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Mathematical Infinity

 
 
ughaibu
 
  1  
Reply Mon 12 Apr, 2010 07:09 pm
@trismegisto,
trismegisto;150996 wrote:
You mean eternally.
No I dont. Your objection was that there's a beginning, while I dont think that objection is sensible, in any case, I have illustrated that it's false for these triangles, because there is no triangle that can be privileged as 'the first'.
trismegisto
 
  1  
Reply Mon 12 Apr, 2010 11:35 pm
@ughaibu,
ughaibu;151149 wrote:
No I dont. Your objection was that there's a beginning, while I dont think that objection is sensible, in any case, I have illustrated that it's false for these triangles, because there is no triangle that can be privileged as 'the first'.


well, since the triangles don't exist until you create them, there has to be a first one in which case, they either get eternally larger or eternally smaller.
Reconstructo
 
  1  
Reply Mon 12 Apr, 2010 11:45 pm
@Reconstructo,
I think the above argument touches on the issue I mentioned in "one as the center of the positives." We have as the smallest positive magnitude 1/infinity and for the largest infinity/1. Here's something to lighten the mood.

YouTube - Pi is an irrational number - Star Trek
0 Replies
 
ughaibu
 
  1  
Reply Tue 13 Apr, 2010 12:22 am
@trismegisto,
trismegisto;151234 wrote:
well, since the triangles don't exist until you create them, there has to be a first one in which case, they either get eternally larger or eternally smaller.
I've explained to you why this isn't the case. Pick a number at will, for example 3695, not only can 1s be added, infinitely, to this number, they can also be subtracted, infinitely. Not only can the number be, for example, doubled infinitely, it can also be halved infinitely, etc.
trismegisto
 
  1  
Reply Tue 13 Apr, 2010 12:56 am
@ughaibu,
ughaibu;151245 wrote:
I've explained to you why this isn't the case. Pick a number at will, for example 3695, not only can 1s be added, infinitely, to this number, they can also be subtracted, infinitely. Not only can the number be, for example, doubled infinitely, it can also be halved infinitely, etc.


You mean eternally.
ughaibu
 
  1  
Reply Tue 13 Apr, 2010 12:58 am
@trismegisto,
trismegisto;151250 wrote:
You mean eternally.
No, I mean and meant what I wrote.
trismegisto
 
  1  
Reply Tue 13 Apr, 2010 09:31 am
@ughaibu,
ughaibu;151251 wrote:
No, I mean and meant what I wrote.


You are confused. I know it seems like you can substitute infinity for eternally but they are much different. You have done a great job of demonstrating eternally ascending and descending numbers they are just not infinite.

You idea is still communicated but it is muddled because of the misuse of the word.
Holiday20310401
 
  1  
Reply Tue 13 Apr, 2010 12:47 pm
@trismegisto,
If ughaibu was to communicate the word "eternally" as opposed to "infinitely", eternally suggests a temporal distinction, but I do not see the need for a temporal distinction to be made. That would seem to me a misrepresentation of what ughaibu was meaning to communicate.
trismegisto
 
  1  
Reply Tue 13 Apr, 2010 01:26 pm
@Holiday20310401,
Holiday20310401;151419 wrote:
If ughaibu was to communicate the word "eternally" as opposed to "infinitely", eternally suggests a temporal distinction, but I do not see the need for a temporal distinction to be made. That would seem to me a misrepresentation of what ughaibu was meaning to communicate.


It is simple, because the numbers or triangles he is discussing do not actually exist until he creates them. How big or how small they get depends entirely on how long he wishes to perform the equations. They do not inherently exist in the physical realm of the universe, they are intelligibles, and therefore are not in themselves infinite.

Like I said, the idea is still conveyed, it is just muddled a bit by the choice of words.
Reconstructo
 
  1  
Reply Tue 13 Apr, 2010 01:34 pm
@trismegisto,
trismegisto;151436 wrote:
It is simple, because the numbers or triangles he is discussing do not actually exist until he creates them. How big or how small they get depends entirely on how long he wishes to perform the equations. They do not inherently exist in the physical realm of the universe, they are intelligibles, and therefore are not in themselves infinite.

Like I said, the idea is still conveyed, it is just muddled a bit by the choice of words.


