Kreyszig, Erwin. Introductory Functional Analysis with Applications. John Wiley & Sons, Inc., 1978.

See also: https://www.uclaextension.edu/sciences-math/math-statistics/course/introduction-hilbert-spaces-adventure-infinite-dimensions-math

for - projection - mechanics of - exploit partial truth of the other - to create the bigger lie

Underwood Touchmaster 5 Typewriter Tabulator Decelerator Demo Operation by [[Phoenix Typewriter]]

Review coordinated by Life Science Editors Foundation Reviewed by: Dr. Angela Andersen, Life Science Editors Foundation & Life Science Editors Potential Conflicts of Interest: None

PUNCHLINE Prostate cancer–associated fibroblasts (CAFs) exhibit conserved and quantifiable differences in morphology and biomechanics compared to matched non-malignant fibroblasts (NPFs). These morphomechanical features—particularly increased stiffness, volume, and nuclear elongation—are correlated with transcriptional programs and clinical outcomes, positioning fibroblast biophysics as a potential biomarker and therapeutic target in prostate cancer.

BACKGROUND Tumor progression is tightly intertwined with the tumor microenvironment (TME), where CAFs play a key role by remodeling the extracellular matrix and altering tissue mechanics. While bulk tissue stiffness has been studied extensively in cancer, the mechanical properties of individual CAFs—and their consistency across patients and link to clinical outcomes—are not well defined. The study leverages a rare resource: 35 pairs of matched CAF and NPF primary cultures from radical prostatectomy specimens, enabling a systematic comparison of morphomechanical traits and their clinical relevance.

QUESTIONS ADDRESSED Do prostate CAFs exhibit consistent morphomechanical changes compared to matched NPFs?

Are these features linked to patient outcomes or tumor grade?

Can CAF biomechanics be modulated by signaling pathways or therapeutic agents?

Do these traits reflect distinct transcriptional signatures, particularly the myofibroblast-like (myCAF) phenotype?

SUMMARY Using real-time deformability cytometry (RT-DC), atomic force microscopy (AFM), and high-content imaging, the authors show that CAFs are consistently stiffer, larger, and more elongated than NPFs across patients. A principal component–derived morphomechanical score integrates five features (volume, Young’s modulus, nuclear area, nuclear circularity, and F-actin alignment) and stratifies patients by clinical outcome. Transcriptomic correlates reveal a link to microtubule dynamics and myCAF signatures. Notably, CAF stiffness can be altered by TGF-β signaling and anti-cancer agents, suggesting potential avenues for stromal reprogramming.

KEY RESULTS CAFs Exhibit Conserved Biophysical Phenotypes

Across 35 matched pairs, CAFs are consistently stiffer (RT-DC, AFM) and larger in both nuclear and cytoplasmic dimensions.

F-actin fibers in CAFs are more aligned, and nuclei more elongated, than in NPFs.

These features were independent of tumor grade but associated with clinical relapse.

A Composite Morphomechanical Score Correlates with Outcome

PCA of the five morphomechanical traits yields a score that stratifies patients.

Higher scores are associated with biochemical and clinical relapse.

Transcriptional Correlates of Biomechanical States

49 genes correlate with the morphomechanical score; top hits include NAV3, MYOCD, and ARHGAP28, implicating cytoskeletal remodeling.

Enrichment for microtubule and myCAF signatures supports a contractile phenotype underlying mechanical changes.

Biophysical Traits Are Pharmacologically Modifiable

TGF-β1 increases nuclear size and stiffness in CAFs, while TGF-β inhibition reduces stiffness.

Docetaxel and axitinib also modulate fibroblast biophysics, suggesting that approved cancer therapies may influence the stromal compartment.

STRENGTHS Large, well-annotated cohort with matched CAF/NPF pairs.

Rigorous integration of imaging, biophysical assays, and transcriptomics.

Clear demonstration of phenotypic consistency and clinical relevance.

Insight into mechanobiological regulation and therapeutic modulation of CAFs.

FUTURE WORK Can morphomechanical profiling be applied to in situ biopsies or circulating fibroblasts?

Is the morphomechanical phenotype of CAFs reversible, and does this influence tumor behavior?

How do CAF mechanics interface with epithelial cell signaling and immune exclusion?

Could targeted reprogramming of CAFs (e.g., via TGF-β blockade) improve therapeutic response?

