If the last thread I made didn't make it clear, I love sci-fi where the main character is a scientist. It allows for very thorough worldbuilding, because the main character is asking questions, but isn't necessarily starting from the very beginning the way a lot of raised-on-a-farm style audience-surrogate protagonists are. So where to start with this series where to start with this series! How about the not-so-spoilery stuff. Bizarre sexual dimorphism: The biology of the aliens is kind of contrived and I'm sure kind of squicky for some people. Spoiler: Gender squicky? Born as pairs of "male"-"female" twins, male eventually induces female to split into two male-female twin pairs (killing her consciousness), takes care of resulting offspring. Females spontaneously split if not otherwise killed. I'm glad that this gets investigated, both as a "should this be allowed to continue" and "what does this mean for society". In fact, my favorite aspect of this is that while the society at the beginning of the series takes it as a reason for patriarchy, since the females are going to die sooner than their male counterparts, it's noted that other societies have taken it as reason for matriarchy, since males don't contribute physically to the offspring. Sexual dimorphism does not translate so easily into societal conventions! Spoiler: Plot spoiler And then the second and third books discussing what happens when nonfatal childbirth becomes possible. I kind of wish the period between the turnaround and the eventual landing was expanded more; when were the two genders merged? How? But I'm not a biologist. I'm a physicist. So onto the spoilery stuff Spoiler: Plot spoilery Oh my god this series is a love-letter to alternate physics. When Yalda went up to the observatory and started drawing diagrams I was just "what the fuck", figuring it out just paragraphs before she did. It's the most audacious idea I have ever seen in a novel, because it's not just ignoring relativity the way a lot of sci-fi does. It's turning it on its head and then paying attention to the result! And the resulting physics is so weird! Spoiler: Electromagnetism Let's talk about electromagnetism for a moment. Electromagnetism, between the 1880s and the 1950s or so, was described by Maxwell's equations, which were really a bunch of other people's equations but he noted that they were all very similar and grouped them together. These equations, nominally relating electric fields and magnetic fields, come together with a few constants that Maxwell noted gave the speed of light. This was the first indication that light and electromagnetism were connected. Lorentz, Poincare and eventually Einstein noticed that if Maxwell's equations held no matter what speed you were going, then the speed of light must also remain fixed compared to you, regardless of how fast you were going. This was the original motivation for special relativity. So if physics is rotational, as in Orthogonal, then there can't be a fixed speed. Which means that Maxwell's equations for electromagnetism go straight out the window. This is partially why the Clockwork Rocket has to run on clockwork: they don't have long-range electromagnetism! All of their stable field configurations have to die off too fast to support anything like electricity! Spoiler: leftors, rightors We get the complex numbers from the real numbers by adding in an element that squares to -1; we call this element i, and say that a complex number is anything of the form a + bi where a and b are real numbers. We can add, subtract, multiply complex numbers, and can divide by any complex number that isn't 0. We can model rotations of the plane by complex multiplication; if a^2 + b^2 = 1, then multiplying a complex number by (a + bi) is like performing a rotation by tan^{-1}(b/a) around the point (0 + 0i). What about in more dimensions? In 3 dimensions we aren't so lucky. There's no type of numbers that takes 3 real numbers and spits out a "triplex" number that acts as rotations in 3-dimensions. In 4-dimensions, however, we can make things work. The quaternions, discovered by Hamilton (no, not the US Secretary of the Treasury) are like the complex numbers; instead of just adding in one square root of -1, we add in three, i, j and k, so a quaternion is of the form a + bi + cj + dk. The multiplication is a little more complicated, because we have that ij = k, but ji = -k. Similarly jk = i = -kj, ki = j = -ik. These rules are necessary to allow for division by nonzero quaternions. But now we can also do rotations in both 3 and 4 dimensions. Given a point (x, y, z) in 3-dimensions, we encode it as a purely imaginary quaternion xi + yj + zk. Then to rotate it, we encode an axis of rotation and an angle of rotation as a quaternion a + bi + cj + dk with a^2 + b^2 + c^2 + d^2 = 1; our axis is (b, c, d), our angle of rotation is a kind of ugly function of a, b, c and d. But we perform this rotation by computing (a + bi + cj + dk)(xi + yj + zk)(a - bi - cj - dk), which ends up as some quaternion Xi + Yj + Zk, and thus the rotated point is (X, Y, Z). The point made in the book is that some particles, instead of multiplying by (a + bi + cj + dk) on one side and (a - bi - cj - dk) on the other, would only have something on the left or on the right, hence leftors and rightors. We need to toss in another dimension, however, because only multiplying on one side could land you with some nonzero real component (i.e. not just Xi + Yj + Zk). In Orthogonal, time serves as that fourth dimension, and they're fine because all of the dimensions look the same. We in our universe have similar particles, except our time looks different from our space. So we can't use quaternions; we have to use a slightly different number system. It's less nice because we can't divide in that system. So from a mathematical standpoint, our universe is in this respect less elegant than the one in Orthogonal. In fact, there are a lot of reasons for the Orthogonal universe to be more...familiar, perhaps, to mathematicians. There's a very well-developed field of mathematics called Riemannian geometry that extends the notion of "distance" and "straight line" to curved spaces, and uses the fact that, over short distances, all the dimensions look the same. That's not the case for our physical universe; the universe in which Einstein's relativity holds is called "pseudo-Riemannian" or "semi-Riemannian", and as the prefixes indicated, the geometry has less going for it. Spoiler: Entropy and large scale geometry I'm not sure I'm so happy with how the discussion of entropy turned out. Yes, if the universe is a sphere then you can make curvature arguments (thanks to the geometry being Riemannian instead of semi-Riemannian) and thus make bounds on the entropy, but in the first book they made arguments against the universe being a sphere, at least in terms of spheres having very strong holographic properties; the universe reflected in grain of sand etc. If the universe is a torus, or indeed is topologically nontrivial, then we don't necessarily have curvature bounds. So I'm not entirely convinced by the arguments they were making. Eh... Spoiler: Esilio The backwards-time segment on Esilio was fun.
