Blog o' Weston

Thoughts on how to find alternate algebra-like systems

noreply@blogger.com (Weston Beecroft) — Sat, 21 Oct 2017 03:20:00 +0000

TL;DR: what if we generalized the notion of an algebraic system in a different way than abstract/modern algebra has, instead focusing on something that may be more at the heart of the utility of algebraic systems: the ability to mechanically alter related mathematical expressions while preserving the underlying meaning, or giving up known degrees of it. It seems possible to me that algebra as we know it retains arbitrary vestiges related to its origins in manipulating symbol sequences (e.g. the usage of inverses to move symbols between related statements), while it may be possible to reach new insights by generalizing from a basis unrelated to sequences or the limitations of handwriting.

Note: There's an annoying mistake running through the article where the only operation type I discuss is 'ortho-semantic'. I realized later there is likely a hierarchy of three operation types: 'ortho-semantic', 'same-relation-preserving', 'some-relation-preserving'. It needs some editing 0_0

It seems like there probably exists a category of systems which exhibit some of the most interesting and useful aspects of algebra, and yet are very dissimilar in other aspects. It’s probably a good starting point for seeking them out to consider what is arbitrary and what is significant in the operation of extant algebraic systems—in other words what is their ‘essence’, and what are their incidental aspects.

My understanding is that their main utility lies in their providing a systematic means of exploring alternate, equivalent representations of values. They let us take two representations which each evaluate to the same thing, and gives us a set of rules for transforming only the representations while the value stays the same (I call these transformations ‘ortho-semantic’ operations since they do not affect the meaning/evaluation of representations—they are orthogonal to semantics). By shifting representations around in this way, while maintaining consistent relations between them, we can discover new patterns and relationships which we would never otherwise have expected to exist.

One especially common/important goal of carrying out these transformations is to 'solve for' unknown elements by taking a pair of equivalent representations and transforming them until one consists only of a single atomic representational element whose value is unknown, while the other representation may be more complex, but readily evaluated. This may generalize to something like: representations may include ‘placeholder’ elements which cannot be evaluated in isolation; however, when equivalent representations are put into some kind of correspondence (e.g. like being placed on either side of an equals sign in traditional algebra), applying sequences of ortho-semantic operations to the representations may put the system into a state in which the correct evaluation for a ‘placeholder’ element is unambiguously revealed.

I think viewing the situation in that way frees the imagination a little to explore new forms of systems exhibiting those properties, while implementing them in potentially radically different ways.

My suspicion is that some of the specific features of algebra as we know it are accidental outgrowths of the historical fact that we had to do these representation transformations by writing symbols on paper. Especially given our familiarity with written language, this would bias us to a sequential, symbolic representation. However, (what I claim are) the essential characteristics of algebra—i.e. the capability of systematically transforming equivalent representations without changing their value/meaning—do not depend intrinsically on symbol sequences.

And the kicker is: the ortho-semantic operations in the various algebras we use all depend on the notions of inverse and identity, since the two together provide a simple means of moving a symbol (or group of symbols) from one representation to its equivalent; and transforming the representations in that manner is of the essence if your machinery for carrying out and recording the transformations consists entirely in symbols drawn on paper via pencil by a human. That’s my central thesis here: we have assumed identity/inverses are part of the essence of systems that behave like algebras—but maybe they aren’t as necessary as they seem.

In the way mathematics has presently generalized specific algebraic systems into an abstract theory, inverse and identities play a very central role. I wonder two main things: 1) Could specific, alternate algebra-like systems be developed which have similar or greater power than traditional algebras, yet do not depend on inverses/identity? 2) Could a generalized mathematical theory be developed which deals more directly with what I claim is at the heart of algebra’s operation (systematically transforming equivalent representations without changing meaning/value), rather than focusing on a particular implementation of that behavior which happens to require inverses and identities? I know many will say that the rich theory around algebra is a sort of proof that it’s the ‘correct’ track—and I would counter that there’s plenty of space in the realm of pure mathematics for more such rich theories. One could also point to uses of abstract algebra in the physical sciences as a kind of proof of the same thing, but if I’m not mistaken it’s often the case already that the ground is covered by alternate theories as well, e.g. Category-theoretic formulations, so I don’t think of success of pre-existing systems as proof of any kind of ultimate correctness.

I think any algebra-like system must have these parts (and only these parts?):

A syntax (i.e. a definition of allowed symbols and how they may be arranged into statements; doesn’t actually have to be symbol sequences though, any consistent representation whose rules may be stated is fine).
A semantics: a mapping of syntactically valid statements into some other domain of ‘values’. For the system to work well it should be the case that the semantics frequently maps multiple unique syntactic statements to the same value.
A set of ortho-semantic operations, describing the ways in which one may convert sets of statements into equivalent sets of statements (equivalent in that the semantics would map the statements to the same values).
(NOTE: this needs to be modified taking into account the introductory note at the top here.)

—maybe the general theory of these systems would use those ‘parts’ as its central terms?

One thing that occurs to me is that it’s not necessarily necessary to isolate single variables (i.e. ‘solve for’ single variables) in order to discover unknown values in other algebra-like systems. It’s necessary in algebra because if you had something like this: x + y + z = a + b + c, where x, y, and z are unknown and a, b, and c are known, it’s ambiguous which variable maps to which since addition is commutative. It’s possible that in alternate, algebra-like systems, you could perform some ortho-semantic operation which causes a number of representational parts to align unambiguously and have their meaning revealed through correspondence to the ‘partner representation’ (I would call each side of an equation one of the ‘partner representations’ in traditional algebra systems).

My best guess is that any alternate, algebra-like systems which are constructed will exist only in software, and would be very inconvenient to try drawing on paper (or at least the set of these is much larger and less explored, so we’re more likely to find something there). It could be that the ortho-semantic operations are much more complex, also, so that it’s not simple to state exactly what it does in any way than reading the algorithm that does it. So, a user of one of these alternate algebra-like systems would probably press buttons corresponding to the ortho-semantic operations in order to shift the representations around and investigate relationships.

——————————

Another mostly unrelated idea:

Why is it that we mathematically represent physical laws with equations? Generally speaking, what we’re attempting to document are how states of physical systems evolve in time after some operation occurs; so wouldn’t it make more sense to use a representation like

[state 1] {static collision} [state 2]

—where two states are related by an operation? If we were to develop an algebra-like system around this, every operation would have its own set of ortho-semantic operations (kind of like the different rules that exist if you relate two algebraic expressions by ‘<‘ or ‘>’ instead of ‘=’). Sounds like a lot of work, but it may be that there’s a more general system which can be used to automatically give sets of ortho-operations for particular physical operations (like ‘static collision’ in this example).

Actually though, I don’t think this would work… —looking at a more concrete example:

[

[mass: 5, elasticity: 0.1, position: {0,0,0}, velocity: {0,0,0}],

[mass: 8, elasticity: 0.25, position: {10,0,0}, velocity: {-2,0,0}]

]

{static collision}

[

[mass: 5, elasticity: 0.1, position: {0,0,0}, velocity: {-3,0,0}],

[mass: 8, elasticity: 0.25, position: {0.234,0.43,0}, velocity: {0.5,0,0}]

]

It is interesting though that scientific laws aren’t generally in the imperative form, like if I have a physical system in state X and do BLAH to it, Y will be the resulting state; my guess is that we use equivalence relations instead because it’s our only means of ‘doing theory’, by encoding results in equations and then looking for new relations by applying ortho-semantic operations to algebraic representations. However, that probably shapes our view of science quite a bit, in a very Sapir-Whorf manner.

Reflections on "Toward a Noncomputational Cognitive Neuroscience"

noreply@blogger.com (Weston Beecroft) — Sat, 27 May 2017 21:47:00 +0000

Note on where this came from: I was bored one afternoon and one of my friends posted this paper ("Toward a Noncomputational Cognitive Neuroscience") on Facebook. I have nothing against it, I just wanted to do some writing and analysis since it had been a while, and this happened to show up. I do feel like my tone ended up being overly harsh, and I guess it did annoy me a little, but it also had some interesting ideas and who knows how off I am—so please do check it out on your own if you're curious.

Since the 'computational' is such an exceedingly far-reaching category, I keep an eye out for things which fundamentally can't be included in it. I only know of one subject totally outside its bounds: immediate conscious experience, all the qualia currently present—the subject matter of phenomenology.

Unfortunately, "Toward a Noncomputational Cognitive Neuroscience," doesn't seem to supply any new instances of the non-computational. Its central argument appears to be a straw man (but mine may in part be too, so make sure to check out [0]): it takes overly restrictive definitions of computation and information processing and then demonstrates how its alternate approach does not fall under said restrictive definitions. Yes, contemporary artificial neural nets don’t adjust their connection weights, transfer functions etc., while operating (i.e. after training), and a dynamical systems analysis of a system which does this is qualitatively different from one which does not—but computation has no intrinsic limits that would prevent someone from architecting such a neural net, even using the paper's narrow definition of computation which requires rules to be operating on representations.

The paper's view on the difference between simplified and realistic nets is most concisely stated here:

"It is the processing of representations that qualifies simplified nets as computational. In realistic nets, however, it is not the representations that are changed; it is the self-organizing process that changes via chemical modulation. Indeed, it no longer makes sense to talk of 'representations.'"

Why would a computation which changes its own rules no longer be a computation? Such computations are at the very heart of computation theory! Additionally, the sense in which the system is no longer operating on representations can only be superficial, since at some level of interpretation, representations are still obviously a component of cognition. The difference is just that they emerge at a higher level, rather than being explicitly defined things which the base system explicitly operates on.

The separate argument about digital computers being classical, non-chaotic dynamical systems also falls flat, in my opinion. The sense in which computers are classical systems is superficial: if I can write a program for it which, at the appropriate level of interpretation, is nonlinear and chaotic—what does it matter if the substrate is classical? If you insist on only modeling the state space of the substrate, rather than something higher level, sure, it’s always classical—but what do you gain by doing that?

The bit on connecting Freud back to the super abstract dynamical systems stuff was a pretty neat idea I thought. Would be interesting to see if there’s a good fit with any ideas of, e.g., William James or Jung.

On the other hand, I suspect the paper's attempt to incorporate the ideas of Derrida et al is part of a flawed justification for considering its notion of the noncomputational to be more significant than it really is.

"Out of that intersection of ‘self’ and ‘other’ the dynamic whole evolves in its spontaneous, unexpectedly bifurcating manner. So the brain does not compute; it permits and supports ‘participation’ between self and other in the evolving whole."

I read that, and many other arguments from the paper, as being circumlocutions avoiding saying, “the system is bottom-up, not top-down.”

"The outside is not represented inside but participates on the inside as a constraint on a self-organizing process."

As far as I can tell, this usage of ‘to participate’ is just refers to something which: 'can’t be modeled top-down', and 'is one among other things involved.' Seems like it's largely, indirectly saying that cognition is emergent—and, erroneously, claiming that you can't create emergent, chaotic systems in classical computers:

"Computation as understood by the tradition is not performed by chaotic systems. Computer computation is not sensitively dependent on initial conditions."

And yet it is capable of executing programs which are.

------------------------------------

[0] To be fair though the sense in which it is a straw man is only this: it doesn't say anything significant about computation in general, only about a special restricted Computation which it is interested in (and which I'm sure many other academics are interested in as well). The reason I take issue with it (it addition to the clickbaitiness of 'Noncomputational') is because the paper also comes with the suggestion of a paradigm shift for Cognitive Neuroscience—but this special Computation it's found a negation of isn't sufficient to constitute a paradigm shift. Anyway, considering that, much of my review may itself be a straw man. Oh well.

The Subtle Narrowness of Human Concepts

noreply@blogger.com (Weston Beecroft) — Sat, 18 Jul 2015 23:33:00 +0000

Note: the first part was mostly just messing around with writing, and the second part is a much more direct statement of the ideas which the first is founded on.

