Really it is quite curious…

May 20, 2010

The universe sings, observes some thing residing on the outside. From a vantage point beyond both space and time, it is an understatement to say the universe appears deterministic. There is no cause and effect from this view, only a single relic with unimaginable beauty and complexity. The minds of animals mimic the happenings of the universe, in memory and foresight, and herein the universe replicates itself like a fugue. The theme of one particularly successful fugue is heard for hundreds of years, from the occasional street musician to the department store radio. The universe favors this fugue.

What happens in choice, when alternate outcomes are considered, one is preferred, and then acted out? The universe has encoded itself within itself, in a simplified model which informs events yet to occur. Equipped only with the knowledge of Newtonian mechanics some observer concludes that a car, headed south along highway 81 en route to Asheville, NC, will collide with a tree in approximately 12.03 seconds. Another observer skilled in the art of brain-state reading concludes that the tree will be avoided as the curve in the highway is followed, and that in approximately 6 hours the driver of the car will meet his son in a restaurant, eat and pay the bill. How mysterious is it that the universe encodes past and future in simplified models contained in mind?

May 5, 2010

May 1, 2010

1.3(i-iii) Cell World

April 29, 2010

The cellular automata universe offers a universe that’s easy to deal with and yet rich enough to give us all the complexity of our universe. Indeed, I argue that the details are essentially irrelevant at high enough levels of complexity; that no particular material nor specific fine-scale mechanics are necessary for consciousness, and that we might expect quantum mechanics to inform our understanding of pop music or hedge fund management as well as it informs our understanding of the brain. Thus, the cellular automata world is rigid enough to grant the most stringent determinism, it is also rich enough to birth arbitrarily deep levels of complexity, and house any imaginable intelligence. I want to also distinguish my position from those who insist free will (or consciousness) is an illusion. At best this is misleading, more likely it is just plain wrong.

i. Objectness

Long before we need worry about free will and consciousness, we need to worry about what objects are. These will be the nouns of any truth claim we make. Before there is *choice*, there is *person*, and how to deal with the distinction of being a *person* object is not as easy as it may seem. Even in a low resolution cellular automaton (i.e., one with few cells) the problem remains. Is a glider an object? Is every configuration of cells an object? We might suppose that every configuration of cells theoretically has a name, or could be given a name, and even that names in our language must be shorthand for collections of cells (that meaning in language must essentially be built from these building blocks). But then something so simple as ‘glider’ is necessarily shorthand for a list of trillions of configurations. This seems like a faulty way of looking at things. If glider includes not only the same two 5-cell configurations of cells, up to translation, but also larger things which exhibit a gliding property, the problem is harder. Certainly if an object appeared to maintain its shape more or less, as it translated itself through space, perhaps even fizzling out at some time, we’d be tempted to call it a glider. This is especially true if our instruments of detection are unable to detect individual cells, so we cannot discern a glider’s states at that finest level. No one argues that natural language is not fuzzy, as it unarguably is, but then how do we interpret a fuzzy truth claim, in reductionist terms?

ii. Diagonalization

We’ve built in our imaginations a cellular world with trillions of cells, and in this world a creature has been formed. That creature is constantly bombarded with gliders of various sizes and from these collisions, (and internal happenings), the creature processes thought and outputs gliders, as statements. This creature I’m thinking of is essentially a human, or a near approximation. Now, let’s say we agree on an interpretation of its language (i.e., the waves of gliders it sends out of its mouth, each wave differing in shape enough so that a discrete language can be understood, as English is). What can it say in this language? One thing it can say is “the universe is a cellular automaton with the following rule of evolution…” What can it not say? It cannot say “I will now give names to the 10^(10^10) cellular configurations possible in this universe, beginning with ‘aardvark,’…” Indeed, since each utterance takes up space (for the gliders to carry the waves of speech) the utterances are quite limited in the amount of information they can carry (necessarily less than the total number of configurations possible in the same tiny amount of space, let alone the universe). Now, theoretically we can offer the utterer all the time he wants to longwindedly describe each fine detail (indeed each cell) of some object, and terminate after finite time. But who, or what, is his audience that can reassemble the information into a model that contains as much information as the original object? This is one reason computers cannot calculate the evolution of the universe, because you don’t even get to specify the initial condition without generating an infinite descending loop! It almost seems absurd to expect more than fuzziness from meaning in language, but of course our language is not fuzzy, and perhaps this is where some of the confusion lies. Language is ridiculously precise. Unlike facial expressions or performed music, it is exact and codifiable. Yet still we discern subtlety and nuance in our favorite authors, after reading hundreds of thousands of their words (or even a good cadence in a paragraph or sentence).

