Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Bill S on 18/11/2014 23:12:53
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Sorry; I couldn't resist the initial question. It's really infinity I'm after, but discussions about nothing tend to be linked.
Infinity finds its way into many threads, causes a distraction, then fades away, usually, with no semblance of resolution. Questions about infinity are often linked to questions about time and about nothing.
I propose asking a few questions, in the form of a poll, which may help to ameliorate the situation. Each question requires only a yes/no answer, but hopefully these would be accompanied by some thoughts.
1. Is infinity a number?
2. Is eternity a length of time?
3. Is it possible to define Cantor’s “absolute infinity”?
4. If there had ever been (absolutely) nothing, could there be something now?
5. Could there be change without time?
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1. No
2. no
3. read Cantor
4. there obviously is something now, so the question is meaningless
5. there would certainly be no notion of time without change
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Alan's number 5 hits the nails on the head. Change never stops. We assume heat death will mean no change. What if there is no heat death of the universe? What if it is just not possible? I agree with Alan's 1 and 2. Cantor I have no knowledge of. I don't believe there was ever nothing.
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Q1. Is infinity a number?
A1. No.
Q2. Is eternity a length of time?
A2. No.
Q3. Is it possible to define Cantor’s “absolute infinity”?
A3. No.
Q4. If there had ever been (absolutely) nothing, could there be something now?
A4. Yes
Q5. Could there be change without time?
A5. No.
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As for 3.
It's a very important question, and quantum mechanics defining a Planck scale seems very related to it, to me that is. Also the idea of many paths co-existing, as well as its opposite, the idea of a infinite, or at least undefined, amount of 'universes' branching at any observed outcome, only one apparent 'per observer'. They all go back to that question, and most interesting is the one about what happens under or close to that Planck scale.
5. change is 'time'', can't get one without the other. Causality is something added to that idea, giving us a commonly agreed on universe.
4. I don't know, wish I did. But, it depends on how you define it too, take 'Cantor's infinity' as a example. Or any of the other ideas above, what is the state of 'the instant' before a outcome? Does it belong to a arrow, or is it separated from it?
1. is meaningless, to me that is, and it's taken me some time to decide on that one. Alternatively, use any of the arguments above to define a 'infinity'.
2. Eternity? As ill defined as 'infinity' to me, doesn't tell me a thing. The 'instant in between' before that outcome, is that existing a 'eternity'?
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don't get stuck on the arrows linearity for 2. Just assume opposites, a arrow, as contrasted to what is not a arrow. If you think of it from a arrow, then 'splitting eternity' from that, you just defined the arrow as the primary reason. That's not correct, both are as important and can be seen as a symmetry possibly, balancing out into a universe. Well, maybe :)
Or think of in terms of 'observer dependencies', giving both a equal 'local' importance. Then you will get both your 'infinity', as well as 'eternity' on one side, the arrow on the other. But they are meaningless to me anyway. I can't comprehend what they should mean from that side, only from 'inside' a universe.
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Thanks for the responses, hopefully there will be more to come. As soon as I have a few spare minutes I will come back to the thread.
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4. There can't 'be' nothing, and it can't exist. 'Nothing' is an abstract concept of negation. Colloquial language makes it appear otherwise (e.g. "there's nothing in the box"), but generally refers to absence of certain types of stuff. A box that really had nothing inside wouldn't really be a box, because its sides would be touching each other.
To make a Hackenthorpe Vacuum: Take a bottle containing an ordinary vacuum, and suck all the vacuum out...
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As always, wish I was perfectly sober here. Dlorde, you just make a perfectly consistent defense for a container.
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3. read Cantor
Alan, I accept full responsibility for the unhelpful nature of this response. My mistake was trying to make this question amenable to a yes/no answer. As a non-mathematician I have struggled with much of Cantor’s work, but I think I have grasped the basics; particularly, I think I have a fair understanding of his thoughts on “absolute” infinity. What I was really looking for was the thoughts of other posters about this.
4. there obviously is something now, so the question is meaningless
“there obviously is something now,” No question about that.
“so the question is meaningless” I don’t accept that the question is meaningless. Perhaps I need to rephrase it.
Given that there is something now, can there ever have been nothing?
There would seem to be three possible answers to this: 1. Yes 2. No and 3. Don’t know. Any one of these would benefit from a bit embellishment.
5. there would certainly be no notion of time without change
I would not argue with that, but it’s a “sociologist’s” response: it’s an answer, but not to the question that was asked.
Could there be change without time?
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nope. no change no time. You measure it.
(and as always, locally)
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Alan's number 5 hits the nails on the head.
Jeffrey, I agree; shame it was not quite the right nail. Can we go back to “Could there be change without time?”
I too have grave doubts about heat death. I think it has to do with something Heisenberg said.
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A3. No.
Pete, I appreciate clear, concise answers like this, but I would be interested to know why you say “no”.
A4. Yes
How could that be?
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Yor_on, as so often happens with your posts, I read this one and thought: I’m sure he’s saying something significant here, I’m just not certain I know what it is. I’m going to have to read it again and give it some thought.
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Regarding time and change:
We can think of a more generalized change as the partial derivative of some characteristic of the universe (or any system) with respect to some parameter. ∂something/∂time is one of the most common meaning of change, but we could chose many other parameters, such as position, temperature, pressure, composition etc. We could discuss the fundamentality of these parameters, but then again, how fundamental is time?
Can there be time without change? Sure, even if ∂something/∂time = 0, that doesn't mean that there is no time, it's just not relevant to that "something". For instance, think of all the parameters that are conserved in Newtonian physics and thermodynamics--as far as the total momentum of the universe is concerned, time is meaningless.
Causality gives time its directionality, and entropy is the proof.
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Dlorde; “Though shalt not with semantics round enmesh me……..” With apologies to Omar Khayyam.
“There can't 'be' nothing, and it can't exist………… A box that really had nothing inside…..” No comment.
Go on! Answer the questions, in spite of yourself. [:)]
Seriously; I would value your answers.
BTW, I agree, in general, with your definition of nothing, and would like to say more about it, but at this point it would introduce thread drift, so I will come back to it later. Prod me if I forget.
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Go on! Answer the questions, in spite of yourself. [:)]
OK, here's my take:
Q1. Is infinity a number?
A1. No.
Q2. Is eternity a length of time?
A2. No.
Q3. Is it possible to define Cantor’s “absolute infinity”?
A3. Not as far as I know. He's supposed to have identified it with God, but I don't know how he defined 'God', and we can't ask him because he's dead. However, it's possible he did define God and left a record somewhere.
Q4. If there had ever been (absolutely) nothing, could there be something now?
