Install Theme

The Kyoto Journal variably categorizes butoh as dance, theater, “kitchen,” or “seditious act.”

(Source: menpale, via jollityfarm)

“Enough!” he commanded, the voice emanating from the same cold well as pale frogs with blind embryonic eyes and hairless rats and nights of no return.

studyinglogic:

Ulam has much the same sentiment as the man in the last two panels. Rota quotes Ulam (in his book Indiscrete Thoughts, p. 58) as saying:

What makes you so sure that mathematical logic corresponds to the way we think? Look at that bridge over there. It was built following logical principles. Suppose that a contradiction were to be found in set theory. Do you honestly believe that the bridge might then fall down?


My personal view is that the sentiment above is wrong: if 1 and 1 don’t equal 2, then the bridge couldn’t be built in the first place, and civilisation couldn’t get off the ground from the start, since counting couldn’t work. 

What Ulam and the man above are suggesting is that it’s possible for mathematics as we know it to go wrong, and for the world to remain the same. But I cannot agree with that assumption: mathematical truths are (to me) paradigms of necessary truths.


To see which side you’re on, try this thought experiment (not original to me):

Imagine that in this world, whenever people add 2 objects and 2 objects together, a malicious demon always adds 1 object. So two oranges stacked with two oranges become five oranges, and so on. Do you think our mathematical calculations would come out any different? Would we conclude that 2+2=5, or would we still have our normal law of 2+2=4?

In 800+ notes I’m sure someone else has already made the following argument, but:

This thought experiment relies on a confusion about the relationship between math, physical law, and reality.

Before I flesh that out, here is my answer to the thought experiment.  We would still ultimately conclude that 2+2=4, because the demon apparently has a well-defined notion of what counts an object.  For instance, if (as stated) you have to get four oranges together to make the demon do its magic, then the demon considers “an orange” to be an object, but not “half an orange” (since two oranges, put together, do not turn into 2 and a half oranges).  So, in this hypothetical world, the usual counting rules (including 2+2=4) would work except in special cases, and we could discover all of ordinary science by looking at the behavior of every piece of the word that is not a “complete object” according to the demon.

Now if I understand correctly, this is the conclusion OP wants me to draw: 2+2=4 is a necessary truth, so it’s true even in a world where it superficially appears to be false.  But I think this is confused.  We are conflating two very different things:

(1) which statements are true in a given formal system (in this case, some version of arithmetic with the natural numbers)

(2) which truths about reality can be reliably derived using a model based on that formal system

There are plenty of well-defined formal systems that don’t make good models of certain parts of reality, and this has no bearing on the a priori truth value of theorems in those systems.  In F_2, the finite field with 2 elements, 2+2=0 (indeed, 1+1=0).  This doesn’t make a good model of what happens when you put oranges together, but it’s still a true theorem.

Without specifying which physical system we are trying to model, the question “does 2 plus 2 equal 0?” doesn’t even have a well-defined answer.  It does in F_2, it doesn’t in Z.  If we are using addition to model putting oranges together, Z is the right system.  If we’re using addition to model XOR on binary digits, F_2 is the right system.

I think Ulam is referring to a rather different issue.  When we build bridges (etc.), we use some principles of reasoning and calculation that seem to work (i.e. to be good models); additionally, people have tried to axiomatize these principles.  Ulam is saying that some axiomatization may turn out to be bad, and that this may not in itself repudiate the principles, which seems undeniably right to me.  There is more involved in the axiomatizations than is necessary for individual applications like building a bridge, which is why (for instance) we are able to dispute whether to include the Axiom of Choice without physical applications simply settling the matter one way or the other.

(via studyinglogic)

xxxdragonfucker69xxx:

ok listen as a kid i thought science had to be super rigorous 100% exact all the time but it turns out at high levels it is all approximations all the time, theres not really a point to this post i just want to spread awareness of something we have to do

the equation for force on a spring is pretty well known, kx^2 (quadratic, goes with the square of the distance). the graph looks like this

here comes part one of the bullshit: theres a mathematical technique called a taylor expansion where you can take any equation (as long as it doesnt do a few mathematically rude things) and turn it into a bunch of polynomials (a+bx+cx^2+dx^3), which makes things a lot mathematically simpler

part two of the bullshit: if you zoom in real small you can ignore most of the latter terms, so its basically just a x^2 equation

so basically if you draw any goddamn squiggle and zoom in REAL close it looks like a parabola and therefore any REALLY small thing acts like a spring

atoms in a molecule. bumps on a road. electrons in an atom (before you get to the nasty stuff). just now i was thinking about bubble wrap. a weight on a pendulum. probably, like, interpersonal relationships. its all springs. boing

This is one of those physics things I wish more people knew

Back in 2014 I started trying to write a book about “the methods of mathematical physics” for a lay/popular audience, and I didn’t get very far, but this is how it started

image

(via prospitianescapee)

birdblogwhichisforbirds:

This is my video for Project 4 awesome, which is an annual YouTube-based fundraising event run by John and Hank Green.

