A fascinating book providing a mind-bending romp through ideas on the 4th spatial dimension (not time). Small and well-stocked with conceptual drawings, the book is written in a way that is usually understandable for this non-mathematician. I also appreciated the regular humor and humility of the author, as demonstrated in this quote: “…a pseudosphere is a sphere with imaginary radius, whatever that may mean.” (p50)
The author provides a very open-minded survey of ideas on visualizing, calculating, accessing, and considering the implications of the 4th dimension. This encompasses established mathematics, psychedelics, consciousness, the occult, and fringe theories. The author is methodical about pointing out the difference between what is known and what is speculative while commenting on pseudoscientific ideas. You will find ideas on not only antiparticles, but also antigalaxies and antipeople (p97). And there is plenty on hypercubes and other 4D objects, light, the shape of space-time, gravity, black holes, white holes, geodesics, world lines, singularities, time, and the idea that mass particles could be tiny black holes or hyperspheres (p114).
My only minor complaint is that the book would benefit from an index and glossary. But the bibliography for additional reading on the 4th dimension and related topics is extensive, and each chapter is capped with word problems for conceptualizing and calculations.
Quotes and interesting ideas:
* “The fact that something is difficult does not mean it has to be confused.” (p10)
* The passage of time in an illusion (p60). “Time arises when we grasp at the world with our irrational minds” using a 4D viewpoint to “see the universe as a single object.” (p117)
* The eyes perceive the structure of space, while the ears perceive the structure of time (p62).
* “Simultaneity is not an intrinsic property of space-time; it is only an artifact of the manner in which we perceive.” (p73) “It is meaningless to speak of two distant events as being simultaneous.” (p77)
* “Objects do not have length in any absolute sense.” (p77)
* “Moving objects appear to be contracted in their direction of motion.” (p79)
* Light cones can be used to visualize you past and future events, and elsewhere (p83-34).
* The author concludes that space-time is toroidal in shape, where nothing is moving and therefore reinforcing his belief that the passage of time is an illusion (p105,60).
* Albert Einstein suspected that space was hyperspherical and expanding, before the expansion of the universe was actually discovered (p108).
* The three geodesics of space-time: space-like, light-like, and time-like (p109).
[https://www.goodreads.com/review/show/6052081645](https://www.goodreads.com/review/show/6052081645)
by ChristopherCFuchs