When I read an Egan's book I cannot tackle it on a purely literary level. Egan's fiction makes me think about things I didn't know I wanted to think about. This is another one of those novels with a mind-boggling universe.
Egan's world has far consequences:
The space won't be isotropic any more. Thus, things would behave differently if you rotate them around the zz-axis and any linear combination of xx and yy. The laws of the physics would behave differently in the different (space) directions.
On the Noether theorem, the symmetries of the Universe have a deep connection to its conservation laws. The isotropy of the space results in the conservation of angular momentum. In a non-isotropic Universe, the angular momentum isn't a conserved quantity any more. Any effect will be instant around any direction, for which dx2+dy2-dz2=0dx2+dy2-dz2=0. It would effectively mean, that moving any point-like particle on such an axis, you get the same system. This would be a new symmetry, which would result in a new conservation law, which doesn't exist in our Universe. To calculate, which conservation law is it, is complex but it doesn't require much more math/physics skills as in high school.
Note: this all depends on if the (non-curved) space-time of your Universe is still governed by the Special Relativity, as ours.
NB: Things would significantly change if you calculate what happens with gravitation, too. Gravitation changes the geometry of the spacetime, thus the distances wouldn't be calculated like ds2=dx2+dy2-dz2-dt2ds2=dx2+dy2-dz2-dt2, instead you have a tensor (essentially a table) for which
gn1n2gn1n2 is determined by the mass and impulse distributions, it is essentially the General Relativity analogy of the gravitational field. For small (much lighter as black holes) and slow (much slower as speed of light) you get the Newtonian gravitation from it.
It is possible, that near strongly gravitational objects the space-time would be multidimensional again. I think this universe is so remarkable, because most universes would not give rise to stars, planets, and intelligent life. From my perspective, this may be one of the crappier universes I’ve ever read. I personally think humans are a scourge. But the fact remains it required a great deal of fine-tuning of physical constants to produce a universe with stars, planets, and at least one intelligent life form. I am a true solipsist. I believe everything we experience could be a virtual reality that the universe we experience does not exist anywhere. Whereas, this is a distinct possibility, I would not say it is probable. If our universe was just a dream, mathematics would not be the helpful too it is. The universe would be more irrational. I am certain the universe we see only exists in our minds. Real objects in our universe do not possess the property of color. Our brains colorize the universe. Moreover, we see large solid objects, when reality is quite different. Every particle is in some manner of speaking is spread-out through all of space-time. We only see a limited number of dimensions. We don't perceive time as spatial dimension. The universe we see with our eyes is nothing the universe that really exists. More than likely the universe is a multidimensional complex field filled with colorless, odorless, tasteless, silent multidimensional waves, branes à la String Theory or what have you. Your body like most matter is mostly empty space spread-out over space-time…
There is no evidence anything infinite or infinitesimal actually exists. More than likely space-time is finite, but unbounded.
I believe micro-states increases with space-time inflation, and decreases with space-time deflation. It is, therefore, space-time inflation that gives rise to the 2LoT and the arrow of time. I believe the number of micro-states decrease, entropy increases, matter and energy congeals and unifies with space-time implosion that we could travel backwards in "time" without revisiting Earth history. Time started at the Big Bang, but there are many ways back to the Big Bang. Our past is only one of those ways. All black holes lead back to the Big Bang, and the beginning of time.
I imagined the nascent in the exact same predicament as Buridan's ass. Buridan's ass was a perfectly logical creature the starved to death between two equidistant bushels of hay.
From one assumption, I have been able to deduce a large part of modern physics. I assume the universe is perfectly logical, that the universe is not capricious, random, or arbitrary. I admit I can be wrong. This is merely a working hypothesis on my part. If it is true, then the universe had a near infinite number of equally good pathways it could have taken. If the universe was not conscious, if it did not have free choice, how could it choose one random path over a near infinite number of equally good paths? I concluded that like electricity, the universe took every possible pathway. Moreover, this is the only way Feynman's path-integral, sum-over-histories solution to QED makes any sense. It is the only way it could be true. Max Tegmark expands on this very concept, though he dismisses my analogy to Buridan's ass.
My conjecture explains why there is so much balance and order in our universe. According to it, the universe has to balance out. The multiverse must have zero energy. It explains why for every action there must be an equal and opposite reaction. It explains the laws of matter-energy conservation, and all the other conservation laws. I believe the universe is completely balanced, that there is a hidden symmetry, that the universe is a perfect unity, that the universe is not capricious, random, or arbitrary. Every scientific discovery with the exception of Borh's and Heisenberg's interpretation of Quantum Mechanics supports my conjecture, that the universe is completely deterministic, unitary, and holographic. "Entanglement" is more evidence for my overly speculative, wild conjecture. The existence of vacuum fluctuations would falsify my theory. Vacuum fluctuations and virtual particles appear to exist. I predict they will disappear as our knowledge of physics increases.
Bottom-Line: How about another 5-dimensional universe Mr. Egan like you did on “Diaspora”, but this time using 5-fold-eigenvalues? Greg Egan keeps on producing SF like no other. 5 stars for the physics, 0 stars for the story which is crap; rounded to 4 stars overall.
NB: Ah! It feels good to be back at reviewing books…
SF = Speculative Fiction.