The False Lexical Constituent Riddle Game

A false lexical constituent pun looks like this:
There's a fake meaning (to acquire a pub) derived from breaking the word "bargaining" into false lexical constituents. Here are some more lexical constituent puns presented as tricky riddles. If you saw these before on Twitter or Slack, you may want to skip the first seven.

1. Fake meaning: A hollow metal cylinder that was born under the first sign of the Western zodiac.
Real meaning: Yellow finches native to islands off the coast of Portugal and Morocco.
Hyphenation pattern: 3 letter - 5 letters.

2. Fake meaning: An Oriental or Eastern Orthodox painting of a religious figure which people like to brush their fingers against.
Real meaning: The river separating Gaul from Italy.
Pattern: 3-4.

3. Fake meaning: A mesh for catching a falling male descendant.
Real meaning: A form of poem in 14 lines.
Pattern: 3-3.

4. Fake meaning: A sheep made from the remains of a fire.
Real meaning: An Indian monastery.
Pattern: 3-3.

5. Fake meaning: A lord of immoral transgressions.
Real meaning: Gradually entering into the ground.
Pattern: 3-4.

6. Fake meaning: A furry animal that can be caressed when it sits on your thighs.
Real meaning: A small fold in a garment. (This one was a little obscure to me.)
Pattern: 3-3.

7. Fake meaning: 2000 pounds of intercourse.
Real meaning: A groundskeeper for a graveyard or parish.
Pattern: 3-3.

8. Fake meaning: The edge of a garment that has been sewn by a ground-dwelling eusocial insect.
Real meaning: An uplifting song associated with a nation or other social group.
Pattern: 3-3.

9. Fake meaning: A large saline body of water in the shape of a torus which is connected to an ocean.
Real meaning: Hot enough to scorch.
Pattern: 3-4.

10. Fake meaning: To prohibit Scottish bonnets.
Real meaning: The miniature, dwarf variety of any chicken breed. Also a publishing house that uses a chicken as its mascot. Also a weight class in boxing between fly- and feather-.
Pattern: 3-3.

11. Fake meaning: A place to lie down and rest in a pub.
Real meaning: Having jagged spines, as on a fish hook.
Pattern: 3-3.

12. Fake meaning: The era in which an item of clothing was worn.
Real meaning: Trash.
Pattern: 4-3.

13. Fake meaning: A person who cooperates with a lower limb.
Real meaning: Done in a licit manner.
Pattern: 3-4.

14. Fake meaning: A single object which reflects light at the lowest end of the visible spectrum. 
Real meaning: To have performed again.
Pattern: 3-3.

15. Fake meaning: When NBC tries to make a new version of an 80s sitcom featuring an alien anteater. 
Real meaning: A pasta sauce made with parmesan cheese, named after its inventor.
Pattern: 3-4.

16. Fake meaning: A billion years of geological time following the domestication of boars. 
Real meaning: A dove, especially one which is not white.
Pattern: 3-3.

17. Fake meaning: A person who shoots down several enemies in combat while riding a wave.
Real meaning: The outer or uppermost layer of a thing.
Pattern: 4-3.

18. Fake meaning: A skinny monarch.
Real meaning: Cognition.
Pattern: 4-4

19. Fake meaning: A safari park ruled by a dynasty of Emperors of Han Chinese ethnicity. (This one is easier to get if you know about my love for adjectives pospositional.)
Real meaning: Moving quickly, or adjusting a camera smoothly between long-shot and a close-up.
Pattern: 3-4.

20. Fake meaning: A regular stopping place on a public transportation route for shrew-like mammals.
Real meaning: Sexual assault, especially of children. (Sorry.)
Pattern: 4-7.

21. Fake meaning: A long serrated blade re-purposed as a weapon in battle.
Real meaning: The capital of Poland.
Pattern: 3-3.

22. Fake meaning: White cereal grain stored in a baseball hat.
Real meaning: A sudden change of mood or behavior; eccentrically impulsive.
Pattern: 3-4.

23. Fake meaning: The speed at which molten metal is poured into a mold.
Real meaning: To remove the testicles of a male animal.
Pattern: 4-4.