FINAL TAKEAWAY This study establishes that prostate CAFs are not only functionally distinct but also physically distinct in measurable and clinically relevant ways. The morphomechanical phenotype of CAFs emerges as a novel dimension of tumor biology—potentially serving as both a biomarker and a therapeutic target. By placing CAF biomechanics in the context of differentiation state, gene expression, and treatment response, the work opens new avenues for integrating stromal biology into precision oncology.

Review coordinated by Life Science Editors Foundation Reviewed by: Dr. Angela Andersen, Life Science Editors Foundation & Life Science Editors. Potential Conflicts of Interest: None.

PUNCHLINE: Chromatin organization, orchestrated by the epigenetic reader MeCP2, governs nuclear stiffness in a concentration- and differentiation-dependent manner—providing a mechanistic link between heterochromatin compaction, mechanotransduction, and the severity of Rett syndrome phenotypes.

BACKGROUND: Nuclear mechanics are critical for how cells sense and respond to physical forces, yet most attention has focused on the cytoskeleton and lamin network. Chromatin, particularly heterochromatin, has been considered a secondary contributor, despite its dominant nuclear occupancy. MeCP2, a methyl-CpG-binding protein abundantly expressed in neurons and mutated in Rett syndrome, is known to cluster heterochromatin and modulate chromatin structure. Rett syndrome mutations impact MeCP2's binding and chromatin compaction abilities, but changes in gene expression do not strongly correlate with disease severity. This study proposes an alternative hypothesis: MeCP2 mutations impair the physical properties of the nucleus via disorganized chromatin architecture, offering a new framework to understand the mechanobiology of neuronal development and disease.

QUESTIONS ADDRESSED:

How does MeCP2 concentration influence nuclear stiffness, and is this linked to chromatin compaction?

Do Rett syndrome mutations disrupt MeCP2’s role in nuclear mechanics?

Is chromatin-mediated nuclear stiffness regulated independently of canonical mechanotransduction gene expression?

SUMMARY: Using atomic force microscopy (AFM) to directly measure nuclear stiffness in purified nuclei, the authors show that MeCP2 levels strongly correlate with increased nuclear stiffness. MeCP2 overexpression in myoblasts leads to heterochromatin clustering and ~15–20x increases in nuclear stiffness. During neural differentiation, wild-type cells exhibit dramatic stiffening of nuclei, which is largely abolished in MeCP2 knockout cells. Rett syndrome mutations, including R106W and T158M, differentially impair this function—with T158M inducing nuclear softening even below baseline. Importantly, these mechanical changes occur without global alterations in expression of mechanosensitive genes, implicating chromatin structure itself as a mechanical determinant.

KEY RESULTS

Chromatin Stiffness Is Cytoskeleton-Independent Nuclei purified from cells retain stiffness comparable to the nuclear region of intact cells, showing that chromatin contributes autonomously to nuclear mechanics. In the absence of cytoskeletal components, MeCP2-dependent changes remain robust.

MeCP2 Induces Heterochromatin Compaction and Increases Nuclear Stiffness MeCP2 clustering activity scales with concentration: untransfected myoblasts show 1.4 kPa stiffness, while MeCP2-overexpressing nuclei reach 23.5 kPa. Heterochromatin becomes fewer in number but larger in volume, indicating fusion and compaction.

MeCP2 Is Required for Nuclear Stiffening During Neural Differentiation Differentiation of ESCs into neurons leads to a ~10x increase in nuclear stiffness in wild-type cells, but not in MeCP2 knockouts. NSCs and neurons from KO mice show both impaired heterochromatin clustering and lower stiffness, especially at timepoints when MeCP2 expression peaks in wild-type neurons.

Rett Syndrome Mutations Impair MeCP2-Dependent Stiffening Of 9 Rett-linked mutations tested, several (e.g., R106W, T158M) failed to increase nuclear stiffness, clustering with untransfected controls. Other variants (e.g., A140V) retained or exaggerated MeCP2-like effects, correlating with milder phenotypes.

Mechanostiffness Is Not Driven by Mechanotransduction Gene Expression RNA-seq and qPCR reveal only minor changes in mechanotransduction-related genes (e.g., Tgfbr1, Notch2), and ChIP-seq does not show MeCP2 binding at these loci—supporting a model where stiffness arises from structural chromatin effects, not transcriptional changes.

