koganbot: (Default)
[personal profile] koganbot
OK, start talking. This is what I'm calling the First General Comments And Questions (C&Q) Thread. The article under consideration is Thomas Kuhn's "What Are Scientific Revolutions?" which you can find your way to here, pp 13 to 32. I'm asking six questions but you can ask your own as well, and you don't have to answer mine 1, 2, 3, 4, 5, 6 separately in that order (though you can if you want). You should have a good idea how to answer the first three, however. Questions 4 through 6 are generated by the essay (at least in my mind), but they're not specifically asked and definitely not answered in it.

1. Kuhn starts the essay by distinguishing between "normal" and "revolutionary" scientific development, saying that the former is "cumulative" and the latter "noncumulative." He uses the metaphor of the brick: "normal science is what produces the bricks that scientific research is forever adding to the growing stockpile of scientific knowledge." Not sure he isn't mixing his metaphors here, "brick" and "stockpile," since I think he means the brick metaphor to give us a picture of bricks being layered atop one another to build an enduring structure.

What do you suppose he means by "cumulative" and "noncumulative" change? Surely he's not saying that in a science that's undergoing normal change there are no widely believed ideas that turn out to be in error. So what's the difference between a normal correction and a correction that leads to a revolution? What's the difference between a normal new idea and a revolutionary new idea? Is the idea that Pluto is not a major planet a revolutionary idea? How about the idea that the demise of the dinosaurs 65 million years ago was not drawn out but was one of the relatively sudden after-effects of a strike by one or more meteors?

2. What's a paradigm and what's a paradigm shift? Kuhn doesn't actually use the terms in this essay; but nonetheless, the revolutions he describes are paradigm shifts. What do you think he means by "paradigm" and "paradigm shift"? (If you click on the "thomas kuhn" tag up above you can find your way to some previous talk on the subject. He uses the term in both a narrow and a broad way, and it's good to be clear on the difference.)

3. What does Kuhn mean by "incommensurability"? This is another term that doesn't appear in the piece, but the concept gets well-described in it. In a different essay he uses the words "residue" and "loss" in association with "incommensurability." What's the residue? What's lost?

4. Is Kuhn's conception of "normal science" a good one? Are there really periods when a science undergoes no noncumulative adjustments, where all the basic terms are at ease with themselves and with each other?

5. Do any of the nonsciences* have equivalent periods, or is what Kuhn is saying is "normal" in normal science not normal elsewhere?

6. If competing paradigms are incommensurable, how does one choose between them? If Kuhn's model is right, an entire field can and sometimes does end up abandoning one paradigm as wrong and embracing another as right. How does it do so? Another way of putting the question - one that obviously doesn't just apply to the sciences - is: if different premises (and their related models and frameworks) generate different "facts," facts that support the premises, how do you go about testing your premises and, when there are competing, incompatible premises, how do you choose one set of premises over another? Is there a rational way of doing so, or is this really just a matter of taste? How would you test the contention that motions or changes must have endpoints, or the competing contention that motions or changes need not have endpoints?

*For example, math, psychology, music criticism, art, politics, situation comedies, girls night out, organized sports, etc. etc. etc.

further to (5) and (6)

Date: 2009-01-27 04:14 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
i think we have to explore what actually constitutes a "field" here -- kuhn's theory seems to presented as if science as a whole is a field, at the same time that physics-as-a-whole is a field and and biology-as-a-whole is a field and maths-as-a-whole is a field, even though all of physics and all of biology and (arguably) all of maths do not combine to be all of physics

this matters because it's not clear to me that a revolutionary shift in the use of the word "planet" had any implications for biology or maths -- somewhere late in the essay, p.29 in fact, TK says that the first shared characteristic of the kind of scientific revolution he's looking at is that it's "somewhat holistic", where "somewhat" is a giant massive handwave! (haha someone on a popular comments thread just used the phrase "slightly objective" and i think "somewhat holistic" falls in the same category of "we know what it means even tho it's strictly speaking meaningless")

i have a bunch more thoughts to come, some of which will be questions and some answers -- i am intermittently busy today and tomorrow so they will be a bit piecemeal

Re: further to (5) and (6)

Date: 2009-01-27 04:49 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
"kuhn's theory seems to presented as if science as a whole is a field" -- mmmmph, what i meant here is "kuhn's theory seems to GET presented as if science as a whole is a field", which i think is more defensible

your response pretty much matches my feeling, that science is more like a looser accretion of disciplines, of different histories and revolutions which don't need to cross from one to another

but i wonder why then it's felt useful to have an overall project of the excloration of "scientific revolutions" -- why maintain a project unity?