Understanding is partially and significantly a generative capacity; and, being able to generate instances of our generic grasping, we feel ourselves to have some ambiguous command of reality. To look upon a house and consequently feel it recreated in the center of one’s self is surely a more profound act of possession than any deed could confer; but to extract from multiple unplanned viewings that which makes a house a house, and turn it around, and freely and fluidly construct never-constructed new variations, in that same most personal inner chamber—perhaps no form of ownership could be more complete. But what is the true value of this ability? In offering even a superlative commendation of the human capacity to know, one inevitably compares its worth against those of its contenders; an act of measurement, always comparative, necessarily precedes our praise. It seems, however, that we are too apt to mistake beating all contenders as furnishing proof of transcendent superiority, when really, as far as we know, the match was rather local and our champion would be devastated outside his hometown. There is a negative and a positive side to considering the situation thusly. The ostensibly negative side is that understanding begins to look more like our various other capacities—like, for example, the one which allows us to determine with our noses whether a shirt is unclean or not. The positive side is that we may attribute to reality—which, if we aren’t solidly a part of, what are we?—a dazzlingly less bounded potential, to say nothing of the general merits of taking a more realist stock of things.

-----

For most of my life I'd assumed that human concepts were this limitless sort of thing capable of making fundamental connections to what's going on in the universe at some deep level. In more recent years I've come to consider them as almost like another sense: they are symbolic patterns consistently formed when we are exposed to certain stimuli (like our experience of smells consistently reappearing when exposed to similar molecules). Our conceptual faculty augments the pure pattern-correspondence of our more primitive senses in that the patterns can be associated with other internal patterns, and in that we can generate new patterns purely from existing patterns (using logical and analogical processes), which at some future time may be usefully associated with some never-encountered external stimulus. This is of course extremely useful—but we really must be falling into what should be an obvious trap of anthropocentrism in ascribing to them much more than that.

Improving Idea Representation and Debate

noreply@blogger.com (Weston Beecroft) — Fri, 12 Jun 2015 04:53:00 +0000

Note: you can skip the prelude by scrolling past the screenshot.

No category of invention has ever been more influential than that of concept representation schemes, which claims such notable alumni as natural language and mathematics.

Concepts have deeply symbiotic relationships with their representations; our inklings are pitiful, delicate agoraphobes without some formal carapace to curl inside of. And, once linked, the two inevitably fuse; discerning a point of separation becomes an endless task: their boundary expands into infinite, alluring detail whose completion always appears near.

Further, our choices of formalization accrete in layers, each developing its own character, without ever fully concealing its origin.

Some representations excel at distinguishing multitudes and attaching to them, separately, myriad, manifold impressions; others have no memory for names, but are remarkably intuitive with relationships. There are factions, and contests: there are those who would have it that rigor stably supports life, and those who claim it the first sign of death. Others plead vociferously, and vaguely, for a kind of harmony.

It was said, in a representation long forgotten, that, "no two forms possess intrinsic merit disparity; the worth of a form exists only in relation to a thought,"—but then! There arose a structure so impossibly well-balanced, so gloriously lacking in error, so frustratingly perfect, that psychotic murmurs of, "messiah," crying whispers of "divinity," and hopeless exhalations of, "God" filled the once heathen mound of abstract rabble. The one true form emerged:

The text in this screenshot is unfortunately misleading—each node should have a single sentence, plain, statement of some 'claim'—a 'proposition,' if you prefer.

Actually, no—my mistake—that's just a screenshot of a project I started nearly a year ago. Ah, well, I guess I'll just talk about it instead.

Natural language has many virtues. Formal mathematical languages also have many virtues—in fact, in a certain sense, it may even be said that they are the more virtuous of the two. Unfortunately, however, even if that is the case, in some sense, it is irrelevant: people have to actually use the language, and nobody has the time for something much more formal than natural language—not even mathematicians!

So, the idea here is to add just the smallest amount of structure to natural language: one must break their overall idea into the separate claims one desires to make—then state those claims with whatever level of formality you'd like. Furthermore, arrange your various claims so that some are supporting others; the supporting claims will be rendered as children in a hierarchy.

Once you have represented some idea, or hypothesis, in this manner, you may do a number of things with it: you can re-use its parts to state new ideas, you may share their parts or whole (though they'll be subject to rating at this point), you can request that a whole 'hypothesis' be critiqued—or, you can put it up for public debate, in the CRUCIBLE (or private debate, not in the crucible, is also fine).

The debate system emphasis the constructive qualities of argumentation: two competing hypotheses are reconciled into one improved hypothesis, with individual claims having been treated individually.

It's possible that a more refined taxonomy of rhetorical devices could be sequestered from conventional expository essay structure than just claims/justification. For instance, why not have 'alternate phrasings' or 'examples' or 'empirical evidence' be node types in the hierarchy of one's hypothesis?

Using such a system, one could represent: political arguments, business decisions, philosophical or scientific ideas—you name it!

How to Make View-Independent Program Models

noreply@blogger.com (Weston Beecroft) — Mon, 08 Jun 2015 00:09:00 +0000

In Part 1 of this two part series, I made an argument that the standard way of structuring program authoring tools involves a peculiar and unnecessary model/view coupling that makes a number of problems in the programming tools domain more difficult than they need to be. Here I'll be describing a simple, general way of constructing generic 'program models,' which have much in common with ASTs, but improve on them in a couple of critical ways. I'll be referring to this method as the 'path formulation' of program models.

Why this structure?

Short answer: because it's simple and general, and bears a very close relation to the essential activity in high-level program construction.

The 'path formulation,' a particular way of creating program models, comes from asking the question, "what are we really doing when writing source code?" and finding the answer, "selecting and configuring abstractions provided by a programming language." In that case, writing source code is just one way of doing a more general and essential activity: selecting and configuring abstract 'language constructs.' Here's a short dialogue illustrating the point a bit more.

So, let's say your programming language provides an abstract language construct called 'function_declaration'; it is comprised of a few parts: a 'name,' a 'return_type,' and an 'argument_list.' A configuration for this construct would be a particular 'name,' 'return_type,' and 'argument_list.' What makes it 'abstract' is that none of these entities are tied to a representation. In other words, while it has become reflex to think of these sorts of constructs in terms of character sequences, here we intentionally leave open the question of how they should look.

Making Program Models using the Path Formulation

The idea behind the path formulation is: if you have a model of a programming language in the form of a graph, then individual program models are just paths through the graph.

Here's a high-level, three step recipe for making these language/program models:

(1) Represent your programming language 'abstractly,' using a formal grammar that has no lexical section (now called an 'abstract grammar'): its fundamental units are the fundamental units from your language in the abstract, rather than character sequences. Only consider which abstractions your language should include and the rules for composing them; worry about how to represent them visually elsewhere. For example, we can say that a 'class' is made up of a 'name,' a set of 'variables,' and a set of 'methods,' without any assumptions about how these things are going to look. (I talk about this in the first part, too.)

(2) Convert your abstract grammar into a graph, which will serve as the 'model' for your language. (I have some Java code that will do this for ANTLR grammars, btw, which I can clean up and share on Github if there's interest.)

(3) Represent individual programs as specific paths through the language graph.

So, if your grammar contains a subsection like this ('class_reference' is for inheritance, indicating a parent class):

program

: class+

interface*

;

class

: name

class_reference?

function_declaration*

;

function_declaration

: etc. etc. etc.

Your graph-based language model will have a subsection like this (black nodes are 'language constructs,' orange nodes are 'language atoms'):

And a particular program in your language, consisting of one simple class might look like this:

These paths could be represented by just listing the edges taken—though of course you have to number the edges:

Taking that approach, the model of our simple program looks like this:

(2 2 0 1 3 0 0 3)

If we would like a little structure in our model representation, we can distinguish between 'language constructs' and 'language atoms' (black nodes and orange nodes), by using opening and closing parentheses to mark the start and end of language constructs.

(2 (2 0 1 (0... 1... 2... 3) 0 0 3))

Note: the ellipses are where we followed some hypothetical edges in 'function declaration.'

Language constructs are just composite abstractions, made up of more than one part; language atoms cannot be broken into smaller units. Actually, 'language constructs' and 'atoms' have a relationship that mirrors S-expressions in Lisp, so it's no surprise that the notation for program models resembles Lisp (here, however, we aren't tied to using this as the visual interface for the programmer).

Using Insight from the Language Model

A big advantage of the path formulation of program models is that it maintains a strong connection between elements of a user's program, and the programming language itself (since programs are paths in the language graph). This connection can be taken advantage of by programming tools to guide programmers in using the language.

As an example, let's say a programmer has just selected a 'class' construct (maybe by typing out the keyword 'class'—or in some new way); the program model now contains a node for that 'class' construct, and the editor, just by examining the 'class' node in the language model, knows all the legal options for proceeding, because each option corresponds to an edge going out of the 'class' node:

To make this as concrete as possible, I'll show one possible UI that takes advantage of this connection to the language graph. Keep in mind, though: you could still render it like a traditional text editor, using the UI contemporary IDEs use for 'auto complete' to display alternatives. It's like automatic auto complete for all aspects of the language—at the least, this would be tremendously useful to new users of a language.

In this hypothetical editor, the UI is split into two main sections: the top is our document, which is just a rendering of the program model; and the bottom contains controls for selecting and configuring language constructs.

Let's say we've just instantiated a class definition by supplying all the necessary parameters; it has the name 'InputHandler,' and our editor has 'collapsed' it, so we just see the name and type:

Since our editor is following along in the language graph, it knows we're back in the 'program' node, from which point we can begin specifying either a class or an interface. Let's say we select 'class.' Our editor now looks like this:

Notice the whole 'class' construct and the 'name' section have red borders; this is to indicate that 'class' hasn't been fully instantiated: it still has 'free' parameters that must be bound to something (in this case 'name' must be bound to something). Also notice that in the bottom section, the options appearing in the grid are just the neighbors of the 'class' node in the language graph.

I imagine that in using a system like this, the cells in the bottom area would map to keys on your keyboard: this way you could accomplish a task like creating the skeleton of a new method declaration with a single keystroke. Something along these lines would also be much better than text editors for programming with virtual/augmented reality systems and mobile devices. Anyway, this UI is a just a quick sketch of one possible approach. The document region could also be something like this (in that video, I'm rendering the AST in manner identical to how I'm suggesting we render program models).

Conclusion

It's been a long time since we laid down the character sequence and parsing-based architecture of program authoring tools, and contemporary work on programming languages is deeply invested in that established approach. It seems like the program model approach could be an improvement—but who knows what lethal oversights might still be lurking. What's especially needed at this point is a concrete implementation. I'm working on it, slowly, in my free time—but my hope is that others will read the ideas here, and if the they prove to be generally interesting after all, expand and solidify them into serious tools that will improve the experience of programming for the upcoming years. If you'd like to hire me to work on something related, I can be contacted at 'westoncb[at google's mail service]' (or even if you just want to talk about it—though the comment section is probably best for that).

----------------------------------------

Appendix:

Identifiers etc.

Let's take a look at the abstract program graph one last time:

Notice that 'class reference' and 'name' are language atoms, but these things need structure of their own, so where does that come from? First I'll point out the reason we don't include identifiers in the language definition is that they are mnemonics for humans, not part of the abstract structure of a language; all the language needs is a unique identifier, so we just generate a random one. As for the mnemonic, maybe it should be a string, maybe something else—accordingly we leave it outside of the language spec. In the program model, we just attach the random ID (discussed earlier, too) which can be associated to some representation specified by the programmer (probably totally without their notice, by just typing in their editor as always). A program model with IDs might look like:

(2 (3 (#49843345) 0 0 (#95728745) 0 1 (... ... ... 3) 4))

There's an external file that maps these IDs to representations (often it's just a string) for editors to use.

The following section discusses how to handle the 'class reference' node and others like it.

