Math is the language of science, and science is all about facts and theories. So, for higher-order philosophy or religion, the language, and the concepts contained, should be somehow be both compatible with and reflected by higher-order math.
Here's what I'm thinking. Language has all sorts of descriptors,
adjectives, adverbs, whatever, that you could describe as dimensions, with levels of their own, described by adverbs like 'very,' 'not much,' 'a little,' etc.
But what we do with those descriptors inside a sentence is really pretty basic, if we shifted it into a math domain.
So what kind of new stuff could you come up with if you did a little mathematical modeling using some of these linguistic descriptors? If you threw math and poetry together, what would you have? Shakespeare meets Maxwell or something. Would such a concept be gibberish or would it allow us to understand language on a more complex level?

Start with a very simple complete sentence. Assign some values to the descriptors, sort of like a Laplace Transform.
Throw in whichever mathematical function suits your fancy. Re-translate. Now what do you have? The re-translation is likely to be gibberish to us, but I propose that this is because the operands in common language are too limited to understand the complexity of what's there. Just like higher math glosses over the eyes of many, this retranslation would be the same. But it might provide a useful tool in explaining philosophic ideas, or even expanding upon them in new ways.

Loglanhttp://www.loglan.org/what-is-loglan.html Only a teensy bit more sensible... [rmutt, Jan 08 2002, last modified Oct 21 2004]

lojbau meksohttp://www.lojban.o...grammar/chap18.html [prometheus, Jan 08 2002, last modified Oct 21 2004]

Lojban Beowulfhttp://www.lojban.org/files/texts/beowulf [prometheus, Jan 08 2002, last modified Oct 21 2004]

Oulipo (in English)http://www.raintaxi.com/oulipo.htm The joining of "the mathematicians' delirium to the poets' logic"- [hello_c, Jan 10 2002, last modified Oct 21 2004]

Mathworld's transformshttp://mathworld.wo...ubmit=Search&as_lq= There are lots of 'em, but you'll probably have to devise one more complex than all of them put together, considering strict mathematics is only half of your equation. [yabba do yabba dabba, Oct 17 2004]

To what does "it" in the second sentence refer? It looks like RS wants math or science to be compatible with math, which I would say is baked. It might be an idea to learn English before you try to write poetry in it.

This is 95% useless, 83% badly described, and 8% an idea.

Loglan link was interesting, but not quite what I had in mind, although you might have to impose it in order to ensure compatibility.

'mathematical poetry' is missing the point altogether.

Contrary to jutta's opinion, I do understand poetry and mathematics. One is a hobby, the other is a large part of my job. The difficulty here was that when I have what I feel is a good idea, I get in such a hurry to scribble it out that it comes out like a mess. I've since refined the verbage.

I'm not talking about just throwing a few operators into some sentence or making poetic comments on math.

What I'm trying to describe is an expansion of context and function inside language. And the fact that language itself has certain limiting factors makes that description process difficult, any one person's linguistic limitations not withstanding. My ambiguous pronouns probably don't help, either. ;-)

Just as math contains concepts such as quantity, value, logical operations, containment, sets, operation, modification, etc., language might benefit from the same in terms of an expansion to the context of linguistic communication. Obviously there's alot of cross-over already, but probably not fully. I'd be curious as to how such an exploration would change us.

It might be useful in some practical aspect, it might not. How much so I frankly don't care. I guarantee it would be useful in terms of a mental exercise.

where exactitude is required - i.e., sciences, engineering, etc., - descriptors and quantifiers are carefully spelled out in mathematical language. Where it is not required - or where it is not appropriate - less numerocentric valuations are used. That's part of the fluidity of language, folks.

There's nothing to be baked here.

Each of us is free to use whatever level of mathematical precision we wish.

Some people would/could cogently argue that mathematicization of language would degrade its richness, shallow it up, suck the life out of it.

Anybody who reads the sentence that starts, "It was a dark and stormy night," and thinks, "Hey, how dark? How many candlepower ambient light was available? What was the rainfall in inches per hour, and the temperature, and the wind speed," just doesn't get it.

Though I myself tend to find objective, quantifiable statements more accessible than the colorful, metaphor-rich, artsy-fartsy language of the literati, I am cultured enough to appreciate what of that style I do grasp.

Put another way: I suppose it would be possible for a man to express his love in terms of heart rate over sedentary normal, erectile turgidity on some objective scale, and state the exact percentage of waking time spend thinking about me. But I'd rather just hear, "Man, I can't get you off my mind. I am so hot for you, my dick could split bricks."

