Metamagical Themas: Questing for the Essence of Mind and Pattern

I: Snags and Snarls

1. On Self-Referential Sentences

• Many systems have the capability to represent or refer to themselves somehow, to designate themselves (or elements of themselves) within the system of their own symbolism. Whenever this happens, it is an instance of self-reference.
• Self-reference is often associated with paradox, but this is not necessarily the case.
• The classic paradox is 'Epimenides the Cretan said "All Cretans are liars."'
• It seems that all paradoxes involve, in one way or another, self-reference, whether it is achieved directly or indirectly.
• The philosophical problem of the connections among Platonic ideas, mental activity, physiological brain activity, and the external symbols that trigger them is vividly raised by these disturbing sentences:
  • I am the meaning of this sentence.
  • I am the thought you are now thinking.
  • I am thinking about myself right now.
  • I am the set of neural firings taking place in your brain as you read the set of letters in this sentence and think about me.
  • This inert sentence is my body, but my soul is alive, dancing in the sparks of your brain.
• Content is just fancy form. Content is just a shorthand way of saying "form perceived by a very fancy apparatus capable of making complex and subtle distinctions and abstractions and connections to prior concepts.
• When self-reference (or reference in general, for that matter) is indirect, mediated by form, then fluidity is required. The understanding of such sentences involves a mixture of deriving the content and yet retaining the form in mind, letting qualities of the form in mind, letting qualities of the form conjure up flavors and enhance the meaning with a halo of not-quite-conscious pseudo-meanings, connotations, flavors, that flicker in the mind, not quite out of reach.

2. Self-Referential Sentences: A Follow-Up

• David Moser's: "This is the Title of this Story, Which is Also Found Several Times in the Story Itself":
  • This is the first sentence of this story. This is the second sentence.
  • This sentence is questioning the intrinsic value of the first two sentences. This sentence is to inform you, in case you haven't already realized it, that this is a self-referential story, that is, a story containing sentences that refer to their own structure and function.
  • I mean, there is such a thing as free will, there has to be, and this sentence is proof of it!
  • This is the last sentence of the story. This is the last sentence of the story. This is the last sentence of the story. This is.
  • Sorry

3. On Viral Sentences and Self-Replicating Structures

• Walton and Going saw self-replicating sentences as similar to viruses - small objects that enslave larger and more self-sufficient "host" objects, getting the hosts by hook or by crook to carry out a complex sequence of replicating operations that bring new copies into being, which are then free to go off and enslave further hosts, and so on. "Viral sentences, as Walton called them, are "those that seek to obtain their own reproduction by commandeering the facilities of more complex entities."
• Both W and G were struck by the perniciousness of such sentences; the selfish way in which they invade a space of ideas and, merely by making copies of themselves all over the place, manage to take over a large portion of that space. Why do they not manage to overrun all of that idea-space? A good question. The answer: competition from other self-replicators. One types of replicator seizes a region of the space and becomes good at fending off rivals; thus a "niche" in idea-space is carved out.
• Roger Sperry in 1965, "Mind, Brain, and Humanist Values":
  • "Ideas cause ideas and help evolve new ideas. They interact with each other and with other mental forces in the same brain, in neighboring brains, and, thanks to global communication, in far distant, foreign brains. And they also interact with the external surroundings to produce in toto a burstwise advance in evolution that is far beyond anything to hit the evolutionary scene yet, including the emergence of the living cell."
• Jacques Monod in 1970, "Chance and Necessity":
  • The performance value of an idea depends upon the change it brings to the behavior of the person or the group that adopts it. The human group upon which a given idea confers greater cohesiveness, greater ambition, and greater self-confidence thereby receives from it an added power to expand which will insure the promotion of the idea itself. Its capacity to "take", the extent to which it can be "put over" has little to do with the amount of objective truth the idea may contain. The important this about the stout armature a religious ideology constitutes for a society is not what goes into its structure, but the fact that this structure is accepted, that it gains sway. So one cannot well separate such an idea's power to spread from its power to perform.
  • The spreading power - the infectivity - of ideas, is much more difficult to analyze. let us say that it depends upon preexisting structures in the mind, among them ideas already implanted by culture, but also undoubtedly upon certain innate structure which we are hard put to identify. What is very pain, however, is that the ideas having the highest invading potential are those that explain man by assigning him his place in an immanent destiny, in whose bosom his anxiety dissolves.
• Richard Dawkins in 1976, "The Selfish Gene":
  • As a library is an organized collection of books, so a memory is an organized collection of memes. And the soup in which memes grow and flourish is the soup of human culture.
  • Memes should be regarded as living structures, not just metaphorically but technically. When you plant a fertile meme in my mind you literally parasitize my brain, turning it into a vehicle for the meme's propagation in just the way that a virus may parasitize the genetic mechanism of a host cell. and this isn't just a way of talking - the meme for, say, "belief in life after death" is actually realized physically, millions of times over, as a structure in the nervous systems of individual men the world over.