(i mean, "*we're* looking at the usefulness of the theory OUTSIDE science, so we need a boundaryline for other reasons, but does kuhn ever even need to reach a generalised definition of "scientific revolution"? why can't he just carry on accumulating locally specific example? is this in fact what he's doing?)

Re: further to (5) and (6)

Date: 2009-01-27 04:56 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
sorry, bunch of rhetorical questions you mostly answered in the previous post!

there's arguably a paradigm shift in the understanding of how science-as-a-whole coheres, in that -- from sometime in the mid-18th century to sometime in the mid-20th century -- it was widely assumed that the "major" sciences were nested WITHIN one another, very roughly maths >> physics >> chemistry >> biology >> psychology

so that a full scientific explanation of some "law of psychology" would (eventually, given enough science) turn out to be explicable in terms of the laws of maths

Date: 2009-01-27 08:46 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
"usually classed in the humanities" is probably more related to administrative requirements = "doesn't need labs o fancy equipment, just books"

it's interesting that two of the three examples TK deploys in this essay -- the first and the last -- actually hinge on a shift of attitude to a highly mathematical concept

it's infinity in the first, in newton's highly weird) concept of an infinitely extended rectilinear nothingness in which the world of matter tidily sits, essentially unaffected by the entirety of the nothingness

it's the distinction between continuity and particularity in the third, which was a very fought-over area in 1th-century mathematics (the mathematicisation of continuity involves some fantastically dodgy algebraic tricks, including another fabulous weirdness invented by newton and/or leibnitz, viz the idea that you can divide zero by zero and get a meaningful and precise answer

(i actually have to say i'm not quite sure i understand how the batteries example constitutes a "revolution" -- the word "resistance" changes meaning and useage, with a certain degree of institutional er resistance, but TK doesn't give much of a sense of all the lower-layer bricks which had to be unlaid and tossed aside...

o ffs

Date: 2009-01-27 08:48 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
"very fought-over area in 1th-century mathematics" = "very fought-over area in 19th-century mathematics"

Date: 2009-01-28 03:15 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
I have no idea about this concept, but I also don't see where it's relevant to the example that Kuhn gives, comparing Aristotelian motion to Newtonian

pp19-20: "I shall instead conclude this first example with a last illustration, Aristotle's doctrine about the vacuum or void... If there could be a void, then the Aristotelian universe or cosmos could not be finite... [E]xpanding the stellar sphere to infinity would make problems for astronomy, since that sphere's rotations carry the stars above the earth. Another, more central, difficulty arises earlier. In an infinite universe there is no centre--any point is as muc hte cnetre as any other--and there is thus no natural position at which stones and other heavy bodies realise their natural qualities."

Your argument is that the example given depends or hinges only on a change in meaning and use of the word "motion": but this seems problematic in two ways, One is simply that Kuhn does include the above, as a "last iluustration" (unnecessary addition if, as you say, it's irrelevant); two is that we surely have to make a distinction between the (backwards) path Kuhn took (spurred by his recognition that "motion" meant incommensurably different things to different people) and the path that cosmology took, as it moved from Aristotle's paradigm all the VERY long way to Newton's (2000 years!). Surely a key point Kuhn is making here is that a whole bunch of things move around and change -- you can boil it down to the tale of motion for purposes of dramatisation, and to help isolate the (important) fact that certain words seem radically to change their meanings during such a revolution, but this is not the only thing going on, nor (necessarily) the central caustive element in the transformation (in fact it's very likely NOT the central cause: centrality would probably imply change of terminology -- retained words with greatly shifted meanings are very probably words that been dragged from where they once sat by convulsions elsewhere in the revolution).

