Language and the Art of Theory Maintenance

Fraggle, this is more or less a direct appeal: I know you have expressed an interest in things physical - where the universe got energy from and so on, so without further prevarication, and since I feel safer appealing to an older, perhaps worldly-wiser owner of porch real-estate, what do you think of theories of language, and do you consider logic is a language in itself - possibly the "root' of language, so that, we really should discuss logic, or is that too logical?

What, for instance, does a dog tell us when it barks? Some owners can train dogs to communicate varying "bark signals" that alert the owner -most dogs have an innate sense of territory, so they bark instinctively and we just "train" ourselves, along with? When we construct such arbitrary "languages" what role does vocalization really play, in that case - seeing as how dogs don't speak American?

 

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Ok, try this: do you think the world is fairly "Carollian"? The person who wrote Alice's tales was also a mathematician - I'm convinced he must have read Spinoza, because there are so many "easter eggs" in the stories.

He used the red/blue pills as vehicles to get small enough to see a stranger world, and plenty of people today think the world looks strange when you get small enough. So linguistically, what is the least "Carollian" term you can think of that refutes this hypothesis, given you won't be able to stress any vowels or restrict them?
(I mean, you can just go "Caaaaaaaaaaa...." instead and sort of yawn all this away)

 

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About curry.

This is a "universal" function of functions.
You have to have uncurry as well, to curry some function. It's actually easier to do backwards, you imply that there is a function that "takes" a function and an argument, and returns a function of the argument.
So if you now "apply the curry" then you can "curry the apply", by saying the composition of a function, argument -> function_of_argument is an apply (function), the first is the inductive step that yields "curry".

Maybe this makes some kind of linguistic sense too (or maybe we should use less curry and more uncurry). p.s. sorry about the CS shop-talk. but I think jargon is another Carollian.
And yes, it's a bastard when you know everything.

 

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Well, ok. I just thought I'd throw the idea of currying at linguistics and functions of language.

As to the complexity or putative "structure" of what I termed an arbitrary language - I know that shepherds can train, say, a team of 5 or 6 dogs to herd sheep cooperatively, using whistles and calls. I once watched a trainee shepherd use just two dogs, a header and a huntaway, to get about 400 sheep into a corner of a 10-acre or so run. Took him about 4 minutes.

So back to the linguistic theme: Is it logical that we most probably started naming places, or each other initially? After all a place where food or water is known to exist (Aboriginal ground maps etc) would have been more important to hunter-gatherers than identifying each other with "locators", since the tribe that hunts together stays together. Naming people possibly wasn't needed until societies became more structured.

So is the name of a place, say a river or a mountain, a more significant word? Lots of nouns are also used as verbs, in English for example we use the word coordinate to mean "a place", and to mean "locating a place".
Hence the use of extensions such as coordinatize, coordinatization, to distinguish the different applications of the noun/verb, so they are "located" better. Clearly both extensions are meant to mean "apply coordinates", and "the process of application of coordinates". So they apostrophize a preposition such as "to, with, ...". Currying is like a quote function that changes or switches context - inversely apply a verbalization -, so it's fairly intuitive once you get past apply(curry).

 

No, I mean when we use the nominative form "a coordinate", it's a place.

The adjective was the past part. of the verb coordinare, which "tenses out" as coordinatus.
The ordinare, ordinatus means "to regulate, to account for" and "regular, accounted for". Hence
ordinatio, or "regularized, proper and orderly, rank & file", etc the word we get ordination from.

 

Hello, I don't know enough about linguistics to see how it is relevant, but here's what currying is:

Consider a function that takes two arguments and returns one, say,
f(x,y) = z
We can write this as
f : (x, y) -> z .

This function is considered "uncurried".

The curried version of this function would be:
g x y = z, or g: x -> y -> z .

This might seem like petty difference, but it turns out it can be a very important difference in programs. We prefer the "curried" version.

"Currying" is just the process of turning an uncurried function into an equivalent curried one.
Sorry to butt in.

 

Another simple way to look at currying/applying is using a standard algebraic-entry calculator. It's more helpful if you also have a stack-entry model that uses reverse polish.

Anyhoo, algebraically, to add two numbers x and y say, you enter (push or press keys) "x + y =" to see an answer "z".
When you press "x +" you are composing a function (x+), or "add x", then "y =" means "to y".
So you actually curry two applied functions, with an algebraic-adder, namely (x+) and (y=), the "apply" is the pressing of keys; with RPN the sequence of presses corresponds to also pushing x and y on a stack, so "x push" is applied to "y+".

So that, the "push" operator is the apply function, and the compositions are then curried together - curry(apply(f)) -> f

Simple huh? You can do this on paper too.

 

See, my thinking goes: if the apply function is universal (as far as functions are concerned), then all you need is a function and a variable.

But, of course the variable has to be within the "sight" or range of the function, and physically you can't swap metres for kilograms, so "nature" provides a set of restrictions, as far as apply() being general goes.

Greg Egan, the SF writer, raises an interesting point about observation and mathematical logic. Ultimately, the story goes (in one of his novels) there will only be mathematics. If this is true, there is only mathematics, or, all observables are ultimately numbers.

The Rubik's cube is "dangerous" because it functions in so many mathematical settings, including, as I have been trying to demonstrate, the construction paradigm. Or "you have to build a machine, to use a machine". Restricting the numbers to a built-only model is "unrealistic" you figure out eventually, so all by itself, it forces you to apply different settings and paradigms - it "vanishes" up its own spout recursively. Ultimately, there is only a cube... you are welcome my son, to the machine.