  • The survival value of the god meme in the meme pool results from its great psychological appeal. It provides a superficially plausible answer to deep and troubling questions about existence. It suggests that injustices in this world may be rectified in the next. The "everlasting arms" hold out a cushion against our own inadequacies which, like a doctor's placebo, is none the less effective for being imaginary. These are some of the reasons why the idea of God is copied so readily by successive generations of individual brains. God exists, if only in the form of a meme with high survival value.
  • There need not be an exact copy of each meme, written in some universal memetic code, in each person's brain. Memes, like genes, are susceptible to variation or distortion - the analog to mutation. Various mutations of a meme will have to compete with each other, as well as other memes, for attention - for brain resources in terms of both space and time devoted to that meme. Not only must they compete for inner resources, but, since they are transmissible visually and aurally, they must compete for radio and television time, billboard space, newspaper and magazine column-inches, and library shelf-space.
  • Unconscious memes have ensured their own survival value by virtue of those same qualities of pseudo-ruthlessness which successful genes display. The idea of hell fire is, quite simply, self-perpetuating, because of its own deep psychological impact. It has become linked with the god meme because the two reinforce each other, and assist each other's survival in the meme pool.
  • Faith - Means blind trust, in the absence of evidence, even in the teeth of evidence... Nothing is more leghal for certain kinds of meme than a tendency to look for evidence... The meme for blind faith secures its own perpetuation by the simple unconscious expedient of discouraging rational inquiry.
• A manuscript sent to an editor may be considered viral, even though it contains no explicit self-reference, because it is attempting to secure its own reproduction through an appropriate host; the same manuscript sent to someone who has nothing to do with publishing may have no viral quality at all.
• In a democracy, nearly any idea will tend to replicate since the only way to win an election is to convince other people to share your ideas. Most political ideas are not properly self-replicating, since the motive for spreading the idea is separate from the idea itself. But ideas can sometimes take on a life of their own and drive their own propagation.
• Some statements like "The bourgeoisie is oppressing the proletariat." drive a desire to propagate them through a wish to protect a victim figure from a villain figure.
• Most extremist mass movements are based on a belief of victimhood.
• "The self-replicating ideas are conspiring to enslave our minds" - this paranoid statement is the Epimenides Paradox.
• Groups of memes are "meme complexes" for Dawkins, or "schemes" for Hofstadter.
• When a thing - a sentence, book, system, person - seems to refer to itself but does so only by allusion to something resembling itself, it is called indirect self-reference.
• This depends upon the ease with which our perceptual systems convert a mirror image into its reverse, and upon other qualities of translation without being aware of the layers - like looking through many feet of water and seeing not the water but only what lies at its bottom.
• Reagan evoked the memory of Truman to implicitly menace Iran with nuclear attack.
• Can self-reference really be direct or indirect? Or are these two points on a continuum? Is there even "self"-reference? One thing refers to another whenever, to a conscious being, there is a sufficiently compelling mapping between the roles the two things are perceived to play in some larger structures or systems. Conscious being, here, is an analogy-hungry perceiving machine that gets along in the world thanks to its perceptions; it need not be human or even organic. The mapping of systems and roles that establishes reference need not actually be perceived by any such being; it suffices that the mapping exist and simply be perceptible to such a being were it to chance by.
• In the movie of the The French Lieutenant's Woman, as two stories unfold in parallel, a number of coincidences arise that suggest ever more strongly that a mapping should be made. But it is left to the movie viewer to carry this mapping out; it is never called for explicitly. After a time though it simply becomes unavoidable.
• Indirect reference of the artistic type is much less precise than indirect reference of the formal type. The latter arises when two formal systems are isomorphic - they have strictly analogous internal structures, so that there is a rigorous one-to-one mapping between the roles in the one and the roles in the other. The existence of genuine reference becomes as clear to us as in the case of someone talking about their mirror-image: we take it as immediate, pure self-reference, without even noticing the indirectness, the translational steps mediated by the isomorphism. In fact, the connection may seem too direct even to be called "reference", some may see it simply as identity.
• This perceptual immediacy is the reason that Gôdel's famous sentence G of mathematical logic is said to be self-referential.
• Indirect self-reference suggests the idea of indirect self-replication, in which a viral entity, instead of replicating itself exactly, brings into being another entity that plays the same role as it does, but in some other system, perhaps its mirror image, perhaps its translation into French, perhaps a string of the product numbers of all its parts, together with pre-addressed envelopes containing checks made out to the factories where those parts are made, and a list of instructions telling what to do with all the parts when they arrive in the mail.
• The arbitrary and peculiar aspect of the Quine sentence is that its seed is half as complex as the sentence itself. But is there one which is made of smaller, less complex parts? Is there a self-documenting or self-building sentence that builds both its halves - its quoted seed and its unquoted building role - out of words or letters? All structure in the built object must arise exclusively out of some principle enunciated in the building rule, not out of the seed's internal structure.

