. That reflects as character in Storyline, which reflects over shared Thing to the individual Thing, the 2 into 1 and 1 into 2 at the shared scale, and I accept that because it’s kinda difficult to argue against something with the attractive weight of a black hole. As a fun ride!