Yes exactly true, this would be the case. I keep it a bit simpler using distance rather than area but area is more complete for the Flatlander reality
Catastrophe
"Science begets knowledge, opinion ignorance.
Is it not the case that distance, r, experienced by D+, is area the flatlander's universe?
They each have a different concept of distance.
D+'s measure r is unknown in flatland.
We must not confuse D+ concept of length with flatland length.
Cat
They each have a different concept of distance.
D+'s measure r is unknown in flatland.
We must not confuse D+ concept of length with flatland length.
Cat
Catastrophe
"Science begets knowledge, opinion ignorance.
This gets very confusing if we try to think only of geometry.
For the flatlander, r is unknowable. Only D+ understands what r means.
r is a separation in the dimension of which flat (=flatlander) has no knowledge.
What we are also calling 'r' is a separation which is, for flat, a separation, in his total observed universe, involving his total universe.
For D+, r is simply a length appearing as the radius of a sphere, a dimension unknown to flat.
The two beings, D+ and flat, have totally different understandings of what r is.
For flat, D+'s r is totally beyond flat's comprehension.
A change in D+'s length r results in an expansion of flat's whole universe.
To D, it is an insignificant change in an insignificant sphere, amongst, perhaps, zillions.
To flat, it is an intrinsic part of "all there is". A dimension beyond his understanding.
Cat
It would make more sense to rename D+'s "r" to R, and flat's "r" to x.
R is a linear dimension for D+.
x^2 is an increase on flat's entire universe, represented by the spherical surface.
For the flatlander, r is unknowable. Only D+ understands what r means.
r is a separation in the dimension of which flat (=flatlander) has no knowledge.
What we are also calling 'r' is a separation which is, for flat, a separation, in his total observed universe, involving his total universe.
For D+, r is simply a length appearing as the radius of a sphere, a dimension unknown to flat.
The two beings, D+ and flat, have totally different understandings of what r is.
For flat, D+'s r is totally beyond flat's comprehension.
A change in D+'s length r results in an expansion of flat's whole universe.
To D, it is an insignificant change in an insignificant sphere, amongst, perhaps, zillions.
To flat, it is an intrinsic part of "all there is". A dimension beyond his understanding.
Cat
It would make more sense to rename D+'s "r" to R, and flat's "r" to x.
R is a linear dimension for D+.
x^2 is an increase on flat's entire universe, represented by the spherical surface.
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"Communication across the great divide is inevitably partial." -- Thomas S. Kuhn.
Gibsense,
Your diagram is partial, incomplete, as such always is. If you did an exact copy transparency of it, turned it around to mirror reverse your diagram and would overlay it over your diagram you'd have a start on the hypersphere. The travelers' maps of the territory . . . the frontier.
This might help you see it in (possible) action as I do:
forums.space.com
Gibsense,
Your diagram is partial, incomplete, as such always is. If you did an exact copy transparency of it, turned it around to mirror reverse your diagram and would overlay it over your diagram you'd have a start on the hypersphere. The travelers' maps of the territory . . . the frontier.
This might help you see it in (possible) action as I do:
Page 26 - From a drop of water....
Page 26 - Seeking answers about space? Join the Space community: the premier source of space exploration, innovation, and astronomy news, chronicling (and celebrating) humanity's ongoing expansion across the final frontier.
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Suppose we assume for simplicity the 2D flatlander Universe. Its world is described by 2 dimensions a x b to give area. The D+ observer knows another dimension say 'd'. So D+ understands the volume. Even so, D+ recognises distance. 3 Dimensions.
Extending the logic we can see both the flatlander and the D+ recognise 'a' and 'b' as distances. Each is agreed (between them) as the same 'a' and 'b'. Adding 'd' to give a volume is still a distance, not an area. Adding a further dimension still is a distance.
But maybe I misunderstand
Ah, I read this ' out of turn'. That statement I would challenge. The flatlander could conceive of a circle. His mathematicians might suggest an extra dimension at right angles. They might then be able to imagine a vertical circle passing through their plain—a dot changing to an expanding line and then shrinking before disappearing.
