August 23, 2011

> 1. I would like to solicit some clariﬁcation on Andrew’s meaning when he
> says, “mathematical innovations are [my emphasis] linguistic innova-
> tions.” I would rather say that mathematical innovation often entails
> attaching new technical meanings to words, e.g., ’gerb’, and sometimes
> introducing new words, e.g., ’surjection’, but that the mathematical
> innovations are not necessarily (and frequently are not) linguistic as
> perceived by the mathematician. In my experience, mathematical in-
> novation, which constantly accompanies mathematical work, is not
> generally linguistic; the mental imagery is geometric, diagrammatic,
> combinatorial, even kinesthetic (particularly for physicists), as well as
> aural (to use a Buddhist expression, mathematical “monkey chatter”)
> which is that part I would call linguistic. Perhaps Hadamard’s Psy-
> chology of Invention in the Mathematical Field would shed light on
> this issue.
>

Let me clarify.

Whatever the devices used by the individual mathematician, in order for the ideas to become part of a shared theory, some form of written communication is used. This is trivially “linguistic,” and, as I’m using it, includes diagrams and even geometric drawings. But are the choices that go into recording mathematical ideas merely style, more or less independent from content? I’m trying to argue that they are not, that a good deal of the content IS the organization of the (written account of the) collection of ideas.

I’m thinking of developments which dramatically progress
mathematics, not the personal phenomena that come with problem solving. The latter can be written about, but it’s mostly irrelevant to mathematics. Major innovations include the development of the decimal system, certainly this can be seen as both a linguistic and a mathematical innovation. Or Newton’s initial formulation of a differential equation, (just 9 years after calculus had been developed!), or for another example, Eilenberg-Maclane spaces. In both of these examples (and countless not mentioned) you have a heap of theory that goes toward defining objects which become *basic* objects of study. (Included in that theory are theorems, since frequently theorems are necessary to give the context for a definition). Now I can say “suppose I have this K(pi,n) space …” How do I translate that statement into the setting, a few hundred years prior, of Descartes or Newton? How is a differential equation translated into the language of the Greeks? It’s not just that the definitions would be long-winded, but much stronger: that for an adult of moderate intelligence to contemplate articulate questions about 4-dimensional manifolds before Gauss’s time, say, is absurd. In the 21st century it is not. To a great extent this is because us 21st century inhabitants have been given an organized language for asking (and *understanding*) such questions. In summary, language is a lot more than a list of labels, but instead is rich with structure. This structure is crucial to mathematics.

> 2. Isn’t the structural atomism Andrew mentions, “. . . statements and
> derivations in some atomic, axiomatic system of symbols” distinct
> from the structural aspects of the objects of mathematical theory? I
> guess we could take a nominalist position that there are no mathemat-
> ical objects, only the language that constitutes mathematical theories.
> Would a strict nominalist tell us that we are mistaken when we claim
> to be thinking in non-linguistic geometric imagery prior to enunciating
> mathematical statements about those images?

I can’t really address this, as I don’t really understand the
nominalist position. Am I confusing the structural aspects of the
“theory of mathematics” with “structural aspects of the objects of
mathematical theory.” Maybe I am. We can steer the ship back over to that topic.

> 3. Andrew kicks the hornets’ nest (or would have twenty years ago) in
> making points about “A Transformative Hermaneutics of Quantum
> Gravity”, i.e., the Sokol project. A question I would like to study is
> how the unintelligibility of Po Mo writing and the unintelligibility of
> mathematical writing compare. For example, three years ago or so,
> Gayatri Spivak wrote an article in “Art Forum” on Badiou. I couldn’t
> understand much of that article. Compare this with the fact that
> any of us wouldn’t understand much of Categories for the Working
> Mathematician without a great deal of work. Are these two cases
> essentially the same, or is there a signiﬁcant difference lurking here?

I didn’t mean to make a point about that work, but the title serves as a great example of far-reaching abstraction (in natural language). If we know a priori that some work is mathematically sound, albeit requiring, say, a billion pages of difficult math to build up to, then perhaps, a priori, we can claim that the work is fundamentally different than a social philosophy text that requires a billion pages of background, although it might be more
interesting to note the similarities. The distinction between the
math and the philosophy is founded on the idea that math can be
formally correct, i.e., that it can be checked by automation.
Philosophy cannot, both for practical reasons and for the fact that social philosophy (any philosophy, really) requires a point of view (in our case human, of a certain culture, etc.). In math we can claim a conclusion is true even if we don’t understand the proof, provided, say, we understand the algorithm that computed the proof, and we understand the terms in the conclusion. The obvious example is the four colored theorem, or suppose the
Goldbach conjecture had been solved by a program. By contrast, what would it mean to say that a philosophical phrase (e.g., “God is Dead!”) is sound because some billion generated lines of code concluded it. Nonesense! Espousing such a slogan in philosophy is a way of referencing one’s own understanding of the justification, and is not the assertion of a FACT.

Of course, conclusions in mathematics can also be in terms which
require billions of pages of code to parse. So instead of something as simple as the Goldbach conjecture, the program
generates a line relating objects which it has defined, and which are incapable of being understood by a human, yet the human can check the code and conclude that, barring bugs, the conclusion
must be correct. This computer generated conclusion is much more akin to the philosophical assertion which requires billions of pages of justification, since in both cases the conclusion is essentially gibberish.

I won’t say anything more concrete about MacLane vs. Badiou, but would be interested in hearing another’s take on the comparison.