All this is underlined somewhat the relative rhetorical weakness of the the meaning-change aspects of the second two examples: the battery meaning-change is interesting and very suggestive, but really the old meaning of battery hasn't vanished from the world; and in the third example, he handwaves at a word-substitution, "resonators" for "oscillators", which frankly FAILS to do the work Planck is said to want it to ("oscillators" is hardly disconnected from all possible acoustic analogy, any more than "resonation" is incapable of being used in non-acoustic contexts).

In general my argument is generally going to be that one of the reasons Kuhn's discussion of revolutions sometimes gets very lost in vagueness is because he doesn't pay consistent enough attention to the role that willed change in physical practice* is (always?) playing -- choices made at THIS level may well be just as reasoned (tho doubtless often aren't)** as than choices made at the theoretical or verbal levels...

*as you'll see later i have a slightly eccentric definition of physical practice
**exploring this will be my non-evasive answer to point 6

telling vagueness (p.31)

Date: 2009-01-28 03:40 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
"If the exhibit succeeds, the new initiates emerge with an acquired list of features salient to the required similarity relation -- with a feature-space, that is, within which the previously juxtaposed items are durably clustered together as examples of the same thing and are simultaneously separated from objects or situations with which they might otherwise have been confused."

This is terribly clumsily written and woolly -- in a piece which is generally vivid -- and I think the reason is, tellingly, that he is attempting a generalised spatial metaphor as opposed to a particular or concrete one (concrete: "hinges on").

some very rough and hurried answers (1-2)

Date: 2009-01-27 08:33 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
1. What's the difference between cumulative and noncumulative change?
Kuhn starts the essay by distinguishing between "normal" and "revolutionary" scientific development, saying that the former is "cumulative" and the latter "noncumulative." He uses the metaphor of the brick: "normal science is what produces the bricks that scientific research is forever adding to the growing stockpile of scientific knowledge." Not sure he isn't mixing his metaphors here, "brick" and "stockpile," since I think he means the brick metaphor to give us a picture of bricks being layered atop one another to build an enduring structure. What do you suppose he means by "cumulative" and "noncumulative" change? Surely he's not saying that in a science that's undergoing normal change there are no widely believed ideas that turn out to be in error. So what's the difference between a normal correction and a correction that leads to a revolution? What's the difference between a normal new idea and a revolutionary new idea? Is the idea that Pluto is not a major planet a revolutionary idea? How about the idea that the demise of the dinosaurs 65 million years ago was not drawn out but was one of the relatively sudden after-effects of a strike by one or more meteors?

I would parse this thus: An error during cumulative change require the change of content of the single brick currently being laid; not of an brick lower in the wall, which would require the displacement and replacement of other bricks level with but distinct from the current brick. So cumulative means never having to go back a layer; non-cumulative means you have to go back a layer -- or at least demolish and replace more of the current layer than the brick in which error was discovered. Pluto's relabelling is revolutionary if it requires us to rethink the celestial mechanism as a whole; not if it just means we relabel some of the bodies based on better observation of where they;re go (round what etc); the meteor strike is revolutionary if fast-extinction changes our undersanding of eg what is descended from what, how descent works, but not if it simply means we have to redraw the dating of extinctions. Revolution -- in terms of the "brick" metaphor -- means having to pull out bricks that other bricks were on top of.

2. What's a paradigm and what's a paradigm shift?
Kuhn doesn't actually use the terms in this essay; but nonetheless, the revolutions he describes are paradigm shifts. What do you think he means by "paradigm" and "paradigm shift"?

I'm not sure your collapse (on an earlier thread) of paradigm and model (the former a "fancypants" word for the latter) is helpful, though it's entirely defensible by ordinary usage. Model comes from "modello", which straps a diminutive onto the latin-italian (modus/modo) for the noun "a measure"; a model would thus something physical that you can keep on your desk-top (or imaginably equivalent to same). Paradigm (from the greek, to show beside) was originally *grammatical*, a verbal exemplar to demonstrate rules of language: Kuhn uses it -- incorrectly considering its root but usefully -- to mean the "system we are operating in; the system whose coherence is being threatened or validated"... just as the exemplar as a synecdoche for the language it sits within and demonstrates. Kuhn is correct I think that small p-paradigms and large p-paradigms sometimes get confused with one another; or moved up off the "small p" onto the "large p"and vice versa -- but I think that at any given moment, the model and the paradigm will be pointing the pupil or researcher in different directions, the one towards a simplified or neatened or pocket-size version so that specific relationships or characteristics are more easily graspable; the other towards a sketch of the system that "everything" (ie everything pertaining to the relevant discipline) operates with in. So a paradigm shift would be when the discipline changes in a significant way. (You can of course have a model of a paradigm; can you have a paradigm of modelling?)