24. Fake meaning: The sound of sonar pulse reflected off of gauze fabric. (The fabric is a little obscure. It's the five-letter component, if that helps.)
Real meaning: Being thrifty.
Pattern. 5-4.

25. Fake meaning: A commercial for a solid sphere.
Real meaning: A narrative poem or song presented in short stanzas.
Pattern: 4-2.

26. Fake meaning: The last stop on a line of the San Francisco metro.
Real meaning: To serve alcoholic drinks from behind a counter.
Pattern: 4-3.

27: Fake meaning: Anger experienced in a small sheltered bay.
Real meaning: The extent to which something has been placed beneath another thing, especially for concealment or protection.
Pattern: 4-4.

28. Fake meaning: Having the poor visual acuity of a cloistered religious mendicant.
Real meaning: Tampered with a machine in the manner of a curious primate.
Pattern: 4-4.

29. Fake meaning: A Native American from a tribe indigenous to Colorado and surrounding areas who has chemically reshaped their hair into curls.
Real meaning: To change, especially to reorder the elements of a mathematical set.
Pattern: 4-3.

30: Powdered resin used in laser printers which is pale in color.
Real meaning: A person who is unrestrained, unruly, or unchaste.
Pattern: 3-5.
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Identifying The Soul

There are lots of recently coined terms for mental objects which I mostly don't use except in quotation.
As for historical terms, I'm not yet resolved either way as to whether the term "soul" has a referent. If there is no soul, then how do we account for soul food and soul music? We have lots of good words for mental objects that aren't so laden with supernatural associations, and which can often stand in for "soul" in common expressions, and I'd like to make up my mind on the question of whether the the soul should be thought of as equivalent to any of them or distinct from them but also naturalistic.

Light-hearted proposals:

1. The soul is the mind-like thing which is tethered to the body but does not reside in the brain. Therefore the soul is the processing capacity of neural reflex arc pathways.

2. The soul is the mental image of a person in which their skin is still attached to their face. Saying a person has a soul = thinking they still have a face. Think about it.

3. The soul is what we called the brain's (magnetic) aura before we realized it was computationally impotent.

4. The soul is the thing that's confused when you learn about a new genre of fetish pornography.

Serious but low quality proposals:

1. The soul is whatever fragment of yourself you can identify with and appreciate finding in other moral agents and moral patients. This is less an identification of the soul and more a procedure for identifying it.

2. The soul is just one's mind or mental identity, but sometimes we call it the wrong name for poetry's sake, especially when a person has died and we want to be reverential. In support of this, notice that "psyche" is a synonym for both "soul" and "mind". By the transitive property of equality, we can derive ... nothing, because synonymy isn't equality. Still, they're plausibly the same.

3. A thing has a soul precisely if we attribute moral decision making capacity (agenthood) or moral value (patienthood) or both (personhood) to it.

Serious proposals:

1. The soul is the moral or immoral content of personality. The soul of a person is the set of stable traits or tendencies of decision-making which we call virtues and vices. I'm not sure how much of personality could be called morally neutral in contrast with this. Maybe the soul is just personality and "morally-charged personality" is redundant? Not sure either way.

2. The soul is what motivates us to moral action or inhibits us from immoral action. If the excitatory component, which works by inspiring pride through self-praise, is called "ego" and the inhibitory component, which works by inspiring guilt through self-shame, is called "conscience", then the soul is just the combination of ego and conscience.

3. The soul is the capacity to valuate behavioral policies. We could say that every formal decision theory is a different soul architecture. Similarly, but with a little more psychological realism, we could say that the soul is the set of human emotive valuation mechanisms, which I've taken to categorizing as liking/disliking, wanting/dreading, and approving/disapproving. In contrast with those two capacities of valuation, I think it's abundantly clear that the soul, if anything, is not a set of valuations itself: the soul is not a utility function of any stripe.

4. The soul is the unconscious mind viewed as a separate person. Like everything else, this is largely done through the use of the unconscious mind.