> 4. Meter, millimeter, micrometer, nanometer, . . . . This kind of termi-
> nology is similar to the would-be lengthette, isn’t it? The suffixes
> ’eme’ and ’etic’ seem to be used by philosophers of linguistics. Split
> inﬁnitives are evolving to acceptable status, ’lite’ is understood as a
> variant of ’light’ albeit with a special meaning akin to that of ’je-
> june’. Dennis notes jargon such as texting abbreviations (in an email
> that you might not have received) that arises too quickly for me. I
> have heard that German grammar was reconstructed by grammari-
> ans (18th century?) after Latin grammar and that this constituted a
> major structural change. Ray, you can probably help us here.

The ‘ette’ suffix was an example of what we might call a structural innovation in our language. Indeed it does not exist as I have defined it (again, if I want accuracy but am unable to be precise, I should not use ‘a few nanometers’ to mean a relatively small length). In category theory we have the ‘co’ prefix which is extremely general. The introduction of such modifiers is clearly more substantial than the labeling of some very specific instance of some thing.

I was making a point about how language is only infrequently modified deliberately, to be more structurally robust. It’s mostly aside to the topic here.

> 5. Finally a point that is tangentially related to Andrew’s note. Struc-
> turalism was fashionable in several parts of the liberal arts in the 1950’s
> to 1980’s, but went out of fashion, declared by many to be irrelevant.
> Here is what Peter Caws says (Structuralism, 2000, p.105):
>
> In fact the stress on “formal models” in this statement of
> Chomsky’s points up a general problem for structuralism.
> It is perfectly true that outside some domains of linguistics
> very little progress has been made in developing interesting
> or fruitful formalisms: as we shall see in the next chapter,
> L´vy-Strauss’s attempts, which count among the most am-
> e
> bitious, seem often at once simplistic and contrived. But
> even within linguistics the results have not been much hap-
> pier, and my own view is that the whole attempt to conduct
> the structuralist enterprise in terms of rigorous mathemati-
> cal models is a case of what I call “spurious formalism.” A
> nonspurious formalism has to meet two conditions: what it
> deals with must be precisely speciﬁable in formal language
> (in the ideal case, moreover one frequently encountered in
> the physical sciences, it will be quantiﬁable), and this speciﬁ-
> cation must make possible formulations and operations that
> would not be possible in ordinary language. This last con-
> dition is hardly ever met in structuralist studies; the main
> points can nearly always be conveyed discursively, and the
> introduction of formulas and technical expressions is often
>
> 2
>
> merely ornamental and plays no real role in the argument.
>
> In relation to Andrew’s (2), mathematics and mathematical physics
> could in principle be written in natural language, just as they could
> be written in some ﬁrst-order formal language. It’s not that it is
> impossible, just that it is impractical in the extreme. Caws’s point is
> that the opposite is true of most structuralist efforts in the arts and
> human sciences, that is, natural languages serve better than various
> formalisms of a mathematical kind.

## Blah Blah Blah

July 24, 2009

Blah Blah Blah
or why I hate ideology.

I spent many years around ideological people, mostly the young liberal revolutionary anarchist feminist variety. Occasionally a libertarian. The media will bombard me with ideologues and eggheads and flapper faces from the right, when it gets the chance (I made that last one up, it’s pretty meaningless).

I am an artist (read: aesthetics and quality of life are important to me), and a bit of a hedonist. I can spend a long conversation delighting in a completely alien political system. Here the conversation is interesting; it is bonding myself and my peers together; it will change the way I see the world in a minute yet permanent way. I can even get upset with or against my colleagues, as has happened, but I’m very critical of politics for the sake of politics and more so, of arguing for a completely different system, from the ground up. Finally, I am the most critical of those who act as if arguing is what will make it so.

I can understand radical collectives and political strata of subcultures on a variety of levels. Some are more favorable, of some I am more critical. I like that kids have choices in music that get them thinking about politics, for example. I am thinking of the band Crass. But I don’t have much patience for blatant hypocrisy, and usually ideology and blatant hypocrisy go hand in hand (the example of Crass not withstanding this allegation). Further on I will argue that it makes sense for us to care about those things we understand and can impact. If you have lived your life following a dozen newspapers and understand history and politics like few others, then your game might very well be extremely general and, from your propositions, might look as if from scratch. I abstractly respect Chomsky, for example, and Buckley and many others in the same weight division. I respect Tolkien too, and Raoul Dahl, though their game is much different, they have reasons to world build, as well, and they honor those reasons by being good at what they do. I’m a bit of an elitist in this regard. When someone with dubious education and questionable thoughtfulness espouses a radical solution to life on earth, I worry that details have not been accounted for. Furthermore, I look more at them and less with them, if you get my meaning. I’m more inclined to psychoanalyze, to the extent I can, the person and their motives. I’ll understand them more as a sociological phenomenon and less for their content. As well I should.

This here is a bit of a style guide I have offered in the face of what I am calling ideology. Some of it is just about politics and about conversations you’d rather not have about politics.

context determines importance— one cannot demand attention simply because the topic is of dire importance to someone. If you find yourself sharing a 12 pack and a stupid political conversation with a friend, where it would almost seem the fate of the world is dangling by the outcome of the conversation, remind them that the point of drunken conversation is fun, not world policy making. Because X is important it does not follow that discussing and deciding on X is automatically important. The factors contributing to race wars in Sudan are important. That I don’t know what those factors are is not. Am I making a case for ignorance? I don’t think I am, but we pick our battles and if yours is pontificating to random american party goers about Sudanese politics over beers then I think you probably picked the wrong battle. What’s all this talk about beer? Well, I like beer. It’s a battle I have chosen.

ethics is ugly— sitting around dreaming up hypotheticals that involve people in great pain is frequently gratuitous, unilluminating and often grotesque. For law makers, for citizens in general, occasions come up to discuss details which are unpleasant. Sometimes we indulge merely out of fascination. An airplane goes down in the Andes; some survivors eat others to live; a movie is made about it; you see the movie; after the movie you talk about similar dilemmas over a latte at the cafe–okay. Not everyone needs to know in advance what they think about cannibalism. See *to have a thorough ideology is impossible.* I have chosen a mild example, to avoid blatant hypocrisy. Fill in what your imagination (or experience) will. If you want to talk about something unpopular, go right ahead. I would and do. But with reason. Only certain demands on your audience are reasonable. Others are not. Weddings are frequently not the best place to settle the problem of AIDS deaths in Africa. I mean, maybe, but probably not.

