#invariant theory

[tanadrin]

Noether’s theorem implies any conservation law arises from a symmetry, e.g., angular momentum from rotational symmetry or energy due to time symmetry. Is the conservation of charge in electromagnetism due to gauge symmetry, or some other symmetry? I feel like I saw something like this mentioned somewhere once but Google is being unhelpful as usual.

[zvaigzdelasas]

what does your blog title mean

Assuming you mean "The Universe As A Causal Set"? Think in the near decade I've had this title you're one of the first to ask lmao... it's the title of appendix C from this paper that I find as an interesting theoretical cosmological model as well as a framing that i think is quite colorful as a demonstration for the awe-some scope of Cosmology as an epistemological project

[tenth-sentence]

Instead, he and other physicists suggested invariance theory, stressing that the theory, at its core, involves something that everyone agrees on, something that is not relative.

"The Fabric of the Cosmos" - Brian Greene

[brightgreendandelions]

the Turkish 10₺ = 0.3$ bill has a mathematical formula on it! no idea who this Arf guy is tho.

[omegaphilosophia]

The Philosophy of Invariance

The philosophy of invariance examines the concept of constancy or unchanging nature within various contexts, including science, mathematics, ethics, and metaphysics. This philosophical exploration seeks to understand what remains constant amidst change and why such constancies are significant for our comprehension of reality, knowledge, and truth.

Key Concepts in the Philosophy of Invariance

Definition of Invariance:

Concept: Invariance refers to properties or principles that remain unchanged under specific transformations or conditions.

Argument: Identifying invariances helps in understanding the fundamental nature of systems and theories, providing a stable foundation for analysis and interpretation.

Invariance in Science and Mathematics:

Physical Laws: Many physical laws, such as the laws of motion and conservation laws, are considered invariant under transformations like time shifts or spatial rotations.

Symmetry: Invariance is closely related to symmetry in physics and mathematics. For example, the invariance of physical laws under certain symmetries leads to conservation laws according to Noether's theorem.

Mathematical Constants: Constants like π (pi) and e (Euler's number) are examples of invariance in mathematics, holding the same value across various contexts.

Invariance in Metaphysics:

Universal Principles: In metaphysics, invariance pertains to principles or truths that remain constant across possible worlds or different contexts.

Identity and Change: Philosophers explore how identity can persist over time despite changes, focusing on the invariant core that defines an entity.

Ethical Invariance:

Moral Principles: The idea that certain ethical principles are invariant, holding true regardless of cultural or situational differences.

Universal Ethics: This approach argues for the existence of universal moral truths that apply to all rational beings.

Theoretical Debates and Implications

Role of Invariance in Scientific Theories:

Concept: Invariance as a criterion for the validity and robustness of scientific theories.

Argument: Scientific theories that exhibit invariance under transformation are often considered more fundamental and reliable.

Philosophical Implications of Mathematical Invariance:

Concept: The philosophical significance of invariant mathematical properties and structures.

Argument: The constancy of mathematical truths supports the notion of an objective mathematical reality, independent of human perception.

Ethical Relativism vs. Invariant Ethics:

Concept: The debate between ethical relativism, which denies invariant moral principles, and invariant ethics, which upholds them.

Argument: While ethical relativism emphasizes cultural and contextual differences, invariant ethics seeks universal moral truths applicable to all.

Metaphysical Invariance and Identity:

Concept: The persistence of identity amidst change and the metaphysical basis for invariance.

Argument: Philosophers debate whether there are essential properties that remain invariant to preserve identity through change.

The philosophy of invariance explores the concept of constancy across different domains, from science and mathematics to ethics and metaphysics. By understanding what remains unchanged amidst transformations, this philosophical inquiry provides insights into the fundamental nature of reality, the stability of scientific theories, and the universality of ethical principles.