-

I'm glad that I've explicated these hypotheses. Some of them feel a little plausible. Still, maybe soul rhetoric should be left to the super-naturalists. In the absence of feedback from other naturalists, I guess I'll just see what word choices I make in the future and that will be a telling sign of whether these ideas have led me to believe that the word "soul" is a useful word with a clear enough natural referent.

Edit 1: I found myself using the world "soul" to refer to the part of myself which (at the least) reaches profound conclusions about the value of my behavior, where profundity means something like "possessing strong emotive force". So that's cool. The soul reaches emotional conclusions or suggests them to us for conscious consideration.

But what is "strong emotive force" really? I understand intense emotion, but what's that "force" word doing there? It's some persuasive influence on our decision process, clearly. Maybe it's like getting angrier as you prepare for a fight; it's a condition wherein you're planning and rehearsing the behaviors that you would begin performing upon adopting a belief, and then that focus and simulation somehow irrationally influences your belief, and that's the persuasion.

Or maybe emotive force is more like getting angry with someone as your suspicion grows that you would *win* in a confrontation with them. For example, you decide that their behavior is indeed immoral as you realize that other people would agree with your assessment and support you in criticizing and standing up to your opponent.

More generally, suppose there's a contemplated belief, an emotion that you would feel upon adopting the belief, and a course of behavior which the emotion generally promotes to attention. When you judge that the promoted behavior would be good in your situation, then you've got an emotion waiting to flare up, and so the contemplated belief is associated with the possibility of a strong justified emotion, and that may be enough to convince you to adopt the belief and take the adaptive action, regardless of other evidence which should weigh upon our consideration of the belief. So, again, briefly: we see a valuable behavior, we want to have a reason to perform the behavior, and sometimes that's enough to sway our judgement and convince us that we do have reason. And sometimes the behavior is not "fight" but "keep your head down" and the belief is "you're not so special" and the emotion is shame. Omission and inhibition can have moral force too. Or, in a domain other than interpersonal confrontation, the soul might lead you believe that someone is worthy of moral consideration because it calculates that expressing that belief would be politically advantageous for you, and then we call the moral force "empathy".

I kind of like this hypothesis for it's naughtiness: the soul is preconscious, epistemically irrational, and politically motivated. The soul might give us our sacred conclusions, but it's operating principle is calculating and profane. Unconscious motivated cognition, folks. I'm calling it Serious Soul Identification Proposal #5. Best one yet, I'd say. In the top five at least.

Edit 2: On twitter, one Hope S. suggests that her lack of soul is related to her not finding inspiration in seeing a flower growing up from cracks in the pavement. Perhaps a soul is "the ability to be inspired by things like stories of perseverance through adversity".
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Giving You Heads On An Unmade Bed

To the tune of "Chelsea Hotel #2" by Leonard Cohen
-
I remember you well looking at a brain cell;
You were talking of mental elites.
Joining up neural threads from all of their heads,
Oxygenating them with your heartbeats.

You were the brain child and I the brain stork,
Delivering tissues and skulls in the flesh.
And you always knew when I'd bundled them wrong
Because the grey matter wasn't quite fresh.

Then you got away - Didn't you, babe? -
From the normal bell curve of the crowd.
In a few short days with Cas9 endonuclease
You'd augmented and then jumped to the cloud.

I remember you well, looking at a brain cell;
You were famous, your mind was a legend.
You told me again you preferred genius men,
But for me you would make an exception.

You pulled my hips close. I put a hand on your blouse,
But you had in mind something hotter.
Live electrodes snaked in, deep under my skin,
And pierced through my brain's pia mater.

I don't mean to suggest that I served you the best.
I can't keep track of each sub-personality.
I remember you well, looking at a brain cell,
And that's all I've become in your mental plurality.
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Generating Meaningful Sentences

When we model the English language statistically and then use our learned model to make new sentences, we get meaningless garbage. It's a little disappointing; we'd like our computers to say intelligent things to us instead.

Is there a test that we can run on sentences to see if they're meaningful, so that we can save ourselves some disappointment and only look at model outputs which pass that test?

