antinegationism reblogged your post and added:

Unfortunately, in a truly physical context, your…

(Replying like this because the post chain is becoming very large)

About the weights: that was supposed to be a hypothetical setup in Newtonian mechanics, not a thought experiment about something you could actually do.  Sorry if I didn’t make that properly clear.

My point is that there are cases in physical theories when an infinity really should appear, either corresponding to some process that can continue without bound, or to some breakdown in one of the postulates of the theory, or both.

The point is that that infinity is telling us something accurate, and shouldn’t be renormalized away or otherwise removed.  Here’s another example – this is a cool one because it’s an actual infinity rather than just a potential one:

In inviscid gas dynamics, solutions with discontinuities can form in finite time from smooth initial data.  In some sense, these discontinuities are unphysical, because the idea of a bulk quantity like density having a true discontinuity is hard to square with the idea that such quantities are only defined as averages over large sets of particles.  This is an example of the theory going beyond its own strictly defined range of validity, like piling together more and more weights until Newtonian mechanics stops being accurate.

However, these discontinuities (shock waves) can be dealt with in a self-consistent and useful way.  They are a limit of the large-but-finite slopes you’d get in systems with very small viscosity, and often it’s simpler and better to just use inviscid theory and shocks than add a tiny viscosity to get rid of the infinities.

The point of this example is that the infinite slopes in gas dynamics, though they technically correspond to something finite in the physical world (there are no “density discontinuities” in reality), should really be infinite if the viscosity is truly zero.  (This is a widely accepted concept, not something I’m making up.)

Now, can we connect that example to the sum of the natural numbers?  Well, it’ll be pretty contrived, but really we can connect anything infinite to the sum of the natural numbers.  Write the slope as a function of time, rescale time so the divergence happens only as t –> inf rather than at finite time, take some function of the slope so that it grows like t^2 or slower (if it didn’t before), then say that that function is bounded above by (some constant times) the quadratic staircase thing defined by f(x) = (sum of natural numbers up to ceil(x)).  But that f is the partial sums of the natural numbers, and the natural numbers sum to something finite while the slope goes to infinity, so we have a contradiction.

You’re undoubtedly groaning right now because that was a hugely convoluted and belabored way of saying that if you use the usual definition for the sum of a series (which says the sum diverges) together with one that says it doesn’t, you can derive a contradiction.  Duh.

But that’s the whole problem here: we need to know which is valid in which case.  You could say “it’s obvious we can’t do the -1/12 thing here because we’re talking about something that really diverges.”  But when we’re talking about the sum of the natural numbers, we’re talking about something that always “really diverges,” in the ordinary sense.  When are we allowed to treat the sum as finite, and what licenses us to do so?  (That’s a non-rhetorical question, and if you know the answer I would love to hear it.)

As for the complex numbers issue, I think we may not disagree so much.  I am speaking from my historical moment, which is one in which ideas like “complex eigenvalues” and “complex exponentials” (and even maybe “contour integrals”) are things the average physical scientist gets comfortable with in their undergrad days and doesn’t lose any sleep over thereafter, while “renormalization” is this mysterious, creepy thing which still hasn’t been put on a fully rigorous foundation.

It’s true that there are cases where complex numbers work but are mysterious, but the paradigm cases are all unambiguous.  I use complex numbers in my day-to-day work and don’t even think of them as stranger than real numbers anymore, because they’re built into the theories I use in a well-defined and self-consistent way that I’ve become comfortable with.  No one thinks of the -1/12 thing that way because no one is sure how to do the same thing with it.

What you’re saying is that you’re really confident that one day we will view the two the same way, that one day we’ll understand how to wield the -1/12 thing rigorously.  And that we should be, as it were, “mathematical progressives” and speak as though we lived in that more enlightened age to come.  Which is fine if you are actually 100% sure of that prediction.  I’m not.  Some old mysteries have turned into unmysterious tools of the trade; that doesn’t entail that every current mystery will become an unmysterious tool of the trade.

aprilwitching:

nostalgebraist:

pluspluspangolin:

nostalgebraist:

[snip]

I mean, I think that is all true, but it doesn’t strike me as something the original poster would agree with

The original post was full of stuff like

You are free to interpret anime how you wish but performing a “feminist analysis” over it? No, don’t do that. Feminism is very political and it is deeply rooted in Western thought.