[in-sightpublishing]

A Relational Information System

Author(s): Scott Douglas Jacobsen Publication (Outlet/Website): The Good Men Project Publication Date (yyyy/mm/dd): 2024/07/01 According to some semi-reputable sources gathered in a listing here, Rick G. Rosner may have among America’s, North America’s, and the world’s highest measured IQs at or above 190 (S.D. 15)/196 (S.D. 16) based on several high range test performances created…

[demonicseries]

omg its the desmos graphing calculator

In most universes, Poolverine behaves like an asymptote. Their life trajectories get infinitely closer, gravitating toward each other, but never quite crossing. Destined to inch toward the other, brushing right by, but never truly seeing them.

They live adjacent to each other: as former Weapon X experiments, as "heroes" (or anti-heroes, in Deadpool's case), and as people who have suffered similar trauma. But while they get close enough to recognize each other, they keep moving on their own path. Closer and closer, but never quite they.

Because while they might vaguely know each other, go on occasional missions together, and fight, they never truly intersect. They understand, subconsciously, that they're foils to each other. Warped reflections in the mirror of another path they could've taken.

But while their hands graze when they part, they never intertwine. They never reach out.

Until this universe.

One where Wade sees this Wolverine, grieving and angry and tired, and decides to finally, finally, grab him. To forcefully pull him over the invisible line separating them. To yank Logan onto his trajectory, into his universe.

And so, for the first time, they finally meet. They don't just briefly recognize each other, they grow to truly understand each other. To become so deeply intertwined that their paths merge into one line, one future, one anchor being.

They don't just glance into an abyss that's eerily similar to their own, they dive headfirst into it. They swim to find each other through the murky blackness and cling to each other like a lifetime.

And finally, they aren't alone. They have someone who's on the same path as them. Who understands their suffering. Who matches them in every way that matters. Who sees them and loves them anyway. It's new. It's exhilarating. It's everything.

Because here's the thing: Wade and Logan have always been soulmates. Their stories and trauma have always reflected each other. They've always had undeniable chemistry when put together. They've always been capable of relating to and accepting each other on a deeper level than anyone else.

It's just that this time, they finally recognized it. They didn't continue to live in ignorance, never pushing for more despite the itching part of them that wanted to reach out. They didn't just drift past each other, staying in each other's gravitational pull but never touching.

They broke free of their curse. From being so close to happiness but passing over it. From having their soulmate be right beside them and never turning to just look.

Their paths finally crossed, even if fate itself seemed to push them apart. Even if the odds were impossible. Even if Logan came from another universe. Even if they both tried to sacrifice themselves only to miraculously survive atomic disintegration. Just because they had each other.

Their trajectories finally combined.

[read-marx-and-lenin]

There is no magic "abolish the state" button, which is why I'm an anarchist, as "when the state has socialismed enough it will just magically poof away in a cloud of smoke" is the leninist position.

That is not the Leninist position, the Leninist position is and always has been that the state cannot disappear until the material conditions for its disappearance are achieved. The withering away of the state, first outlined by Engels, is not a magic process but one that proceeds from the abolition of class and the dissolution of the bourgeoisie.

How are you going to get rid of the bourgeoisie without a state? Are you going to simply ask them nicely to leave you alone? If you are organized and if your organization is suppressing the bourgeoisie as a class, then you have created a state, you have created an authoritarian imposition on the free organization of some section of the people. If you are not doing any of this, then the bourgeoisie who you have left unmolested will invariably come to dominate you once more.

Anarchists have always played word games to get around these simple facts. There are the practical anarchists who will admit to some amount of authority, but always with the caveat that theirs is *just* authority, *necessary* authority, and that is is the *unjust* authority that they condemn. Just authority is not the State, because the State is unjust, and so if they see an authority as just then it cannot be the State. Fair enough, you can call things by whatever names you like, but if you put these ideas in practice you basically end up with Leninism. You want to create dual power? You want to abolish the bourgeois state and replace it with a democratic organ of the working class? Well so did Lenin, and now you know why the Mensheviks accused him of anarchism.