A4. Invalid/meaningless question. There can't 'be' nothing. Redefine 'nothing' as 'empty' (zero energy) spacetime for this question, and I'd say 'yes' (e.g., I'm told that the energy of matter & radiation, etc., is balanced by the 'negative' energy of gravity, resulting in an overall zero energy for our universe).
Q5. Could there be change without time?
A5. No. Change either requires or defines time.
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There can't 'be' nothing. Redefine 'nothing' as 'empty' (zero energy) spacetime
Perhaps I should reword the question:
If there had ever been a complete absence of anything, definable or otherwise by us, could there be anything now?
I would certainly not choose to redefine 'nothing' as 'empty' (zero energy) spacetime. I suspect you would point out that spacetime is something.
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Perhaps I should reword the question:
If there had ever been a complete absence of anything, definable or otherwise by us, could there be anything now?
Same answer as before - it's a meaningless question. There can't 'be' a complete absence of anything - time itself is meaningless without spacetime.
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There can't 'be' a complete absence of anything
OK, Dlorde, over to you. If absolutely everything ceased to exist, what term would you use to describe that. This is a thought experiment, so don't point out either that that couldn't happen, or that if it did you wouldn't be around to describe it.
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If absolutely everything ceased to exist, what term would you use to describe that.
Meaningless. How would you describe it?
If an irresistible force meets an immovable object, what happens? Just a thought experiment, so don't point out that it couldn't happen [;)]
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1. Is infinity a number?
No. It's not a number. It's a concept/idea.
2. Is eternity a length of time?
No. Just like eternity it's a concept. Think of it as infinite amount of time.
3. Is it possible to define Cantor’s “absolute infinity”?
I don't know what that is so I can't say.
4. If there had ever been (absolutely) nothing, could there be something now?
Yes.
5. Could there be change without time?
No, because can is defined as change.
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We have matter, lots of it. If it ceases to exist where does it go? It can't become nothing because then it would be included in the nothingness. Therefore absolute nothingness cannot exist.
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We have matter, lots of it. If it ceases to exist where does it go? It can't become nothing because then it would be included in the nothingness. Therefore absolute nothingness cannot exist.
Agreed, and this is the very reason I disagree with the notion that nothingness lies outside our observable universe. And if nothingness does not exist beyond our present universe, the cosmos is infinite.
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... if nothingness does not exist beyond our present universe, the cosmos is infinite.
I don't think this is necessarily the case; the universe may be finite and closed and still be all there is.
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Dlorde, I admire your evasive subtlety. Let's consider a more mundane example. You and I look into a room which we agree is devoid of human occupants. I say: "There's no one in that room." You say: "There cannot be no one in that room, because "no one" is a negation, so it cannot "be". Is that not tantamount to your saying that there must be someone in that room?
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Thanks Pete.
If there had ever been (absolutely) nothing, could there be something now?
Yes
You have still not told me how something can emerge from nothing.
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...the universe may be finite and closed and still be all there is.
Agreed, but what is beyond the outer boundary of the finite universe?
Let me guess; the question is meaningless. [8D]
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Alan, there are still a couple of unresolved points lingering in #8; I hope you will return to give us at least one more injection of down-to-earth scientific opinion before this thread meanders off into the bog of eternal nothingness.
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Alan, there are still a couple of unresolved points lingering in #8; I hope you will return to give us at least one more injection of down-to-earth scientific opinion before this thread meanders off into the bog of eternal nothingness.
The bog cannot be eternal as nothingness has nothing to do with time. Nothing would change so time would not exist. How do you measure a period of nothingness and what parameters do you use?
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Thanks Pete.
If there had ever been (absolutely) nothing, could there be something now?
Yes
You have still not told me how something can emerge from nothing.
That's because I don't know how it could happen. I only know that it can happen by which I mean that there's nothing in the laws of physics so far that prevents it. That may change in the future.
The laws of physics only tell us what can happen, not why. For example, when two elementary particles collide there may result many different things. Sometimes it's only the energy and momentum of each particle that changes, the sum being constant, i.e. unchanged. If I knew whether particles A and B could change into particles C and D it doesn't imply that we could tell you why it happened. It could be that someday we'll why but today we can't. As Feynman once said regarding particle physics "If anything can happen it will happen. It's possible that it's similar here.
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Dlorde, I admire your evasive subtlety.
I'm not trying to be evasive, I'm giving the opinion that you asked for.
Let's consider a more mundane example. You and I look into a room which we agree is devoid of human occupants. I say: "There's no one in that room." You say: "There cannot be no one in that room, because "no one" is a negation, so it cannot "be". Is that not tantamount to your saying that there must be someone in that room?
No. I already mentioned the colloquial use of 'nothing' as referring to the absence of certain types of stuff. Using 'no-one' is quite reasonable. It says that in a certain context there are no objects of a certain type. If you think about it, it's a relative statement.
To talk of 'nothing at all' is meaningless because there's no context and no relativity. There's literally nothing to say about it. It doesn't and can't exist because it is the negation of all existence.
I had hoped my example of a 'box' containing 'absolutely nothing' (that isn't really a box because sides must touch each other) would enable you to visualise the meaninglessness of the idea in physical terms.
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Agreed, but what is beyond the outer boundary of the finite universe?
There would be no boundary. We've been through all this before. Finite and unbounded, like the surface of a sphere, but in 4 dimensions. There would be no 'outside'.
Let me guess; the question is meaningless. [8D]
The premise is mistaken.
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The bog cannot be eternal as nothingness has nothing to do with time. Nothing would change so time would not exist.
Thanks Jeffrey! This is precisely the point I have been trying to make (one of them, anyway). Eternity/infinity has nothing to do with time, so there can be no change in eternity/infinity.
Do google “Bog of Eternal Stench” if you have and lingering doubts on the subject of eternal bogs. [;D]
How do you measure a period of nothingness and what parameters do you use?
You don’t. Nothingness is a concept that is no more measurable than an “infinite” sequence. If either “exists”, it exists in infinity and is therefore not accessible to our measurement.
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Alan, there are still a couple of unresolved points lingering in #8; I hope you will return to give us at least one more injection of down-to-earth scientific opinion before this thread meanders off into the bog of eternal nothingness.
Sitting here in my grease-stained overalls and muddy boots (it's the weekend - theatre scrubs and radioactive dust suits are for work days) here's the answer to
How do you measure a period of nothingness and what parameters do you use?
It's the smallest vector between two somethings.
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How do you measure a period of nothingness and what parameters do you use?
It's the smallest vector between two somethings.
[8D] Yes indeed. It's meaningless without the context of things (thingness?).
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That's because I don't know how it could happen. I only know that it can happen by which I mean that there's nothing in the laws of physics so far that prevents it. That may change in the future.
Could it not be said that the laws of physics militate against there ever being “nothing”?
The laws of physics only tell us what can happen, not why
“How” and “why” are vastly different questions. When you said “I only know that it can happen” I wondered if you knew of, or theorised, some method that would facilitate it.
