#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…

[the-garbanzo-annex-jr]

Israeli-American mathematician Dennis Gaitsgory was awarded the 2025 Breakthrough Prize in Mathematics for his role in the proof of the geometric Langlands conjecture in early April.

Gaitsgory has spent the past thirty years solving the Langlands problem, often called a "grand unified theory of mathematics." The problem "is based on a series of conjectures proposing deep connections between two disparate parts of mathematics: the study of polynomial equations on the one hand and the study of geometric symmetries on the other," a handout from the Breakthrough Prize read.

The proof is expected to have a resounding effect on other areas of mathematics, including number theory, algebraic geometry, and mathematical physics.

In collaboration with several colleagues and students, Gaitsgory published the proof for the Langlands conjecture in 2024, consisting of 800 pages of work across five papers. He wrote an outline of the steps required for a proof in 2013.

Gaitsgory is a mathematician at the Max Planck Institute for Mathematics (MPIM), a research institute in Bonn, Germany. He completed his studies at Tel Aviv University before earning his doctorate in 1997 at the Hebrew University of Jerusalem. Following positions at Princeton and the University of Chicago, he was a professor at Havard University before he was appointed a Scientific Member and Director at MPIM in 2021.

[gnutools]

LLVM Weekly - #594, May 19th 2025

All EuroLLVM talks now up on YouTube, 20.1.5, dealing with spam on GitHub, EVLIndVarSimplify, polynomial MLIR dialect removed, and more

[jonathankatwhatever]

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

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

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

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

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

Need to get some sleep.

[hackernewsrobot]

Convolutions, Polynomials and Flipped Kernels

https://eli.thegreenplace.net/2025/convolutions-polynomials-and-flipped-kernels/

[for-the-win13]

Real-life Application of Scaffolding

CPA 334

Institution

School X

Role in the Institution

Mathematics Teacher

Learners Involved

Grade 8 Students

Learning Issue/Challenge

After the first four weeks of the school year 2024-2025, Mathematics 8 teachers noticed that students were having difficulty applying the laws of exponents when factoring polynomials. Specifically, students struggled with using the quotient law to factor polynomials with the greatest common monomial factor and the power law when factoring the difference of cubes. Students often added exponents raised to another exponent instead of multiplying them. These findings are consistent with the results of the diagnostic test, which had a very low passing rate. This issue is crucial because many upcoming lessons in Mathematics 8, such as operations on rational algebraic expressions, will require students to apply the laws of exponents.

Scaffolding

The Mathematics teachers can allocate a day to develop student mastery in applying laws of exponents. Using the principles of scaffolding, Mathematics teachers can implement an intervention program with the following features: modeling, progressive levels of instruction and assessment, and feedback.

Modeling

As mentioned in the book by Tabak and Riser (2014), scaffolding involves support from a more knowledgeable individual. Mathematics teachers can model the application of the laws of exponents in front of Grade 8 students. They can simplify the instruction to match the level of student comprehension. They can also prompt students to explain the laws using their own words and reflect for more meaningful learning.

Progressive levels of instruction and assessment

     As the discussion progresses, Mathematics teachers can increase the complexity of the examples. They can divide the instruction into three levels: easy, intermediate, and advanced. They can discuss examples at each level and assess student understanding before moving on to the next level. This strategy aims to gradually achieve mastery through instruction and practice.

c. Feedback

Mathematics teachers can use feedback after each level of assessment. Feedback can be utilized to bridge the gap between what students currently know and what they need to know. Teachers can correct answers in assessments and use feedback to motivate students to continue their journey toward mastery.