STRENGTHS:

Direct mechanical measurements using AFM in purified nuclei across multiple cell states.

Dissects MeCP2 function independently of its transcriptional effects.

Uses Rett syndrome mutants to connect biophysics to disease severity.

Establishes chromatin structure as an autonomous determinant of nuclear stiffness.

Integrates epigenetics, mechanics, and disease in a novel conceptual framework.

FUTURE WORK:

Can modulating MeCP2 levels or chromatin compaction rescue mechanical defects in Rett models?

Do neurons use MeCP2-mediated stiffness to regulate mechanosensitive gene expression or signaling?

Are similar chromatin-stiffness mechanisms active in other cell types or diseases?

Could small molecules targeting chromatin modifiers restore nuclear mechanics in disease?

FINAL TAKEAWAY: This study redefines the role of chromatin—particularly MeCP2-organized heterochromatin—as a critical regulator of nuclear stiffness during neuronal differentiation. By decoupling mechanical properties from transcriptional changes, it provides a mechanistic explanation for how MeCP2 mutations contribute to the pathophysiology of Rett syndrome. These findings suggest that chromatin organization is not merely a regulator of gene expression but also a physical architect of the cell’s mechanical identity.

How does this speak to (or not) the idea of coherence in quantum mechanics?

Doctorow analogizes his reading and writing in the same sort of chemistry/statistical mechanics method as I have in the past.

https://en.wikipedia.org/wiki/Infinite_monkey_theorem

for - consciousness - incomplete knowledge of science - hole in understanding - physics - neuroscience - quantum mechanics - Federico Faggin

for - quote - no cloning theorem - quantum mechanics - extended to consciousness and qualia - Frederico Faggin - hard problem of consciousness - no cloning theorem and private inner world of qualia - Frederico Faggin quote - no cloning theorem - quantum mechanics - extended to consciousness and qualia - Frederico Faggin - (see below) - What I feel what I feel is private. - What you feel is private. - You cannot transfer it to me - In order to tell you what I feel, I must translate that private feeling into classical information bit saying what I say. - The symbols must be this. - They must be sharable. - They must be copyable to share. You need to copy. Yeah. - My inner experience cannot be copied. And there is something in physics that cannot be copy. - In Quantum state, there is the "no cloning theorem", which says do not copy. - Not only that, but the maximum information that you can get if you make a measurement of the quantum state is one bit per quantum bit. - Olivas theorem says that and we have or Labor's theorem ourselves. What I can say about what I feel is much, much less

Calculus and mechanics should be though together. The first one is boring without the second. The second one cannot be understood without prior knowledge of the first.

Reasonable estimate it would seem. I haven't seen any others before.

Eraser Table Spring install Olympia SM3/4 by [[The HotRod Typewriter Co.]]

Part 2: COMPLETE Olympia SM3 Typewriter Service/repair- SO YOU WANT TO BE A MECHANICAL ENGINEER?!? by [[The HotRod Typewriter Co.]]

An excellent video in terms of coming to understand the functionality of a typewriter versus how the pieces interact to effectuate those functionalities.

Mechanics, dynamics and aesthetics

organization<br /> : specialized systems carrying out concerted actions toward a stated goal or purpose

Note that even if some members of the organization create statistical noise in their actions, the larger organization may still move in a useful direction

Definition of degrees of freedom of a system

quote from Christoph Adami at https://twitter.com/ChristophAdami/status/1711583362647814485

Re: George Ellis https://www.nature.com/articles/d41586-023-03061-y

Physicists and quantum mechanics as solution to consciousness.

See also: Physics in Mind: A Quantum View of the Brain by Werner R. Loewenstein

| physics/mathematics | Classical Physics | Quantum Mechanics |<br /> |---|---|---|<br /> | State Space | fields satisfying equations of laws<br>- the state is given by a point in the space | vector in a complex vector space with a Hermitian inner product (wavefunctions) |<br /> | Observables | functions of fields<br>- usually differential equations with real-valued solutions | self-adjoint linear operators on the state space<br>- some confusion may result when operators don't commute; there are usually no simple (real-valued) numerical solutions |

https://www.youtube.com/watch?v=5qGRPOzMWnA

Watched the first 46:39 on 2023-02-02. His personal communication style is a bit off-putting, but remedied slightly by watching at 1.25 or 1.5x speed. He's broadly covering pieces directly from his text which seems much more compact and elegant. Questions from the viewers in real time is a bit muddy with respect to understanding what they're saying.