I think you are touching on a good issue. An infinite series can be processed without the time element, but the time element in intuition-ally involved. It's really quite a tricky subject. D.F. Wallace wrote a great little book on this issue called Everything And More. I think it touches on Zeno, Aristotle's potential infinity, Cantor's aleph, and the beautiful concept of the infinite series as divergent or convergent.

The O.P. is aimed more at the word infinity, but I agree that time is involved in the issue, as our concept of time is often mathematical, and we often(usually?) conceive of time spatially. And "spatially" takes us back to Euclid and Kant.

---------- Post added 04-13-2010 at 02:36 PM ----------

ughaibu;151245 wrote:
I've explained to you why this isn't the case. Pick a number at will, for example 3695, not only can 1s be added, infinitely, to this number, they can also be subtracted, infinitely. Not only can the number be, for example, doubled infinitely, it can also be halved infinitely, etc.



I agree. If infinite means "without end," which is manifest (in- finite), it's a useful word for this sort of thing. Perhaps you will agree that it's an exciting and tricky enough concept to be worth our examination.
0 Replies
 
polpol
 
  1  
Reply Tue 13 Apr, 2010 02:22 pm
@trismegisto,
trismegisto;151436 wrote:
" It is simple, because the numbers or triangles he is discussing do not actually exist until he creates them. How big or how small they get depends entirely on how long he wishes to perform the equations. They do not inherently exist in the physical realm of the universe, they are intelligibles, and therefore are not in themselves infinite. Like I said, the idea is still conveyed, it is just muddled a bit by the choice of words."

You are wrong, Trismegisto. You are confusing logic and empirical thinking. Ughaibu is not actually creating any numbers or triangles. As you say, they do not exist in the physical realm, they are intelligibles and that is precisely why they are infinite ie. they have no limits, they are "potentially real" but do not exist empirically as there is no such thing as "one", only one this or one that. Something eternal means that it always existed and will always exist, hence Ughaibu's triangles are not eternal, they are infinite because they do not exist by themselves.
I think Reconstructo was talking more about the aesthetics of mathematics and the mystic aspect of that type of human reasoning which is indeed very astonishing. The concept of "zero" is also very interesting and it is almost certain that those that came up with this mathematical "idea" were also mystics.
Reconstructo
 
  1  
Reply Tue 13 Apr, 2010 03:01 pm
@polpol,
polpol;151462 wrote:

I think Reconstructo was talking more about the aesthetics of mathematics and the mystic aspect of that type of human reasoning which is indeed very astonishing. The concept of "zero" is also very interesting and it is almost certain that those that came up with this mathematical "idea" were also mystics.

I will agree with you an the aesthetics! Actually the mystic is not so important for me in the context of this thread. I am quite fascinated by the transcendental, though, and I feel that this is mixed with the mystical.

What is the number one, for instance? It's an "intelligible. " Or an abstract object. And we seem to have built all mathematics from this one in relation to itself. Infinity is a useful and even necessary concept exactly because we can infinitely halve or double or add or subtract to any magnitude, and this possibility seems inherent in positional notation. Or really, as soon as fractions are invented. I'm fascinated with the root structure of human thinking. And infinity and unity are excellent points to investigate. :bigsmile:
polpol
 
  1  
Reply Tue 13 Apr, 2010 03:48 pm
@Reconstructo,
Yes Reconstructo, The structure of human thinking capable of grasping such concepts is astonishing and till recently we marveled at our capacity to speculate on such systems but now scientists describe the real physical universe as infinite from micro to the macro, an infinite system of possibilities so much so that mathematics can be seen as the expression of some sort of intuitive understanding about the nature of our world. As if our brain does not allow us to grasp the reality directly but serves us well in inventing the tools necessary to do so. We are indeed a curious species and it's a wonderful world! You went back to the avatar you had before. I see the signs express infinity? What does it mean?
trismegisto
 
  1  
Reply Tue 13 Apr, 2010 04:05 pm
@polpol,
polpol;151462 wrote:
trismegisto;151436 wrote:

You are wrong, Trismegisto. You are confusing logic and empirical thinking. Ughaibu is not actually creating any numbers or triangles. As you say, they do not exist in the physical realm, they are intelligibles and that is precisely why they are infinite ie. they have no limits, they are "potentially real" but do not exist empirically as there is no such thing as "one", only one this or one that. Something eternal means that it always existed and will always exist, hence Ughaibu's triangles are not eternal, they are infinite because they do not exist by themselves.


