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Personal project: Using mathematics as a spoken language

  1. Dec 26, 2003 #1
    This is purely speculative and deals with a quirky concept that quite probably no one else will have any interest. Still, I offer it nonetheless, in the hope that some of you might respond.

    Suppose there was a society in which the people spoke in mathematical terms. They have a complex, highly advanced civilization in which everyone spends their time working on advanced problems in math, science, chemistry, physics, etc. Now, because they are so specialized they are forced to trade with the outside world for common, mundane goods like shoes, clothing, food and other manufactured goods. You run a general store and in walks one of these people who wants to buy, oh say, some apples. What would that conversation sound like? How would they communicate, in a spoken way, to let you know (other than strict pantomime or pointing or some other variation of sign language) what it was that they wanted? Realzing you, as a layperson running the store, would not grasp or understand the higher mathematical forms of their language and for various reasons cannot or will not speak your language but understand what you're saying. And you've done enough business with them in the past that you've picked up a few of their phrases and concepts.

    If I walk into a store I might say, "Let me have a dozen apples please." But if they walk into the store, they would first have to speak in simple sentences in order for the clerk to understand. Much like any foreigner today would speak in small, broken words to ask a question in English, what for us might amount to little more than baby talk, but because of the language barrier they are forced to communicate the key concept as best they may without the fluidity one would have of native fluency.

    So my fancy first led me to try and put things in terms of plane geometry, the first advanced subject in math to be taught in most schools after long division. It's concepts are at an elevated level from basic addition, subtraction, etc. but not as abstract as other fare, like for instance, Algebra. So such a person might first want to indicate the desire to enter into a transaction by first stating, "Line AB intersects Line CD at point E". They're basically saying, "I want to engage this good grocer in some trade and his store is the meeting point". They might ask the price of his goods by saying, "What is the Ratio?", meaning how much to buy this item? If a price were agreed upon they might conclude the transaction by saying, "The shortest distance between two points is a straight line".

    How would they say, "Hello" or "Good-bye"? How would they differentiate an apple from an orange or a new hat? What if they were under the weather and wanted to buy some medicine? Assuming that mathematics can be used to describe everything, how could it be accomplished so that it might be used as an everyday language, and more than that, used to converse with people who only have a rudimentary ability to translate? I'm interested in formulating a basic vocabulary and hoping to pick a few brains of people who, like myself, have a fondness for the frivolous and excess capacity for the imaginative.
    Many thanks in advance.
  2. jcsd
  3. Dec 26, 2003 #2
    I'm thinking if you ever wanted to utilize this idea, you would find a way to meld Sign Language with Mathematics...
  4. Dec 26, 2003 #3
    Hmmm... Maybe some form of coordinate system (for the store)? Something would be said to give the dimensions of the room in whatever unit the speaker chooses (the unit used is irrelevant, but the total size of the room in those units is necessary), then an x y coordinate could be given of the location of what the person wanted to buy... Then you would have to describe the slope and direction of a line passing through that object and the buyer. (This is assuming, of course, that the objects aren't simply numbered). To ask the price a variable x would be used for the items price and compared to a known price (or the value of an item wished for trade) to ask for the value of the item (x) in terms of the value of the item with the known value.

    Hmm and "Hello" and "Goodbye"... Hello is a greeting, acknowledging someone's presence, goodbye is the opposite. So they would probably use an equation to say that the coordinates of themselves equals the coordinates of the person they are greeting, and say the coordinates are not equal when departing.

    That mathematics thing is a very interesting idea- I don't think communication between the Mathists and the Linguists would work though. In Mathist society there would probably have to be a lot of protocols understood (just like there are in Linguist society- but the Mathist protocols would be vastly different).
  5. Dec 26, 2003 #4


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    It's not possible to have a pure math language. Mathematics is, by itself by definition abstract. As soon as you start adding concrete objects to the language, you might as well just go with give me 12 apples suitable for eating raw please. Technically, the mathematically oriented might add a whole slew of extra qualificaitons that might not occur to someone else.

    You can certainly create alternative language syntaxes that would boggle the mind. My friend wants to have RPN languages. The idea is that words modify the things that come after them. For example
    If Give You to me five apples Pay I you one dollar da.
    Might translate into "If you give me five apples, I will pay you one dollar." Da is a no-op word. The notion is that you can identify the words in a stack moving left to right. It's pretty brain-intensive because it involves elaborate state tracking -- something that humans are not particularly good at.
  6. Dec 26, 2003 #5
    Some great concepts in there, Sikz. I like the ideas for hello and good-bye.