iii. Emergence

I want to draw attention to the fact that fuzzy terms (as in the referent is fuzzy, such as with natural language) aren’t just ‘fuzzy,’ as opposed to being precise, as a sort of deficit. But instead, that there is meaning in a fuzzy term that is essentially lost with the attempt to make it precise. I am thinking of the cellular human, and imagining her, let’s call her Frida, holding a ball and commenting “it is round.” This roundness property, which seems so elementary, is in reality a reflection of the ball’s resemblance to other objects previously perceived by Frida. So the process goes: an object is in front of Frida, some waves of gliders emanate from it (or rather “bounce” off it), carrying information about the object into Frida’s sensory apparatus, then Frida’s brain momentarily gets a hold of that information. Within a few seconds most of the information is gone, but some faint ghost remains, a ghost which somehow holds information about the object which is general, and connects to yet other things Frida has seen. This object would not be classified under the blanket abstraction ’round’ were it not for the ‘intrinsic’ cellular make up of the ball, but the abstraction cannot be said to be an intrinsic quality of the ball, supported only by the physical state of that ball. I think some would find this distinction too subtle, but it’s an absolutely crucial difference to understanding how meaning works and how the reductionist is wrong.

It is only too easy to imagine ’roundness’ is a concrete quality either enjoyed intrinsically by an object or not. However, terms which are overtly contextual as opposed to physical are readily available and make up the majority of the words we use. Take ‘majority,’ for example, and define it in terms of cells in such a way that nearly all usages found in English literature can be said to reference it. It can’t be done. We can say what a majority of cells being on in a given region means, more or less, but that is not directly referenced by my usage above, nor when we stumble upon it in literature, say in the phrase “tyranny of the majority.”

It is observed, also, that terms which don’t lend themselves easily to reduction, are frequently not necessarily more complex, given a context. This is exactly the point, for if it was necessary to give a description of X with complexity proportional to the extent X resists reduction, then we are in a reductionist framework, and X is just really complex. But the human mind doesn’t work this way. It is frequently possible to communicate great generalities to children, who would have no way of understanding the reduction to finer physical parts. How can one insist “being on one’s best behavior in a restaurant” is really a property or action of physical particles, or even a deep sociological action, when neither of these can be comprehended by the child, while the statement itself is easily understood? Part of the answer is that in building a vast framework of complexity, certain terms become contextually simple, while being intractably complex from a ground-up perspective. You don’t build “one’s best behavior” from scratch. The other part of the answer is that a child begins with such a framework. Knowledge does not stick to an empty slate (not even a blackboard!), but children have a robust way of making sense of generalities from the beginning. My main point here is that meaning is emergent, held together by a framework harder to imagine than a strict partial order. There are more lateral connections in the network of meaning.

1.2 The Land of Counterexamples

January 26, 2010

We will now take Borges’ Library of Babel as the discrete analog of what might be called the land of counterexamples. Specifically, suppose we agree that space is continuous, and matter exists in this continuous space in some array of forms at each point. I mean by this that there is a set $X$, possibly a space in its own right, and that each point in space can be occupied by vacuum or by a value from $X$. Then if $I_k$ is the cube of side lengths $k$, we denote by $A_k=X^{I_k}$ the set all possible configurations of matter which fit into the cube $I_k$. Then we sit back and dream about $A=A_\infty$ which is the direct limit of the $A_k$. For those to whom this description is too mathematical the translation is: $A$ is the collection of all possible (bounded, meaning not stretching off to infinity) configurations of matter. This we might call the Continuous Library of Babel (CLB), since it is essentially just the continuous analog of said library. Now, if nature wants for half-rhino-half-chickadees, CLB does not. Think of it as a sort of library of congress, where every physical creation sits, on cubby shelves of increasing size which eventually get arbitrarily large. A philosophers’ Costco.

Exercises: what might be wrong with this parameterization? (hint: there are quite a few things possibly wrong). What are some interesting shelf-lifes to objects in $A$?