Referencing the Program Model

There is an aspect of programming languages that isn't captured by the 'abstract grammar' that I've described so far. The abstract grammar only allows us to describe 'free' language constructs which, when supplied with specific parameters, are 'instantiated'; program models contain only instantiated language constructs. However, the 'abstract grammar' should describe the full capabilities of the language, and programming languages always contain mechanisms for referencing already instantiated language constructs: e.g., I have instantiated a 'function_declaration,' which had its 'name' parameter bound to the value 'testFunction'; other parts of my program should be able to reference this specific, instantiated 'function_declaration' by using it's 'name,' 'testFunction,' as a reference.

To be honest, I'm very curious to hear other people's ideas on how to go about doing this, though I do have an approach that seems like it would work well: extend the notation of our 'abstract grammar' (which is just some variation of BNF at the moment) to express 'queries' on program models: i.e. "select all the nodes from the program model of type 'class'." More concretely, let's say our 'class' construct is defined as follows:

class

: name

class_reference?

function_declaration*

visibility?

;

(The 'class_reference?' component is used to reference a parent class.)

'class_reference' would be defined in our grammar as follows (except using some appropriate notation, not English):

class_reference
: "select nodes on program model of type 'class' in same 'package'"
;

So, in order to instantiate a 'class_reference' the programmer would have to select a node from the program model that meets the criteria in the query. Ideally, the programmer's IDE would parse the query, run it on the program model, and offer up a selection of valid nodes. Present IDEs do this sort of thing of course, but including the necessary information in a unified, abstract language specification would be beneficial.

Why Programming Languages Use Only One 'View,' and How to Fix That

noreply@blogger.com (Weston Beecroft) — Sun, 07 Jun 2015 19:19:00 +0000

(note 1: This is the first of a two part series; part two is here: How to Make View-Independent Program Models)

(note 2: In the interest of a little more context/concreteness: here's a video of an editor I made that works by rendering a tree-based program model as described in the article (this just uses an AST, though, not a 'pure' model): Tiled Text)

---------------

It's pretty well acknowledged that the reason source languages exist is that they are better interfaces for program creation than, say, typing and reading machine code. And yet, it's kind of weird to call them 'user interfaces'—probably because they are each comprised partly of the concrete interface to some external text editor and partly of an abstract specification, this combination being a more nebulous construct than we're accustomed to labeling 'user interface.' At the same time, however, even if its form differs from our typical user interfaces, its function matches well: programmers use a text editor and programming language features as their interface to program creation.

User interfaces are something we've learned a lot about since the original architecture for program authoring software was laid down (which determines that programs will arrive in the form of character sequences and then be parsed into something more useful). Among these things learned is a useful way of analysing systems into 'models' and representations of those models, called 'views'. Furthermore, probably the strongest reason for an architecture to adopt a model/view split is that the software will require multiple representations of one model. This is very much the case for program authoring tools: for instance, source code and machine code could be generated as two representations from a pure program model (which I describe how to build here)—and we could far more easily allow multiple source views.

There are a few points I've come to believe are true which have led to a new perspective on program creation systems:

(Note: I'm going to use 'machine code' as catchall for any kind of target/output language in any kind of interpreter/compiler.)

(1) The only reason we have source languages (as opposed to machine code) is because they are better interfaces for human programmers.

(2) Program source and machine code are two representations of one abstract thing. This common 'abstract thing' is much like the models in MVC systems; accordingly, I call it a 'program model' here.

(3) ASTs are an approximation to this 'program model,' but they are biased towards one potential representation: source code.

(4) It's possible to construct generic program models, which are better at capturing the essential properties of programming languages (including, e.g., 'type' information), and which are not tied to any particular representation.

The more I think about 'program models,' the more our treatment of program source code seems bizarre. Why aren't the models of computer programs prior to their source code representations? Shouldn't program models be the basis for generating program views? Shouldn't we store models on disk and build views when using our programming tools? Shouldn't we pass models around the internet instead of views?

This more symmetric relation of the various views of a language to a single generic model, as in the image, seems more natural:

Among the many benefits we could expect to arise from structuring things this way:

Swappable views for programming languages (think, e.g., personally configurable 'syntactic sugar,' but on a much grander scale—definitely edging in on the realm of meat and potatoes. A primitive example: you check a box in your editor, and now your Python-like language is rendered with curly braces instead of just tabs. A little more complex: instead of 'new Color(20, 30, 50);'—your editor renders a color picker).
Experimenting with UI concepts for program construction would be far less costly.
No need for parsing at all.
Dead simple for tools to give feedback on what's possible to do within your language, significantly reducing the learning curve of using a new language. (More on this in Part 2.)
More diverse, interesting textual representations are possible since you don't have to parse.
Program models could be much simpler than source code (aside from LISP: my particular formulation ends up looking like this: (2 (3 0 0 0 1 (0 3) 4))), hence they are easier to manipulate via algorithms.

Program Views on Generic Models

The editor 'Moonchild' has some examples of the sorts of 'node views' I'm imagining in the section below.

So, assuming we now have a generic program model (I describe how to actually build these in part two: How to Make View-Independent Program Models), what would it look like to build views based on such a model? There is a powerful, natural approach to this, which is for programming tools to mimic web browsers, whose displays are built up using algorithms on DOM trees. Our 'program model' is very similar to a DOM tree: first, it's a tree, and second, it contains the abstract structure and content of the thing to render, but doesn't say how to render it. The modern web is ample evidence that this kind of structure works well as the basis for rendering complex, diverse, text-centric layouts, with varied interaction styles.

It's probably not hard to see that we could use this structure to build visual representations of programs that exactly mirror the look of present day, pure text source code—so if 100% text is preferred, that's absolutely possible. But imagine, now that it's built on a structure that matches the web, how we could evolve pieces of our document into rich, interactive elements, when desired.

What I mean to propose here isn't that we use one view or another, though; rather, only that we maintain a more direct correspondence between elements in the visual display of our programs, and their backing models (as in the image). This is in strong contrast to the unfortunately indirect relationship found in most modern programming systems, which is necessarily mediated by parsing. For example, with this more direct relationship, just by placing your cursor somewhere in the document your programming tool knows which node in your program's model you are considering interacting with. The node might have an "on click" script attached—it might expand its visual representation, pushing the views for other nodes to the side, or shrinking nodes whose types are irrelevant to what you're interacting with.

Again though: I don't know what the better interface is, just that this opens up our freedom to explore. In our current systems, the only time we experiment with alternate views is when designing whole new programming languages; using generic program models, we can keep every other aspect of the language and just change how it's rendered for programmers.

The Difference Between ASTs and 'Program Models'

While ASTs are a sort of approximation to program models, It's probably more accurate to call them models of program source, than of programs themselves. Well, what if we model 'programs themselves' instead of 'program source'? After all, modeling program source does imply that unhealthy dependence on one view; can't we consider 'language constructs' in the abstract, separate from a visual representation? We can!

It's very common to use formal grammars to generate software for building ASTs out of program source. These grammars define the set of abstractions (i.e. 'language constructs') available to the programmers of a given language—but they do so in terms of a textual representation of these abstractions. However, if our grammars were to not bottom out in a 'lexical section,' i.e. without describing the decomposition of abstractions into character sequences—we could more directly address the 'essence' of our programming language, handling representation later.

More important than the actual act of omitting the lexical section, though, is the different way of thinking about grammars when you aren't tied to characters as the 'atoms' of your language. What would your primitive types be if not characters? Well, why not the abstract primitive types of your language?

Here's an example of the difference: let's consider how a simple function call is represented in an AST first, then in a generic program model. Here's our function call:

doCoolThing(intVar, boolVar);

And this is what it might look like as represented by an AST:

Now, as represented by a generic program model:

Notice how in the AST the function name and both arguments all appear to be the same kind of thing? That's because in the model of the source code, they are all the same thing: they're all character sequences following the rules for identifiers. In the program model, the node types relate to meaningful types within the programming language—it's not talking about character sequences at all. This makes it a much more useful model for programming systems to work with: it's a structure that relates more closely to meaning within a programming language.

The long numbers you see in the program model diagram are IDs used to associate certain nodes with arbitrary, external representations. If you'd like, there's no reason this representation couldn't just be a sequence of characters—but now it could be interchanged with any number of other things, without changing the rest of the language.

The next half of this essay: How to Make View-Independent Program Models

You might also check out: A Short Dialogue on How Crazy Human Programmers Are

Some more examples of editors that operate on models instead of text, but aren't visual languages: Lamdu, Unison, JetBrains MPS, eco

A Short Dialogue on How Crazy Human Programmers Are

noreply@blogger.com (Weston Beecroft) — Fri, 05 Jun 2015 15:14:00 +0000

This was initially part of my explanation for why people should be interested in 'syntax free' programming, but I decided to separate it. Here is the original essay.

Aliens have landed on earth. One of their computer scientists has been speaking with one of our own. They understand each for the most part, at high levels of abstraction—but they find plenty of discrepancies in the details. Now the alien is trying to grok how our programming tools work:

Alien: I understand that you have added abstractions over your 'machine code' because people find it unmanageable to build systems in a binary alphabet—but I don't see how your programmers interact with the abstractions, how they specify which they would like to use.

Human: Okay, I think I see what you mean. Well, whenever we write programs, it is in a particular 'programming language'; this language contains a set of abstractions which a programmer is free to choose from and use how they'd like. Each language assigns names to its abstractions; so the programmer types the abstraction's name in order to use it.

Alien: Alright. Maybe I do understand then—it's not so different at home: we don't usually type out the name, but we might say it out loud, or reach our hand toward it, if we see it on the 'program construct' list. I'm curious, though, after you have typed the name of an abstraction, how does this update the 'machine code' for the program you're building?

Human: Well, it's not usually just one name that has been typed, but there's a whole 'document'—just like we talked about for email, or academic papers. This document is then 'parsed,' which is a way of converting the document into a 'model': a form suitable for a running program to interact with—the program being a 'compiler' in this case. So, once the document is parsed—if it was well-formed—the compiler uses the resulting model as a basis for generating machine code.

Alien: I understand what you mean by 'parsing'—we have something similar, too. But this seems strange to me that you would involve something as complex as inferring semantics through syntax in order to update the model of your program. You mean to tell me that in order to change a single part of a program's model, you must use a document editor, find the part of the document that corresponds the part of the model you want to change, recall from memory all of the abstractions available, type out the replacement abstraction's name one character at a time, and re-parse the changed document!? Just to change one thing in the model!? You guys must be much better programmers than us after all; that would be far too difficult for us: we need to see which abstractions are valid to use at different times, and when we replace one, or add a new one—or anything like that—the program's model is updated directly, which lets our software give feedback on how to proceed.

Human (grinning and slicking hair back, then shrugging): well, it's not too hard: we've gotten really good at automating parsing, and our programming tools have document editors built in. But yeah... I guess we are pretty good!

(In case it's not obvious: the aliens were the better programmers.)

Flow and Grothendieck-like Problem Solving

noreply@blogger.com (Weston Beecroft) — Sun, 03 May 2015 23:15:00 +0000

Flow: a pleasant, efficient, focused state of mind.
Alexander Grothendieck: revered mathematician living between 1928 and 2014 who had an unusual approach to mathematics.

The idea that being in a state of flow is desirable for computer programming is now commonplace; good information on the nature of this mind-state and techniques for inducing it are more sparse. My idea here is that the meditative mind-state and flow are one and the same—which I suspect is uncontroversial. From there, however, I'd like to address a general problem in learning how to flow at will, which I think can be made more clear by analogy to a style of problem solving that Grothendieck was especially known for (not that it was unique to him by any means, but it seems to have been a sort of trademark because he took it to such extremes).

***************

After spending years dealing with a computer-related repetitive strain injury, I found that using computers was not the same even after I’d resolved the physical component of the problem. Eventually, in trying to discover the source of the problem that remained, I came across the notion of ‘flow,’ which instantly connected with certain common occurrences from my pre-injury programming days. Recent occurrences of this state were utterly absent; and, in fact, the more I thought about it, the more sense it made that my current problem in using computers could be clearly characterized as ‘anti-flow.’ If there’s some axis in the space of mental states where a large positive value indicates being in flow, my problem was that I had a large negative value on this axis (such an axis could sensibly be named ‘acceptance of things as they are’—which will make more sense by the end of the essay). So, my interest in flow began.