some very rough and hurried answers (3-4)

Date: 2009-01-27 08:34 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
3. What is incommensurability?
What does Kuhn mean by "incommensurability"? This is another term that doesn't appear in the piece, but the concept gets well-described in it. In a different essay he uses the words "residue" and "loss" in association with "incommensurability." What's the residue? What's lost?

In the example we discussed -- the isoceles right triangle -- the residue turned out to be the bit that would always be left behind; whatever whole number you assigned as length to the shorter sides, whatever unit of measure derived from this, there would be a little piece of length left over. It's the gap between measurement as bridge-builders (and space-rocket builders) define it, which rwhen you come eright down to it always has a "good enough for jazz shimmy; and measurement (or number) as it functions within mathematics. The latter has given the former all kinds of tricks to get the engineer's estimate incredibly exact - logarithms, to cite something you and i are old enough to have learnt to use via printed tables -- but the latter still exists in a different realm of thought. Maths is (with certain cranky caveats) a realm where infinity is a real thing, for example. For other paradigm shifts, what's "lost" is possibly better defined as "what can no longer be observed".

4. Is Kuhn's conception of normal science a good one?
Are there really periods when a science undergoes no noncumulative adjustments, where all the basic terms are at ease with themselves and with each other?

I would hesitate to periodise this so strictly: it's not a matter of TIMES when science is non-normal, it's a matter of PLACES. Obviously in an abstract sense the "basic terms are no longer at ease with one another" across the board once they are ill-at-ease anyway, but in practice this unease spreads gradually, not instantaneously. (The danger I think is assuming we have a place to stand, above the fray, where we can see the different projects and zones clearly and make perfectly rational-managerial distinctions: there is in fact no such place... )

a redherringvolk of bad analogies

Date: 2009-01-27 09:40 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
For other paradigm shifts, what's "lost" is possibly better defined as "what can no longer be observed". -- ok this is (or may be) a better definition, sez me, but it's just as adly misleading as "lost"... the thing that's "missing" (the "residue") is really an artefact of an early, no-longer-used observational or documentary or calculating technology...

(the paradigm-shift between engineering and post-pythagoras mathematics seems to be different in type than other revolutions: since both fields contined to exist and evolve in tight embrace -- the "residue" isn't lost in this instance, it just stays hovering between the two fields, a bit of exact but unmeasurable number that one system can work with and the other just throws away)

some very rough and hurried answers (5-6)

Date: 2009-01-27 08:35 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
5. Do any of the nonsciences have periods equivalent to a science's normal periods?
Do any of the nonsciences* have equivalent periods, or is what Kuhn is saying is "normal" in normal science not normal elsewhere?
*(For example, math, psychology, music criticism, art, politics, situation comedies, girls night out, organized sports, etc. etc. etc.)


Paradigms aren't periods really -- they're more like territories; they have location in space as well as time, and their placing in time is determined by their placing in space (which lab the revolution starts in, and what its relationship is to the other labs). Those who fail to accept -- or be accepted by -- the new paradigm don't necessarily vanish from the world; and, as they continue to use the tools of observation or documentation (or creation) that others have rejected, the nature and the purpose of their practice shifts, or is shifted.

6. How does one choose between incommensurable paradigms?
If competing paradigms are incommensurable, how does one choose between them? If Kuhn's model is right, an entire field can and sometimes does end up abandoning one paradigm as wrong and embracing another as right. How does it do so? Another way of putting the question - one that obviously doesn't just apply to the sciences - is: if different premises (and their related models and frameworks) generate different "facts," facts that support the premises, how do you go about testing your premises and, when there are competing, incompatible premises, how do you choose one set of premises over another? Is there a rational way of doing so, or is this really just a matter of taste? How would you test the contention that motions or changes must have endpoints, or the competing contention that motions or changes need not have endpoints?