I gave up on the video due to streaming issues.

One of the problems in approaching quantum gravity is the choice for how to best represent it mathematically. Most of quantum mechanics is algebraic in nature but gravity has a geometry component which is important. (restatement)

This is similar to the early 20th century problem of how to best represent quantum mechanics: as differential equations or using group theory/Lie algebras?

This prompts the question: what other potential representations might also work?

Could it be better understood/represented using Algebraic geometry or algebraic topology as perspectives?

[handwritten notes from 2023-02-02]

reply to u/New-Investigator-623 at https://www.reddit.com/r/antinet/comments/10r6uwp/comment/j6wy4mf/?utm_source=reddit&utm_medium=web2x&context=3

Ideas, concepts, propositions, et al. in this context are just the nebulous dictionary definitions. Their roots and modern usage have so much baggage now that attempting to separate them into more technical meanings is difficult unless you've got a solid reason to do so. I certainly don't here. If you want to go down some of the rabbit hole on the differences, you might appreciate Winston Perez' work on concept modeling which he outlines with respect to innovation and creativity here: https://www.youtube.com/watch?v=gGQ-dW7yfPc.

I debated on a more basic framing of chemistry or microbiology versus statistical mechanics or even the closely related statistical thermodynamics, but for the analogy here, I think it works even if it may scare some off as "too hard". With about 20 linear feet of books in my library dedicated to biology, physics, math, engineering with a lot of direct focus on evolutionary theory, complexity theory, and information theory I would suggest that the underlying physics of statistical mechanics and related thermodynamics is precisely what allows the conditions for systems to evolve and emerge, for this is exactly what biological (and other) systems have done. For those intrigued, perhaps Stuart Kauffman's Origins of Order (if you're technically minded) or At Home in the Universe (if you're less technically oriented) are interesting with respect to complexity and emergence. There's also an interesting similar analogy to be made between a zettelkasten system and the systems described in Peter Hoffman's book Life's Rachet. I think that if carefully circumscribed, one could define a zettelkasten to be "alive". That's a bigger thesis for another time. I was also trying to stay away from the broad idea of "atomic" and drawing attention to "atomic notes" as a concept. I'm still waiting for some bright physicist to talk about sub-atomic notes and what that might mean... I see where you're going with phenomics, but chemistry and statistical mechanics were already further afield than the intended audience who already have issues with "The Two Cultures". Getting into phenomics was just a bridge too far... not to mention, vastly more difficult to attempt to draw(!!!). 😉 Besides, I didn't want Carol Greider dropping into my DMs asking me why didn't I include telomeres or chancing an uncomfortable LAX-BWI flight and a train/cab ride into Baltimore with Peter Agre who's popped up next to me on more than one occasion.

Honestly, I was much less satisfied with the nebulousness of "solution of life"... fortunately no one seems to be complaining about that or their inability to grapple with catalysis. 🤷🏼

To resolve the measurement problem from quantum mechanics into the classical realm, one can use the observables principle and the Born rule.

re: https://hypothes.is/a/HqT-lG1fEeqHX7fnzQAfGg

A zettelkasten provides a catalytic surface to which ideas in the "solution of life" can more easily adhere to speed their reaction with ideas you've already seen and collected.

Once combined via linking, further thinking and writing, they can be released as novel ideas for everyone to use.

https://www.math.columbia.edu/~woit/QM/spring2022.html

https://inference-review.com/article/woits-way

link to: text: https://hypothes.is/a/macvwJ5zEe2kdF_K9kCN-A

Woit, Peter. Quantum Theory, Groups and Representations: An Introduction. Revised and Expanded version [2022]. Springer, 2017. https://www.math.columbia.edu/~woit/QM/qmbook.pdf.

https://ncase.me/polygons/

An interesting interactive model for segregation here. See also https://www.bloomberg.com/news/articles/2014-12-10/an-immersive-game-shows-how-easily-segregation-arises-and-how-we-might-fix-it for press coverage.

https://en.wikipedia.org/wiki/Aleatoric_music

There is a direct analogy to statistical mechanics and thermodynamics to be drawn here.

How can we frame the science of poverty with respect to the model of statistical mechanics?

