When I started doing Sudoku puzzles from my local newspaper, I just filled in what numbers I could on the page. I learned to solve the easier ones this way but the harder ones defeated me. So I looked up more advanced Sudoku logical techniques such as “naked doubles” and “hidden triples” that required me to keep track of which numbers were candidates for the unsolved spaces. To help me with this, I created a “markup sheet” in Word that had the 9x9 Sudoku grid with all possible numbers that I could check off as possibilites were eliminated. This served as an external memory that allowed me to keep track of more data than I could ever hold in my head, and helped present the available information to me in a format that made spotting patterns easier.
But even this was insufficient to solve the very hardest of the Sudokus. So I downloaded the freeware program Simple Sudoku that automates much of the puzzle solving. When you decide to mark a cell as solved, SS automatically makes sure that that number is eliminated from the rest of that 3x3 subgrid, row, and column. It warns you if you accidently enter an invalid number. It provides filtering that allows you to highlight all of a particular number 0-9; and allows you to mark cells in up to four different colors to enable you to follow the extremely extended logic of some very advanced solving techniques (“X-Y Wing”, “Multiple Colors”, etc.
Which leads to my question: as I become more dependent on these external tools, at what point do I no longer deserve to claim that “I” am solving the puzzle? When does it become cheating? For instance, using Simple Sudoku lets you avoid making boneheaded mistakes- but is avoiding boneheaded mistakes part of the challenge? On the one hand, virtually no one would insist that you are cheating if you don’t memorize the puzzle in the newspaper and solve the whole thing in your head; but simply taking the clues, plugging them into a computerized Sudoku program and hitting the “Solve Puzzle” button wouldn’t be considering “doing” the puzzle either.
I’m reminded of a controversy in chess I read about. The best chess programs can now defeat even grand master chess players. But some people claim that the way chess programs are written effectively gives them what’s called an “opening move book”, which allows one to eliminate most of the unproductive moves. Chess players claim this gives the computer an unfair advantage, and insist that they could defeat even the best chess computers if they could use opening move books too (which have never allowed in tournaments). The pro-computer side of the argument claims that that’s the whole point: not only do computers calculate faster but they have larger and more reliable memories- if humans can’t memorize an entire chess opening move book, too bad.
On the whole, I don’t consider using Simple Sudoku cheating, because Sudoku is still challenging even with it. I can now use some very advanced logic tools that just wouldn’t be workable without it. But I’d be interested in hearing the Dopers input on this. Like the characters in the cyberpunk novel True Names, who augmented themselves into superbeings, at what point can’t you really say it’s “you” doing it anymore?
I think this question is the kind that’s going to come down to a rather arbitrary assignment of identity.
You can, for instance, think of your own memory, in your head, as something external to “you.” Your memories, after all, are not themselves conscious: they are arguably something percieved by your conscious mind. Or you can include thoes memories as part of “you” since they are part of how you operate, part of defining who you see yourself as, moment to moment.
But can we go farther in this game of definition? I would say that my memory for facts is pretty speedy, but unreliable and sometimes gets stuck (“tip of the tounge” hangups). What if I included, say, wikipedia as part of myself, part of my memory? I can access and “remember” things in great detail from wikipedia almost as fast as I can things from my own head: sometimes even faster. And certainly always in greater detail. So why not?
This might seem a little crazy, but remember: it’s not even going to be a decade before many people will have 24/7 portable access to resources like wikipedia everywhere they go: maybe even embedded in their visual and auditory fields. It won’t be decades from then until those resources are even more integrated into people.
How do we define ourselves then?
Within two or three years, people will have instant 24/7 access to as many people as they want in any form they want as cell tech and IM concepts merge (say goodbye to dialing, say goodbye to rings: just speak to as many people as you want, no matter where they are in the world). It would happen even sooner if cell companies were scared shitless of what this will do to their ARPU (i.e. the amount of money they can extract from each user). What will happen to our self-identity when we can talk to other people anywhere, anywhen, as easily as we can think to ourselves?
None of this is science fiction. It’s already happening now. Most of what I’m talking about is merely a means of making things slicker, more embedded, faster. By the basic revolution has already started.
I agree that eventually people will have almost unlimited storage capacity that everyone will have essentially photographic memories and access to whatever external data they want at the time. This will essentially give us immortality (assuming you can do a core dump to some offline storage device*). Yet, the majority of people will still be sitting on their asses watching Survivor or American Idol, etc. It isn’t what you know that counts, it is what you do with it that matters*.
*obviously for immortality to occur once you’re downloaded to a computer you’d have to have a processor and O/S that could process that data in such a way that the output would be indistinguishable from your bio body. Luckily for the Survivor watchers out there this will require no more than an 8088 to simulate the sound of mouth breathing and the occasional belch .
Classical identity theories would hold that you lost your identity the moment you picked up a pencil. For it to be your mental solution, you should solve it in your head. But modern theories generally hold that the bounds of identity are the same as the bounds of existence; i.e., you are your experience. Physics on our scale dictates that no two of us can ever have the same experience because no two of us can occupy the same space at the same time and thus experience the same event in the same way.