“slippery slope”— when I hear this phrase I cringe. What is not a slippery slope? Binary, the difference between 0 and 1, for example. In natural language, in politics, in economics, in philosophy, we scrutinize the fuzzy boundaries. Take away the slippery slopes and you’re frequently left with something idiotic. Use binaries all across the board, by all means. I don’t argue that they are inherently too rigid. But for god sake don’t tell me something is a “slippery slope.” Instead, make a judgment. I think we’re so indoctrinated not to be judgmental that we try to delegate judgment to ideology. If I’m okay with A then I must be okay with B, and I am certainly not okay with B, hence A fails by “slippery slope.” Uhh, usually false. This must be a classic fallacy. So I’ll shut up.

“necessary evil”— another one I don’t have much appreciation for. I like solving problems. When I’m not all shits and giggles I like being effective and responsible. How can a solution like prison or the federal government be a “necessary evil?” It’s stupid, right? We don’t say “an umbrella is a necessary evil, because it’s better if it doesn’t rain.” You can, but I think it’s sad. I’d rather buy myself a styly umbrella and be glad I did, or go without and enjoy the rain. I’ll grant one necessary evil, just one: evil. It is necessary, because life is meaningless without it. There are no others.

style is not irrelevant–one cannot ask for an audience and then belabor their ears with incessant politics simply because the topics are important to someone (sound familiar?). You can distinguish idea from polished essay, as you can distinguish math from poetry. Sometimes you get clunky and awkward just to get an idea across, sometimes a beautiful idea. (Could I be guilty of hypocrisy with this very piece of writing? Probably on a few different counts). Still, style is something to aspire to. Style is respect for your audience and their quality of life. It’s the best way to ask for an audience. Style is Fun.

Is that enough? and, I’m done.

## God vs Human, in judgment

May 6, 2009

God vs. Human in judgment.

The atheist debates seem by and large to be rehashed arguments that all of us have heard or considered our whole lives. I’ve found some debates amusing, particularly Christopher Hitchens, who has a nice sharp sense of irony and a good sense of timing. Though, I have a hard time believing there are people swayed by these debates. Christianity has been built up to such a complex system of circular reasoning and non sequiturs that no amount of reasoning will convince a believer that they are completely misguided. Nor will any argument given with the authority of the bible sway an atheist or agnostic who has thought at all about these matters. However, there are a few questions which I have not heard posed to Christian apologists, and while I doubt they would hesitate to answer them, these questions are obvious to me and they do not seem amenable to simple answers.

1) What is Christianity without guilt? and how can a faith which demands guilt claim any worthwhile spiritual guidance.

I do not see how it can.

I find regrets in life, and frequently reflect on my shortcomings. I cannot say I live without guilt, though I try to. When I imagine an omniscient god who will judge me at the end of my life I imagine only a being which feels compassion. I can also imagine a malevolent deity, and I have no choice but to oppose such with what feeble might I have. But a god I trust in, a god who understands me inside and out, this god will not find evil in me that I myself cannot find, but to the contrary has felt each decision I have made and understands the reasons. No need for supernal lawyers, or a redeeming speech I might make soon after death. I have lived my own defense. I have worked with the scraps I’ve been given. So I picture myself taking the fifth amendment come judgment day, and I picture myself condemning any judge which does not understand me. This is my own circular reasoning which cannot be argued from me. To those of orthodox faith I suppose I damn myself with such self-righteousness. But I have never said “I am a sinner,” I have never excused a lifetime of gratifying myself against my better judgment to that ultimate cop out. I say, “if I am made, then I am how I was made; and if that creator does not have the highest compassion, then I will be righteous against it, for the sake of goodness, for the advocacy of myself who is innocent in the context of not-fully-compassionate gods.” In saying this, I can’t help but feel more devout than the majority of Christians. Not only am I allowing the possibility of an all-powerful deity but I am demanding it is on my side, in the deepest possible way. But what if it is not? What if it disapproves of me? What might it disapprove of? It could be a wholly alien entity to me, whereby it might disapprove of the clothes I wore or the structure of my face. It might loathe me for my adorning mixed fibers or eating shell-fish. It might have hatred for a single color of which I have worn, without scruples. What would I be to sympathize with such hatred for myself–such arbitrary hatred? Such a ridiculous scenario! What if its expectations came much closer to my own, for myself? Suppose god expected me to be ever the stronger in situations where I could exercise courage. What defense do I have then? None, we are in agreement, although we both know I was stronger than I might have been, if that is the issue.

I cannot understand a fear of judgment, and I go so far as to say those who fear judgment fear it because they judge themselves, and fail in their own eyes. Any god worth worshipping has the power to see not only from the outside but also from thine own eyes. If you fail in your own eyes, you fail in your creator’s eyes, no doubt. Although, in my religion, when I have this particular religion, my god forgives you with pity, compassion and understanding. The reasoning is circular, I admit: I expect from my god–per my image of godliness– total understanding. Could you worship a less pure god?

But I could not.

