The End of the Road is Haunted (and a bit more Ruliad)

Two different and completely unrelated topics (OR ARE THEY?) today, just because they’re both small, and hearkening back to the days when I would just post utterly random unconnected things in a weblog entry those title was just the date (and noting again that I could easily do that now, but for whatever reason I don’t).

First, whatsisname Wolfram and his Ruliad. Reading over some of his statements about it again, it seems like, at least often, he’s not saying that The Ruliad is a good model of our world, such that we can understand and make predictions about the world by finding properties of the model; he’s saying that The Ruliad just is the world. Or, in some sense vice-versa, that the world that we can observe and experience is a tiny subset of The Ruliad, the actual thing itself, the one and only instantiation of it (which incidentally makes his remarks about how it’s unique less obviously true).

I’m not exactly sure what this would mean, or (as usual) whether it’s falsifiable, or meaningful, or useful, or true, in any way. My initial thought is that (at the very least) every point in the Ruliad (to the extent it makes sense to talk about points) has every possible value of every possible property at once, since there is some computation that computes any given bundle of properties and values from any given inputs. So it’s hard to see how “beings like us” would experience just one particular, comparatively immensely narrow, subset of those properties at any given time.

It might be arguable, Kant-like, that beings like us will (sort of by definition) perceive three dimensions and time and matter when exposed to (when instantiated in) the infinite variety of The Ruliad, but how could it be that we perceive this particular specific detailed instance, this particular afternoon, with this particular weather and this particular number of pages in the first Seed Center edition of The Lazy Man’s Guide to Enlightenment?

The alternative theory is that we are in a specific universe, and more importantly not in many other possible universes, and that we experience what we experience, and not all of the other things that we could experience, as a result of being in the particular universe that we are in. This seems much more plausible than the theory that we are in the utterly maximal “Ruliad of everything everywhere all at once”, and that we experience the very specific things that we experience due to basically mathematical properties of formal systems that we just haven’t discovered yet.

We’ll see whether Wolfram’s Physical Project actually turns out to have “vast predictive power about how our universe must work, or at least how observers like us must perceive it to work”. :) Still waiting for that first prediction, so far…

In other news, The End of the Road is Haunted:

These are in the cheapest one-credit mode, because I was in that mood. Also I kind of love how the AI takes “haunted” to mean “creepy dolls”.

“The Ruliad”: Wolfram in Borges’ Library

I think people have mostly stopped taking Stephen Wolfram very seriously. He did some great work early in his career, at CalTech and the Institute for Advanced Study, and (with a certain amount of intellectual property mess) went on to create Mathematica, which was and is very cool.

Then in 1992 he disappeared into a garret or something for a decade, and came out with the massive A New Kind of Science, which got a lot of attention because it was Wolfram after all, but which turned out to be basically puffery. And a certain amount of taking credit for other people’s earlier work.

Being wealthy and famous, however, and one imagines rather surrounded by yes-folks, Wolfram continues in the New Kind of Science vein, writing down various things that sound cool, but don’t appear to mean much (as friend Steve said when bringing the current subject to my attention, “Just one, single, testable assertion. That’s all I ask”).

The latest one (or a latest one) appears to be “The Ruliad”. Wolfram writes:

I call it the ruliad. Think of it as the entangled limit of everything that is computationally possible: the result of following all possible computational rules in all possible ways.

It’s not clear to me what “entangled” could mean there, except that it’s really complicated if you try to draw it on a sheet of paper. But “the result of following all possible computational rules in all possible ways” is pretty clearly isomorphic to (i.e. the same thing as) the set of all possible strings. Which is to say, the set of all possible books, even the infinitely-long ones.

(We can include all the illustrated books by just interpreting the strings in some XML-ish language that includes SVG. And it’s probably also isomorphic to the complete graph on all possible strings; that is, take all of the strings, and draw a line from each one to all of the others. Or the complete graph on the integers. Very entangled! But still the same thing for most purposes.)

Now the set of all possible strings is a really amazing thing! It’s incomprehensibly huge, even if we limit it to finite strings, or even finite strings that would fit in a reasonably-sized bound volume.

And if we do that latter thing, what we have is the contents of the Universal Library, from Borges’ story “The Library of Babel”. As that story notes, the Library contains

All — the detailed history of the future, the autobiographies of the archangels, the faithful catalog of the Library, thousands and thousands of false catalogs, the proof of the falsity of those false catalogs, a proof of the falsity of the true catalog, the gnostic gospel of Basilides, the commentary upon that gospel, the commentary on the commentary on that gospel, the true story of your death, the translation of every book into every language, the interpolations of every book into all books, the treatise Bede could have written (but did not) on the mythology of the Saxon people, the lost books of Tacitus.