4. Nomic: A Self-Modifying Game Based on Reflexivity in Law

• Reflexivity dilemmas of the Protagoras vs Euathlus (I'll teach you law and you pay me when you win your first case) type and problems of conflicting omnipotence crop up with astonishing regularity in the down-to-earth discipline of law.
• Reflexivity can include:
  • The self-reference of signs
  • The self-applicability of principles
  • The self-justification and self-refutation of propositions and inferences
  • The self-creation and self-destruction of legal and logical entities
  • The self-limitation and self-augmentation of powers,
  • Circular reasoning, circular causation, vicious and benign circles, feedback systems, mutual dependency, reciprocity, and organic form
• A good scheduling system strives to be equitable, but all kinds of conflicts can arise, in which interrupts interrupt interrupts and are then themselves interrupted. The scheduler has to be able to run its own internal decision-making programs with high priority, but not so high that nothing else ever runs. It can get bogged down in "introverted" computation deciding what it should spend its time doing and meanwhile very little real computation is going on.
• In government, supermajorities and the concurrence of many bodies are necessary to protect the foundations of the system from hasty change, but that protective purpose is frustrated if those foundations are reachable by rules requiring merely a simple majority of one legislature. Although all the rules in the American system are mutable, it is convenient to refer to the less mutable constitutional rules as immutable, and to the ones below them in the hierarchy as mutable.
• Normal social life is just such a system of indefinite tiers. Near the top are actual laws, rising through case precedents, regulations, and statutes, all the way up to constitutional rules. At the bottom are rules of personal behavior that individuals can amend unilaterally without incurring disapprobation or censure. Above these are rules for which amendment is increasingly costly, starting with costs like furrowed brows and clucked tongues, and passing through indignant blows and vengeful homicide.
• Nomic:
  • After a few rounds the game being played by the players may in a certain sense be different from the one they were playing when they started. In a similar way, human beings undergo constant development and self-modification, and yet continue to be convinced that it makes sense to refer, via such words as "I", to an underlying stable entity. The more immediately perceptible patterns change, whereas deeper and more hidden patterns remain the same. From birth to maturity to death, however, the changes can be so radical that one may sometimes feel that in a single lifetime one is several different people. Similarly, in law, many have acknowledged that an amendment clause, even a clause limited to piecemeal amendment, could, through repeated application, create a fundamentally new constitution.
  • The continuing identity of the game, like that of a nation or a person, is due to the fact (if fact it is) that all change is the product of existing rules properly applied, and that no change is revolutionary. Once could even argue that revolutionary change is just more of the same, where rules that were assumed immutable are simply rendered mutable by other rules that are more deeply immutable, but that previously had been taken for granted and hence had been invisible or tacit.
  • Stare decisis - precedents should be followed.
  • Nomic affords the blurring between constitutive rules (which define lawful play) and rules of skill (which define artful play), ie a blurring between the permissible and the optimal.
  • A game can embrace anything at the vote of the players. The line between play and non-play may shift at each turn, or it may apparently be eliminated. Players may be governed by the game when they think they are between games or when they think they have quit.
  • For most games, there is an infallible decision procedure to determine the legality of a move. In Nomic, by contrast, situations may easily arise where it is very hard to determine whether or not a move is legal.
  • Some rules, all of which can become immutable:
    • Immutable (113): A player always has the option to forfeit the game rather than continue to play or incur a game penalty. No penalty worse than losing, in the judgment of the player to incur it, may be imposed.
    • Immutable (114): There must always be at least one mutable rule. The adoption of rule changes must never become completely impermissible.
    • Mutable (202): One turn consists of proposing a rule and having it voted on and throwing a die and adding the number to your score.
    • Mutable (213): If the rules are changed so that further play is impossible, or if the legality of a move is impossible to determine with finality, or if by the Judge's best reasoning, not overruled, a move appears equally legal and illegal, then the first player who is unable to complete a turn is the winner. This rule takes precedence over every other rule determining the winner.
  • Some possible rule changes:
    • Remove the unanimity requirement for changing mutable rules
    • Add new tiers above, below, or between the two initial tiers.
    • Add special procedures for changing some rules (incomplete self-entrenchment)
    • Devise sunset rules that expire automatically after a certain number of turns
    • Allow private consultation on future amendments
    • Allow secret ballots
    • Allow constitutional conventions or revolutions
• How we make analogies determines how we make choices, and that is the essential nature of all judgment.
• The crux of any legal system is the ability of people to distinguish between the incidental qualities and the essential qualities of various events and relations, resulting in recognition of what a given item is, which category it belongs to. This is "choice".
• Coming to grips with the contrast between explicit rules and implicit principles or guidelines is of great importance if one wants to characterize how flexible category recognition (choice) takes place. In any attempt to make a machine capable of choice, one runs headlong into the problem of inconsistencies, level-collisions, and reflexivity tangles.
• In any modality, perception consists of many layers of processing, from the most primitive or syntactic levels, to the most abstract or semantic levels. The zeroing in on the semantic category to which a given raw stimulus belongs is carried out not by a purely bottom-up (stimulus-driven) or purely top-down (category-driven) scheme, but rather by a mixture of them, in which hypotheses at various levels trigger the creation of new hypotheses or undermine the existence of already-existing hypotheses at other levels. This process of sprouting and pruning hypotheses is a highly parallel one, in which all the levels compete simultaneously for attention, like billboards or radio commercials, or advertisements on the subway.
• Any recognition program must have at its core a tiered structure precisely like that of government or Nomic in which there are levels that are easily mutable, moderately mutable, almost mutable, and so on, and so a "choice" program is inevitably to be riddled with reflexivity.

II: Sense and Society

5. World Views in Collision: The Skeptical Inquirer vs The National Enquirer

• At its core, rationality will always depend on inscrutables: the simple, the elegant, the intuitive.
• Human perception and categorization underlie all that we take for granted in terms of common sense, and in more primordial ways that are so deeply embedded that we even find them hard to talk about. Such things as:
  • how we break the world into parts,
  • how we form mental categories,
  • how we refine them certain times while blurring them other times,
  • how experiences and categories are clustered associatively,
  • how analogies guide our intuitions,
  • how imagery works,
  • how valid logic is and where it comes from,
  • how we tend to favor simple statements over complex ones, and so on.
• This question of the interaction of form and content fascinates me deeply. I believe that if one has the right "terraced scan" mechanisms, one can go very far in separating the wheat from the chaff.
• Where does one draw the line? Where is the borderline between open-mindedness and stupidity? Or between closed-mindedness and stupidity? Where is the optimum balance? That is such a deep question that I could not hope to answer it. Even if we have no adequate theory to formalize such decisions, we nonetheless are all walking instantiations of such decision-making beings, and we make decisions for which we could not formally account in 1m years. Such decisions include all decisions of taste. We do not yet know how we make such decisions, but that does not mean we have to allow in indecisiveness.

6. On Number Numbness

• If we can develop a sense for the number of chairs in a room, why not as good a sense for the number of zeroes in a numeral?
  • 10 - (1) - Tens
  • 100 - (2) - Hundreds
  • 1,000 - (3) - Thousands
  • 10,000 - (4) - Tens of Thousands
  • 100,000 - (5) - Hundreds of Thousands
  • 1,000,000 - (6) - Millions
  • 10,000,000 - (7) - Tens of Millions
  • 100,000,000 - (8) - Hundreds of Millions
  • 1,000,000,000 - (9) - Billions
  • 10,000,000,000 - (10) - Tens of Billions
  • 100,000,000,000 - (11) - Hundreds of Billions
  • 1,000,000,000,000 - (12) - Trillions
• Some other kinds of big numbers
  • 100m cells in your retina
  • 100b neurons in your brain
  • 1t glia in your brain
  • 70t cells in your body
  • 6b trillion hemoglobin molecule in your body (400t being destroyed and the same number being created each second
• When numbers get too big, our perceptual relaity begins to shift. We cannot visualize the actual quantity and our perceptual reality becomes the string of zeroes
• Your estimate should be within ten% of the correct answer at the level of your perceptual reality

7. Changes in Default Words and Images, Engendered by Rising Consciousness

• The ability to ignore what is very unlikely - without even considering whether or not to ignore it - is part of our evolutionary heritage, coming out of the need to be able to size up a situation quickly but accurately.

8. A Person Paper on Purity in Language

• What if linguistic sexism were linguistic racism?

