- I apologise if I break any rules of netiquette,

as this is my first send on this post. I am but an

independent mathematician out of Dallas, TX and have

an insatiatable appetite for mathematics and logic. So

here are my two cents on the prime coordinates issue:

There is a way to make the addition of

coordinates work, but you step outside the realm of

integers by doing so. Taking upon the idea presented

by Sergio Ribeiro, you could take the main X, Y, and Z

poles and use the ln of all of the coordinates. Then

by adding X+Y+Z them you get unique coordinates for

all normal (X,Y,Z). Reason is due to Unique

Factorization Theorem: just like multiplied

coordinates in Sergio's system have a unique

factorization, the addition of the three ln

coordinates also equals ln XYZ and this number is

always unique by construction.

I'm not sure if it can be scaled to integers,

using a system such as floor(C*(ln X + ln Y + ln Z)),

finding a C that would give each coordinate a unique

integer value. The reason is due to the distribution

of primes: ratio of primes is 1/ln n, so I would

assume that as you approached (inf,inf,inf) you would

find coordinates (x1,y1,z1) and (x2,y2,z2) such that

ln x1y1z1 - ln x2y2z2 is arbitrarily close. Any takers

on a proof or disproof?

I couldn't forsee the use of such a system,

however. Cantor already proved that Z^3 and Z are the

same cardinality and this would also prove the same,

albeit more romantically (not necessarily more

elegant, but more aesthetically pleasing ;). You

already have a real number for every R^3 coordinate,

in a somewhat more dense fashion. I could see the

interesting possibility of adding two ln XYZ

coordinates together, because the pair of coordinates

added together could be deconstructed from the sum,

using the same reasoning above. (three coordinates

however IS impossible by the presented method)

As far as the philosophical debate, I say

whatever floats your boat. What matters except for the

mathematics? Why step outside of the mathematics? It's

only symbols; It's inherent in nature; It's man-made;

it's created by God; Man is God whatever. What matters

is the mathematics. To put in my two cents though,

this is how I see it: Logic is god, and reality is

just the symbols of god flying around to the winds of

logic. No personification. Mathematics is simply the

practice of putting symbols on paper and letting them

dance on the winds of logic. But does it matter to the

mathematics? As long as math doesn't try to supercede

logic, we're on solid ground.

--leadhyena

__________________________________________________

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http://auctions.yahoo.com >ratio of primes is 1/ln n, so I would

ln x1y1z1 - ln x2y2z2 is minimum when x1y1z1-x2y2z2=2.

>assume that as you approached (inf,inf,inf) you would

>find coordinates (x1,y1,z1) and (x2,y2,z2) such that

>ln x1y1z1 - ln x2y2z2 is arbitrarily close. Any takers

>on a proof or disproof?

Assuming this happens infinitely often, then ln x1y1z1 - ln x2y2z2 tends to

zero.

Jon Perry

perry@...

http://www.users.globalnet.co.uk/~perry

http://www.users.globalnet.co.uk/~perry/maths

BrainBench MVP for HTML and JavaScript

http://www.brainbench.com

-----Original Message-----

From: Leadhyena Inrandomtan [mailto:leadhyena_inrandomtan@...]

Sent: 31 January 2002 20:45

To: primenumbers@yahoogroups.com

Subject: [PrimeNumbers] About that coordinate system...

I apologise if I break any rules of netiquette,

as this is my first send on this post. I am but an

independent mathematician out of Dallas, TX and have

an insatiatable appetite for mathematics and logic. So

here are my two cents on the prime coordinates issue:

There is a way to make the addition of

coordinates work, but you step outside the realm of

integers by doing so. Taking upon the idea presented

by Sergio Ribeiro, you could take the main X, Y, and Z

poles and use the ln of all of the coordinates. Then

by adding X+Y+Z them you get unique coordinates for

all normal (X,Y,Z). Reason is due to Unique

Factorization Theorem: just like multiplied

coordinates in Sergio's system have a unique

factorization, the addition of the three ln

coordinates also equals ln XYZ and this number is

always unique by construction.