To conceive of a sphere passing through their plain would be much more difficult to explain and understand; their mathematicians would need to add another spatial dimension. But, our guys have managed it -
Imaginary time is needed to achieve some calculations regarding Quantum Mechanics. It runs at 90 degrees to 'Real-time' and is spatial (Stephen Hawking, The Universe in a Nutshell).
Mathematicians talk about the beauty of formulae and express satisfaction as if only they can appreciate, through mathematics, the universe. As if in some Magical process their sums add up. But it isn't Magic and 'Imaginary time' is real (IMO).
To a Flatlander of the 'Flatland Universe', extra dimensions are step increases and decreases in magnitudes of Flatland. There is no other dimensionality, no outside dimensionality to Flatland, other than 0-point and 1-d string, directions of and in magnitudes . . . breadths and depths of Flatland (MULTIVERSE) Universe magnitudes to infinities . . . of "Mandelbrot Set."
The "Mandelbrot Set" defines the territory of the Flatland Universe!
The "Mandelbrot Set" defines the territory of the Flatland Universe!
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Catastrophe
"Science begets knowledge, opinion ignorance.
Yes. Flatland is two dimensional. But we have established that a sphere (surface) is 2D.
I really do not understand this. A flatlander cannot perceive depths.
A D+ observing a flatland area can also see the radius R, but flatlanders cannot.
We must distinguish between what is perceivable to flatlanders and D+ beings. No?
Cat
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Catastrophe
"Science begets knowledge, opinion ignorance.
Gibsense, how do you add a third dimension to flatland?
That would make it 3D, and it would no longer be flatland.
What can such verbal shenanigans prove?
Cat
Shenanigans = tricky or questionable practices or conduct.
I hope you consider this a fair description?
Catastrophe
"Science begets knowledge, opinion ignorance.
Gibsense:
Again, we must distinguish between our geometry and the world of a flatlander.
They are very different. To us (with 3D geometry) it is very simple.
We can see the first dot when the sphere touches the flatland plain.
As we see the sphere (remember in geometry, a sphere is a 2D surface - not a ball) the dot becomes a growing circle, which reaches maximum, and then decreases to a dot, and then disappears. We see the passage of the sphere through flatland. Flatlander does not.
The flatlander sees the dot-circle-dot sequence, but not anything in 3D.
I do not see any problem here.
Cat
Again, we must distinguish between our geometry and the world of a flatlander.
They are very different. To us (with 3D geometry) it is very simple.
We can see the first dot when the sphere touches the flatland plain.
As we see the sphere (remember in geometry, a sphere is a 2D surface - not a ball) the dot becomes a growing circle, which reaches maximum, and then decreases to a dot, and then disappears. We see the passage of the sphere through flatland. Flatlander does not.
The flatlander sees the dot-circle-dot sequence, but not anything in 3D.
I do not see any problem here.
Cat
Catastrophe
"Science begets knowledge, opinion ignorance.
Gibsense,
Did you perhaps not realise "adding 'd' to give a volume" can only refer to flatlander?
And "adding a further dimension", also, can only refer to flatlander.
D+ already has volume, so adding length does not give a volume.
Cat
Did you perhaps not realise "adding 'd' to give a volume" can only refer to flatlander?
And "adding a further dimension", also, can only refer to flatlander.
D+ already has volume, so adding length does not give a volume.
Cat
Cat,
You are going in the wrong direction in your dismissal of depth to a "Mandelbrot Set" 2-dimensional Flatland and Flatlander. The depth is in the breadth of a reach to 0-point asymptote that goes to infinities in magnitudes of reaching for the 0-point . . . never attaining 0-point.
Flatland flattens volume toward zero ('0'), keeping it -- the flattening -- up to infinity. Volume will still exist because 0-point is an unattainable absolute. String 1-dimensionality goes from the well of infinite breadth to infinitesimal breadth which will still be infinite breadth in its entire depth of a vertical-like length to the horizontal.
