I would be very pleased to receive any comment on the strength of an analogy, described (inter alia) as:

The analogy in question is my posting in respect of the perspective of a "flatlander".

To clarify the terms of the first analogy, by 'flatlander' I am following in principle the use of the term by Edwin A Abbott (originally anonymously) in the book "Flatland - The Classic Speculation on Life in Four Dimensions". In a Preface (entitled "Limitations") Isaac Asimov describes the book as "probably the best introduction one can find into the manner of perceiving dimensions" although I have seen some comment also from Google:

My use of the idea is not to repeat or criticise the idea, but to try to extract some "similarity in known respects to similarity in other respects"; viz., analogy.

By flatlander, I mean a 2-D being living in a 2-D 'universe'. By consulting mathematical sources, I was able to confirm that a sphere is actually a 2-D surface existing in 3-D. It is similar to the idea that, inhabiting (at least, historically) only a tiny portion of the Earth's surface, mankind once thought the Earth to be flat. There is, of course, the difference that we are a 3-D (spatial) lifeform inhabiting a 3-D (spatial) 'universe'.

The first analogy considers our simplistic view that we inhabit a 3-D space 'universe' travelling through a 4th dimension, which is how time is commonly considered. (Spacetime will be considered later).

To the flatlander, there is no 3rd spatial dimension, no 'up' or 'down', although these are, of course, apparent to us.

Thus, his 'universe' is bounded by the surface of the sphere. If his 'universe' is to be perceived as expanding, this would be viewed as increase in surface area with time, and his spherical surface would be judged as expanding by increasing distance between points on the surface. Of course,

If we now change perspective to what our own would be, if we were able to view flatland, we would see his 'universe', his curved 2-D surface, increasing in radius, and his "time axis" would be the increase in radius of this sphere. Whilst we might (but not necessarily) relate flatland 'time' to our time, it is easy to see it as akin to a linear dimension

The points I wish to draw from this analogy, are:

That the flatlander's 'universe' is limited to that spherical surface existing in his 'time. For us, as a D+ being, meaning a being able to perceive and process at least one more dimension than the flatlander, it is simply akin to an expanding soap bubble. Note that this is a common analogy for us, but not so in the later example. We should at least be prepared for some differences. Thus a D+ being (e.g., us) could observe a million or more of what a flatlander considers to be 'his' 'universe'. Hence my use of 'around' the word universe. That means that 'universe' is no longer "all there is", but "

"Universe" is a relative term, which may be replaced by "observed universe".

The second analogy follows directly from the first. The difference is that, in distinction to our "natural" viewpoint of dividing space from time, we simply ( ) substitute spacetime as the spherical surface (or 'bubble' if you will). This means that what we (D+) observe as radius no longer corresponds to time, whether 'our time' or 'flatlander time', but to something akin to time for a D++. It means that we understand our (D+) "expansion of the universe"

What do you think? It is not a proof, but might it help conceptualisation?

Cat

Logic

a process of arguing from similarity in known respects to similarity in other respects.

The analogy in question is my posting in respect of the perspective of a "flatlander".

To clarify the terms of the first analogy, by 'flatlander' I am following in principle the use of the term by Edwin A Abbott (originally anonymously) in the book "Flatland - The Classic Speculation on Life in Four Dimensions". In a Preface (entitled "Limitations") Isaac Asimov describes the book as "probably the best introduction one can find into the manner of perceiving dimensions" although I have seen some comment also from Google:

What is Flatland a satire of?

In 1884, the English minister, headmaster, and biblical and Shakespearean scholar Edwin Abbott Abbott produced a thin volume titled Flatland: A Romance of Many Dimensions. It was both an introduction to the notion of higher dimensions and a satire of Victorian society and norms.

My use of the idea is not to repeat or criticise the idea, but to try to extract some "similarity in known respects to similarity in other respects"; viz., analogy.

By flatlander, I mean a 2-D being living in a 2-D 'universe'. By consulting mathematical sources, I was able to confirm that a sphere is actually a 2-D surface existing in 3-D. It is similar to the idea that, inhabiting (at least, historically) only a tiny portion of the Earth's surface, mankind once thought the Earth to be flat. There is, of course, the difference that we are a 3-D (spatial) lifeform inhabiting a 3-D (spatial) 'universe'.

The first analogy considers our simplistic view that we inhabit a 3-D space 'universe' travelling through a 4th dimension, which is how time is commonly considered. (Spacetime will be considered later).

To the flatlander, there is no 3rd spatial dimension, no 'up' or 'down', although these are, of course, apparent to us.

Thus, his 'universe' is bounded by the surface of the sphere. If his 'universe' is to be perceived as expanding, this would be viewed as increase in surface area with time, and his spherical surface would be judged as expanding by increasing distance between points on the surface. Of course,

*radius of a sphere*has no meaning for him.If we now change perspective to what our own would be, if we were able to view flatland, we would see his 'universe', his curved 2-D surface, increasing in radius, and his "time axis" would be the increase in radius of this sphere. Whilst we might (but not necessarily) relate flatland 'time' to our time, it is easy to see it as akin to a linear dimension

__.__*to us*The points I wish to draw from this analogy, are:

That the flatlander's 'universe' is limited to that spherical surface existing in his 'time. For us, as a D+ being, meaning a being able to perceive and process at least one more dimension than the flatlander, it is simply akin to an expanding soap bubble. Note that this is a common analogy for us, but not so in the later example. We should at least be prepared for some differences. Thus a D+ being (e.g., us) could observe a million or more of what a flatlander considers to be 'his' 'universe'. Hence my use of 'around' the word universe. That means that 'universe' is no longer "all there is", but "

__all that can be perceived or generally recognised by the entity__.*owning*that 'universe*'*"Universe" is a relative term, which may be replaced by "observed universe".

The second analogy follows directly from the first. The difference is that, in distinction to our "natural" viewpoint of dividing space from time, we simply ( ) substitute spacetime as the spherical surface (or 'bubble' if you will). This means that what we (D+) observe as radius no longer corresponds to time, whether 'our time' or 'flatlander time', but to something akin to time for a D++. It means that we understand our (D+) "expansion of the universe"

*into what?*, we need perception of an additional dimension, which we do not have. If a comprehension of "universe" needs perception of an additional dimension, why not also comprehension of an "additional time" dimension, which, after all, is only part of comprehension of "universe"?What do you think? It is not a proof, but might it help conceptualisation?

Cat

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