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Tlagwv Yagwanta!

  1. Mar 23, 2008 #1
    That's Cherokee for "I just don't know"

    If it hadn't been for the TV show Medium and my wife's love of watching it I would have never known that Mathematicians still existed, but I do know that I have had a love of mathematics for many years. Living in SW Kansas we don't exactly have many people who care for this kind of stuff, and so I had been afraid to tell anyone that I wanted...um...not wanted, lusted for mathematics.
    So I had done things on my own, with no help and with no idea where to start. So for about 15 years I had done a few things that I just don't know where or how to look up information. Only recently I had become less afraid of it and more open, and well, with the advent of finding wikipedia and some other things recently, I have learned a great deal more, but again, not nearly enough.
    So what I would like is some help on where to start.

    The first thing would be to understand the different symbols and functions used in mathematics. I have seen things such as an upsidedown delta symbol, T used for 2 or 3 different purposes, and although I can find lots of equations that are written with them, I can't seem to find anything that explains what they are and how exactly they are used.

    The next areas cover the things that I have done on my own. Some are very complicated, easy for me to understand, but difficult to explain to others. As I have stated, I did all this on my own, so came up with my own rediculous styles and explanations.

    Numerical Systems.
    I define #Ss differently than a Numerical Sequence. Numerical sequences are nothing more than a set that generates a single answer, whereas a #S creates a series of numerals, and has two sets of rules.
    The first rule of a Numerical system is based on the fact that a Numerical Sequence (The answer of a Numerical System) is multi system. Which can be easily seen in a polynomial.
    (3x+5)(x-3)=0 In this polynomial there are two numerical systems, -5/3 and 3. This is shown by the format of Ax+-S.
    I should have mentioned about the 3 different forms of numerical systems that I have defined, but I'll define them now before I show any other formats.
    Each of these numerical systems can be of one of 3 different subsets.
    Simple: The Numerical Systems can be easily understood by viewing.
    Broken: Can be simple or difficult, but for the most part are not in the correct format. Such as if we were to use 32,47 to represent a two digit value in decimal, which of course would be 3,247 and have 4 digits, not two.
    Complex: These Numerical Systems are fairly difficult to understand. Imagine a place value of -4/5, well if we were to move up the ladder, so to speak, the next place value would be 16,25. So 1,0 would be larger than 1, but 1,0,0 would be smaller than 1,0.
    Those are the three subsets, the major sets are as follows.
    Perfect: Perfect numerical systems are easily solved. Each place value follows the same rule. Mayan 20*20*20.../(20*20*20...), Decimal (10*10*10...)/(10*10*10...). This can be shown by the formula Np+-i. The N is the Numeral at the p Place value, the +-i defines the increment. So the decimal system could be shown as (0 to 9)10+-1, the Mayan system would be shown as (0 to 19)20+-1.
    Inflected: Inflected Numerical Systems are very complex. Each place value does not have to be exactly the same as the previous place value. This can be shown in our way of viewing time. Year is an infinit integer, Month is based on either names or numbers 1 through 12, days are defined by month and/or year and/or century, hours are either 2 twelves or a single integer between 0 to 23, and so on so forth, even the decimal is commonly changed, either in science to show smaller amounts of time, or in financial situations in which only minutes and hours are necessary.
    Equational: These numerical systems are based on a series of equations. However, they can be either perfect or inflected, but I have classified them by themselves. Look over the example of the 4th increment of the numerical system.
    +1+1-1-1 Zeroeth place
    +1+1-1-2 1
    +1+1-1-3 2
    +1+1-1-4 3
    +1+1-2-1 4

    The fourth place value of this system does not go into the range of 1,0. Actually this system is based on the Byte, there are 256 numbers per place value.
    However, one interesting thing about this is it returns to zero multiple times before it reaches the next place value.

    Well, this is the first part, something I have done for many years. Studying this has caused me to rethink about numbers. I do believe that our understanding of them is a complete farce and that although they may work, they are not anywhere near actuality.
    My feelings on this came about when I was looking at equations of the formats -n(-p), n(p), n(-p), -n(p). Looking these numbers over I began noticing a very subtle difference between them. They are nowhere alike in anyway shape or form.
    I feel that these forms can not be equal. For if we were to place these forms out in how a true number line works, they do not function out at all.
    5(7) = 35. 5 is the starting point, 7 amounts of 5's is 35. Reversed, 5 amounts of 7's is 35. A perfect Incremental Equation, however, this can never be inversed.
    -5(7) = -35. Hold the phone. Starting point -5 move down 7 5's it would be -35, it checks out in an inversed equation, but not an incremental equation. If 7 is the starting point then -35 is wrong. So how can this be correct? It isn't correct for anything less than or equal to 0 does not exist, it is impossible. Which would explain why certain tangents blow up.
    The reverse 5(-7) holds true to the last example, too.
    -5(-7), now this is fun. This equation is only inversed. It is never Incrementive.
    Which leaves me with a very wierd feeling. If numbers of zero and all numbers less than zero do not exist, therefore what is the correct plane? The Cartesian would have to be false then, at least in truth. However, in practicality of human understanding it functions well.