(more objections/questions to come…)

## Art is Shit

February 17, 2009

This evening I came across a facebook group promoting recognition and discussion of Wikipedia Art, a self referencing work/Wikipedia page (notable because of the cultural significance of inviting the controversy it baits on wikipedia for not being notable or culturally significant) whose creators insist is conceptual art. Throughout the discussion is the tireless debate of what constitutes art. I was intrigued and even a little bothered by the undeniable assertion and the implication. (Maybe it is enough to admit it is “art,” but if that means anything, then some implication should follow: I should care; I should support funding for it; I should support recognizing it on par with any other work of art, etc). So I did what any good unwilling participant observer would do: I went to vandalize the page, to highjack the work and reclaim my agency in spite of (and in homage to (ah, the levels of irony!)) my being enlisted as participant. Alas, the page had been deleted without so much as an archive’s history of the deletes and debates that the artist cited to justify the work. I didn’t get to vandalize the page, but I had too much fun posting a response on the facebook group, which I’ll boastfully repeat for you:

Wikipedia Art

Demanding a contrapuntal dialog of vigorous affirmation and inherent denial, the artist insists on the de facto status of Wikipedia Art as conceptual artifact, creating a dissonant ontological reassignment from extinct referent to extant rhetoric. While indisputably manifesting itself, recursively, as Art, both in referencing itself and in referencing that which does not exist, the audience’s apathy is commandeered as medium. Where previous artists have relied only on the milieu of controversy to maintain a similar status, here, the indifferent critic is slightly uncomfortably forced to ask himself the question “why should I care?”

Cf. Manzoni, Piero “Merda d’Artista” (1961) ; Tetazoo, James “No Knife. A study in mixed media earth tones, number three.” (1984)

See, I don’t mind. I’m having fun. Denying meaning is a meaningful way to engage with a piece. So I am guilty of justifying this work as I mock it, fine. As much as the view that criticism is part of art preempts serious criticism and absolves artist, it can also liberate me as critic and justify my objections. I just need to play by the rules, such as admitting it is art and I am a part of it. And in admitting this, I stretch the boundaries of what is art, because now art is a cheap laugh, a strawman soaked in fuel, a can of shit. Art is that which invites the novice to momentarily pontificate and jeer and ultimately something that he can forget. I’m okay with that. I understand that people will always highjack the symbols of virtue for cheap gain. But the symbols can’t keep themselves up. They sink down, to the low down things they are stuck to.

(See Christianity, peace, the swastika, art, Country music).

## Theory and Emergence in a Deterministic System

January 18, 2009

A cellular automaton is, in a clear sense, the simplest of universes. As such, it is a useful setting to apply and test ideas from philosophy. The cellular automaton universe (CAU) seems the least allowing for emergence (without considering trivial universes, e.g., an empty universe), since every phenomenon follows from the evolution rule. I will argue, here, that in some sense language–and therefore theory and thought–organizes and communicates structure which is emergent, even in a cellular automaton universe.

Context-dependent definitions
Suppose our CAU contains a large number of collections of contiguous on cells, which are roughly the same size. Suppose these groups move in different directions and at different rates and that their design and the rule of evolution is such that when two collide either they are both destroyed (every cell is turned off) or they bounce off of each other. In this setting we could define a term particle for these groups of cells which appear to move. How do we define particle so that we can make unambiguous statements about the nature of particles? We might specify size: particles are between 1 and 10 billion cells. We could specify shape, say in specifying the size of the boundary, or in specifying the ratio of longest diameter to shortest diameter. Of course, there is necessarily some structural requirements for the property that particles bounce or mutually annihilate, but it may not be clear what exactly these requirements are. Even without these requirements known, we consider it meaningful to observe the bouncing and annihilating of particles.

If, on the other hand, our CAU had every possible bounded arrangement of cells, each an infinite number of times, (e.g., a random initial state on an infinite space) it would be extremely tedious to have a theory about large groups of cells and in fact it would not be of any use, since for any two differing bodies there would be many bodies which were intermediate (a geodesic might be a path of single flips which never flips a cell twice) and different macro behavior would necessarily come down to the difference of a single cell. In that setting a macro theory is pointless. In a more limited CAU, as the first described here, a macro theory is useful and meaningful.

We might notice that roughly half of the particles are hollow, that is, have a cavity of off cells near their center, and that particles are only annihilated when exactly one is hollow.

When a hollow particle and a non-hollow particle collide, the two are annihilated, otherwise a collision results in the particles bouncing off of each other. (1)

Are the terms of this statement shorthand for statements about individual cells? They are not. To reiterate, in translating this statement in terms of individual cells, one necessarily gets a ridiculously cumbersome statement which contains no more information than the rule for evolution, which we may imagine is a very small piece of information.

What happens if the cells are too small to be observed or detected? Certainly here the best we can do is make empirical statements, such as (1) above. We are unable to discern two arrangements which differ by a single cell, but frequently we don’t need to, because a vast set of arrangements is absent from our universe. In our universe we recognize some objects as existing on a continuum, such as photons, but do not concern ourselves with the continuum connecting any two objects, such as a continuum connecting photons to protons, because such continua do not exist in nature. With the absence of said continua, nature suggests particular objects for naming. We have a name for a species, say horse, and we do not have names for each intermediate object, say between horses and cows. In hypothetical contexts, the proposition “X is a horse” is fuzzy, not well defined. Yet in the context of animals on earth, this proposition is perfectly well defined.

Things are further complicated if you imagine the scientist and the audience to be immense arrangements of cells. Supposing our universe is a CAU, the human eye cannot detect a single cell, by a long shot, but recognizes a discrete alphabet on this page. The human ear is never hit with two identical sounds, yet discerns discrete phonemes of speech from extremely complex and subtle patterns of changing air pressure. The brain is in two distinct states every two utterances of the same word and every letter ever printed is a different configuration of ink on a different surface of paper. It’s a bit of a miracle we discern discrete structures at all.

