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Source: (consider it)
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Thread: I understand that the universe is big
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LeRoc
Famous Dutch pirate
# 3216
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Posted
Although I agree with some of his arguments, I'm not exactly sure which definition of 'countable' Schroedinger's cat is using here. I'm familiar with the concept of countable sets and the related notion of 'countably infinite' but he seems to be talking about something else here.
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Schroedinger's cat
Ship's cool cat
# 64
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Posted
Countability means that you can assign a single ordinal number to each object. I am arguing that this cannot be done, because the time it would take is significant, and at cosmological scales, time is crucial.
There are parts of the universe that we cannot reach. Or rather objects that we cannot count, because they are outside our time cone. In this case, I would consider them uncountable.
And this is not a rigorous scientific argument, but a way of understanding the universe which explains how the number of objects can be uncountable.
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LeRoc
Famous Dutch pirate
# 3216
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Posted
quote:
Schroedinger's cat: Countability means that you can assign a single ordinal number to each object. I am arguing that this cannot be done, because the time it would take is significant, and at cosmological scales, time is crucial.
I guess this confirms my suspicion that this is different from the usual mathematical definition of a countable set. Thank you for the clarification.
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I know why God made the rhinoceros, it's because He couldn't see the rhinoceros, so He made the rhinoceros to be able to see it. (Clarice Lispector)
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Schroedinger's cat
Ship's cool cat
# 64
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Posted
quote:
Originally posted by LeRoc:
quote:
Schroedinger's cat: Countability means that you can assign a single ordinal number to each object. I am arguing that this cannot be done, because the time it would take is significant, and at cosmological scales, time is crucial.
I guess this confirms my suspicion that this is different from the usual mathematical definition of a countable set. Thank you for the clarification.
I am not sure it does. I thought my definition fits with the wikipedia definition you linked to.
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LeRoc
Famous Dutch pirate
# 3216
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Posted
quote:
Schroedinger's cat: I am not sure it does. I thought my definition fits with the wikipedia definition you linked to.
Not really. Countable sets are a mathematical concept, whether we are prohibited from counting things by physical constraints (for example because of time constraints, things are moving, or things being created or because of the speed of light) doesn't really enter. If you look at the Wikipedia page, there's nothing in it about time, movement, change, light cones or stuff like that.
Once again, if you want to use a definition of 'countable' that's somewhat different from the standard mathematical one, that's fine by me. I was just looking for clarification.
[ 11. September 2014, 21:31: Message edited by: LeRoc ]
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I know why God made the rhinoceros, it's because He couldn't see the rhinoceros, so He made the rhinoceros to be able to see it. (Clarice Lispector)
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sharkshooter
Not your average shark
# 1589
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Posted
quote:
Originally posted by mousethief:
...
quote:
Originally posted by sharkshooter:
If it is infinite, there can be no boundary.
You err because you do not understand mathematics.
...
Interesting how quickly some resort to personal attacks.
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Let the words of my mouth, and the meditation of my heart, be acceptable in thy sight, O LORD, my strength, and my redeemer. [Psalm 19:14]
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mousethief
Ship's Thieving Rodent
# 953
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Posted
Interesting what some people interpret as personal attacks.
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mousethief
Ship's Thieving Rodent
# 953
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Posted
quote:
Originally posted by Schroedinger's cat:
quote:
Originally posted by LeRoc:
quote:
Schroedinger's cat: Countability means that you can assign a single ordinal number to each object. I am arguing that this cannot be done, because the time it would take is significant, and at cosmological scales, time is crucial.
I guess this confirms my suspicion that this is different from the usual mathematical definition of a countable set. Thank you for the clarification.
I am not sure it does. I thought my definition fits with the wikipedia definition you linked to.
Countability means exactly that you can assign a single integer (ordinal or cardinal doesn't matter on this side of infinity) to each element of a set. But it doesn't mean that you can do this yourself, personally. It means you can in theory.
