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The Number One as center of the Positives

 
 
Reply Sun 4 Apr, 2010 10:17 pm
It occurs to me lately that the number one is the center of all positive numbers. The smallest number is 1/infinity and the largest number is infinity/1. This puts "1" smack in the middle. Of course that's an oversimplification, but perhaps you get my point.

If we multiply any number by any number less than one, we are essentially dividing it. And if we divide by a number less than one, we are multiplying or increasing the first number. So 1 functions for multiplication/division in the same way that zero functions for addition and subtraction.

-1 is the center of all negative numbers. Zero is the number that is neither positive or negative, and the exact meeting point of the these inverse/mirror twins, the negatives and positives.

The smallest negative number is -1/infinity, and the smallest positive number is 1/infinity. How close are these two numbers? They both tend toward zero. Their only real difference is their signs, the badge of which dimension they hail from.

This sort of thing amuses me. I hope it amuses someone else.
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Type: Discussion • Score: 0 • Views: 1,345 • Replies: 28
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Jebediah
 
  1  
Reply Sun 4 Apr, 2010 11:02 pm
@Reconstructo,
I believe the Mandelbrot set:

http://www.clausewitz.com/images/MandelbrotSetSM.gif

Is based on that. The numbers that are less then one go extinct (approach zero, leaving the black spaces) and the numbers above 1 go to infinity, creating the infinite detail.
0 Replies
 
Deckard
 
  1  
Reply Sun 4 Apr, 2010 11:13 pm
@Reconstructo,
Reconstructo;148426 wrote:


The smallest negative number is -1/infinity, and the smallest positive number is 1/infinity. How close are these two numbers? They both tend toward zero. Their only real difference is their signs, the badge of which dimension they hail from.

This sort of thing amuses me. I hope it amuses someone else.


Did you really mean to say "smallest negative number"?
The small hole is greater than the large hole though both are still less than nothing. The rules are different on the other side of the looking glass: small things are greater than large things; or is the meaning lost in translation? "Small" and "large" are used analogous to their positive meanings. Are the pictures in your mind similarly analogous?
Reconstructo
 
  1  
Reply Tue 6 Apr, 2010 08:26 pm
@Deckard,
Deckard;148437 wrote:
Did you really mean to say "smallest negative number"?
The small hole is greater than the large hole though both are still less than nothing. The rules are different on the other side of the looking glass: small things are greater than large things; or is the meaning lost in translation? "Small" and "large" are used analogous to their positive meanings. Are the pictures in your mind similarly analogous?


Yes and no. I suppose it depends on how one views the negatives. In the usual sense, I'm wrong of course. I guess I was automatically thinking of absolute value. I can't help, when it comes to multiplication, but see the negatives as a twin mirror number continuum. And these twin mirror continuums are separated by an infinitely thin border known as zero.

I'm immersing myself in math at the moment, but sadly have much to learn. On the other hand, I'm passionate about the subject and come at from a root level. What is number? And one and zero seem like the strange twin fulcrums of this strange discontinuous continuum. After all, we can't divide by zero. But we have the limit concept.

Anyway, I appreciate your response. I sort of dashed off what I wrote. The essence I meant to focus on is Unity or One as the center of either twin spectrum.
0 Replies
 
mister kitten
 
  1  
Reply Tue 6 Apr, 2010 08:53 pm
@Reconstructo,
One raised to the power of infinity would equal one?
Reconstructo
 
  1  
Reply Tue 6 Apr, 2010 09:21 pm
@mister kitten,
mister kitten;149045 wrote:
One raised to the power of infinity would equal one?


Yessir, it does seem so. I think a limit concept would be used, but the game is the same. 1 to the power of x, as x tends toward infinity, still equals one.

It seems to me that 1 times 1 is the same as 0 plus 0. 1 is the zero of multiplication/division. And 0 is the 1 of addition/subtraction.

Ratio is basically division. In some ways, division is the root of it all. But in a practical sense, adding is the root. But the rub is this. What is 5, if not 5/1? For 5 is just five ones. 5 is a shorthand symbol for 5 unities.

I also can't help but think of the important fact that any number can be written in any base. And computers do all their math in binary, for instance. So the arabic numerals and the base of 10 mean NOTHING, not essentially. We happen to have 10 fingers. That's all. And Pythagoras and the gang were fond of 10.
Deckard
 
  1  
Reply Tue 6 Apr, 2010 11:40 pm
@Reconstructo,
Reconstructo;149048 wrote:

It seems to me that 1 times 1 is the same as 0 plus 0. 1 is the zero of multiplication/division. And 0 is the 1 of addition/subtraction.


