Friday, January 8, 2010

Indescribable

Blog post # 33:

Today's picture, made today:

Oblate Superposition


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And some typewriter art:

1!1!!1!!!111!11!1!

A little tidbit, that was.

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I noticed the other day with my latest poll, almost every word to vote on starts with the letter P. And my "jokes" are mostly puns, so we could replaced that with "Puns", starting with a P. And switch "Anagram" and "Palindrome" around, appropriately, to get that topic starting with P too.

Coincidence?

Probably! Positively!

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WPMD's

Because of the expanding lower class here in America, what our leaders SHOULD be afraid of aren't "Weapons of Mass Destruction", but rather are

We Pawns of Mass Destitution!

Sing it! (and dance!):
.

WPMD's!
WPMD's!

We Pawns of Mass Destitution
We Pawns of Mass Destitution

Rise up!
Rise up!

Go downtown, now.

We Pawns of Mass Destitution
We Pawns of Mass Destitution

Rise up!
Rise up!
Rise up!
Rise up!

Go downtown, now.

We Pawns of Mass Destitution
We Pawns of Mass Destitution
WPMD's! WPMD's!
WPMD's! WPMD's!
We Pawns of Mass Destitution
We Pawns of Mass Destitution

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Our government has gone rotten on all of us. This is our dystopia.

We are ruled by a...

Mal-archy!

What our leaders tell us is all...

Malarky!

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Are there words that, speaking of malarky, are so complicated to define that they essentially are undefinable, no matter how complicated a definition one could try to come up for them?

I know there are some words and phrases in mathematics, say, where you practically need a PHD, or literally need a PHD, to understand what the Hell they mean.
But they ARE definable, in principle.

And I am not talking about nonsense words, because they essentially have no definition at all, not an indescribable definition.

And I am not talking about poorly defined words, because we have some idea what they mean.

I mean, are there words so convoluted in their definitions that NO ONE could come up with definitions for them -- even a definition such as "something indescribable" -- in principle?

Can we comprehend such a word or words?

Such words might describe "life" (if there is such a thing as life there) in another universe where things are so different that even the laws of physics and mathematics and logic are different from what they are in our universe.

The strangest dream ever dreamt by the craziest madperson would seem quite trite when compared to what these words define.

Can such a word even be proven to exist?

It all reminds me of Godel's theorem. And I think that a linguistic analog to this math theorem is quite possible.

Maybe there are a group of such words, and they each can be used to define the other. But there is NO way for any of these words to be defined with any language in our universe. These words are on another continent, if not an island, separated from all human understanding.

Just sayin'...


Update: It is possible to have such a "word" that is defined with an infinitely long definition. There are numbers -- reals, decimals -- in mathematics that cannot be defined with any FINITE definition, NO MATTER HOW complex that definition is. As a matter of fact, 0% of all (but not no) reals are finitely definable. All the rest (100% minus an infinitely small percentage) are so-called "uncomputable numbers". (Google it.)

So, if a word refers to a SPECIFIC uncomputable number, then the ONLY way to express the definition of this word (beyond that it is an uncomputable number in a given range) is to use a definition with an infinite number of characters, math symbols, numbers, etc -- such as simply listing the infinite decimal expansion of the number.
Still, as I said, SOME aspects of this word-number's definition are indeed definable in this universe, such as the range (with any precision except exactly) this number falls into and the fact that it is incomputable. But it cannot be described
EXACTLY with any finite alphabet and with any finite numbers of elements of that alphabet.

So, therefore, there can be words, not necessarily mathematical (although I didn't prove they can ever be non-mathematical), that are not definable completely with a finite number of words written in a finite alphabet.
QED.

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By the way, thanks to the very few people who have voted in my polls so far.
And even greater thanks to those (or she or he or it) who read(s) my blog.

Leroy

5 comments:

dennis hodgson said...

I don't want to dissect your post in its entirety, just a few observations:

1. There is no such thing as a word that cannot be defined, unless you're talking about concatenations of letters of infinite length, which aren't really words. Real words are created because there is a need; they don't simply spring out of nowhere.

2. I think Godel's incompleteness theorem is applicable outside mathematics.

3. I didn't read far past the update, but transcendental numbers like pi and e, despite being of infinite length, are definable without invoking infinity.

Amorphous Trapezoid said...

I agree completely with you as far as points 2 and 3.
As far as point 1, I wonder if this is a counterexample. (I may be on the wrong path here.)
Let yujix = 1.375408..... Now I will say that yujix is a SPECIFIC uncomputable number, yet I -- the definer of the variable/word yujix -- do not yet know any more decimal digits, let alone all infinity of them. I could at a later date refine my definition by adding more and more decimal digits based on some completely truly random number-picking process. But I will never completely define yujix.
In the meantime, I could use mathematical phrases like 'yujix+1' and 'yujix/2'. These too are uncomputable reals. But they are yet to be defined and cannot ever be defined exactly, although their definitions can become more and more precise as the random-number generator picks more and more digits.

So, we have a linguistic/mathematic universe, separate from what we are usually familiar with, of all phrases (not necessarily mathematical) involving yujix in a significant way.
"I thought of the number yujix today," for example.

Note: I DID think of the number yujix today -- just now, in fact. So, this phrase is definitely true. But I certainly didn't think of ALL aspects of yujix today, since I don't know its, say, 100th digit at this point.

Amorphous Trapezoid said...

Hmmm. Just thought about what I wrote.
NO ONE knows more about yujix than I do at this point. But aren't ALL words not known in their entirety? Sticking with mathematics, the number 1 is known to infinite accuracy. But not EVERY mathematical theorem about 1 is now known or will ever be known by humanity.

Same goes for cats. Human beings, especially vets, know a lot about cats. But not EVERY little thing about them will ever be known by humanity.

Back to yujix: Let us say that I don't know ANY of its digits, and I never care to generate them. But what if I still use the variable yujix in conversation? Yujix could simply be an undefined word. But I could define it as that SPECIFIC number which would be generated if I had chosen to do so.

Hmmm...

By the way, yujix brings up more than 3000 hits on Google. I guess it is a homonym.

Amorphous Trapezoid said...

More:PS: So I guess there are at least words that we will never know the complete definitions of. (I guess all words are like this.) We could even "define" a word by saying: Randomly pick letters of the alphabet and place them in a string arbitrarily long. Continue doing this until an English phase appears, preceded by nonsense, that defines our word. Now, let us say that we won't generate our random definition. But WE COULD HAVE. IF WE HAD generated our random definition, then our word does have the definition we would have gotten. We could even use this word in conversation as a place-holder. So, our word isn't undefined in the sense that the definition is too complicated for human beings to understand. But the definition is UNKNOWN, and could potentially (but not necessarily) remain unknown forever. Hmmmm...

Anonymous said...

Leroy here.

It is much easier to think of a word with an unknown definition this way: Have a computer with a truly random number generator randomly pick a word out of the dictionary, but not tell you what it is. Define, oh, say, "ovsoss" as being a synonym of the random word. Then this word, in a way, has an unknown definition. But in a way, its definition is "the synonym of the word randomly picked on such and such a date by such and such computer from the such and such dictionary. So, like all words, we know something about its meaning and we don't know something about its meaning. It is in essence like a foreign word we don't know the translation of. But in this case, NO ONE (but the computer) knows the definition. And the computer doesn't know it knows the definition. :)