Unemployment numbers have very little to do with levels of poverty. They definitely don't seem to be correlated with poverty levels, in fact perhaps inversely so. Many would say that people are lazy and don't want to work when the general reality is that they do want to work (for a variety of reasons including identity and self-esteem), but the amount of work they can find and the pay they receive for it are the bigger problems.

Can poverty be modeled after a statistical thermodynamic framework? How might we move the set point for poverty up significantly to prevent the ill effects of regular, repeated poverty?

What does the complexity of poverty indicate? Within the web of potential indicators, what might be done to vastly mitigate the movement of people in and out of poverty? What sorts of additional resiliency can be built into the system?

TLDR Hyperion is a moon orbiting Saturn and has chaotic motion about its CoM. This chaos is modeled correctly with classical mechanics but incorrectly with quantum mechanics. The catch being that if the average of all wavefunction collapses due to decoherence with interactions particles+photons is included then the prediction is correct. However, averaging is a non-physical process and, furthermore, collapsing a wavefunction requires instantaneous transfer of information which is nonphysical.

• Saturn's moon, Hyperion, has chaotic motion due to the orientation of the moon about the orbit. Due to chaos, we can't predict orientation due to chaotic tumbling.
• This can be described classicly with relativity.
• Quantum Mechancis has been falsified because it fails to recreate or predict chaotic behaviors of the moon after 20 years.
• Due to the linear nature of the eigenvector in Schrodinger's equation, it can not contain chaos.
• By applying the correspondence principle, we only see chaos for up to the Ehrenfest time upon having the time function applied.
• Physicists explain this incongruence in theories because the Schrodinger equation isn't including the entangled interactions of light/dust. These effects result in decoherence.
• By averaging over the predictions we achieve the same solution as classical mechanics. Howevering averaging isn't a physical process. (e.g. rolling a 6 sided dice many times gives an average of 3.5 which is nonphysical)

For a model to be real, we require that each individual prediction is true not the average. One solution is that Hyperion interacts and is having it's wavefunction updated nonlinearly resulting in decoherence. * Collapse of a wavefunction is said to not be physical due to instantaneous transfer of information being impossible. However, this wavefunction collapse due to interactions is required for the chaos of Hyperion to be modeled correctly. This is the issue.

Mario interjects in the conversation to clarify Barry's question to Carlo, which is concerning the subjective aspect of experience and how it fits into science as the observer. It comes down the the question of existence of reality and the obrserver's role in that, epitomized in the question: If a tree falls in the forest, does anybody hear?

This will depend on a very specific and narrow definition of fitness--perhaps one from a very individualistic and libertarian perspective.

There is fitness at the level of the gene, the organ, the individual, and the group, and even possibly larger groupings above that.

What if, by starving out and leaving "uneducated" people like Srinivasa Ramanujan, for example, who surely was marginalized for his time, society is left without them? While on an individual level Ramanujan may have been less fit on some levels as G.H. Hardy and may have otherwise dwindled and disappeared, Hardy adopted him and made both mathematicians better while also making dramatic strides for mankind.

From a statistical mechanics perspective, within some reasonable limits, we should be focusing on improving ourselves as well as the larger group(s) because the end results for humanity and life in general may be dramatically improved. (Though what we mean by improved here may be called into question from a definitional perspective.)

Compare this with [Malcolm Gladwell]]'s argument in My Little Hundred Million.

On a nationalistic level within human politics, Republicans should be less reticent to help out marginalized Americans because it may be from this pool of potential that we may find life saving improvements or even protection from other polities (ie, in our competition or threats from countries like China, Iran, North Korea). Consider how different things may have been had the U.S. not taken in Jewish or other foreign nationals like Albert Einstein, John von Neumann, etc. in the early to mid-1900s.? Now consider, which life changing geniuses we may be preventing reaching their potential by our current immigration policies? our current educational policies?

Interesting list - from the procedural to the motivational.

I wonder a bit here about the idea of what in a meme might have a substrate type of effect to decrease the overall energy of the process to help it take off.

in other words, it's just statistical thermodynamics. Eventually small pieces will float by each other and stick together in new and hopefully interesting ways. The more particles you've got and the more you can potentially connect or link things, the better off you'll be.

The interaction of forces on objects is Newtonian but in our case when the force is applied the objects are changing shape within themselves. Newtonian only discusses the in between. While we will talk in terms of forces it is really continuum but we talk like it's Newtonian.

Solved Exams and Problems in advanced classical mechanics. Great Source!