Reading more, it would’ve been difficult not to connect this concept to the ‘meditative mind-state’: a state in which all experience is accepted as okay, lacking in self-awareness, and characterized by direct interaction with the objects of experience. The opposite involves the heavy presence of meta-thought, analyzing what one is doing as one does it.

Reading more, I discovered this excessive meta-thinking is basically synonymous with anxiety. This makes intuitive sense: you meta-think about something you’re doing when you think there might be something wrong with it. And, being in a state of flow, characterized as behavior lacking meta-thought, has an intuitive reason for being more efficient: it’s like the difference between running a procedure encoded in software, executed on a general purpose chip—and having the procedure directly represented in hardware. In both cases you have this trade off of efficiency for mutability. Further, it makes sense that flow would be enjoyable and meta-thinking not: anxious experiences are unpleasant ‘by design’—they encourage the experiencer to change something, to get out of that mode; by contrast, the more you’re able to stay in a state that doesn’t require meta-thought, the better things must be going for you, and your mind rewards you.

So, in order to resolve my computer use issues, which I could now more usefully state as, “in order to move toward Flow on the ‘Acceptance Axis’” or “in order to reduce anxiety while using computers”—I could draw from methods in Western psychology, or Eastern philosophy. I have explored both and both have been useful. Ultimately, however, the literature surrounding Eastern meditation practice and, to a surprising extent, life perspective—was the most directly applicable. Isn't it strange, though, that 'life perspective' should concretely affect my ability to engage in some activity? I thought it was, and I spent a lot of time thinking about how that could work. Here's how I think of it now.

‘Life perspective’ is another way of referring to the conceptual framework in which one thinks, their total set of Schemas, the conceptual categories available for organizing experience and the rules relating those categories. Just to give an idea the kind of thing I’m talking about, I’ll give two ridiculously stripped down, simplified examples of personal conceptual frameworks.

(1)I am an autonomous entity with a fixed set of actions and senses. I exist in a universe made up of small objects that follow fixed rules. I am made up of these objects. After a certain duration I will cease to exist. While I exist I will experience some things that are good and some that are bad, and the proportion of good and bad experiences will depend in part on my actions.

(2)I am an eternal soul that can suffer or feel joy. Temporarily I exist in a ‘physical’ universe, and depending on the moral character of my decisions while here, I will suffer or feel joy eternally afterward.

One’s ‘life perspective,’ as a framework, provides a special kind of vocabulary—a set of terms to make statements 'in terms of.' What makes this kind of vocabulary special is that it provides terms that could be ordered based on how general or particular they are, where the more particular terms are arrived at by supplying parameters to the more general terms. For instance, if you say, “the most fundamental things in existence are ‘physical entities’,” then you have the general term ‘physical entity,’ and everything else in your framework must be expressible as some parameterization of that general term (e.g. "that is a physical entity with location X, Y, Z, smelling like W, with color R". So, the more general a term is, the more other terms are potentially impacted by it. This is the same as in any framework, and modifications to these very general terms are what we call 'fundamental' changes. In science, such changes are often called ‘revolutions’; they are how we change ‘paradigms’ (this is Thomas Kuhn’s popular terminology anyway), rather than elaborate the present one. These changes of very general framework terms are also what take place in significant software refactors; they are what determine whether you work with elegant structures, or whether you become an expert in the application of duct tape.

Personal ‘life perspectives’ are this same way. Incidentally, this is why some people are so interested in metaphysics: it’s a field explicitly addressing the most general structures of personal conceptual frameworks or ‘life perspectives.’ But what difference does it make if you personally have one framework or another? Consider the difference in behavior that results when someone really, truly believes that an afterlife with eternal suffering or pleasure exists and they’ll go to one or another based on their actions, or if someone were to believe that people are essentially robots with no real experience of pleasure or pain. Or, if someone were to believe that all of the universe, including all of humanity, was truly one indivisible whole, so that it becomes meaningless to say "this part of the universe is me, that part is not"; is selfish behavior possible if you deeply believe this? Is fear of death or any form of material loss? Those are extreme examples, with extreme consequences for adoption, but: people's beliefs, their conceptual frameworks (the true contents of which are actually quite hidden from us!), have a pervasive influence not only on how we behave, but on how we interpret our experience.

Let's switch to Grothendieck for a minute. I’ll quote from Pierre Cartier’s essay on him:

“Grothendieck’s favorite method was similar to Joshua’s for conquering Jericho. One must seize the place by sapping it; at a certain point, it succumbs without a fight. Grothendieck was convinced that if one had a sufficiently unifying vision of mathematics, if one could sufficiently penetrate its conceptual essence, then particular problems would be nothing but tests that no longer need to be solved for their own sake.” -Pierre Cartier, “A country known only by name” (http://inference-review.com/article/a-country-known-only-by-name)

This sounds like the same wisdom we hear about refactoring in software: you can change the framework so that the problems within it are easy, or you can work hard solving the problems in the framework. Here’s another quote on Grothendieck's approach:

“My friend Bob Thomason once told me that the reason Grothendieck succeeded so often where others had failed was that while everyone else was out to prove a theorem, Grothendieck was out to understand geometry. So when Grothendieck set out to attack the notoriously difficult Weil Conjectures, the goal wasn’t so much to solve the problems as to use them as a test for the philosophy that if you generalize sufficiently, all difficult problems become easy.” -Steven Landsberg, “The Generalist” (http://www.thebigquestions.com/2014/11/17/the-generalist/)

Okay, back to meditation for a minute.

If you try to meditate, you are immediately faced with a problem: “how do I go about intentionally doing something which requires that I do nothing?” If you try to get into a state of flow, you will run into the same problem: it’s characterized by effortlessness; you don’t monitor your actions and decide beforehand which to take next; it's often described as a cognitive mode where you act without taking actions (non-paradoxically: acting without consciously choosing your actions). In the terminology of Taoism, this is called ‘wu wei,’ or ‘non-action.’ To be in this state is a normal part of human experience; it 'just happens' under all sorts of circumstances. The intentional cultivation of wu wei, or flow, is important largely because circumstances often act to prevent it—and if your environment is particularly stressful, those circumstances may be ever-present.

Here's the problem in another form: if practice as a general human activity requires monitoring performance and making corrections, how do you practice the skill of non-monitoring, or intentionally avoiding meta-thought? My proposal is that all valid forms of solution use a Grothendieck-like method, restructuring one’s personal conceptual framework, so that there's nothing to do when it comes time to 'practice,' and yet, in time, you do improve. By contrast, normal practice consists in monitoring yourself as you take some action, then revising your way of taking the action and repeating; this is like proving individual theorems within some existing framework.

As an example of the framework revision approach: one of the first things one learns when studying Eastern frameworks is a formulation of ‘self’ that differs from the typical Western conception: we think of it as what’s often called the ‘ego’ or the ‘will’—that which decides; but if you think that your most essential identity is the part of you that makes decisions, how are you going to take actions without deciding to take them? Interestingly though, it seems that, most often, the ‘insights’ leading to fundamental personal conceptual revisions are derived from direct, personal experience. Regarding one's conception of self: if you consistently experience yourself doing things without consciously deciding to do them, while still feeling that it was yourself doing them, you are collecting data that implies the ‘ego’ or ‘will’ is too narrow a definition of 'self' and you're inductively led to a revision. So, in this way, meditation is a sort of strictly empirical metaphysics. I think the efficacy of the empirical approach is what makes it possible for Eastern philosophy to not philosophize, rather insisting on non-conceptual approaches.

When starting to learn to meditate, one inevitably imagines the process will be similar to other things they’ve learned before and they generate all sorts of images of what success would look and feel like; they imagine that they’ll one day be able to say, “now I’m going to meditate” and they’ll begin using this skill called ‘meditation’ that they’ve developed. My understanding is that, in actuality, you will have learned no skill whatsoever; you will have just changed your understanding of self and life so that you arrive at ‘nothing needs to be done’ (where 'be done' refers to intentional action) in more and more situations. Alternatively, it could be said that you more often find yourself in a state of mind where “it’s not necessary that I do anything, but it’s okay to do things if I like,” which is probably also a description of being in the mindset for ‘play.’

Why There's Nothing Rather Than Something

noreply@blogger.com (Weston Beecroft) — Mon, 10 Jun 2013 00:56:00 +0000

It seems like despair over the emptiness of existence is something like an occupational hazard for philosophers. Maybe it only seem this way because society especially pushes this image -- or it may be that it primarily affects amateur philosophers who know only enough to be dangerous. Whatever the case, we can at least say that some large number of people who make a habit of analyzing their relation to the universe end up dissatisfied with the results. Probably the only substantial error here is to waste the time analyzing something essentially irrelevant and unanalyzable; but since poorly directed analysis is an entrenched habit of mine, I have a cause to propose for this unfortunate conclusion.

We understand things by analogy, or in other words, "in terms of what we already know." When we attempt to understand the universe itself in terms of things more familiar, we expose the severe limitations of our capacity to understand, to an extent that's almost embarrassing. It's true we can do pretty well predicting some of its behaviors, if we radically isolate the attribute in question and delegate some of the processing to adjunct calculation machinery -- but to me this cannot be called understanding. Understanding is a more rich experience that occurs only with sufficiently complex subject matter which we're able to interact with from many angles.

We create specialized frameworks for anticipating some facet or another of the universe, and we can gain an understanding of several of these with time -- but the degree of their specialization prevents any holistic comprehension. Imagine you must try to understand humans without prior knowledge, but the only route available is to study endocrinology, followed by neurophysiology, followed by rheumatology, etc. When you complete these studies, you will have very good understanding of humans for many definitions of "understanding" -- but as a human, you will find the result dissatisfying, probably because we have divergent modes of understanding which work well only for their respectively appropriate subject matter.

When we ask questions like, "what is the nature of reality?" or "what is the essential character of the universe?" -- questions outside the domain of science -- and seek answers by improving our understanding through the scientific/analytical mode, we have chosen a route than can end only in dissatisfaction. What was confusing to me, though, was which domain these questions are in if not the scientific. What valid modes of understanding could possibly exist besides those grounded in observation and logic? It sounds like since I'm being asked to not use scientific understanding, that I should not observe the phenomena in question, and use some transformations other than logic to elaborate the dubious unobserved starting point of my speculations. This is overreacting.

Why do we ask the question, "what is the nature of reality?" ? One reason is that we are following a chain of causes to some root, because that's what we do. But I think another important and mostly overlooked reason is that it's something we have to co-exist with, and decisions about whether or not to live in the company of some thing are among the most important to humans. So, I propose that "what is the nature of reality?" is really a social question. We want to know whether we can trust the universe, whether he tells good jokes or is always getting into trouble, etc. Our brains are trying to figure out whether a relationship with the universe is the best decision for spreading our genes.

Clearly there's something funny about this question. It gets back to what I was saying about our embarrassingly limited capacity for understanding the universe: our brains try relating it to something already understood and the nearest match is a ways off.

And, when the depressed philosopher reaches the conclusion that reality is fake or empty, what is he getting at? To me, this sounds like a social imputation; that the universe promised to be one thing at some earlier point, but time bore out that it was all pretense. Of course the universe makes no promises, so that she is flaky cannot be a very meaningful claim -- but we did get the idea from somewhere.

When we are young, we just do things, and it's fun. When we get older, and develop our tendencies to abstraction, we want to name things -- especially if we're into creating functional symbolic systems that can compute predictions for us, if only we can find the right set of names for things. To be more precise, we come up with layers of definitions for things, and at the bottom of these definition strata, lie indefinables. Also, it's not always clear to us that these systems are separate from their referents; that a rock flying through the air and F=MA are two different things. So, when we were young, the universe was just mystery -- filled with potential; by the time we lay the groundwork for a more sophisticated comprehension of the universe, we find that it is a series of representations, resting on top of indefinables (i.e. something about which there is nothing whatsoever interesting to say), and no substance. Substance does not exist, only representation. The universe is a charlatan.