The modern view also settles quaint puzzles about replication identities. Suppose, for example, that you were replicated into a person just like you in every way, including memory of all your past experiences. Are you two different people? Just a few decades ago, this was a head-scratcher. But now, it is clear that your experiences are not the same. The replicated you has an experience of emergence that you do not share, and from the moment of its existence, its subjective reference frame is unique, viewing its world from a completely different place in space and time than yours.
So, the short of it is that you are still solving the puzzle even when you use tricks like computer programs. It is your mental acuity that derives using software as a possible solution avenue. You could, if you wish, make it even less taxing on you mentally by hiring someone to solve the puzzles for you. That also is you solving the puzzles assuming you thought of doing the hiring.
Of course, none of this has any bearing on your Sudoku skills because it isn’t just your identity that matters; it is also the identity of the puzzle itself. By using pencils and computers and other people’s labor, have you solved Sudoku or have you solved something else? You have in fact solved something else — namely, that task of solving Sudoku. That is, you have solved how to be efficient. And your solution is useful generally for other tasks. No good at chess? Use a computer. No good at spelling? Use a computer. And so on.
So, the clash between classical and modern theories is still ongoing. And even less mainstream theories come into play. What of temporality, for example? Are you even the same person before and after the solution? After all, when you’re finished the knowledge you have is different from the knowledge you had before you began, and therefore you are different. This theory holds that basically there is no such thing as identity, since you cannot be the same from one moment to the next. And in general, nothing in the universe has an identity since a particle cannot be at rest. (It would violate the Uncertainty Principle: you would know both its location and its momentum.)
What an interesting idea; if my recollection of a given memory is wholly dependent on a written aide memoire - and if identity is based on memory, which seems reasonable -then that part of my identity exists partly as pencil markings on paper.
I don’t have a problem with that; I doubt SentientMeat will have a problem with it; I expect TibbyCat will.
Lumpy, you might be interested in the works of Andy Clark and Teed Rockwell . Both are fascinating investigations into the concept of “extended mind”.
(Clark’s book is dense and fairly technical; good if you’re into AI. Rockwell’s book takes a broader and more philosophical view of the subject. --Disclaimer: I haven’t read Rockwell’s book in it’s entirety… I’m basing my recommendation on the summarized chapters available on his website , and a few exchanges I’ve had with him in online debates.–)
As a chessplayer, I’m used to relying only on my memory + ability when playing. So I try to solve Sudoku only by writing in answers (in pen!). But I can only do many grids by writing in two possible numbers, and crossing one out later.
You could argue that I’m extending my memory onto paper, so I’m using an ‘aid’.
Allow me to discuss chess examples. It is true that computer programs are becoming stronger than us carbon-based life-forms. (Personally I think it’s amazing we’ve held out for so long!)
However the ‘chess opening book’, while useful, is not at the heart of the matter. There are chess openings which do not lead immediately to sharp tactical positions (such as 1.d4 and 2. Nf3), which mean the game will be decided by the better player after the opening is over.
Computers also use totally different methods to humans to play chess. Computers analyse every move, no matter how ‘absurd’ it appears, leading to a vast number of positions to be assessed. Depending on the speed of the processor and the quality of the programming, they can get through x million positions before time constraints kick in.
Humans eliminate 90% of possible moves ‘at a glance’. Of course, we can miss something vital, but we can also see further ahead - provided our ‘judgement’ is sound…
The scary thing for human chess players are endgame databases. Basically you take all legal positions with n pieces left, sort them into a database and can then announce any position is either a win or a draw (and how many moves the win will take against best defence). There is no possibility for a mistake, and no calculation is needed - just a lookup on the database. They are up to n=6 as far as I know: when n=32 chess will be solved.
Good question. Back in the 80’s, I had one of those books that told how to solve Rubik’s cube. With the book in front of me, by looking up and applying the necessary sequence of moves, I could solve the cube. But did that count? Was I solving the cube, or was I+the book solving it, or could what went on really be called “solving” at all? And what if I had memorized the contents of the book?
Is this related to the questions that come up in mathematics education, about whether (or to what extent) students should be allowed to use calculators etc. and how much they should know how to do on their own? i.e. are you still doing multiplication, or solving equations, or evaluating integrals, or whatever, if you’re just entering the problem into a calculator or computer algebra system? And if you can just do things electronically, why—or to what extent—should you learn how to do them “by hand”?
Reminds me of the Chinese room argument. If I’m shut up in a small room with a bunch of reference books, and somebody slides a message written in Chinese under the door, and I, not knowing any Chinese, look up the symbols in my reference books and copy down what the books tell me would be an appropriate response and slide it back, can the room (I + the books) be said to be communicating or to understand Chinese?
If I’m not mistaken, this is physicall impossible, because the number of positions to analyze is so great. But theoretically, given an infinitely powerful computer and an infinite amount of time, etc…
I’ve heard the complaint that chess computers “cheat”, but not because of opening books or endgame databases. The claim was that the computer was fed every move every made in previous matches by the human opponent the computer will play. This is normal and fine, as chess players will indeed study “game film” on their opponents. The problem, and why it’s cheating, is that the computer has no history of games that its opponent can study in preparation for playing it.