It's the problem, the blessing and the curse, with being able to see and think and go vastly multi-dimensional MULTIVERSE from fundamental binary base2's '0' and/or '1', including the Trojan "parity" out of ((+1) (-1)) = 1/0 ("there will never be 'One World' until there are two or more worlds (division will have its null unity '0' of [quantum-discrete quanta] portion if it has to take it out of the 'GUT' -- the guts -- of '1' (the guts of 'unity')))! (I keep wanting to designate '0' 'Null-A' instead of "null unity" but no one, except maybe you, Cat, would even begin to understand what it means!)
You are going in the wrong direction in your dismissal of depth to a "Mandelbrot Set" 2-dimensional Flatland and Flatlander. The depth is in the breadth of a reach to 0-point asymptote that goes to infinities in magnitudes of reaching for the 0-point . . . never attaining 0-point.
Flatland flattens volume toward zero ('0'), keeping it -- the flattening -- up to infinity. Volume will still exist because 0-point is an unattainable absolute. String 1-dimensionality goes from the well of infinite breadth to infinitesimal breadth which will still be infinite breadth in its entire depth of a vertical-like length to the horizontal.
It's the problem, the blessing and the curse, with being able to see and think and go vastly multi-dimensional MULTIVERSE from fundamental binary base2's '0' and/or '1', including the Trojan "parity" out of ((+1) (-1)) = 1/0 ("there will never be 'One World' until there are two or more worlds (division will have its null unity '0' of [quantum-discrete quanta] portion if it has to take it out of the 'GUT' -- the guts -- of '1' (the guts of 'unity')))! (I keep wanting to designate '0' 'Null-A' instead of "null unity" but no one, except maybe you, Cat, would even begin to understand what it means!)
Ad #37:
I realized this is not that bulky so brought it over in whole from "From a drop of water...." #643:
I know it is difficult to visualize and understand, but all outer-space is Flatland (infinitely) 2-dimensional mass-surface that is naturally set upon and can be artificially built upon in any number of ways, directions, and magnitudes!
1.) "0-point."
2.) "Superstring."
3.) "Sierpinski carpet."
4.) "Menger Sponge."
It's too bad so few see it as "Flatland Universe" surface, much less understand it or understand the potential to usefully custom manipulate it at large (warp SPACE (cutting curvatures), creations of soliton bubble waves, and so on) and small (facilitation and colonizing, and so on building to live upon or to work), as needed and wanted!
I realized this is not that bulky so brought it over in whole from "From a drop of water...." #643:
I know it is difficult to visualize and understand, but all outer-space is Flatland (infinitely) 2-dimensional mass-surface that is naturally set upon and can be artificially built upon in any number of ways, directions, and magnitudes!
1.) "0-point."
2.) "Superstring."
3.) "Sierpinski carpet."
4.) "Menger Sponge."
It's too bad so few see it as "Flatland Universe" surface, much less understand it or understand the potential to usefully custom manipulate it at large (warp SPACE (cutting curvatures), creations of soliton bubble waves, and so on) and small (facilitation and colonizing, and so on building to live upon or to work), as needed and wanted!
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There are no 4 spatial dimensions. This is an idea that I also had a while ago, but this is not the case. There are 3 vector dimensions. And then there is a time or density scalar.
You take a sheet of paper and increase the compression around a central point, the paper will deform under the action of the change in length and the spherical symmetry. This deformation occurs in the height dimension, which is not in the plane. The 2-dimensional plane thus deforms in the 3rd dimension.
Like this :
CuriouSTEM - Gravitational Waves, Part 1: Ripples Across Spacetime (Introduction)
On September 14, 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) observed gravitational waves for the first time. These waves were the results of a collision of two black holes of 29 and 36 solar masses.
www.curioustem.org
In a 2-dimensional space there is only one plane but in a 3-dimensional space there are 3 planes.