Borges — The Library of Babel

It also contains this essay, and A New Kind of Science, and every essay Wolfram will ever write on “the Ruliad”, as well as every possible computer program in every language, every possible finite-automaton rule, and to quote Wolfram “the result of following all possible computational rules in all possible ways.” (We’ll have to allow infinite books for that one, but that’s a relatively simple extension, heh heh.)

So, it’s very cool to think about, but does it tell us anything about the world? (Spoiler: no.) Wolfram writes, more or less correctly:

it encapsulates not only all formal possibilities but also everything about our physical universe—and everything we experience can be thought of as sampling that part of the ruliad that corresponds to our particular way of perceiving and interpreting the universe.

and sure; for any fact about this particular physical universe (or, arguably, any other) and anything that we experience, the Library of Babel, the set of all strings, the complete graph on all strings, “the Ruliad”, contains a description of that fact or experience.

Good luck finding it, though. :)

This is the bit that Wolfram seems to have overlooked, depending on how you read various things that we writes. The set of all strings definitely contains accurate statements of the physical laws of our universe; but it also contains vastly more inaccurate ones. Physicists generally want to know which are which, and “the Ruliad” isn’t much help with that.

Even philosophers who don’t care that much about which universe we happen to be in, still want correct or at least plausible and coherent arguments about the properties of formal systems, or the structure of logic, or the relationship between truth and knowledge, and so on; the Universal Library / “Ruliad” does contain lots of those (all of them, in fact), but it provides no help in finding them, or in differentiating them from the obviously or subtly incorrect, implausible, and incoherent ones.

There is certainly math that one can do about the complete graph over the set of all strings, and various subgraphs of that graph. But that math will tell you very little about the propositions that those strings express. It’s not clear that Wolfram realizes the difference, or realizes just how much the utter generality of “the Ruliad” paradoxically simplifies the things one can say about it.

For instance, one of the few examples that Wolfram gives in the essay linked above, of something concrete that one might study concerning “the Ruliad” itself, is:

But what about cases when many paths converge to a point at which no further rules apply, or effectively “time stops”? This is the analog of a spacelike singularity—or a black hole—in the ruliad. And in terms of computation theory, it corresponds to something decidable: every computation one does will get to a result in finite time.

One can start asking questions like: What is the density of black holes in rulial space?

It somewhat baffles me that he can write this. Since “the Ruliad” represents the outputs of all possible programs, the paths of all possible transition rules, and so on, there can be no fixed points or “black holes” in it. For any point, there are an infinite number of programs / rules that map that point into some other, different point. The “density of black holes in rulial space” is, obviously and trivially, exactly zero.

He also writes, for instance:

A very important claim about the ruliad is that it’s unique. Yes, it can be coordinatized and sampled in different ways. But ultimately there’s only one ruliad.

Well, sure, there is exactly one Universal Library, one set of all strings, one complete graph on the integers. This is, again, trivial. The next sentence is just baffling:

And we can trace the argument for this to the Principle of Computational Equivalence. In essence there’s only one ruliad because the Principle of Computational Equivalence says that almost all rules lead to computations that are equivalent. In other words, the Principle of Computational Equivalence tells us that there’s only one ultimate equivalence class for computations.

I think he probably means something by this, well maybe, but I don’t know what it would be. Obviously there’s just one “result of following all possible computational rules in all possible ways”, but it doesn’t take any Principle of Computational Equivalence to prove that. I guess maybe if you get to the set of all strings along a path that starts at one-dimensional cellular automata, that Principle makes it easier to see? But it’s certainly not necessary.

He also tries to apply terminology from “the Ruliad” to various other things, with results that generally turn out to be trivial truths when translated into ordinary language. We have, for instance:

Why can’t one human consciousness “get inside” another? It’s not just a matter of separation in physical space. It’s also that the different consciousnesses—in particular by virtue of their different histories—are inevitably at different locations in rulial space. In principle they could be brought together; but this would require not just motion in physical space, but also motion in rulial space.

What is a “location in rulial space”, and what does it mean for two things to be at different ones? In ordinary language, two things are at different points in “rulial space” if their relationships to other things are not the same; which is to say, they have different properties. (Which means that separation in physical space is in fact one kind of separation in “rulial space”, we note in passing.) So this paragraph says that one human consciousness can’t get inside another one, because they’re different in some way. And although you might somehow cause them to be completely identical, well, I guess that might be hard.