It's syllogistical and syllabical, volumetric and metered in stanzas. It's busting with computational ability all over the place, so why only "let it be a permutation puzzle"
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I want to pursue this functional Haskell Curry thing.

Note in the above example using calculators, the compositor apply() consists of pushing arguments on the stack by pushing keys. You compose the outer descriptive: "add x" as well because that's what you want the new 'operator' to do, since it's uncurried, which means "not activated yet".
The "to y" part is equivalent in the RPN to "x push" (on an HP the "push" function that sends a variable to the stack is ENTER), so the operations are reversed.
There's a swap-around because of the difference between RPN and algebraic entry.
Algebraically "add x to y" is apply((apply(x,+),apply(y,=))); in RPN it's "to x add y", the curry is equivalent to de-stacking or the "pop" or "peek" addressing op in computer languages.

Pop acts by default - you can see the whole stack in RPN, Push has to be "pushed".
So, the ENTER key is also apply(push,x)...

 

Rabbiting On

Well, the questions are, cubically speaking, what of the 4-color problem? What about Golomb's conjecture, and Baez' comment about the twist group?

Who, or what is M? M is she or he that you need to "report" to. M is always M - there is always a cube somewhere you can put together.
You, are on a mission - to understand what M is, of course.

Now you can "communicate" after a fashion, by drawing a square and using four different colors on the edges, then quartering the square, like a set of coordinates. You have a kind of receiver, but it can't tell you much unless you inflate it, and project the "components".

This is much like first using a noun and verbalizing it. Thus the kitset of a puzzle that is "in" the same class, is also a kind of verbalizable noun, linguistically speaking, the assembled cube with no stickers is an equation (of the "twist group") in black & white, which you then "activate" (you construct the declension: qubus, quba, qubum) or verbalise with colors, to see how transitive different "stresses" "extensions" etc are, and what conjugations do. You are of course, also M. M is a putative "mind-machine" construction, that you construct from the parts you use. The user is U.

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"We", or in other words you, and I can see that with language and communication there is something we call "humor".
This is the stuff physicists try to use at the start of a session or during a conference.
Dodson used it in stories he told his niece initially, Monty Python exemplifies the extent language can be taken to, by "normally funny" examples.

But funny means "not normal, or usual" in terms of using it accurately and concisely - without this room there would be only body language, I suppose.

You don't normally find humour in America, you find humor, but both are in the same group of "slack" usage, or imprecise communication and the choice made by the "receiver". Humor is an "H" word, in the normal group of communications.

The thing I think Shannon realized is that a channel is just something like a pipe, made of a material, which might be rigid or otherwise, but its "nature need not concern us here", only that it act as a carrier for information. This "rigid" material is the very same that Einstein used.

So you have a tube or pipe of some kind, with some kind of message sent and received. Universally the tube is made of Planck "material" and the messages (message) is frequency. So any material channel is a carrier we use "artificially" to send time-encoded information. It has to be sent and received though.

So badabing and badabeesh, you got a little this, you gotta little that...

 

Everything is real. Reality is everything.

 

I think Ethics could be seen as Spinoza in 42 stanzas. He more or less says that all a mind can do is learn. Mind, in Spinoza is universal, so the corollary is that a universal human knowledge not only exists, but necessarily.

If you start at the end and work backwards, it "falls like a house of dominoes", the way all the objections to the necessary pursuit of knowledge, to its own end are laid low.
So then, the Ethics is a logical proposition, which is consistent in both directions.

Next Kant, and then with Maxwell's equations Einstein lays out so many stanzas, in a sequence of papers which has much the same structure and consistency as Spinoza used to present an infallible argumentum.

In black and white however.
Nonetheless both are efforts of logical deduction alone. Einstein's 1916-17 papers have few if any references. Both stand alone as individually brilliant deductive works of logic.

 

Some of the ways I've tried to characterize the character/characters of or in the cube, as I "color" it, are that it's a castle with a king, or a deck of some kind, etc.
I think of this guy Harry, who is the guy you get hold of, to get the deck finished. Harry is the guy you call when you want things done. He always seems to know someone who knows.

So all the King's men are the pieces, and their moves apart, then back together - Harry must know Humpty.

 

So having presented the innards of a problem, so to speak, the guts of this problem is this:
Computation uses iterative machines, and algorithms are designed to encode "programs" recursively.

This is the iteration/recursion problem. The symmetry in the cube "declension" is possible because (and only because) that's how spacetime is, symmetry-wise.

So what is recursion or a recurrence? The latter is what you try to induce when designing an algorithmic solution (to a computational problem - a recurring "theme"). You want to derive the smallest step that will change some data, so that a sequence of similar steps will, like clockwork, reach the solution and "print" the answer.

With the stickering "problem" you need to start with no colors and find a recurrence that gets you the required symmetry for a 2-polytope. Say you start with only 4 stickers, and all are different colors, what happens if you randomly sticker four edge pieces?
If you gradually increase the number of stickers but not colors, should the previous ones be taken into account in the recursion?

 

"Faster than a speeding bullet, smaller than a locomotive, look, up in the sky...
Is is a Fukawe bird? Is it a Euclidean plane?

No! It's Categoryman!"


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