If the density is increased around a point in a 3-dimensional space, the space will curve but not in a 4th dimension, its three dimensions are sufficient for this. A 3-dimensional space therefore has the ability to fold back on itself without the need for a 4th. Just imagine an infinity of superimposed curved planes. Each will produce a curvature in the dimension orthogonal to it and ultimately there is no need for a 4th vector.
It should be seen like this:
Ask Ethan: How Can We Measure The Curvature Of Spacetime?
It's been over 100 years since Einstein, and over 300 since Newton. We've still got a long way to go.
www.forbes.com
The geometry of the universe is elliptical and quaternionic :
Elliptic geometry - Wikipedia
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I have been a firm believer that time has been speeding up since the BB.
i think there is likely a relationship between space and time much similar to electro and magnetism
so the question becomes does time dilation cause the expansion or does the expansion cause the time dilation?
perhaps Dark Energy is just that feedback loop.
it is starting to look like we live in a steady state universe that follows the laws of entropy.
that BB singularity is just an mathematical illusion just like the distant horizon is.
it is just a product of time dilation over time.
i think there is likely a relationship between space and time much similar to electro and magnetism
so the question becomes does time dilation cause the expansion or does the expansion cause the time dilation?
perhaps Dark Energy is just that feedback loop.
it is starting to look like we live in a steady state universe that follows the laws of entropy.
that BB singularity is just an mathematical illusion just like the distant horizon is.
it is just a product of time dilation over time.
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Catastrophe
"Science begets knowledge, opinion ignorance.
What do you mean by "time"? Universal time? No such thing.
Even with clocks, time is subjective for every individual.
Wake up and know exactly how long you have slept, without a clock.
Cat
Even with clocks, time is subjective for every individual.
Wake up and know exactly how long you have slept, without a clock.
Cat
There is only a "universal now" and by time i mean a local rate at which change can happen.What do you mean by "time"? Universal time? No such thing.
Even with clocks, time is subjective for every individual.
Wake up and know exactly how long you have slept, without a clock.
Cat
a second is the basic unit of time
it is the duration it takes for light to travel 299,792,458 meters in a vacuum
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Catastrophe
"Science begets knowledge, opinion ignorance.
Catastrophe
"Science begets knowledge, opinion ignorance.
Time (entangling concurrent REALTIME NOW (t=0) instant) is the universally vibrating (the quantum discrete fluctuation) instant that records all change and the passing rate of changes. It doesn't make changes nor does it stretch out or contract the rate of change.
My! How people are blind! Has anyone here other than me ever seen how cartoons used to be made by page flipping sequenced frames of instants of entangling concurrent REALTIME NOW. Those page flipped sequenced frames of instants being light's coordinate points past-future histories' SPACETIME . . . a multiverse deck of cards, of time-frame instances, that can 'mirror' sequence to the length and breadth of "observable universes."
No one here apparently, that I've read, knows why there is that warning message on auto rearview mirrors telling drivers that those autos speeding at any apparent speed oncoming behind the driver on the road, are always closer to the driver in space and time than light at the speed of light shows them to be! The constant time-frame sequences are always old history and those drivers are actually -- in reality -- out front of that descending SPACETIME (t=+1) past history "observed universe" of time ascending in of some future history (t=-1) "un-observed universe " of time. That "un-observed universe" is always issuing brand new frame sequences of framed instances of an "event horizon" of quantum fluctuation (string vibration), of change (which is at that exact moment a back to the future moment that will NOT arrive to drivers ahead (always as past history (t=0, t=+1, +2, +3, +4, t=+5....)) until a future time (t=-..., -5, -4, -3, -2, t=-1, t=0)) at the speed of light ('c' (t=0)).
What keeps the universal quantum fluctuation instant (t=0), the universal string vibration instant (t=0), rigidly, inflexibly, diamond hard (so to speak) constant for all time?! I've answered that question several times over in several ways already! Einstein answered it once in his vision of....! Hawking answered it once in his imagination of....!