Like, yeah, tell that to academics who write feminist analyses of stuff written thousands of fucking years ago (and publish them in prestigious journals).  It’s clear that the OP has a giant philosophical disagreement with these people and probably thinks that academic feminists writing about ancient Roman love poetry are just as full of shit.  But that disagreement goes way beyond anime — the OP just does not approve of feminist literary analysis as a genre, and that puts them at odds with way more people than just queer anime fans

(Many of whom would be much more socially difficult to take potshots at, which is I guess why the post annoyed me enough to get me to say something about it)

actually, i used to get pretty exasperated at feminist analysis of medieval english texts that i felt did not respect their cultural and historical context (though that doesn’t mean looking at, say, saints’ lives featuring virgin martyrs through a feminist lens is never worthwhile, period, just because there was no concept of feminism in thirteenth century europe— but you still can’t treat the work as ahistorical and without a specific cultural context and meanings within that context, imo)

if i recall correctly, the post you’re complaining about may have seemed a little too broad with some of its criticism, but it was also reacting specifically to some really presumptuous, facile, shallow, not-at-all-researched analysis that was (i think) supposed to be part of an educational presentation (at some nerd convention, but still!)

i would be upset, too, if someone not from my country or culture presented themselves as an expert on its popular media or as having insight into that media’s themes and social implications, and then gave this analysis that paid no attention whatsoever to the original cultural context of its subject and was also quite superficial and hyper-simplified in general…?

i’m 100% on board with death of the author and all interpretations of any work of fiction being potentially defensible/valid and stuff, but i’m not on board with lazy thinking, lazy research, and willful ignorance about other cultures being excused with, “oh, it doesn’t really matter what the author intended, anyway…”

By the time I saw this post the original presentation had been deleted (and so had the responder’s copy of it), so I have actually never read it.  I am certainly willing to believe it is as bad as you say.

I was treating the response as its own thing because people seem to be reblogging it for its own sake even without the original presentation, and it goes way beyond saying “you shouldn’t pretend to be an expert if you aren’t” to saying

If you are not Japanese then you don’t have any right to decide which parts of our media are definitely sexist or feminist

and

All you tumblr anime feminists went off to interpret her as a trans man and continued to piss on anyone that tried to tell you otherwise.

and

Femininity isn’t revolutionary and weaponized femininity is bullshit.

and various other gigantic, sweeping, and/or contentious claims that depend on the author’s specific ideas about what person X is allowed to say in context Y, or on their very particular brand of feminism.  (E.g. that last quote – declared without qualification or justification, as though they’re bringing the final word about “femininity” down from Mt. Sinai.  Good we’ve got that one cleared up!!)

I guess I agree with the basic “learn about the cultures you try to talk about” sentiment, but there’s so, so much more than that in the post.

(via aprilwitching-deactivated201808)

the eucatastrophic lifestyle

There’s a continual pattern in my life where I will have somewhere between a few hours and five days of intense productivity – during which period I’ll tend to assume this hypercompetence will last forever, and extrapolate endless rapid progress – and then, having gotten some concrete thing done, will suddenly crash and literally accomplish nothing on any major project for several weeks.

It’s almost always like this.  The proportions are usually about the same, too: “on” periods last between one and seven days and “off” periods last 2-3 weeks (occasionally much more).  Unfortunately, despite this statistical regularity, these periods aren't quite regular enough to be predicted in advance.  This creates a lot of stress that isn’t the result of uncertainty about my literal ability to do my work, but rather the result of uncertainty about how these patterns will map onto the worldly patterns of deadlines and the like.  When given any major responsibility, I never know, even days (sometimes even hours) before the deadline, whether I will enter one of my competent periods or not before it arrives.  If I do, I’ll do it effortlessly and well; if I don’t, I’ll scrape something together at the last minute, I’ll feel ashamed because it sucks, I’ll go in sleep-deprived and present what I’ve done and bullshit about it and people will be forgiving because they know that sometimes I can do good work.  Or something.

