## Book Review – Schild’s Ladder

“It’s beautiful, isn’t it?” his father said.  “This is called Schild’s ladder.  All throughout geometry, all throughout physics, the same idea shows up in a thousand different guises. How do you carry something from here to there, and keep it the same?  You move it step by step, keeping it parallel in the only way that makes sense. You climb Schild’s ladder.” – Chapter 14

This is just one of the passages from Schild’s Ladder by Greg Egan, an author of Hard Sci Fi.  I’d come across the author while reading a series of posts by John Baez on his blog Azimuth on Platonic Solids and the Fourth dimension (it was part 8 that mentioned Egan). The book opens wonderfully,

“The Sarumpaet rules let you trace the history of the universe back to the vicinity of the Diamond Graph, and everything you could ask for in a creation, low entropy, particle creation, rapidly expanding space.” – Chapter 1

It’s 20,000 years in the future and the Sarumpaet rules explain all of physics.  It’s based on quantum graphs and Egan’s characters go at lengths to explain this to us on and off during the novel.  The characters are all well trained in physics and mathematics, given that their Qusp minds (a quantum computer/digitized sentient mind) last forever and can be backed up and beamed across space.  In fact, bodies are optional as the following quote indicates,

Yann replied affably, “My earliest memories are of $\mathbb{C}P^4$ – that’s a Kahler manifold that looks locally like a vector space with four complex dimensions, though the global topology’s quite different.  But I didn’t really grow up there…” – Chapter 5

The story begins around an experiment with creating a new vacuum and goes from there.  Heavy mathematics and physics are central to the crux of the story as our heroes try to solve the problem that emerge.  Egan clearly likes talking about this stuff because even with the big picture dilemmas he pauses to have the characters reflect on such things as romance in this future,

“Fair enough. But what do you do instead?”

Yann sat up and leaned against the side of the bed. “All the other things the embodied do.  Give gifts. Show affection. Be attentive. Sometimes we raise children together.”

“Art. Music. Theorems.”

“Original Theorems?”

“If you’re serious.”

That’s great on it’s own, but it continues,

Yann nodded.  “When I was ten years old, all I gave my sweetheart was a pair of projections that turned the group of rotations in four dimensions into principle bundles over three-sphere.  Ancient constructions, though I did rediscover them for myself.”

These quotes are only meant tempt you.  The reviews on Amazon were mixed but the one that hooked me confessed that this book just had too much science and math and went right over his head.  The reader would have to have degrees in the subjects to make sense of this novel.  Sold.