Language and the Art of Theory Maintenance

Ok sorry about that.
It's just that I figured out the Fukawe bird is the Norwegian Blue.

I mean in Einstein's puzzle, one of the nationalities lives next to the blue house.
He's the Norwegian. This clue is the pivoting relation in the color-symmetry, which is pentagonal. Pentagons are dodecahedral and so is the Mathieu group.
What I need to do in practice is show that the problem can be encoded in a way that generates the M12 group (or even a subgroup).

But that's neither here nor there - the thing is the problem is one of the SAT kind, called NAE or not all equal, to do with finding an order in sets of partially ordered elements.

Sorta like switching a phone call through a network, but deterministically. I would really like to know when he wrote it, I have this idea it was when he was at the Polytech,.
The Prolog code I found is problem-specific ("find the fish owner") so a general version might mean I can "slice" the problem better.

I'm sure he was thinking about something else, you see, that is also 5-dimensional. If this is true the clues could be relevant to the kinds of problems he thought about - his ideas of tensor calculus possibly. He may have been able to categorize things physical and abstract more efficiently.

The problem is supposedly Mensa level - if you can't solve it on paper you get the wooden spoon, you are officially dumber than Einstein.

So now, is the parrot dead?

 

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Time to go hard.

I see some posters who might be young people asking about calculus, or the Schrodinger equation.

Calculus, is a word direct from a Latin dictionary, where it means "counting stone". In differential calculus you find a sum of terms which are parts of the whole problem. In the case of a traveling salesman problem the calculus is a graph with a path through it, that does not visit any node twice.

This is another NAE type of problem, in which none of the edge-transitions in the graph are equal, so there must be sufficient transitions in it that no edge is traversed more than one either. The problem is satisfied if such a path can be found.

The calculi in the cube-solving (or pattern-making) problem, are the black and colored elements made of PVC plastic. We know that black isn't a color, and that "colorless" also applies to transparent material. White light divides into a spectrum, and we partition it (we can do this and make a color-symmetric circle or wheel). We see more than the colors blue and yellow, because of a pigment that absorbs red in our visual system.

The light from the average computer screen is at optical infinity for the lenses of most people's eyes at a distance of 0.3-0.5 metres. If there is an animated figure on the screen (the light pattern changes in time) it moves in an XY plane, perpendicular to your line of sight, The calculus here is the sum of all the pixels, at any small interval of time dt.

These are actually rapidly switched transistor elements or possibly plasma or phosphor based, but the mechanics is the same.
In each case a transistor controls the current or voltage to brighten the element so it emits more or less light, at subperceptive frequencies (>70Khz is too rapid for mammalian eyes to notice). Current intensity and voltage level control pixel intensity and background, The transistors are closely manufactured to be as identical as possible. The addressing of pixels row and column wise is the tensoring of the equal-volume but variable capacitance (red, green, blue) of fixed partitions of electric charge.

The electronic solution is normalised to strings of 1 and 0 addressing that "refresh" the matrix. The extrinsics are your retinal cells at infinity for the colors, and the screen is like a kind of artificial prism that scatters white light into a spectrum, or rather a matrix of small prisms that "bend" light.

The symbology used formally in mathematical calculus and physics is something you can abstract (more easily than you might think) to computer programming and computer science. This is not that surprising because computer science is applied mathematics, or at least a field of it. Not many mathematicians do not use computers, and indeed computer models of the Rubik's cube appeared almost as soon as it did.

If you can write a program that simulates a physical system, it's also a calculus of the problem. Here the counting stones are the steps in real time the computer will need and the amount of memory in real space it will use to calculate the answer(s). Simulating the cube puzzles means the actual physical rotations become redundant.

The redundancy in the full group is I believe the most fundamental calculus, and the most fundamental element is a black one next to a colored one.

Calculus often finds a way to count from both ends of a sum - or what CS calls top-down, bottom-up parsing. In functional programming languages, the "way" is a function that can traverse a list from head to tail or reverse this. List reversal is a common tool in functional programming, because it allows forward recursion with backtracking.

If you can learn how to program some problem in GAP, say, you should get a better idea about this calculus thing. If you learn a programming or coding language you are also learning a calculus. In pure math the languages are restricted to conventional symbols and grammar, which must be context-free and unambiguous. Coding allows few of these rules to be broken, in fact a grammar which is not either strictly typed or bound by rules of compilation isn't very useful.

So there are rules of computation, which are primarily Boolean logic. One of the least logical things about this is that it's affine, which means it can't be universal (it isn't free).

 

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What does "free" mean in the context of logic? We choose things axiomatically, the permutation puzzles and symmetries they have exist because of this freedom (to choose a geometry and color it).