I do think there's a good idea here: the use of mathematical operators in prose. There are a lot of times you want to say something like 'for all x, y is true', or 'there exists x such that for all y, z is true' or 'consider a0...an where ai=(some operation on bi), then...'. There are English idioms to express most of these thoughts, sometimes succinctly and accurately, but too often vaguely and ambiguously. Incorporating into English the forms of expression that mathematicians have found useful would only enrich the language, make it more versatile and expressive. It would not (as qb implies) require us to quantify everything we say --- that's arithmetic, not mathematics.

Rayford, I didn't say you don't understand poetry and mathematics, I said you don't understand linguistics and mathematics.
I'm assuming that you think mathematics is part of your job, not poetry? What is your job, then?

Formulas are geared towards being read visually, often slowly, often many times over. Human language is optimized towards being heard spoken quickly; it is shallow and redundant.

Trying to merge the two forms of expression will be about as successful as growing breast implants from earth in a plastic bag. It's sympathetic magic. By introducing formal elements of a written languge into a primarily spoken language you hope to pick up the expressiveness and complexity of the written language, but you won't; all you'll end up with are unpronounceable formalisms that don't lend themselves to the kind of parsing and production humans do well when conversing.

//Language has all sorts of descriptors... that you could describe as dimensions... described by adverbs like 'very,' 'not much,' 'a little,' etc. So what kind of new stuff could you come up with if you did a little mathematical modeling using some of these linguistic descriptors.//

Language already is *mathematical* in this sense. Aren't you just talking about nominative or ordinal measurements instead of the usual interval or ratio measurements we generally consider as "maths"; and doesn't this type of measurement system necessarily limit the mathematical operations permissible?

Responsibility for precision of a particular locution lies with the locutor, not with the language. Language is completely capable of any range of mathematical accuracy or logical precision. As I said, there really is nothing to be baked here. If you find particular texts or spoken works to be failing, then the problem lies either with the speaker/writer, or with your own expectations, but certainly not with language itself.

While quantifiers such as "few" and "some" lack apparent precision when compared to enumeration, they nonetheless are logically well-defined as "at least one."

Lurking within this idea is a popular misconception that precision itself is always meaningful. For a simple pragmatic counterexample, describing an ingredient in a food recipe as "0.375 grams salt" instead of "a dash of salt" will not result in a more accurate rendition of the recipe (actual volume of tablespoons and teaspoons in different kitchens vary greatly, yet that has no relevance to the variation in quality of food produced in those kitchens). In a chemical process, that kind of precision is probably appropriate.

Even in the sciences, excessive enumeration occurs in various guises. For example, whenever quantified measurement differences are smaller than measurement error, reports of discrete values is not just misleading but erroneous.

When one psychologist says that there are 7 stages in the heirarchy of needs and another says there are 9, do you really think that one of them has made a mistake in counting or basic arithmetic?

But if your interest is in mixing of genres (which the Maxwell/Shakespeare sentence implies), may I suggest reading Stanislaw Lem's Love Poem in Tensor Algebra, found in the Cyberiad. But that kind of genre fusion is an artform unto itself, and quite a different beast than the concerns with linguistic precision. So perhaps it is most accurate to say that RayfordSteele as two ideas here, rather than just one. But even that is probably a misapplication of quantification.

If we go to Wittgenstein, we see that language is a game. We use language in certain situations for certain purposes. It doesn't have any mysterious relation to meaning, truth or the external world. It works simply because people share it and we know that words produce a similar effect in others to that which they produce in ourselves.

Mathematical notation/formalism is a language used to play the game of mathematics: to prove theorems and calculate results. Mathematics as an activity/job/pastime admits intuition, creativity and play, not to mention a standard of beauty as exacting as that of poetry; but mathematics as a language is rigid and formal and designed to be as unambiguous as possible.

Human language (English, Tagalog, Navaho, etc) can be used for formal specification, where we assume words have a narrow, logical meaning, or for jokes and riddles, where we assume their meanings may be suddenly upended or far from common. We can use language for anything we want, subject to the proviso that it has to be understood by someone else. If it doesn't need to be understood we may be using words, but we might as well be using grunts and farmyard noises.

I still don't understand what RayfordSteele's on about, though.

"If we go to Wittgenstein"? Have children colonized him, has he become a world?

yesterday I see my man Wittgenstein & I go "Yo!"