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Could it not be said that the laws of physics militate against there ever being “nothing”?
It could indeed be said, but like what politicians say, it's just a collection of words with no relationship to the truth. The laws of physics are discovered mathematical approximations to what actually happens. They have no power nor even an enforcing agency.
But if you look at my parameter of nothingness, I think you will find it entirely logical and consistent with the known properties of everything.
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No. I already mentioned the colloquial use of 'nothing' as referring to the absence of certain types of stuff. Using 'no-one' is quite reasonable. It says that in a certain context there are no objects of a certain type. If you think about it, it's a relative statement.
Surely you are not saying that turning “nothing” into “no-thing” would make a significant difference to the meaning.
To talk of 'nothing at all' is meaningless because there's no context and no relativity. There's literally nothing to say about it. It doesn't and can't exist because it is the negation of all existence.
There can never have been a complete absence of any-thing?
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Could it not be said that the laws of physics militate against there ever being “nothing”?
It could indeed be said, but like what politicians say, it's just a collection of words with no relationship to the truth. The laws of physics are discovered mathematical approximations to what actually happens. They have no power nor even an enforcing agency.
Considering how often, in threads of this nature, the laws of physics are cited as something akin to “the Word of God”, that’s a consoling quote to have to hand.
But if you look at my parameter of nothingness, I think you will find it entirely logical and consistent with the known properties of everything.
It's the smallest vector between two somethings.
In order to avoid being “something”, would it not have to be infinitely small?
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Surely you are not saying that turning “nothing” into “no-thing” would make a significant difference to the meaning.
That's right, I'm not saying that.
There can never have been a complete absence of any-thing?
If by 'absence of any-thing' you mean the 'absolutely nothing' we've been talking about, that's correct. I refer you to my several previous answers.
No offence, but I'm not sure whether you're being deliberately obtuse, or you're unwilling or unable to articulate the point you want to make. Repeatedly asking the same question in different ways doesn't seem very productive. What's on your mind? Can you not just describe what you find unsatisfactory about the answers given?
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No offence, but I'm not sure whether you're being deliberately obtuse, or you're unwilling or unable to articulate the point you want to make.
Earlier this evening when I was tending to the "calls of domestic duty" I was thinking that I would have apologise for appearing obtuse and repetitive. You, and others, are probably well aware that I have been involved in discussions about infinity with various people in different threads and forums for quite some time. I have found, from experience, that it pays to be absolutely sure what other people are saying before drawing conclusions.
If that makes little sense, blame the single malt. [:D]
I'll come back to it tomorrow when I can think clearly.
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It's the smallest vector between two somethings.
In order to avoid being “something”, would it not have to be infinitely small?
Depends how far apart the somethings are. The definition holds for all values of any dimension.
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Depends how far apart the somethings are. The definition holds for all values of any dimension.
You’ve lost me there, Alan. Could you give me an example in which (say) the somethings are 1m apart?
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Okay, way out in deep space there are two hydrogen atoms a meter apart, with no other entities between them. Then we have a meter of nothing in at least one dimension, and quite possibly a lot more nothing elsewhere.
You might argue that photons and particles of stuff are passing through the gap in any observable part of the universe, but these transits are momentary, interspersed by periods of nothing. Which is just as well, since if there were something, the particles wouldn't be able to transit without interacting.
Which leads me to a whole new train of thought. I have just defined absolute nothing, but there is probably an infinity of relative nothings, defined as the absence of anything significant betwen two points. This is for instance a pleasant aspect of aviation, when I request a zone transit, say of a military range, on a specific course, and get "nothing known to affect": i.e. plenty of air, but no chunks of metal about to intersect my intended vector.
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Okay, way out in deep space there are two hydrogen atoms a meter apart, with no other entities between them. Then we have a meter of nothing in at least one dimension, and quite possibly a lot more nothing elsewhere.
You might argue that photons and particles of stuff are passing through the gap in any observable part of the universe, but these transits are momentary, interspersed by periods of nothing. Which is just as well, since if there were something, the particles wouldn't be able to transit without interacting.
As I understand it, quantum field theory says that the gap contains continuous fields, all of overall zero energy, except the Higgs field. If this isn't enough 'something', the zero-energy fields are only zero on average - uncertainty means that they oscillate, continually generating excitations, virtual pairs of particles that quickly annihilate. However one interprets these quantum oscillations, they too are something rather than nothing. I suspect it could be said that spacetime is these oscillating fields.
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Which leads me to a whole new train of thought. I have just defined absolute nothing, but there is probably an infinity of relative nothings, defined as the absence of anything significant betwen two points
Thanks for the explanation, Alan. Dlorde is ahead of me with the sort of questions I would want to ask, so I'll sit back for a while to see what happens.
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Yor_on, I’ve been giving some consideration to your post #4 and I have some questions.
Also the idea of many paths co-existing, as well as its opposite, the idea of a infinite
In what way do you consider the “many paths” to be the opposite of infinity?
1. is meaningless, to me that is,
Is it meaningless because you need a definition of infinity before you can decide if it is a number, or not?
2. Eternity? As ill defined as 'infinity' to me, doesn't tell me a thing. The 'instant in between' before that outcome, is that existing a 'eternity'?
Can you be equating an instant with eternity? I’ve been down that road myself, I would be interested to know where it leads you.
Then you will get both your 'infinity', as well as 'eternity' on one side, the arrow on the other.
I always have infinity and eternity on the same side; definitely no arrow (of time) associated with either. How could it be any other way?
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Which leads me to a whole new train of thought. I have just defined absolute nothing, but there is probably an infinity of relative nothings, defined as the absence of anything significant betwen two points
Thanks for the explanation, Alan. Dlorde is ahead of me with the sort of questions I would want to ask, so I'll sit back for a while to see what happens.
It's stuff like this that made me tired of conversations about infinity. The concept is simply to someone who's taken their first year of calculus or taken a real analysis course.
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It's stuff like this that made me tired of conversations about infinity. The concept is simply to someone who's taken their first year of calculus or taken a real analysis course.
Perhaps those who find these things simple (I assume you meant simple) should post simple explanations for the benefit of lesser mortals, instead of bald statements that are presumably meant to be taken on faith.
For example, you have still not explained how you believe something can emerge from nothing.
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I'd like to hear about that one too Bill.
Okay, way out in deep space there are two hydrogen atoms a meter apart, with no other entities between them. Then we have a meter of nothing in at least one dimension, and quite possibly a lot more nothing elsewhere. You might argue that photons and particles of stuff are passing through the gap in any observable part of the universe, but these transits are momentary, interspersed by periods of nothing. Which is just as well, since if there were something, the particles wouldn't be able to transit without interacting.