The ideas of opacity and clarity are used in conjunction in Boolean logic, or any predicate calculus.
Black is opaque and clear is transmissive - clarity, the lack of opacity is how few attributes remain hidden - if these are all irrelevant to the answer we choose (the "important" one) then they can be "black".

Black is color-blocking, and clear is color-sending. Transmission is the sending, so blocking a whole puzzle means leaving it black (or covering all the facets with the same color, which will be a "new" black in that case).

Therefore in Rubik's original puzzle ca 1980, transmission is the relocation of 1/3 of a layer at a time (turn), over adjacent face-groups of layers. Blocking is both "being black" since color is blocked, and simply rotating one layer continuously, or equivalently leaving it skewed. The original can "spin" two layers at once, if the third is fixed somehow. Like say, the D layer is held in a frame which is at rest.

So "black/block" and "clear/transmit" are the color relation to the computational logic here.

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When you look at something like the above picture on a computer display, you see colors.

Color vision is a function of certain pigments arranged in retinal cells, and also the function of those cells and neural signalling.

Color is a common physical reference, we have it because "evolution with common descent gives mammals trichromatic vision, which is an adaptation".
Or we see color because it's an advantage to the survival of our species. So colors are a default "labelling" we use. Spectra are a function of the visual system's capacity to respond to light at different frequencies and intensities.

White is a "balanced" response, that abstractly we can say is continuous neural output from all three kinds of cone cell, so the visual system registers equal amounts of red, yellow and blue light. Black is no response, so represents the "body" of color in terms of black body radiation (not temperature). This is true because a flourescent light source can output light with a higher frequency than an incandescent light source, but the latter depends on thermodynamic heating of a thin metal filament,

Black plastic is the "Planck line" for the colors, in the above figure. Colors are in fact a complex phase space of frequency and amplitude, damping and "interference", and surface-effects (butterfly wings, beetle shells, iridescence, ...); colors are an Hilbert space H_color, with infinite dimension, in fact.

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So the puzzles are a heuristic for the rotations of parts of the structure - if there is only black (no color response) the device can only output an infinite string of "b", or bbb... to infinite rotations (r). The rotational symmetry is extended by being partitioned with colors, since there is a simplex "under b". Or black is any point at an apex of the figure.

"Common descent" into G (using an agreed color-protocol) has to adapt the branching factor that combining b with c, c', ..., gives the structure - there is zero branching with a sequence bbb..., you have to partition this.

The maximum branching factor is conditional on the number of colors used: if you use the same number of colors as there are elements, you only replace bbb... with cc'c''...

In the case of the above 2x2x2 structure, there are 3,674,160 combinations of 24 different colors, for instance. It's easier to tell these apart with fewer colors - divide 24 by 4, say, the number of elements per face.

 

Another thing that's occurred: Einstein stuck with the idea of a general form of radiation as a photon gas, moving through a frictionless adiabatic fluid.

These days we also have the idea of packets of information (photons as bits) traveling down a channel. Information is both the message that a channel exists (even if nothing is sent or received), and the content a channel can deliver--even in principle. So that information is also a form of energy, and since energy is also massless, massless information exists as momentum energy. If this were a false proposition we wouldn't have optoelectronics and LEDs.

As to equivalence: the equivalence of mass and energy is characterized by the free energy of radiation, which is massless and for which, time is irrelevant.

The time-relevance of massive energetic forms of energy is that they have the greatest probability of being relevant, when they have zero relative velocity. So relative velocity, which changes inertial mass, decreases the time-relevance or the observational "suchness" of any mass-energy, as its kinetic energy becomes more relevant.

On the other hand, photons have zero mass-relevance, but a probability of being energetic enough that they gain (create) mass, by splitting into a particle-antiparticle pair. Thus relevance, for a massive body at rest, is time-dependent, and the relation is to kinetic energy; for a massless body which cannot be at rest, with fixed kinetic energy, the relevance is the information content.

So that momentum energy is always a carrier, it can carry massless frequency or massive kinetic energy, the only problem in retrieving the information is determining the baseline.
This is always a local timebase, and observations are always in terms of space and time, which are respectively coordinates and relative changes in them.

 

Have you heard of "the vocabulary of alarm"?
Vervet monkeys for instance, use different sounds for different predators. If you record all the alarm sounds that a vervet monkey makes, hide it in a bush and play it, "snake" makes them look at the ground, "eagle" makes them look up and "leopard" makes them run for the hills, or trees.

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Some animals make subtly different sounds for different animals - prairie dogs, for example, will describe a human in a blue shirt differently from a human in a yellow shirt. Meerkats will announce both the type of predator and how close it is. Chickadees from North America will inform their neighbors if a predator is resting or flying. Since pygmy owls are more likely to eat their babies than horned owls, they will kick up way more fuss if they see a perched pygmy owl than if they see a perched horned owl.