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orfeo
Ship's Musical Counterpoint
# 13878
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Posted
quote:
Originally posted by sharkshooter:
quote:
Originally posted by Schroedinger's cat:
... The argument I had above provides for an infinite but bounded universe, that is, however far you go in any direction, you will never find an end - but it is possible to have something "outside" the universe.
I don't buy that. If it is infinite, there can be no boundary. My argument is that, if there is a boundary, we cannot call it infinite - very large, certainly.
Well, in mathematics, there are plenty of infinite series with boundaries.
Not that that's an exact analogue of a physical world. It just struck me that the words 'infinite' and 'boundary' can be quite readily used together and make sense - at least in a mathematical context.
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mousethief
Ship's Thieving Rodent
# 953
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Posted
quote:
Originally posted by orfeo:
Not that that's an exact analogue of a physical world. It just struck me that the words 'infinite' and 'boundary' can be quite readily used together and make sense - at least in a mathematical context.
I think the world is a whole lot more mathematical than most people realize.
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itsarumdo
Shipmate
# 18174
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Posted
quote:
Originally posted by mousethief:
quote:
Originally posted by orfeo:
Well, in mathematics, there are plenty of infinite series with boundaries.
Not that that's an exact analogue of a physical world. It just struck me that the words 'infinite' and 'boundary' can be quite readily used together and make sense - at least in a mathematical context.
I think the world is a whole lot more mathematical than most people realize.
An example of an infinite boundary is the equation for heat or water entering a point source - the boundary is effectively infinite for as long as the "signal" of the input takes to reach whatever real boundary there is, and for the reflection from the boundary to make a "substantial" difference for an observer. The maths can't be formulated unless the boundary at infinity has some property - just some unknown something at infinity means that what goes in inside is undefined once the boundary's presence starts to have an effect. You can assume some random property at infinity, but at some point in time if that assumption is incorrect, it will affect the "maths" and the maths will not represent the processes very well. Infinity has a habit of affecting non-infinity surprisingly quickly. Boundary conditions are the bread and butter of any attempt to model real processes using maths. And they are often the hardest thing to define.
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"Iti sapis potanda tinone" Lycophron
Posts: 994 | From: Planet Zog | Registered: Jul 2014
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Schroedinger's cat
Ship's cool cat
# 64
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Posted
quote:
Originally posted by mousethief:
quote:
Originally posted by Schroedinger's cat:
quote:
Originally posted by LeRoc:
quote:
Schroedinger's cat: Countability means that you can assign a single ordinal number to each object. I am arguing that this cannot be done, because the time it would take is significant, and at cosmological scales, time is crucial.
I guess this confirms my suspicion that this is different from the usual mathematical definition of a countable set. Thank you for the clarification.
I am not sure it does. I thought my definition fits with the wikipedia definition you linked to.
Countability means exactly that you can assign a single integer (ordinal or cardinal doesn't matter on this side of infinity) to each element of a set. But it doesn't mean that you can do this yourself, personally. It means you can in theory.
And my point is, it cannot be done in theory, because there is no point in the universe to distribute all of the series of numbers from that would capture every object.
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Blog
Music for your enjoyment
Lord may all my hard times be healing times
take out this broken heart and renew my mind.
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itsarumdo
Shipmate
# 18174
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Posted
There was an interesting paper posted on a different talk board a few years ago - unfortunately I lost the link, and have not been able to re-discover the paper. It was an analysis of the universe using information theory. If you consider the moment-by moment manifestation of the material world as a computer program, then you have active registers (memory), you have registers being used to prepare the next event, and you have registers being used to dispose of the processing and data remaining from the last event. The proportions of these three, when calculated, gave relative memory required as being almost the same proportions as ordinary matter (now), dark matter (past) and dark energy (future).
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"Iti sapis potanda tinone" Lycophron
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que sais-je
Shipmate
# 17185
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Posted
quote:
Originally posted by Schroedinger's cat:
And my point is, it cannot be done in theory, because there is no point in the universe to distribute all of the series of numbers from that would capture every object.
I wish I knew (though not very much) what this meant. Is it a statement about mathematical physics or mathematics?