This does not seem like a major advance in either psychology or philosophy.

Then he gets into speculation about how we might be able to communicate between “different points in rulial space” by sending “rulial particles”, which he identifies with “concepts”. The amount of hand-waving going on here is impressive; Steve’s plea for a falsifiable claim is extremely relevant. In what way could this possibly turn out to be wrong?

(It can, on the other hand, easily turn out to be not very useful, and I think so far it’s doing a good job at that.)

He also proceeds, hands still waving at supersonic speed, to outline a Kantian theory that says that, although “the Ruliad” contains all possible laws of physics, we seem to live in a universe that obeys only one particular set of laws. This, he says, is because “for observers generally like us it’s a matter of abstract necessity that we must observe general laws of physics that are the ones we know”.

What “observers like us” means there is just as undefined as it was when Kant wrote the same thing only with longer German words. He goes on like this for some time, and eventually writes:

People have often imagined that, try as we might, we’d never be able to “get to the bottom of physics” and find a specific rule for our universe. And in a sense our inability to localize ourselves in rulial space supports this intuition. But what our Physics Project seems to rather dramatically suggest is that we can “get close enough” in rulial space to have vast predictive power about how our universe must work, or at least how observers like us must perceive it to work.

which is basically just gibberish, on the order of “all we have to do is find the true physics text in the Universal Library!”.

It’s hard to find anyone but Wolfram writing on “the Ruliad” (or at least I haven’t been able to), but the Wolfram essay points to an arxiv paper “Pregeometric Spaces from Wolfram Model Rewriting Systems as Homotopy Types” by two authors associated with Wolfram Research USA (one also associated with Pompeu Fabra University in Barcelona, and the other with the University of Cambridge in Cambridge, and one does wonder what those institutions think about this). That paper notably does not contain the string “Ruliad”. :)

I may attempt to read it, though.

Mach’s Principle

I wrote my 750 words again! (Answers to even-numbered exercises are in the back of the book.)

The blinking light on the side of your laptop computer actually represents the average heartbeat of every human on Earth who is within one mile of a monitoring node.

Which is approximately 45% of the population of the planet.

Most of the time it is rock-steady, as any excitement in one heart, or in one group of hearts, is exactly balanced through the vast mushy laws of large numbers, by the ebbing of excitement in the same number of hearts elsewhere.

And vice-versa.

But on some days, if you are watching the blinking light as I often do, you will notice it slowly subtly down, or speeding suddenly up, as somewhere there is a large anomaly, a sudden gasping, a thrill, an excitement, in the entire population of a small city in Rawanda, or every Girl Scout in the USA; or somewhere else an entire continent goes to bed, and on the other side of the world, due to an international holiday, their usual counterbalancers are sleeping in.

Because, vast and sprawling and numerous though we are, humanity is still finite. There are only so many left-handed people, only so many people about to open a soda can, only so many Lutherans. The number of religious sects is large, but smaller than the number of grains of sand on the beach, which is smaller than the number of atoms in one grain of sand, which is smaller than the number of possible Sudoku grids, which is itself still finite, and so smaller than nearly all of the positive integers.

Looking down Platform 29, across all those people waiting patiently, or impatiently, for the 6:45 to arrive, and thinking that each of them has a history, and a set of beliefs, a complicated web of preferences and fears, we are already far beyond the vastness that any one of us can comprehend (one, two, three, seven, many), but if all of those people were to vanish suddenly, spirited off by aliens or vaporized by more mundane means, the size of the world as a whole would be reduced by only an imperceptible fraction.

So your laptop’s light blinks, almost always, at the same steady pace, as all of our hearts (or the hearts of all of us within one mile of a monitoring node), average out into a signal with just one bit of content (“still the same, still the same, still the same”); all the complexity nicely smoothing out, a hill here balanced by a valley there, a hundred orgasms in one set of college dorms nicely making up for a hundred hearts drifting off to sleep in another set one time zone away.

Take a breath. Feel yourself breathing, and what it feels like to breathe. Feel yourself thinking, and what it feels like to think. If you are worried, feel what it feels like to worry. Feel your own heartbeat slowing. Look at the reflection of the blinking light on the Ethernet connector, or the shiny tabletop, or your fingernail. As your heart slows down, imagine that you can see the light slowing down, by the smallest imaginable amount.

Imagine that you can feel, somewhere deep in your gut or your inner ear, the Earth turning under you, and the stars whirling around.