The official names for what you are observing

Additive identity
x + 0 = x

Multiplicative identity
x times 1 = x


Are these axioms?
Reconstructo
 
  1  
Reply Wed 7 Apr, 2010 12:06 am
@Deckard,
Deckard;149119 wrote:
The official names for what you are observing

Additive identity
x + 0 = x

Multiplicative identity
x times 1 = x


Are these axioms?


Yes. The identities. And I think they are axioms. And axioms in this case would seem to be transcendental. We must have the identities. No math works without them? It seems to me that all is derived from one...and that zero is the second most important number. And then perhaps infinity? WHich is not a number but maybe a function? I don't know what they are calling it officially. I have been reading on Cantor lately. His Alephs are amazing. The Continuum is amazing. That irrationals outnumber the rationals is amazing. It all touches hard-core on the transcendental, in my opinion. Math seems to touch on something deep and eternal as far as the structure of human thinking goes.

What about this? If number is essentially ratio, then the number one becomes the absolute ground of everything numerical. A ten-digit number is still a single quantity, or a unity. 1 is like the primal unity, and a number like google is just a complex unity. Made systematically out of simple unities by means of positional notation. (And isn't positional notation a piece of genius?)

Excuse the length. The subject is an exciting one.
Deckard
 
  1  
Reply Wed 7 Apr, 2010 12:30 am
@Reconstructo,
Reconstructo;149131 wrote:

What about this? If number is essentially ratio, then the number one becomes the absolute ground of everything numerical. A ten-digit number is still a single quantity, or a unity. 1 is like the primal unity, and a number like google is just a complex unity. Made systematically out of simple unities by means of positional notation. (And isn't positional notation a piece of genius?)


Is infinity a "complex unity"?
0 Replies
 
jeeprs
 
  1  
Reply Wed 7 Apr, 2010 12:32 am
@Reconstructo,
The Monad, the One, has an especially significant place in many of the ancient philosophical and theosophical systems.

From Wikipedia
Quote:
n many Gnostic systems (and heresiologies), the Supreme Being is known as the Monad, the One, The Absolute Aiōn teleos (The Perfect , αἰών τέλεος), Bythos (Depth or Profundity, Βυθός), Proarchē (Before the Beginning, προαρχή), and Hē Archē (The Beginning, ἡ ἀρχή) and The ineffable parent. The One is the high source of the pleroma, the region of light. The various emanations of The One are called . Within certain variations of Gnosticism, especially those inspired by Monoimus, the Monad was the highest god which created lesser gods, or elements (similar to ). Some versions of ancient Gnosticism, especially those deriving from Valentinius, a lesser deity known as the Demiurge had a role in the creation of the material world in addition to the role of the Monad. In these forms of gnosticism, the God of the Old Testament is often considered to have been the Demiurge, not the Monad, or sometimes different passages are interpreted as referring to each.
This Monad is the spiritual source of everything which emanates the pleroma, and could be contrasted to the darkness of pure matter.


[CENTER]
[/CENTER]
north
 
  1  
Reply Wed 7 Apr, 2010 12:57 am
@jeeprs,
jeeprs;149148 wrote:
The Monad, the One, has an especially significant place in many of the ancient philosophical and theosophical systems.

From Wikipedia




sounds religious to me
Deckard
 
  1  
Reply Wed 7 Apr, 2010 01:00 am
@jeeprs,
jeeprs;149148 wrote:
The Monad, the One, has an especially significant place in many of the ancient philosophical and theosophical systems.


Was the Monad infinite. I seem to remember the Greeks having a preference for a limitted universe. The unlimited was somehow undesirable, unrefined, perhaps for aesthetic reasons, the infinite is sloppy. The Monad is finite?
0 Replies
 
north
 
  1  
Reply Wed 7 Apr, 2010 01:02 am
@north,
the jews believed in and believe in one god ( they did have many gods in the begining as many did at the time , but it got boiled down to one , in time )
0 Replies
 
jeeprs
 
  1  
Reply Wed 7 Apr, 2010 02:08 am
@north,
north;149151 wrote:
sounds religious to me


Everyone was religious in the past, North.

---------- Post added 04-07-2010 at 06:14 PM ----------

Deckard;149152 wrote:
Was the Monad infinite. I seem to remember the Greeks having a preference for a limitted universe. The unlimited was somehow undesirable, unrefined, perhaps for aesthetic reasons, the infinite is sloppy. The Monad is finite?