In mathematics there are infinite sets which are countable but bounded. To take the simplest example, all the fractional points between 0 and 1 but excluding 0 and 1 ( sometimes written ]0,1[, sometimes (0,1) ). All the points are distinct, their positions (or values) are bounded: all are < 1 and > 0.
In mathematical physics we'd have to take into account the Uncertainty Principle, spontaneous creation/disappearance of photons, black holes where, even in theory, we can't look inside the event horizon and so on. Conceivably that could make a difference.
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"controversies, disputes, and argumentations, both in philosophy and in divinity, if they meet with discreet and peaceable natures, do not infringe the laws of charity" (Thomas Browne)
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itsarumdo
Shipmate
# 18174
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Posted
quote:
Originally posted by que sais-je:
quote:
Originally posted by Schroedinger's cat:
And my point is, it cannot be done in theory, because there is no point in the universe to distribute all of the series of numbers from that would capture every object.
I wish I knew (though not very much) what this meant. Is it a statement about mathematical physics or mathematics?
....
What I was trying to say previously - you can't count using zero resources over zero time - your counting process inevitably takes up a finite proportion of the universe, and takes a finite length of time. There is a flow of information. So given that fact, it is possible to look at the universe as exactly that - a flow of information.
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"Iti sapis potanda tinone" Lycophron
Posts: 994 | From: Planet Zog | Registered: Jul 2014
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Schroedinger's cat
Ship's cool cat
# 64
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Posted
quote:
Originally posted by que sais-je:
In mathematical physics we'd have to take into account the Uncertainty Principle, spontaneous creation/disappearance of photons, black holes where, even in theory, we can't look inside the event horizon and so on. Conceivably that could make a difference.
That is what I am getting at. There are more issues than just black holes and uncertainty. These problems are inherent in the universe.
The time cone means that even outside event horizons, there are many places that we cannot have any information about.
As itsarumdo is saying, I think, there are parts of the universe that we cannot have information about from where we are. Irrespective of where we are, there will be places that we can have no information about. Therefore we cannot count the objects in them.
In most systems represented by mathematical models (the models of number theory for example) these factors are irrelevant. It is only when you start to work in cosmological scales that these are issues. Mathematical models do also work for these, but they are more complex models, taking into account factors like uncertainty and event horizons.
These places where we cannot receive information from are important, meaning that the number of objects in the universe is uncountable. That does not necessarily mean infinite, but I suspect it does in reality.
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Blog
Music for your enjoyment
Lord may all my hard times be healing times
take out this broken heart and renew my mind.
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que sais-je
Shipmate
# 17185
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Posted
quote:
Originally posted by itsarumdo:
What I was trying to say previously - you can't count using zero resources over zero time - your counting process inevitably takes up a finite proportion of the universe, and takes a finite length of time. There is a flow of information. So given that fact, it is possible to look at the universe as exactly that - a flow of information.
I agree but describing something as 'countable' in the mathematical usage doesn't involve actually counting or using any resources. It is only necessary to create a thought experiment or do a proof. To take a trivial example, the set of words formed from the 26 letters of the Latin alphabet is countable. Imagine all possible words written order as a numbered list so that first we have all one letter words
1. a
2. b
...
26. z
then all two letter words (in alphabetical order),
27. ...
28. ...
....
then three letter then four and so on. Clearly each and every word appears at just one point in the list and at every point (in our infinitely long list) corresponds to a possible word. Thus the set of all possible words is countable in the mathematical sense. Very little information required or consumed.
I think information as a conserved quantity is an interesting idea but it determines whether stuff can be counted within certain resource constraints - mathematics (like God) is not so constrained.
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"controversies, disputes, and argumentations, both in philosophy and in divinity, if they meet with discreet and peaceable natures, do not infringe the laws of charity" (Thomas Browne)
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mousethief
Ship's Thieving Rodent
# 953
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Posted
quote:
Originally posted by itsarumdo:
quote:
Originally posted by que sais-je:
quote:
Originally posted by Schroedinger's cat:
And my point is, it cannot be done in theory, because there is no point in the universe to distribute all of the series of numbers from that would capture every object.