Then there are the quite impractical capital-A Anarchists, who are adamant that anarchy means anarchy and that even voluntary hierarchy and submission to democratic authority is impermissible. Whether pacifistic or militaristic, they are generally unremarkable and ineffective at their goals because they eschew most effective forms of organization as ideologically impure. Even the most advanced anarchists, the CNT in Spain and the Maknovists in Russia, were plagued by economic confusion and disorganization. Their lack of discipline led to their downfall.

If you want to read more, here are some pertinent links:

[max1461]

I've said this before but human societies are complicated and human psychology is complicated. Often people who do bad things are also themselves suffering. Often people in positions of power are unhappy. Often there are systemic factors which hurt some people and benefit others, and different systemic factors that benefit the first group and hurt the second, and this doesn't line up into a neat "oppressor/oppressed" binary. Sometimes it does line up into a fairly neat binary on the whole, but the edges are messy. Always, always the edges are messy. Sometimes people do good things for bad reasons and bad things for good reasons. Sometimes you have to work with people you hate, just to get things done. There are only lessors-of-many-evils. There are only ever lessors-of-many-evils. You are always, always, invariably choosing the lesser of many evils.

You are also choosing the greater of two goods! There is some worth in everyone, everyone, there is some way to improve every bad situation, there is some kernel of good in the world always (I claim).

But! Your model is wrong. Your theory is wrong. Your model will always be wrong, that is the nature of models. Some are useful, but never forget they are still wrong. The world is too big for your model to be right. An endless stream of caveats and exceptions and carve-outs is the nature of living in reality and not imagination. It cannot be pretty, it cannot be elegant, it is necessarily ugly. Sorry.

[psychotrenny]

I really do hate the way people use the phrase "Conspiracy Theory" to refer to everything from "Supernatural Bullshit" to "Technically Possible but all the actual evidence is against it" to "We know for sure that this happened like we have declassified documents and decades of testimony from dozens of people and..."

Like it's just such an actively counterproductive conflation of different phenomenon that mostly serves to discredit actual investigation into the activities of those in power. Because sure, it's stupid to act as though the world is primarily driven by the hidden schemes of the powerful. But it's just as stupid to act as though powerful individuals and institutions don't ever get together and enact hidden schemes. Even though these sorts of entities invariably engage in many more equally bad (if not worse) activities in the open, for certain programmes the maintenance of some sort of secrecy does have worthwhile advantages. The fact of the matter is that high level conspiracies happen and they happen for a reason. Along with all the conspiracy "theories" out there, you'll find plenty of conspiracy facts

And sure, broader structural forces are much much more important than any individual project could be. State and Corporate conspiracies generally serve the ultimate purpose of maintaining or accelerating processes that were happening openly and/or "naturally" (i.e. without large scale co-ordinated planning) anyway. But these sorts of plots are still worth talking about not only because of their direct impacts (the greatest of which can change the fate of entire small countries) but also because of the ways they reflect and reinforce the overarching structures that produced them. At the very least, you shouldn't dismiss them out of hand because you think "A powerful entity did something and tried to keep it a secret" is a claim made only by people who've been watching too much X-Files

[demonicseries]

it gets worse. The plot involved me accidentally coming up with a new interdisciplinary subfield of mathematics that is so dense it would take me years to learn all the foundations necessary to explore it. So, um, it looks like I’m gonna have to tweak the plot.

me explaining how they accidentally made lokius canon using mathematical concepts such as chaos theory and dynamical systems

[autonomystic]

Adorno against "nothing ever happens":

Criticism of tendencies in modern society is automatically countered, before it is fully uttered, by the argument that things have always been like this. Excitement - so promptly resisted - merely shows want of insight into the invariability of history, an unreasonableness proudly diagnosed by all as hysteria.

The accuser is further informed that the motive of his attack is self-aggrandizement, a desire for special privileges, whereas the grounds for his indignation are common knowledge, trivial, so that no-one can be expected to waste his interest on them. The obviousness of disaster becomes an asset to its apologists - what everyone knows no-one need say - and under cover of silence is allowed to proceed unopposed.

