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Mathematical Infinity

 
 
Holiday20310401
 
  1  
Reply Tue 13 Apr, 2010 09:26 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.


By that logic, we might as well take the word 'infinitely' right out of the English language for it would have no use.
ughaibu
 
  1  
Reply Tue 13 Apr, 2010 09:37 pm
@Holiday20310401,
Holiday20310401;151637 wrote:
By that logic, we might as well take the word 'infinitely' right out of the English language for it would have no use.
In any case, the thing can be finitely described as a supertask. So, I dont think that Trismegisto is offering a lucid objection.
0 Replies
 
Reconstructo
 
  1  
Reply Tue 13 Apr, 2010 09:39 pm
@Reconstructo,
Personally, I think the word is quite valuable, even if difficult to work with. Many of the best words are, just as some of the best numbers are. Pi and e are certainly on another level than 4 or 6. And words like infinity and God are on another level than dog or tree. Yes? I would say that the math pros have made it quite workable. The limit concept seems to imply an infinitesimal, but they have figured out how to word it gracefully, to minimize possible confusion. This is just wiki, but it's also free.
Infinity - Wikipedia, the free encyclopedia

I just finished this book (hardback, but found it on google. Some excellent ideas in this book.)
Mathematical fallacies and paradoxes - Google Books
0 Replies
 
Alan McDougall
 
  1  
Reply Wed 14 Apr, 2010 02:31 am
@Reconstructo,
Infinity is an impossible absolute truth, an enigma rapped up in a paradox of eternal dimension's
Reconstructo
 
  1  
Reply Wed 14 Apr, 2010 03:26 pm
@Alan McDougall,
Alan McDougall;151720 wrote:
Infinity is an impossible absolute truth, an enigma rapped up in a paradox of eternal dimension's

I welcome your thoughts. However, I do hope to keep this thread aimed at mathematical infinity. For me, philosophy is more about the transcendental than the transcendent, and the difference between the two is "infinite."
0 Replies
 
trismegisto
 
  1  
Reply Wed 14 Apr, 2010 04:06 pm
@Holiday20310401,
Holiday20310401;151637 wrote:
By that logic, we might as well take the word 'infinitely' right out of the English language for it would have no use.


Only when applied to the Infinite Supreme does it have any meaning everything else is a misuse of the idea contained within the word.
Reconstructo
 
  1  
Reply Sun 18 Apr, 2010 06:50 pm
@trismegisto,
trismegisto;152011 wrote:
Only when applied to the Infinite Supreme does it have any meaning everything else is a misuse of the idea contained within the word.


If you mean that our idea of the All is paradoxical, I agree. One might say that the all cannot be written in closed form. I have suggested that "being is negative one," but this is probably misunderstood by most, as they are not necessarily even interested in the same aspect of philosophy that I (we?) am/are.

I must insist that math uses the infinity concept in important ways, but they understand it, IMO, as a potentially infinity. Or in the sense of no-limit. For instance, that lovely number e is defined by means of a limit. The bigger the value we use for n, the closer our approximation to e. But we can never represent this number perfectly. No limit on our precision except strangely a limit on perfect precision. And also strange is this: our calculation of e becomes slower and slower exponentially in terms of magnitude, which is poetically related to what this number represents. Every next digit is ten times less important than the one before, if we are calculating its decimal value.

e = limit as n tends to infinity of (1 + 1/n)^n .....and this is basically the polite and careful way of saying that e = (1 + 1/infinity) to the power of infinity. A number that is limitlessly close to one multiplied by itself a limitless number of times. Hmmm.
trismegisto
 
  1  
Reply Tue 20 Apr, 2010 01:30 am
@Reconstructo,
Reconstructo;153782 wrote:
If you mean that our idea of the All is paradoxical, I agree. One might say that the all cannot be written in closed form. I have suggested that "being is negative one," but this is probably misunderstood by most, as they are not necessarily even interested in the same aspect of philosophy that I (we?) am/are.


The story of the blind wise men and the elephant is still the best way of explaining this in terms we can digest, don't you think.

Every thought we individually have about the infinite is correct in that they all describe aspects of the infinite but no single thought no matter how eloquent can ever convey the entirety of the infinite'



Reconstructo;153782 wrote:
I must insist that math uses the infinity concept in important ways, but they understand it, IMO, as a potentially infinity. Or in the sense of no-limit.


I am sure that the concept used in mathematics makes for some very exciting equations, I am just saying that the concept, while still valid, is just one aspect of the infinite and is not capable, simply by the limits of communication, of incorporating the immensity of the infinite into its expressions.



Reconstructo;153782 wrote:
For instance, that lovely number e is defined by means of a limit. The bigger the value we use for n, the closer our approximation to e. But we can never represent this number perfectly. No limit on our precision except strangely a limit on perfect precision. And also strange is this: our calculation of e becomes slower and slower exponentially in terms of magnitude, which is poetically related to what this number represents. Every next digit is ten times less important than the one before, if we are calculating its decimal value.

e = limit as n tends to infinity of (1 + 1/n)^n .....and this is basically the polite and careful way of saying that e = (1 + 1/infinity) to the power of infinity. A number that is limitlessly close to one multiplied by itself a limitless number of times. Hmmm.


Yikes, I don't speak that language. But I bet there is a way to express the same exact thing in a story, I do better with stories. If it is real there is probably some example of it in nature, don't you think?
Reconstructo
 
  1  
Reply Tue 20 Apr, 2010 02:08 am
@trismegisto,
trismegisto;154366 wrote:
The story of the blind wise men and the elephant is still the best way of explaining this in terms we can digest, don't you think.

I don't know that one. Do share...oh wait. They all feel a different part? Great story!

---------- Post added 04-20-2010 at 03:09 AM ----------

trismegisto;154366 wrote:

Every thought we individually have about the infinite is correct in that they all describe aspects of the infinite but no single thought no matter how eloquent can ever convey the entirety of the infinite'

I sometimes like to think of 'God" as the sum of all human experience (and alien, etc.), much of which is presumably quite unlike my own little piece.

---------- Post added 04-20-2010 at 03:10 AM ----------

trismegisto;154366 wrote:

I am sure that the concept used in mathematics makes for some very exciting equations, I am just saying that the concept, while still valid, is just one aspect of the infinite and is not capable, simply by the limits of communication, of incorporating the immensity of the infinite into its expressions.

I agree that your use of the word is bigger, as math intentionally limits its use. Still a debated issue.

---------- Post added 04-20-2010 at 03:12 AM ----------

trismegisto;154366 wrote:

Yikes, I don't speak that language. But I bet there is a way to express the same exact thing in a story, I do better with stories. If it is real there is probably some example of it in nature, don't you think?


Your right! Imagine an ooze whose growth rate is exactly proportional to its current size. Instantaneously proportional.

An actual example would be the half life of radioactive material. But this is the inverse. It slows its rate of decay. Its decay is exactly inversely proportional to the amount still there.
0 Replies
 
 

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