Now, think about what the library of Babel has to say, on its shelves, about the CLB. Other than gibberish and lies, one finds guides to understanding the contents of CLB. Like a book that tells you about different birds, so too the library of Babel has guides to help you understand the beasts of the CLB. One problem becomes immediate. The entire library does not contain enough information to specify any object but possibly an infinitesimally few special objects, such as the empty object, or an object that consists of 2 points of matter, exactly 3 meters apart. The majority of everyday objects seem to be indescribable. For example, if one insists that common nouns should reference specific configurations of matter, thereby allowing English sentences about matter to fall into the two categories TRUE and FALSE, then what is a “book”? If one takes a book–just a common book mind you, one whose “bookness” would not be in question– and alters it physically by removing a point of matter, then it should still be a “book,” since no human would ever even detect the difference, indeed vast more differences are occurring molecularly within any given book within any given second. But according to our parameterization there are an infinite number of such configurations, all of which easily fall into what is indisputably understood to be a book. Then it is hopeless to think we can even describe what it means to be a book, let alone have any sort of theory of anything physical at all.

This brings to my mind Zeno’s arrow paradox, which essentially asks the question “is motion inherent in a physical state?” I.e., said in this way, are there configurations of matter that would spring forth as a flying arrow, upon their creation, since matter in motion is different than matter at rest? or is the standard model of matter and motion accurate, that they are independent. Certainly some kinds of potential energy are purely physical, such as a cocked spring, or the head of a match. In theory we could build, atom by atom, pool balls which are pressed into the banks of tables, ready to instantly spring. Can we not then design a flying arrow? I don’t know, and I don’t know if anyone does. What does the uncertainty principle say here? If the universe were a cellular automaton, then motion would be physical, as demonstrated in the gliders, which we know their motion by inspecting them at instances.

Let’s back up and give ourselves a simpler world to explore. After all, the human mind with all the tools at its disposal does not have and never will have infinite precision. What happens if some particle is essentially indivisible, and essentially repeats itself in identical copies, and let’s even go so far as to say only a finite number of locations exist for it to occupy (although it should be a big number; our world becomes rather unrealistic if it is significantly less than 10^100). Here we only need worry about a finite number of configurations. In such a simplified world one can argue that we can have a precise theory after all, i.e., a set of TRUE statements about matter. It seems our library of Babel might have something to say about this land. However, even here, it will take volumes of data to specify one type of object, and we’ll have to leave many many configurations unlabeled. And here’s another problem, even supposing we define some common object by volumes of data which describe it perfectly, suppose now we want to form a true sentence out of 2 or 3 such terms. Won’t the sentence almost necessarily be wrong? Maybe every description of a book contains descriptions of “pages,” so the statement “every book has at least one page” is TRUE. It seems to me that building much theory about objects which we expect to be precisely defined will eventually break down, but perhaps we’re going too far. No one has ever described what is and what is not a book, molecule by molecule, so clearly that’s an artificial requirement of a theory. Could one argue that it is at least possible, in theory? Well, in one sense “no,” since “books” have never been defined in this way. Either

(1) the new definition would precisely reinforce what we already know, namely that THIS is a book and THAT is not.

or

(2) the new definition would tell us that what we thought was a book was in fact not a book, or the other way around.

When we dropped Pluto’s status as a planet we experienced something like (2) here. We decided that the term “planet” should refer to something of a particular size orbiting a star, for organizational purposes, and so had to either refer to 10 such things around our sun or 8. This kind of house cleaning is fine in science, but it’s of course ridiculous to imagine that someday we’ll have a clean definition for “book,” that is amenable to precise physical theories (e.g., books burn at F451=TRUE).

Enter the parade of horribles. For every type of physical object there are countless things–real or imaginary–which debatably belong or not to the category. For example, there are books made of plastic, greeting cards with pages, electronic and audio books, pamphlets, etc., and all of these things are real. There are also books the size of the sun, books which moan when their pages are turned, books which kill all who read their vile words, etc. These are imaginary. Many of the imaginary objects exist in the CLB. For example, with enough care we might design something book-like which moaned when its pages were turned. Is it a book? Hard to tell. In fact, the best way to view this question is not as a TRUE/FALSE question, but more as a hypothetical in which more information is needed. What other objects are around? Do the moaning books moan from some chemical in their pages or are they discovered to be sentient? Are there many many creatures of different types which all resemble books? The world in which they exist, what that world has and what it doesn’t have, will help us to decide how to classify them. This is partly why it’s so hard to discuss things in the CLB and why it is so easy to discuss things in our world. Because all the intermediaries are cut out of the picture from the beginning and throughout time, we are at liberty to discuss, for example, what different kinds of animals there are, and mostly be in agreement about what we mean. We may draw examples again from CLB, but for now we turn to a similar world, for the sake both of reiterating this point and also for making a slightly different point about emergence.