I wish I knew (though not very much) what this meant. Is it a statement about mathematical physics or mathematics?
....
What I was trying to say previously - you can't count using zero resources over zero time - your counting process inevitably takes up a finite proportion of the universe, and takes a finite length of time. There is a flow of information. So given that fact, it is possible to look at the universe as exactly that - a flow of information.
The point is not physically counting them. "Countable" doesn't mean "someone could count them." This is constructionist nonsense.
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itsarumdo
Shipmate
# 18174
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Posted
quote:
Originally posted by mousethief:
quote:
Originally posted by itsarumdo:
quote:
Originally posted by que sais-je:
quote:
Originally posted by Schroedinger's cat:
And my point is, it cannot be done in theory, because there is no point in the universe to distribute all of the series of numbers from that would capture every object.
I wish I knew (though not very much) what this meant. Is it a statement about mathematical physics or mathematics?
....
What I was trying to say previously - you can't count using zero resources over zero time - your counting process inevitably takes up a finite proportion of the universe, and takes a finite length of time. There is a flow of information. So given that fact, it is possible to look at the universe as exactly that - a flow of information.
The point is not physically counting them. "Countable" doesn't mean "someone could count them." This is constructionist nonsense.
I think that if you wish to deal with a real universe ...
instead of Counting (without actually counting) imaginary items in a hypothetical series in a mathematically constructed universe, you will necessarily have to descend to the less elegant and rather mundane effort of physically counting real objects.
If this is not the case, I guess you will be able to count the sheets of paper remaining in my printer without having to open the drawer. At least you know it's less than 501 and probably more than zero.
Even the alphabetical example you gave does't work, because e.g. there are no words spelt Wxcrtta, Wxcrttb, Wxcrttc, Wxcrttd, ... etc, and there are no clear rules for knowing exactly which words are real and which not in any specific language except by physically counting them
[ 17. September 2014, 21:43: Message edited by: itsarumdo ]
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"Iti sapis potanda tinone" Lycophron
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mousethief
Ship's Thieving Rodent
# 953
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Posted
At this point I have no idea what your point is. I didn't say ANYTHING about words. And the question is whether the number of stars is countable, which is a precisely mathematically defined adjective and has nothing to do with physically counting. Nor your printer. I can confidently state that you have fewer than an infinite number of sheets in your printer, so it's not really comparable.
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itsarumdo
Shipmate
# 18174
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Posted
quote:
Quote by mousethief:
At this point * have no idea *hat your point is. * didn't say ANYTHING about *ords. And the question is *hether the number of stars is countable, *hich is a precisely mathematically defined adjective and has nothing to do *ith physically counting. Nor your printer. * can confidently state that you have fe*er than an infinite number of sheets in your printer, so it's not really comparable.
Apologies about the *ords - the edit time on these boards seems to be only several microseconds.
* had a look at countable sets, and it doesn't appear to apply to real items. If you try to count (e.g) electrons - they are theoretically countable, but it impossible to label them, so then it becomes necessary to compartmentalise their physical location - counted, not counted. *hich is implicit in a theoretical enumerated set, but has to be e*plicit *ith real objects. One basket contains counted oranges, each *ith a neat label displaying a unique integer, and over there *e have a basket of oranges *ith no label. So - ho* does one compartmentalise the universe of electrons to make sure that its constituents are not double-counted or that *e have not missed any? This is the basis for information theory, *hich requires that the countable information is substantially less than (maybe 10%) the total space available. *e are so far also ignoring state and relationship, *hich increase counting comple*ity. Similarly, the time that may be taken to count "may be infinite" - so that comes across practical objections in a universe that apparently has a finite lifespan. *hat may be theoretically enumerable is not the same as *hat is effectively enumerable, and if it takes longer than the life of the universe to enumerate its contents, it is effectively VERY BIG (to use the appropriate jargon).
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"Iti sapis potanda tinone" Lycophron
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