First off there is an error here in that it sounds like we've discovered some metaphysical property of the universe -- unfortunately an overly ambitious hope: instead the discovery is epistemological. We don't experience substance directly; our minds operate through representations. This seems to merely transfer the source of the problem, leaving its effects in place. The error here, however, is to think that this is a problem in the first place, that we understand anything about what it means to experience a reality through representation versus directly, or if such a notion is anything but nonsense. The problem is something like trying to imagine the edge of the universe or time travel. Our brains construct a model of the situation when we query them to, but we know better than to trust the model for much more than amusement.

Again, the solution probably is to admit defeat and go play outside.

Solving Wrist Pain by Writing an IDE

noreply@blogger.com (Weston Beecroft) — Fri, 01 Mar 2013 21:58:00 +0000

This originally appeared on the my project website for Tiled Text, which can be found here: http://westoncb.com/projects/tiledtext

Late in my 19th year I was writing the third iteration of my ongoing game engine project, when I felt the first typing induced twinge. Saw doctors, half-heartedly tried a number of remedies and some ergonomic upgrades, continued programming. Nothing phased it, the pain got worse. After a few months I decided I would have to stop programming, maybe for a year or so. That was okay: I needed to get caught up in mathematics if I was going to be very good with real-time graphics. Took time off, no improvement. Dropped out of school.

Years passed. I didn't understand compromise then and preferred the prospect of working in another field over being crippled in the one I loved; though I eventually finished a CS degree despite having no real hope of returning to software development. I became more academic in the interim. I thought a lot rather than just building things. I liked philosophy and science (and philosophy of science!) and suspected there was some mathematics out there that would be as good as software. After graduating, my project was to discover why people thought mathematics was beautiful; failing that, at least acquire some rudimentery facility with it. That went so so, made a lot of progress—but it wasn't coding. About a year in, though, while explaining to a friend why coding with the Microsoft Kinect wasn't a real solution (with existing IDE's), the kernal of the idea behind Tiled Text occurred to me.

And, like the warrior who has put killing behind him, I blew the dust off my keyboard and set to work: my wrists would hold out for a few months until I could build this thing.

The initial idea was an early form of the code generation concept (didn't understand what a formal grammar was well enough to see how it would relate; thought of making some kind of linguistic constraint description system—thankfully my dad put me off the path of re-inventing the wheel here), but it was augmented in the early days by a few epiphanies. Real, old-fashioned epiphanies: if I were religious I might have thought they were gifts. The first was on the cycling behavior—the other half of the core concept. The second gave the UI concrete form (was still thinking of building it on top of an existing text editor before this). The third mostly related to the architecture, and led to generalizing beyond just code editing.

Then there was work. And more work. I worked three days a week stocking groceries and four days a week on the project. I did this for about five months, with constant wrist pain. Then I got Type 1 diabetes. I had medical bills in addition to student loans and was barely scraping by. Then I worked for another 9 months or so, with progress slowing some.

I needed a change. I'd been thinking about moving to Boston for a while, inspired by Paul Graham's comments on it from "Cities and Ambition." And now, here I am, in Harvard Square, excited about whatever's next. I'd like to continue with Tiled Text and GIDE, but I realize that may not be possible. What I really want now is to get in an environment where I can learn from others. I've been working in relative isolation for most of the time I've been programming, but I know the only way for me to progress is working with experts. Of course that will involve typing/mousing, but: ironically, I have learned how to mitigate my wrist pain from mouse/keyboard while working on software to obviate my usage of those devices.

And, incidentally, when I would procrastinate work on Tiled Text, I would often go to math books. My studies at these times were very fruitfull and I think now that mathematics has a chance at contending with coding, and I have finally seen some glimpses of mathematical structures that should be called beautiful.

An Architecture for Deliberate Thought

noreply@blogger.com (Weston Beecroft) — Wed, 02 Jan 2013 01:44:00 +0000

Some time ago I realized that when I think very abstractly, what's going on in my mind is not for the most part natural language; instead it's more visual. Specifically, the visuals seem to be of a schematic nature, focused on indicating relationships between things. The ideas in this essay came out of my thinking about what sort of cognitive system underlying thought could allow one do it both in natural language and in something as diverse as the 'schematic thinking' I was doing. The more general system accounts for thinking in various domains; e.g. chess or algebra might be other domains you think in.

This is actually part of a larger piece I started on schematic thinking, intending to build up to something like a tutorial—but for now I just have this fragment which I think is kinda neat on its own.

(If you'd like to know more specifically what I mean by 'schematic thinking' check out the two excerpts I include at the end of this document. They are from Hadamard's "The Psychology of Invention in the Mathematical Field," but they are essentially descriptions of what I have in mind when I say 'schematic thinking'.)

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     Deliberate thought can take place in a number of different substrates, which I shall call "Domains," each of which corresponds to a domain in a more ordinary sense. The mental counterparts to Chess, algebra, social situations, physical situations, drawing, and playing the flute are all different Domains.

     When a Domain is active in the brain, some State is present. A State in Chess is the board layout at a single moment of a particular game; a State in algebra is an algebraic expression or equation; a State in a social situation is mostly made up by the estimated mental state, facial expressions, and bodily gestures of a group of people; a State in a physical situation is a group of objects relatively oriented under the constraints of one's understanding of physical law; a State in drawing is the contents of a piece of paper; a State in playing the flute is the configuration of the fingers of the player combined with an exhalation strength. When thinking in some Domain, words are not present (unless language is the active Domain -- but more on that later), only a chain of States from the Domain. Although, in practice, when playing Chess for instance, the Chess Domain will be your substrate for thinking only a fraction of the time: you may swap in a social situation Domain, or a language Domain, and then jump back to the Chess Domain with new ideas -- but at that point (probably an image of the board is the principle contents of consciousness), words disappear.

     Each of these Domains is defined by a set of assertions considered always true while the Domain is the active substrate; these state the elements of a Domain and limit the valid relationships between those elements. In chess the assertions would comprise the rules of the game and constraints on how a board/pieces may appear; in social situations they would correspond to an experience based collection of verities in human interaction: if I behave violently toward a person, they will return with violence -- etc; in drawing the assertions are that a mark will be left at the point of contact between pencil and paper, and a pencil may be moved while in or out of contact with paper. Each of the States mentioned before has a particular format which is a result of the assertions of the Domain; and so, it is useful to think of the assertions of the Domain as a sort of grammar for the Domain -- this will be returned to later. Now let's view the theory in the abstract.

     A Domain is a collection of assertions considered always true while that Domain is active, and a collection of valid States.

     A State within a Domain is a configuration of mental elements in some arrangement allowed by the assertions of a Domain.

     A Line is a sequence of States, corresponding to the notion of a "line of thought."

     Deliberate thought within a particular Domain consists primarily of finding a desirable Line. Between each State in a Line there is considered to be an operation which changed one State into the next; this collection of operations for a Line forms a set of actions to take in the external counterpart domain (e.g. actual game of chess).

     It is useful to consider a space of all of the possible States within a Domain, called a State-space: each point is a State; each axis of the space corresponds to an operation which may take place in the Domain (e.g. a valid move in chess, yelling in a social situation), resulting in another valid State in the space; any path through this space would be a Line.

     Consciousness, the work table of deliberate thought, holds a small list of States in view at any given time, with the most recently occurred being most prominent. These active States are the input to a recursive process for determining which State to add to the list next. Choosing a next State is identical to selecting an operation, i.e. selecting a direction to step in a State-space.

     Thought within a Domain is exploration of a State-space. The decision making about which direction to move in next is subconscious, and does not operate in the narrow confines of the Domain itself. Every Domain has two assertions which guide this decision making process: the first is that contradictions may not occur, and the second is that composite mental constructs with similar internal relationships are interchangeable to some degree. The first assertion allows the mind to use logic, and the second enables analogy.

     The Domains considered so far are of a primitive type, which presumably showed up in brains so that animals could carry out simulations within particular domains in order to estimate an optimal decision in that domain. These primitive types all seem to have a clear notion of what an operation within the domain is: moving a chess piece, adding to both sides of an equation, grinning, etc., which results in a successor State to the current one. When we consider a language as a Domain, where its assertions are the grammar and lexicon for the language (e.g. "each sentence must contain a verb," "'triumphant' is in the lexicon"), we find that it has the same basic role in the mind as the others: subconscious processes serve up successive States (sentences in the case of language) to consciousness, and the States in consciousness have an important role in determining which States will follow -- but, when we look at two successor states, no operation which transformed the first into the second is apparent with language. Now, in any Domain, the process which selects the operation is always complex and hidden, but in the primitive domains, given a State and a successor for it, we are at least able to identify the operation, once selected; not so with language.

     It is a hypothesis of this theory that language is a later evolutionary development which generalized the more primitive Domain "simulation" machinery. But with language, there is no counterpart domain external to the thinker, instead language seems to be a meta-Domain, for thinking about other Domains. Its generality also allows it to translate between Domains. (Perhaps analogy didn't appear as a method for navigating State-spaces until language showed up.)

     Before, I said that the assertions of a Domain define a format which the States of the Domain must be in, and that this was good reason for considering the assertions to form a grammar for the Domain -- hopefully this is more clear now that we have a Domain where the assertions are a grammar and lexicon, so that the definition of grammar undertakes only a slight expansion. But viewing them as a grammar is not just an amusing conceit, it gives an idea about how the brain is able to derive meaning from States. In linguistics and computer science, systems exist which can take expressions conforming to a given grammar and analyze them into atomic units which each have a pre-defined role; this is called parsing and is the first step to incorporating semantics in a linguistic machine. Since States in a Domain have a consistent grammar, States can be parsed and each of their elements assigned some role in the context of a semantics for a particular Domain. In this form, a subconscious process could take the labeled elements and determine a value for a State, so that some States can be considered good and others bad, and we have a system in place for preferring certain Lines over others. It is probable that the value determination of a State manifests emotionally.

     In this theory then, the complex system of meanings that we experience when thinking in language is an outgrowth of the semantic systems of the more primitive Domain simulators. It is possible that the correct way of viewing a language's State-space is as an infinite-dimensional space: since it is a meta-Domain rather than a proper Domain, and must be able to talk about all other Domains, it doesn't have a finite set of operations for transforming its States -- instead, it has the general notion of operation itself, which includes all operations. Or it may be that there isn't enough structure between its States to usefully view a State-space for it; perhaps its lack of operations is a testament to its freeness -- it can jump between any States that logic or analogy suggest, guided by semantic-emotional responses to candidate Lines.
----------------------------------------
Excerpts from "The Psychology of Invention in the Mathematical Field":
"Indeed, every mathematical research compels me to build such a schema, which is always and must be of a vague character, so as not to be deceptive. I shall give a less elementary example from my first researches (my thesis). I had to consider a sum of an infinite number of terms, intending to valuate its order of magnitude. In that case, there is a group of terms which chances to be predominant, all others having a negligible influence. Now, when I think of that question, I see not the formula itself, but the place it would take if written: a kind of ribbon, which is thicker or darker at the place corresponding to the possibly important terms; or (at other moments), I see something like a formula, but by no means a legible one, as I should see it (being strongly long-sighted) if I had no eye-glasses on, which letters seeming rather more apparent (though still not legible) at the place which is supposed to be the important one."

"About the mathematicians born or resident in America, whom I asked, phenomena are mostly analogous to those which I have noticed in my own case. Practically all of them -- contrary to what occasional inquiries had suggested to Galton as to the man on the street -- avoid not only the use of mental words, but also, just as I do, the mental use of algebraic or any other precise signs; also as in my case, they use vague images."