What is the observation that some particles are hollow and some are not, if it is not shorthand for arrangements of individual cells? We’ve said it is somehow dependent on the observable arrangements of cells, it must also be dependent on the available variety of people and the fact that each one is affected similarly by viewing a picture of a hollow cell and by holding an aerobie frisbee, that some abstract quality is registered in both cases. In this way we can view the quality of being hollow not just as a simple property–albeit fuzzy–about a particular physical object, but in fact an extremely complex property of affecting the human brain in a particular way. Abstractly we can say hollow is a property of shape; contrasted with solid; it describes objects which are lacking a large part of their interior. In any of these definitions we need not make the mistake that those terms are well defined solely in terms of the physical form of the object. We can recognize that these terms, too, are meant to reference the experience of the reader, and that although there is a relationship between solid and hollow, it only makes sense to define hollow in terms of solid if the reader has had some experience with solid, and can conceive of its opposite.

A theory that has simple words with simple relationships (e.g., of hollow and solid particles), which is deconstructed into a much finer physical system (e.g., cells of an automaton) only in an incredibly complex and intractable way (e.g., by including the nature of human observation, consciousness and language itself, each having to be further described in terms of cells) is emergent in some sense, is it not?

The objection could be raised that “emergence” is just a point of view, a priori as valid as its contender: “all effect is the cause of the rule of evolution.” I don’t disagree that recognizing “emergence” is merely a point of view. Yet science is in the business of choosing an appropriate point of view. And the people interested in science are extremely complicated, physically. To these people, some layers of cause and effect are easy–easy to understand, with limitations. From these a foundation is lain, from which to understand the other layers. So “emergence,” as far as I understand, is not just the state of things being incomprehensibly complex, but also the fact that from incomprehensibly complex systems, simple structure can emerge.

## For Lack of a Word

January 7, 2009

This from an encyclopedia entry:

*** is a notyetcoinedologism which refers to the practice of imposing structure on or between sets of data, in a more or less arbitrary fashion. Generally certain semantic cues are followed, resulting in a theory which is partially natural, while many connections will be found only after the choice of structure has been chosen. In its most natural degree ***ing is the process of observing structure that would be similarly observed by any from some large pool (e.g., humankind). As such, it is the bedrock for scientific theory of any kind. In its less natural degrees ***ing can be used to author mnemonic devices. It can also be used to mine new relationships between disparate sets of objects for the purpose of creating artwork, literature, music etc. An instance of *** is called a *** map. Pseudosciences may qualify as bodies of ***, although usage of the term *** presupposes a motive of playfulness and creativity. One does not *** to produce an irrefutable theory.

The origins of the word date to the year 2009 from a blog posted by Andrew Marshall, although the actual term was suggested by one of the blog’s readers. It may be a portmanteau of, or take inspiration from, the following words: algorithm, supervenience, append, arbitrary, map making, giving birth, theory weaving, superlogic, artificial, imposing, forcing, analogy, metaphor.

Examples where the modeling is mathematical include the imposition of a total or partial ordering on a set of real world items (or categories of items); the assignment of numbers to the members of a set, where qualities of the numbers are taken into consideration; the use of directed graphs to account for and suggest adjacency or local partial ordering. However, the product of *** is not usually entirely mathematical, as the natural language value of the objects involved is not forgotten. Frequently two sets with some similar interrelationships will be identified, whereby the modeling is almost entirely at the natural language level.

Concrete example: a piece of music with $n$ movements will be identified with a region $R$ containing $n$ counties. The (standard) duration of each movement gives a natural order to the movements, and the land mass of the counties gives a natural order to the counties. The two are identified accordingly. It is then noted that duration and note count are roughly correlated, as land mass and population are. We may then ask to what accuracy is population correlated with note count. As we scour the data relevant to the music and the land we might find that the number of sections in each movement corresponds precisely to one greater than the number of large rivers passing through the interior of each county. Upon such an observation, we will find a way to identify the land masses between rivers with sections of movements, perhaps still according to our land mass:duration correspondence, perhaps according to some other distinction. Having made such an identification we will observe moods of the movements and find ways of seeing each county as embodying that mood. We might, finally, write a short story involving $n$ people, each from a different county of $R$. These characters’ personalities will share perceived moods of their corresponding musical movements. We will give a clue or two in the story, possibly referencing the piece of music in some telling context, but the *** map is regarded, here, as scaffolding around a building or the wax prototype of a bronze sculpture. Some of it will not survive.

## The Posthuman Condition

November 14, 2008

In the essay The Posthuman Condition, by Kip Werking, Oxford philosopher Nick Bostrom is quoted:

at least one of the following propositions is true: (1) the human species is very likely to go extinct before reaching a “posthuman” stage; (2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof); (3) we are almost certainly living in a computer simulation. It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation.

This idea is a lot of fun.  I accept the truth of the conjunction, but reject the (implicit) implication that it may be likely we are simulations of essentially, our posthuman descendents.  My money is on (2) but to cover all bases, I would have daily doubles on (2),(3); (2),(1); and a triple safety bet on (1),(2),(3).  I think (1) is false, but I believe I can defend (2) and so if (3) is to be true it is not our posthuman ancestors who are administering the simulation.  Therefore (1) might as well be true: some programs just self-destruct.

