Strange but True: Infinity Comes in Different Sizes
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Strange but True: Infinity Comes in Different Sizes
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Strange but True: Infinity Comes in Different Sizes
Glendower: I can call spirits from the vasty deep.
Hotspur: Why, so can I, or so can any man;
But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:
go with the flow the river knows . . .
Frank
I do not know, therefore everything is in pencil.Tags: None
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If one were to apply a mathematical notion of infinity to multiple universes, it would be in the sense of "no upper bound". {1, 2, 3, ...}
And if one were to assign a transfinite cardinal to this concept, it would be aleph-null, although I don't recall ever seeing the "no-upper-bound" concept mixed with transfinite cardinals.
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Originally posted by klaus54 View PostWhat does the set theory abstraction of uncountable infinities have to do with the real world of matter and energy?βλέπομεν γὰρ ἄρτι δι᾿ ἐσόπτρου ἐν αἰνίγματι, τότε δὲ πρόσωπον πρὸς πρόσωπον·
ἄρτι γινώσκω ἐκ μέρους, τότε δὲ ἐπιγνώσομαι καθὼς καὶ ἐπεγνώσθην.אָכֵ֕ן אַתָּ֖ה אֵ֣ל מִסְתַּתֵּ֑ר אֱלֹהֵ֥י יִשְׂרָאֵ֖ל מוֹשִֽׁיעַ׃
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Originally posted by klaus54 View PostIf one were to apply a mathematical notion of infinity to multiple universes, it would be in the sense of "no upper bound". {1, 2, 3, ...}
And if one were to assign a transfinite cardinal to this concept, it would be aleph-null, although I don't recall ever seeing the "no-upper-bound" concept mixed with transfinite cardinals.
JimMy brethren, do not hold your faith in our glorious Lord Jesus Christ with an attitude of personal favoritism. James 2:1
If anyone thinks himself to be religious, and yet does not bridle his tongue but deceives his own heart, this man’s religion is worthless James 1:26
This you know, my beloved brethren. But everyone must be quick to hear, slow to speak and slow to anger; James 1:19
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Originally posted by oxmixmudd View PostBut as I proposed in the other thread, what about the set of potential initial conditions for any universe about to be born? What if the set of potential initial states can only be represented by the power set of aleph null, i.e. aleph one? And suppose the probability distribution for initial states is even, with the probability of any specific initial state then equal to zero? Then the probability any newly born universe will match any of its predecessors would also be zero.
JimGlendower: I can call spirits from the vasty deep.
Hotspur: Why, so can I, or so can any man;
But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:
go with the flow the river knows . . .
Frank
I do not know, therefore everything is in pencil.
Comment
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Originally posted by shunyadragon View PostYes, this a possibility, but very unlikely. IF this extreme view is true we would be the only universe. There is an assumption in science of uniformity that it is unlikely that there is 'only one' of anything, which is unique. If science discovers something, there has always been more than one. Based on our present knowledge of Quantum Mechanics there is the possibility that the initial conditions of singularities may result from variations in the physics constants that result in the formation of our universe, and the formation of the universe fails, or one forms that will not result in a universe like ours that supports life. At present this possible range of constants is unknown, and they may be limited to the point that all possible universes will form when the same initial conditions of the singularity that forms a universe.
In our universe, as far as I/we know, continua does not actually exist except as a mathematical abstraction. Everything from matter to energy to space itself appear defined as some sort of discrete quanta of energy or time or both. Yet something in the early universe defined what those quanta would be. Are these values fixed across all possible universes, or are then themselves a variable, something that can take on a continua of possible values. And if so, what do differing quanta (different energy, space, or time 'packet sizes' do to the constraints of the resulting universe. Is quantization itself a variable - are there possible universes without quanta?
The essence of science, of exploration is to be capable of thinking outside the box of currently accepted norms when the evidence shows there is more than was thought to be. When you start talking about a multiverse, you have left the norm. So why not ask questions of what might be beyond this universe, why not at least explore the possibility some of the things we take for granted as fixed properties are in fact not? This is what Einstein did - space and time are not absolutes. Yet the prevailing view at the time was that they were. That was a big part of his genius - being able to see the possibilities. He saw the evidence and explored a possibility for reconciliation of the evidence that others did not. I'm not Einstein by any stretch, but I do embrace the idea of exploring what might be that is different from what is the accepted norm.
JimLast edited by oxmixmudd; 02-13-2016, 10:15 AM.My brethren, do not hold your faith in our glorious Lord Jesus Christ with an attitude of personal favoritism. James 2:1
If anyone thinks himself to be religious, and yet does not bridle his tongue but deceives his own heart, this man’s religion is worthless James 1:26
This you know, my beloved brethren. But everyone must be quick to hear, slow to speak and slow to anger; James 1:19
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Originally posted by oxmixmudd View PostI take exception to the term 'extreme' view. It is simply a possibility. What do we know about whatever it is that provides the 'substrate' for multiple universes, assuming there is >1? And without knowing much of anything about it, why should we necessarily extend observations about our universe to it? It by definition must be in some ways different in that somehow it contains or facilitates all the universes - yes?