I have been browsing The Pythagorean Sourcebook, which covers this topic, but have not gotten far into it. But I recall it saying that the Limit was placed on the Limitless which is how anything particular came to be, or manifested.

The idea of The One has mystical significance in all the ancient traditions but it is hard for us to recapture that sense. We are at a different 'station of consciousness' from them. However, as the OP was hinting, there is this sense in which The One precedes the duality within which all of the manifest world dwells, so in a sense it is also a symbol of the Divine, although not necessarily in a theistic sense.
ughaibu
 
  1  
Reply Wed 7 Apr, 2010 02:55 am
@Reconstructo,
Reconstructo;149048 wrote:
I also can't help but think of the important fact that any number can be written in any base.
You'd have problems writing any number in any random real base.
Reconstructo
 
  1  
Reply Wed 7 Apr, 2010 03:29 pm
@jeeprs,
jeeprs;149163 wrote:
But I recall it saying that the Limit was placed on the Limitless which is how anything particular came to be, or manifested.


To me that is the meeting of the discrete and the continuous. This ties into the number mysticism of the Kabbalah, which influenced Cantor to name his new transfinite numbers with an aleph symbol, and yet Cantor's math was the real thing, despite its mystical influences.

---------- Post added 04-07-2010 at 04:30 PM ----------

Deckard;149152 wrote:
Was the Monad infinite. I seem to remember the Greeks having a preference for a limitted universe. The unlimited was somehow undesirable, unrefined, perhaps for aesthetic reasons, the infinite is sloppy.


Spengler writes all kinds of stuff on this. He sees us Faustians as essentially in love with the infinite, and therefore we build cathedrals, calculus, impressionist paintings, polyphonic music, etc.

Spengler is juicy.

---------- Post added 04-07-2010 at 04:32 PM ----------

ughaibu;149172 wrote:
You'd have problems writing any number in any random real base.


I'm sure you know what I meant. I bet I would also have a problem using pi as a base, but do I really need to mention that?
Reconstructo
 
  1  
Reply Sat 10 Apr, 2010 10:31 pm
@ughaibu,
ughaibu;149172 wrote:
You'd have problems writing any number in any random real base.


I suppose that radians (based on pi) are a sort of number system, but only for the measurement of angles. Still, pretty amazing, to make pi work like that. Sadly, I've only lately discovered the beauty of radians and steradians.
0 Replies
 
Deckard
 
  1  
Reply Thu 15 Apr, 2010 03:11 am
@Reconstructo,
Reconstructo;149338 wrote:
To me that is the meeting of the discrete and the continuous. This ties into the number mysticism of the Kabbalah, which influenced Cantor to name his new transfinite numbers with an aleph symbol, and yet Cantor's math was the real thing, despite its mystical influences.

We are both of us eventually going to have to read Badiou...after we better understand Cantor...
Reconstructo;149338 wrote:

Spengler writes all kinds of stuff on this. He sees us Faustians as essentially in love with the infinite, and therefore we build cathedrals, calculus, impressionist paintings, polyphonic music, etc.

e.g. the Parthenon and the Leon Cathedral. It is such an excellent contrast. So rich! So full of meaning. A building is worth a million words.
TuringEquivalent
 
  1  
Reply Thu 15 Apr, 2010 06:54 am
@Reconstructo,
Reconstructo;148426 wrote:
It occurs to me lately that the number one is the center of all positive numbers. The smallest number is 1/infinity and the largest number is infinity/1. This puts "1" smack in the middle. Of course that's an oversimplification, but perhaps you get my point.

If we multiply any number by any number less than one, we are essentially dividing it. And if we divide by a number less than one, we are multiplying or increasing the first number. So 1 functions for multiplication/division in the same way that zero functions for addition and subtraction.

-1 is the center of all negative numbers. Zero is the number that is neither positive or negative, and the exact meeting point of the these inverse/mirror twins, the negatives and positives.

The smallest negative number is -1/infinity, and the smallest positive number is 1/infinity. How close are these two numbers? They both tend toward zero. Their only real difference is their signs, the badge of which dimension they hail from.

This sort of thing amuses me. I hope it amuses someone else.


I guess something so simple as a 1 is amusing to many people. I guess some people are happy about everything.
Deckard
 
  1  
Reply Thu 15 Apr, 2010 08:49 pm
@TuringEquivalent,
TuringEquivalent;152223 wrote:
I guess something so simple as a 1 is amusing to many people. I guess some people are happy about everything.

Some intellects are more playful than others.
0 Replies
 
 

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