One answer is "No, we can't". There are lots of languages that could be formed from English words, and a given sentence could well have a different meaning or no meaning in each of these languages. But of course we don't care about possible languages that associate words and meanings: we care about the specific language that we already have and share, and its associations between words and components of the world.

Perhaps we feel that we should be able to algorithmically determine what a sentence is talking about just from language usage data. Having no vision and no instilled linguistic faculties, a competent newly born AI should still be able to reason about atmospheric optics from reading the Wikipedia article on Rayleigh Scattering, should it not? With enough deep thinking? AIXI could do it, presumably! Why not my shitty Python program?

And indeed, amazingly, we *can* translate between languages using just language usage data - even using just mono-lingual non-parallel corpora we can do this! - without modelling the associations that languages make between words and the world as it presents to our sensors.

But if our conventional statistical methods paired with merely terrestrial amounts of data and computing resources can't reliably make sentences from scratch that meaningfully refer to the world, well, that's not so unreasonable. It's a hard task. And it's not so tragic, either: all that we need in order to make Language Generation meaningful is to jointly model the world and language. We just have to get our programs to look at things while people talk about them and then our programs can be "grounded", and they too can talk about things while looking at them. We know it can be done in some circumstances: AI programs right now can label images with grammatical sentences and paint new images from sentence prompts. We have not yet foreseen the date when AIs will be able to talk about more abstract concepts like justice as fluently as they can already talk about the colors of birds' wings, but we will get there or be killed trying.

I suspect that the language grounding literature to date is all about grounding language in sensory categories, which are different from concepts. There are some fairly simple sensory categories for "mother" such as "a woman who is seen caring for children that look like her and her mate", while the concept of "mother", which is more complicated and built on top of the sensory category, can involve inferences to unseen events in the woman's history like "childbirth" or "adoption". Concepts are just one step on the path to intelligent language generation, but my hope is that the first step alone (sensory grounding of language terms) is enough to generate lots of meaningful speech, if not intelligent speech.

While present research in language acquisition almost uniformly leverages parallelism between a linguistic source and a sensory channel, maybe the task can even one day be done with merely non-parallel visual and linguistic data streams, as we are just now learning that translation can be done even without a corpus from each language which is parallel to the other in meaning at the sentence level.

Below are some titles of academic papers that I'm looking forward to reading soon which I think are relevant to the project of meaningful language generation. Not all of them are about grounding language acquisition in perception: I do still have some hope that language can be grounded in itself so to speak: that usage data has a good amount of as-yet-uncaptured structure that can be used to constrain language models so that they only output sentences which are sensical (if not sensorially referential). In particular, selectional restrictions and subcategorization frames are really cool to me and I want to play with them and see if they can help me to make broad sensical grammars.

* A Cognitive Constructivist Approach To Early Syntax Acquisition
* A Comparative Evaluation Of Deep And Shallow Approaches To The Automatic Detection Of Common Grammatical Errors
* A General-Purpose Sentence-Level Nonsense Detector
* A Neural Network Model For Low-Resource Universal Dependency Parsing
* A System For Large-Scale Acquisition Of Verbal, Nominal And Adjectival Subcategorization Frames From Corpora
* Combining Language And Vision With A Multimodal Skip-Gram Model
* Detecting Grammatical Errors With Treebank-Induced, Probabilistic Parsers
* Ebla: A Perceptually Grounded Model Of Language Acquisition
* Experience-Based Language Acquisition: A Computational Model Of Human Language Acquisition
* Exploiting Social Information In Grounded Language Learning Via Grammatical Reductions
* Grounded Language Acquisition: A Minimal Commitment Approach
* Grounded Language Learning From Video Described With Sentences
* Grounded Language Learning In A Simulated 3d World
* Integrating Type Theory And Distributional Semantics: A Case Study On Adjective–Noun Compositions
* Interactive Grounded Language Acquisition And Generalization In A 2d World
* Learning Perceptually Grounded Word Meanings From Unaligned Parallel Data
* Learning To Connect Language And Perception
* Parser Features For Sentence Grammaticality Classification
* Reassessing The Goals Of Grammatical Error Correction: Fluency Instead Of Grammaticality
* Selection And Information: A Class-Based Approach To Lexical Relationships
* Solving Text Imputation Using Recurrent Neural Networks
* The Generality Constraint And Categorical Restrictions
* Unsupervised Alignment Of Natural Language Instructions With Video Segments

Why don't I have a bunch of references to Deep Learning papers like "Generative Adversarial Text To Image Synthesis"? Because I read what I want. Or I don't read what I want, but I make a blog post about what I kind of want to read so that I can close some of these browser tabs.

