Out of Time - Predicting the Science of Future Centuries and Millennia (Edition 2)

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Immersing (not embedding) the figure-8 Klein bottle in the 3rd dimension + Imaginary time makes the 4th dimension both space and time (since the Klein is 2-dimensional, the statement in the file [in the section BITS AND TOPOLOGY] about a couple of two-dimensional Mobius strips uniting to form a three-dimensional figure-8 Klein bottle needs further explanation) - A manifold is a collection of points forming a certain kind of set, such as those of a topologically closed surface or an analogue of this in three or more dimensions. (https://www.bing.com/search?q=meaning+of+manifold&FORM=QSRE7) A Klein Bottle is a 2-dimensional manifold whose inside is its outside. It can only exist in 4-dimensions! A Klein Bottle cannot be embedded in 3 dimensions, but you can immerse it in 3-D. A photograph of a stapler is a 2-dimensional immersion of a 3-dimensional stapler. (An immersion may have self-intersections; Embeddings have no self-intersections.) (https://www.kleinbottle.com/whats_a_klein_bottle.htm#:~:text=A%20true%20Klein%20Bottle%20live) Since the figure-8 Klein bottle referred to in this article can only exist in 4 dimensions, it can be termed a structure of 3 space dimensions which includes the 4th (time) dimension described by Wick rotation. The bottle's immersion in 3 dimensions means its self-intersection allows it to possess only one surface - its inside is its outside (other 3-D objects like wine bottles, for example, have both an inside and an outside). Self-intersection is possible because the 4th dimension of time unites the present with the past and future (explained in the downloaded file) and permits its surface to, in words borrowed from quantum mechanics, occupy more than one location at once i.e. to occupy the position which the bottle's hole would if it were a 3-dimensional object manufactured by the company "Acme Klein Bottle" (mentioned in the website above, "What's a Klein Bottle?") The implied motion from being in more than one place at once is a result of Klein bottles being ultimately composed of the BITS or binary digits of 1 and 0, and switching between those states. These 3+1 dimensions may also be called "an analogue of a topological surface in three or more dimensions". Of course, the 4th dimension can be thought of as spatial instead of temporal. Mathematically, imaginary time (the text explains why it isn't merely mathematical trickery) is real time which has undergone a Wick rotation. Popularized by Stephen Hawking is the fact that measuring time with imaginary numbers, such as i^2 = -1, makes the distinction between space and time disappear completely (self-intersection by means of a 4th space dimension, rather than the previous paragraph's time, is familiar in topology - but we should remember that both apply in reality since we live in space-time). If a figure-8 Klein bottle is analogous to 3+1 dimensions, what is the reality behind the analogy / similarity / correspondence? All of the information in the universe is contained in two-dimensional packages trillions of times smaller than an atom (in this case, the 2D package is the Mobius Strip) - see Afshordi, N. & Corianò, C. & Delle Rose, L. & Gould, E. & Skenderis, K. From Planck Data to Planck Era: Observational Tests of Holographic Cosmology. Phys. Rev. Lett. 118, 041301. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.04130 (2017). Therefore, the 3rd dimension (and the distances within it) wouldn't objectively exist but would be the way our perceptions and expectations interpret information contained in the Mobius strip. The implication is that the universe we live in needn't be described as 3 spatial dimensions plus one temporal dimension (3+1 space-time) but, in keeping with the theory of a holographic universe's 3 spatial dimensions being a projection from 2 dimensional information, as 2+1 space-time. Also, using future technology, it should be possible for the time it takes a spacecraft to reach its destination to be the same amount of time as reaching the launchpad from the craft’s position on the launchpad (travel may oneday be instant - the distance to the ship's destination and the time to arrive both equal zero.) If the spacecraft travels through the 4th space dimension, that is equivalent - thanks to imaginary time making the distinction between space and time disappear completely - to taking a trip through time and visiting any point in the past or in the future.

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