The whole Oulipo might be relevant here; they played many games with mathematical quirks carried out in literary forms. I think my favorite is the "10^14 Sonnets", but the novel written without the letter E has been translated into English.

When I was a wistful undergraduate, I wrote a sonnet to my absent dear that used every letter but "u" ("Missing You!" haw!). (It ended "Q.e.d.".)

I'm an automotive restraints engineer, for the curious. It's all about energy management, some math modeling, etc. So yes, math is a part of my job.

And no, I'm not at all talking about precision in language. I'm talking about greater capability for description by using expanded functions. Just as math with just addition and subtraction would be quite dull and limited, even though a 1st grader knows little more, so might our language be hindered without our knowledge of what's really possible.

RS - you'll have to provide some samples in order for your intent to be clear. You keep on saying, essentially, that language can do "more" (more *what*, exactly?).

Furthermore, you seem to be operating under the assumption that careful study/development of language will reveal some hidden or mystical truths about the way the world works. Much of the 19th and 20th century developments in philosophy have pretty much undermined that view.

You ask for "greater capability of description" yet what exactly do you wish to describe?

In no way do I think you are a doofus. The construction of your original idea, in and of itself, indicates a special kind of intelligence. But, as I have (repeatedly) said, I think you're misguided about the way language works. Pottedstu mentions Wittgenstein - I highly recommend him to you. The Philosophical Investigations is incredibly accessible.

While I don't think you're a doofus, I do find it highly ironic that your advocacy for superarticulate description in language is itself lacking in meaningful description.

Or perhaps that was your point, and your idea is really a self-referential joke. In which case, you certainly wouldn't be a doofus (but that kind of cleverness is really a pain in the ass).

RayfordSteele seems to be confusing mathematics as a language with mathematics as an activity. If you have math with only addition and subtraction, what is prescribed is not the language, but the set of operations that can be performed. Mathematics is different from ordinary language in this way: that nothing can be done unless some notation exists to specify it.

In the wider world of people, what we do is not limited by language. Language is used for certain tasks but there are generally ways of performing these tasks without language. Mathematics as a discipline is equivalent to the representation of it (you can view maths as a collection of proofs and results).

Possibly RayfordSteele believes that natural language enjoys a similar relation to thought as mathematical notation enjoys to mathematical practice; if this were the case, increasing the language increases the tasks that can be performed. Just as in maths the invention of calculus gave a whole new set of symbols, operations, definitions, theories, results and proofs, so new subdisciplines of language could be created to extend human thought and activity.

However, mathematical language develops in a quite distinct way from natural language. Natural language constantly undergoes developments through processes like metaphor and metonymy, changing and extending the reference and use of words. Innovation is constant, happening all around the world in numerous subcultures. Are there things that language cannot yet describe? If so, what are they? And why haven't we wanted to talk about them (language already has a good go at the ineffable and sublime, as in theology and poetry)?

There is a philosophical debate as to whether and in what way language constrains thought. For instance, can a meaning ever be translated from one language to another? Does someone who speak English think differently from someone who speaks French? If so, then creating a new language might lead to new possibilities. But even if you admit that language constrains thought, it is questionable whether a new language created by a speaker of other languages could ever contain anything that could not be expressed in those other languages. In short, could the creation of a math-modified language give anything new?

Mathematical praxis (proofs and theorems) can be defined using the English language. Not as elegantly, and not as intuitively understood. I do not believe that combining two systems (English and math) that are both present in one individual could produce anything that was not already in that individual. Mathematics is not a subset of natural language, although it is a subset of human practice.

Natural language may have difficulty describing the feeling of being a mathematician; communicating this may require some appreciation of maths. But this appreciation can be conveyed by a combination of natural language and maths. There is nothing mystical about this; the two have been used in conjunction since mathematical formalism was first conceived.

Finally, consider the creation of language. New mathematical concepts must be explained in terms of old ones in conjunction with English; ultimately it goes back to definitions in natural language. Similarly, Esperanto can only be described in terms of translations. In this sense, although new languages (formal like math or faux-natural like Esperanto) may lead to new discoveries -- theories and artworks -- they can only be understood on the basis of existing language.

So unless RayfordSteele plans to give us a dictionary or examples, I don't think we can proceed.

_pottedstu: If you do turn into Vernon, be wearing a head restraint -- the man is a wall.

¯RayfordSteele: /…greater capability for description by using expanded functions… / excellent!

I need better ways to say:
If, and only if …
My first choice was …
How completely erroneous!
I don't know.
and similar nosological quandries that I struggle with many times daily.