It the Earth turning, or the stars? We know, these days, that motion in a straight line is relative; that jogger is the one who is moving, and I on the park bench here with my peanuts am the one sitting still, only because the math is simpler that way; but either one might be true. It’s not so simple for rotation, though, for things spinning around. Ernst Mach thought, at least if we listen to Einstein (and we might as well, since we listened to him on that whole “motion in a straight line” thing), that the universe has a large-scale structure (large as large, larger than anything), that determines what counts as spinning and what doesn’t; but I hear down at the corner pub that this is not true in all solutions to the field equations.

Feel your breath, and what it is like to breathe. Feel your heart beating, and what it is like to have a heart, beating. Watch the blinking light, and feel your heart beating with all of the other hearts (the ones within a mile of a monitoring node). Feel the Earth turning under you, and the stars whirling around you (with or without closed timelike curves). Be still.

Quantum Physics and (not really) Free Will

It turns out that there is a well-known thing in quantum physics called “The Free Will Theorem”, developed by smart persons John Conway and Simon Kochen.

(I haven’t heard of this before, which I suspect means that, like L. Ron Hubbard’s science fiction, it didn’t exist in my original birth universe; I wonder if that means I’ve switched again recently. Always hard to tell.)

Anyway, the Free Will Theorem, which is described in two papers that are both quite readable really, is not actually about Free Will to speak of, at least not if you are a sensible compatibilist like we are, and I want to write down my thoughts here as to why and how that is.

What the Theorem actually shows is that, if some generally but not universally accepted parts of quantum physics and relativity are true, then if there is some behavior of some humans that can’t be predicted, even in principle if you knew every fact about the universe up to that point, then there is also some behavior of some elementary particles (as evidenced by the behavior of some macroscopic detection apparatus) that can’t be predicted, even in principle if you knew every fact about the universe up to that point.

Which is not a big surprise really; it’s hard to imagine a universe in which all elementary particle behavior was predictable but human behavior was somehow not, humans being made of elementary particles and all. But this Theorem puts a solid example under that intuition (as well as bringing up some other issues in physics that I won’t talk about more here).

Conway admits somewhere in the coverage of this that he chose the name, the Free Will Theorem, intentionally to get attention. But he’s also responded to criticism of the name by saying things worth noting.

The most obvious criticism is that being unpredictable even in principle isn’t the same as having free will (and if you’re a compatibilist it’s not even a necessary condition). Conway has said a couple of things about this.

First, he’s said informally that humans and particles are the same in this way, and since we say that humans have free will we should say that about particles too:

“That’s why I insisted on using this evocative language,” Conway says. “Many people thought I should say the particle’s behaviour is indeterminate. But it would be really rude if I told you that you were indeterminate! It’s the same property and I don’t see why we should be required to speak of it as if it were a different property. Our theorem says that if humans have it, then so do particles.”

But that’s sort of silly. The fact that humans and particles share some property X, and humans have free will, doesn’t imply that particles therefore have free will; it’s just a non-sequitur.

He’s also responded to the “randomness isn’t enough for free will” argument by claiming that the indeterminacy they’ve proved for particles isn’t just randomness. From that same link above:

and which action the particle does is free in this sense, it is not a predetermined function of the past. And that’s not the same as randomness, oh dear me no!”

Exclamatory cuteness aside, if “not determined by anything that’s come before, and not predictable even in principle” isn’t the same as randomness, I don’t know what is.

What Conway apparently has in mind here is that the randomness is weird and quantumly nonlocal: when the behavior goes from undetermined to determined, it does it at two places at once, and the places can be sufficiently far apart that no signal can get between them in time. That doesn’t mean it’s not random, it just means that as well as being random it’s also bizarre in the usual QM way; the Free Will Theorem doesn’t tell us anything particularly new about the weirdness, it’s just one of the three assumptions that it starts from.

Conway gets all sort of Penrose-like and speculates that while all the little “free decisions” made by particles usually sort of cancel out, our brains somehow avoid this canceling out, and that through some as yet unknown process our human-level free will pops out as a result. This, he says, makes the whole Compatibilism thing a moot point; since the universe isn’t deterministic, it just doesn’t matter whether free will is compatible with determinism. Compatibilism, the second of the papers says, is just “a now unnecessary attempt to allow for human free will in a deterministic world”.

Which is not quite right. :) Compatibilism is the recognition that indeterminicity is neither necessary nor sufficient for free will. Free will has to do with the freedom to express one’s preferences and goals in the world, not necessarily the ability to escape prediction by a hypothetical omniscient seer. Free will is possible with or without random or undetermined bits of fundamental physics (and those people who told Conway he ought to just say the particle behaviors are undetermined were right).

