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Author Topic:   A definition of infinity?
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 4 of 41 (372003)
12-24-2006 12:55 PM
Reply to: Message 1 by dogrelata
12-24-2006 7:34 AM


I don’t know if I’m making any sense, but can the second scenario be considered to be an example of infinity?
Yes, absolutely. It is what we call a semi-infinite line. Just like the positive x-axis on a graph: starts at 0, the origin, and continues without upper bound. The entire x-axis, including the -ve branch, is obviously infinite in both directions. Whether you can actually realise such a line in the universe depends upon whether the universe is itself infinite in spatial extent.
However, as you point out, there are many types of infinity. The usual infinity considered is that in the sense of an infinite number of objects - the countable infinity, aleph null. It has quite different properties to the infinity represented by the infinite x-axis.
Given my pseudo-Platonist outlook, infinite distances are of no concern, as I can simply map them into finite distances. Likewise, finite distance can be mapped into infinte distances. Similarly with time. This is why a universe that has always existed, and a universe that began in a big bang 14 billion years ago have exactly the same issues regarding a need or lack of need for a creator.

This message is a reply to:
 Message 1 by dogrelata, posted 12-24-2006 7:34 AM dogrelata has replied

Replies to this message:
 Message 6 by dogrelata, posted 12-25-2006 4:24 PM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 8 of 41 (372215)
12-25-2006 8:38 PM
Reply to: Message 6 by dogrelata
12-25-2006 4:24 PM


how would it work?... ...what would cause them to be semi-infinite?
I'm sorry, I don't understand. Why would they have to be "caused" to be semi-inifinte? Nothing causes the +ve x-axis to be semi-infinite, nor any other line radiating out of any point in the x-y plane, they just are...
I wonder if there’s also a possibility that there are things within this universe that might be infinitely small
In mathematics, the infinitely small - the infinitessimal - is exceptionally common and is the basis of calculus. In physics there are complications such as the idea of length breaking down at the Planck scale, so it becomes difficult to continue sub-dividing a length. However, it is entirely possible that the deepest underlying physical layers contain the concept of the infinitessimal, which is obscured as the quantum elements are built up. This is very much in the realms of the philosophy of physics/reality, rather than in hard science.

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 Message 6 by dogrelata, posted 12-25-2006 4:24 PM dogrelata has replied

Replies to this message:
 Message 9 by Chiroptera, posted 12-25-2006 9:17 PM cavediver has replied
 Message 13 by dogrelata, posted 12-26-2006 6:58 AM cavediver has not replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 10 of 41 (372223)
12-25-2006 9:34 PM
Reply to: Message 9 by Chiroptera
12-25-2006 9:17 PM


Re: Pedantic point.
Completely agree... just detest theory of limits with a passion - it may be their constructivist flavour or just that I was in a decidedly non-mathematical mood when I first had to study the subject - gigs and girls were my predominant study at the time - and I have always avoided teaching the subject like the plague.
I'm not so sure about use in Planck scale physics, which is very much finite scale, but it may be useful in looking at the emergence of finite scale physics from the underlying topological structure... and don't asy 'what underlying topological structure?'
Edited by cavediver, : No reason given.

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 Message 9 by Chiroptera, posted 12-25-2006 9:17 PM Chiroptera has not replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 35 of 41 (374898)
01-06-2007 9:36 AM
Reply to: Message 33 by Son Goku
01-04-2007 2:25 PM


Re: Measurement, paths and Zeno freezing.
Hi SG, two points regarding your post that may sound a bit negative but they're really there to spark discussion on how we appraoch this whole area... let me know what you think.
1) I think you've introduced a bit of confusion with your negative probabilities by (unintentionally) suggesting that a specific path can be associated with a -ve prob. I bring forth dogrelate as my first evidence
I must admit I've never liked the "classicalisation" explanations of quantum phenomena (look what happens to this *particle* or consider this *path*) as they perpetuate much of the voodoo nonsense. Quantum behaviour is fascinating but it quickly leads down the road to the confusion we often see expressed by certain individuals here at EvC.
The truth is that classical behaviour is the weird stuff, and quantum the mundane. The fact that a classical regime emerges is what amazes me. And trying to explain the quantum world by reference to the classical is like explaining the chemistry of liquid water by reference to oceanic currents. But can we do better?
2) Now I do like your write up of Zeno freezing... very nice. However, you're sort of playing the magician:
So I've managed to stop an atom from decaying by not interacting with it, in other words, by doing nothing to it.
Flourish, take a bow, curtsy from your beautiful assistant, rapturous applause from the thoroughly baffled and now slightly even more ignorant audiance I think us physicists are so guilty of turning physics into magic just to persuade the masses that it is exciting. I do it all the time...
Think of how you used to view black holes as these truly mystical objects, baffling beyond belief in terms of their ability to screw around with space and time. And then you saw the simplicity of Schwarzschild... were you disappointed or blown away by the elegance and beauty? It is that elegance and beauty I wish we could express better... but could we make anyone else appreciate it?

This message is a reply to:
 Message 33 by Son Goku, posted 01-04-2007 2:25 PM Son Goku has replied

Replies to this message:
 Message 36 by Son Goku, posted 01-06-2007 11:05 AM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 37 of 41 (374903)
01-06-2007 11:50 AM
Reply to: Message 36 by Son Goku
01-06-2007 11:05 AM


Re: Measurement, paths and Zeno freezing.
I never said it was easy. And please don't take it too hard. We're all in the same boat with this.
However this is a lame explanation, that can be made less lame by picking an ontology, but which one? And why one above any of the others?
Reminds me of picking a gauge... whichever one seem most appropriate to your desired outcome!
Will get back later...

This message is a reply to:
 Message 36 by Son Goku, posted 01-06-2007 11:05 AM Son Goku has not replied

  
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