In a more gentle time, the mark of one's word was a down payment that could be trusted to be upheld -- and without evidence to support my belief, let me just speculate that interest in modifying language has declined steadily in the last century as the pool of private thinkers has been incrementally pulled into the arena of public scrutiny (compare "Highly Visible" parents of today, versus the private home life enjoyed by millions just a few years ago).

Today, by contrast, I feel that adherence to an encoded proof of concepts would strangle creative expression and encourage some already dilatory people to demand more and more from their superiors. In that there is such a disregard for authority, merit, and fact, can we expect a mass acceptance of information based on the sense contained in that information?

There are grammatical rules which exist only on paper, or in discussions of form. There are interpretations of written work and writing style that are solidly grey from the thesis statement to the closing statement. I do wish that I could personally do what the central idea here suggests, and that is to experience first hand the receipt of information as an unbiased reader and quickly make the determination that the information was suitable or not for my needs based on criteria intrinsic to me. The information would be more or less in tune with my subjective standards of acceptability, or reasonableness, or precision.

// Possibly RayfordSteele believes that natural language enjoys a similar relation to thought as mathematical notation enjoys to mathematical practice; if this were the case, increasing the language increases the tasks that can be performed. Just as in maths the invention of calculus gave a whole new set of symbols, operations, definitions, theories, results and proofs, so new subdisciplines of language could be created to extend human thought and activity. //

Yes! I wish I could've written it so succinctly. Call it an experiment. Ironic that in trying to describe it I'm bumping into my own rather elementary linguistic difficulties.

Since I'm more of a right-brained guy in practice, my raw ideas run abound, but my linguistic ability to describe them frequently runs dry. Naturally when I get frustrated I tend to run towards the safety of my less-linguistic self.

Perhaps what I was aiming at was not exactly 'increasing the tasks that could be performed,' but combining the tasks we already perform in new or shortcutted ways.

Since most new ideas are simply new combinations or variations of baked ones, this seemed like a natural extension.

// and doesn't this type of measurement system necessarily limit the mathematical operations permissible? //

Yes, exactly. And it's that limitation which I'm attempting to get around. In order to give concrete examples, the concept itself would already need to be baked, since it grasps for expression outside of linguistic limitations.
The basic theory I'm using is if you push the capability of language, you push the capability of communication, and thought itself, to some extent.

BTW, I do understand linguistics, having minored in a foreign language.

// I do not believe that combining two systems (English and math) that are both present in one individual could produce anything that was not already in that individual. //

Except that most people don't understand maths. Most people know a subset of their own language and nothing more. The benefits of this idea could be more easily achieved in ordinary people by getting them to learn another existing language - be it a human one, a programming one or mathematics.

Rayford is (I think) suggesting that beyond that stage, there are ideas that can only be effectively explored by progressing beyond existing language barriers. It's a nice idea, but if he has a clue how to do it he's smarter than I am. Which of course, he is.

And as a final pearl to throw in here for those interested in the relationship between human and more formal languages, look at Lingua::Romana::Perligata, a module that allows you to write almost-free-text Latin that is executed with the semantics of Perl. It's a while since I did Perl, and even longer since I was avidly resisting learning Latin, but it appears to be quite successful.

I've sometimes thought it would be useful to have punctuation marks in English that would serve a function similar to parentheses in mathematics (parentheses in English already exist but serve a different function). Without such marks, it can be difficult to describe events which should occur if (a or b) and ((c and (d or e)) or not (f and g)) occur.

Perhaps ambiguity of meaning creates more opportunity for new plateaus of understanding. If we pin down the meaning of words using math or create new words with math that have specific meaning we may be denying ourselves opportunities. One way ambiguity can create new understanding is in arguments. If someone misinterprets your statement you will have to clarify and in the process may see the issue from their point of view.

I was looking at the link that thumbwax had put up which points to the mathematical poem by Kaz Maslanka it shows the physics equation for Energy but in place of numbers Maslanka has chosen words. He seems to me that he is talking about reincarnation thru karmic energy and misfortunate paranoia is what drives humanity through the ages from the beginning of time to the end. You may see something else
Maslanka says points out the physics equation for energy … Energy = mass times acceleration over a distance. -- In place of the mass he puts in the phrases: The conscious embryo, rampart, through the viridian passage ß that is the mass … then he accelerates that mass by the phrase “misfortunate paranoia” so here we have force (mass times acceleration) then he uses the distance formula in algebra to show this mass being accelerated over the distance between two points. The first point being where we have single cell intelligence and the discovery of the wheel. Next we move the mass across to the next point where we have omniscience and extra dimentional travel. ---Sounds kinda like reference to Alpha and Omega

I believe this is what Rayfordsteel was talking about earlier … using math as a language in a connotative way instead of denotive. Whaddya think Rayford?