Cough. Space isn't nothing. When a seismic wave moves through the ground, the ground waves. When an ocean wave moves through the sea, the sea waves. When a gravitational wave or an electromagnetic wave moves through space, space waves. And then you can perform pair production and make matter out of one of these waves. Don't think of matter as something and space as nothing, because matter and space aren't all that different. Have a read of Does Matter Differ from Vacuum? (http://arxiv.org/PS_cache/gr-qc/pdf/9610/9610066v1.pdf) by Christoph Schiller.
Which leads me to a whole new train of thought. I have just defined absolute nothing, but there is probably an infinity of relative nothings, defined as the absence of anything significant betwen two points. This is for instance a pleasant aspect of aviation, when I request a zone transit, say of a military range, on a specific course, and get "nothing known to affect": i.e. plenty of air, but no chunks of metal about to intersect my intended vector.
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I'd like to hear about that one too Bill.
Sorry John, I'm not sure what you want to hear more about. Could be I'm having a "senior moment". [;)]
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Perhaps it is time to look at some of the things I might be able to take from this thread so far.
I am aware of the fact that scientific veracity does not depend on democratic vote, but “hitch-hikers” like me do well to seek and heed the opinions of the more knowledgeable.
I have often been asked why I think there can be no change, or meaningful division in infinity. Answers like “Because it makes sense to me”, or “because infinity has a lot in common with Barbour’s Platonia”, are obviously not of the best, so I try appealing to such reasoning as “time and eternity are entirely different concepts”, and my answers always seem to be countered by Cantor-type responses which do little more than muddy the waters.
Let’s see if the responses to these questions help the situation. The majority view seems to be:
Is infinity a number? No.
Is eternity a length of time? No.
Could there be change without time? No.
A sequence is a number of things/concepts/etc.
Infinity is not a number; therefore it cannot be a sequence.
An “infinite sequence”, such as the natural numbers, is not truly infinite. Boundless – yes; infinite – no.
Eternity is not a length of time. It is not time at all. Without time there can be no change, therefore there can be no change in eternity/infinity.
Now I need to square that with the idea that the cosmos is infinite, and our Universe is “part” of the cosmos.
There are many scientists who believe the Universe is finite. Many of those who opt for an infinite Universe see it as being infinite in the way that they see the sequence of numbers as being infinite. It really makes little difference which one believes.
We exist in an infinite cosmos in which there is no change or differentiation. Every “part” is the whole. Nothing happens, everything just “is”.
We are conscious of time as being linear, and experience our Universe as passing through time; but that is because we are restricted to 3+1 dimensions, we cannot see or experience infinity, and in order to survive in this “illusion” must be able to make sense of our world.
I this science? Yes.
If there had ever been nothing, there could be nothing now. There must always have been something. That something must be eternal/infinite, and therefore changeless.
Will we, as individuals ever experience/understand the infinite cosmos? The answer to that is not science, it may be philosophy, theology or plain old guesswork, but not science.
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An “infinite sequence”, such as the natural numbers, is not truly infinite. Boundless – yes; infinite – no.
This is incorrect. There is such things as infinite sequences. Being an infinite sequence means that the value of the partial sequence has no bound. For example: the sequence
1, 2, 3, .... , etc.
1, 22, 32, .... etc.
are both infinite sequences. Each has no bound. The sequence
1, 2, 1, 2, 1, 2, ..., etc.
is an infinite sequence as well but this one is bounded.
Bill - Have you ever considered picking up a book on calculus and read the first couple of chapters? You can do it in a day or two and after that you'll have answers to all the questions you've asked over the last month or so. You'll do much much less work reading too.
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A sequence is a number of things/concepts/etc.
Infinity is not a number; therefore it cannot be a sequence.
That needs some explanation - it makes no sense to me as it stands. A sequence is an ordered list; there's no requirement I'm aware of that it must be finite. (it can also have zero elements (http://en.wikipedia.org/wiki/Sequence#Finite_and_infinite))
An “infinite sequence”, such as the natural numbers, is not truly infinite. Boundless – yes; infinite – no.
What is the justification for this? What is the difference between 'infinite' and 'truly infinite' ?
Eternity is not a length of time. It is not time at all. Without time there can be no change, therefore there can be no change in eternity/infinity.
Eternity is defined as endless time, time without end, infinite time, time of indefinite or infinite extent, etc. So whatever it isn't, it is some sort of time; that's what the word means.
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That needs some explanation - it makes no sense to me as it stands.
Same here.
Bill - It's best to back up assertions like this when you make them, otherwise they're not of much use.
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I'd like to hear about that one too Bill.
Sorry John, I'm not sure what you want to hear more about. Could be I'm having a "senior moment". [;)]
How you get something from nothing. By the way, I was reading your post, and I spotted this:
"Without time there can be no change, therefore there can be no change in eternity/infinity."
Thar's your problem! You got it back to front. It should be without change there can be no time. Or motion of you prefer. A clock clocks up some kind of regular cyclical motion and shows you some cumulative display that you call the time. But it doesn't literally "measure the flow of time". It isn't some kind of cosmic gas meter.
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This is incorrect. There is such things as infinite sequences. Being an infinite sequence means that the value of the partial sequence has no bound. For example: the sequence
1, 2, 3, .... , etc.
1, 22, 32, .... etc.
“…the value of the partial sequence has no bound.”
Precisely! It is unbounded, you could never establish that it was infinite, other than in principle.
In the first half of the 1980s when I started a science based degree course with the Open University, I dabbled in calculus. Unfortunately, a major career change, and the learning curve that accompanied that prevented any further study, and 30+ years on I have suffered from the “use it or lose it” syndrome, but I recall nothing that would influence my thoughts about non-mathematical infinity. Mathematical infinities, as I have said before, are not a matter of contention to me.
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“…the value of the partial sequence has no bound.”
Precisely! It is unbounded, you could never establish that it was infinite, other than in principle.
I was talking about the following statement
An “infinite sequence”, such as the natural numbers, is not truly infinite. Boundless – yes; infinite – no.
and not whether someone could sit down in a lab with pen and paper and do it. Those are two entirely different things. You keep talking about boundless as being different than infinite when in actuality they are synonyms. To be exact - Something is infinite when it has no limit. When someone writes 1, 2, 3, 4, .... the "..." actually is defined to mean that it has no limit, that it keeps going and never ends. It is therefore infinite.
You really should study this again. It's not as if it'd be a waste of time for you because you'll spend less time talking about it here then actual study time. It's only a few pages long and doesn't require much math background at all because this is the foundation of math. Just a bit of friendly advice from your buddy Pete! :)
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There is such things as infinite sequences. Being an infinite sequence means that the value of the partial sequence has no bound. For example: the sequence
1, 2, 3, .... , etc.
1, 22, 32, .... etc.
are both infinite sequences.