I'm not sure if it can be scaled to integers,

using a system such as floor(C*(ln X + ln Y + ln Z)),

finding a C that would give each coordinate a unique

integer value. The reason is due to the distribution

of primes: ratio of primes is 1/ln n, so I would

assume that as you approached (inf,inf,inf) you would

find coordinates (x1,y1,z1) and (x2,y2,z2) such that

ln x1y1z1 - ln x2y2z2 is arbitrarily close. Any takers

on a proof or disproof?

I couldn't forsee the use of such a system,

however. Cantor already proved that Z^3 and Z are the

same cardinality and this would also prove the same,

albeit more romantically (not necessarily more

elegant, but more aesthetically pleasing ;). You

already have a real number for every R^3 coordinate,

in a somewhat more dense fashion. I could see the

interesting possibility of adding two ln XYZ

coordinates together, because the pair of coordinates

added together could be deconstructed from the sum,

using the same reasoning above. (three coordinates

however IS impossible by the presented method)

As far as the philosophical debate, I say

whatever floats your boat. What matters except for the

mathematics? Why step outside of the mathematics? It's

only symbols; It's inherent in nature; It's man-made;

it's created by God; Man is God whatever. What matters

is the mathematics. To put in my two cents though,

this is how I see it: Logic is god, and reality is

just the symbols of god flying around to the winds of

logic. No personification. Mathematics is simply the

practice of putting symbols on paper and letting them

dance on the winds of logic. But does it matter to the

mathematics? As long as math doesn't try to supercede

logic, we're on solid ground.

--leadhyena

__________________________________________________

Do You Yahoo!?

Great stuff seeking new owners in Yahoo! Auctions!

http://auctions.yahoo.com

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com

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Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/- --- In primenumbers@y..., Leadhyena Inrandomtan

<leadhyena_inrandomtan@y...> wrote:> I apologise if I break any rules of netiquette,

Hello,

> as this is my first send on this post. I am but an

> independent mathematician out of Dallas, TX and have

> an insatiatable appetite for mathematics and logic.

It is nice to welcome someone with an interest in logic.>

Yes, but symbols of reality. Therefore the 3-d cartesian co-ordinate

> As far as the philosophical debate, I say

> whatever floats your boat. What matters except for the

> mathematics? Why step outside of the mathematics? It's

> only symbols;

system is a real 'discovery' which will affect humankind for all

generations. You also have the possibility to contribute.

It's inherent in nature; It's man-made;> it's created by God; Man is God whatever.

Man is A God. Man is not THE God. We are 'chips off the old block.'

But I digress.

What matters> is the mathematics. To put in my two cents though,

This is a nice metaphor for 'streams of consciousness' that we have

> this is how I see it: Logic is god, and reality is

> just the symbols of god flying around to the winds of

> logic. No personification.

> Mathematics is simply the

> practice of putting symbols on paper and letting them

> dance on the winds of logic.

been discussing as the 'matrix' for collective thought. The 'out

there'.

But does it matter to the> mathematics? As long as math doesn't try to supercede

Yes, logic oversees mathematics as an elder brother to a younger

> logic, we're on solid ground.

brother.

Nice comments. Do you have any of your own work you would like to

share with the group?

regards,

Paul Mills

Kenilworth,

England.

> __________________________________________________

> Do You Yahoo!?

> Great stuff seeking new owners in Yahoo! Auctions!

> http://auctions.yahoo.com - Dear Colleagues,

I never expected so many emails about the 3d

coordinate system. I must thank everyone for

contributing. In the original Email I sent to this

group I had a typo on my email I was missing the

number 19. One to many beers that night :). Now I

realize that as long as xp>Yp>Zp etc.. that any group

or grouping of prime numbers can be used for the

system, As long as they are larger prime numbers than

the 1st group.

Regards,

Jason Kurtz

__________________________________________________

Do You Yahoo!?

Great stuff seeking new owners in Yahoo! Auctions!

http://auctions.yahoo.com