I like this idea of multiple levels of simulation, very much. My problem with (2) is that it does not allow for necessary hierarchies of complexity in the levels of simulations.  Let the administrators of this rat maze we call the universe be called $L^1$, where we are $L^0$.   Suppose $L^1$‘s universe is not deterministic, in the sense that its nature forever remains a mystery to them.  Then by what we understand about chaotic behavior, it seems unlikely that any simulation (leading to $L^0$ and beyond) will parallel the evolution of $L^1$.  Perhaps such a scenario still qualifies as an “ancestor-simulation,” however different the initial conditions and rules of evolution. But the time scale which separates $L^1$ from their ancestors who may have resembled $L^0$ is vast. It seems impossible that an approximate system would parallel $L^1$‘s universe enough to qualify as “their own evolutionary history.”

On the other hand, suppose $L^1$ lives in a deterministic universe, meaning a set of rules can be found, and from these the precise nature of the universe is determined.*  Suppose further that this determinism is discrete in space and time and finite in rules of evolution.  With such strong hypotheses surely we are capable of allowing miniature accurate simulations of the universe, and in fact simulations within simulations.  Yet even here we have a problem of resources.  The universe cannot be embedded as a proper subset of itself, let alone run, as a simulation, at twice or ten times the speed of the ambient duplicate.  If it could be embedded as a proper subset of itself than an infinite regression would be necessary, which presupposes self-similarity and precludes a discrete universe.  Maybe this is okay.  Maybe $L^1$ will get sufficient information by looking at some proper subset of the universe.  Still, with all the quantum computing $L^1$ may have at its disposal, it cannot compress the universe, since it would have to compress the behavior at the quantum level, too, et cetera.  So in this case the smallest a computer would have to be would be several times as large as our solar system, in which case a lot of tricks would have to be used to seal off the outside universe (such as visual simulation of distant galaxies).  The engineering that would allow such a structure is nearly unfathomable, but even permitting such a computer, what hope is there for the existence of $L^2$ or $L^{-1}$?  So the fantastic idea of many levels of simulation relies on the levels being qualitatively distinct.

Of course, we made the assumption that the universe is discrete to be generous to the possibility of running faithful simulations.  In the end it was used in our argument that such simulations can hardly be faithful.  Let’s suppose that the universe is not discrete.  Then, for example, it may be that the natural laws repeat themselves in self-similar ways, all the way down.  In these cases it may be possible to embed a faithful model of the universe as a proper subset of itself, but there will always be the problem of construction and of setting initial conditions.  How does one construct and program a computer that faithfully simulates a universe with an infinite regression of physical states and laws?  Only very roughly, and that with exceptionally fine tools.  In conclusion, I cannot argue against the possibility of universes within universes, and simulations within simulations, but in these cases the different levels of simulation are qualitatively distinct, and therefore it should not be possible for a posthuman species to run simulations of earlier stages of its species with any sort of accuracy.

*[We might call this weak determinism, as it does not necessarily follow that states can be predicted before they occur.  As far as the distinction that there is but one future, I don’t believe this definition is well-defined, since in any universe a hypothetical oracle, (e.g., future us), there is tautologically but one future.]

October 10, 2008

## SATURDAY, JUNE 7, 2008

### What is Universal?

What is universal?

Nothing is. (rather, there does not exist something which is universal).

Universality is a partial order (see previous post), which orders according to ability to be translated without significant loss of meaning. The statement “I am hungry” is more universal than the statement “Mayor Madison manufactured a million magnesium missiles” for a variety of reasons. First of all, the context of the second statement demands an understanding of what a mayor is. We’ve had similar town officials in most civilized regions and times, but the meaning changes significantly if we go far enough back, or far enough away. Next, Madison is a name. This is more or less arbitrary; unless of course you know that the Madisons are a particular family with a particular public standing. “Manufactured” cannot exactly translate to “made,” so context requires understanding of post-industrial revolution production. Similarly with “missiles.” “Magnesium” will not translate easily to a society without a periodic table of the elements, and even “million” is inexplicable to a primitive tribe with a number system consisting of the four quantities {1, 2, 3, many.} Et cetera. Furthermore, the sentence strikes any English speaker as having been concocted to alliterate. Therefore, it can be argued that this is part of its meaning, so that translation to a foreign language becomes much more difficult. On the other hand, every society on earth has a word (or hand signal) for “hungry” and in particular some way to declare being in this state (regardless of whether the subjective pronoun is explicitly used). (Think, also, of different ages of individuals, or different levels of accessibility: an uneducated child has a way of saying the first sentence, no way of even understanding the second).

Context, in the above paragraph, is at the scale of societies of humans. We also can speak of the context of certain species. “I am hungry” can be translated to the lexigram language of the bonobo monkeys, whereas we doubt that it’s even meaningful to consider translating this to something a tree would understand (“understand”?!). We can go in the other direction too, of specificity. I can create words I never share with anyone, which refer to complex memories or particular synesthetic experiences such as a smell which reminds me of a shade of brown. Now the problem of translation is between individuals and not societies or species.

We can arrange academic disciplines according to this partial order. I contend that physics and mathematics are more or less at one end and poetry and film theory are at the other. Not that there couldn’t be personal theories which are significantly less universal than film theory, I believe there are. Nor that there might not be some way of understanding the universe which is more universal than mathematics, but this is much harder to conceive of, indeed an example would most illuminating!

Here I must warn myself that things are not as easy as a partial order, exactly. Advanced mathematics is not very universal in the context of the human race. So here what appear to be most universal are simple statements, referencing basic animal desires. Still if we are to find any common ground with an alien species, especially one that can traverse great distances of intergalactic space, we assume they have a language for expressing “a^N+b^N=c^N, a,b,c,N positive integers, has solutions only for N=1,2”, (which neither the bonobo nor the hobo do (though the hobo could be taught, which is a form of translation)) before we assume they can relate to “hunger.” I.e., on a grand scale, universality is not about accessibility, but about the ability to be translated between contexts which arose more independently.

