# Other ways of counting

1. Nov 25, 2003

### alflud

Hello all! First of all, please excuse me for barging in on you all like this. I am a nobody with little formal education in ANY field and I apologize if I seem a little mad. The bottom line is this - I just CANNOT find any satisfactory answers to my questions across the whole of the net and having read in this site I deem this to be the best of all candidates for probable answers to my crazy daydreaming .
Ok, so I am a nobody with feck-all know-how, but that doesn't mean I don't know what I'm seeing when I'm looking at it. Now, there's an exception: when I look at the number 9 I just dunno wtf!!!
Can anyone tell me what is going on here? I have even approached professors with my queries and ALL of them more or less told me the same thing: 'ah, it's just a funny number, that's all'. I kid you not! Now maybe you all know what a 'funny' number this is, maybe you all don't, but mess about with your calculators there for a while and go about adding the digits of your resluts and you will begin to see some pretty wierd relationships. And it IS wierd considering that we have a decimal number system. For instance:
if we take 9, multply it by ANY number and add the resulting digits together we will get 9 -> 9*3=27, 9*137=1233, 9*27=243.
And this is just multiplication. Add 9 to any number and you will get a result the same as the original number, e.g. 43+9=52 (4+3=7 5+2=7) (Is there a name for this process of adding the digits of a number?)
A sphere is 360^*360^, a torus: 360^*360^*360^.
This 'thing' - whatever it is - is wound into the very fabric of our universe (well I believe it to be anyway or at least Cicular Motion(gives everything it's FORM - take away spin:take away form)). And it gets wierder: like WHO devised the decimal, imperial, and metric systems - and did they somehow incorporate into thier thinking that a 9 should 'convert' neatly? 9 miles = 14.484096 kilometres: 1+4+4+8+4+9+6=36 (3+6=9)etc. etc. etc. etc..............
What's this all about? WTF????? And also, is it wierd that lines of latitude are more or less 111km wide and longitude only 111km wide at the equator? 3 is the square-root of nine and therefore just as noticable for IT'S peculiar qualities also.
I took 365*4 and added 1 for the leap year = 1461
divide by 9 = 162.33333333333333333333333333333
divide by 9 = 18.037037037037037037037037037037
divide by 9 = Feynmans 'cute' little cycling sequence!
(Don't ask me why I did this as I'm sure I haven't a clue.) Is this just a coincindence or what? Guys - I feel as if my brain is gonna burst or something here! Does ANYONE here know what the BEEP is goin' on? Are any of you even curious at all? How can you NOT be? Well at the very least, this thread will stay here for a long time and maybe will throw us up an answer or two someday - who knows?
Thank you all for your time and patience. Believe me, I tried to keep this initial thread as small as I could (and still get across my point[OUCH]) but there are a LOT more coincidences and funny relationships here than what I have just touched upon. (Check it out but not unless you're prepared to spend a LOT of time at it.) Can anybody, anywhere shed some light on this for me please? And please - let's not hear anything about 'Gematria'. The Net is full of it - and it suxx. There is a scientific explanation for this - there HAS to be. It MAY be mystical also but who cares? There is science here and I am only interested in that so for all you would-be jokers - leave it out please.

2. Nov 25, 2003

### HallsofIvy

This is called "casting out nines" and works because 9 is one less than the base of our number system, 10.

For example, if you start with any number 100a+ 10b+ c, with digits a, b, c, and add 9 that's 100a+ 10b+ c+ 10- 1= 100a+ 10(b+1)+ c-1.
The sum of the digits is a+ (b+1)+ c-1= a+ b+ c so it hasn't changed.

If you multiply 100a+ 10b+ c by 9 you get

(100a+ 10b+ c)(10-1)= 1000a+ 100b+ 10c- 100a- 10b- c
= 1000a+ 100(b-a)+ 10(c-b) - c.
Of course, the last "digit" is not c, it is 10- c so
the second digit is not c-b , it is c-b-1 (assuming that is positive, if not continue to the next digit).

The sum of digits is a+ (b-a)+ (c-b-1)+ (10- c)= 10-1= 9.

3. Nov 25, 2003

### Guybrush Threepwood

a simple example:

5684 +9 = (5*1000 + 6*100 + 8*10 +4) +9 =
= (5*1000 + 6*100 + 8*10 + 4) + (10 - 1) =
= 5*1000 + 6*100 + (8 + 1)*10 + (4 - 1)
= 5*1000 + 6*100 + 9*10 + 3

you can do that with any number and if you add the digits you'll get the same sum from both numbers. Hope it's clear why....

I'm not sure what are you trying to say with this, but in the same way you can say a sphere is aprox 6,2831853*6,2831853....