Interpretation of David Foster Wallace's "Mister Squishy"

noreply@blogger.com (Weston Beecroft) — Wed, 19 Dec 2012 00:27:00 +0000

After reading the story "Mister Squishy" by David Foster Wallace and really liking the design of it, I found myself uncertain whether certain aspects were actually there or just something I read into it. So, I looked around online for interpretations of the story, especially one given by Wallace, but I couldn't find anything too useful—and I felt that many popular summaries were doing the story a disservice by describing its marketing language as 'noise' or 'random,' since it appeared as a stream of coherent concepts in my reading. So, here's my interpretation.

The story is about the deception, manipulation, and unwavering self-interest that underlies the operation of modern corporations, particularly those whose success is highly dependent on the public's perception of the company and its products. The story is set in a downtown skyscraper, and the structure of the story matches this setting, its layers being displayed one at a time in an upward journey that reveals the figures of each lower level to have been duped by someone above.
At the start of the story we are shown a focus group in progress, and are introduced to its coordinator, Schmidt. Then we are shifted up a level for the first time: it is revealed that the company isn't interested in the immediate results of the focus group, but is instead using it as a component in a larger experiment involving a parallel focus group being conducted with a slight difference. In particular, the group which we are shown is given information on the the processes behind the development of the product (a chocolate snack-cake), particularly the concepts behind its marketing; the other group will not be given this information. The aspect monitored for variation between the two groups is a measure of difference between individual surveys of members within the group, and a single group survey which each group will fill out together; in other words, deviation between their private and public responses to the product—though "public response" is probably too much of a simplification: the story treats groups of people as isolable, abstract organisms, the organisms studied by statistical methods; so really, the group evaluation contains the responses of this group organism.
Now it seems that the purpose of the focus group, rather than gathering information about consumer response to the snack-cake, is to improve the design of future focus groups. Schmidt, however, informs the reader through glimpses we are given to his thoughts during the session, that the focus groups have no material impact: rather than using the collected data to make inferences about consumer preferences, it is desirable to end with a nebulous analysis which could conclude one outcome or another based on which direction the client company is already planning on moving in: the focus groups can only confirm a decision which has already been made: a deviation on this will result in the termination of the marketing firm. And so, the focus group facilitator, Schmidt, presumes that the real purpose of this inter-focus group experiment is to generate multiple conclusions so that a desirable data set may be selected at a later date.
Then we ascend another level. We are introduced to the perspective of a member higher up in the marketing firm—Awad, and a peer of Schmidt's who has the favor of Awad: Mounce. Awad shares with Mounce that the true purpose behind the inter-focus group study is to explore a class of marketing strategy where a depiction of the inner workings of the company is the subject of advertising material. So, Schmidt, without knowing it, is effectively delivering to the focus group a primitive form of this behind-the-product advertising, and his peer Lilley gives a similar presentation absent the behind-the-product information to another group.
Then we ascend another level. We are introduced to the perspective of a member higher up in the marketing firm than Awad: Britton. Britton also has a mentee, who he discusses strategy with while smoking cigars: Laleman. Britton and Lalemen have a sub-surface power struggle between them, Lalemen thinking he is on an approach to surreptitiously overtaking Britton, while Britton is fully aware of Lalemen's machinations. Still, they discuss the future of demographic analysis which they anticipate will be carried out by monitoring websites rather than running focus groups. The only problem is all of the presently employed focus group coordinators. Here is shown the penultimate deception of the plot: the inter-group experiment is actually a device that will be used to demonstrate to the coordinators their own inimical influence on the focus groups, using a statistical argument which the coordinators, themselves statisticians, will be forced to accept, followed by their resignation—or, if they are so unreasonable as to protest, as evidence against any case they may form in a lawsuit regarding their termination. The argument which Britton is devising centers on the fact that humans are random components interfering with the demographic analysis process, and in order to concretely represent this fact the focus group will have a "stressor" appear who pushes the coordinator to behaving erratically.
There is another character, nearly silent, who plays an important part in my interpretation of the story as a whole: a participant in Schmidt's group, who is referred to as "I" in the story's narration, so that we must identify this character with the narrator of the story; however, the narration is omniscient, switching between the thoughts of many people in the course of the story; so, I conclude that this character is different from the others—he is a meta character who is a character in the story, but also represents the story itself. This "I" is covered in sensors, has been given a script which he must stick closely to, and wears an "emetic prosthesis," that can be used to simulate vomiting. He is the stressor which Britton has inserted in order to effect his strategy of giving the coordinators "enough rope."
It is important to note also that this strategy of introducing a stressor and observing the results is demonstrated several times in the story (most vividly when Britton has Awad make unwanted sexual advances toward Lilley, just to observe her character), and becomes a symbol for the concept of applying scientific methods in a callous fashion.
Similarly, by various approaches the concept of the consumer's awareness of marketing activity is presented, the conclusion generally being that at best the consumer has a superficial sort of awareness which the marketing agencies have already easily accounted for.
Two other facts have evolved in parallel with the story's principle structure outlined above: Schmidt is a deeply dissatisfied person (probably) interchangeable with the typical white collar worker, and Schmidt has been developing (and implementing?) a scheme for injecting a lethal poison into the snack-cakes.

So, we are introduced to an experiment where one group of people is given the (appearance of the) marketing strategy behind a product, and a control group is not; in this experiment is a character present who will stress the group so that some outcome may be observed (using his emetic prosthesis)—and this character represents the story itself; and, the reading of the story represents a sort of experiment analogous to the inter-focus group experiment: we have just been given a generalized version of the story-behind-the-product—we have been told the story behind products. Thus another layer of deception has been revealed: the real purpose behind the experiment was to inform readers of the more complex and insidious reality behind product marketing—but, this character, who is the story, also played the role of a stimulus used to provoke a reaction which could be scientifically observed, so the story must play that role also, and the author wins the pinnacle seat on the tower of deception, and proves himself the master of calculating manipulation.
And there's another question left fairly uncertain: did Britton know about Schmidt's development of the poison or not? If so, then the emetic prostheses is supposed to trick Schmidt into thinking that one of the members of his group is vomiting in reaction to a poisoned snack-cake. If not, then the final scene where Laleman notes a chocolate cake stain on Britton's finger, laughing internally in reply, would seem to indicate that Laleman was exulting in consideration of Britton's demise. But, we are informed in the story that the chosen poison would take 24-36 hours to take effect, so I'm inclined to go with the latter interpretation, which seems to imply that the cog-like victims of the marketing machine eventually get their revenge.
There's also a guy scaling the wall of the building and drawing a crowd that speculates on his activities throughout the story, who in the end, while carrying a gun or gun replica, inflates his costume which bears the image of "Mister Squishy" (the logo for the snack cake company). I see this scenario as representing the reality of the interaction of marketing firms with consumers: the marketers put on a carefully designed show and the consumers are drawn to it inexorably, their awareness of their situation never reaching more than superficial levels, though many take satisfaction in their delusions of knowledge.

I Who?

noreply@blogger.com (Weston Beecroft) — Thu, 26 Apr 2012 10:22:00 +0000

An excess of thought circulating in a young mind trammeled by habit and hopelessness drove the first of two unusually precise friends to complain, "I'm bored, Ramij. I'm tired of thinking about all the things I usually think about. I feel like all of the philosophical questions I've had have already been answered by derivations off of the universe being governed by rules..."

Ramij sat opposite his friend at a weathered and graffitied park table; he'd been silent for some time, contemplating, but the interruption was welcome at this point.
"Well Illya, if you're up for it, I think there's a question of self-identity that's important to consider, though people generally neglect it, thinking it's either too obvious or too impossible. Specifically, I think it's important to go beyond looking at self-identity in the in the sense that we use the word 'I' to refer too; its usefulness seems to be primarily in distinguishing one person from another, which is of course a very practical thing to be able to to do, but what I'm more interested in, once we've isolated an individual, is figuring out what is that individual. In other words, how does the individual relate to the rest of existence?"

Illya nodded his assent, despite being a little disconcerted by his friend's barrage.

Ramij continued, "Probably we'll make the best progress if we can nail down a little more precisely what an individual is first—what 'I' refers to in the way it's commonly used. Ideas?"

Illya began to apprehend what he'd gotten himself into; he roused himself from his lazy boredom, sat up a little straighter, and managed to articulate, "Well, I'd say it's the atoms making up a person's body... Although... I'm tempted to go a step further and say most of the body is irrelevant and that when we speak of 'I,' it's primarily in reference to our preferences and decisions, which seem to belong to the mind particularly. So maybe 'I's and brains are one and the same."

Ramij knew fully well from the outset that they'd have to trudge through these preliminaries; he responded with patience, "I agree for the most part, but there's a tricky question of awareness that I think this misses—"

"—Consciousness?"

"Possibly, depending on exactly what's meant by consciousness. Ninety nine percent of what's usually meant by it is pretty mundane, and brains are obviously responsible for it: it's a part of the brain that's aware of—or, processes data from—the rest of the brain, the rest of the brain being aware of data received externally from sensory input, as well as what it has stored internally. The only quasi-mysterious aspect of it is self-awareness, which seems to come from the fact that the computations occurring in consciousness—which are about the rest of the brain—are fed back into the rest of the brain, so that some of the rest of the brain's computations end up being about itself. In either case, it's a sort of awareness that seems entirely possible in mechanical systems, and which I think is insufficient for defining 'I's.
"I think a definition of 'I' must include the aspect of brains which causes them to feel the data they process; which gives red or cold data the particular feeling of redness or coldness—though this must not be mistaken with the sensory input itself: I mean the mind's experience of processing those symbols. I think 'I,' as it's generally understood, refers to this sort of awareness... in conjunction with the operation of mundane consciousness and of the rest of the brain..."
But Ramij had a habit of thinking as he spoke, and a potential shortcoming in his statement occurred to him, "—Err, I guess this could just be a property of the functioning of brains then—something everywhere-intrinsic in their operation rather than something adjoined; though I still don't see how to account for it materially and I suppose we won't get anywhere if this definition we seek ends up using elements from some hypothetical extra-reality..."

For Illya the park then dropped out of consciousness. The thoughts that had ground circularly round too worn neural haunts appeared to slip outside the trammel. Tentatively, something new was happening.
"Hold on a sec—you've given me an idea. If we define 'I' to be simply the sum of all the matter composing a particular person's brain, then I think we would both agree that 'I' in the common sense will have been accounted for, absent this final awareness that you speak of. You said that maybe this awareness is just a property of brains—what if it's instead a property of matter generally, which just becomes interesting when matter forms arrangements with certain kinds of complexities, like human brains. In other words, maybe this final awareness is just how it is for the matter comprising a mind to process the data that flows through it; or rather, for that matter to exist in time⁽¹⁾.
"Then again, it's unfortunate—"

With quick perception Ramij saw the implications in full.
"—Oh! That's good!"
He Hardly paused before moving on to applications.
"Actually, seeing all of mind reasonably accounted for by ordinary matter, you've just given me a more satisfactory solution to the 'would I be my mind-duplicate' question than I've had before. If we take your definition of 'I' as all of the matter comprising a particular brain at a single instant of time and expand it to instead be the world line of that definition—"

"—wait, wait—world line?"

"I figured you'd know that one! A world line is an object in space and time, rather than just space. So, take a ball, say it pops into existence in 1952 and pops back out in 2005 and it stays in one place in space this whole time; its world line is a sort of cylinder with spherical ends extending from 1952 to 2005 along the time axis. Well, close enough anyway—that's a three dimensional approximate visualization of a four dimensional object. If you take a two dimensional object, say a circle, and extend it through time, then you actually get a cylinder.
"Anyway, with the world line definition of an 'I,' whose implications I think form a complete correspondence with our common understanding of the notion, it becomes very clear that duplicating a mind would create a new world line, hence a new 'I.' Awesome."