Assent is given to what has been drummed into people's heads by philosophy of every hue: that whatever has the persistent momentum of existence on its side is thereby proved right. One need only be discontented to be at once suspect as a world reformer. Connivance makes use of the trick of attributing to its opponent a reactionary and untenable theory of decline - for is not horror indeed perennial? - in order by the alleged error in his thinking to discredit his concrete insight into the negative, and to blacken him who remonstrates against darkness as an obfuscator.

But even if things have always been so, although neither Timur nor Genghis Khan nor the English colonial administration in India** systematically burst the lungs of millions of people with gas, the eternity of horror nevertheless manifests itself in the fact that each of its new forms outdoes the old. What is constant is not an invariable quantity of suffering, but its progress towards hell: that is the meaning of the thesis of the intensification of antagonisms. Any other would be innocuous and would give way to conciliatory phrases, abandoning the qualitative leap. He who registers the death-camps as a technical mishap in civilization's triumphal procession, the martyrdom of the Jews as world-historically irrelevant, not only falls short of the dialectical vision but reverses the meaning of his own politics: to hold ultimate calamity in check. […]

Horror consists in its always remaining the same - the persistence of 'pre-history' - but is realized as constantly different, unforeseen, exceeding all expectation, the faithful shadow of developing productive forces. The same duality defines violence as Marx demonstrated in material production: 'There are characteristics which all stages of production have in common; and which are established as general ones by the mind; but the so-called general pre-conditions of all production are nothing more than … abstract moments with which no real historical stage of production can be grasped.'

In other words, to abstract out historically unchanged elements is not to observe neutral scientific objectivity, but to spread, even when correct, a smoke-screen behind which whatever is tangible and therefore assailable is lost to sight. Precisely this the apologists will not admit. On one hand they rave about the derniere nouveautés [latest news] and on the other they deny the infernal machine that is history. Auschwitz cannot be brought into analogy with the destruction of the Greek city-states as a mere gradual increase in horror, before which one can preserve tranquillity of mind. Certainly, the unprecedented torture and humiliation of those abducted in cattle-trucks does shed a deathly-livid light on the most distant past, in whose mindless, planless violence the scientifically confected was already teleologically latent. The identity lies in the non-identity, in what, not having yet come to pass, denounces what has. The statement that things are always the same is false in its immediateness, and true only when introduced into the dynamics of totality. He who relinquishes awareness of the growth of horror not merely succumbs to cold-hearted contemplation, but fails to perceive, together with the specific difference between the newest and that preceding it, the true identity of the whole, of terror without end.

**I think Adorno's remark about India here is diminishing of the gravity of colonialism and creates an unjustified distance between Auschwitz and EIC/British rule over India, which was likewise marked by horrific butchery and the deaths of millions, and thus he bends the stick too far in the opposite direction of his criticism - but I don't think this really diminishes the claim overall.

[literaryvein-reblogs]

The Basic Elements of Tragedy

When we think of tragedy in the context of literature in English, we think first of Shakespeare: of the ‘great tragedies’, Hamlet (1600– 1), Othello (1604), King Lear (1605) and Macbeth (1606). With such plays in mind, and adapting Aristotle’s definition in the Poetics, we could suggest that tragedy comprises 4 basic elements.

There is a central character (the protagonist), someone who is ‘noble’ and with whom we are able to sympathize or identify.

This character should suffer and (preferably) die, and his or her downfall or death should roughly coincide with the end of the play.

The downfall or death of the central character should be felt by the spectator or reader to be both inevitable and ‘right’ but at the same time in some sense unjustifiable and unacceptable.

It has to feel apocalyptic. As we have already indicated, it is not just the death of the protagonist with which we are presented in a tragedy: in identifying with the protagonist who dies, we are also drawn into thinking about our own death. And because the protagonist’s death is invariably shattering to other characters, tragedy always engages with a broader sense of death and destruction, a shattering of society or the world as a whole.

Without these 4 elements, there cannot be a tragedy.