But let's get back to the main question: is there a test that we can run on sentences to see if they're meaningful? Well, if you ground an agent's language faculty, then it will understand some sentences and not others, just as I understand lots of English sentences but my eyes lose focus when I hear people talk about category theory. So by grounding an agent's language usage, we can push back the question of "Is this sentence meaningful?" to the questions of "Is this sentence meaningful to the agent?" and "Is the agent conceptually fluent in this domain?". If the agent is well versed in the plumage of birds but doesn't have a good guess for the meaning of a sentence that mentions feathers, then we can suspect that the sentence is semantically ill-formed, even if a syntactic parser tells us that the sentence is grammatical. That leaves us with a problem of judging to what degree an agent is conceptually fluent in a domain and a problem of how to handle sentences in domains where our agent never becomes fluent (for example, because a conceptual faculty is required, whereas the agent only has sensory categories).

Right now I just want to read some papers and write some code and see what I can do when I commune with the spirit of the academic times. I'll let you know how it goes. Take care of yourselves.
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Finding Short Rubik's Cube Codes

When you see codes for the 3x3x3 Rubik's cube, they're generally used for manipulating the top layer while keeping the lower two layers intact. I'd like to discover all of the last-layer algorithms for various short lengths.

6-Move Codes
There aren't many at first. If we constrain ourselves to a set of 18 moves consisting of clockwise quarter turns of the six faces, (U, D, L, R, F, B), counter-clockwise quarter turns (denoted by appending a typewriter apostrophe ' to the letter of the turned face), and half turns (for which we append a 2), then even though there are 18^6 distinct sequences that are six moves in length, there are, up to rotations and mirror reflections, only two last-layer algorithms among them:

<F  U  R  U' R' F'> and its inverse <F  R  U  R' U' F'>

7-Move Codes:
What about codes that are 7 moves in length?

Let's normalize our presentation of codes in the following way:
  • If a code's first move is on one of the faces (L, R, or B), it should be transformed by rotation into a code that begins with a turn of the F face.
  • Any code which then begins with F' should be transformed into one that begins with F through a left-right reflection.
  • What about codes that begin with F2? A left-right reflection won't change the first move, but it will change any quarter turns that show up later in the move. If a code begins with F2 and contains a quarter turn later on, prefer the left-right variant for which the first quarter turn is made to be clockwise rather than counter-clockwise.
  • Any code that has a turn of the U face at its beginning or end should have those moves simply cut off.
  • Any code that begins with a turn of the D face should have that turn moved to the end.
  • Any two successive turns on the same face should be combined into one turn, and they should also be combined if they're only separated by a turn of the (independent) parallel face.
  • I haven't added this into my normalization procedure yet, so the codes below might not adhere to this rule, but if a code has two successive moves on opposite faces, the two moves can be swapped without changing the result, so perhaps we should establish some ordering (such as U, D, L, R, F, B), and prefer that opposite faces occur in that order, unless the reverse order would result in a reduction according to one of the other rules. For example, "U D" would be preferred to "D U" in the interior of a code, but if "U D" appeared at the end of a code, then by switching to "D U" we could shorten the code by removing the U turn.
Using those normalization rules, there are 5 distinct last-layer codes in 7 moves. These are

<F  U' B' U  F' U' B > | The inverse of which, in normal form, is same code.
<F  U2 F' U' F  U' F'> | <F  U  F' U  F  U2 F'>
<F  R  B' R  B  R2 F'> | <F  R2 B' R' B  R' F'>

Again, this is kind of weird: the number 18^7 is much bigger than 5. It's not as if the number of distinct last-layer configurations (about a thousand, depending on which symmetries you ignore) is the real limiting factor, because I would happily separately count two codes that produced the same configuration. There are just very few sequences that are codes. Oh well. At least it's an easy set to memorize.