In fact free will requires that various of our actions are in fact influenced by, reflective of, if not determined by, past facts about the universe, those facts being the preferences, plans, and goals of the person acting with free will.

Hope that clears that up. :)

Friday, October 21, 2011

So I don’t understand this kind of spam:

Hello,

My name is Franco Cavalier am sending you this email regarding in Purchasing Product from your company,I will like to know if you can ship directly to France , I also want you to know my mode of payment for this order is via CC . Get back to me if you can ship to that destination and also if you accept the payment type I indicated

Kindly return this email with your price list of your products..

Franco.

201, rue de Grenelle

FR – 75357 PARIS

FRANCE

Slightly even more puzzling because it was sent to my work address (in ibm dot com), and it was sent from an email address of “dummy” at somewhere in France (with a reply-to at a gmail dot com address).

What value does anyone get by spamming out a request for lists of goods that can be paid for by credit card and shipped to France?

I suppose he might just be gathering email addresses in general, to spam or to sell? But surely if you want to test to see if a vast number of email addresses are valid, you’d want to maximize the chance that the person will write back, and in that case asking for lists of products that can be bought via credit card and shipped to France doesn’t do that.

They could just be validating a big list of email addresses by sending any old junk to them and seeing what bounces, but (1) email agents don’t send “no such user” replies anymore, as I recall, for exactly this reason, and (2) this is an awfully weird “any old junk”. I’d hate to think that some spammer address-collector had this nice a sense of the absurd.

Ah, mysteries, mysteries…

I just got The Physics Book from Amazon (I think I’d pre-ordered it or something), and it’s lovely. Bigger and fancier than I’d expected, a nice weighty hardcover with lots of short entries about interesting physics things, and great pictures.

You should get it, too! And not just because the author’s office is more or less across the hall from mine or anything. :)

I’ve just started reading it (the introduction and then a few completely random pages), but I think I will enjoy it greatly; it’s nice and bite-sized (a box of intellectual chocolates!), which fits my current (tiny) attention span nicely.

I’m also enjoying The Quantum Thief quite a bit, in the digital edition, despite having sort of forgotten about it for long enough that starting out again I didn’t quite remember just who everyone was, or what had happened to whom previously. But it’s the kind of book in which you’re enjoying trying to figure out what’s going on anyway, so that hasn’t been a big problem. And the tech and the world and the culture(s) and all are interesting while one is trying to work it all out.

It occurs to me that I could just sort of leave this entry, with the date at the top, open in WordPress all day, and hit Publish in the evening or whenever I felt like I wasn’t going to write anything elsemore to speak of.

Maybe I’ll do that. Although I might forget. And it’s also nice to Publish shortly after writing, and get that sense of Accomplishment.

So for NaNoWriMo this year, assuming I convince myself that I have time, I’m thinking about a nonlinear hyperlinked novel. Say, 100 interlinked pages at 500 words per page? Or 500 100-word pages, or anything on that curve. Something like The Forked Stick, only I would “finish” it in a month, and not leave it hanging forever like I did with that. :)

Water Street runs close by the river, into the Dun Quarter, which is quiet but far from silent in this moony night, breathing with the sharp stillness of the river and the easy aches of poverty and long practice.

To one side is the pier, and across the street is an old building where a sign shows a cup and a hen. Far down at the other end of the street, the Long Temple broods in a feverish silent sleep.

(I am still quite proud of the Tic Tac Toe game embedded in The Forked Stick. Wow, that was some time ago!)

Didn’t you mean to say you assassinate your enemies
Didn’t you mean to say you kill journalists and artists
Didn’t you mean to say you give orders for the murder
Didn’t you mean to say you sell drugs to make your fortune
— Holly Near, “Edge”

I don’t actually recall how Edge got onto the iPad here, but I’m enjoying it very much. Energy, novelty.

Also enjoying The Dresden Dolls:

and you can tell
from the smoke at the stake
that the current state is critical
well it is the little things, for instance:
in the time it takes to break it she can make up ten excuses:
please excuse her for the day, its just the way the medication makes her…
— girl anachronism

What else should one mention in one’s weblog? I’m sure there are other things that will occur to me later in the day. But at the moment the desire to see it published and In The Can seems sort of strongish. So I will probably push Publish sometime in the next minute or so, assuming the universe and its laws continue more or less unchanged (something that it’s not clear how justified we are in assuming, or whether it matters whether we are).

Yep, here we go!

See you on the other side! :)