I'm not sure that "one" does choose between them; almost better to say "they choose between us". We pick the tools we favour and the companions we prefer -- which would include the language and the mythologies -- the problems we tell ourslves we're solving, as opposed to the effects we're actually having -- and how language and mythology are used "within the field". By doing so, we open ourselves to the shaping energies of the paradigm -- old or new, if that's a distinction -- the full extent and implications of which we may not have any grasp of, yet. Also, to "different premises (and their related models and frameworks)", I would append "different technologies of observation, comparison and documentation": I think paradigms are cultured round practice, and practice is a matter of physical as well as mental tools and skills. A seamstress can see facts that a metallurgist can't, and vice versa. Does an "entire" field ever abonadon a paradigm? More usually I think the field splits into two: the two then drift away from one another, sometimes a very long way, in terms of cultural status and usefulness (astrology and astronomy, for example).

can't draw = can't think

Date: 2009-01-27 09:52 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
it occurs to me that the way i -- intuitively -- distinguish between a science-y zone of near-each-other paradigms and an arty zone of near-each-other (haha) para-paradigms is actually somewhat to do with the likely geoemtry of nearness -- the former having a tree-ish type connectivity (which could be modelled with bricks); the latter very likely not (and couldn't)

whether i can explain this without a picture i don't know

restating

Date: 2009-01-28 02:41 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
fair enough (esp. for (6)): my intention was to get SOMETHING said before i got diverted into a superbusy three weeks, so we actually start a discussion at all instead of it tailing off into you posting six questions and no one responding for months on end (particularly aggravating as i am on a two-month cycle busy-unbusy which is too long for anyone not me to carry in their heads)

Date: 2009-01-28 04:50 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
maybe with two and three -- but restate them according to this now non-secret agenda: viz "based on the information in this essay, can we say what ______ means"

see spot SIT

Date: 2009-01-28 10:59 pm (UTC)
From: [identity profile] dubdobdee.livejournal.com
sorry, i was being a bit flippant -- i know you'd suggested that earlier exercise ("exercise: definition of a project you are advised to do but also in fact secretly excused from doing, like practicing scales") but when tuesday came you posted these six quite big questions, which actually seem to be nudging the answerer in another direction -- i'm bad enough as it is (as you know) at hurtling off onto my own tangents and jumping way ahead of where we should have got to and dragging bizarre semirelevant roadkill in from other unrelated sprees -- so really all i meant it, keep asking really direct questions, it may help me stay focused


Date: 2009-01-27 09:46 pm (UTC)
From: [identity profile] skyecaptain.livejournal.com
I'll be able to comment on this tonight -- might take it to my own LJ for repost if my thoughts end up being substantial enough.

Date: 2009-02-01 10:13 pm (UTC)
From: [identity profile] petronia.livejournal.com
I'm going by my own feel for these words first, before analyzing Kuhn's text (which in any case I'm finding difficult to do within the parameters you laid out ^^;): to me a "paradigm" is a trick of the mind, where a "model" is external - I won't use the word objective... An open cube made of sticks is a model. A Necker Cube drawing is also a model, but the brain's interpretation of the Necker Cube's conflicting perspective is paradigmatic. The corner points either inward or outward; it's not merely difficult to hold both views at once but actively inpossible. The mind is trapped by its own design, a biological computer optimized to match input with preexisting stored patterns... IOW I almost feel like the usefulness of the word is more in describing the scientist than in the science, that if there were no mental conflict (i.e. in periods of cumulative change where what came before can be assumed) there would be no need for the concept at all. The battery example fits with my definition, I think, because it pretty much is an optical illusion. (A misnomer, as they have nothing to do with optics.)