It seems that not all mathematicians agree with this.
https://www.math.toronto.edu/mathnet/answers/infinity.html
“Number systems come in many sizes. There is the "natural number system", which is just the set of numbers used in counting: 1, 2, 3, 4, and so on. Or, one can expand this number system to include additional concepts, such as negative numbers, fractions, even the so-called "imaginary" numbers (which are not really imaginary at all). Each of these concepts exists provided we look for it in the context of a large enough number system.
Now the question is, does infinity exist in the same way that these concepts (negative numbers, fractions, etc.) do?
In other words, does there exist any number system which, as well as including the familiar numbers we are used to, also includes an "infinity" concept?
The answer is no;”
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It seems that not all mathematicians agree with this.
I suspect there's no field of human knowledge where everyone agrees about everything.
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Take a sphere of set radial dimension. Draw two lines from the center of the sphere to its surface separated by a set angle. We can describe the arc that joins them at the surface by a mathematical formula. Now make the radius infinite and carry out the same procedure.
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It seems that not all mathematicians agree with this.
https://www.math.toronto.edu/mathnet/answers/infinity.html
Nope. You're wrong. I believe that in your haste to attempt to prove me wrong you didn't take the time to completely absorb the material and as such you didn't understand that they said that there's no number which equals infinity. But that's not what I argued, Bill. Was it?
“Number systems come in many sizes. There is the "natural number system", which is just the set of numbers used in counting: 1, 2, 3, 4, and so on. Or, one can expand this number system to include additional concepts, such as negative numbers, fractions, even the so-called "imaginary" numbers (which are not really imaginary at all). Each of these concepts exists provided we look for it in the context of a large enough number system.
Now the question is, does infinity exist in the same way that these concepts (negative numbers, fractions, etc.) do?
In other words, does there exist any number system which, as well as including the familiar numbers we are used to, also includes an "infinity" concept?
The answer is no;”
You misread it. They are not talking about infinity as most other mathematicians do. It's a VERY poor webpage. Look at their proof at: https://www.math.toronto.edu/mathnet/answers/infnotnumber.html
No "infinity" concept exists in the context of any number system, if by number system one means a collection of concepts that have operations like addition and multiplication the way familiar numbers do, operations which obey the usual properties of arithmetic.
One way to see this is to think, what would infinity minus 1 be? It couldn't be a finite number, since no finite number plus 1 equals infinity. So it must be infinite, and this would mean
infinity - 1 = infinity
From this one can immediately see that the rules of arithmetic must be violated, since if they held one could subtract infinity from both sides to conclude that -1 = 0, which isn't true.
Did you see what they're talking about? They mean
...in which "infinity" would mean something one can treat like a number.
which is what nobody thinks of as being infinite. That's merely ONE instance/version in which your article speaks of infinity which doesn't exist. However they also give to other examples in which it does.
In this argument they're proving that there is no such thing as a number which equals infinity which is not what everyone else means by infinity. They claim that they're talking about the "concept" of infinity but they aren't. This is a really bad argument and is written extremely poorly.
Bill - I'm sorry but I can't respond to anymore of your responses on infinity unless I know that you took the time to read a section in a calculus text about it. You'd end up reading less than you do in all the internet articles that you've read in the past few days and you wouldn't keep making these errors. But I'm taking a lot of time out of my internet time to respond to your comments to help you. But you haven't been appreciative enough to take my advice and read what I suggested. I feel as if you're being disrespectful to me when the fact is that I'm being as respectful to you as I possibly can by doing a lot of work trying to help you understand this and all you do is skirt around my one single suggestion which will help you. I beg you to understand my point of view. It is not my intention to come across as a jerk to you by any means. The fact is that I consider you one of my best internet friends and an intelligent man to boot. I'm merely expressing my dissatisfaction with you not taking my word on this. You've known me for years now, right Bill? As such you should know that I don't take such strong positions unless I'm absolutely certain that what I'm suggesting will be helpful more than anything you're going to read from me or anybody else on the internet. So please don't get angry with me my friend. Okay? :)
See the attachment which completely defines the concept of infinity
[ Invalid Attachment ]
Do you see this, Bill? This is all that I was asking you to read all these days. Do you see how small it actually is? And it completely covers the concept and shows that "becomes infinite" is identical to "increases without bound" by definition. :)
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It seems that not all mathematicians agree with this.
I suspect there's no field of human knowledge where everyone agrees about everything.
I beg to differ!
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I suspect there's no field of human knowledge where everyone agrees about everything.
I beg to differ!
[:o)] [;D]
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Bill S:
1. Is infinity a number?
No.
infinite: not limited, not measurable, not countable, without a specific value
By definition, infinity is not a number, but a state of indeterminacy.
2. Is eternity a length of time?
No.
eternity: time without a beginning and an end
Its definition implies an infinite duration, and therefore cannot be measured.
3. Is it possible to define Cantor’s “absolute infinity”?
No.
Cantor was a self appointed spokesmen who thought he could explain infinity, i.e. things without end, despite the fact that no human experience encounters it, thus the mind has no ability to conceptualize it. If you study something to a greater degree than the masses, they will consider you an expert. This would require a separate topic.
4. If there had ever been (absolutely) nothing, could there be something now?
Yes.
There is something now, and something cannot come into existence without a cause/reason.
5. Could there be change without time?
Yes.
Time does not cause changes. As far as known, energy does. Time is like an accounting system, recording events of interest to a standard (clock) event.
This was done long before philosophy was augmented with measurement to become science.
In the quantum world, particles change states, A to B, and B to A. The physicist observes both while his clock accumulates ticks. One transition is the reverse of the other, not one moving backward in time. Change of states for basic entities is acceptable behavior, but a shattered glass reassembling itself off the floor, and moving to the top of the table would be suspicious. To maintain perspective, running the film backwards (in real time) is not equivalent to an actual reconstruction of a complex object.
Ponder this.
If time is a causal factor, why are quantum predictions expressed as probabilities?
For a 24 hr period, people enter a restaurant off the interstate, eat and leave. Their circumstances vary, so there is no causal chain of events, i.e. their visits are random. Time did not cause their visits. It's memory that allows the mind to make fictitious connections for a sequence of events.
While watching animations on the display, are there really 'moving pictures'?
While watching a plane fly toward the horizon, is it the plane or its image, getting smaller?
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Pete, please don’t think that I lack appreciation for the time and patience you and other experts expend trying to help “hitch-hikers” like me. As the main carer for two disabled family members I have little time to spare, and I have to say that when I hind a few minutes I tend to spend it interacting with others on line rather than trying to find the specifics of calculus or complex numbers that might, or might not, help.
Thanks for your attached explanation; it is perhaps the best I’ve seen to date. If this is what we have been discussing, and coming close to falling out about, we have certainly been at cross-purposes. As far as I understand it, in my mathematically challenged way, I have absolutely no problem with it.