The difference between these two states is like night and day.  It’s really as though I wake up some days on a serious dose of some strong stimulant, but I don’t get to choose which days and never know in advance which ones they’ll be.  I can try all sorts of healthy strategies in the “off” periods, I can try diet and exercise patterns and mental tricks and let myself do all sorts of fun things to relax (indeed, since I can’t work, I don’t do anything but “fun relaxing things”), but none of these will let me open up the major project on my computer without it feeling like pulling teeth and quitting after 30 minutes, max, because I realize I’m expending massive amounts of effort for pathetically little gain.  Then one day I wake up and I’m “on” again and the idea of doing anything but work is very strange and unappealing, and all of the shit I’ve gotten behind on in the last few weeks just dissolves.  And I go in to work/school feeling like a conquering hero, or at least some sort of very successful con man.  I feel vindicated.

And in some ways that might be worse than unequivocal failure.  Failure would force me to realize that the kind of work I’m doing might not be right and I should maybe find something else.  This kind of frequent but unpredictable success lets me keep doing this stuff while nonetheless feeling intensely uncertain in a way that can’t be good for my health.  (Chronic stress is bad for you, right?  And every time one of these “major responsibilities” is over, even if I’ve screwed it up, I feel physically so much better, like the way you feel when an illness clears up … )

For a very long time I’ve wondered what it meant that my life involves these types of cycles.  This isn’t the only one – my sex drive also cycles between “asexual” and “very much not asexual,” again with a typical “off” period of 2-3 weeks and a typical “on” period of 1-7 days.  These sex and work periods don’t always coincide, though, which makes it much harder to come up with a hypothesis that explains them.  I feel like this is the kind of thing that must have some sort of biochemical explanation, but I have not been able to figure it out for myself, and I haven’t had much success trying to talk to medical professionals about it.

(To clarify, my mood doesn’t cycle in this way, so I strongly doubt I have anything like bipolar disorder)

There’s stuff I need to actually be doing now, but my mind keeps rewriting some long stupid post tangentially inspired by that J. Campbell shit, and in order to exorcise it I’ll say the gist which is basically 

• at some point in the last N years I stopped thinking I “deserved” anything in particular, even life itself, and in fact stopped thinking in these terms entirely and more in terms of what I can do and what its concrete effects would be
• for instance, even if I don’t deserve to live, I’m not going to kill myself on that basis because that would severely harm some people close to me and have a negligible effect on stuff like the earth’s ability to support human life
• so at that point why does it matter what I “deserve”
• I don’t think I should be part of any kind of radical, directly acting movement because I think there are numerous indicators that the concrete effects of me doing so would be negative
• the previous point has nothing to do with ideology, it has to do with me being bad at this kind of stuff.
• you don’t want my version of direct political action.  have you talked to me?  I’m good at taking rigid systems to their logical conclusions, I’m very obtuse and bad at understanding people
• most of this tumblr blog is about how constantly confused I am by other people
• my father grew up very poor and was involved in radical politics for around a decade in his youth and in a lot of ways it ruined his life (via getting involved with the worst, most manipulative people in his subculture) without doing any apparent concrete good, because he has the same kind of cold, rigid, and easily manipulable mind that I do
• lots of people have insurmountable limitations and cannot “get serious” and start “really trying to change things” the way they tell you heroes do in movies, or if they do they’ll fuck it up in ways very directly predictable from their personal characteristics
• if I were to go into radical politics, I know one concrete effect would be that my father – who is still far left, just a little bit more aware of what people like him and me are like and what’s wrong with us – would feel like, now, near the end of his life, he had essentially failed at raising a child who wouldn’t fall into the same pointless abyss he did
• I’m a mathematics student living in an expensive city, not really “doing anything” about anything except slowly working on math stuff (which I feel like I’m shit at, but I feel like I’m shit at everything) which might, if things go unreasonably well, in some tiny way help us understand some things that might be important about out planet or something
• I’m not saying that as a way of proving my “worth” or that I “deserve” anything, I’m saying it’s better than what would probably happen if I were to start “giving up illusions” and “really trying to change things”
• people like me acting on guilt and self-justification and a feeling of “needing to do something” are not good and you don’t want us, trust me

thefemaletyrant:

princessnijireiki:

latinagabi:

saturnsorbit:

Let’s not forget to acknowledge Alexandre Dumas this Black History Month

The writer of two of the most well known stories worldwide, The Three Musketeers and The Count of Monte Cristo was a black man. 