    Thanks also to NateTG and Yahweh for responding. I'd agree, some concessions would have to be made. For instance, they might just pick up an apple, point to it and say, "What is the ratio to monetary units?" to ask for the price. Or they may even use the word apple to say, "What is the ratio of monetary units to apples?" Although this admittedly takes some of the fun out of speculating, it brings up a valid point. Afterall, what is an apple?

    Or rather the word we use, 'apple' is actually an abstract representation and not the thing itself. The concept of Plato's apriori, if I remember correctly. Too lazy to look it up at the moment. In other words, we have in our minds and through experience built up an image of an apple, a prototype, and it is this prototype we have in mind when we say, "I feel like eating an apple". We all (hopefully) know and intuitively understand what was said, but it is, in it's own way, abstract. Afterall, did I mean a Granny Smith, Golden Delicious, Red Delicious, Roman, etc. ??

    There certainly would be difficulty in such an encounter but our Mathists and Linguists (thank you Sikz), being intelligent, reasonable people, would certainly want to persevere. Necessity is the mother of invention, afterall. Our grocer must sell his apple before it goes rotten, and our apple patron wants to eat before he goes hungry. But being smart, our Mathist apple eaters, they wouldn't want to overpay. He or she might be on a budget, to save money for shiny new beakers, glass slides, maybe chalk and a scalpel or two, and other sundries.

    Our grocer might quote a price of .50 cents. How would they bargain? It might go something like, "Given two angles of a triangle are 60 and 80, the missing angle is 40". Now, they've just offered to pay .40 cents.

    Oh and NateTG, the example of your friend reminds me of Gene Wolfe, who's writing is partially responsible for this thread. He's done some very interesting work on language in several of his books. Your buddy might want to take a look, esp. in Wolfe's Sun series (New, Long and Short).
    Last edited: Dec 26, 2003
  7. Dec 26, 2003 #6
    I don't think they would use this, seeing as the triangle part of their sentence only serves to come out with their answer, not explain their reasoning. For instance, if you were talking in English and offering to pay 40 cents for something, you would not say "99 bottles of beer on the wall; if 59 fall there are 40". You would say "I can't afford/I don't want to pay 50 cents, howabout 40?" So our Mathists would probably say something more like this: "x-50<0" where x is how much money they have (or rather, are willing to spend) to show that they can't afford/don't want to pay 50 cents. Then "x=40; y=40?" y being the actual price required to pay for the apple.

    Naturally there would be other ways of phrasing this, using different variables or explaining more of the thought process. But basicly what I was saying is that math, by definition, is logical- so any Mathist Language would have to flow logicaly, not simply throw ideas out about the angles in a triangle or such.

    As for naming apples... It would probably go about like this: Originally people would refer to apples by location, untill this became frequent- at which point it would no longer make sense to say "The object at this location...", but rather "The object like this". So then it would turn into a description of the colour (in terms of wavelengths) and size, density of the apple. This would soon be condensed for utilitarian purposes (for instance, if we said wavelengthMin=300 wavelengthMax=800 avsize=50 avdensity=43, that would be shortened to 300/800/50/43). Before long it would be shorteneed even MORE (averaging 300 and 800 together, for instance) into something like 550/50/43. Since these are pretty even the 0s would eventually be dropped in common use and the resulting 4.3 would be rounded to 4, and we have 55/5/4. If the word became EXTREMELY commonly used a variable would be substituted in, and apple would just be "r" or some symbol. :)

    Are we reffering to a Mathist speaking in semi-Linguist terms, or pure Mathist? If we mean the former, that makes sense, but if we mean the latter... In pure Mathist there would be no "What" no "is" no "the". Also, "ratio to monetary units" is really just another way to say "price" (as you pointed out)- so if a Mathist progressed far enough in his Linguistic studies to say "ratio to monetary units", he could probably simply rephrase it to "price". A Mathist trying to speak English would probably sound something like "What is x/1 [insert description of apple, probably in Mathist terms]?" The first difference he would learn between English and Mathist would be "is" instead of "=" and "What is ___?" instead of just "__=__?". It would actually be written and spoken as that "might equal" symbol, I believe, not an "equals" and a "question mark".
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