From an Aristotelian perspective we might want to propose additional elements, in particular the notions of:

peripeteia (‘reversal’),

anagnorisis (‘revelation’ or ‘coming to self-knowledge’) and

hamartia (‘tragic flaw’ or ‘error’).

Tragedy is offensive, it generates disunity and exposes disharmony.

Like psychoanalytic theory (itself of course crucially indebted to Sophocles’s Oedipus the King), tragedy makes the unconscious public.

It leaves us uncertain about our very identities, uncertain about how we feel, about what has happened to us.

Source ⚜ More: Writing Notes & References

[thegildedbee]

:: March 4 :: Selection for Week 10 of 2025 :: 🐝"a study in scarlet" (1887) from sherlock holmes: a year of quotes* 🖊️

"I never read such rubbish in my life." "What is it?" asked Sherlock Holmes. "Why, this article," I said, pointing at it with my egg spoon as I sat down to my breakfast. "I see that you have read it since you have marked it. I don't deny that it is smartly written. It irritates me though. It is evidently the theory of some armchair lounger who evolves all these neat little paradoxes in the seclusion of his own study. It is not practical. I should like to see him clapped down in a third class carriage on the Underground, and asked to give the trades of all his fellow-travellers. I would lay a thousand to one against him." "You would lose your money," Sherlock Holmes remarked calmly. "As for the article, I wrote it myself."

The first two chapters of A Study in Scarlet are a master-class in writing -- and although I've made desultory dissections of them multiple times, it seems that no matter how much I deposit into the dusty trunk in my mental lumber room, oddly enough, the interior space never seems to fill up. Hmmmm.

So, the appearance of this article, "The Book of Life," which sports a "pencil mark at the heading," occurs simultaneously with the curious incident of the flatmates at the breakfast table. What curious incident, you may ask? That Holmes was already ensconced at the table before Watson's arrival, when -- heretofore -- "he had invariably breakfasted and gone out before I rose in the morning." And yet, on March 4th, Watson arrives somewhat earlier than is his norm (some manipulation on Holmes's part?), and it seems likely Holmes lingered somewhat later than his norm, and there, placed to hand, the periodical in question, containing an article that not so subtly announces: "read me!"

You can see, no doubt, where I'm going with this :-) Watson has been fascinated by Holmes over the many weeks they've shared digs, and one of the objectives of his Sherlock-sleuthing has been the effort to fathom what in the devil his fellow lodger's occupation may be, reticent as he himself is to inquire straight off. I imagine Holmes has been equally fascinated by Watson, and fascinated by Watson's responses to Holmes's being, and has been deliberately mum on the topic of his lifework just to see how Watson proceeds in consequence. How likely is it that Holmes has ever had such an up-close and personal continuous opportunity to observe another individual? That in itself was likely an addictive circumstance. I find it hard to believe that Holmes was unaware of Watson's perplexity, and therefore had, for whatever reason, decided that March 4 was the day the question was to be answered, in a manner of his own choosing. So: in which periodical did "The Book of Life" appear? This is, admittedly, a tangential question and likely there is little to be gained by trying to posit a realistic option (and here I've no doubt made it obvious as to why it is taking me so long to process two (!) chapters). . . . Nonetheless :-) I reckon that the periodical would be a weekly, because that would allow Holmes, after however many weeks he and Watson had been not-answering the question, to be able to arrange for the article to appear at a non-too-distant time, once he had hit on the idea of using TBofL as his door-opener -- to the world, and to Watson. That is, I don't think it is a coincidence that this event happens when it does (and the universe would never be so lazy, correct? :-) After pondering and hunting, my candidate is Nature, which was founded in 1869, and in which it was not unusual for articles to appear without an attributed author. I think that the Proceedings of the Royal Society are unlikely as Holmes isn't FRS, and the dry exactitude of the essay rules out a general interest publication intended for entertainment. Nature seems to hit the sweet spot between these two poles. As editor Walter Gratzer notes in A Bedside Nature: Genius and Eccentricity in Science, 1869-1953, the journal was filled with material such as "leisurely ruminations on phenomena involving rainbows and lightning and the curious behaviour of ants and pet spaniels," and of reports from all over the globe, such as those of the Astronomical Society of Riga and the Montevideo Natural History Association. I propose, therefore, that Nature is likely to be a congenial home for the purported article.