I think this was Kasparov’s complaint like 10 years ago, so probably worthless for this discussion.
Yeah, that reads as a major contradiction to me.
For n=32 to be realized would mean that white cannot possibly lose to black, wouldn’t it? And even in such a case, couldn’t you pull a Data from Star Trek:TNG and just change tactics to play for a draw, thus confounding the unbeatable database?
I think you put the emphasis on the wrong word. At what point do you no longer deserve to claim that you are “solving” the puzzle. Liberal addressed this nicely:
Much like using an adding machine solves the task of addition, you don’t deserve to claim that you actually did the addition.
Since part of the actual Sudoku experience involves using a pencil to fill in the blanks, IMO the entire world of pencils is fair game. (Meaning an endless supply of pencils and scrap paper is fine.) But I’d draw the line there. Anything beyond that would mean that you solved it with help, and you’d have to add that qualifier when bragging about your accomplishment.
Those all seem pretty benign. You could do the same thing yourself with scratch paper, colored transparency film, and attention to boneheaded mistakes. You’re still solving the puzzles, just like an author who uses a word processor is still writing.
I think that if the computer is only catching errors–or pointing out opportunities–that you’d be embarrassed to miss yourself, the kind of stuff that anyone who had played the game a few times would know to look for, then you’re fine. There’s still plenty of room for strategy left to distinguish good players from bad ones.
Personally I consider it cheating to make ANY MARKS AT ALL on the paper other than the final number that gets written in each square. And the numbers must be written in pen – no backtracking. I like the challenge of keeping all the possibilities for the different squares in my head.
Of course that means that sometimes I stare at the paper for the better part of an hour without making a single mark. But that’s part of the fun!
As a game designer, here’s my take on the OP’s philisophical question: “Play”, as defined by Huizinga in Homo Ludens, requires three things: a rule set, a bounded playfield, and a lack of real-world consequences. Solving Sudoku remains “play” so long as you don’t cross any of those lines. Using software solving tools doesn’t cross a line because there still remains a set of artificial constraints (“a rule set”) that you can push against. If you solve the puzzle by pressing a single button or by hiring someone to solve it for you the “rules” go away and “play” evaporates.
FWIW, this is why I haven’t bothered to play Sudoku. I took a look at it and thought “I could write a computer program to solve this in about 10 minutes” and went back to the crossword. It’s tedious without computational aids, and pointless with them. I already know that computers are better at brute-force searching limited domain problems than I am.
I suck at the crossword, but at least I do so knowing that it’s not trivially solvable.
Not necessarily. It could also be that with perfect play on both sides, the game is drawn (this is considered the most likely result, AFAIK). It could even be that black can force a win, though this isn’t likely at all and would startle people.
No. First, some definitions:
A position is said to be won for white if, no matter what moves black makes, white can make moves such that white eventually wins. This doesn’t mean that white will win no matter what moves s/he makes, merely that no matter what black does white can always reply with a countermove that leads inexorably to victory.
Similarly, a position is said to be drawn for white if black can’t prevent white from forcing a draw, but white can’t defeat black (given perfect play on both sides).
A position is lost for white if, no matter what moves white makes, there exist countermoves for black such that black wins.
A position is solved if we know whether it’s a win, a loss, or a draw for white.
So if a position is solved, it doesn’t matter whether the human player is trying for a win, a draw, or a loss: the computer can always choose a move that leads to a win (or a draw, if the position is drawn). Note that if the human player screws up, the computer could win from a position that’s solved as a draw, or come back to win or draw in a position that’s “supposed” to be a loss. This means that when a computer is in a position that it knows is lost, it’s to its advantage to keep playing, and give the human player as many chances to make mistakes as possible. This requires the machine to understand what makes positions hard for humans to solve, and is still very much an open problem.
Back to the sudoku, my own philosophy is that using computers or pencils is “cheating” - I allow myself only pens and my head. Just because those are the rules that make it most fun for me. If I thought it would be more fun to input the givens into a computer and hit the “solve” button, I’d do that.
By the way, I solved one that was published in the newspaper last week, in two minutes and 20 seconds. That was a record for me.
Well, just to play devil’s advocate here… why do you need the pen if you have your head? If you’re dependent on an external tool to remember which numbers you’ve solved, isn’t that a form of cheating too?
The **goal ** of sudoku is to fill in the squares. You **can ** play by your own personal rules where you calculate the whole thing in your head and never write anything down, but that’s a non-standard variant.
(For example, I sometimes work easy puzzles by trying to fill in all the 1’s first, then all the 2’s and so on. Imposing this additional constraint increases the play value of a task that would otherwise be too simple.)
In order for cheating to occur the rules of the game must be violated. The only official “rule” of Sudoku is to fill in the squares. Other “rules” are self-imposed handicaps employed by individual players to heighten their enjoyment. I personally feel as though I’ve cheated if I make any mark on the paper other than the final solution. But I wouldn’t impose that standard on others.
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