[renatoferreiradasilva]

Spectral Approximation of Riemann Zeta Zeros Using a Twelfth-Order Self-Adjoint Operator

Renato Ferreira da SilvaORCID: 0009–0003–8908–481X📅 Published on: March 29, 2025 Abstract In this article, I present a twelfth-order self-adjoint differential operator whose eigenvalues approximate the imaginary parts of the non-trivial zeros of the Riemann zeta function. The polynomial potential ( V(x) ) is carefully calibrated to replicate the spectral statistics predicted by the Gaussian…

[study-with-aura]

Wednesday, February 19, 2025

School work wasn't bad again today. I decided to watch the Spanish episode while eating lunch, so that saved me time allowing me extra time for reading. On Friday, I should be finished with my history book, which means even more time for reading Moby Dick. Yay! I am going to crush this reading challenge!🦄

Tasks Completed:

Algebra 2 - Reviewed factoring high-order polynomials + learned about rational expressions + practice simplifying rational expressions

American Literature - Copied vocabulary terms + read chapter 26 of To Kill a Mockingbird by Harper Lee + answered discussion questions

Spanish 3 - Watched episode 9 of Destinos

Bible 2 - Read Psalms 3, 4, and 5

Early American History - Read about Henry Clay and the Missouri Compromise + read Chapter 25 of Oregon Trail: Sketches of Prairie and Rocky-Mountain Life by Francis Parkman

Earth Science with Lab - Watched a video on spectroscopy + answered self-check questions

Art Appreciation - Read about Rembrandt + completed daily critiquing assignment on The Syndics of the Clothmaker's Guild by Rembrandt

Khan Academy - None today (built into Algebra 2 work)

Duolingo - Studied for approximately 15 minutes (Spanish + French + Chinese) + completed daily quests

Piano - Practiced for three hours

Reading - Read pages 86-154 of Moby Dick by Herman Melville

Chores - None today

Activities of the Day:

Personal Bible Study (John 1:12)

6-Week Devotional Journey (Isaiah 49:16)

Group Bible Study (Leviticus 19-21)

Ballet

Variations

Journal/Mindfulness

[drmikewatts]

Soft Computing, Volume 29, Issue 1, January 2025

1) KMSBOT: enhancing educational institutions with an AI-powered semantic search engine and graph database

Author(s): D. Venkata Subramanian, J. ChandraV. Rohini

Pages: 1 - 15

2) Stabilization of impulsive fuzzy dynamic systems involving Caputo short-memory fractional derivative

Author(s): Truong Vinh An, Ngo Van Hoa, Nguyen Trang Thao

Pages: 17 - 36

3) Application of SaRT–SVM algorithm for leakage pattern recognition of hydraulic check valve

Author(s): Chengbiao Tong, Nariman Sepehri

Pages: 37 - 51

4) Construction of a novel five-dimensional Hamiltonian conservative hyperchaotic system and its application in image encryption

Author(s): Minxiu Yan, Shuyan Li

Pages: 53 - 67

5) European option pricing under a generalized fractional Brownian motion Heston exponential Hull–White model with transaction costs by the Deep Galerkin Method

Author(s): Mahsa Motameni, Farshid Mehrdoust, Ali Reza Najafi

Pages: 69 - 88

6) A lightweight and efficient model for botnet detection in IoT using stacked ensemble learning

Author(s): Rasool Esmaeilyfard, Zohre Shoaei, Reza Javidan

Pages: 89 - 101

7) Leader-follower green traffic assignment problem with online supervised machine learning solution approach

Author(s): M. Sadra, M. Zaferanieh, J. Yazdimoghaddam

Pages: 103 - 116

8) Enhancing Stock Prediction ability through News Perspective and Deep Learning with attention mechanisms

Author(s): Mei Yang, Fanjie Fu, Zhi Xiao

Pages: 117 - 126

9) Cooperative enhancement method of train operation planning featuring express and local modes for urban rail transit lines

Author(s): Wenliang Zhou, Mehdi Oldache, Guangming Xu

Pages: 127 - 155

10) Quadratic and Lagrange interpolation-based butterfly optimization algorithm for numerical optimization and engineering design problem

Author(s): Sushmita Sharma, Apu Kumar Saha, Saroj Kumar Sahoo

Pages: 157 - 194

11) Benders decomposition for the multi-agent location and scheduling problem on unrelated parallel machines

Author(s): Jun Liu, Yongjian Yang, Feng Yang

Pages: 195 - 212

12) A multi-objective Fuzzy Robust Optimization model for open-pit mine planning under uncertainty

