Flatlander 3D: Hypersphere to Flat Space

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But this is relative. Entropy if time was positive and you are there in a contracting universe continues the same - or does it/can it?
"Verse" means "turn", to turn, wheel turning, rounding, returning. "Entropy", both positive and negative entropy (one way or the other), is the constant of return to the "Wild (weedy chaos)Frontier" universe, including the Hawking constant of life migration in mid-turn to the "Life Zone" 'Midway' between the eternally present constant of 'Perfect End' in and to the equally eternally present constant of 'Endless Beginning' . . . one and the same 'Schrodinger', if not 'Dirac' as well, constant.
 
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Catastrophe

"Science begets knowledge, opinion ignorance.
Gibsense,

Come back to ABCD for a moment. Let them look at their watches.

B will hear the sounds from A and C simultaneously (and if they were further apart and/or sound travelled more slowly and/or their watches were extremely more accurate - you get the parameters) they would see that B heard the sound a tiny interval after A and C produced it.

If they compared their "perfectly accurate" watches, they would see that D received the sounds slightly later than B.

Cat :)
 
From "From a drop of water...." post #577:

-------------------------------

"From a drop of water, a logician could infer the possibility of an Atlantic or a Niagara without having seen or heard of one or the other...." -- 'Sherlock Holmes: A study in Scarlet; by Arthur Canon Doyle.
 
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Time dilation is a hiccup to the hypersphere model.
Those TD radii progress more slowly and distort a uniform hypersphere.

Black holes would be the most extreme case.

Space would have to stretch further to conjoin the span of temporal variances.
 
Time dilation is a hiccup to the hypersphere model.
Those TD radii progress more slowly and distort a uniform hypersphere.

Black holes would be the most extreme case.

Space would have to stretch further to conjoin the span of temporal variances.
What I call Hawking time, among others who have tied to it (including me), entangled and entangling concurrent REALTIME NOW t=0, instant and eternal ("for all time"), doesn't stretch. Holographical observable light's coordinate point SPACETIME (t=+1) (t=-1)), yes . . . spontaneous REALTIME NOW instant (t=0), no way (universally instantaneously spontaneous, thus not a chance)! (It has -- comes with -- a guarantee and guarantor, collapsed cosmological (Horizon) constant (/\) P/BB T=1.)
 
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Catastrophe

"Science begets knowledge, opinion ignorance.
Gibsense,

I do not understand your reply.

I stated in forming the analogy:

Consider four observers A, B, C and D standing in straight line, say each 100m from the next.

yet you say that they are on a circumference. Surely the speed of sound and 100 metre separations are strictly Newtonian, not Einsteinian, in context.

You posted:

Have I made a logical error - it seems so.

Is this the source of your logical error? :)

Cat :)
 
I'm angry as can be at my two favorite physicists, Einstein and Hawking, among so many others I've read over almost seventy-years!

I've suddenly realized that "emergent SPACE" (hyperspace) (subspace) (warp space) (JUMP-SPACE (wormhole(s)) (emergent gravity (including 11-dimensions of it, if not more)), as I've been seeing and describing it dimensionally for so long, can't be more than a 0-dimensional "vacuum void" in total actual dimensionality I keep "turning" to. And given that I see and describe, picture and model, REALTIME NOW as entangled, entangling, spontaneous concurrent REALTIME NOW instant (t=0)! And, given again, that I see and describe light's coordinate points' SPACETIME past-future histories as being strictly "observable universe" holographical universe.

Both space and time are infinitely multi-faceted, multi-dimensional, many worlds, and, simply, "Infinite MULTIVERSE Universe" complexity and chaos!
 
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f A and C cause a loud noise "simultaneously", B will hear both at the same time.
However, D will hear the noise from C before the noise from A.
(This assumes nothing intervening changes the speed of sound)

This may be a simpler caveat than you had in mind, but it does show simply that "now" is different for different observers.
Cat Hi, your statement has forced me to think more about how to answer your points. Consequently, I realise that answers to this and many other questions discussed have been staring me in the face for years. So much so that I think we need a new thread probably titled "Onions, Spheres, Time, Light Cones and Gravity.
I am not sure about Gravity but it probably gets included.
There is no doubt I need help to express the stuff mathematically. I got an 'A' level GCE in maths but my further education was too diverse a subject to build on it. I am 80 and have lost most of that knowledge except simple arithmetic. Simple geometry is still within my grasp though, lol.
To convince you that it is worth bearing with me I would like to state something that you can verify easily (if you are good at arithmetic). It is stunning and simple.