III: Sparking and Slipping

• Human thoughts have a way of slipping easily along certain conceptual dimensions into other thoughts, and resisting such slippage along other dimensions. A given idea has slightly different slippabilities - predispositions to slip - in each different human mind that it comes to live in. Yet some minds' slippabilities seem to give rise to what we consider genuine creativity, while others' do not. What is this precious gift? Is there a formula to the creative act? Can spark and slippability be canned and bottles? In fact, isn't that just what a human brain is - an encapsulated creativity machine? Or is there more to creativity and mind than can ever be encapsulated in any finite physical object or mathematical model?

9. Pattern, Poetry, and Power in the Music of Frédéric Chopin

• Phenomena perceived to be magical are always the outcome of complex patterns of nonmagical activities taking place at a level below perception. The magic behind magic is pattern. The magic of life itself is a perfect example, emerging as it does out of patterned but liefless activities at the molecular level. The magic of music emerges from complex, nonmagical - metamagical - patterns of notes.

10. Parquet Deformations: A Subtle, Intricate Art Form

• What's the difference between music and visual art? Temporality. Pieces of music consist of sounds intended to be played and heard in a specific order and at a specific speed. Music is thus fundamentally 1-D - it is tied to the rhythms of our existence. Works of visual art, by contrast, are generally 2-D or 3-D. Paintings and sculptures seldom have any intrinsic "scanning order" built into them that the eye must follow. Your are free to come and go as you please.
• Regrouping - in which the boundary line of the uit cell shifts so that structures jump out at the eye that before were completely submerged and invisible - while conversely structure that a moment ago were totally obvious have now become invisible, having been split into separate conceptual pieces by the act of regrouping, or shift of perceptual boundaries. it is both a perceptual and conceptual phenomenon, a delight to that subtle mixture of eye and mind that is most sensitive to pattern.
• Is there an architecture to creativity? Is there a plan, a scheme, a set of principles that, if elucidated clearly, could account for all the creativity embodied in the collection of all parquet deformations, past, present, and future?
• The essence of any artistic act resides not in selecting particular values for certain parameters, but far deeper: it's in the balancing of a myriad intangible and most unconscious mental forces, a judgmental act that results in many conceptual choices that eventually add up to a tangible, perceptible, measurable work of art.
• Once the finished work exists, scholars looking at it may seize upon certain qualities of it that lend themselves easily to being parametrized. Anyone can do statistics on a work of art once it is there for the scrutiny, but the ease of doing so can obscure the fact that no one could have said, a priori, what kinds of mathematical observables would turn out to be relevant to the capturing of stylistic aspects of the as-yet-unseen work of art.
• What kind of architecture is responsible for all of these ideas? Or is there any one architecture that could come up with them all? I would say that the ability to design good parquet deformations is probably deceptive, in the same way as the ability to play good chess is; it looks more mathematical than it really is.
• Good chess moves spring from the organization of a good chess mind: a set of perceptions arranged in such a way that certain kinds of ideas leap to mind when certain subtle patterns or cues are present. This way that perceptions have of triggering old and buried memories underlies skill in any type of human activity, not only chess. But in chess the skill is particularly deceptive, because after the fact, it can all be justified by a logical analysis, a fact that seems to hint that the original idea came from logic.
• For computers to act human, we will have to wait until we have good computer models of such human things as perception, memory, mental categories, learning, and so on.
• For a machine to make simple variants of a given design, it must possess an algorithm for making that design which has explicit parameters; those parameters are then modifiable. But the way people make variations is quite different. They look at some creation by an artist and then they abstract from it some quality that they observe in the creation itself. This newly abstracted quality may never have been thought of explicitly by the artist yet it is there for the seeing by an acute observer. This perceptual act gets you more than half the way to genuine creativity; the remainder involves treating this new quality as if it were an explicity knob: "twiddling" it as if it were a parameter that had all along been in the program that made the creation.
• That way, the perceptual process is intimately linked up with the generative process; a loop is closed in which perceptions spark new potentials and experimentation with new potentials opens up the way for new perceptions; The element lacking in current computer are is the interaction of perception with generation. Computers do not watch what they do; they simply do it.
• Each of us is at the very center of our own personal web, and each one of us things "I am the most normal, sensible, comprehensive individual." And our identity - our shape in personality space - springs largely from the way we are embedded in that network - the identities (shapes) of the people we are closest to. We help to define others' identities even as they help to define our own.

11. Stuff and Nonsense

• What marks something off as being nonsense?