edit: damn, I'm late

4. Nov 25, 2003

### alflud

Add those digits -> 6,2831853 -> 6+2+8+3+1+8+5+3=36 -> 3+6=9 HOW IS THIS?
what I mean is that the number nine, being the highest WHOLE number, is representative of all of our fundamental shapes. Add together the digits that represent most, if not all of our fundamental values and we will almost always get a 3, 6 or 9. I don't have sufficient Mathematics know-how to express what I mean more clearly. Everything is fractal-like also, yes? The microscopic universe has massive similarities to the macroscopic universe and even tho I don't have any proof or assertions on the matter I am sure there are also similarities in the quantum universe also. Quantum is wierd - think about this: the particle is probably heading that way at this probable speed: there are no clear defining edges are there? We are forced to look for a balance in order to get any clear value at all. Our base10 system doesn't allow for division by 3 very often and the binary system we compute with doesn't either. With 2 one can only have yes/no values, ok? Black or White - clear, DEFINED lines, yes?
It is how we are used to thinking. Give a computer 3 bits to work with and we introduce a chaotic element into the system (i.e. chaotic to 'our' way of seeing things). If you have 2 people in a group there can always be a stalemate when it comes to decision-making - but if you have 3 there will always be a casting vote. This is important. THIS is what staves off stagnation and drives evolution! A minimum of 3! You need at least three rockets for a balanced ride. 3 points for a triangulation. Give the computer 3 bits and see what happens! Could it be the first steps towards artificial intelligence? Who knows - probably loadsa baloney! Anyway the point is this: why is absolute zero exactly -273.15: why is the tilt of the earths axis 23.4 degrees: and why is 1AU 150million kilometres? Why do all of these resulting digits all add up to 3, 6 or 9? Ok, so there are many things that do NOT show resulting 3's, 6's or 9's but I only 'watch' for these occurences - I don't actively research it (doing so only hurts my head! lol) so I only see that which tallies with my thimking. Sorry if that is unacceptable.

5. Nov 26, 2003

### Guybrush Threepwood

actually that is 2*pi truncated at the first 0. pi has a infinity of digits so you're welcome to add them all and demonstrate that you get 9
http://www.cecm.sfu.ca/projects/ISC/data/pi.html [Broken]

still I don't know why did you multiply 360 with 360 to represent a sphere.......

You might want to rethink that.....

Last edited by a moderator: May 1, 2017
6. Nov 27, 2003

### uart

Hi alflud, before you start you really need to adopt the mindset that there is a simple mathematical explaination and that there is no "magic" involved with these properties of 9. Also try to tackle and understand the concepts one at a time.

Now both the properties of 9 that have alread been explained above (that is that both "add 9" and "mult by 9" leave the digit sum unchanged) can be explained from just one simple property of 9.

That one property is :
In modulo 9 arithmetic every postive whole number is the same as the sum of it's digits

Take one of your numbers (137) for example,
137 = (1 * 100) + (3 * 10) + (7 * 1)

= (1 * 1 + 1 * 99) + (3 * 1 + 3 * 9) + (7 * 1)

= (1 + 3 + 7) + ( 1 * 99 + 3 * 9 )

= ( Digit Sum ) + ( Exact multiple of nine )

It should be reasonably easy to see that this same approach can be applied to any whole number. In other words every whole number is always equal to the sum of it's digits plus an exact multiple of 9

7. Nov 27, 2003

### alflud

uart - thank you for your reply. First, if there is such a thing as magic it is only science that we do not understand yet. Magic is a word for children and parties please Coincidence has always been a driving factor. What seems to be a coincidence at first nearly always ends up being explained in a rational way but only after our curiousity (first aroused by this 'coincidence') has sought out the explanation. ->

If we take item A and experiment with it, and say someone else has item B and is experimenting with that and later when the two people are talking, discussing their respective work, one person says to the other: 'that really happened? You really got those results? Man that's some coincidence! There's something going on here - I need to go back and correllate all this to try find out whats going on here.'

We all know that there really isn't such a thing as a coincidence. Everything can be explained and we strive to do just that because we really don't believe in coincidences - we KNOW there is a relationship there somewhere and we feel driven to discover it.

There are too many coincidental things about the number 9 for this to have a 'simple explanation'. I know I do not have the mathematical abilities of all of you guys, that is why I came here, and I do defer to your knowledge, but I don't need the experience of all of you to know that what I am curious about here is possibly one of THE biggest coincidences of our time.

Is it easy to convert a known equation from base10 to some other, say base9, system? Would someone be willing to do that for me and study the result for extra 'tidiness' (the equation would therefore have to be untidy to begin with) or 'slopiness'?

Also, uart, I have been investigating Modulo9 Arithmethic - very unusual stuff - also very interesting. Thank you for the pointer.

8. Nov 27, 2003

### Guybrush Threepwood

you can always try....

not more unusual than the other modulo arithmetic (say modulo 2, or modulo 122545343143548434212224588897)

9. Jan 12, 2004

### pallidin

Interesting...

10. Jan 12, 2004

### Jeff B

people who ramble make me happy :)

Indeed I've spent half my life going over this quiery......

Jeff

11. Jan 16, 2004

### matt grime

And do you realize that isn't even true?

9*11 is 99, add the digits an we get 18 which isn't 9.

If you're going to point out the delights of mod 9 arithmetic at least get it right.

12. Jan 19, 2004

### Guybrush Threepwood

he means keep adding the numbers if you have a number of more then 1 digit. You get 1+8 = 9
some king of numerology stuff I think.....

13. Jan 19, 2004

### matt grime

I knew what he meant, but only from experience.

I wish that everyone who found some 'new and amazing' numercal facts would take a second to think why it's true rather than just saying 'wow! would you look at that.' But perhaps that's too demanding if no one gets taught simple modular arithmetic at high school anymore.

Wonder if the OP has figured out how to determine divisibility by 11 yet?

14. Jan 27, 2004

### red_fox77

Remember, mathematics was invented/discovered by us as a way to describe observations of nature. By that premise alone it is probably flawed by the observer (us) and will never be more than a tool, not the gateway to 'magic' that some people claim.

Mathematics is the tool to truth, not the truth itself.