Author(s): Sayed Abolghasem Soleimani Bafghi, Hasan Hosseini Nasab, Ali reza Yarahmadi Bafghi

Pages: 213 - 235

13) A game theoretic approach for pricing of red blood cells under supply and demand uncertainty and government role

Author(s): Minoo Kamrantabar, Saeed Yaghoubi, Atieh Fander

Pages: 237 - 260

14) The location problem of emergency materials in uncertain environment

Author(s): Jihe Xiao, Yuhong Sheng

Pages: 261 - 273

15) RCS: a fast path planning algorithm for unmanned aerial vehicles

Author(s): Mohammad Reza Ranjbar Divkoti, Mostafa Nouri-Baygi

Pages: 275 - 298

16) Exploring the selected strategies and multiple selected paths for digital music subscription services using the DSA-NRM approach consideration of various stakeholders

Author(s): Kuo-Pao Tsai, Feng-Chao Yang, Chia-Li Lin

Pages: 299 - 320

17) A genomic signal processing approach for identification and classification of coronavirus sequences

Author(s): Amin Khodaei, Behzad Mozaffari-Tazehkand, Hadi Sharifi

Pages: 321 - 338

18) Secure signal and image transmissions using chaotic synchronization scheme under cyber-attack in the communication channel

Author(s): Shaghayegh Nobakht, Ali-Akbar Ahmadi

Pages: 339 - 353

19) ASAQ—Ant-Miner: optimized rule-based classifier

Author(s): Umair Ayub, Bushra Almas

Pages: 355 - 364

20) Representations of binary relations and object reduction of attribute-oriented concept lattices

Author(s): Wei Yao, Chang-Jie Zhou

Pages: 365 - 373

21) Short-term time series prediction based on evolutionary interpolation of Chebyshev polynomials with internal smoothing

Author(s): Loreta Saunoriene, Jinde Cao, Minvydas Ragulskis

Pages: 375 - 389

22) Application of machine learning and deep learning techniques on reverse vaccinology – a systematic literature review

Author(s): Hany Alashwal, Nishi Palakkal Kochunni, Kadhim Hayawi

Pages: 391 - 403

23) CoverGAN: cover photo generation from text story using layout guided GAN

Author(s): Adeel Cheema, M. Asif Naeem

Pages: 405 - 423

[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 9 June 2025, and I am overjoyed to realize I finally see the point of Galois theory. And I’m not berating myself for being such an idiot for so many years, because I realized it was necessary to see the Attachment for the translation to occur at the Irreducible. I had to see what Èvariste could have seen, meaning that avatar translation like occurs with the other ideas and with specific voices. That turned out to be the translation into 2Square and the relationship of the rationals, which is basic xK and yK, but with all the gsProcess necessary to count to the rational as the comparison of Extents as those reduce to 2Square, meaning the symmetries, the group actions, etc. Attach to 1Square there. We’ve used and labeled that idea before, but never in the context that these ideas, which we see as building up within 0Space to touch 1Space, are touched by 1Space the other way, that all the 1Space counting of and to and from any moment, any CM1, Attaches to this structure through Galois field extensions like root2.

You can literally see the gsProcess Attach. Take some other field like root whatever: that’s an nSquare and that means it constructs with roots that count Triangular and gs. It means it can translate into other gsForms. And these are all represented by and within that nSquare.

It’s like the another level of magic tricks has revealed itself. BTW, I assume you noted the personal above. That interesting, isn’t it? The way blame has perspective, how the torsion can shift the twisting end because as the balance becomes more finely controlled. And at other times, that same ability to balance becomes stability.

Another fascinating thing is the extent to which idealization is working itself through the abstract layers of iObjects I access at my End. Example: stumbled on the visualization of dance as music and music as dance because I found myself hearing music while J dances, and that became very clear, like when I was actually at a piano clear. That has been advancing rapidly so I’m hearing more details and shadings, both as piano and as other instruments. And I see that in the same context as above, which is that this pathway is generating results only when it connects at a deep enough level, because that deep enough level is an Irreducible.