Further and way more interesting, other animals can also decode these warning signals. Diana monkeys for example, don't use the same sounds for leopards as Campbell monkeys, but they respond to the "leopard" sound that Campbell monkeys make in the same way as they respond to the "leopard" sound that Diana monkeys make. Yellow casqued hornbills, who are not prey for leopards, will ignore the Diana monkey when he shouts "leopard" but will react when he shouts "eagle"

Not only that, the predators also recognise these calls, after the Diana monkey calls "leopard!", the leopard will also come out of hiding and walk away.

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Cool, huh?

So how do they know what the sounds mean? Is it innate or experience? Probably both. Young vervet monkeys will scream "snake" at long thin sticks on the ground and "eagle" at any flying bird or falling leaf.

Sources:

For vervet monkeys responding differently to different alarms, and for young vervets being trigger happy, see Seyfarth, R. M., Cheney, D. L. and Marler, P. 1980. “Monkey responses to three different alarm calls: evidence of predator classification and semantic communication.” Science 210: 801-803; for a more lengthy, and fascinating, discussion of all this, see Hauser, M. D. 1996. “The Evolution of Communication.” MIT Press. (The description of a young vervet being smacked by its mother for making the wrong call is given on page 309.)

For Diana monkeys making different sounds for leopards and eagles, see Zuberbühler, K., Noë, R. and Seyfarth, R. M. 1997. “Diana monkey long-distance calls: Messages for conspecifics and predators.” Animal Behaviour 53: 589-604. For the same phenomenon in Campbell’s monkeys, see Zuberbühler, K. 2001. “Predator-specific alarm calls in Campbell’s monkeys, Cercopithecus campbelli” Behavioral Ecology and Sociobiology 50: 414-422.

For human shirt colors being announced by prairie dogs, see Slobodchikoff, C. N., Paseka, A. and Verdolin, J. L. 2009. “Prairie dog alarm calls encode labels about predator colors.” Animal Cognition 12: 435-439. For meerkats giving information about predator type and the urgency with which listeners should respond, see Manser, M. B., Seyfarth, R. M. and Cheney, D. L. 2002. “Suricate alarm calls signal predator class and urgency.” Trends in Cognitive Science 6: 55-57. For different call types in black-capped chickadees, including assessments of predator danger, see Templeton, C. N., Greene, E. and Davis, K. 2005. “Allometry of alarm calls: black-capped chickadees encode information about predator size.” Science 308: 1934-1937.

For an interesting discussion of the difficulties in interpreting animal noises, see Hauser, M. D. 2000. “A primate dictionary? Decoding the function and meaning of another species’ vocalizations.” Cognitive Science 24: 445-475.

For Diana monkeys understanding the calls of Campbell’s monkeys, see Zuberbühler, K. 2000. “Interspecies semantic communication in two forest primates.” Proceedings of the Royal Society of London B 267: 713-718. For yellow-casqued hornbills tuning into Diana monkey shouts of “eagle!” but not “leopard!” see Rainey, H. J., Zuberbühler, K. and Slater, P. J. 2004. “Hornbills can distinguish between primate alarm calls.” Proceedings of the Royal Society of London B 271: 755-759.

For leopards giving up when they realize they’ve been detected, see Zuberbühler, K., Jenny, D. and Bshary, R. 1999. “The predator deterrence function of primate alarm calls.” Ethology 105: 477-490. For an excellent general overview of what we know about alarm calls, see Zuberbühler, K. 2009. “Survivor Signals: The Biology and Psychology of Animal Alarm Calling.” Advances in the Study of Behavior 40: 277-322.

For Gunther’s dik-dik responding to calls of the go-away bird, see Lea, A. J. et al. 2008. “Heterospecific eavesdropping in a nonsocial species.” Behavioral Ecology 19: 1041-1046. For moose that have lost calves to wolves becoming sensitive to wolf calls, see Berger, J., Swenson, J. E. and Persson, I.-L. 2001. “Recolonizing carnivores and naïve prey: conservation lessons from Pleistocene extinctions.” Science 291: 1036-1039. For a review of animals learning about predators by observing others, see Griffin, A. S. 2004. “Social learning about predators: a review and prospectus.” Learning and Behavior 32: 131-140. For an example of how pre-release predator training can help captive-reared animals to survive in the wild, see Shier, D. M. and Owings, D. H. 2007. “Effects of social learning on predator training and postrelease survival in juvenile black-tailed prairie dogs, Cynomys ludovicianus.” Animal Behaviour 73: 567-577.

 

I think the more interesting approach is to our own language development, and how we can train animals using languages that aren't "human", as in how shepherds and stockmen train dogs to respond to calls and whistles.