Increases in the radius of a circle and therefore the increase in its circumference equal the Hubble Constant.

NB It is necessary to accept the interchangeability of length and time units i.e. a light year = a year ( plus 1 second = approx 300,000km)
Variations 'in reality' are easily explicable and the answer to your statement is contained in the description of light cones, onions, balloons, Spatial 4D and Time. However, the 'imagination energy' needed is large and hence the above statement shows it would be worthwhile if you verify it.

It is all geometry. Even, I think, the expansion of space and gravity-bound areas but the nature of time is an essential factor. I am frustrated by the fact that diagrams are much easier. I tried to set up something on a free website as I published one on the subject many years ago called "Timewave" to illustrate the statement above. It is now lapsed and the new methods although simpler I find confusing - it must be my age!

I can draw some diagrams and email them to anyone interested. Also, I can email an Excel worksheet that gives the Hubble Constant for any given age of the Universe (without locking so the working is visible but it is arithmetic and probably an intelligent person can drastically simplify it).

I must cease for now and get my partner a cup of tea (6.30 am) to keep her onside, lol.
 
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Catastrophe

"Science begets knowledge, opinion ignorance.
Gibsense, You seem to be complicating ABCD unnecessarily. Is it not simply that the speed of sound is (here, correctly) assumed constant, and therefore it takes longer to travel further distances?

As far as maths is concerned, I took pure and applied maths (separately) at A level, and then both at S level.
I then did a degree in Chemical Engineering, which did entail much more complicated maths, but, then again, I am now 85, so it was a while ago. And I don't think we need much complicated maths here.

I may be wrong (as always), but I do think that you are overcomplicating issues.
Perhaps I am not understanding something here? More to follow . . . . . . . . .


Cat :)
 

Catastrophe

"Science begets knowledge, opinion ignorance.
. . . . . . . . .

I am finding it a bit difficult here because I am using the spherical surface in a different analogy.
I have to work out your analogy, then check how it works with mine. Interesting if it works for both.
Of course, both are just analogies so both can be right (useful) in context.

"Onions, Spheres, Time, Light Cones and Gravity"

Could you provide, please, a very short summary of this? I am trying to compare the assumptions.
In my analogy, See below. ***

I have looked in detail at yr #1 and #2. Have you seen my ref in #3. Also please see #7.

I do have a problem with the number of words you are using. I do understand that it is a difficult matter to understand. I am sorry you have had problems with other sites, but I don't stop easily, so let's try to find some common linguistics? :)

In my analogy, the surface of the sphere is the "universe" for a flatlander. Thus his/her observed universe can be boundless, yet still expand. This universe can be understood as expanding, but solves the paradox of "expanding into what?". The answer is apparent to a being capable of understanding "one dimension higher". In this case, us. Granted it is only an analogy, it postulates an answer which could work. ***

Can you state your analogy as simply as that? It may not be possible, I grant you. . . . . . . . . .

Cat :)


P.S. Increase in radius, in my analogy, represents view by observer of higher dimension.
 
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. . . . . . . . .

I am finding it a bit difficult here because I am using the spherical surface in a different analogy.
I have to work out your analogy, then check how it works with mine. Interesting if it works for both.
Of course, both are just analogies so both can be right (useful) in context.



Could you provide, please, a very short summary of this? I am trying to compare the assumptions.
In my analogy, See below. ***

I have looked in detail at yr #1 and #2. Have you seen my ref in #3. Also please see #7.

I do have a problem with the number of words you are using. I do understand that it is a difficult matter to understand. I am sorry you have had problems with other sites, but I don't stop easily, so let's try to find some common linguistics? :)

In my analogy, the surface of the sphere is the "universe" for a flatlander. Thus his/her observed universe can be boundless, yet still expand. This universe can be understood as expanding, but solves the paradox of "expanding into what?". The answer is apparent to a being capable of understanding "one dimension higher". In this case, us. Granted it is only an analogy, it postulates an answer which could work. ***

Can you state your analogy as simply as that? It may not be possible, I grant you. . . . . . . . . .

Cat :)


P.S. Increase in radius, in my analogy, represents view by observer of higher dimension.
The analogy is identical. I identify your one dimension higher as being a hypersphere. That validates the surface as 3D.