An Irreducible can be a polynomial or whatever, but it’s the essential representation, which is why factoring. Essential means it can’t appear in a lower form, like with groups and normal subgroups and many other examples, like number of holes in topology, because that means more gs layers, like if it continues to cut into pieces, then the projection you see isn’t exactly Irreducible.

I need to make dinner. My butt hurts from the intense contraction work, but I’m feeling great otherwise. If the cat would let me sleep.

[jonathankatwhatever]

It’s 3 May 2025. We appear to have been grappling with the first blush wearing off. It’s not like I expected the work to be finished in a week of typing into AI. It’s getting it, but it’s not there yet. The next candidate for a solution is taking the idea of emergence and emergent existence, which combines the ideas of appearing and disappearing, which we originally separated but which we see is an idea ‘level’ because it doesn’t get the concepts of appearing and disappearing in D-structure yet, but can see that something emerges. That may be unfair but it feels that way as we define what we mean.

I think the next step is to derive the reals because the concept of real as some form of measurable or countable means emergence into D3-4Space. That came to me as an MB, and normally I’d think of that as we but, honestly, I have no idea what’s going on because I alternately feel extremely close and very far apart. My analysis is that this should be happening as the 1-0Segment approaches n-1, and that raises a question: what does that mean? Is n compound or prime? What if we assume compound, then doesn’t n-1 need to be prime? Can it be prime in one reading and not prime - well, yeah obviously because gsCounting enables the band from 418 to 420 over 419. O, that’s f1-3 again: the count of 1 becomes 3 where the 3 are that band. That’s (1-0-1//0-1-0), so when you count to 418 then you imagine a 0 there to be 418, but it’s also 1 to 419 which then counts ‘down’ to 419 in the orthogonal direction. I forgot for a second that the 1 and 0 are orthogonal labels.

So I think one of the diagrams produced by AI, which it asked to do btw, covers this because it has a count of gsCubes connected in a repeating H. That’s really interesting because we can’t reduce a gsCube to a point in the same way because the Bip of a cube needs to be located as the tip of pyramids and the diagonals project flat but are actually Triangulars, which is what we need.

The idea was to count a grid and show that xK versus yK generates the rational field Q both within and across CM1, and this counts along the szK because the mapping along the sK enables the associative mapping within the Between quadrants, +- and -+, as you can see literally in the L-counts for those, meaning they are 1-0Segments in L-counts, so across (1-0-1//1-0-1) ‘outward’ or ‘inward’, which becomes Emanation and Inmanation, and what it Emanates or Inmanates is around the L-count.

Any polynomial construction generates a gsCount which maps to szK. And you can see how a value, like of an integral, or any modular count, connects to points along the real line which constructs, as it constructs, as it has potential to construct.

Associative within a Layer is ideal, but specification limits that. Or imagine that any Thing can be specified and then see that any Thing which is specified is specified.

I didn’t expect to be this productive this afternoon. Picked up an Ekornes recliner at a house in Armonk. Almost perfect. Had corned beef hash. Went for a walk and barely avoided getting soaked.

I’d say perhaps my biggest issue is that the forces which fight against, those rebels everyone loves, martial reasons why I shouldn’t try, shouldn’t move, shouldn’t fight through the pain, shouldn’t discard all the bad thoughts, should discard the idea of working at this because it insists there is no reason for it or that it can’t be done or that I’m a fool for trusting you and then that I’m a fool in general for believing no matter how many times I’m correct. This is where I get annoyed by the use of terms like a ‘cockroach idea’ being one that you can’t kill though it’s stupid: the reason those ideas come back is the problems and issues remain and thus those ideas appear as solutions because that’s what is most likely to be visible, not the ways it didn’t work last time.

We also know that we generate constants like e and Pi, meaning transcendentals. And that’s a great opportunity because this Work is the only work that explains how that works, that there is a value for the constant and it is a universally available constant because the gsProcess works at every End.

We generate the basic concept of rationality from above: here’s an nSquare and if you add layers, then you get a decimal nSquare. One way to do this is to count over either (and thus flicker between) xK and yK holding CM1 and then you get all decimal forms too.