12. Variations on a Theme as the Crux of Creativity

• In the mind of each person who perceives a Rubik's Cube there arises a concept that we could call "Rubik's-Cubicity". It's not the same concept in each mind, just as not everyone has the same concept of asparagus or of Beethoven. The variations that are spun off by a given cube-inventor are variations on that concept. In a discussion of perception and invention, this distinction between an object and some mind's concept of the object is simple but crucial.
• Invention is more like falling off a log than like sawing one in two. A mind follows its path of least resistance, and it's when it feels easiest that it is most likely being its most creative. Mozart: Things should "flow like oil".
• Making variations on a theme is really the crux of creativity.
• If a concept is a machine with knobs on it, we have to stretch the very concept of "knob". New knobs must be able to sprout, depending on the settings of other knobs. On each concept, there are potentially an infinite number of knobs, and at any moment, some new knobs may get revealed as a consequence of the settings of other knobs.
• Nondeliberate yet nonaccidental slippage permeates our mental processes, and is the very crux of fluid thought. This subconscious manufacture of "subjunctive variations on a theme" is something that goes on day and night in each of us, usually without our slightest awareness of it. It is one of those things that, like air or gravity or 3-D, tend to elude our perception because they define the very fabric of our lives.
• It is very hard to slip mentally into a world in which people would not think by slipping mentally into other worlds - very hard to make a counterfactual world in which counterfactuals were not a key ingredient of thought.
• The hidden fault lines of the mind, which things are solid and which things can slip. Nothing is reliably unslippable. Context contributes an unexpected quality to the knobs that are perceived on a given concept. The knobs are not displayed in a nice, neat little control panel, forevermore unchangeable. Instead, changing the context is like taking a tour around the concept, and as you get to see it from various angles, more and more of its knobs are revealed. Some people get to be good at perceiving fresh new knobs on concepts where others thought there were non, just as som people get to be good at perceiving mushrooms in a forest where others see none, even when they stare mightily.
• One of Knuth's main theses is that with computers, we now are in the position of being able to describe not just a thing in itself, but how that thing would vary.
• I call it the implicosphere (implicit counterfactual sphere) referring to things that never were but that we cannot help seeing anyway (or sphere of implications surrounding any given idea.
• One way to imagine how slippability might be realized in the mind is to suppose that each new concept begins life as a compound of previous concepts, and that from the slippability of those concepts, it inherits a certain amount of slippability. that is, since any of its constituents can slip in various ways, this induces modes of slippage in the whole.
• As the space of possibilities of the new concept - the implicosphere - is traced out, the most common and useful of those slippages becomes more closely and directly associated with the new concept itself, rather than having to be derived over and over from its constituents. This way, the new concept's implicosphere becomes more and more explicitly explored, and eventually the new concept becomes old and reaches the point where it too can be used as a constituent of fresh new young concepts.
• The test of whether a concept has really come into its own, of its genuine mental existence, is its retrievability by that process of unconscious recall. That's what lets you know that it has been firmly planted in the soil of your mind. It is not whether that concept appears to be "atomic", in the sense that you have a single word to express it by. That is far too superficial.
• When one story from a friend triggers the retrieval of an old memory, the two subjects can appear to be completely unrelated, but at some deeper conceptual level, these really are the same idea. There is just one idea here, and this idea I call a conceptual skeleton. Try to verbalize it. It's certainly not just one word. It will take you a while. And when you do come up with a phrase, chances are it will be awkward and stilted - and still not quite right.
• The point is that the concept itself has been reified - this much is proven by the fact that it acts as a point of immediate reference; that my memory mechanisms are capable of using it as an "address" (a key for retrieval) under the proper circumstances. The vast majority of our concepts are wordless in this way, although we can certainly make stabs at verbalizing them when we need to.
• Variations on a them - the notion encompasses knobs, parameters, slippability, counterfactual conditionals, subjunctives, "almost"-situations, implicospheres, conceptual skeletons, mental re-ification, memory retrieval, and more.
• My own mental image of the creative process involves viewing the organization of a mind as consisting of thousands, perhaps millions, of overlapping and intermingling implicospheres, at the center of each of which is a conceptual skeleton. The implicosphere is a flickering, ephemeral thing, a bit like a swarm of gnats around a gas-station light on a hot summer's night, perhaps more like an electron cloud, with its quantum-mechanical elusiveness, about a nucleus, blurring out and dying off the further removed from the core it is. if you have studied quantum chemistry, you know that the fluid nature of chemical bonds can best be understood as a direct consequence of the curious quantum-mechanical overlap of electronic wave functions in space, wave functions belonging to electrons orbiting neighboring nuclei. In a metaphorically similar way, it seems to me, the crazy and unexpected associations that allow creative insights to pop seemingly out of nowhere may well be consequences of a similar chemistry of concepts with its own special types of "bonds" that emerge out of an underlying "neuron mechanics'.
• Making variations is not just twiddling a knob before you; part of the act is to manufacture the knob yourself. Where does a knob come from? The question amounts to asking; How do you see a variable where there is actually a constant? More specifically; What might vary, and how might it vary? It's not enough to just have the desire to see something different from what is there before you. Often the dullest knobs are a result of someone's straining to be original, and coming up with something weak and ineffective. So where do good knobs come from? I would say they come from seeing one thing as something else. Once an abstract connection is set up via some sort of analogy or reminding-incident, then the gate opens wide for ideas to slosh back and forth between the two concepts.
• When two things can both be seen as instances of one abstract phenomenon, it is a very exciting discovery. Then ideas about either one can be borrowed in thinking about the other, and that sloshing-about of activity may greatly illumine both at once.
• Projection of oneself into a situation: "How would that be for me?" People are remarkably fluid at seeing themselves in roles that they self-evidently could never fill, and yet the richness of the insights thus elicited is beyond doubt.
• Experience with a wide variety of things refines your category system and allows you to make incisive, abstract connections based on depp shared qualities.
• Seeing clear to the essence of something unfamiliar is often best achieved by finding one or more known things that you can see it as, then being able to balance these views.
• Once you have decided to try out a new way of viewing a phenomenon, you can let that view suggest a set of knobs to vary. The act of varying them will lead you down new pathways, generating new images ripe for perception in their own right.
• Like a planet orbiting a star, and whose orbit brings it so close to another star that it gets" captured" and begins orbiting the second star. As it swings around the new star, perhaps it find itself coming bery close to yet another star, and fickly changes allegiance.
• You can think of concepts as stars, and knob-twiddling as carrying you from one point on an orbit to another point. If you twiddle enough, you may well find yourself deep within the attractive zone of an unexpected but interesting concept and be captured by it. You may thus migrate from concept to concept. Knob-twiddling carries your from one concept to another, taking advantage of their overlapping orbits.
• Can "concept" become a legitimate scientific term? This goal could be taken to be the central goal of cognitive science.
• Of course not all implicospheres have the same radius. Some people's tend to have bigger radii than others, and consequently they overlap more. This can be good but it can be overdone:
  • Too much overlap and all you have is a mush of vaguely associated ideas, a tasteless mental goulash
  • Too little and you have a very thin, watery mind, one with few big surprises
  • There is, in other words, an optimum amount of overlap for useful creative insight.
• When a new idea is implanted in a mind, an implicosphere grows around it. Since this means, in essence, the linking up of this new idea with older ideas, I call it diffusion in idea-space.