That’s excellence.

Let’s not forget that he was played on screen by a white man. And the fact that he was black is barely ever mentioned or the book he wrote inspired by his experiences.

Other things not to forget about Alexandre Dumas:

• chose to take on his slave grandmother’s last name, Dumas, like his father did before him.
• grew up too poor for formal education, so was largely self-taught, including becoming a prolific reader, multilingual, well-travelled, and a foodie, resulting in his writing both a combination encyclopedia/cookbook (which just— is fucking outrageous to me) AND the adaptation of The Nutcracker on which Tchaikovsky based his ballet
• he also wrote a LOOOOT of nonfiction and fiction about history, politics, and revolution, bc he was pro-monarchy, but a radical cuss, and that got him in a lot of hot water at home and abroad.
• even beyond that, he generally put up with a lot of racist bullshit in France, so he went and wrote a novel about colonialism and a BLATANTLY self-insert anti-slavery vigilante hero (which he then cribbed from to write the Count of Monte Cristo, the main character of which, Edmond Dantés, Dumas also based on himself).
• (…a novel which also features a LOAD of PoC beyond the Count, and at LEAST one queer character, btw, bc EVERY MOVIE ADAPTATION OF ANYTHING BY DUMAS IS A LIE; seriously, at LEAST one of the four Musketeers is Black, y’all.)
• famously, when some fuckshit or other wanted to come at Dumas with some anti-Black foolishness, Dumas replied, “My father was a mulatto, my grandfather was a Negro, and my great-grandfather a monkey. You see, Sir, my family starts where yours ends.”
• 
• for the bicentennial of his birthday, Pres. Jacques Cirac was like, “…sorry about the hella racism,” and had Dumas’s ashes reinterred at the Panthéon of Paris, bc if you’re gonna keep the corpses of the cream of the crop all together, Dumas’s more widely read and translated than literally everybody else.
• and they are still finding stuff old dude wrote, seriously; like discovering “lost” works as recently as 2002, publishing stuff for the first time as recently as 2005.

ALSO IMPORTANT:

SWAG

This is IMPORTANT!

(via waltzingwithmonsters-deactivate)

kadathinthecoldwaste:

nostalgebraist:

Honestly though I do find thinking about these kind of ethical puzzles really interesting, because it reveals things about ethical sentiments that I would never have thought about otherwise

E.g. I think part of why the dust speck scenario seems so obviously preferable is that if I were someone who knew someone was being tortured to prevent me getting a dust speck in my eyes, I would feel horrible about it.  Knowing that would ruin my life.  And if someone offered me the option to excise this knowledge from my mind, I wouldn’t at all feel like this option would make everything OK again — so clearly it isn’t the knowledge that I think matters, even if it’s what directly causes unhappiness

I feel like the possibility for empathy needs to be somehow incorporated into the utilitarian framework even in cases where empathy isn’t actually felt — because that’s what people would want, if they knew

(On a more boringly technical note, there are unresolved problems with summing up utilities over more than one person the way E.Y. wants to in those posts, although I am sure he is aware of this fact and has some proposed solution)

Could we view this at least in part as a distinction between Act utilitarianism and Rule utilitarianism? It seems like “don’t torture innocent people” is a rule that in the great majority of cases produces the greatest good, and this corresponds fairly well to the notion that “following rules that tend to lead to the greatest good will have better consequences overall than allowing exceptions to be made in individual instances, even if better consequences can be demonstrated in those instances.” (Source: wikipedia.)

I’m that rare person who’s actually pretty pro-Omelas. To my mind the lesson of the story is mostly one about the lengths to which people will go in order to avoid feelings of guilt and moral responsibility. There are thousands, maybe millions of children right now living in conditions a hell of a lot like those of that one child in Omelas, without even the direct provision of happiness to others to give their suffering justification. Yet the vast majority of people who are sure that they would leave Omelas, and pat themselves on the back for their rectitude in so imagining, spend very little time concerned for this huge number of actual suffering children. Or, to put it in a humorously crass manner, the exchange rate on child misery is much worse in the real world than in Omelas, and yet none of these righteous readers seem to care all that much. (This relates to your post a few days back about your frustration, which I share, at people who think that being as concerned about people far away as people close by is somehow contrary to morality and compassion.)

