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what is the meaning of “concentric rings round the world” in this context?

In his spiritual vision Davis saw an arrangement of the universe which corresponds closely with that which Swedenborg had already noted, and with that afterwards taught by the spirits and accepted by the Spiritualists. He saw a life which resembled that of earth, a life that may be called semi-material, with pleasures and pursuits that would appeal to our natures which had been by no means changed by death. He saw study for the studious, congenial tasks for the energetic, art for the artistic, beauty for the lover of Nature, rest for the weary ones. He saw graduated phases of spiritual life, through which one slowly rose to the sublime and the celestial. He carried his magnificent vision onward beyond the present universe, and saw it dissolve once more into the fire-mist from which it had consolidated, and then consolidate once more to form the stage on which a higher evolution could take place, the highest class here starting as the lowest class there. This process he saw renew itself innumerable times, covering trillions of years, and ever working towards refinement and purification. These spheres he pictured as concentric rings round the world, but as he admits that neither time nor space define themselves clearly in his visions, we need not take their geography in too literal a sense. The object of life was to qualify for advancement in this tremendous scheme, and the best method of human advancement was to get away from sin—not only the sins which are usually recognized, but also those sins of bigotry, narrowness and hardness, which are very especially blemishes not of the ephemeral flesh but of the permanent spirit. For this purpose the return to simple life, simple beliefs, and primitive brotherhood was essential. Money, alcohol, lust, violence and priestcraft—in its narrow sense—were the chief impediments to racial progress.

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    For me there is some clash of meaning between “spheres” and “rings”. Picturing rings around the world brings the rings of Saturn to mind - a ring situated above the equator (or some other circumference). Picturing a sphere around the world is quite different - the entire surface of the world is enclosed. Perhaps “spheres” is being used in a figurative sense (as in “spheres of influence”) in which case imagining the spheres as rings seems slightly more sensible. – Orbital Aussie Feb 15 at 22:35
  • I failed to state the obvious though: concentric rings around the world are rings (circles) that share the same centre - presumably the centre of the Earth. – Orbital Aussie Feb 15 at 22:40
  • A ring has two dimensions; a sphere has three. – Michael Harvey Feb 16 at 0:42
  • The language is imprecise, but the meaning is clear. Perhaps if this passage is old enough it was acceptable usage at the time. – CJ Dennis Feb 16 at 9:53
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"Concentric" refers to shapes of different sizes which share the same centre. For example, the ripples in water after something has been thrown in are usually circles within circles that ripple outwards from the centre. These are concentric circles.

Spheres can also be described as concentric if one is within another and the centre of both spheres is exactly the same point.

There is something of a contradiction in the statement you are asking about:

These spheres he pictured as concentric rings round the world

It says he pictured spheres as rings - which does not make sense as a sphere is a 3-dimensional solid shape whereas a ring is a hollow circle and normally 2-dimensional.

One possible explanation is that this "spiritual vision" was seen from a fixed perspective. From any given point, a sphere looks like a circle. If the Earth (a sphere) was seen within a series of other semi-transparent spheres, they might look like circles, or rings around it.

Alternatively, the person just lacked the correct language to describe what they saw.

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