The issue of 'expanding into what' is not a problem the way I think. The canvas or embedding space is 4 spatial dimensions (or more - doesn't matter). The 'outside' existence or not is at this level irrelevant I think.

The point is the 3d Shape is a hypersphere. NB I use that technically to mean the surface of a ball.
 
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Each passing second extends the radius (of the hypersphere; your balloon) by 299,792,458 meters.
Each second added (299,792,458 meters) to the radius adds 2Pi(r) to the circumference of the hypersphere. That added circumference represents added space from expansion as time passes (space is added as a function of time).

The yuck bit is converting the added amount into the terms of the Hubble Constant and working the arithmetic. In the case of reality 13.8 billion years = Hubble Constant 70.855 when you work it out.

Hence I stated, "Increases in the radius of a circle and therefore the increase in its circumference equal the Hubble Constant."

You referred to some of your previous posts - I need to check them now. Oh partner asking for help to do something - will check soon
 
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Catastrophe

"Science begets knowledge, opinion ignorance.
Cat Hi, your statement has forced me to think more about how to answer your points. Consequently, I realise that answers to this and many other questions discussed have been staring me in the face for years. So much so that I think we need a new thread probably titled "Onions, Spheres, Time, Light Cones and Gravity.
I am not sure about Gravity but it probably gets included.
There is no doubt I need help to express the stuff mathematically. I got an 'A' level GCE in maths but my further education was too diverse a subject to build on it. I am 80 and have lost most of that knowledge except simple arithmetic. Simple geometry is still within my grasp though, lol.
To convince you that it is worth bearing with me I would like to state something that you can verify easily (if you are good at arithmetic). It is stunning and simple.

Increases in the radius of a circle and therefore the increase in its circumference equal the Hubble Constant.

NB It is necessary to accept the interchangeability of length and time units i.e. a light year = a year ( plus 1 second = approx 300,000km)
Variations 'in reality' are easily explicable and the answer to your statement is contained in the description of light cones, onions, balloons, Spatial 4D and Time. However, the 'imagination energy' needed is large and hence the above statement shows it would be worthwhile if you verify it.

It is all geometry. Even, I think, the expansion of space and gravity-bound areas but the nature of time is an essential factor. I am frustrated by the fact that diagrams are much easier. I tried to set up something on a free website as I published one on the subject many years ago called "Timewave" to illustrate the statement above. It is now lapsed and the new methods although simpler I find confusing - it must be my age!

I can draw some diagrams and email them to anyone interested. Also, I can email an Excel worksheet that gives the Hubble Constant for any given age of the Universe (without locking so the working is visible but it is arithmetic and probably an intelligent person can drastically simplify it).

I must cease for now and get my partner a cup of tea (6.30 am) to keep her onside, lol.

To keep this idea separate, you stated:

Increases in the radius of a circle and therefore the increase in its circumference equal the Hubble Constant.

This needs modifying. There is a very useful technique called dimensional analysis.
In this case, you talk about length = increase in radius, e.g., in metres of feet.

Now,

Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving away from Earth. Wikipedia

Thus, speed is proportional to distance (expansion).
Mathematically, speed = constant times distance (radius is related to distance), so you would need speed of recession involved to invoke Hubble's Law.

Cat :)
 

Catastrophe

"Science begets knowledge, opinion ignorance.
The analogy is identical. I identify your one dimension higher as being a hypersphere. That validates the surface as 3D.

The issue of 'expanding into what' is not a problem the way I think. The canvas or embedding space is 4 spatial dimensions (or more - doesn't matter). The 'outside' existence or not is at this level irrelevant I think.

The point is the 3d Shape is a hypersphere. NB I use that technically to mean the surface of a ball.

NB I use that technically to mean the surface of a ball.

Now that does help.

Cat :_
 

Catastrophe

"Science begets knowledge, opinion ignorance.
Each passing second extends the radius (of the hypersphere; your balloon) by 299,792,458 meters.
Each second added (299,792,458 meters) to the radius adds 2Pi(r) to the circumference of the hypersphere. That added circumference represents added space from expansion as time passes (space is added as a function of time).

The yuck bit is converting the added amount into the terms of the Hubble Constant and working the arithmetic. In the case of reality 13.8 billion years = Hubble Constant 70.855 when you work it out.