Date: 2009-02-01 10:23 pm (UTC)
From: [identity profile] petronia.livejournal.com
Also: this is how I would generalize the concept to social sciences as well, and to the arts. Psychology and economics certainly have/had paradigms... With art it is a little different, less axed on theories re: what is happening than on systems/hierarchies of value judgment, perhaps... i.e. I wouldn't want to call the rise of abstraction in the visual arts (say) a paradigm shift so much as a change in an entire nexus of beliefs concerning originality, intellectual property, tradition, progress...

Date: 2009-02-02 01:57 am (UTC)
From: [identity profile] skyecaptain.livejournal.com
Since I can jump ahead and speculate wild 'n' recklessly here, I should just state flat out that one reason my readings haven't been super close so far is because I keep thinking about how to or not to apply this stuff to not-science. (A teacher of mine once told me, "You always jump straight to the end. What must your girlfriend think?") Specifically to discussions of culture -- my feeling so far is that Kuhn's ideas of revolutionary change aren't applicable to matters of culture, because the nature of the change in cultural matters is always cumulative, and there are no systems of understanding (through language) that are "violated" in order to include some new idea. (I like Kuhn's use of "univocal" to describe our understanding of a given word or concept in only one way, so that the Ptolemaic planet and Copernican planet can't coexist as one word, "planet," with one meaning in the same sentence.)

Social ideas co-exist, if not peacefully, then at least in ways that aren't categorically incompatible. But I am encouraged by how wrong I have been so far and haven't given up hope that I may well be quite wrong now, too. I say "hope" because I would LIKE to be able to (1) understand Kuhn better and then (2) apply to stuff that, frankly, I like talking about anyway. But I'll try to keep Dick 'n' Janing it for the time being...

Date: 2009-02-02 03:10 am (UTC)
From: [identity profile] petronia.livejournal.com
I'm also a jump-straight-to-the-end-then-fill-in-the-middle type! That's why the start-with-basic-definitions approach is hard for me.

Mmm I see what you mean... I admit the examples I was considering when I wrote the above have nothing to do with progress/change, per se, but rather cultures/value systems coexisting in time if not space. (And that by analogy only with the process of discovery described by Kuhn, going from superficial "wrongness" - "Why are you being knowingly rude to me?" - to a realization of fundamental and systematic differences - "Oh, it's not that you don't respect my property, it's that we don't have the same definition of ownership or what causes it to be transferred.") But this was the idea I was groping at in my comments anyway: that a "paradigm" can only be recognized/defined insofar as it comes into conflict/contrast with another. Otherwise you're fish trying to describe water. Aristotlean physics only came into existence as the destruction was underway... I think the idea that social paradigms can coexist when scientific paradigms cannot is a paradigmatic belief in and of itself, i.e. that when one is able to hold both social models in one's head (and move between them) it makes them both somewhat/possibly true, whereas understanding both scientific models doesn't make them both true. But both the relativism of the former statement and the objectivism of the latter are modern ideas.**


** I'm likely to have sinned here in using words without being certain about their meanings, as [livejournal.com profile] koganbot has previously griped. XD;

Date: 2009-02-02 06:12 pm (UTC)
From: [identity profile] petronia.livejournal.com
I think you misunderstood my sentence, but only because it was constructed terribly. XD; It really should have been something like
I wouldn't want to call the rise of abstraction in the visual arts (say) a "paradigm shift", so much as I would reserve the term for a change in an entire nexus of beliefs concerning originality, intellectual property, tradition, progress - a coherent example of which is not currently coming to mind.

I am only groping toward what I really mean here. Something along the line of: the appearance of abstract painting in Western fine arts is only a symptom, what really changed was the system of values underlying the artists' work, i.e. the definition of what it means to "paint" (or create art) changed, and thus the activity and its goals naturally broadened to take in strategies unavailable under the definition that previously held sway.
Edited Date: 2009-02-02 06:14 pm (UTC)

Date: 2009-02-02 06:15 pm (UTC)
From: [identity profile] petronia.livejournal.com
W00t! XD

Profile

koganbot: (Default)
Frank Kogan

July 2025

S M T W T F S
  12345
6789 101112
13141516171819
20212223242526
2728293031  

Most Popular Tags

Style Credit

Expand Cut Tags

No cut tags
Page generated Jul. 14th, 2025 08:59 am
Powered by Dreamwidth Studios