In a number like 1/9 with only one decimal; I can’t access the numbers moving to the left with a normal calculator; this has become bothersome to the degree that I’m more and more requiring to splice in certain points of infinite decimal readouts.
1414/9
157(1/9)
157.1111111111111111…
<---------157-------->.<---------111111111----------->
Every number in a specific composition like this has an infinite number of algorythms (in the form of structured scales - what most consider ‘complete songs’) running through it spacially from all directions.
157.10^6backwards.(1/9).3 <----------
157.0000001<---------…11111111111…<--------3
^
take a well known one like 1/7 0.142857.142.8437
857
142
857
V
Right now I’m using it for composition signiture frequency modulations to compose music and recursively narrow down the most likely signature for a given body of work. I require these spacial edits for dimensions of timbre, tone, velocity, rhythm and whatnot…
It’s a benchmark I set for myself to keep pace. It only get messier after this =)
It’s a means to circumvent the floating point problem I keep running into. For a specific decimal readout; I turn it into a whole number by applying it’s base inversion against it; creating something like a physical structure from which I can observe intersecting themes and isolate various operators (in the form of numbers) working within the structure.
D’oh… figures it wouldn’t format correctly. Move that gibberrish by the word “take” over to the 142. This pictoral certainly doesn’t do it justice; but I think it conveys the general idea of what type of calculator I’m searching for.
So, I think I actually understand what your getting at Justhink. What you want is a way of appending different number sequences onto each other.
So you have
a = 467346554
b = 3557674354865
so a.b.a = 4673465543557674354865467346554. In that case, I would suggest using a symbol other than . becauseyou need that as a place holder… If you have any knowledge of programming, I think the easiest thing to do would be to convert each number into a string, append the strings together and then turn them back into integers. Perl would be good for this I suspect.
You guys do know that computers and calculators are using binary, don’t you? There’s a whole other aspect to the question posed in the OP regarding decimal fraction conversion to binary that results in inaccuacies at the least significant digits.
I have never seen nor heard of numbers with multiple decimal points, but then again I’m not a math major - does such a thing actually exist?
I more or less think I understand what you want to do, and if I’m right, I worked on something very similar.
Take a musical note, it can possibly be expressed by four parameters, say, frequency, amplitude, timbre and duration. If we asign an arbitrary number to timbre that corresponds to a preset on a synthesizer, we might get the following values for a note:
220.2
5000
3
254
However, because these four parameters correspond to a single note, you want to express them as a single value. The way this is done, is by writing them down as a 4-dimensional vector, written: (220.2, 5000, 3, 254). Thus, in a composition, each note becomes a single point in 4-d space, and, using vector arithmetics, you can then perform statistical analyses on your data set (the composition).
As has been mentioned, binary conversions and multiplication/division are both pretty sensitive to rounding errors. That’s pretty much what this all comes down to.
I think jovan is right on as for what you really want to do. There’s no such thing as multiple decimal points in mathematics.
-----------------------------157.
…111111.11111…1111.11111…
---------------------1
----------------1---------1
--------------1-------------1
----------------1---------1.4141…0…111111…
---------------------1
Basically, the process of division allows one to select two numbers in a very structured setting. One of the ‘numbers’ is motion; charachterized by a repeating decimal output. By seperating the two numbers one can use both numbers to speak about themselves by calling slots in their own respective structures; ultimately speaking about the higher order as well; that created the decimal condition in the first place from the process of division. Think of the number 157 here as a mount on top of a ring; being expressed as perched atop a ring of repeating ones; the ring is 157 loops of 157 1’s running trough each 1 157 different ways. The point is that I require numbers to be able to speak about themselves by reading the values of their repeating output and then dropping a mark on that output for further recursive exploration to grab the higher order out of the system. That would be ONE area of the decimal number. When mapping an operator; these loops are converged with another series of abstractions on the same layer; at which point this convergenge is marked itself by a repeating decimal output which is eventually extracted into a whole number readout of ratios. The additional decimal points are used as markers that recognize the first order reading itself in the context of the numbers reflected in the output; effectively translating itself to that degree.
Additional calls can be made to numbers than cannot divide equally when selected; at which point another division is procured at the designated mark.
Part of this system as well is to allow the efficiency of expressiong a number like:
Where it would only be expressable as as
0.11111111111…
before.
One of my largest problems is expressing numbers like this:
000011111111111111112222222222222000000000000
As an answer for a specific process. Often times I’ve run into areas where these types of answers are implied; but calculators will only save them on the side where the decimal point is.
This has become a problem when dealing with ‘backwards reading’ and other uses I’ve found necessary as of late.
I’m just having lots of fun with decimals right now; but this can be a bit annoying when running a loop bewteen process and answer; when I’m expecting this type of output on the other end; only to know that it has been lopped off; at which point I do the division by hand.
so a.b.a = 4673465543557674354865467346554. In that case, I would suggest using a symbol other than . becauseyou need that as a place holder… If you have any knowledge of programming, I think the easiest thing to do would be to convert each number into a string, append the strings together and then turn them back into integers. Perl would be good for this I suspect.
I need . as a placeholder on two sides. I tried working symbolically by oscillating between bases; and isolating an additional number to that degree; but it still gives me the floating point issue with respect to a placeholder I need on both end (I still get infinite regress in this process)
It’s not satisfactory for me to place a symbol like this without the symbol itself describing how it arrived there.
One of my challenges involves mapping all the other operators into division itself. How does division read a 3 and tell me what is in the 3rd place? These are the types of issues I’m working on resolving.
Is there a question left re the OP because most of what you seem to be (apparently) discussing at this point is quantatative data analysis programming strategies which might be better served with a separate thread addressing these issues.
The translation process will typicall render something like:
333334 (depending on the other number I’m working with).
However; I can observe that there is another number back there which requires articulation in the process I’m using. It makes a big difference what’s back there!
0333334?
1333334?
2333334?
3333334?
Without two decimals I can’t resolve it using a calculator.
I try reversing the decimal output, and the obvious occurs:
0.43333333333333333
is it
0.4333330
0.4333331
0.4333332
0.4333333
??
I find that accessing these numbers is critical towards knowing which part of the repeating fraction I’m opening up to insert a value. That’s why I’m using this convergence method; with the right side designating the values until I can nullify it and recieve a purer decimal output. At first I started taking random pop-shots to locate it, have lately figured out how to apply slightly more efficient factorization; yet the amount of data being factorized is phenomenal. At least I know some system boundaries now - so it’s not as bad as a needle in a haystck; but still pretty damn close. I can always cheat by using addition; but I’m trying to map addition!! I can’t do that =)
I’ll stop with this topic; thanks for the replies. I don’t know programming languages; I’m trying to create a natural one through base conversion using the process of division; so that programming languages can be scanned for function (composition signature) and recalled through a direct command in english for a specific function (composition signature frequency).