Some time ago I downloaded a calculus course which has remained unstarted somewhere on my external HD; maybe I should find it and have a go. [:-\]
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Phyti39; you raise some interesting points, some of which I would like to return to when time permits. In the meantime, this puzzles me:
4. If there had ever been (absolutely) nothing, could there be something now?
Yes.
There is something now, and something cannot come into existence without a cause/reason.
Shouldn't that have been "No"?
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Ponder this.
If time is a causal factor, why are quantum predictions expressed as probabilities?
Time is an abstract mental picture we humans define as change in progress. Time does not cause change, change is the evidence that time has passed.
While watching animations on the display, are there really 'moving pictures'?
No, but photons are moving between the screen and your eyes. And pixels have also changed places and colors.
While watching a plane fly toward the horizon, is it the plane or its image, getting smaller?
This question is a bit silly. Hold your finger up very close to your eyes, observe it's apparent size then move it to arms length. If you'll notice, it now appears smaller compared to when it was very close to your eyes. Are you prepared to suggest that just because your finger now appears smaller than when very close to your eyes that is has somehow shrunken?
The divergence of light is the reason for the phenomenon of perspective, not because the object has reduced in size.
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As the main carer for two disabled family members I have little time to spare, ..
Yes. I know that and that's why I wanted you to trust me and read what I suggested to you what I did. I.e. because you would have spent a great deal of time less in reading and discussing the point otherwise then actually reading the very small amount on the definition. And when I say that it'd be less reading I mean that'd it take less than one minute! :o
You saw and read the attachment that I created and inserted into my last post. Thus you saw now how little there actually was to read, didn't you? The reason I asked you to take my advice and my word and read it was because I would have had to do less work creating that attachment because I couldn't easily type it out since limit notation is hard to do by typing. I told you many times how little where was to read and you kept thinking that it would take too long. Do you now understand how little there was to actually read? Will you please take my word for it next time? :)
..when I hind a few minutes I tend to spend it interacting with others on line rather than trying to find the specifics of calculus or complex numbers that might, or might not, help.
You mean to tell me that when I (or someone else) posts a URL to something like a Wikipedia article of a webpage of mine that you've never looked at it? If you did then why would you think that reading a paragraph or two in a text would be any different or require more work? I would never repeatedly suggest reading a portion of a text it wasn't actually a mere paragraph or two. I just wish you would have trusted me on this. :(
Some time ago I downloaded a calculus course which has remained unstarted somewhere on my external HD; maybe I should find it and have a go. [:-\]
That'd be a great idea.
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I suspect there's no field of human knowledge where everyone agrees about everything.
I beg to differ!
[:o)] [;D]
My sentiments exactly, dlorde. :)
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Ponder this.
If time is a causal factor, why are quantum predictions expressed as probabilities?
Time is an abstract mental picture we humans define as change in progress. Time does not cause change, change is the evidence that time has passed.
While watching animations on the display, are there really 'moving pictures'?
No, but photons are moving between the screen and your eyes. And pixels have also changed places and colors.
While watching a plane fly toward the horizon, is it the plane or its image, getting smaller?
This question is a bit silly. Hold your finger up very close to your eyes, observe it's apparent size then move it to arms length. If you'll notice, it now appears smaller compared to when it was very close to your eyes. Are you prepared to suggest that just because your finger now appears smaller than when very close to your eyes that is has somehow shrunken?
The divergence of light is the reason for the phenomenon of perspective, not because the object has reduced in size.
I think you get the point. Perception is not what it appears to be. Time does not cause change is my argument against "change cannot happen without time". People still cling to this idea that there is something invisible orchestrating the sequence of events. Maybe it's some form of security blanket in a world where things are so temporary, including life.
Nevertheless, the history of time as a concept and as applied science, shows it as an alias for distance. Look at a Minkowski diagram and notice the vertical axis is ct.
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Bill S #51
We exist in an infinite cosmos in which there is no change or differentiation. Every “part” is the whole. Nothing happens, everything just “is”.
I hope you don't believe in fatalism.
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Phyti39; you raise some interesting points, some of which I would like to return to when time permits. In the meantime, this puzzles me:
4. If there had ever been (absolutely) nothing, could there be something now?
Yes.
There is something now, and something cannot come into existence without a cause/reason.
Shouldn't that have been "No"?
There was nothing (a physical universe), then one came into existence. Since the elements (energy or matter) had no prior existence, they can't be used to bootstrap themselves into exixtence.
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There was nothing (a physical universe), then one came into existence. Since the elements (energy or matter) had no prior existence, they can't be used to bootstrap themselves into exixtence.
When you say the bolded above, do you mean there was a physical universe? because it seems to me a physical universe isn't nothing.
If you mean instead that there wasn't a physical universe (i.e. there wasn't anything at all, so no causes or reasons), then you seem to be contradicting yourself - if something cannot come into existence without a cause/reason (i.e. the elements (energy or matter)... can't be used to bootstrap themselves into existence), and there is something now, then it follows that there can't have been nothing (no cause or reason).
I'm puzzled...
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Time does not cause change is my argument against "change cannot happen without time".
It's not really an argument - "change cannot happen without time" doesn't imply that time causes change. It just says time is a necessary condition for change.
Having said that, there are good arguments for the inverse dependency, "there's no time without change", which does have more of a causal flavour...
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There was nothing (a physical universe), then one came into existence.
That's not known at this point. The Big Bang theory cannot be used to trace back to t = 0 but to only a short time after that. Therefore we cannot say what came before that time. There is a theory called the Pre-Big Bang theory which uses string theory to address some of those scenarios.
Since the elements (energy or matter) had no prior existence, they can't be used to bootstrap themselves into exixtence.
We don't know that either. There are particles which do "bootstrap themselves into existence". In fact many particles do that. There's a whole slew of them in particle physics which have been seen in the lab merely "popping into existence" from the inertial energy which is already there.
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There's a whole slew of them in particle physics which have been seen in the lab merely "popping into existence" from the inertial energy which is already there.
This is one of the fascinating things about science; scientists seem to be able to claim that the "inertial energy which is already there" is nothing, yet maintain that it can give rise to something.
I'm willing to believe that I have missed something; but I wish someone would explain what it is. My suspicion is that "nothing" is used in different ways, with different meanings, in different contexts, and that the trouble comes when the contexts get crossed over.
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BTW. If anyone is interested in seeing how the discussion, starting with the same OP, developed on another forum, you might be interested in looking at SAGG. Just for fun.
http://www.scienceagogo.com/forum/ubbthreads.php?ubb=showflat&Number=53488&page=1
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This is one of the fascinating things about science; scientists seem to be able to claim that the "inertial energy which is already there" is nothing, yet maintain that it can give rise to something.