In our universe, as far as I/we know, continua does not actually exist except as a mathematical abstraction. Everything from matter to energy to space itself appear defined as some sort of discrete quanta of energy or time or both. Yet something in the early universe defined what those quanta would be. Are these values fixed across all possible universes, or are then themselves a variable, something that can take on a continua of possible values. And if so, what do differing quanta (different energy, space, or time 'packet sizes' do to the constraints of the resulting universe. Is quantization itself a variable - are there possible universes without quanta?
The essence of science, of exploration is to be capable of thinking outside the box of currently accepted norms when the evidence shows there is more than was thought to be. When you start talking about a multiverse, you have left the norm. So why not ask questions of what might be beyond this universe, why not at least explore the possibility some of the things we take for granted as fixed properties are in fact not? This is what Einstein did - space and time are not absolutes. Yet the prevailing view at the time was that they were. That was a big part of his genius - being able to see the possibilities. He saw the evidence and explored a possibility for reconciliation of the evidence that others did not. I'm not Einstein by any stretch, but I do embrace the idea of exploring what might be that is different from what is the accepted norm.
Jim
Glendower: I can call spirits from the vasty deep.
Hotspur: Why, so can I, or so can any man;
But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:
go with the flow the river knows . . .
Frank
I do not know, therefore everything is in pencil.
Comment
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Looking at an infinity being at the decimal point.
...000.000... or ...999.999... being the same infinity.
G64 not infinity ...987.000...
Gn where n is infinity. ...987.000... having no left starting digit. Is a smaller infinity than ...999.999... Infinity.. . . the gospel of Christ: for it is the power of God unto salvation to every one that believeth; . . . -- Romans 1:16 KJV
. . . that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again the third day according to the scriptures: . . . -- 1 Corinthians 15:3-4 KJV
Whosoever believeth that Jesus is the Christ is born of God: . . . -- 1 John 5:1 KJV
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Originally posted by 37818 View PostLooking at an infinity being at the decimal point.
...000.000... or ...999.999... being the same infinity.
G64 not infinity ...987.000...
Gn where n is infinity. ...987.000... having no left starting digit. Is a smaller infinity than ...999.999... Infinity.Glendower: I can call spirits from the vasty deep.
Hotspur: Why, so can I, or so can any man;
But will they come when you do call for them? Shakespeare’s Henry IV, Part 1, Act III:
go with the flow the river knows . . .
Frank
I do not know, therefore everything is in pencil.
Comment
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Originally posted by shunyadragon View PostThe belief that there would be only one universe, ours, is an extreme view. Since the more general view of science is that more universes within a multiverse matrix is possible, and more likely. The substrate of the multiverse would be the timeless Quantum zero-point energy existence at T=0.
JimMy brethren, do not hold your faith in our glorious Lord Jesus Christ with an attitude of personal favoritism. James 2:1
If anyone thinks himself to be religious, and yet does not bridle his tongue but deceives his own heart, this man’s religion is worthless James 1:26
This you know, my beloved brethren. But everyone must be quick to hear, slow to speak and slow to anger; James 1:19
Comment
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Originally posted by oxmixmudd View PostBut as I proposed in the other thread, what about the set of potential initial conditions for any universe about to be born? What if the set of potential initial states can only be represented by the power set of aleph null, i.e. aleph one? And suppose the probability distribution for initial states is even, with the probability of any specific initial state then equal to zero? Then the probability any newly born universe will match any of its predecessors would also be zero.
Jim
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Originally posted by shunyadragon View PostThe belief that there would be only one universe, ours, is an extreme view. Since the more general view of science is that more universes within a multiverse matrix is possible, and more likely. The substrate of the multiverse would be the timeless Quantum zero-point energy existence at T=0.
But it does make some very interesting points. Though not definitively so, this point seems to run counter to your view: "The Casimir force is widely cited as evidence that underlying the universe there must be a sea of real zero-point energy. This argument follows from Casimir's analysis and prediction. It is not necessarily true, however. It is perfectly possible to explain the Casimir effect by taking into account the quantum-induced motions of atoms in each plate and examining the retarded potential interactions of atoms in one plate with those in the other.
This point may be interesting to some: "Zero-point energy behaves differently. For ordinary radiation, the ratio of pressure to energy density is w=1/3c2, which is customarily expressed in units whereby c=1, and thus the ratio is expressed as w=+1/3. But for zero-point energy the ratio is w=-1. This is owing to the circumstance that the zero-point energy density is assumed to be constant: no matter how much the universe expands it does not become diluted, but instead more zero-point energy is assumed to be created out of nothing."
In general, the idea that dark energy is in fact zero-point energy is very interesting. So thanks for that. A patent for tapping zero-point energy as a usable source of energy, what an incredible idea!βλέπομεν γὰρ ἄρτι δι᾿ ἐσόπτρου ἐν αἰνίγματι, τότε δὲ πρόσωπον πρὸς πρόσωπον·
ἄρτι γινώσκω ἐκ μέρους, τότε δὲ ἐπιγνώσομαι καθὼς καὶ ἐπεγνώσθην.אָכֵ֕ן אַתָּ֖ה אֵ֣ל מִסְתַּתֵּ֑ר אֱלֹהֵ֥י יִשְׂרָאֵ֖ל מוֹשִֽׁיעַ׃
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