8-Move Codes:
How about codes in 8 moves? Surprisingly there are just 19.... probably. The program that I ran in order to find these had a stupid optimization which might have skipped a valid code or two. My guess however is that these are the full set.

<F  R  B  R' F' R  B' R'> | <F  R  F' L  F  R' F' L'>
<F  R  B  U' B' U  R' F'> | <F  R  U' B  U  B' R' F'>
<F  R  B' R' F' R  B  R'> | <F  R' F' L  F  R  F' L'>
<F  R' F  R  F2 L' U2 L > | <F  U2 F' L2 B  L  B' L>
<F  R' F' L  F2 R  F2 L'> | <F  R2 B' R2 F' R  B  R'>
<F  U  F  R' F' R  U' F'> | <F  U  R' F  R  F' U' F'>
<F  U  F' L' B' U' B  L > | <F  R  U' R' F' L' U  L>
<F  U  F' U' F' L  F  L'> | <F  R' F' R  U  R  U' R'>
<F  U2 F' U2 F' L  F  L'> | <F  R' F' R  U2 R  U2 R'>
<F  U  F2 L  F  L2 U  L > | Whose normal-form inverse is the same.


I wish I could say which of these are newly discovered and which are known. Probably all are known, given how small the set is and how much computing power has been thrown at Rubik's cubes, but it's hard to know. People online don't put their codes into normal form, so even if Google can't find one of my codes online, maybe that just means someone has posted a transformed version of it.

9-Move Codes:
How about Last Layer codes in 9 moves? I really don't have any guess as to the size of this set. The search space is huge. If I were to limit myself to codes where each face besides U had face turn conservation (that is, the turns to each face must add up to 0 modulo 4, counting each counter-clockwise turn as -1), then I think I could find all such Last Layer codes in a few days. Maybe I will. It would be pleasing to know that I had exhaustively found all 9-move codes even in that restricted class.

Here are the 9-move normal form codes that I have so far - 76 in total, but I still need to filter out a few equivalent codes that remain unnecessarily due the fact that I haven't yet normalized the order of successive moves on parallel faces.