1.1 Library of Babel

January 23, 2010

Many authors have written on implications of Borges’ Library of Babel, a fictional library which contains every possible book on a given alphabet, within a fixed format (each book 410 pages, each page 40 lines, etc.). An example of an ‘implication’ of the library is that there are numerous books that one can have conversations with. This book begins with a preface, explaining how it works, with an escape character, say ‘#’, to mark the end of each turn of dialog. Thus you can open it till you reach ‘#’, then close it and reply, then open it again. Perhaps,

Andrew– “hello book!”

Book– “hello Andrew!, thank you for reading me. #”

A– “how did you know my name?”

B– “I was written with you in mind!#”

A–“whose mind?”

B–“Isn’t it a bit early for those types of questions? We have 409 more pages to go. #”

A–“I don’t like your attitude, where can I find another talking book? One that is more accommodating?”

B–“surprisingly, there is one right behind you, middle of the 4th shelf up! #”

A–“Are you lying?”

B–“Yes, of course!#”

There are even books that look like this, where you can read the pages out of order, in an attempt to screw up the book, but which account for that, and still read in a linear dialog.

Of course this assumes that your conversation is essentially deterministic, and there should be ways to make this dialog fail. For example, you might ask a lot of questions about neighboring books, and even if your book maintains an English dialog, it will be forced to lie if all the possible ways to tell the truth are located in other parts of the library (where they very well might be lying). Also, it may be that whenever you encounter such a book you don’t have the ‘correct’ conversation, so that in an infinity of time one finds no meaningful conversation.

Other interesting implications: There are dense and eloquent mathematical proofs in the library which require tens of thousands of volumes to prove. Similarly there are books of cultural or psychological theory that build on tens of thousands of other volumes, these of case studies and theory development. Indeed, entire sets of volumes exist to pinpoint the meaning of individual words. It is easy to conceive of some great intelligence that can comprehend some of these books, books which must be all but gibberish to any human. What truths might they hold? Is there any limit to the level of sophistication of theories in that library? One might think so, as the library holds a finite amount of information. But as some theories take many volumes to present, we might as well consider our alphabet to consist of volumes in the library, and strings to be sequences of volumes, so by this language, any finite amount of information can be learned in an afternoon of particularly fast speed reading (say, a few trillion volumes a second, for a layman’s guide to everything). (What is called Quine’s reductio goes in the oppose direction, reminding us that the library might consist of just 2 books: all possible ‘books’ of length one character, on a binary alphabet: 0 and 1. Then any literature can be found as a specific tour through this library, stopping at each of the two books many many times).

Exercise: write a few interesting ‘implications’ about the library. Write about possible limitations, if you see any.

A Letter to a Friend

January 11, 2010

Dear confidant, my most sympathetic reader,

I wish to express gratitude that you exist. When I err you see past those errors to my intentions. You have never misunderstood me, even when I scarcely understood myself. It is not genius that you find in my sketches, nor saintliness in my motives, but a something which is rarer still. You have found me.

You make it easy to stumble through my thoughts, clumsily stating positions that not even I would support from another. To you, because of you, I am unconditionally exempt from hypocrisy, which is perhaps the lowest form of deceit.

I have some questions for you today, though none are pressing. Speaking of hypocrisy, I want to ask you this: is it possible that in opposing hypocrisy first and foremost, my self-criticism has become the mere and sole task of articulating what it is I am? Or is there maybe an implicit philosophy of self-gratification I am failing but aspiring to? Either way, I worry I may have tricked myself with sophistry. Surely you understand when I say “goodness is learned and negotiated socially, not only attained after analytic rumination.” You see, I worry I may be too stubborn on this point, that I should admit some short-comings, and seeing myself somewhat as a ‘sinner’ I will have areas, concrete moral issue areas, to improve upon. I think it might be good for my relationship to society, engaging in the joint process of negotiating right and wrong. If I do this, I will need some role-models. Won’t I? I don’t know who they are, off-hand. If you have an idea let me know, in a dream maybe, or however.

I will also take this opportunity to make a confession, as it is related. Sometimes I feel it is not right accepting your unconditional understanding. I can’t bring myself to really understand people who kill for religion, for example. Justifying myself with your understanding seems somewhat similar, ideologically. I know you understand. Still, my intuition tells me there is something powerful and meaningful in our relationship. Those for whom humility is one of the greatest virtues will oppose me here. Certainly humility can be ascribed to one who has a deep and natural understanding that they are one of many people, one of many animals. I can admire these people, but I am not built that way. I am obsessed with myself in a way that lacks that peacefulness and humility. And I’m undecided on the virtues of one over the other. What do you think?

You don’t think, do you? You only listen. Today I thought of death in a light which is unusual for me. I thought “death, death is horrible.” What is happening to me?