13. Metafont, Metamathematics, and Metaphysics

• The mathematicalization of categories - the idea that any abstraction or Platonic concept can be captured as a software machine with a finite number of knobs, like a meta-font, a meta-waltz, a meta-shoe.
• But to fill out the full "space" defined by a category such as "chair", or "waltz" or "face" is an act of infinite creativity, and no finite entity will ever be capable of producing all possible "A"s and nothing but "A"s.
• This amounts to positing that any conceptual or semantic category is a productive set, namely a set whose elements cannot be totally enumerated by any effective procedure without overstepping the bound of that set.
• A system that contains at least one unprovable truth is said to be incomplete, and a system that not only contains such truths but that cannot be rescued in any way from the fate of incompleteness is said to be essentially incomplete (or productive). The requirement that one must stay within the bounds of a conceptual category could be called consistency.
• The frame problem is about the question: What variables (knobs) is it within the bounds of normalcy to perceive?
• Trying to capture the essence of each separate concept in a separate "knobbed machine", to isolate the various Platonic spirits will not work. Those spirits overlap and mingle in a subtle way.
• No letter is an island. There has to be much mutual knowledge spread about among all the letters. Letters mutually define each others' essences, and this is why an isolated structure supposedly representing a single letter in all its glory is doomed to failure.

IV: Structure and Strangeness

14. Magic Cubology

• This Magic Cube is much more than just a puzzle. It is an ingenious mechanical invention, a pastime, a learning tool, a source of metaphors, and inspiration. It now seems an inevitable object, but it took a long time to be discovered. Somehow, though, the time was ripe, because the idea germinated and developed nearly in parallel in Hungary and Japan and perhaps even elsewhere.
• It is necessary to find a general algorithm for doing it from any scrambled state. No one can restore a messed up Magic Cube to its pristine state by mere trial and error. Anyone who gets back to START has built up a small science.

15. On Crossing the Rubicon

• The cube has some kind of primordial appeal:
  • It is small and colorful, fits snugly in the hand and has a pleasing feel. Twisting is a fundamental and intriguing motion that the hand performs naturally. There are not many puzzles or toys that give the mind and fingers a genuine 3-D workout.
  • That it manages to stay in one piece when it has so many independent ways of twisting is initially amazing, and remains mysterious even after you've seen its "guts".
  • It's a miniature incarnation of that subtle blend of order and chaos that our world is.
  • There are plenty of patterns, some attainable, some unattainable. Sometimes they are simple to generate, but one can't see how they emerge. Sometimes they are hard to generate, yet one clearly understands how they arise.
  • They are many routes to any state, and the shortest is nearly always completely unknowable.
  • The Cube is a rich source of metaphors. It furnishes analogies to particle physics, to biology, to problem-solving in everyday life, to entropy and path-finding, and even touches theology.
  • There is a strong contrast between the algebraic or mathematical approach (long sequences of operations compounded out of shorter sequences, which become increasingly abstract) and the geometric approach (using eye and mind to compose twist after twist along a carefully charted pathway.
  • Aside from cubies and modes of twisting, there is flippedness and twistedness.
• Getting into a scrambled state and getting out of it are operations of different computational complexity. It is easier to find routes out than routes in, even though there are the same number of each. Clearly there is something deeply asymmetric about such a situation, and the whole thing smells of the second law of thermodynamics, stating that entropy will tend to increase with time in a closed system.

16. Mathematical Chaos and Strange Attractors

• The motion of a point in phase space must always be non-self-intersecting. This arises from the fact that a point in phase space representing the state of a system encodes all the information about the system, including its future history, so that there cannot be two different pathways leading out of one and the same point.
• All systems that exhibit turbulent behavior are dissipative: they dissipate or degrade energy from more usable forms such as electricity into the less usable form of heat
• Metrical universality (as opposed to structural universality) shows the parabolic case with the onset of chaos happening through periodic-doubling attractors.
• When you are searching for a memory that eludes you but that you kno is there, what you in effect do is release ten "dogs" in your brain and let them go "sniffing" in parallel. Each dog will start to rummage around here and there, sometimes going in circles, sometimes smelling down wrong alleys, but since there are a bunch of them you can afford to let them smell out many false pathways. They don't need to be very bright; they just need to have had a whiff of the original idea, and they will follow that spoor high and low. Eventually it is likely that one dog or another will trot home carrying the desired memory in its mouth.
• Locking-in - a system that seeks and gradually settles into its own most stable states, and the mechanism whereby it seeks and attains such loci of stability is feedback. A system that locks into a state is in a stable equilibrium, which means that if you perturb it somehow, it will swiftly return to the state is was in - there are restoring forces that push it back.
• As long as we're willing to "up" the dimensionality of the space, we can store more and more information in a single point. Thus fixed points and stable orbits are very close concepts.
• Generally speaking, the stablest behavior of a system seems also to be its simplest behavior.
• Starting somewhere random and relying on feedback to get you somewhere better is the most likely way to discover a fixed point.
• The tangledness of one's own self is a perfect metaphor for understanding what renormalization is all about. Begin by imagining yourself as a 0th order person - someone totally unaware and inconsiderate of all others, a baby. Then imagine how you would be modified if you started to take other people into account, always considering others as perfect babies, or 0th order people. This gives a first-order version of you. You are beginning to have an identity emerging from this modeling of others inside yourself. Now iterate: second order people are those who take into account the identities of first-order people. An on it goes. The final result is renormalized people: people who take into account the identities of renormalized people. I know it sounds circular, and indeed it is, but paradoxical it is not.
• Memory retrieval - How do things that are only vaguely similar to each other stir up rumblings of recollection, and eventually trigger the retrieval of amazingly deep abstract resemblances? If the initial input is a seed - a vector in a very high-dimensional space, then the seed is fed into memory-retrieval mechanisms, which convert it into an output vector that is then ged back in again. This cyclic process continues until it either converges on a stable fixed point - the desired memory trace - or is seen to be wandering erratically without any likelihood f locking in, tracing out a chaotic sequence of "points" in mind-space
• Perception - the bottom-up processing is complemented by concurrent top-down processing driven not by the input, but by expectations of what is "out there" to be recognized. The swirling activity in which bottom-up and top-down processes seek a reconciliation with each other leads to a gradual kind of "crystallization" in which many small pieces of evidence align with, and mutually reinforce, each other. The ultimate justification for some of them resides, of course, in the raw perceptual input, while for others of them it resides in the richness of previous experiences stored in memory. The combination of all these mutually confirming hypotheses results in a globally optimal interpretation of the input: an act of recognition. Once again, locking-in carries the day.
• Locking in seems to be a key to the metamagics of snarls, of society, of slipping, of strangeness, of substrate, of stability, of survival.