These are all specific to different animals in a working pack, so in other words a shepherd with a team of 6 dogs has that many individually-tuned sets of commands, for each animal to bark, stop barking, move left or right, forward or back, etc.
If they replace a dog, it will have an individual custom-made "language" the shepherd has trained it with. The commands have to be specific to each animal, of course.

So working dogs require the maintenance of a theory of animal communication, and that the owner of a dog team knows this language well enough to be the alpha male, and lead the pack. Dogs are animals that seem quite happy with this arrangement--maybe the only animals that are this easy to control in a "linguistic" way...

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The segue here is towards scientific theories and the languages they use--how are ideas maintained when languages change? Do we think of something like color differently because nowadays we know about quantum mechanics, and computer screens??

 

Actually, I'd rather understand what animals are saying. Knowing their language should make it easier to communicate, yes?

Think of it this way, the Campbell monkeys are not insisting that the Diana monkeys or the yellow casqued hornbills speak their language.

There is an important lesson right there.

 

Hmm. I wonder if animals understand humans and noises they make.
[..if they havent been domesticated and trained to respond]

Studies apparently indicate that there is one form of human language and communication, that most other animals--even our closest relatives in the evolutionary tree--aren't interested in, which is what we call music. Birds are believed to be "musical" but this is anthropomorphic, attributing something that doesn't (necessarily) exist.

This is also in the same kind of tread-carefully domain as humans observing animals communicating with each other. But I think it's fairly incontrovertible--if they don't communicate at some level, how do they cohabit? I would say animals in general have a "vocabulary" of some kind, which would be a necessary adaptation, since being able to warn others in the group of danger, or that food or water has been located, etc, must mean a species adapts and survives better.

Languages or noises are of course, part of the theory of maintaining a theory...

 

Didn't you give an example of this with the shepherd dogs?

You can see another example of this in Orleanders thread on the alpha male, where beggar dogs who ride the subway learn to recognise the names of stations as the conductor calls them out.

Even more fascinating is the deer who wait with pedestrians when the signal colour says stop and cross with them when it changes to walk.

 

Ok, thanks I'm not someone who has looked into this that closely or in much detail, but my understanding is that animal appreciation of human art, and music in particular are largely anecdotal.

For the most, or largest part, there is little firm evidence that animals other than humans appreciate harmonic structure and rhythm. The birds in that study may be reacting to something else than either of the two most fundamental things we identify "musically" and so we project this identity onto animal sounds and nature--a laughing stream, rustling wind, etc, even the phrase "bird song" rather than "bird language"or more general "bird calls".

At least that was my understanding, although I'm not overturned exactly by the research as such, it's just it isn't overwhelming. I think humans are musical because of our developed cortex, because simply put, the brain is rhythmical, and so, it isn't a big leap to a musical or harmonic(ally patterned) brain structure--which is neurons cooperating, to "think" etc.

Thought must also be a kind of harmonic rhythm. When you're on horseback, you think differently. Somehow you or part of your mind is aware that the animal you're sitting on is going to go where you want it to, but you have to "communicate" this; in a sense you "are" the horses mind, sort of thing.

After a while, it just sort of happens all by itself. Getting a horse to go charging up a hill, you're on the back of a "domesticated" and saddled and bridled horse, which is maybe 10 times as strong as you are, which is kind of musical I think. Once your ass gets the hang of the rhythm, and you can get it to stop charging so it doesn't wipe you off against a tree or something. Here, the musical theme is pretty obvious--something pastoral perhaps...

So there it is; there are two other kinds of mammal we share a niche with. One cooperates instinctively, the other has to be trained to by being husbanded and reared close to humans. Dogs being pack animals cooperate best in groups and farmers with working dogs are exploiting the innate group behaviour--the dogs are hunting in a pack, with an alpha male who has "trained" them to follow "barks" and whistles; they understand commands like "up" "down" "back" "go" "in" "out" "behind" "away" "stop" "shut up" "speak up" "be quiet", and phrases like "get into it', "stop there, Blue" etc. You may have seen how closely this association is tested, on TV shows where they have sheep penning contests, with one dog and three or more sheep, say. Pups are trained early though, like horses. Horses get a worse deal than dogs, they aren't hunting or pursuit animals instinctively. So dogs work for humans partly because they are allowed to express their natural behaviour, though not to actually attack any prey--the alpha male will provide meat from the day's hunt, they just have to be patient, and play the stupid hunting game, what the hey.

Horses usually are indifferent to being saddled or even whistled up, and prefer to be lead rather than ridden. I can recall a sense of a horse giving me some gyp (they turn and shake their head at you, as if trying to make eye contact, and you get this "when do we get there" impression) about carrying my sorry ass around, after a fairly long ride they definitely get stroppier.