<F  B' U  R  U' R' F' U' B > | <F  U' B' R' U' R  U  F' B >
<F  B' U' R' U  R  B  U  F'> | <F  U' B' R' U' R  U  B  F'>
<F  D  B2 D' F  D  B2 D' F2> | <F2 D  B2 D' F' D  B2 D' F'>
<F  D2 B2 L  U2 B2 D2 R  F > | <F  L  D2 B2 U2 R  B2 D2 F >
<F  D2 B2 R  B2 D2 F2 L  F > | <F  R  F2 D2 B2 L  B2 D2 F >
<F  L' U2 L  U2 L  F2 L' F > | <F  R' F2 R  U2 R  U2 R' F >
<F  R  B  U' B' U2 R' U' F'> | <F  U  R  U2 B  U  B' R' F'>
<F  R  F  U  F' R' F  U' F2> | <F2 U  F' R  F  U' F' R' F'>
<F  R  U  R' F' U  F  U2 F'> | <F  U2 F' U' F  R  U' R' F'>
<F  R  U  R2 F  R  F' U' F'> | <F  U  F  R' F' R2 U' R' F'>
<F  R  U' R' F' U' L' U2 L > | <F  U2 F' U' L' B' U' B  L >
<F  R  U' R' U  F' L' U  L > | <F  U  F' L' U  B' U' B  L >
<F  R  U' R' U  R  U  R' F'> | <F  R  U' R' U' R  U  R' F'>
<F  R  U' R' U' F' L' U  L > | <F  U  F' L' U' B' U' B  L >
<F  R  U' R' U2 F' L' U  L > | <F  U  F' L' U2 B' U' B  L > 
# Both of the above are equivalent to <U2>. That's a trivial result, but they're still very pretty codes.
<F  R  U' R' U2 R  U  R' F'> | NF-inverse is the same.
<F  R  U2 B  U  B' R' U2 F'> | <F  U2 R  B  U' B' U2 R' F'> 
# The above are equivalent to <U> and <U'> respectively.
<F  R' F  L2 F' R  F  L2 F2> | <F2 R2 F  L  F' R2 F  L' F >
<F  R' F  R  F2 U  L' U  L > | <F  U  F' U  L2 B  L  B' L >
<F  R' F  R2 B' R  B  R2 F2> | <F2 L2 B  L  B' L2 F  L' F >
<F  R' F' U' F  U  R  U' F'> | <F  U  R' U' F' U  F  R  F'>
<F  R' F2 L  F2 R  F2 L' F > | NF-inverse is the same.
<F  R2 B' D  B' D' B2 R2 F'> | <F  R2 B2 D  B  D' B  R2 F'>
<F  U  F  D  F' U' F  D' F2> | <F2 D  F' U  F  D' F' U' F'>
<F  U  F' L' U  L  F  U' F'> | <F  U  F' L' U' L  F  U' F'>
<F  U  F' R' F  U' F' U  R > | <F  U  R' U' R  F' R' U  R >
<F  U  R  U2 R' F' L' U  L > | <F  U  F' L' B' U2 B  U  L >
<F  U2 F  D  B' R2 B  D' F2> | <F2 D  B' R2 B  D' F' U2 F'>
<F  U2 F  D  F' U2 F  D' F2> | <F2 D  F' U2 F  D' F' U2 F'>
<F  U2 F' L  F' L' F2 U2 F'> | <F  U2 F2 L  F  L' F  U2 F'>
<F  U2 F2 U' F2 U' F2 U2 F > | NF-inverse is the same.
<F2 D  B' D' F' D  B  D' F'> | <F  D  B' D' F  D  B  D' F2>
<F2 L2 R2 B2 D  B2 L2 R2 F2> | NF-inverse is the same.
<F2 L2 R2 B2 D  F2 L2 R2 B2> | <F2 R2 L2 B2 D  F2 R2 L2 B2>
<F2 R2 F  L2 F' R2 F  L2 F > | <F  R2 F  L2 F' R2 F  L2 F2>
<F2 R2 L2 B2 D  B2 R2 L2 F2> | NF-inverse is the same.
<F2 U  L  R' F2 L' R  U  F2> | NF-inverse is the same.
<F2 U  R' L  F2 R  L' U  F2> | NF-inverse is the same.
<F2 L  F  L' U' F2 R' F' R > | <F  R' F' R2 U' B' R  B  R2>
# The above are both equivalent to <U'>.
<F  L  F2 L' F  U  F2 U' F2> | <F2 U  F2 U' F' L  F2 L' F'>
<F  U  F' L' U2 L  F  U' F'> | NF-inverse is the same.
<F  R' B2 R  F  R' B2 R  F2> | <F2 L  B2 L' F  L  B2 L' F >

Gosh, that was fun. If you know of someone who's already done or even started this work, please do let me know.

EDIT: While testing for remaining 9-move codes, I did some online searching and found a handy little github repository from Lars Petrus containing a (large) text file with all possible Last Layer algorithms up to fifteen moves here. After normalizing those, I was pleased to find that there were no codes in fewer than 9 moves that I had failed to find, and that for codes of exactly 9 moves, there were only 4 new pairs:

<F  R2 B' R' B  U  R' U' F'> | <F  U  R  U' B' R  B  R2 F'>
<F  R2 D  R  D' R  F2 U  F > | <F  U  F2 L  D' L  D  L2 F >
<F  R2 D  R  D2 F  D  F2 R > | NF-inverse is the same.
<F  U  F' L2 B  L  B' U' L > | <F  U' R' F  R  F2 L' U  L >

None of those violate face turn conservation except in the U face, so I would have found them all eventually, though it would have taken days, and I wouldn't have had this warm satisfaction of knowing that I was done with the project. I'm free!
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The Meaning Of Identity

What is identity? It's a long story.