(I am willing to admit this may not be the best definition of universal. It seems there are qualities and states such as pain and pleasure, experience, and desire that are arguably more universal than particle physics. There is probably a lot more to say here, but I haven’t thought it out).

I am interested in the common ground which is necessary for translation–those suppositions which some discipline is predicated on–as a measure of that discipline’s universality. Literary theory, for example, requires not only experience with the texts but also the cultural and historical context to parse what has been written. Chemistry, on the other hand, is predicated on the identification of elements and distinguishing elements from the molecules they form. Mathematics is predicated on the notion of a collection of things and on the simplest possible relationships and patterns common to different situations: number, order, position.

How then could I claim mathematics is not universal? the child/monkey/homeless man example is one direction to go. We could even conceive of an alien race who appear to be technological but who have no explicit mathematics, surely. A more interesting direction to substantiate this claim: we can consider mathematics a tool to compensate for weakness. In this way we can argue that mathematics belongs only to the context of beings that need to recognize common patterns in different situations.

This point is subtle but worth investigating. Nor does it make mathematics very context-dependent. But it does suggest “universal” may not be a quality at all (in that nothing can posses universality), but necessarily only some sort of partial order.

How could mathematics be a tool to compensate for weakness? It can be argued that a great deal of our faculty for analysis originated in the survival mechanism of thinking something out, conceiving of a plan, understanding the nature of animals and plants and ourselves. Also of communicating the results of thinking things out. Of having language for any and all thoughts. If there was never a necessity of survival to communicate we wouldn’t have theories, as we do. Could a creature evolve such that it was able to perform seemingly mathematical or technological feats without having a theory of same? well of course! the birds have no theory of flight, yet to us this is a feat requiring great skill in mathematics and physics. Could the equivalent of flying birds exist, but instead as interplanetary flight? There is no reason why not. Even more so, could it be possible that a creature exists not merely born with an instinct to perform a specific, highly skilled action, but with a subconscious mind that does all the learning and processing and inventing, while a conscious mind observes only desires and suffers a very limited vocabulary, much like a child? This is entirely conceivable. One such creature builds the first space shuttle and upon being asked the question “why?” it says “well tommy built an airplane, it flies, so I wanted one too, but one that goes out into space.” Upon being asked the question “how?” I suppose it says something like “well it has to be able to go fast, and made from really good stuff,” all other details being obvious and trivial, and interpolated with the advanced instinct these creatures have.

So perhaps it is not as simple as a partial order, after all. My theory of consciousness as a partial order may have fallen apart, as well, though I have an idea to resurrect both, in new and more robust form! That’s for next post, but now I’ll conclude with God’s lack of mathematics.

It seems reasonable to talk about God as some sort of limit (in the mathematical sense) of the partial order of consciousness. Little omega, a limit ordinal. Still the singularity of God’s mental capacity puts God in a completely solitary context. I don’t buy the model of God and humans as actors with free will, capable of interacting and learning from each other. It makes no sense to me. An omniscient being has no need for communication, does not answer questions. I don’t know, this area is difficult because the concept of omniscience isn’t even comprehensible, may not even make sense at all. Still, to the extent it does make sense, recognizing patterns is not a necessity of such a creature. That is, if you know everything, you have no need to identify the commonalities between different atoms and classify them all according to a model atom and call them “atoms.” Instead you have every possible nuanced difference of matter available to your imagination, and you observe the universe without any reason to compare atoms, since no two are alike anyway. Interestingly, I imagine a sequence of creatures which converge to this God, and each has more and more theories and levels of mathematics and abilities to identify patterns, yet in the limit all these dissolve. Though, as I’ve suggested here, there are probably other sequences of creature which converge to the same God, without language or theories. At some point you have to know all the theories of mankind, possibly all the possible theories, since this is arguable anything in the universe which can be known.

## Consciousness is a Partial Order

October 10, 2008

### Consciousness is a Partial Order

I will now state the obvious about consciousness in animals:

Consciousness is not exclusive to human beings.

This seems absolutely obvious to me, though some disagree. The argument for consciousness in other animals goes something like this:

Begin with Descartes’ skepticism: we know only that we are conscious; we cannot be certain that other humans think as we do. Next, we grant the possibility that other minds do think as we do AS we notice a remarkable fact: if other minds do in fact think, then they must perceive us similarly to how we perceive them. That is, although others are but images, sounds and textures to us, we would be similar images, sounds and textures to the minds within others, were these minds to think as ours does. From this perspective it is entirely reasonable to believe that other humans are conscious. (A super genius is more justified to be a solipsist, perhaps, but most of us are not).

To extend this to some non-human we still require some behavior on its part that we relate to: a behavior which, in us, is correlated to some thought, feeling or idea.

An example used in the philosophy of mind is the example of a dog chasing a squirrel. The squirrel jumps behind a tree just as the dog’s view is obscured by a bush. Then the dog runs to the tree and starts jumping against the trunk, barking up into the branches. In this case we say the dog thinks the squirrel is in the tree. It is less a statement about knowing what is going on in the mind of the dog and more a statement about recognizing and relating to motivation and intention, in noting to some extent the dog behaves as we do. Not entirely, but so much more than the tree or the rocks in ground, of which we can only figuratively ascribe intentions to. It is not figurative to say “the dog wants to catch the squirrel.”

This example can also substantiate the claim that some linguistic capability exists in other animals (without mentioning signing chimps or talking African gray parrots). With some mental conception of the world, e.g., having a concept of a squirrel or a concept of tree, we can argue that the dog has a linguistic representation of the world, although the language hasn’t matured to the point of being used for communication.