Also please go and vote for EA charities in p4a, it can result in $25k per charity!
The three links below are all to the lists of videos for each charity. You can click on each video to vote - as all the charities have more than one video, you can vote for each video and the votes among all the videos get aggregated. There is also still time to submit a video yourself.
http://projectforawesome.com/?charity=WUDGW89r
http://projectforawesome.com/?charity=JZ2iuLvs
http://projectforawesome.com/?charity=TgF1CvOw

Also @argumate you better fucken reblog this.

My own contribution, ft. Ryu in the first appearance of his fledgling film career

Once again, to deliver the actual payload here you need to vote for videos, so here are the links again:

http://projectforawesome.com/?charity=WUDGW89r

http://projectforawesome.com/?charity=JZ2iuLvs

http://projectforawesome.com/?charity=TgF1CvOw

(via nostalgebraist)

birdblogwhichisforbirds:

This is my video for Project 4 awesome, which is an annual YouTube-based fundraising event run by John and Hank Green.

Also please go and vote for EA charities in p4a, it can result in $25k per charity!
The three links below are all to the lists of videos for each charity. You can click on each video to vote - as all the charities have more than one video, you can vote for each video and the votes among all the videos get aggregated. There is also still time to submit a video yourself.
http://projectforawesome.com/?charity=WUDGW89r
http://projectforawesome.com/?charity=JZ2iuLvs
http://projectforawesome.com/?charity=TgF1CvOw

Also @argumate you better fucken reblog this.

The Furniture Ombudsman claims that it is ‘inspiring consumer confidence’. But what it is actually doing is giving furniture retailers licence to browbeat their customers to despair – to the point that they simply capitulate.

But now a copy of Sexual Habits of the Adélie Penguin has been unearthed, thanks to sleuthing by Douglas Russell, curator of birds at the Natural History Museum, who discovered a copy among records of the work of Scott’s expeditions and has had it published in the journal Polar Record, with an accompanying analysis of Levick’s work.

@the-grey-tribe

This is from 1999, and was written in the context of MacOS classic, BeOS, DOS, and Windows 95. KDE 1.0 had already been released.

Windows NT, OSX, BeOS, Amiga, had relatively similar GUIs but different underlying principles.

Symbolics, Plan9, Squeak/smalltalk-80, Oberon, and web bowsers have a completely different UI that reflects the difference in underlying concepts. All existed in the 90s, but they weren’t made for ordinary people. Ordinary people GUIs all followed the same pattern.

This continued until the iPhone arrived.

You have to differentiate the abstractions from the metaphors: A file is an abstraction. A floppy disk “save” icon is the metaphor. The picture of a file as a binder is a metaphor.

Stephenson was pointing out that the metaphor promises things it cannot deliver, while offering a familiar conceptual scaffold to users. The point is not just that files and directories are leaky abstractions, and that you don’t need to know how they work except when you do. The point is that the VISUAL metaphors are not explained.

When the visual metaphors are inaccurate, it’s in a way that is not exactly lying. The images are not even wrong: They don’t tell you anything explicitly.

Plain text is discrete and explicit in a way images and Word documents are not. You cannot hide things in an ASCII file. You can hide things in a .doc or .psd file. These files have metadata land layers and scripts and WYSIWYG is a deception. What you see might be what you get, but what you see is not all there is.

Thanks for the pushback on this.

I take your point about abstractions vs. metaphors.  A metaphor like “the desktop” has no precise specification, and there is no firm way to differentiate when lower levels are “leaking through.”  All you have is a system that looks like a literal desktop but doesn’t entirely behave like one.

Insofar as GUIs tend to involve a lot of “metaphors” in this sense, I suppose that graphics probably lend themselves to metaphors.  Nonetheless, I want to note that Stephenson seems equally concerned about the verbal side of GUI metaphors.  Long quote to representatively sample from his examples (the omitted paragraph is one I quoted in the OP):

At the upper (which is to say, closer to the user) levels, this is done through a set of conventions–menus, buttons, and so on. These work in the sense that analogies work: they help Eloi understand abstract or unfamiliar concepts by likening them to something known. But the loftier word “metaphor” is used.