17. Lisp: Atoms and Lists

• Psychologically, one of the great powers of programming is the ability to define new compound operations in terms of old ones, and to do this over and over again, thus building up a vast repertoire of ever more complex operations:
  • It is quite reminiscent of evolution, in which ever more complex molecules evolve out of less complex ones, in an ever-upward spiral of complexity and creativity.
  • It is also quite reminiscent of the industrial revolution, in which people used very simple early early machines to help them build more complex machines, then used those in turn to build even more complex machines, and so on, once again in an ever-upward spiral of complexity and creativity.
  • At each stage, whether in evolution or revolution, the products get more flexible and more intricate, more "intelligent" and yet more vulnerable to delicate bugs or breakdowns.

18. Lisp: Lists and Recursion

• Speaking recursively, an n factorial is simply the product of n and the previous factorial. It reduces the given problem to a simple sort of the same type. That simpler one will in turn be reduced, and so on down the line, until you come to the simplest problem of that type, which I call the embryonic case or the bottom line. People often speak, in fact, of a recursion bottoming out.
• Shapes with substructures that goes on indefinitely, never bottoming out in ordinary curves, are called fractals.

19. Lisp: Recursion and Generality

• Since the whole thing is recursive, every needle (in the Tower of Brahma puzzle) will be switching hats many times over during the course of the transfer. That's the beauty of this puzzle and in a way it's the beauty of recursion.
• In Lisp, one has the ability to "elevate" an inert, information-containing data structure to the level of "animate agent", where it becomes a manipulator of inert structures itself. This program-data cycle, or loop; can continue on and on, with structures reaching out twisting back, and indirectly modifying themselves or related structures.
  • Certain types of inert, or passive, information-containing data structures are sometimes referred to as declarative knowledge (aka "knowledge that") - because they often have a form abstractly resembling that of a declarative sentence, and encode facts about the world in some way, accessible by looking in an index in somewhat the way "book-learned" facts are accessible to a person
  • By contrast, animate, or active, pieces of code are referred to as procedural knowledge, since they define sequences of actions that actually manipulate data structures, and can be viewed as embodying the program's set of skills, something like a human's unconscious skills that were once learned through long, rote, drill sessions (aka "knowledge how").
• This distinction should remind biologists of that between genes - relatively inert structures inside the cell - and enzymes, which are anything but inert. Enzymes are the animate agents of the cell; they transform and manipulate all the inert structures in indescribably sophisticated ways. Genes dictate the form of enzymes, and enzymes manipulate genes (among other things). Thus Lisp's procedural-declarative program-data loop provides a primitive but very useful and tangible example of one of the most fundamental patterns at the base of life: the ability of passive structures to control their own destiny, but creating and regulating active structures whose form they dictate.
• If you know enough English, you can bootstrap your way further into English; there is a point beyond which explanations written in English about English are indeed quite useful, and that point is not too terribly far beyond the beginning level. You need a kernel, and then you can begin to life yourself by your own bootstraps. For children, it is an exciting thing when, in reading, they begin to learn new phrases all by themselves, simply by running into them several times in succession. Their vocabulary begins to grow by leaps and bounds. So it is once there is a Lisp kernel in a system; the rest of the Lisp interpreter can be - and usually is - written in Lisp.
• When one interpreter runs on top of another one, there is always the question of what level one chooses not to look below. I personally seldom think about what underlies the Lisp interpreter, so that when I am dealing with the Lisp system, I feel as if I am talking to someone whose native language is Lisp. Similarly, when dealing with people, I seldom think about what their brains are composed of; I don't reduce them in my mind to piles of patterned neuron firings. It is natural to my perceptual system to recognize them at a certain level and not to look below that level.
• For some reason, many people in AI seem to have a deep sense that recursivity in some form or other is connected with the trick of intelligence.
• Gödel's construction revealed in a crystal clear way that the line between direct and indirect self-reference/reference is completely blurry, because it pinpoints the essential role played by isomorphism (or coding) in the establishment of reference and meaning.
• Semantics is an emergent quality of complex syntax.
• Certain orally produced screeches or manually produced scratches (such as word, say, language, sentence, reference, grammar, meaning, etc) can stand for elements of language itself - pieces of language talking about language. How amazingly magical it must have felt to our ancestral cave people when such powerful concepts as words about words first sparked. In some sense, human consciousness began then and there.
• Gödel got a system to talk - in code - about itself. He had snuck self-reference into systems that were presumed to be incapable of self-reference.
• The central data structure of Lisp, the list, was at the core of Gödel's work, and the crucial need to distinguish between atoms and lists was resolved by him with his odd-even distinction. Also critical were the idea of quoting and recursive functions.
• Gödel's remarkable series of 46 function definitions is, IMO, the world's first serious computer program - and it is in Lisp
• A programmer's instinct says that you can cumulatively build a system, encapsulating all the complexity of one layer into a few functions, then building the next layer up by exploiting the efficient and compact functions defined in the preceding layer. This hierarchical mode of buildup would seem to allow you to make arbitrarily complex actions be represented at the top level by very simple function calls. In other words, the functions at the top of the pyramid are like cognitive events, and as you move down the hierarchy of lower-level functions, you get increasingly many ever-dumber sub-routines, until you bottom out in a myriad calls on trivial subcognitive ones.
• But this is a crazy vision - the top-level behavior of the overall system must emerge statistically from a myriad independent pieces, whose actions are almost as likely to cancel each other out as to be in phase with each other.