I hear what you are saying. However, just as I do not consider the Universe to be infinite I cannot consider Creation to be infinite either and if Creation is not infinite then the ideas and objects within Creation cannot be infinite either.

The Ideas and Objects of Creation manifest in the universe as thoughts and things and thoughts are just as temporal as things, even if we just contemplate doubling or halving numbers or triangles they are still dependent on how long we choose to contemplate or enact.

There are no infinite thoughts or things and very few eternal ones, ie. seemingly endless thoughts or things. The universe itself may be the only eternal thing.
polpol
 
  1  
Reply Tue 13 Apr, 2010 04:16 pm
@trismegisto,
What do you mean Trismegisto, that the universe nor creation are infinite and that few things are eternal? Tell us how it all began and how it will all end but try to put some math in it since it's our friend Reconstructo's thread.
Reconstructo
 
  1  
Reply Tue 13 Apr, 2010 04:29 pm
@polpol,
polpol;151516 wrote:
Yes Reconstructo, The structure of human thinking capable of grasping such concepts is astonishing and till recently we marveled at our capacity to speculate on such systems but now scientists describe the real physical universe as infinite from micro to the macro, an infinite system of possibilities so much so that mathematics can be seen as the expression of some sort of intuitive understanding about the nature of our world. As if our brain does not allow us to grasp the reality directly but serves us well in inventing the tools necessary to do so. We are indeed a curious species and it's a wonderful world! You went back to the avatar you had before. I see the signs express infinity? What does it mean?


I think that we can only truly process the finite.. And that the concept of infinity is itself finite. I go into this in my Real is Rational thread, and I stole it all from Hegel and Wittgenstein. But it clicks for me, and it seems like a resolution to certain famous philosophical dichotomies.

Infinity in that avatar represents qualia or sensation. Kant would call it intuition, but this word now has a different meaning for us. We never experience meaningfully any sort of sensation without its organizing concept. Not can we experience pure concept without some mixture of contingent qualia. For instance, number is quite abstract, but it still represented visually, and even if we dodge that, we still have contingent names for numbers and must learn their manipulation from a social context.

All human life occurs at the top of that triangle. The plus sign symbolizes the clash of sensation and concept, just like the triangle does. The plus sign is actually just another way to draw the triangle. The most we can do, in my opinion, is to deduce that we are the collision of sensation and concept, and this triangle is a diagram that presents that thought. You might say that the plus sign (cross = Logos --gnostic, etc.) is the self-consciousness of the triangle as the whole. I could have put another triangle up there. It's not actually mystical, although its poetic presentation might suggest so. In my opinion, structure is beautiful/numinous, but not supernatural. For me, all is integrated into the system of sensuous concepts that i am. The self is the limit of the world. I could go on, as it's quite a network of relationships...
0 Replies
 
trismegisto
 
  1  
Reply Tue 13 Apr, 2010 04:30 pm
@polpol,
polpol;151532 wrote:
What do you mean Trismegisto, that the universe nor creation are infinite and that few things are eternal? Tell us how it all began and how it will all end but try to put some math in it since it's our friend Reconstructo's thread.


This isn't really the place for all that went into Creation but you can check out my thread on that if you are interested.

Let's just say that even the concept of infinity is only eternal.

There is a vast difference in the philosophy of "without beginning or end" and "seemingly endless" and yet the distinction is rarely made.

To get back to the OP, in mathematics there is no distinction between infinite and eternal as mathematics is not as precise as philosophy and no one has the energy to find out if an equation is without end or seemingly endless.
0 Replies
 
Reconstructo
 
  1  
Reply Tue 13 Apr, 2010 04:30 pm
@Reconstructo,
Oh yes, the minus sign! Well synthesis is just the negation of accident, which is simultaneously the production of essence. It's must simpler than it sounds. But that is indeed the thought in simple terms. For me, essence and accident is crucial.

I think we experience the intelligible structure of the world as a system of essences, or concepts.
trismegisto
 
  1  
Reply Tue 13 Apr, 2010 04:36 pm
@Reconstructo,
Reconstructo;151542 wrote:
I think we experience the intelligible structure of the world as a system of essences, or concepts.


I can get behind that
0 Replies
 
Reconstructo
 
  1  
Reply Tue 13 Apr, 2010 04:39 pm
@Reconstructo,
Someone should start a thread perhaps on eternity. I would join in there as well, after I take a break from this screen!
0 Replies
 
 

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