I'm willing to believe that I have missed something; but I wish someone would explain what it is. My suspicion is that "nothing" is used in different ways, with different meanings, in different contexts, and that the trouble comes when the contexts get crossed over.
Yes; the articles I've seen by Krauss, Carroll, and others usually clarify what they mean by 'nothing' - and it's generally not the conceptual 'absolutely nothing' we've been kicking around here; for example (http://www.ttbook.org/book/transcript/transcript-lawrence-krauss-marcelo-gleiser-something-nothing):To a physicist, the first version of nothing of is simply empty space with nothing in it. You wouldn' t have any particles, all the radiation and so, there's literally nothing in it. But that nothing is actually quite complicated because of quantum mechanics and relativity. It turns out empty space is a boiling, bubbling brew of virtual particles, popping in and out of existence in a time so short that you can' t even measure them.
So clearly it is important to specify exactly what you mean; and, to your credit, you did, when you talked of 'absolutely nothing'; albeit in my view it isn't meaningfully applicable to the physical world.
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My favourite quote from Lawrence Krauss is:
“By nothing, I do not mean nothing…..”
OK, it's a bit unfair, but it makes a good quote.
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There was nothing (a physical universe), then one came into existence. Since the elements (energy or matter) had no prior existence, they can't be used to bootstrap themselves into exixtence.
When you say the bolded above, do you mean there was a physical universe? because it seems to me a physical universe isn't nothing.
If you mean instead that there wasn't a physical universe (i.e. there wasn't anything at all, so no causes or reasons), then you seem to be contradicting yourself - if something cannot come into existence without a cause/reason (i.e. the elements (energy or matter)... can't be used to bootstrap themselves into existence), and there is something now, then it follows that there can't have been nothing (no cause or reason).
I'm puzzled...
Should have put "no" in place of "a". Nothing to me is literally "no thing", no matter, no energy, no physical laws. These things had to be introduced somehow. They do not bring themselves into existence. The "big bang" states the universe starts from a singularity, and even assigns an age. That just replaces one question with another.
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There was nothing (a physical universe), then one came into existence.
That's not known at this point. The Big Bang theory cannot be used to trace back to t = 0 but to only a short time after that. Therefore we cannot say what came before that time. There is a theory called the Pre-Big Bang theory which uses string theory to address some of those scenarios.
Since the elements (energy or matter) had no prior existence, they can't be used to bootstrap themselves into exixtence.
We don't know that either. There are particles which do "bootstrap themselves into existence". In fact many particles do that. There's a whole slew of them in particle physics which have been seen in the lab merely "popping into existence" from the inertial energy which is already there.
Quantum fluctuations, virtual particles, etc. result from energy and processes already in place. Prior to the "big bang" or whatever, that could not be the case, unless you propose a 'forever' universe.
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Quantum fluctuations, virtual particles, etc. result from energy and processes already in place. Prior to the "big bang" or whatever, that could not be the case, unless you propose a 'forever' universe.
Frankly, that's exactly what I'd propose. I'll explain:
If our universe once sprang up within nothingness, as a few might suggest, it is quite likely it can happen again. The question is; How do we understand this nothingness from which our universe first came into existence?
There are those that will contend that nothing lies outside our present universe. In fact, they will suggest that there simply is no outside at all. If that's the case, and our universe is finite in both size and age, it came to being within an region that did not formerly exist. And that logic simply does not make any sense at all. If that region didn't exist, nothing could arise within it.
If the Big Bang is an accurate understanding of our universal evolution, we still can only go back to a very short time after this initial event. I therefore suggest that because space is here now, it has always been. And our local Big Bang is just that, a local event within an infinite cosmos of both size and age.
Nothingness is, IMHO an impossibility!
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Much earlier, I said:
“Dlorde; ……I agree, in general, with your definition of nothing, and would like to say more about it, but at this point it would introduce thread drift, so I will come back to it later.”
I tend to write my notes as though I were trying to explain points to someone else. In this instance that was the case, so please excuse the style. These are my thoughts on nothingness from a few years ago.
I suggest a visualisation exercise. For the sake of the exercise, we will assume the correctness of a number of theoretical positions: First, the Big Bang itself; secondly, that before the Big Bang, there was nothing and, thirdly, that inflation caused the infant universe to expand extremely quickly. Now for the mental image: The Universe appears, out of nothing. It inflates rapidly to the size of a beach ball. Freeze the scene at this point and describe what you see in your mind’s eye. Do not bother too much with the appearance of the Universe, it is the image of “nothingness” that is of interest.
All the people I have asked to undertake this exercise have described a sphere of light, surrounded by blackness which extends (some qualify this with such words as “presumably”) to infinity in every direction. There is a second part to the exercise. Now imagine two universes coming into existence simultaneously. Freeze the action at the same point, and describe what you see. The picture that emerges from those who have undertaken the exercise is of two spheres of light, separated by blackness, and surrounded by infinite blackness. Two points need to be addressed here. One is: does the second mental image really describe two objects with nothing between them? The other must be: is this what nothing looks like?
If we talk of two runners, for example, finishing a race with nothing between them, we mean they are so close together that it is almost impossible to separate them. Obviously, this is a figurative use of the term, because, unless they are actually in physical contact at all possible points, which is very unlikely, there will be at least a small amount of space between them. Strictly, then, can we talk of two things having nothing between them if there is any sort of gap between them? We might argue that there is nothing in that gap, but the gap itself must be space, and space, as relativity tells us, is something in its own right. This must lead us to reason that if our two imagined universes have nothing between them, then they must be contiguous, with maximum surface contact. This must prompt us to question the nature of the nothingness surrounding both the pair of universes, and the earlier single universe. If we cannot have a space between them with nothing in it and justifiably call this “nothing”; how can we have space around our universe, or universes, and call that “nothing”? This brings us to the second question: “is this what nothing looks like?” The answer must be “no”, because nothing cannot look like anything. Where does this leave us? I believe it leaves us having to acknowledge that we cannot actually visualise nothing. Many popular science books assure us (and rightly so) that we cannot visualise a fourth dimension of space, let alone the ten, or more, dimensions required by string theory, because we have no experience upon which to base such a visualisation. In the same way, I suspect that our life experience prevents us from forming a mental picture of nothing, because we have never experienced it, either first hand, or through someone else’s description of it. Our nearest experience is of “empty” space, so when we try to visualise nothingness, we use empty space, as a convenient substitute. If space has ever been a suitable substitute image for nothingness, it certainly is not now, because, according to quantum theory it is far from empty. Of course, there may be mystics somewhere who can visualise “nothing”. Perhaps Fred Alan Wolf could find us a yogi who could do this. The possibility must not be ruled out, but for the vast majority of us the fourth spatial dimension and “nothing”, together with the moment of creation of the Universe, will probably remain concepts we can acknowledge only intellectually, but never actually visualise.