    well, that is the first part of what I have done. There are lots of things I have written down about this stuff, and if I need to write more things down about it, or define something better, tell me and I'll try. I would like to know where to go with this, and who might have studied things such as this before so I would be able to know more about what I have done on my own, as well as figuring out how to write it out where it is more mathematically correct...
    Wado, Takk, Kolaval, Thanks...
  2. jcsd
  3. Mar 23, 2008 #2
    The upside down triangle is called Nabla (in typography) and it's standard mathematical referent is the del operator, which is a vector differential operator that in 3-dimensional cartesian coordinates can be represented:

    [tex]\nabla = \mathbf{\hat{i}}\frac{\partial}{\partial x} + \mathbf{\hat{j}}\frac{\partial}{\partial y} + \mathbf{\hat{k}}\frac{\partial}{\partial z}

    Here is a reference:


    (as a side note, as fun as it is too learn math from wikipedia it is also important to cross-reference what you learn with professionally curated sites such as Mathworld)

    Since the Del operator is a part of vector calculus, you should be familiar with both calculus and vector geometry before studying this topic. I highly recommend to learn these subjects because they have advanced applications to science and are very highly polished.

    Your original investigations, although I do not fully understand them, seem that they would be classified as number theory (which is far away from Calculus discussed above).

    Unfortunately people without formal training in Mathematics do not usually get a good response to their original investigations and thoughts. This happens for many reasons, but the bottom line is that I recommend putting your original thoughts on the side while you learn to speak the language of math; then you will get a much more positive result. We already have established meanings for "number sequence" and "number system" that seem to differ from yours; we also have a somewhat standard procedure for defining new concepts, as you seem to be trying to do.

    Start by enrolling in a Precalculus or Calculus course at a local university!
    Last edited: Mar 23, 2008
  4. Mar 23, 2008 #3
    The language of math was what I am interested in. I do not live in an area that information of this sort is easily found. However, I had alread presumed that Wikipedia was not the best place to look for information, but quite frankly was the only thing I knew of at the moment till I found this place...However, you did help me in figuring out where to start, so thanks...
    By the way, I have often times come off as very confusing to people, what I meant by the Nabla was just in reference to 'The Language of Math' as you put it. I just didn't know what else to call it so I used examples.
  5. Mar 25, 2008 #4
    You obviously have access to the internet. And as Crosson said you appear to be interested in number theory. I agree with him in the sense that your investigations make little or no sense to us because we are not speaking the same language. There are plenty of people here who can recommend good books that you can order on Amazon.com and have them shipped to you. This way you can start reading them, take notes, ask questions here, in a language we can understand.
  6. Mar 25, 2008 #5
    How close is the nearest university? Usually a university library will have mathematics books that go much further in depth than a public library. Math books can be expensive to purchase, and there is no guarantee that you will find it readable when it arrives!

    A formal introduction to number theory is somewhat advanced, you'll find that it probably depends on either calculus or abstract algebra. You might find a taste of abstract algebra to be interesting, since it eventually allows us to better see the essence of the operations that I think your talking about:

    Search for the topics: Groups, Rings, and Fields.
  7. Mar 25, 2008 #6
    Thanks diffy...

    Traveling to the nearest university would probably cost far more than purchasing a book. I live almost in the middle of Amarillo, Wichita, and Denver. A little city named Garden City in the southwest part of Kansas.
    Truthfully, I do not have much money, but I have been able to gain a few books, and I will look up what I can into abstratct algebra.
    I can try the college library here, but I don't think there is much it can offer. This community is based on agricultural sciences, very little in other areas.
    Thanks again...
  8. Mar 25, 2008 #7
    You know that one of the worst things I've ever heard in my life is the advice Crosson has given you: telling someone like you to go to a university and enroll in a precalc or calc course (like it's free to attend a class full of nothing but a bunch of jerks who think they know everything about everything). But at least it's true that mathematicians have their own methods of arriving to conclusions and have defined things certain ways and all that jazz...but still it was always those free thinkers and people who never had training (a person to reference on the subject would be ramanujan) that usually changed the face of mathematics while people like those who study math spend all their time just trying to understand the genius of others. Aside from the lame advice given by others, props to you, in whatever you decide to do.
    Last edited: Mar 25, 2008
  9. Mar 25, 2008 #8
    It sounds like you had a very rough time in university, but that does not mean that formal training is a bad thing in general. Ramanujan is an example of a mostly untrained raw genius, but it would make more sense to say that such a thing is "rare" or happens "once in a while" then to say, as you do, that it is "always" or "usually" the case. A statement like that suggests an ignorance of the history in favor of personal fantasy: for every Ramanujan there have been at least 1000 untrained amateurs who wasted their time and breath to at best rediscover a defective version of the proverbial wheel. It's fine to complain about the high cost of education and the arrogance of the other students, but where will that attitude get you, compared to perseverance?