For Illya however, the discovery was not made without misgivings; it may have been, technically, a new region for his thoughts to roam, but the new land appeared as barren as the last.
"I'm glad you can feel good about it; I think its a depressing confirmation of the idea that the self is insignificant; it's just a matter aggregate with enough similarity through time for human abstraction to call it the same object now and ten years from now. It's unfortunate to have a material account of experience—if all it is is some configuration of matter 'being,' I'm tempted to say that experience doesn't exist after all; if data in the brain essentially dies after being consumed by consciousness, I don't think it ever does anything useful at all. I have a kind of longing for there to be something there that actually experiences—whatever that means; and I know that's useless: nothing material will satisfy me, and I'll never be convinced of the non-material..."
Illya's head drooped slightly; his boredom was forgotten.

Ramij could empathize with Illya, but the new notion had struck him from another angle. He shrugged, "I feel differently about it—I think we've arrived at a good definition for 'I' in the way that it's traditionally used, but I think the more interesting question, which we originally set out to answer, is a little different; that was the question of identity in the deepest sense, really of how an 'I' relates to the rest of existence. This greater question we can form as 'what is self?' for convenience. I became curious about self after noticing that I'd been answering the question with 'self is "I",' which of course isn't really answering it at all. So yes, I agree with you that the 'I' is far less significant than it's been considered in the past, but the question of self still has potential.
"We see the 'I' as less significant because it's material; it doesn't differ in any essential way from any other object in the universe⁽²⁾. This makes the 'I' a much more arbitrary construct than it's traditionally been held to be; it doesn't make as much sense for our existential identity to be so strictly bound to it. If experience is just what it's like for matter to exist in time, then the essence of our selves is just being matter, not being the matter that our bodies comprise, but just generally being matter. That being the case, and since the universe is the only source of matter and nothing but matter, I feel a deeper identity with the universe as a whole rather than with just my body. "Matter" of course is slightly inaccurate, but by it I just mean "fundamental universe parts." Follow?
Illya considered, then gave a minor nod, not indicating his comprehension so much as his desire for Ramij to continue.
Ramij considered: his words were accurate, but their import significantly compressed; a new approach was required. A demonstration.
"There's a way of visualizing the universe that will help to make the notion more concrete. In actuality the universe has some extents in time and spatially, and perhaps along other unknown dimensions as well, and these extents may or may not be infinite. In order to hold some concept of the universe in my mind, I strip it down—it becomes finite in all of its extents, it now has two spatial axes and one time axis which behaves exactly as the spatial axes—the whole universe, throughout time mind you, then becomes one massive, luminous glass cube with the most intricate conceivable patterns filling it. Since we started with two spatial axes only, from outside the cube we see all the objects within as their three dimensional world lines⁽³⁾.
"Now lets say this cube is actually glass—the material doesn't really matter, just that it's homogeneous, as the actually universe is in the sense that it's matter everywhere, or even better, rules everywhere—we can peer into it and see the full life of some two-dimensional being before us, one branch of a massively networked glass sculpture. When I contemplate the life of this being and ask myself what it is essentially, the only answer that comes to me is, 'part of the sculpture.' The only way that it differs from any other part of the sculpture is that it is in the space that it occupies—and its boundaries are extremely arbitrary: its only a consequence of my own mind's pattern forming routines that it can be called a separate object in any sense at all. Since the only boundaries between parts of the sculpture have a subjective origin, objectively there is just a single whole.
"When I add back on to this glass sculpture each of the pieces I originally stripped out, making it matter again rather than just glass, giving it infinite extent and all of the dimensions it deserves, but pausing after each facet I rejoin to ask whether my conclusions about the object and its parts have changed, I must answer 'no,' even when the universe is whole again. And for that reason I think the universe is the most sensical source of identity for anyone in it. 'I's have no objective significance; your mind is how it feels to be the universe in one particular area, the same way that the sensations from a patch of skin on your arm are how it feels to be you in one particular area."
Content that he'd made his case, Ramij leaned back, placing his hands with interlocked fingers behind his head.
"The only question remaining then is whether it's any better to be the universe rather than some person in it. My answer to this is that although the glass cube approximation is a miraculously wondrous thing in itself, the true universe is still incomprehensibly grander. I think I would not have felt this way in the past, but the more I learn about the universe the more incredible I find it; and it doesn't hurt that it's probably infinite and eternal. I think even man's earlier overblown conceptions of the 'I' are meager next to this self I see."

Illya had listened closely, and caught the spark of something in the proposition, but held on to reservation. His suspicion that reality was a disappointment still lurked nearby, hardly budged; but the prospect of a potential fatal flaw within it inspired a little cheer.
"We'll see."

(1)
Unfortunately, now that I am done writing this, I realize that I'm actually uncertain on the existence of qualia (the stuff making up "final awareness," the way it "feels" to process the symbol "red")—I've got doubts. And I've expressed the doubt before: "A complex self-monitoring system would have the illusion of a meaningful interpretation of its own data." Fortunately the main thesis is untouched if they turn out not to exist (it'd be quite a lot stronger in fact). The material account of qualia I gave was only to give a fully material specification of mind; if the mind does not include qualia then its specification was already completed before broaching the subject. Ramij gets excited when qualia are accounted for because it troubled him before as a potentially non-material aspect of mind, but his important insight about self is due only to the fact that the mind had been fully materially accounted for; if Qualia is stripped out as part of the description, as may be appropriate, the mind remains material and the argument stands.

(2)
I see the most basic constituent of the universe as being the actual laws that govern it. My understanding of the modern view of fundamental particles, in physics, is that "particle" is really just a convenient way of referring to something which in fact doesn't represent a physical object at all, but is something closer to a consistent behavior. Now I say the universe is homogeneous because its laws appear uniform throughout. And even if there were more variation in its fundamental behavior than I've described, it's still just a bunch of rules being carried out; I don't think someone would find the essential character of the universe as one thing under A, B, C and another under D, E, F. The only thing which could make the character of these rules different, that I can conceive of, is if they were embedded in some kind of infinite nesting doll of meta realities—which is absolutely impossible to determine. So if nothing else, our universe is a homogeneous locus of rule application. (Later edit: interesting seeing this serious and detrimental error in thought here: the idea that the universe IS rules; clearly mistaking a system of description with the thing being described, mistaking the "finger pointing for the moon itself" as it's sometimes said.)

(3)
I think some would object to viewing the universe in this crystallized form even in principle due to a supposed lack of determinism in reality, the idea that what will happen next isn't actually determined until the current instant occurs. Perhaps that's the case—but I think we lack a reason for thinking it is. The idea of this non-determinism comes from quantum physics, which is non-deterministic; but quantum physics is not a direct description of physical reality, but a modeling of our knowledge of physical reality instead. So, just because this system we've invented for making approximate determinations of certain physical quantities (granted, with great precision) isn't deterministic, it should not be taken as an indication that the system it approximates is itself non-deterministic. The non-determinism in physics comes directly from the fact that its statements are in terms of probabilities, which are a result of speaking of our knowledge rather than the system itself—this should have no bearing on the qualities of the system itself.

A Sinister Morning

noreply@blogger.com (Weston Beecroft) — Mon, 19 Apr 2010 03:35:00 +0000

At 4am, just before bed, I entered a morning perhaps sinister, though not gloomy, perhaps menacing, though not sad. After a day of relative ease, I decided to end with a cigarette and mug of Brazilian evening tea. Unexpected, however, was the fog laden morning I soon found before me. The streetlights glowed yellow and the trees, though expectant of Spring, knew leaves not yet; instead their branches jutted bare like broken swords, unfriendly and austere. But the morning was undecided, and knew not whether to emerge evil or amicable. In partnership with the darker elements it did proffer, were the morning birds and their sweet chirp. At first sparse, their sounds left me only wanting more; and as my desire fulfilled, the morning and I grew more in accord. At last its visage showed nothing worse than mystery, not any hidden threat; and as I dragged the cigarette I rolled, then expelled my contribution to the early fog, a sense of wonder grew within me. My thoughts roamed to ancient man in my position, amid the fog but less knowing. Would it be fearful to him? Without modern images, what is a densely fogged night? Is it the mantle of some goddess, or the oily smoke of war? I knew not. My cigarette was done now, ready for tea was I; and happy to find its temperature somewhat slaked by chilling mist, which now surrounded on all sides, my first warming gulp took I. Before me I spotted wet accumulations, water gathered just to fall, too weak to bear its weight; and across the way, objects earlier plain to see had been pulled with greed into the mist. This revealed something new. Perhaps the fog was not so friendly; it would not maul or bite at once, but one should not recline in ease amidst it. And the birds -- their chirping was now everywhere -- but was it calling in the sun? or were the creatures not themselves? Things trembled in the grass unseen. The birds, it's possible, were diseased. Their hearts had blackened, and together they conspired. This morning, after all, was cruel and hungry, and the birds its siren call.

Some Thoughts on a Potentially Immaterial Piece of Mind

noreply@blogger.com (Weston Beecroft) — Sat, 13 Mar 2010 06:59:00 +0000

      As a consequence of the apparant mechanical nature of the human mind, consciousness and its adjunct mental processes must work by the manipulation and storage of patterns. The use and effects of patterns in this manner are not unfamiliar to scientists and engineers; they've been building pattern manipulators for many years (e.g. computers). And during this time, it has always been plain that the nature of the machine's operation resides in the patterns themselves, rather than in the material used to represent them. Indeed, there were certainly theories of pattern manipulators before a material to build them with was selected; and the choice of materials has changed over the years to meet our requirements for efficiency, and it continues to change.
      This suggests that a scheme for replicating our minds in different materials is possible -- and there has been much writing related to this idea during the past two decades (perhaps especially due to Ray Kurzweil). We know that our minds function as they do because of their ability to store and modify patterns; how could this ability be altered by changing the underlying mechanism from neurons to transistors? Well, it seems that it might be made more efficient and durable; aside from that, it shouldn't make one bit of difference.
       Subsequent to my learning of them, and prior to my thinking which produced this essay, I had yet to doubt the possibility of a transfer of this sort; its plausibility seemed necessary. I still do believe them to be possible even, but with a certain important limitation now. I believe minds can be transferred, but I also believe something could be lost.
      Imagine a variation on the substrate transfer theme: imagine sitting isolated within a small cube with plain blue walls and even lighting, awaiting your complete duplication: bones, blood, viscera, memories, habits, fears, moods, moles, scars, chromosomes, bacteria -- everything -- copied from yourself to an identical form, with consummate fidelity, two meters left in a cerulean womb a lot like your cube.
      Would the creation of this duplicate have any effect on you? Would that part of you that's consistent throughout your life, which is often termed 'self' or 'soul' indiscriminately, be multiplied? If you were killed off at this point, would 'you' persist in the next blue cube over? You may not, though this is essentially what is suggested as possible in mind transfers. Something could be lost. Maybe we can make new, even enhanced, consciousnesses -- but we can't transfer ourselves without risk of losing something.
      This seems to suggest that some part of our being may be non-material. Consciousness, i.e. self-awareness, emotion, creativity -- none of these are difficult to conceive of as having a material basis; perception at the final level, however, that's difficult. Perception at this level is useless in our materiel existence, it serves no purpose. Every last detail of human, or animal, functioning makes sense without it; and if it were taken away, no one would ever know the difference. Even now, we don't know whether it's there or not; but it feels like it is, and the chance of losing it is a very high stake.
      The conundrum of the final observer arises from the following: our minds are pattern manipulators whose state at any given time is the product of internal self-modifying processes and external sensory input. It's likely that a self-monitoring system, which we call consciousness, sits atop the remaining unconscious mental hardware for the purpose of monitoring an enormous array of variables representing select aspects of the unconscious mind. The values of these variables are interpreted by consciousness and responses are fed back into the unconscious. The unconscious mind is tied into the nervous system which exerts influence on the 'physical' body (it is, of course, all physical); and through the interaction of the physical body with the environment, data is sent back to the nervous system, back to the unconscious mental components, and back to consciousness. It's an endless interactive cycle resembling: environment, body, mind, consciousness, mind, body, environment. At the level of consciousness, the pinnacle of the cycle, all of the data for the rich experiences we have do exist; the problem is, there's nothing to interpret the data at this level; indeed, you face the problem of an infinite regress and must introduce the non-material in order to have meaning.
      Data is meaningless without something to interpret it. This is made clear in computing systems: meaningless binary sequences are stored in memory and are given meaning when an interpretation for them is provided. An example: 0101 is stored in memory. A piece of software can treat this as whatever it chooses: if we want it to represent a numeric value, then it would be a decimal 5; if we want it to map to a standard set of alphanumeric characters which start with "A" at zero, then it could be the letter "F"; or if we want it to represent a simple image, then it could be a four pixel image with alternating white and black pixels.
      However, the computer has still not provided anything intrinsically meaningful: it has provided an interpretation that truly does affect the physical world, but another level of interpretation is required for the data to become more to us than an arbitrary arrangement of atoms. Take the case of the bit string interpreted as an on-screen image: when your eyes catch the photons from the screen, your mind has to organize the signals from your photon receptors into something meaningful to itself. Of course it does do this, and then consciousness picks up on it, reacts, and feeds the interpretation back to other parts of mind -- and at this point we're satisfied with calling the interaction meaningful. But that is all that we can tell happens; the mind just keeps reading data, modifying itself, and feeding data elsewhere.
      So, does the final, meaningful interpretation happen at all? The question has well disguised depths; it provokes facile and specious responses; and the glowing, recondite heart of it is that we would react as if it did in spite of the truth. A complex self-monitoring system would have the illusion of a meaningful interpretation of its own data. And, were it to exist, anything fulfilling the role of the self, soul, final interpreter/observer, or whatever you'd like to call it, would necessarily reside someplace beyond material existence, leaving it forever beyond our definite discovery.
      Maybe then there is nothing we stand to lose. Certainly we have no reason to assume there is, and it is very unclear what it could be. Still, the above duplication scenario evokes some discomfort in myself, and reminds me that there is potentially a non-material part of mind.
      Progress the scenario to a few seconds after the duplication. One of the staff of the experiment approach the cube containing the clone, open it, and issue a first question to its occupant: "How do you feel?"
      "Well I feel fine, of course; have you spoken to the clone yet?"