Really, though, I think any moral system that is purely utilitarian or purely consequentialist is going to lead to ethical injunctions that are at best counterintuitive and at worst utterly repugnant. Yud’s argument is a good example of this for pure utilitarianism, but our discussion a couple years back about Kantian morality in law and governance, and the notion of a government that won’t shoot down a hijacked plane even if doing so would save tens of thousands of lives is an analogous case for consequentialism/deontology. Or, say, the notion that because acts are morally neutral there’s nothing inherently wrong with causing the extinction of the human race as long as one *truly* didn’t mean to.

Act vs. rule utilitarianism could be one way to look at it, but it’s distinct from my objection.  I don’t even think that the torture scenario serves the “greater good” better than the dust speck scenario, so I don’t think the problem with it is that it’s an exceptional case.  I feel like a correct, non-broken version of act utilitarianism should choose dust specks over torture, too.

I’m still not sure about the best way to formalize that feeling.  Some of it may have to do with empathy.  The simplest utilitarian treatment of empathy is that it’s just another kind of pain, albeit one that can do good by causing people to help others.  If the 3^^^3 people in the torture scenario knew about the tortured person, and felt awful about it, this would be bad, but (on this account) this problem could be removed by just preventing them from knowing about it.  This doesn’t actually feel like it addresses how we feel about empathy, though.  Most people feel that ordinary pains like toothaches are things they straightforwardly want to avoid, but I don’t think most people want to avoid empathetic pain in the same way.  Part and parcel of the emotion is a desire for its cause to be gone; when in empathetic pain we don’t think “I wish I didn’t hurt” but “I wish they didn’t hurt.”  It seems to me – though I don’t know how to formalize this – that the fact that the 3^^^3 people would feel bad if they knew must be morally significant, even if they don’t know, because if they did know they wouldn’t feel like a removal of their empathy would solve the problem.

In other words, I guess I think that morality involves minimizing the number of situations that could cause empathetic pain if people knew about them.  Note that the 3^^^3 dust specks are not such a situation.  No one would naturally feel that this is a tragedy.  (Yudkowsky would, but not intuitively, only on the basis of theory.  I’d bet that he wouldn’t really be in empathetic pain if such a thing happened, though who really knows.)

It’s possible that my focus on “things that cause empathetic pain” vs. “things that don’t” here is just a way of getting at the more general ideas that not all pains can be lumped together.  EY’s analysis involves the idea that small pains when added up equal large pains, and that if one doesn’t think this way one runs into absurdities (along the lines of “arbitrarily many people in pain state X are better than one person in pain state X+epsilon, where X and X+epsilon are very similar”).  However, this doesn’t seem to accord with our actual experience of pain.  For instnace, some pains feel “bearable” and others feel “unbearable”; dust specks are a prototypical instance of the former and torture is the latter pretty much by definition.  And – even if our own individual lives – we tend to act almost as if infinitely many bearable pains are less bad than one unbearable pain.  Bearable pains are merely annoying, while unbearable pains feel fundamentally wrong or unjust – they interact with the moral sense in a way bearable pains don’t.  (If I am feeling a very intense kind of pain I will usually have thoughts along the lines of “this shouldn’t be allowed to happen to people” – I don’t have anything like these thoughts, not even scaled-down versions of them, when dealing with bearable pains.)

I always interpreted the Omelas story as asking the reader “yeah, you feel like you’d be one of the ones who walk away, but would you really be?  Really?”  I have no idea if that was the intent, though.

(via dagny-hashtaggart)

kadathinthecoldwaste.tumblr.com →

Lockhart’s painting analogy is possibly even better than his music analogy:

Meanwhile, on the other side of town, a painter has just awakened from a similar nightmare… 

I was surprised to find myself in a regular school classroom– no easels, no tubes of paint. “Oh we don’t actually apply paint until high school,” I was told by the students. “In seventh grade we mostly study colors and applicators.” They showed me a worksheet. On one side were swatches of color with blank spaces next to them. They were told to write in the names. “I like painting,” one of them remarked, “they tell me what to do and I do it. It’s easy!" 