Here is that link again to the poem “Karmic influences on the double helix”
http://www.kazmaslanka.com/Karmic_influence_on_the_double_helix_image.html

Rayford, what is the difference between poetry and pure mathematics? … both are languages … both can express but what is the bottom line difference between the two? What does math express that poetry(art) can not? And what does poetry(art) express that math can not?

This was a really early idea post of mine; I danced around it but couldn't explain it very well the first time around. It was an analogy that didn't work very well.

In a nutshell: language provides a certain framework around which we must adapt our thoughts, but sometimes there are gaps, and perhaps even borders which are difficult to cross. With an expanded structural freedom that would allow us to manipulate 'linear' sentences into more complicated expressions, such as we see in mathematics, or art, perhaps a new insight could be expressed.

A picture is worth a thousand words, but if those words were more adapted to the task, reorganized, non-linearized, or otherwise combined in a new fashion, maybe a reduction in the amount of verbage could be achieved, with better description.

RayfordSteele said:
“In a nutshell: language provides a certain framework around which we must adapt our thoughts, but sometimes there are gaps,”

Yes Math is logic and logic is the language we use to replicate experience “reproduce with the same results” Poetry is the language that bridges that gap … metaphors bridge the infinite to the concrete.

Lets look at the difference between a simile and a metaphor … “He runs like a deer” is a simile … because he is ‘like’ something i.e. (a deer) … “He is a deer is a metaphor” … when we use the word ‘is’ then we are creating logical confusion … He ‘is’ a deer is nonsense because we know he is a human … it is this logical tension that creates the metaphor and bridges the gap between the infinite and the concrete. It is the same thing as dividing by zero - the function blows up!

So now we look at this artwork which imbeds metaphors inside math equations … bringing culture or cultural ideas into a math equation … This accomplishes part of what you are asking … although when you say, “maybe a reduction in the amount of verbage could be achieved, with better description.” I have a feeling you are thinking in terms of utilitarian purposes instead of aesthetic but I find blending the aesthetics of Math and Art extremely interesting.

I guess my response to that is that I have found at least the similie's requirement of having 'like' or 'as' inserted somewhere as restricting and linear. Metaphors provide a little more freedom, but are still kind of locked in by the rather direct equation between the objects.

Language is quite serial by necessity of communication, while one's thoughts usually aren't. I could eventually expound on the tangle of directions that my thoughts take me, but I'd still have to do it in a serial fashion, one by one. I guess I was looking for a way to break from that linearity.

Rayfordsteele says; Language is quite serial by necessity of communication, while one's thoughts usually aren't.

Yes rayford, verbal language seems linear but mathematical language definitely is not ... so when you mix verbal language inside mathematical language you get the non-linear vision for which you are asking.

Look at the equation for a sphere (non linear): x^2 + y^2 + z^2 = r^2 if you substitute words for the variables then you can create a sphere made of concepts constructed by verbal language. Think of each dimension in the equation as a conceptual number line where you have different values of a concept instead of numbers … example: lets make the x axis a line with different values of justice ( ranging from just to unjust ), lets make the y axis a line with different values of integrity ( ranging from integrity to non-integrity ) lets make the z axis a line with different values of nobility ( ranging from noble to ignoble ) and lets make the radius values of virtue … this is not linear – it is a 3 dimensional sphere but it doesn’t even have to be 3 dimensional, it could be 12 dimensional or 31 dimensional or where ever you want to take it -- just put in different concepts for each dimension.

This idea comes again from Maslanka
http://www.kazmaslanka.com/The_Virtuous_Sphere.html

If you just rewrote it, and didn't annote it, then I wouldn't have read it. I've yet to decide whether that's good or bad.

I like it as a thought experiment, but actually doing it seems impracticable. The biggest question is where to start. And why LaPlace? Is that just an example? Seems like your going for any transform, or probably one that doesn't exist yet.

I don't know where the sunbeams end and the starlights begin--it's all a mystery.
And I don't know how a man decides what's right for his own life--it's all a mystery.

The Fourier Series is not the same as the Fourier Transform.