And in taking a closer look at the period roughly from 1873-1891 (Holmes and Watson are held to have met in 1881), here are some indications of the potpourri of topics one would find within the pages of Nature: observations on how tuning-forks affect garden spiders; whether scorpions are suicide-prone; if sea urchins are capable of altruism; and a weighing of evidence that animals have a sense of humour. Surely there is room for a report within Nature's pages on how observations on "The Book of Life" might best be conducted?

But consider as well: there is an article by Francis Galton on the genetics of criminality; an article on the chemistry of cremation; a review of a work of geometry by Charles Ludwige Dodgson and his construction of an algorithm for finding the day of the week for any given date; reports on the physics of surface tension by Agnes Pockets, a German woman who had not been allowed to attend university and used her kitchen as a laboratory; and "The Remarkable Discovery of a Murder in Bermuda" (of a man who had killed his wife, weighted her corpse, and deposited it in the ocean, calculating "truly enough that the fish would very soon destroy all means of identification; but it never entered into his head that as they did their ravages, combined with the process of decomposition, would set free the matter which was to write the traces of his crime on the surface of the water"). I rest my case :-) Sherlock Holmes himself subscribed to Nature, and announced the arrival of the science of deduction within its pages! The readers of A Study in Scarlet might themselves have made such a comparative observation, underscoring -- between the lines -- a strong indication of Holmes's membership within the scientific community, broadly understood. And, for fun, two more examples of the congeniality of Nature's topics in this time period and the Sherlock Holmes stories: 1) the first is editor Norman Lockyear's stamp of approval for Jules Verne: "For in the author we have a science teacher of a new kind. He has forsaken the beaten track, bien entendu; but acknowledging in him a travelled Frenchman with a keen eye and vivid imagination--and no slight knowledge of the elements of science -- we do not see how he could have more usefully employed his talents." and

2) A rhapsody on the introduction of the Remington Typewriter: "The principal question which this beautiful and ingenious little instrument suggests to our minds is, whether it would not be better for every one of us to learn the Morse telegraph language, and employ it for writing upon all occasions instead of the cumbrous letters now in vogue." (Oh, and it was here that William Gladstone published his argument that Homer was colour-blind, which apparently excited much heated discussion!) [If you're curious about the question of color identification (and how blue and green figure into this in particular) here's a good place to start (in today's world): "The way you see colour depends on what language you speak." . . . And, guess what, I haven't even had time to consider the specifics of Watson's remarks! I am a slave of the digression . . .

...................................................... *Levi Stahl and Stacey Shintani, eds., U of Chicago Pr, 2019

& bespoke notifications as requested :-) [thanks for reading!]: @totallysilvergirl and @winterdaphne2 and @keirgreeneyes and @calaisreno

[galahadwilder]

On the list of favorite Doctor Who theories: the part of the TARDIS’ chameleon circuit that’s broken isn’t the thing that shapeshifts. It’s the thing that decides what to shapeshift into.

So every time the TARDIS lands somewhere new, it takes in huge amounts of data, analyzes its surroundings, runs through multiple forms, and invariably decides that the best camouflage is a blue police telephone box from 1963 England. Which it then turns into.

(She may be doing it on purpose.)

[in-sightpublishing]

The Chosen One

Author(s): Scott Douglas Jacobsen Publication (Outlet/Website): The Good Men Project Publication Date (yyyy/mm/dd): 2024/06/30 According to some semi-reputable sources gathered in a listing here, Rick G. Rosner may have among America’s, North America’s, and the world’s highest measured IQs at or above 190 (S.D. 15)/196 (S.D. 16) based on several high range test performances created…