I invented a number system in 2008 and I've never shared it with the public I thought I might as well...I had my reasons at the time for inventing it, and i think it may be useful...although i invented it, it's features are really natural features of our universe itself, and are therefore much less arbitrary than any number system i've encountered before,,,,,The number system is used as follows,,,,,a equilateral triangle is disected into combinatory permutations of it's sides,,,,there being 3 sides of a triangle there are 7 and only 7 representable permutations, no more, no less, consisting of 3 instances of one side represented, 3 instances of 2 sides represented, and the one instance of the full triangle being represented the reason this number system may be useful is that because of the nature of science and scientific endeavor every effort we make toward finding the truth in turn affects the truth we are trying to find, and our work changes the environment we live in (based on the Heizenburg Principle), we have no choice but to live in it, we have no choice but to operate on the same plane as our experiments and logics. This has been apparent in the usefulness of "Planke's measurements" in physics, where simply by using different scales of measurements that are more related to the subjects of physical interactions the physicist is investigating,,the physicist can !sometimes (caveat) come up with better measurements and predictions,,,,realistically if you look through 2 different microscopes at the same subject you would expect to find the same thing,,,of course if you killed the subject with the first microscope you might end up seeing something different with the second microscope regardless,,,,so my number system could be used to further verify currently proved mathematical theory,,,by actually using it to do all the same mathematics done with current systems,,,,you would actually be strengthening any previous arguement if you found the same answer with another base of number system,,,(my number system is base-7),,this is because you have further tested that your choice of number system was not a factor in coming up with your original answer,,,,so technically you would want to test every major mathematical arguement with my number system and others (perhaps other bases) to make sure the same answer is always found in those other number systems (of course there are WRONG answers to be found if the the number system does NOT define the same points on Y=X),,, Getting back to my number system it is visually represented by drawings of the equilateral triangle,,,,the convention used would be a point directly pointing upward to keep constant the triangle's orientation, and a convention on reading in the direction of the native language of the user of the number system,,,thus from what i said before / = 1.00, \ = 2.00, _ = 3.00, /_ = 4.00, _\ = 5.00, ^ = 6.00, and /_\ = 7.00 in the set of real numbers,,,depending on the writing convention of the user present you would simply add triangles and parts of triangles of any quantity to thus represent any number from 0 to infinity, and from 0 to negative infinity, the negative sign ( - ) could easily be used to expand my system as well as decimal places to represent fractions, and the addition of a zero is easy, i decided on a personal convention of an upside-down equilateral triangle to represent zero further this number system can be adapted into a "base-8" system by adding the zero usage to all real numbers at the "8" place adding a zero after every 8 regular integers also the writing convention can be compacted further by grouping triangles into regular shapes at regular intervals, for example there is a shape used in the video game "Zelda" called the triforce that in my number system would represent 21.00, it being 3 triangles,,,,thus my number system can potentially be adapted to hold and convey more information than the standard 10-base used today, especially if multiple regular shape conventions were invented,,,(why it relates to the symbol in a video game is just by chance) As I said at the beginning my number system relates inherently to the universe itself,,,as a equilateral triangle always disects into seven permutations, no more, no less,,,thus my number system is not arbitrary, it is in fact universal,,,,I am publishing my work here, so that any one can use it, and I am going to keep studying this and also large numbers (see http://answers.yahoo.com/question/i...58eVPQDsy6IX;_ylv=3?qid=20111223022617AAELnv4) Ivery much need and want input on this subject,,,,pls email me at kdunham1@rocketmail.com,,,,and i also welcome any related material any one already has that might help me , send me your links! ))) ty and God bless -K
1. Mathematics has nothing to do with actual, measurable reality. 2. A "number system" is not the end-all be-all of mathematics. Mathematics is not built entirely on the integers, or the reals. There are things called axioms, look those up on google. 3. The fact that you misspell many names and terms scares me. How do you expect anybody to take you seriously if you couldn't care to properly do your own research? Your understanding of what mathematics is as a whole is completely flawed. Your argument as to why your number system is more natural is unsupported and not really try after all. I'm not saying all this to be mean, I commend your efforts and willingness to think about mathematics on your own, but this can be filed under crackpot stuff. did you think that just because you're counting sides of a triangle your method is more natural? How does this help in any way? If you had shown us how some calculations were more efficient in your so-called "base 7", then perhaps it would help your argument. Summary: This is crackpot stuff, and sadly, quite useless. Again, I didn't want to be mean, I am sorry if I come across as harsh. Edit: There are also many, many more things I would have liked to comment on (Ex: why _\ = 2.00, with exactly 2 sig. figs.), however, in an attempt to stay moderately friendly, I will not comment on them. My advice to you: Take some mathematics classes. Read some mathematics books (Courant's "What is Mathematics" springs up in my mind), study more. You have lots of things to learn yet.
then why are you bothering to reply? the accesibility of methematics is an issue, and as you take such a vitriolic reaction to my ideas I assume you don't care about it's accessiblity anyway, if i had just introduced the base ten system over the use of the roman system YOU would still be yelling "this has nothing to do with math" You are wrong. My number system can potentially convey more information than the currently used base ten system, because as i said my system can be not only base-7, but also base-21 and so on at the same time. All I can say is relax, no hard feelings, but you are wrong.