After class I spoke with the teacher. "So your students don’t actually do any painting?” I asked. “Well, next year they take Pre-Paint-by-Numbers. That prepares them for the main Paint-by-Numbers sequence in high school. So they’ll get to use what they’ve learned here and apply it to real-life painting situations– dipping the brush into paint, wiping it off, stuff like that. 

Of course we track our students by ability. The really excellent painters– the ones who know their colors and brushes backwards and forwards– they get to the actual painting a little sooner, and some of them even take the Advanced Placement classes for college credit. But mostly we’re just trying to give these kids a good foundation in what painting is all about, so when they get out there in the real world and paint their kitchen they don’t make a total mess of it." 

"Um, these high school classes you mentioned…" 

"You mean Paint-by-Numbers? We’re seeing much higher enrollments lately. I think it’s mostly coming from parents wanting to make sure their kid gets into a good college. Nothing looks better than Advanced Paint-by-Numbers on a high school transcript." 

"Why do colleges care if you can fill in numbered regions with the corresponding color?" 

"Oh, well, you know, it shows clear-headed logical thinking. And of course if a student is planning to major in one of the visual sciences, like fashion or interior decorating, then it’s really a good idea to get your painting requirements out of the way in high school." 

"I see. And when do students get to paint freely, on a blank canvas?" 

"You sound like one of my professors! They were always going on about expressing yourself and your feelings and things like that—really way-out-there abstract stuff. I’ve got a degree in Painting myself, but I’ve never really worked much with blank canvasses. I just use the Paint-by-Numbers kits supplied by the school board." 

A Problem in Dynamics

An inextensible heavy chain
Lies on a smooth horizontal plane,
An impulsive force is applied at A,
Required the initial motion of K.

Let ds be the infinitesimal link,
Of which for the present we’ve only to think;
Let T be the tension, and T + dT
The same for the end that is nearest to B.
Let a be put, by a common convention,
For the angle at M ‘twixt OX and the tension;
Let V_t and V_n be ds’s velocities,
Of which Vt along and Vn across it is;
Then V_n/V_t the tangent will equal,
Of the angle of starting worked out in the sequel.

In working the problem the first thing of course is
To equate the impressed and effectual forces.
K is tugged by two tensions, whose difference dT
Must equal the element’s mass into V_t.
V_n must be due to the force perpendicular
To ds’s direction, which shows the particular
Advantage of using da to serve at your
Pleasure to estimate ds’s curvature.
For V_n into mass of a unit of chain
Must equal the curvature into the strain.

Thus managing cause and effect to discriminate,
The student must fruitlessly try to eliminate,
And painfully learn, that in order to do it, he
Must find the Equation of Continuity.
The reason is this, that the tough little element,
Which the force of impulsion to beat to a jelly meant,
Was endowed with a property incomprehensible,
And was “given,” in the language of Shop, “inexten-sible.”
It therefore with such pertinacity odd defied
The force which the length of the chain should have modified,
That its stubborn example may possibly yet recall
These overgrown rhymes to their prosody metrical.
The condition is got by resolving again,
According to axes assumed in the plane.
If then you reduce to the tangent and normal,
You will find the equation more neat tho’ less formal.
The condition thus found after these preparations,
When duly combined with the former equations,
Will give you another, in which differentials
(When the chain forms a circle), become in essentials
No harder than those that we easily solve
In the time a T totum would take to revolve.

Now joyfully leaving ds to itself, a-
Ttend to the values of T and of a.
The chain undergoes a distorting convulsion,
Produced first at A by the force of impulsion.
In magnitude R, in direction tangential,
Equating this R to the form exponential,
Obtained for the tension when a is zero,
It will measure the tug, such a tug as the “hero
Plume-waving” experienced, tied to the chariot.
But when dragged by the heels his grim head could not carry aught,
So give a its due at the end of the chain,
And the tension ought there to be zero again.
From these two conditions we get three equations,
Which serve to determine the proper relations
Between the first impulse and each coefficient
In the form for the tension, and this is sufficient
To work out the problem, and then, if you choose,
You may turn it and twist it the Dons to amuse.

(A poem written by James Clerk Maxwell of “Maxwell’s equations” fame)