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# Is this a logical joke.

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Can infinity have a border? In other words, if space is infinite can it be limited by a border of non-space? We have a proposal where infinite distance is squeezed into a finite one, so as to be measured. This is related to the proposal that our visual physical universe may just be an image, a Hologram. It seems that I recall reading both these concepts in Plato's work, mainly in the Philebus dialogue. In the introduction of his English translation B. Jowett comments: The infinite would be no longer infinite, if limited or reduced to measure by number and quantity. The opposite class is the limited or finite, and includes all things which have number and quantity. And there is a third class of generation into essence by the union of the finite and infinite, in which the finite gives law to the infinite;–under this are comprehended health, strength, temperate seasons, harmony, beauty, and the like.

The Hologram. A n t i– de si t t e r spac e ,although it is infinite, has a “boundary,” located out at infinity. To draw this boundary, physicists and mathematicians use a distorted length scale similar to Escher’s, squeezing an infinite distance into a finite one. This boundary is like the outer circumference of the Escher print or the surface of the solid cylinder I considered earlier. In the cylinder example, the boundary has two dimensionsone is space (looping around the cylinder), and one is time (running along its length). For four-dimensional anti–de Sitter space, the boundary has two space dimensions and one time dimension. Just as the boundary of the Escher print is a circle, the boundary of four-dimensional anti–de Sitter space at any moment in time is a sphere. This boundary is where the hologram of the holographic theory lies.

Extract from the Philabus.

Socrates:.....And for this reason
I should like to consider the matter a little more deeply, even though some
lovers of disorder in the world should ridicule my attempt. Now the elements       (Carl Sagans', "We are star stuff")
earth, air, fire, water, exist in us, and they exist in the cosmos; but they are
purer and fairer in the cosmos than they are in us, and they come to us from
thence.
And as we have a soul as well as a body, in like manner the elements
of the finite, the infinite, the union of the two, and the cause, are found to
exist in us. And if they, like the elements, exist in us, and the three first exist
in the world, must not the fourth or cause which is the noblest of them, exist
in the world?
And this cause is wisdom or mind, the royal mind of Zeus, who
is the king of all, as there are other gods who have other noble attributes.
Observe how well this agrees with the testimony of men of old, who affirmed
mind to be the ruler of the universe. And remember that mind belongs to the
class which we term the cause, and pleasure to the infinite or indefinite class.

We will examine the place and origin of both. What is the origin of pleasure?
Her natural seat is the mixed class, in which health and harmony were placed.
Pain is the violation, and pleasure the restoration of limit. There is a natural
union of finite and infinite, which in hunger, thirst, heat, cold, is impaired–
this is painful, but the return to nature, in which the elements are restored to
their normal proportions, is pleasant.

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