Can't the base 10 system we commonly use relay an infinite amount of information already? There's no limit to how many digits a number can have. I don't understand where the alleged limitations lie.
You keep saying that, how it can simplify things, how about you show us? This is what peer-review feels like. It's not about compassion. Get used to it. You have given zero good arguments as to why your idea is worth anything. You're clearly offended when you should not be, this is criticism, it should help you.
To be fair, I only skimmed what you wrote in the OP. However, I fail to see how your "number system" is more accessible. I had a hard time making heads or tails of what you wrote. Another thing to consider is that most of modern mathematics is not dependent on the base we use.
Besides it already being mentioned here that you're just using a base 7 system, which is nothing spectacular, I'd like to know whether you think the triangle is more natural than say, the square? And looking at your link to yahoo answers, it's quite clear that you're trying to come up with some extensions to what we already know but what isn't taught in high school. You're gravely mistaken for thinking it's something new and ground-breaking though. Just look at number systems for your answer in this thread, and knuth's up arrow notation for the big numbers.
i'm not saying I have a new number for gravity constant g, im saying that at the very least it is interesting to represent other bases,,,,here's another sequence that my study will show to be regular and dependent on geometry, if you were to permutate the sides of larger equilateral figures you would get a exact immutable sequence that you nor i can change, starting with the triangle it would be 7, 15 for square, 28 for pentagon, and larger and larger, although i dont know if you could say this number hits infinity or not,,,,another sequence that is interesting which is a derivative of this work is the relation of these numbers to the number of sides they have, so let's make a convention that number of sides can be represented by B and the permutation total can be represented by A,,,so, for the triangle, A=7, B=3, A=2B+1, for the square A=15, B=4, A=3B+3, and so on (also for pentagon, A=28, B=5, A=B^2+3) ,,,these numbers are immutable so it is interesting that they are close to the self multiplication of their number of sides, or B^2, and the differences could also then be represented in a sequence such that the difference from B^2 for each permuation takes the IMMUTABLE sequence of (-2.00,-1.00, 3.00),,,,if this doesnt interest you that's fine, but there's nothing about it to berate thank you for your time, -K
i had already written my reply but didnt see your reply Mentallic, as i showed in my newest reply the square would permutate to a 15-fold system and this is really hard to remember and keep in a standard convention,,,maybe what im saying in the original post sounds like jargon so ill put it simply,,,, here is the codex for my number system (a codex being an agreed upon convention, to emphasize, this is a convention only) /=1, \=2, _=3, /_=4, _\=5, ^=6, /_\=7 then additions to the right are simply added to the total number of triangles which in turn are multiplied by 7, this number system can describe any real number from negative infinity to positive infinity. Thank you for your time, -K
Here again no offense intended but you should show the implication of your number system to other areas of mathematics. In what does this idea help or connect to other ideas/concepts in mathematics? Also if you want people to read your idea, you should write it in a mathematical style presenting definitions, motivations, theorems and proofs. The proofs shouldn't be personal opinions or anything for that matter but rather a rigorous way so that others could check your work. With that said, like others said, I do recommend you get a taste of real mathematics if you haven't already done so. Pick a book in real analysis, topology, algebra or advanced calculus and see the proofs, the concepts and problems. The work great mathematicians have done should show you that any mathematical idea is not isolated: It has connection and rich implications to other branches of mathematics. A humble start will be to learn as much as possible and when one is ready, one could go to tackle problems. It will also be nice if you could tell us your mathematical background and how this problem/thought came about.
Any number system can convey the same information as any other number system. There are lots of number systems in common use, besides the decimal system, such as base 2, base 16, and base 64. The only practical advantage in having a larger base is that a given number can be represented with fewer symbols.