Ascriptions of identity happen in the mind at the level of conceptualization, and not at the lower level of perception. While perception supports a faculty of categorization which is invariant to many sensory perturbations, such as lighting conditions and partial occlusions in the case of vision, this categorical invariance with respect to sensory perturbation is not the same as object identity.

Even the recognition of objects is not the same as recognizing them as having comparable identities. A mind can know about objects, as parts of a data stream which can be modeled separately, and yet still not know about their physical separation, persistence, or identity. Let me explain.

I was trying to imagine different ways an AI could analyze a video in order to tease out my implicit ideas of how the mental processes of conception differ from and build on perception. Here's the hypothetical: An AI could have an assumption of persistence for some features, like that there will keep being a bird with a bowler hat in each successive frame of the video, and not assume persistence in other features, like the AI could be unable to guess that the bird has a cane behind its body which was seen in a previous frame.

Is this AI seeing samples from the class of "bowler hat birds" and not relating them across times? Or is it successfully forming a very limited concept of identity whose only identity criterion is "be a bird with a hat"?

The answer could be either one, depending on the details of the AI, but pondering that question led me to a description of what it means for an agent to identify a thing as existing in two percepts rather than for it to merely make the same sensory categorization about the contents of the two percepts: Percepts of two instances of a category (two different bird pictures) have similarities which are genetic (arising in the past, after which the things could go their separate ways and never meet each other or their maker again) while two views of one object have similarities because of persistence or conservation (locally, spatially, through intervening times). "This bird" isn't the very narrow category of "birds with all features presently observed to be persisting". "This bird" differs from "a bird just like this" in that the mind assumes an intervening history transforming the features observed in or inferred from one percept into those features observed in or inferred from another percept.

If the AI has no conception of identity, it will just see a sequence of samples from the category of Bowler Hat Birds, and the AI will having nothing to say on whether they're the same or different birds. Despite having learned persistence of features and sensory categorization, it will not have learned Identity, and the question of whether the bird in the second frame has a tiny cane behind its back will be answered at some ignorant base rate (for birds or for canes, about which the AI could well reason separately). If the AI does have a notion of identity, then it could tell us it sees a sequence of different Bowler Hat Birds or one persisting Bowler Hat Bird, depending on its personal categories. But whether it sees them as the same or different, that judgement will be based on whether it suspects there was a causal history in which the objects depicted in the first video frame became the object in the second video frame. If such a transformation is plausible, and would not have entailed the destruction of the tiny cane, then hey presto, we have a plausible inference at the level of conceptualization enabled through through the ascription of identity.

In summary, objecthood at its lowest level might be interpreted as something like learning separation of background and foreground in a sensory stream. Learning that the feature values of an object or the sensory categories of an object are persistent in time is not enough to license other inferences across time which Identity allows, such as supposing that this bird has a tiny unseen cane behind its back. Maybe that's not impressive to you because the AI could have learned object persistence for the cane too, but Identity also lets us do counterfactual cross-temporal density estimation for unobserved features of the bird: like if she has cancer in one frame, she'll probably still have cancer three seconds later. And finally, Identity means supposing a local transformative history (as an explanation for the similarities which allow cross-temporal density estimation) rather than a genetic similarity of the category (in which case observed dissimilarities could be written off as within-category variance).

So that's a good start at what I think Identity is. It might be more complicated. Maybe it can only be the same Bowler Hat Bird in the second video frame if the hat stayed on the whole time between frames. If so, would that specifically be part of the criterion of identity for Bowler Hat Birds, or does continued identity require continuity of identity generally? I don't know. Hard question. Important question. Not for tonight.
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Simple Songs For Sarah Sparks

Here are some songs I like, which, if I've sorted through them well enough, can be played on guitar without using any barre chords. Some of the chords do require four fingers, like A/C# and D7/F#, but for these, you can just leave out the bass notes that follows the slash. "Slip Sliding Away" does technically have one barre chord, an F Major, but it doesn't occur during a singing part, so that could also be skipped, I'd say.

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