As previously written about here I, like many others, thought there “must be” a way to solve the Eternity II puzzle… Not deluding myself that I would be the one to win the prize exactly (although there’s a possibility [1] I might have said during last year that I was “about 50% confident” that I would solve it…) but more that ‘surely’ it should be possible, that although no algorithm can exist that would solve ‘all’ problems of this class, that it could be solved by the combination of human intelligence and computing power. Stepping outside the system is what’s required to solve most problems of this type, and why computers are terrible at it (in general) and artificial intelligence is probably, not only light years away, but conceptually not actually possible.
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I mentioned previously that I’d decided to try to solve the Eternity II puzzle game and write a ‘solver’ for it, possibly using some kind of AI. Of course, I haven’t yet found a solution, though I do have a couple of promising approaches. The ‘final’ deadline is December 31st and it won’t be solved by then, though it would be nice to see them extend it for another year (no-one has yet won, and it would be much more satisfying from both a company and buyer perspective to have a winner, rather than it just be abandoned!) but I don’t know if this will happen. See what happens when we get a few days off over Christmas!! You’d think trying to solve a (seemingly) intractable problem (the general class of problems like Eternity II must surely be NP-complete, so an AI approach might come up with a “very good” solution but won’t guarantee to find the exact solution, though it may do of course…) would be quite frustrating and frankly a waste of time but in fact there’s a certain stubbornness and determination that “no-one can solve that, I can solve it!” amongst people like me that makes problems like this almost more worthwhile to work on than mundane things like a ‘solver’ for those sliding number puzzles. What bothers me about all this though is that although an AI algorithm might “happen” across an exact or at least very good solution (which I’d then be tempted to tweak by hand) it’s a fuzzy approach by nature in that a solution evolves or is stumbled across; what I’d really like is to truly understand the puzzle to the extent that a solver could find all possible solutions based on a deep structure or rule. Where I’m starting to look is the number of solutions they mentioned that there are, and how else this number can be generated. I’ve been a bit quiet lately as (among other things) I’ve been foolish enough to start work on a ‘solver’ for Eternity II (TM) – a puzzle game similar to a jigsaw in which 256 numbered pieces have to be re-assembled onto a 16×16 board so that all edges match (the website gives a lot more details), basically it’s a special case of the edge matching problems class with the solution being an arrangement of the pieces so that all 480 edges match in terms of pattern and colour. (The rules of the game say that entrants are not allowed to disclose any of the details of the pieces or of any solution so the information I’ve put here is quite general.) → view the rest of the post: This book is something I initially got for Christmas last year, read once and have recently re-read. It’s the 20th anniversary edition of the book, and not having read the original from 1979 (this one is from 2000 so it is actually a bit longer ago than 20 years now!) I’m not sure how much it has changed from the first version, but as it deals with topics such as AI (Artificial Intelligence) these types of subject areas move on, of course. I read quite a lot of fiction and non-fiction (probably more non-fiction on balance, though) and what strikes me with this book is how different it is in approach from many ‘popular’ science and maths books etc although it is aimed at the general reader, not just the AI/Computer Science/Maths/Music specialists. Rather than expand on aspects of just one subject the emphasis here is how certain aspects of all of these subjects are related and in fact in many cases isomorphic, ie that the same structures and relationships are present in different domains… It’s quite hard to explain without reading the book actually, but the appeal for me is this ‘connectedness’ between ideas.
Originally uploaded by ctsnow It made more sense on the second reading as well, as I was more aware of the overall structure and ‘argument’ of the book, and was very enjoyable to read… in spite of the formidable length (824 pages according to Amazon) it’s certainly not boring or heavy – there was one of the number theory sections that got slightly heavy and had to be re-read a few times but eventually made sense (I think!) I’d definitely like to get hold of more books like this – I’m aware of systems such as the Amazon ‘recommended’ and ‘people who bought X also bought Y, Z…’ but many of these books are linked by subject matter and ‘audience’ rather than approach as such, for instance Fermat’s Last Theorem and The Selfish Gene as popular science/maths books… perhaps there just are no other books quite like this! It’s a good introduction/explanation of all of these subject areas and there are certainly some I’d like to pursue further now (such as Number Theory) which previously I’d dismissed as too ‘dull’ or ‘detailed’ etc… I do get a strong feeling a lot of the time with subjects like this that in reality everything must be much simpler than it’s made out to be with all the Theorems and equations and all the rest of it… like there’s a piece of knowledge ‘out there’ waiting to be discovered that will suddenly make sense of a lot of disparate subjects and cause them to be seen as genuinely related and part of “the same” thing. I haven’t read any of Hofstadter’s other books though will be looking into these as well (though I’ve heard that a lot of the same subject matter is covered). |
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