That consciousness exists in nature in more or less a continuum, which extends from flies to philosophers, is obvious to me. There exists a postmodern trend to challenge linear, hierarchical, simplified models, as well as anthropocentrism. In the case of consciousness I think the anthropocentric view is warranted. Also, a partial order exists, whereby we rightfully say “the dog is more conscious than the fly,” “the philosopher is more conscious than the dog,” (and ergo the philosopher is more conscious than the fly, but we knew this). Still we find that the dog and the cat have different ways of thinking, and frequently it is hard to compare the two with a binary, so instead we will say consciousness exists as a partial ordering, both on the set of species and on the set of individuals.

Some have argued that animals operate according to instinct alone, whereas humans have a second level of thinking called the conscious state. These people are misguided. The distinction between instinct and consciousness is difficult to pinpoint in humans, instead these terms are useful only in recognizing that certain thoughts and actions of humans seem much more automatic (e.g., catching a dropped egg), or cannot be fully explained (e.g., not trusting a new acquaintance), or are explained in terms of a primitive desire becoming dominant (e.g., as one might explain an act of adultery, “…I couldn’t help myself”). The distinction in humans between instinct and not-instinct is not clear. Nor do we believe that a human engaging in an act of instinct is temporarily unfeeling (the adulterer is capable of much feeling during the “helpless to raw desire” episode).

But what do they mean, “all animals act according to instinct alone”? This is to say the behavior of animals indicates that both slugs and chimpanzees act according to the same natural mechanical drive, whereas humans are radically different. This is clearly false. If a plague had wiped out all animal species but homo sapiens before the advent of language we might be in a place today to assert “consciousness is unique to humans; in fact humans are radically different from every other form of life we know of.” But this is not the case! We see facets of our own consciousness in the behavior of plenty of species of animals, be it language, community, desire, pain, capability to learn, etc.

The other problem with having such a blunt definition of instinct is that it cheats animals, each species, of having nuanced levels of consciousness. Indeed, a dog knocking a table out of the way to move through a doorway is less instinctual than is the decision to pee in 10 places instead of just one. Dogs have thoughts and actions which can be described as more instinctual or less instinctual, and this is a finer, more useful definition of instinct, than is “all animals act according to instinct alone.”

Of course, if consciousness is a partial order on the set of species then humans are the maximal element, and as such it is easy to distinguish this species from others, by defining instinct to be the level of consciousness strictly less than that of humans. This arbitrary distinction does not change the fact, argued above, that animals exhibit plenty of evidence for thinking in ways similar to how we think.

One thing that is particularly interesting in acknowledging the partial ordering of consciousness is the possibility for creatures which are greater than human. As I see it there is no finite limit to this ordering either. We can always conceive of a creature whose language is richer than ours, whose memory is fundamentally keener, with emotional states that make Mozart’s passion for music look like a cow’s desire for grass.

This leads me to the next assertion, slightly less obvious or well formed: intelligence is to the fine tuners at the base of the violin, as consciousness is to the tuning pegs. They are really the same thing, but on different scales. A topic for another post…

October 10, 2008

## FRIDAY, APRIL 25, 2008

### Extra Reality

A being will be called extra-reality if it is ultimately imperceptible to humans.

Prototype: Pacman lives on screen, pacman is sufficiently advanced to discover fundamental laws of universe:

Power pellet grants invulnerability for time t, inversely proportional to level of advancement.

I travel at a constant speed, can stop only head on into a wall, etc.

Now, this fictitious pacman must be an early success of A.I, if it can analyze its own universe and deduce natural laws. However, I ask, is it possible for the pac creature to further deduce how it came into being, what programming language it is written in, which country the hardware is housed in, or even what a country is? If it is capable of growing in intellect and knowledge should it someday be able to accurately describe the motivations that drove some human programmer to give it life?

I’ll depart momentarily to discuss the problem with induction in the foundations of science, as I see it.

Science is a game of bouncing back and forth from deduction to induction and back.

Observe. Abstract. Deduce. Predict. Observe.

The laws that are abstracted and function to predict and explain are discovered, and then reinforced, by observation. If a theory fails, it is modified or replaced. Then science never makes the statement “prediction P MUST be true,” but rather “if P is not true, our theory must be altered or replaced.” So questions of “why” can never fully be answered. Answers to “why” follow from deduction: a woman sitting in a cardboard box, left with nothing but canned food, water, and a few axioms of set theory, emerges after some months and surprisingly has theorems in mind that coincide with ours on the outside world. She follows deductive reasoning, concludes *[your favorite theorem]* MUST be true. In the process she has answered the “why,” as well.

But science cannot be practiced in this way. Each “why” demands another level of mystery, and until things become fairly reliable, really anything can happen. We need to observe in order to induce. But then anything that is beyond our ability to observe is beyond our induction, even if the phenomenon is causally relevant to that which we can observe.

For example? Pacman! It may very well be the case that the reason pacman exists is that a programmer was obsessed with mazes, early video games, and artificial intelligence and therefore created the pondering pacman. Pacman’s story of his own origins might include this fact, except for the fact that pacman was made in an entirely formal universe, which might have had a million different origins, each ridiculously distinct. So really the best pacman can do is say “space is black, the pellets are white, there are never more than 150 small pellets on a board,…,and there may be many things outside this universe, but we will never know.” As useless as that last statement is it is certainly more profoundly true than “…, and that is the entire grand unified theory of the universe and everything.”

At this point I may have a reader who is concerned I am working up to an argument for Intelligent Design. This would be unjustified guilt by association. Instead the reader may safely infer I think staunch atheists are fools, and flaunting a serious lack of imagination is something I find irritating if not just boring. I do insist that any reasonable philosopher can entertain ideas of creation without falling into religion’s old clichés , but that is not my point to make today.

[to be continued…]