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This game was the insipid edutainment experience that I had feared when I was preparing to play Junior Arithmancer.
When I first loaded this up and got through the short introductory segment, I thought that I was going to be treated to an extended version of the experience provided by the core mechanic seen in the author's other notable math-themed game. The presentation and the setting were quite similar, and the first few segments (constructing and extending the set of numbers) seemed to support the title's implication that this game would be about learning to appreciate the "cold and austere" beauty of the vast and interconnected web of concepts and reason that is mathematics. Since Arithmancer was so unexpectedly fun, I was looking forward to the experience -- I even hoped that I might learn something.
Unfortunately, the game quickly devolves into something else entirely: an old-school-style puzzler with frivolous mathematical theming that seems almost totally at odds with the implicit premise. The actual reasoning required to make progress is typical for old-school puzzlers, and the game does little to explain or reinforce mathematical concepts. This places the focus of attention in the wrong place and is similar to the shortcomings (as educational tool) of a game like Where in the World Is Carmen SanDiego? (In that case, the game is ostensibly a game about geography, but one can play the deduction game that it presents many times and never learn much about geography at all.)
To be fair, it's hardly this work's fault that it wasn't what I had hoped it to be on the basis of a misunderstanding that it was written after Arithmancer. It was, in fact, written before, and the arrow of causation points the other way; Spivey quite admirably extracted one of the best ideas from this game and crafted a much better experience from it. Perhaps I was reading too much into the title and cover for a second time with one of Spivey's works. However, I was not particularly impressed with this work even when trying to take it on its own terms. The fairness level of many puzzles is debatable, and the only unifying structure is dream logic, i.e. non-logic. The most interesting aspect was (Spoiler - click to show)the roller coaster; with its multiple possible configurations, I had to admire its implementation as either very clever in its design or of impressively large scale in execution, if not both.
I think I would recommend this game to someone who really enjoys the old school puzzle sensibility of wanting to solve a puzzle "because it's there," and I imagine that there would be some appeal to mathematicians in the fact that many props and setting elements come from the history of their field. However, I would expect that the typical player would find much more enjoyment in the author's other work.