The overarching concept of the MacOS was the “desktop metaphor” and it subsumed any number of lesser (and frequently conflicting, or at least mixed) metaphors. Under a GUI, a file (frequently called “document”) is metaphrased as a window on the screen (which is called a “desktop”). The window is almost always too small to contain the document and so you “move around,” or, more pretentiously, “navigate” in the document by “clicking and dragging” the “thumb” on the “scroll bar.” When you “type” (using a keyboard) or “draw” (using a “mouse”) into the “window” or use pull-down “menus” and “dialog boxes” to manipulate its contents, the results of your labors get stored (at least in theory) in a “file,” and later you can pull the same information back up into another “window.” When you don’t want it anymore, you “drag” it into the “trash.”

There is massively promiscuous metaphor-mixing going on here, and I could deconstruct it ‘til the cows come home, but I won’t. Consider only one word: “document.” When we document something in the real world, we make fixed, permanent, immutable records of it. But computer documents are volatile, ephemeral constellations of data. Sometimes (as when you’ve just opened or saved them) the document as portrayed in the window is identical to what is stored, under the same name, in a file on the disk, but other times (as when you have made changes without saving them) it is completely different. In any case, every time you hit “Save” you annihilate the previous version of the “document” and replace it with whatever happens to be in the window at the moment. So even the word “save” is being used in a sense that is grotesquely misleading—“destroy one version, save another” would be more accurate.

[…]

So GUIs use metaphors to make computing easier, but they are bad metaphors. Learning to use them is essentially a word game, a process of learning new definitions of words like “window” and “document” and “save” that are different from, and in many cases almost diametrically opposed to, the old.

If I understand correctly, he is saying: even the verbal parts (like the names of options in menus) are “metaphors” as opposed to “abstractions.”  As Stephenson says, if you take the word “document” here too literally, you will be in for some nasty surprises – but this is not like a technical abstraction springing a leak, since the technical abstraction will have a spec (“you can pretend Precise Thing X is really Precise Thing Y”), while “document” is just a cloud of implicit associations.

Nonetheless!  I think Stephenson is going much too far when he talks about MS and Apple selling an “illusion” that one can usefully interact with the world through such metaphors.  After the passage above, he goes on to talk about how more and more devices are using GUIs, and how

by using GUIs all the time we have insensibly bought into a premise that few people would have accepted if it were presented to them bluntly: namely, that hard things can be made easy, and complicated things simple, by putting the right interface on them.

He’s going too far because no one, in my experience, actually trusts the metaphors for more than a few early moments.  His examples quoted above are good illustrations.  Yes, the word “save” is being used in a strange way, but people do not react to this by getting burned over and over again; people react by learning a new meaning for the word “save.”  More generally, people who interact with a “metaphorical” interface quickly develop a working facility with its actual behavior that obviates most of the dependence on the metaphors.

This is possible because the actual behavior is always largely predictable, even if the metaphors are bad.  By now, we all have a precise sense of what ought to happen when we choose “Save” (or “Open,” etc.) in a GUI menu, and would be rightfully indignant if something different were to happen.  For all I know, there really is some written spec about what these menu items should do on Windows or Mac OS, but even if there isn’t, there’s a de facto understanding which is just as good.  Some little open source gizmo I find on github might prefer to say it will “write a file to disk” instead, but this doesn’t really give me more information than “save” does.

(Indeed, while reading that passage, I had to stop for a moment to notice that I knew two meanings of the word “save” which did not agree.  I’m so used to the actual behavior of the GUI that it takes effort to remember what the metaphor was supposed to be.  Likewise, I can’t remember the last time I thought about the purported connection between GUI drag-and-drop and the act of moving papers around on a desk.  Can you?)

It’s possible that there is a young vs. old difference here – maybe older people who have trouble with computers are unable to make these leaps and have to keep relying on the bad metaphors?  And yes, the essay was written in 1999, and perhaps back then it was less clear how people would react to the ascension of GUIs.  (Still, they’d been around for over a decade.  Also, I first read this essay in 2005 or 2006, and it seemed overblown to me then.)  At best, I think we can say Stephenson raised a worry that may have been reasonable at the time, but which is no longer so.

ETA: to me it seems like Stephenson ignores the true ease and efficiency benefits GUIs can confer even to power users, and thus concludes that GUIs must be popular because of all this metaphor stuff.  Near the end, he says he likes BeOS because (paraphrasing) it has the power of Linux but isn’t as tedious to configure and maintain.  But he sums this up as “sometimes, in other words, I just want to go to Disneyland,” as if convenience requires illusions.  (But you can get a lot of convenience, without losing any power, through well-chosen default behavior.)

(via the-grey-tribe)