As usual, I would appreciate comments/criticism.
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I think this thought experiment might be invalid because it requires the observer to be outside the beach ball universe(s). So you are already starting with a contradiction.
In the case of the two universes: I think this is an argument for considering more than just spatial dimensions. If there are multiple universes, and each is spatially all-encompassing, then they must either occupy the same space or have entirely different coordinate systems. By introducing even one additional dimension (one plus the three spatial and one temporal dimensions we are familiar with), these two universes can exist throughout all of 4D spacetime and still not have any overlap or contact.
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It seems to me a multiverse must consist of some meta-spacetime, particularly models that have universes 'continually' popping into existence and existing in 'parallel'. Whether this meta-fabric is a multidimensional view of the spacetime our universe is part of, or something different, it can't be nothing (because it spawns, or has spawned, universes).
If our universe is the only one and is finite, then it has no outside; it is all there is, and if you keep travelling 'straight' (a geodesic?) you never come to an edge, but may eventually revisit the vicinity of your starting point (if that is meaningful, given the time it would take and the ongoing expansion).
Just speculating...
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Multiverses are an abstraction, so are time without change. Both are important questions philosophically, to me at last. If you believe in the possibility of mutltiverses, do you also believe in the possibility of pure properties? That something to its nature can have a property that defines it?
I usually use linking 'c' to a clock, asking about that clock, ('c') split into Plank scale, one 'light step' at one 'Planck time', when I wonder about that one. Did that 'frozen instant' of one 'Planck step' also meant that we stopped its clock? (locally defined naturally, you can never get away from the observer and so such a experiment would be very hard to prove anything by, as the observers clock won't stop, and the observer defines the experiment.)
But let us assume that we by splitting 'c' into Planck scale also (locally defined) stop its 'clock'. Would you now define it as the property of that 'clock' still exist there?
Also, if we define a 'emergence' of something, to new properties that does not follow from what we know and can theorize about its constituents behavior before?
=
Also it becomes a question of the scale we use, if you think it's possible.
both questions are about properties, and if they are something more than just a idealization. If they are, what would that make a 'multiverse'?
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There are times when I wonder which is the more interesting when posting in these threads. Is it the science, or the psychology?
The three responses so far all raise points that would be valid if my post were actually about multiple universes. In fact, the post was about “nothing”; the single and double universes were introduced simply to illustrate different aspects of considering nothingness.
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It's the most exacting branching out of science Bill. We will build a whole wood here :)
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All the people I have asked to undertake this exercise have described a sphere of light, surrounded by blackness which extends (some qualify this with such words as “presumably”) to infinity in every direction. There is a second part to the exercise. Now imagine two universes coming into existence simultaneously. Freeze the action at the same point, and describe what you see. The picture that emerges from those who have undertaken the exercise is of two spheres of light, separated by blackness, and surrounded by infinite blackness. Two points need to be addressed here. One is: does the second mental image really describe two objects with nothing between them? The other must be: is this what nothing looks like?
...
If space has ever been a suitable substitute image for nothingness, it certainly is not now, because, according to quantum theory it is far from empty.
You have identified the ambiguous words, "nothing" and "space".
If space has properties that are altered by the presence of mass as in gravity, and quantum fluctuations as in the casimer effect, then space, although invisible, has a form or structure. Nothing, being total absence of any thing, would have no properties. It would not have extent or measurement.
The figure of speech, "I see nothing" is more correctly "I do not see any thing".
A miniature universe embedded in a space would not be visible to an outside viewer.
With two, neither would be aware of the other. If the space of each merged then you would have one bigger universe.
The blackness has to be defined as "nothing" or "space".
My exercise would be to turn off photon production, and asking people what they imagine.
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You have identified the ambiguous words, "nothing" and "space".
Why do you say that they're ambiguous? To me they certainly aren't. They have very precise meanings even if space cannot be precisely defined. I.e. see http://users.wfu.edu/brehme/space.htm
Like time and matter-energy, it is not possible to define space in terms of simpler physical entities. Space simply exists. It can be defined only in terms of its properties. Those properties are what we call geometry.
The term nothing simply means the absence of matter, something that does not exist, the absence of all magnitude or quantity; also zero, nothingness or nonexistence.
If space has properties that are altered by the presence of mass as in gravity, and quantum fluctuations as in the casimer effect, then space, although invisible, has a form or structure.
Well stated.
Nothing, being total absence of any thing, would have no properties. It would not have extent or measurement.
The figure of speech, "I see nothing" is more correctly "I do not see any thing".
Seems okay to me.
A miniature universe embedded in a space would not be visible to an outside viewer.
I'm not quite clear what you mean by "miniature universe" since you're speaking of it in a way that is inconsistent with what our own universe is; our universe is not embedded in a space and can't even be though of as being so.
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You have identified the ambiguous words, "nothing" and "space".
Why do you say that they're ambiguous? To me they certainly aren't. They have very precise meanings even if space cannot be precisely defined. I.e. see http://users.wfu.edu/brehme/space.htm
Like time and matter-energy, it is not possible to define space in terms of simpler physical entities. Space simply exists. It can be defined only in terms of its properties. Those properties are what we call geometry.
The term nothing simply means the absence of matter, something that does not exist, the absence of all magnitude or quantity; also zero, nothingness or nonexistence.
If space has properties that are altered by the presence of mass as in gravity, and quantum fluctuations as in the casimer effect, then space, although invisible, has a form or structure.
Well stated.
Nothing, being total absence of any thing, would have no properties. It would not have extent or measurement.
The figure of speech, "I see nothing" is more correctly "I do not see any thing".
Seems okay to me.
A miniature universe embedded in a space would not be visible to an outside viewer.
I'm not quite clear what you mean by "miniature universe" since you're speaking of it in a way that is inconsistent with what our own universe is; our universe is not embedded in a space and can't even be though of as being so.
You know the necessity of good defintions, but Bill uses them with vague and uncertain meanings. The "miniature universe" is used as he presents it, being just as vague. The better his defintions, the less the participants can speculate!
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You know the necessity of good defintions, but Bill uses them with vague and uncertain meanings. The "miniature universe" is used as he presents it, being just as vague. The better his defintions, the less the participants can speculate!
I wasn't aware of that.
Bill. Is that true?
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For the sake of the exercise, we will assume the correctness of a number of theoretical positions: First, the Big Bang itself; secondly, that before the Big Bang, there was nothing and, thirdly, that inflation caused the infant universe to expand extremely quickly.
The reason I included these assumptions was to avoid speculation about where the “universe/s” might have come from; what their nature might be, or anything else about them. The exercise was about “nothing”, and the perception of “nothing”.