20. Heisenberg's Uncertainty Principal and the Many-Worlds Interpretation of Quantum Mechanics

• The main thing to keep in mind is that science is about classes of events, not particular instances. Science explains through abstractions that underlie a potentially unlimited number of concrete phenomena.
• Many people think the quantum-mechanical uncertainty principle actually applies to everyday phenomena. Nothing could be further from the truth!
• In some ways, light waves are simpler than water waves:
  • While water waves of different wavelengths travel at different speeds, all light waves travel at one speed, c.
  • The medium that light waves travel through is nondispersive: all wavelengths travel at exactly the same speed. Vacuum is light's medium - how peculiar for waves to wave even when there's nothing to wave!
• De Broglie proposed the equation p = h/λ:
  • Where p = momentum, h = Planck's constant, and λ = wavelength
  • It is proposed as universal, applying to all matter, so that anything has a quantum-mechanical wavelength whose value would depend on how fast it is moving.
  • Wavelength is inversely proportional to momentum.
  • Arbitrarily accurate measurement of either position or momentum is possible; you just can't get both.
• The uncertainty principle is more than an epistemological restriction on human observers; it is a reflection of uncertainties in nature itself. Quantum-mechanical reality does not correspond to macroscopic reality. It's not just that we cannot know a particle's position and momentum simultaneously; it doesn't even have definite position and momentum simultaneously!
• As long as no measurement is made of a system, a physicist cannot know which eigenstate the system is in. In a very fundamental sense, the system itself does not know this and only decides - at random - at the moment the observer observes. And up to this moment it is not in any eigenstate.
• There is a clear connection between the imaginary worlds of our minds and the alternate worlds evolving in parallel with the one we experience.
• When a novelist simultaneously entertains a number of possible ways of extending a story, are the characters not, to speak metaphorically, in a mental superposition of states? If the novel never gets set to paper, perhaps the split characters can continues to. evolve their multiple stories in their author's brain. Furthermore, it would even seem strange to ask which story is the genuine version. All the worlds are equally genuine.

V: Spirit and Substrate

• How and when could mind and emotions - surely the essence of the animate - emerge from complex inanimate substrates.
• Where is the borderline between the highest inanimate flexibility and the lowest animate sentience. When does a system or organism have the right to call itself "I", and to be called "you" by us?

21. Review of Alan Turing: The Enigma

• This image of a machine that jumped from one state to another according to a finite set of rules became uppermost in Turing's mind. What fascinated him was the idea that such meaningless actions could also be viewed as having meanings. For instance, one rule-obeying machine might be viewed as making moves of chess, another as producing truths of mathematics, and yet another as writing poetry.
• What Gödel had left unsettled was the question of whether, given an axiomatic system and an arbitrary proposition in it, one could determine mechanically whether that proposition was undecidable in that system.
• To Turing's surprise, he discovered that for very Gödelian reasons, no machine could be built that could infallibly recognize undecidable propositions.
• First he supposed that a machine for recognizing undecidable propositions exists; then he showed how that assumption leads to self-contradiction - a universal Turing machine being fed its own description number would instantly send it into a dizzying loop of computational vertigo.
• Undecidable propositions run through mathematics like ineradicable threads of gristle that crisscross a steak in such a dense way that they cannot be cut out without the entire steak's being destroyed.
• Mathematics was revealed to be incompletely mechanizable, no matter how complex the machine involved.
• People, no matter how aware they are of their minds, cannot fully take their own complexity into account in attempting to understand themselves, and, quite like Turing machines baffled by their own descriptions, may be plunged into a vertigo of the psyche when they attempt to calculate their own hypothetical or future acts.
• Lady Lovelace's objection - computers cannot originate anything, but can do only what we explicitly tell them to do. Turing's answer to this - that one does not know what one has programmed a machine to do, except in the most superficial and general way - has a depth that eludes many good minds.

22. A Coffeehouse Conversation on The Turing Test

• Starquakes and earthquakes can both be subsumed into a new, more abstract category. And that's how science constantly extends familiar concepts, taking them further and further from familiar experience and yet keeping some essence constant. The number system is the classic example - from positive numbers to negative nmbers, then rationals, reals, complex numbers, "and on beyond zebra".
• Though, even more than hurricanes, ia an abstract structure, a way of describing some complex events that happen in a medium called a brain. But actually, thought can taked place in any one of several billion brains. There are all these physically very different brains, and yet they all support "the same thing": thinking. What's important, then, is the abstract pattern, not the medium. The same kind of swirling can happen inside any of them, so no person can claim to think more "genuinely" than any other. Now, if we come up with some new kind of medium in which the same style of swirling takes place, could you deny that thinking is taking place in it?
• People give other people credit for being conscious simply because of their continual external monitoring of other people - which is itself something like a Turing Test.
• I think emotions are an automatic by-product of the ability to think. They are entailed by the very nature of thought.
• In my view, consciousness requires a certain way of mirroring the external universe internally, and the ability to respond to that external reality on the basis of the internally represented model. What's really crucial is that it should incorporate a well-developed and flexible self-model.
• Any intelligence has to have motivations. Machines, when they look at a scene, will have to focus and filter that scene down into some preconceived categories, just as a person does. And that means seeing some things and missing others. It means giving more weight to some things than to others. This happens on every level of processing.
• People talk to each other out of conviction - not out of hollow, mechanical reflexes. Even the most intellectual conversation is driven by underlying passions. There's an emotional undercurrent to every conversation - it's the fact that the speakers want to be listened to, understood, and respected for what they are saying.
• When things get complicated enough, you're forced to change your level of description, to adopt the intentional stance. Really interesting things will happen in IA when the program itself adopts the intentional stance toward itself.
• The smarter computers get, the more they'll be in a position to tackle messy real-life domains, so they'll be more and more likely to have inaccurate models. To me, mistake-making is a sign of high intelligence.
• Parry (a paranoid) maintains strict control so that no one can truly probe him. For reasons like this, simulating a paranoid is a whole lot easier than simulating a normal person.
• Each time I could postulate some not too sophisticated mechanical underpinning that would allow that particular thing to happen. I kept on trying to come up with rationalizations for the fact that this program was doing so well. My conclusion was that it was a very vast and quite sophisticated bag of tricks, no one of which was terribly complex.
• The class was willing to view anything on a video terminal as mechnically produced, no matter how sophisticated, insightful, or poetic an utterance it might be.