    As a side note, one of the benefits of learning mathematics is that you start to use language more thoughtfully, which leads to purging your phraseology of such grotesquely sloppy hyperbole as "one of the worst things I have ever heard in my life." Have you ever been informed of the death of someone close to you, is what I said really comparable to that? Turn off the TV and go read a book.
    Last edited: Mar 25, 2008
  10. Mar 25, 2008 #9
    I knew when I wrote a reply that you were going to get all offended. I wrote it anyways. I actually had quite an easy time in college and I didn't knock formal training, it's just that sometimes people like you don't realize that not everyone has the opportunities that you have or have had. It's a cold and heartless world, too bad we all can't be mathematicians, so loving and compassionate.

    Edit: Oh yeah, plus I think if you're going to give someone the advice of take the class or something like it, then you should fund them. No point in telling a drowning man, you should learn to swim. ;)
    Last edited: Mar 25, 2008
  11. Mar 25, 2008 #10
    This argument raised a hair on the back of my neck, so to speak...

    I was thinking about how I view numerical systems and what was mentioned about language, and I think I know a way of explaining language issues on this matter.

    Our numerical system is decimal. When we move from 9 to 10 we move up one place value, the same goes for all other numerical systems. Hexidecimal, Vigesimal, Binary, etc. And there are even more ways in which numbers are changed, and language, also.

    An example is quadrants. They are named I, II, III, and IV, were as I prefer calling them (-,+), (+,+), (+,-),(-,-) which makes it easier to know where they are.

    A parabola, is a name from another language to define a 'curve'.

    Triangles, actually any form, is nothing more than a specific definition of an object with either one or more points with lengths between those points.

    A point could be a triangle where each line has a length of zero, each angle is zero.

    Looking at equations that form a circle I have seen lines created by adding different numbers to the equations, a point is a circle with a radius of 0.

    I guess with all the similarities between them all, yet seeing what I have read, I guess that one of the most difficult things isn't only finding the answers but finding a language that the person in question is comfortable with and is acceptable, too.

    But as an aforethought. I study languages, also, and I really do not put much stock in 'using language more thoughtfully'. Not being rude or anything, but if you could hear how Mayan phrases literally translate to, you'd be baffled as to how they could have come up with the knowledge they had.

    I am not saying it's a good thing either, there does need to be some sort of 'common language' else we would have about a million ways of saying the same thing, which is the main reason I am here, I want to learn how to explain these things more 'universally' as well as if there have been previous works on them as well. Also, to see if someone might have mentioned at least a part of what I have looked into and give me a better way of expressing it.

    Hopefully that made sense...
  12. Mar 25, 2008 #11
    Be sure to check out MIT's OCW website. http://ocw.mit.edu/OcwWeb/web/home/home/index.htm

    Also, in the "Math and Science Tutorials" there are threads called "Free down loadable science texts". They also usually have links to free math texts.

    Some of the links I have are:
    as well as:

    The OCW at MIT is fabulous, and you can learn HUGE amounts of math for free. There are other OCW's as well.

    If you can't get to a University, have the University come to you!
  13. Mar 25, 2008 #12
    Yes everything you said made sense this time. I think you have good taste for what makes a mathematical observation interesting, and it was enjoyable to read these familiar facts in an unusually raw way.

    You see, I am not insisting that everyone mind their p and q letters according to some precisely prescribed grammar, but just asking you to meet halfway.

    Remember that the Mayan people were human beings, not essentially different from us. If you are impressed by the knowledge of their mathematicians, astronomers, and physicists (?), then you should be astounded by the modern cornucopia of knowledge we have today that is figuratively light-years beyond what they had.

    What is the difference that has allowed this accelerating rate of knowledge accumulation since the time of Newton? As Sir Isaac himself said, he "stood on the shoulders of giants." He did so to a greater extent then the Mayan people possibly could with their (according to you) highly figurative language that (according to me must have, as is usual) depended on ostensive teaching (pointing gestures). It has been said that what gunpowder did for war, the printing press has done for the mind; but written transmission depends on exact and thoughtful word choice if it is at all desired that the eventual recipient interpret it with meaning intact.
  14. Mar 25, 2008 #13
    I can understand that, and I surely hope I can be able to learn how to be comprehensible...:)

    Again, thanks for all your help...


    Quantumduck: Thanks a bunch. In just a few hours I figured out the imaginary (a+bi) and I think that I might have a better grasp of vectors from an applet that was used to help in explaining the imaginary numbers, also.
    Last edited: Mar 26, 2008
  15. Mar 26, 2008 #14
    If I were you I would pick up a few textbooks on Amazon.com. Find the subject you're interested in pursuing in mathematics and there will almost always be a few corresponding books on Amazon at an insanely low price - you just have to buy the book used.

    For instance, you could buy this $180 Calculus textbook for roughly $20; and the condition of all the purchases I've made were nearly perfect.

    I'm currently in high school, so I have the option of stealing a book for virtually any subject that piques my interest (don't worry, I return them at the end of the year). Personally I haven't found any other medium that teaches mathematics better than a textbook. Why? Because it contains many different aspects of the subject (Geometry, for example) in a concise, orderly, and progressive manner. I don't have to worry about hopping through a different Wikipedia article every 12 seconds.

    Anyway, I hope you're as successful in your mathematical endeavors as I hope to one day be myself, good luck!
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