Cereal thoughts

noreply@blogger.com (Weston Beecroft) — Mon, 01 Mar 2010 11:35:00 +0000

I had an idea to write some sentences while eating cereal lately. However, they would sense less make. Variety in means and increasing dosages, also. Still, tangent. And syntax violates, diction misinformed, tenses having obtrude. Which, were it as, defines -- no, contradicts, thence; but continue. And, so, tyrannied, nonplussery, sequence. Garble-goble.gourmet;sprocketedrelief. CoN;we,ro.ir"P).####****____

Beer-Pong through College-Colored Glasses

noreply@blogger.com (Weston Beecroft) — Wed, 24 Dec 2008 00:38:00 +0000

     It is the noblest tradition among those entering the latter years of education to undertake a pilgrimage in quest of knowledge divine and extracurricular. These pilgrimages are said to be fraught with peril, and often end in shame; but to those sturdy enough to complete the journey to frat house, their neighbor's up the street, or perhaps even their own living room, questions may be asked of sage Players older and wiser than themselves: "What is Beer-Pong? Whence does it come? By what codes and precepts do its participants abide? Can I just sit out this first round and watch?" And if the proselyte presents himself with obsequious, trembling humility, answers may be given.
     "Beer-pong is the Eternal Game; the game of our roommates and of their roommates before them; the passage from innocence and youth into manhood; and the substance of life. Its origin is unknown, lost to the chaotic drunk that its own creation birthed. It's rules are lewd, numerous, and relative. And you have no choice but to sit out and watch the first round; you aren't even on the list."
     As the initiate takes his place as spectator, waiting the interminable duration to his virgin game, he will see and hear many things unknown to him. He is as a nestling watching its mother fly for its first time. He observes acts that are unexplainable and imagines sensations beyond his experience, all with the growing excitement that he, too, will soon become part of this fantastic alien world. He sees giants of unmatched proportions bearing the weight of monstrous distended bellies, flinging, with the utmost delicacy, opal spiraling spheres. He sees steezy sunglassed playboys swaying like the leafy branches of spring, stumbling and recovering, casting and scoring. The mystery of how one so intoxicated could act with such precision will stay with him, and in shroud, for the next half hour or so. He listens to the powerful intellects in the crowd shout recommendations for re-racks, respectfully deliberate over progressive legislation, and muse over the more philosophic aspects of The Game. Should the cups be arranged with consideration given to horizontal and vertical alignments, or does valency reign supreme? Without a spokesman for the household present, what rules should be established as defaults for in-cup ball retrieval? Does the purity of one's water cup truly reflect the compassion of one's soul?
     The powerful impression of myriad new sites and ideas weigh heavily on the initiate, and he is encouraged to drink of Economy's golden nectar. First he makes libations to the owner of the house and parsimonious supplier of beer; the remainder is drank personally and induces him to frown the Frown of Economy's Golden Nectar. His cheeks flush, and his cup is found wanting.
     Finally his turn is called and he may take his place at the stately game table; the table which is gilt with hardened Venetian leather, heavily embroidered with gold; whose surface is responsive, glistening, and redolent of countless prior games. There is an inscription in the center inlaid in a glowing argent fire:

          Though Beer-Pong be a game
          Beer-Pong be that what shall remain

     The initiate's partner brushes against him with damp and fashionable raiment, entreating him to play with the dignity of a warrior and to not, "fuck up." Unbeknown to him, his opponents are the peerless "Clarence" whose birth was the accident of the passion of a 14 game winning streak consummated in 1985, and the redoubtable "Floyd, bulwark of The South" who himself is now in the midst of a 14 game winning streak. The outcome is set; his fate is sealed with the promise of much more to drink.
     Though his first game has been lost, the initiate is not dismayed; he knows something of Beer-Pong now and sees that it is like life with its changing seasons, victories and losses, joys and sorrows. Whichever way the evening goes, the initiate has taken his first steps to becoming a man, he has tasted of the best life has to offer, and he will surely suffer a formidable hangover come morning. His story is the story of all men throughout the ages who have ascended to the exalted peaks of human knowledge, and who from this eminent platform have truly progressed the vanguard of human experience. His story is eternal and yet timeless; it is the story we all live and learn from. His story, is the story of Beer-Pong.

Mechanistic Beauty Via Conversation

noreply@blogger.com (Weston Beecroft) — Tue, 23 Dec 2008 08:30:00 +0000

[Wherein two eccentric old friends drink whiskey and talk about serious matters under the stars.]

Cannon: "By Jove's sable brow! Didst thou just drink all thy whiskey?"

*Cadwalader's face is contorted in a manner that suggests "yes", but he is unable to reply. Moments later, he sets his countenance straight and clears his throat.*

Cadwalader: "Yes. Unfortunately I had no choice: I know of nothing better to combat those vile change-of-season pathogens."

Cannon: "I see..."

*pause*

Cadwalader: "Anyway.. You were asking me something just before?"

Cannon: "Right. I had meant to ask: do you not think that by taking a purely mechanistic, physicalist view of reality that you limit your own ability to perceive its beauty? And more than that, disregarding how things actually are, and stepping beyond the bounds of your own beliefs, do you hold that the belief would be benevolent, generally applied?"

*Cadwalader lets his head drop near his knees to better consider the proposed question. After a moment of deliberation in this position, he raises his head and begins rubbing his bristled chin, checking a few final details for consistency.*

Cadwalader: "I think it is a powerful view... It has great potential; but it may be misapplied, misinterpreted, and simply incomprehensible for some I'd imagine. Or.. at least they wouldn't be willing to put the work into comprehending it. I say this because to fully understand it requires a reasonable amount of imaginative effort -- not to invent something about reality, mind you, but to understand something about it that is invisible to human minds and eyes."

Cannon: "Well, that's rather vague isn't it?"

*Cadwallader laughs a moment and then thinks silently for another before continuing.*

Cadwalader: "This is where the viewpoint's problems begin: the beauty it has the potential to reveal is everywhere within it; and yet, just as atoms are everywhere and invisible, so to might this beauty be. Both atoms and the beauty in physicalism are at first transparent because of limitations inherent in humans for dealing with: the extremely small, in the case of atoms, and the extremely numerous, in the case of physicalism -- which will require some explanation. However, just as we were able to find an indirect route to atoms in physical reality, an indirect route to beauty in physicalism may be walked."

Cannon: "Why though? Why put effort into 'locating the beauty'? Isn't it a sign that we're on the wrong track if we have to strain to see it?"

*Cadwalader smiles*

Cadwalader: "Not at all. This is an easy mistake to make; one of the many pitfalls along the way to a safe comprehension of physicalism. Just because we have to put effort into seeing the beauty initially does not mean its radiance will be dimmed once spotted; you won't be perceiving beauty through squinted eyes, you'll just have to furrow your brow in the effort to reach it. This is done beforehand. You're still free to relax and enjoy yourself at other times; in fact, it's encouraged.
     The other reason you should bother is because it's useful and gratifying to know the truth. Physicalism is an accessory viewpoint automatically installed when a mind is furnished with man's most current knowledge of the universe. And while this knowledge expands, bits will be revised and scientists will work in changing paradigms; but you can be certain enough that we won't ever take back the universe's deterministic nature (despite what that daft pseudo-scientist who misinterprets quantum theory for you might say); this is all that physicalism requires."

*Cannon takes it all in while contemplating star-ward, then turns back to Cadwalader.*

Cannon: "Okay then, how is the beauty located? As far as I can determine, physicalism sounds dull and plain, uninspiring and.. mundane. I can surmise no redeeming qualities which it might posses in the way of enjoyability."

*Cadwalader acknowledges with a nod.*

Cadwalader: "Well, the first obstacle you have to overcome has to do with comprehending large numbers. When people see numbers like 10 to the 42nd power, the only thoughts they can have regarding it are along the lines of: that's a damn lot! But what's important is how damn much it really is.
     As humans evolved, they were not required to deal with quantities in that range; we are still without the capacity to proceed otherwise, directly. The national debt is incomprehensible, the number of sand-grains on a beach is more incomprehensible, the number of atoms in your thumb is far more incomprehensible. Once you understand how greatly concentrated the units of matter in the universe are, try for a grasp of how large and complicated the universe is.
     Take a moment and try to visualize each step: the lot which your high school and all of its grounds rested on was a great deal less than a single square kilometer; the surface area of the Earth is over 500 million square kilometers. The sun we revolve around is millions of times larger than our Earth. The observable universe contains more than 50 billion trillion stars organized into more than 80 billion galaxies. Now, think about how many atoms must be in the universe.
     This is such a hugely, extravagantly, vast number of interacting parts that I can conceive no limitations of beauty and wonder afforded to the system containing them. Not only that, but the unsurpassed elegance and genius of the laws of physics which define how the parts interact, giving rise to all of the coordinated grandeur of stars, planets, DNA and life, rather than to chaos, is more worthy of reverence than anything else known to me.
     This is the compass of the physicalist viewpoint, this is what it allows for. I have no doubt in my mind that a system with this level of complexity could give rise to perceived emotions as rich as the most profound love or diabolical, raging hatred; to our most awe-inspiring works of art in music, architecture, painting, poetry; to entities which can be moved by them as we are; and finally, to delicate flowers, gurgling streams, epic sun sets, and all of the rest of natural world.
     Once you realize the full import of these statements, you can feel free to discard them. Perceiving beauty has nothing to do with whether you believe in god or atoms; it has a lot to do with observation unclouded by thought. Not just visual beauty either, beauty of the moment, as I like to call it. This is something that can be found when you tune into sounds, smells, appearance, temperature -- in short, everything around you -- without thinking anything about it, just appreciating and waiting for more. All that's required to perceive beauty with physicalism is to remove the obstruction which a false impression of it may leave you with.

*Cannon is silent for a moment.*

Cannon: "I'll have to think about it."

*Cadwalader smiles again.*