To be continued, maybe....
My! How people are blind! Has anyone here other than me ever seen how cartoons used to be made by page flipping sequenced frames of instants of entangling concurrent REALTIME NOW. Those page flipped sequenced frames of instants being light's coordinate points past-future histories' SPACETIME . . . a multiverse deck of cards, of time-frame instances, that can 'mirror' sequence to the length and breadth of "observable universes."
No one here apparently, that I've read, knows why there is that warning message on auto rearview mirrors telling drivers that those autos speeding at any apparent speed oncoming behind the driver on the road, are always closer to the driver in space and time than light at the speed of light shows them to be! The constant time-frame sequences are always old history and those drivers are actually -- in reality -- out front of that descending SPACETIME (t=+1) past history "observed universe" of time ascending in of some future history (t=-1) "un-observed universe " of time. That "un-observed universe" is always issuing brand new frame sequences of framed instances of an "event horizon" of quantum fluctuation (string vibration), of change (which is at that exact moment a back to the future moment that will NOT arrive to drivers ahead (always as past history (t=0, t=+1, +2, +3, +4, t=+5....)) until a future time (t=-..., -5, -4, -3, -2, t=-1, t=0)) at the speed of light ('c' (t=0)).
What keeps the universal quantum fluctuation instant (t=0), the universal string vibration instant (t=0), rigidly, inflexibly, diamond hard (so to speak) constant for all time?! I've answered that question several times over in several ways already! Einstein answered it once in his vision of....! Hawking answered it once in his imagination of....!
To be continued, maybe....
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TIME is a duration. It has a beginning and an end. And it's rate is constant.
This constant rate of time comes from the motion of e. Motion can not be undone. It's a one way dynamic. And all motion takes and consumes time. Time is a necessary nutrient for motion. And one way length plus duration is a product of motion. Time gives us dimension too. Time is the concrete that holds dimension. Motion can not motion without time. No time no motion.
e has quantum motions. These have quantum durations. All of these quantum durations come from and are set by the first ground level duration, which is the longest quantum duration. This will be the fundamental EM frequency in the future. It's a constant for all matter. No matter the velocity of the matter.
These durations are the same everywhere all the time. The spectrum is set and can not be changed.
All physicality even the intangible time comes from e. The same rate everywhere.
When the long lost space brother returns he'll be the same age.
I'm betting it all turns out to be very simple. And a lot of fuss for naught.
I can only work with what I got.
This constant rate of time comes from the motion of e. Motion can not be undone. It's a one way dynamic. And all motion takes and consumes time. Time is a necessary nutrient for motion. And one way length plus duration is a product of motion. Time gives us dimension too. Time is the concrete that holds dimension. Motion can not motion without time. No time no motion.
e has quantum motions. These have quantum durations. All of these quantum durations come from and are set by the first ground level duration, which is the longest quantum duration. This will be the fundamental EM frequency in the future. It's a constant for all matter. No matter the velocity of the matter.
These durations are the same everywhere all the time. The spectrum is set and can not be changed.
All physicality even the intangible time comes from e. The same rate everywhere.
When the long lost space brother returns he'll be the same age.
I'm betting it all turns out to be very simple. And a lot of fuss for naught.
I can only work with what I got.
Catastrophe
"Science begets knowledge, opinion ignorance.
CM,
You are talking about "clock time".
Each person lives by their own time, which inter-relates with clock time, but which is also personal to each.
Time, by its very definition, has been around for billions of years.
Cat
You are talking about "clock time".
Each person lives by their own time, which inter-relates with clock time, but which is also personal to each.
Time, by its very definition, has been around for billions of years.
Cat
I agree sort of. It's similar to "The Big Bang Centre is Everywhere".
Sure individual time variation is described by relativity but that doesn't mean there is no valid time reference from the point of view of D+ (the hyperdimensional 4D person)
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