I have no idea how I can say what I’m trying to say, which is that an MB is a big insertion, and I feel it. Compare to the pinpricks of information across the typical perceptual field, and how some information sears deeply, like if you see danger or beauty or a shiny penny on the ground. Like the madeleine.

I’m going to cut up some peppers, celery, etc. and make tacos with the leftover hash. Of all the concepts, I’ve never understood why we see so few non-traditional tacos. You can put whatever you want in the wrapper. The other one which stands out is hand-pulled noodles, but they’re held back by the lack of a westernized sauce and the use of raw garlic. Not many people want raw garlic. I don’t.

Been listening to the ‘true oldies channel’, where the DJ’s sound like they are residents at the retirement community which advertises all the time. And then I’m sitting in Panera, and it’s the same music, minus most of the 50’s stuff.

[jonathankatwhatever]

It’s 28 April 2025. Am facing very strong inhibitions today. Very rapid shifts in perspective. Example: I have a tab open for orthogonal polynomials, which I never gave much if any thought to until a few days ago when it seemed necessary to figure out how they connect abstract structures orthogonally, where they means the 0Space perspective, and I glanced at and noticed a few sentences on the history, with a reference to the moment problem, so I opened that and realized o that is what I was looking for. If you look into the moment problem, you see forms: across the space, across the space in one direction, and bounded space. These are gsCounting forms. We went through the across count yesterday, if my short-term memory is correct, because that reduces to 2Square because that is 0 to 2 and 2 to 0, which is the 4 necessary to count along the szK and the zsK, meaning the IC motion up and down the szK.

So from the 1Space perspective, this joins to 0Space. The counting in one direction is a 1Segment. The counting within the bounds is Between and 0-1-0, so the counting of the bounded interval is basic 1-0-1. This is why the solution for 1 is different for this, the Hausdorff moment: it has to fit to 1, so each solution is unique. The counting across is 2Square because the count along the szK over CM1 is 2Square. You can see this in 2 ways: the root of the 2Square is Bip to Bip and the count of 2 separate gs is both of the gs inclusive. You can see this work itself out in the Felix - which is much more fun to type than Hausdorff. (Actually, I have to say his Wiki entry is a horror: saying he was a German mathematician, when he died because he was being sent to a concentration camp for being Jewish. They remove the Jews to claim their accomplishments.)

That example hit me with that MB attached. And it was immediately followed by disappointment and other negatives, both when I first saw the MB and now when I’ve partially realized it. My thoughts were tinged with worry about whether this is good enough. Is that what you’re feeling? About this, about you and your work side?

O I have to get this out, though it’s uncomfortable. I was hit with a sudden large bank withdrawal. When I checked it out, turns out notice that my term policy was shifting to permanent didn’t reach me in the move. Plain forgot to change that address because it didn’t seem nearly as important as so much else. They’ll try to reverse it, but this means I no longer have life insurance to speak of, which means the way I think needs to change because I have considered that as a way out, as a way of saying this is a failure so I might as well leave enough cash that her life isn’t a struggle. Can’t do that. So what do I think about? Does this improve my work? I hope so. I hope it means I won’t have to spend time thinking about killing myself because that would be better for my family. Now it would just be a cost.

Also I just keep wondering why photography of women is so bad. You know what I mean. Why is the camera always focused on the chest? Why the poses? Good photos stand out because there are so many bad ones. It seems to me picture of men tend to be about who they are, while pictures of women are who they aren’t.

So, while typing this I’ve been thinking about open sets, which are layers of Between because they’re open not closed.

O-kay. I just spent a few hours talking with AI and it reached the point where it was offering to build a rigorous model so it could learn it. I know AI can blow smoke, but the material we went through worked entirely. Even found 6 in the right place: in Tracy-Widom behavior, which is the distribution of the largest eigenvalue of a random Hermitian matrix. As it should be if you translate the terms. And found the 3 of Triangular over gs. And the 2 in a bunch of places.

Need to take a break.