Hence I stated, "Increases in the radius of a circle and therefore the increase in its circumference equal the Hubble Constant."

You referred to some of your previous posts - I need to check them now. Oh partner asking for help to do something - will check soon


Each passing second . . . . . . . . .

Now that does help. You are bringing in the missing speed.


Cat :)


I find confusing - it must be my age!

No. We just have to keep using our brains. We are. Just keep it up (both of us).
 
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Catastrophe

"Science begets knowledge, opinion ignorance.
Post #8 looks long, but this is what remains after taking out the quotes:

QUOTE

Atlan0001,
Thank you for your comments.

According to Google:

What I actually posted was:

My emphasis.

From:







Would you not agree that this is a perfectly acceptable use of the term "superbeing" in this context, making a comparison, as it does, with a "flatlander"?

Whilst I would thank you again for your extensive comment on this point, I do feel that it was slightly excessive suggesting this,

where mere humans were clearly what I described in parentheses as "superbeings".

I do further stand by this latter comment as possibly relevant to any "higher beings", even when we are describing rabbits to amoebae.

I hope that you will take this reply in the friendly and constructive manner as I intend it.

Cat :)


What I actually posted was:

My emphasis.

From:

Goodbye infinity and all that infinite singularity and infinite density descriptions | Space.com Forums

As you will notice, the first part of this, rendered bold, simply states that the
Thus, in this context, we would qualify as superbeing, and please note that I have put superbeing in quotes to emphasize this.

From the second part, rendered bold,


Whilst I would thank you again for your extensive comment on this point, I do feel that it was slightly excessive suggesting this,

where mere humans were clearly what I described in parentheses as "superbeings".

I do further stand by this latter comment as possibly relevant to any "higher beings", even when we are describing rabbits to amoebae.

I hope that you will take this reply in the friendly and constructive manner as I intend it.

Cat :)


Atlan0001,
Thank you for your comments.

According to Google:

What I actually posted was:

My emphasis.

From:

Goodbye infinity and all that infinite singularity and infinite density descriptions | Space.com Forums

As you will notice, the first part of this, rendered bold, simply states that the
Thus, in this context, we would qualify as superbeing, and please note that I have put superbeing in quotes to emphasize this.

From the second part, rendered bold,
you will see that this further emphasises the point by substituting "beings with the ability to perceive higher dimensions" (we being one such) in place of superbeing.

Would you not agree that this is a perfectly acceptable use of the term "superbeing" in this context, making a comparison, as it does, with a "flatlander"?

Whilst I would thank you again for your extensive comment on this point, I do feel that it was slightly excessive suggesting this,


where mere humans were clearly what I described in parentheses as "superbeings".

I do further stand by this latter comment as possibly relevant to any "higher beings", even when we are describing rabbits to amoebae.

I hope that you will take this reply in the friendly and constructive manner as I intend it.

Cat :)
 
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Sorry, not have a good afternoon, Partner is ill I'd better make tea.
My attempts to get an image up to summarise what we have so far have failed but the link posted does bring it up ok.
I glanced at your last post but am confused again. If the image makes sense to everyone is it ok to post about onions and time as previously mentioned - as a separate post- perhaps tomorrow?
Better make food for her now
 
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Gibsense,



Even if absolute space / time do exist, you are correct about caveat(s).

Consider four observers A, B, C and D standing in straight line, say each 100m from the next.

If A and C cause a loud noise "simultaneously", B will hear both at the same time.
However, D will hear the noise from C before the noise from A.
(This assumes nothing intervening changes the speed of sound)

This may be a simpler caveat than you had in mind, but it does show simply that "now" is different for different observers.

Another question. Does space exist at all if there are no objects present, by which you can measure it? If you are in totally empty space - no stars visible - you would be able to move a finger from shoulder to hand, but would this give you the impression of space which you could move through? If, over a long period, you spoke a number of random different words (say 100) would you know (remember) the order after, say, a year? You would have no need to know either. You would not need to invent words like before, after, nearer, further, since you would have no one to communicate with.

Coming back to the quote, why do you think that that absolute space and absolute time do exist?

Cat :)
I have a moment to respond. I think that - just a guess - for quantum stuff reality is a reaction to events. But for space, there is a sort of independence of events and perhaps mass. Maybe if we can do the onions and time we can tackle this. If we can all agree, lol that should keep us busy!
 
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