i don't have to justify my interest in mathematics, and abiyo that is really distasteful what you are implying, i could ask you to do the same but im not going to because that would be impolite. Yes there are many concerns about the way you look at mathematics and the tools you use, for example physicists are finding the Planke's units to be very useful where they, through a convention, define units of measurement as relating to a baseline number relating the 5 constants in physics. When this is done numbers that are unwielding before with the standard base ten number system and sociologically determined measurement systems (meter, second, etc.) are then transformed into sometimes useful managable numbers. Again although this doesnt always occur it can sometimes in the environments of physics and chemistry which are vastly different from the "meat and potatoes" (pun-intended) environments of everyday meter and second measurements. While I will not ask you to list your mathematics degrees I will put this challenge to you, please dispute, with reasons, my above defence of the need to broaden mathematical tools availible to mathematicians. Or let's put this simple. Does 1.5x10^280 = 1.5x10^280 + 1? Now prove to me that they are not equal. In base 10 you would represent them...exactly the same. When a number system or human lacks processing power what do they do? They approximate. We see this with pi, we see this with the speed of light. And computers utterly trump humans in the numbers of digits they can remember and calculate. Again please explain why each of these points is not valid, and all of them relate to my number system. Or are you just going to refute them because they are new ideas. Are you going to skim the post and then make a broad generalization? Thank you for your time, -K
I think you misinterpreted the intent of his/her post. The first point was essentially that if you expect other people to take your idea seriously, then you need to demonstrate that the idea is useful to them. Since very very few mathematicians do any work at all with different number-bases, you really have not given a sufficient justification why anyone should take your idea seriously. It might not seem like that is how things should be, but it is how they are. The second point was essentially encouraging you to study some serious mathematics and learn how various fields interact. I really fail to see how this is offensive. First, Planck units are not really a tool, just a notational convenience. Second, it turns out that most of modern mathematics is independent of whichever base you choose for the natural numbers and integers. So your idea probably has very few (if any) novel applications to modern mathematics. Assuming that we are talking about N, that they are not equal is essentially a matter of definition. In fact, it is easy to prove that n+1 ≠ n for any n in N. It doesn't matter which base we choose to represent n as! The proof is independent of the base! There are plenty of instances where approximation is useful or necessary in math. This is not one of them. I think the above should explain why nobody is taking your number system seriously.
Nor are we asking you to. And besides, that's not what the discussion is about. What abiyo wrote seemed entirely reasonable to me. What is it that seems so distasteful about what you believe he is implying? No, 1.5x10^280 and 1.5x10^280 + 1 are NOT equal. 1.5x10^280 = 150000...00 (I am not showing the 279 0's that follow the 5 digit.) 1.5x10^280 + 1 = 150000...01 (I am not showing the 279 0's that follow the 5 digit.) If pressed I could easily write out all 281 digits of each number. Clearly these are not the same number, and just as clearly, the 2nd number minus the first produces a difference of 1. That should suffice to show that they aren't equal. Why in the world would you think they are equal? The form you used is scientific notation, not their base-10 representations. I wrote the numbers in base-10 notation (with some digits omitted to save space). Other than using parts of a triangle to represent the numbers in your base-7 system, I don't see much new here. As already mentioned by others in this thread, mathematics is not much concerned with the number system that's being used. In much of mathematics beyond calculus, it is mostly symbols that are used, with very few numerals of any base in sight.
For your convenience, I quoted what I said, since you didn't. What part of what I said seems to be a dichotomy to you?
ok ill quote you mark, Mark44"Any number system can convey the same information as any other number system. There are lots of number systems in common use, besides the decimal system, such as base 2, base 16, and base 64. The only practical advantage in having a larger base is that a given number can be represented with fewer symbols." "a given number can be represented with fewer symbols" While you say this you ignore that this is beneficial depending on the usage of the base, this is in direct dicotomy to what you said above- "Any number system can convey the same information as any other number system" At the same time, a number system can most certainly FAIL to convey the same information as another. There are numerous instances of this in the case of the addition of zero, the change from the roman system to base ten, the adding of decimals. Then in your other above post i see nothing but baiting ideological arguements, I'm not interested in these unimportant small points you have with my ideas that certainly you are free to argue into the dust, for example here- Mark44 "No, 1.5x10^280 and 1.5x10^280 + 1 are NOT equal. 1.5x10^280 = 150000...00 (I am not showing the 279 0's that follow the 5 digit.) 1.5x10^280 + 1 = 150000...01 (I am not showing the 279 0's that follow the 5 digit.) If pressed I could easily write out all 281 digits of each number. Clearly these are not the same number, and just as clearly, the 2nd number minus the first produces a difference of 1. That should suffice to show that they aren't equal. Why in the world would you think they are equal?" "why in the world would you think they are equal?" is just completely baiting and snide tactics, we all know they are not equal. That is not the point of my bringing this up...
jgens "Since very very few mathematicians do any work at all with different number-bases" this is just blatant misinformation the use of base 2 in computing is well documented
Dichotomy is not the word you mean here. This is very plain since dichotomy is a noun while you are using it as a verb. I am nitpicking, but I think the distinction is important. We actually are not talking about number systems at all here. The term number system is usually used to refer to things like N, Z, Q, R, etc. What you are talking about is ways of representing the elements of number systems. As a result, one way of representing the number system must convey the same information as another way of representing it. What is the point of bringing it up? The result is trivially true regardless of which base we choose to represent our number system as.
You are misinterpreting the point. Sure, base 2 happens to be a useful way to represent some things in computablity theory, but that does not mean mathematicians are researching different number-bases and their properties. In fact, it is hypothetically possible to do the same work in base 10! Additionally, from my experience, most mathematicians do work in algebra, algebraic number theory, algebraic geometry, topology, analysis, etc. In these fields, the base-system you choose to represent the natural numbers (or other number systems) are usually irrelevant. So my statement is not incorrect from that standpoint either.